Aqua 1

AQUAMaterials andCross Sections

Version 16.13

� SOFiSTiK AG, Oberschleissheim, 2012

AQUA Materials and Cross Sections

This manual is protected by copyright laws. No part of it may be translated,copied or reproduced, in any form or by any means, without written permissionfrom SOFiSTiK AG. SOFiSTiK reserves the right to modify or to release neweditions of this manual. The manual and the program have been thoroughly checked for errors.However, SOFiSTiK does not claim that either one is completely error free.Errors and omissions are corrected as soon as they are detected.The user of the program is solely responsible for the applications. We stronglyencourage the user to test the correctness of all calculations at least by randomsampling.

Materials and Cross Sections AQUA

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1 General. 1−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1. Task Description 1−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2. Types of sections 1−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.1. Static Properties of Cross Sections 1−1. . . . . . . . . . . . . . . . . . . . . .1.2.2. Standard Cross Sections 1−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.3. Freely Defined Thin−walled Cross Sections 1−2. . . . . . . . . . . . . . .1.2.4. Freely Defined Solid Cross Sections 1−2. . . . . . . . . . . . . . . . . . . . .1.2.5. Freely Defined FE Cross Sections 1−2. . . . . . . . . . . . . . . . . . . . . . .1.2.6. Selection of Section Type 1−3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.3. Creating variants of sections 1−3. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Theoretical Principles. 2−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1. Materials 2−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.2. Holes and Composite Sections 2−1. . . . . . . . . . . . . . . . . . . . . . . . . . .2.3. Coordinate System. 2−2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.4. Normal Stresses. 2−3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.5. Effective Width. 2−5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.6. Warping and Shear Stresses 2−5. . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.7. Torsional Moment of Inertia. 2−7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.8. Shear Stresses in Solid Sections. 2−8. . . . . . . . . . . . . . . . . . . . . . . . .2.8.1. Equivalent Hollow Cross Sections 2−8. . . . . . . . . . . . . . . . . . . . . . .2.8.2. Shear Cuts 2−8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.8.3. Force Method 2−10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.8.4. Displacement Method 2−13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.9. Shear Stresses in Thin Walled Sections. 2−15. . . . . . . . . . . . . . . . . . .2.10. Plastic forces. 2−15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.11. Program Limits 2−16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.12. Bibliography. 2−16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Input Description. 3−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.1. Input Language. 3−2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2. Units 3−2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3. Input Records. 3−4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.4. CTRL − Control of Analysis 3−9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.5. Materials. 3−13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.6. NORM − Default Design Code 3−15. . . . . . . . . . . . . . . . . . . . . . . . . . . .3.7. MATE − Material Properties 3−32. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.8. MAT − General Material Properties 3−38. . . . . . . . . . . . . . . . . . . . . . . .3.9. MLAY − Layered Material 3−39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.10. NMAT − Non−linear Material 3−40. . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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3.10.1. Invariants of the Stress Tensor 3−41. . . . . . . . . . . . . . . . . . . . . . . . . .3.10.2. Material Parameters 3−41. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.10.3. Non−linear State Variables (hardening parameters) 3−44. . . . . . . .3.10.4. Material Law VMIS 3−45. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.10.5. Material Law DRUC 3−47. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.10.6. Material Law MOHR 3−48. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.10.7. Hardening Plasticity Soil Model − GRAN 3−50. . . . . . . . . . . . . . . . .3.10.8. Material Law SWEL 3−57. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.10.9. Material Law FAUL 3−61. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.10.10.Material Law ROCK 3−62. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.10.11. Material Law MISE 3−63. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.10.12.Material Law GUDE 3−65. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.10.13.Material Law LADE 3−66. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.10.14.Material Law MEMB 3−69. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.10.15.User Defined Material Laws 3−69. . . . . . . . . . . . . . . . . . . . . . . . . . . .3.11. BMAT − Elastic Support / Interface 3−72. . . . . . . . . . . . . . . . . . . . . . . .3.12. HMAT − Material Constants HYDRA 3−75. . . . . . . . . . . . . . . . . . . . . .3.12.1. Hydraulic Parameters 3−76. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.12.2. Heat Conduction. 3−77. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.12.3. Hydration of Concrete 3−80. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13. CONC − Properties of Concrete 3−82. . . . . . . . . . . . . . . . . . . . . . . . . .3.13.1. Eurocode / DIN 1045−1 / OEN B 4700 3−83. . . . . . . . . . . . . . . . . . .3.13.2. DIN 1045 old / DIN 4227 / DIN 18806: 3−86. . . . . . . . . . . . . . . . . . .3.13.3. ÖNORM B 4700 / B 4750 3−87. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13.4. Swiss Standard SIA 3−88. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13.5. French BAEL−99 3−89. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13.6. Spanish EHE 3−89. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13.7. Swedish BBK 3−90. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13.8. Danish DS 411 3−90. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13.9. Norwegian NS 3473 3−90. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13.10.Italian design codes 3−90. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13.11. Hungarian design codes 3−91. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13.12.British Standard BS 8110 3−91. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13.13.American concrete institute ACI 318M 3−92. . . . . . . . . . . . . . . . . . .3.13.14.Brasilian NBR 6118−2003 3−92. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13.15.Australian AS 3600 and New Zealand NZS 3101 3−93. . . . . . . . . .3.13.16.Japanese Standards 3−93. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13.17.Chinese Standards 3−93. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13.18.Indian Standards IS / IRC 3−93. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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3.13.19.Egyptian Standard ET RC−2001 3−94. . . . . . . . . . . . . . . . . . . . . . . .3.13.20.Russian Standard SNIP 3−94. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13.21.Linear Elastic Concrete 3−95. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.14. STEE − Properties of Metals 3−97. . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.14.1. Structural Steel 3−98. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.14.2. Aluminium alloy 3−109. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.14.3. Reinforcing and Prestressing Steel 3−112. . . . . . . . . . . . . . . . . . . . . .3.14.4. Relaxation 3−121. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.14.5. Bond Properties 3−122. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.14.6. Stress−Strain Relations 3−123. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.15. TIMB − Timber and Fibre Materials 3−125. . . . . . . . . . . . . . . . . . . . . . . .3.16. MASO − Masonry / Brickwork 3−132. . . . . . . . . . . . . . . . . . . . . . . . . . . .3.17. SSLA − Stress−Strain Curves 3−134. . . . . . . . . . . . . . . . . . . . . . . . . . . .3.18. MEXT − Extra Material Constants 3−137. . . . . . . . . . . . . . . . . . . . . . . . .3.18.1. AIR − Air Contact Ratio 3−137. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.18.2. CNOM − Nominal Cover 3−137. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.18.3. CRW − Crack width 3−137. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.18.4. KR − Equivalent roughness 3−138. . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.18.5. TEMP − Temperature environment 3−138. . . . . . . . . . . . . . . . . . . . . .3.19. BORE − Bore Profile with Beddings 3−139. . . . . . . . . . . . . . . . . . . . . . .3.20. BLAY − Layer of the Soil Strata 3−140. . . . . . . . . . . . . . . . . . . . . . . . . . .3.21. BBAX − Axial Beddings 3−143. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.22. BBLA − Lateral Beddings 3−145. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.23. SVAL − Cross Section Values 3−148. . . . . . . . . . . . . . . . . . . . . . . . . . . .3.24. SREC − Rectangle, T−beam, Plate 3−151. . . . . . . . . . . . . . . . . . . . . . . .3.25. SCIT − Circular and Tube Sections 3−156. . . . . . . . . . . . . . . . . . . . . . . .3.26. TUBE − Circular and Annular Steel Cross Sections 3−158. . . . . . . . . .3.27. CABL − Cable Sections 3−159. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.28. SECT − Freely defined Cross Sections 3−163. . . . . . . . . . . . . . . . . . . .3.28.1. Parametric Sections 3−167. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.28.2. Import of FE−Sections 3−170. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.29. CS − Construction Stages 3−171. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.30. SV − Additional Cross Section Properties 3−173. . . . . . . . . . . . . . . . . .3.31. POLY − Polygonal Cross−Section Element / Blockout 3−175. . . . . . .3.32. VERT − Polygon Vertices in Absolute Coordinates 3−177. . . . . . . . . .3.33. CIRC − Circular Cross Section Elements 3−179. . . . . . . . . . . . . . . . . . .3.34. CUT − Shear and Partial Sections 3−181. . . . . . . . . . . . . . . . . . . . . . . .3.35. PANE − Thin−Walled Cross Section Element 3−187. . . . . . . . . . . . . . .3.36. PLAT − Thin−Walled Cross Section Element 3−190. . . . . . . . . . . . . . .


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3.37. WELD − Welded Shear Connection 3−193. . . . . . . . . . . . . . . . . . . . . . .3.38. PROF − Rolled Steel Shapes 3−195. . . . . . . . . . . . . . . . . . . . . . . . . . . .3.39. SPT − Points for Stresses 3−205. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.40. NEFF − Non effective parts 3−207. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.41. SFLA − Forces Work Laws 3−208. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.42. WPAR − Parameters for Wind Loading 3−210. . . . . . . . . . . . . . . . . . . .3.43. WIND − Coefficients for Wind Loading 3−211. . . . . . . . . . . . . . . . . . . . .3.44. Reinforcement. 3−214. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.45. RF − Single Reinforcement 3−217. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.46. LRF − Line Reinforcement 3−218. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.47. CRF − Circular Reinforcement 3−220. . . . . . . . . . . . . . . . . . . . . . . . . . . .3.48. CURF − Perimetric Reinforcement 3−222. . . . . . . . . . . . . . . . . . . . . . . .3.49. TVAR − Template Variables 3−224. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.50. INTE − Interpolation or Cloning of Sections 3−226. . . . . . . . . . . . . . . . .3.51. IMPO − Import of Data 3−228. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.52. EXPO − Ansi Export of Data 3−229. . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.53. ECHO − Extent of Output 3−230. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Description of Output. 4−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.1. Information about the Design Code 4−1. . . . . . . . . . . . . . . . . . . . . . .4.2. Material Properties 4−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.3. Bedding Profiles 4−6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.4. Overview of the Cross Section Values and Types 4−7. . . . . . . . . . .4.5. Cross Section Properties 4−8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.6. Cross Section Elements 4−12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.7. Wind Coefficients 4−16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.8. Integral Equation Method 4−17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.9. Spring Characteristic Curves 4−17. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Examples 5−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.1. Materials. 5−2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2. Standard Sections. 5−3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3. T−Beam with Effective Width. 5−5. . . . . . . . . . . . . . . . . . . . . . . . . . . .5.4. Polygonal Column Cross Section. 5−11. . . . . . . . . . . . . . . . . . . . . . . . .5.5. Polygonal Cross Section with Inner Perimeter. 5−19. . . . . . . . . . . . . .5.6. Polygonal Cross Section with Interpolation 5−30. . . . . . . . . . . . . . . . .5.7. Thin−walled Steel Box. 5−34. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.8. Composite Section. 5−41. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


1−1Version 16.13

1 General.

1.1. Task Description

AQUA calculates the properties of cross sections of any shape and made out ofany material. The cross section properties for a static analysis are determined,as well as characteristic magnitudes for the calculation of normal and shearstresses. Cross sections need to be defined before input of the static system orthe dimensioning with AQB.

After definition with AQUA, the cross sections can be represented graphicallywith AQUP.

There are four types of cross sections, depending on the complexity of the designtask. Without a licence for AQUA only the first two types may be defined (AQUA−light).

1.2. Types of sections

1.2.1. Static Properties of Cross SectionsAll static properties of cross sections are directly specified. This includes sheardeformation areas and stress resistance values. The values may be taken fromother cross sections with a multiplication factor. These cross sections are mainlyused in the static calculations. Their usage in AQB is strongly restricted.

1.2.2. Standard Cross SectionsA standard cross section (Rolled steel shapes, Rectangle, T−beam, annular sec-tions, cables) is always defined with a single command. All cross sectional prop-erties, including the torsional moment of inertia, are available. Due to the knowngeometric structure, most of the property values may be calculated in a direct way,allowing to skip the time consuming detailed analysis of the shear or plastic resist-ance only available with an AQUA license. In many cases it is also intended tohave these simpler values taken from tabulated data in the literature. On the otherside variability and locations of design points are thus limited. A detailed analysisor a combination with other cross section parts is only possible for the rolled steelshapes.


Version 16.131−2

1.2.3. Freely Defined Thin−walled Cross SectionsA freely defined thin−walled cross section may contain any number of thin ele-ments, whose thickness is much smaller comparative to its length. A thin elementassumes that the variation of the normal stress and most shear stresses over thethickness are negligible. This has the consequence that the moment of inertiaabout the weak axis also vanishes. Available elements are panels, standard steelshapes and welded joints, as well as reinforcements.

Section moduli for all stresses are available at all points of the cross section. Tor-sional moment of inertia and warping resistance, as well as centre of shear andshear deformation areas, are determined for open or closed shapes, but they canalso be specified explicitly for special cases. Composite cross sections can bedefined.

1.2.4. Freely Defined Solid Cross SectionsA freely defined solid cross section consists of any number of outer and inner peri-meters in the form of circles or polygons, as well as of reinforcement elements.Structural steel shapes can be integrated.

Section moduli for all stresses are only available at distinct points of the cross sec-tion. The torsional moment of inertia, the centre of shear and the shear deforma-tion areas can be calculated, or they can be input separately. The warping resist-ance can not be determined. Composite sections or effective widths of thepolygons can be defined.

1.2.5. Freely Defined FE Cross SectionsA freely defined FE cross section will be imported from a FE mesh available ina separate external data base. Stress points, reinforcement elements or shearcuts may be added then. The import may also activate a temperature field for thesection (e.g. hot design).

All sectional values including warping are evaluated. Section moduli for all forcesand moments are available for all element mid points. Composite sections maybe defined.


1−3Version 16.13

1.2.6. Selection of Section TypeThe user has to decide on his own authority, which type of sectional descriptionto choose. Due to the established restrictions a standard cross section may havemore sectional data available than a poorly defined general cross section.

A thin walled section has much in common with a standard frame analysis, whilethe solid section requires a continua solution. This means that the simplificationsof the thin walled approach allow a faster, more robust and more extensive solu-tion, but neglects local effects, which may become visible within a continua solu-tion with integral equations or finite elements.

For example it is to be noted, that for a thin hollow box, the shear stress of thecontinua solution is not really constant across the web thickness and may havehigher intensities at the corners which might require a smoothing of the contour.On the other side a thin walled section has problems to take account of the posit-ive effect of the fillets of a thin rolled steel shape which has a considerable contri-bution to the torsional strength.

The checks for the b/t ratio for steel sections are much more easily performed witha thin walled section and the modelling of discrete dowels is only possible withthis type of approach.

In general problems have to be expected if a section is not modelled with the op-timum method. Especially very thin plates with stiffeners modelled as polygonsneed a very high numerical effort.

1.3. Creating variants of sectionsDue to the fact that most cross sections are build up according to certain rules,AQUA supplies several definition possibilities for these instances:

• You may describe the section via CADINP variables within a block, whichis then used multiple times.

• You may interpolate between two sections linearly

• You can define a cross section template consisting of several constructionpoints. Other points are referenced hierarchically to those original points.You can then generate other cross sections by changing these points.

• You may describe the position of those construction points by a 3D modelwith curved reference lines.


Version 16.131−4

It is also possible for AQUA to update all interpolated or otherwise generated sec-tions with a single command (INTE).


2−1Version 16.13

2 Theoretical Principles.

2.1. MaterialsProperties of materials must be distinguished according to whether they are to bekept as close as possible to real values (e.g. for dynamic calculations) or to beused with a safety coefficient for calculating an ultimate load−bearing capacity.

A small, but subtile contradiction is given by the fact, that many design codes usea factor of 10.0 to convert the density of a material [t/m3] into the weight [kN/m3].To avoid any confusion about that SOFiSTiK has established the following rules:

• All weights have to be specified as the 10 time value of the mass, as it isalso done in the Eurocode, this value will be saved to the database.

• Thus masses for dynamic or thermic analysis will be always deteminedwith a factor of 0.1.

• If the design code or the user allows for more exact loadings, the factor ofthe self weight has to be defined according to the locally effective value ofthe gravity (e.g. 0.981 instead of 1.0).

Whereas the safety factors were formerly assigned more−or−less at random,sometimes to the load and sometimes to the material, more recent regulations(Eurocode) provide a clearer separation between safety factors for the loads andfactors for the material.

Since the material safety factors still depend on the nature of the load or the typeof design, AQUA generates and stores only the genuine properties of the mater-ial. However, AQUA accounts for some safety factors which are independent ofthe particular loading case, such as long term reduction factors.

Nevertheless, a safety coefficient can be entered in AQUA for each material; thisis used in AQUA for calculating the full plastic section forces and moments, andcan be used in AQB for the strain checks.

2.2. Holes and Composite SectionsWith version 2012 the treatment of holes has been redesigned. While older ver-sions required to specify a hole as a special polygon with the type “hole” or by anegative radius of a circle, any type of required hole will be generated now


Version 16.132−2

automatically if poylgons or circles overlap. A true hole is now defined with mate-rial number 0. To avoid anay ambiguities, some rules have to be followed howe-ver:

• A polygon/circle may create a hole in another area only if it has a differentmaterial number and at least one vertex of the periphery within the otherarea.

• If a polygon/circle is completely within another area, it will always createa hole, if the areas overlap partly the sequence of the input will decide: Thearea defined last will be considered “in front of” and will create a hole in thearea laying behind.

2.3. Coordinate System.Cross sections are described according to DIN 1080 in the local y−z coordinatesystem of the beam. Here the x−axis points in the longitudinal direction of the bar.The observer is looking in general at the positive boundary of the section (fromthe end of the bar to the beginning).

The coordinate system of the section is identical with the local beam coordinate−system, i.e. the local x−axis is along the beam on the line between the nodes, they− and the z−axis are right handed perpendicular to it. The z−axis defines themain bending direction and is in general oriented downwards in the gravity direc-tion.

For the description of the forces and moments and the support conditions, threepoints along the beam have to be distinguished within a section:

• Beam axis (0)this point may be given either by the centroids of the sections (centricbeam) or it is defined by the origin of the sectional coordinate system.(beam with a reference axis). Support conditions in the nodes thus are al-ways specified for the beam axis position!

• Center of gravity (S)this point is the reference for the normal force and the bending moments

• shear center (M)this point is the reference for the transverse shear force and the torsionalmoment. The section will rotate about that point in general. If we have arotation about a fixed point (e.g. by a bracing) this point has to be specifiedexplicitly and it will coincide with the beam axis in many cases.


2−3Version 16.13

Deviations between these points will create changes in teh moments betweensupport and end of beam. On the other side it is possible to describe a completegeometry with any eccentricities and unsymmetrical haunched beams and con-struction stages with ease.

M

S

Coordinate system

x, y, z Local beam coordinate system, freely selectable, is defined relative to the global coordinate system with the beam.

y’, z’ sectional coordinate system for minimum moment of inertia (=coordinate system shifted to the centre of gravity)

For rotations the sign is always defined by the rotation about the local x−axis. Thisis clockwise if you look in the direction of the beam and it is counter clockwise iflooking on the positive face. Sections will be saved in the database with the peri-phery in that same orientation. The sign of the radius of a circular arc is definedpositive if the area is increased compared to the secant, and it is negative if thearea is decreased as in the case of a fillet.

2.4. Normal Stresses.

The load−bearing behaviour of a generic bar without foundation according to 1storder theory, yet with warping, can be described with a differential equation mat-rix:


Version 16.132−4

E��

��

Fx �

Fy

Fz

Fw

Fy

Fyy �

Fyz

Fyw

Fz

Fyz

Fzz �

Fzw

Fw

Fyw

Fzw

Fww �

��

�

��

vII�

x

vIV�

y

vIV�

z

�IV �

x

��

��

��

p �xp �yp �z

mx�GIt�Ix

��

(1)

with the following definitions:

vx, vy, vz displacements parallel and perpendicular to the barϑx rotation about the axis of the barpx, py, pz loads parallel and perpendicular to the barmx torsional load

The rest of the parameters are static properties of the cross section (geometricalarea moments). Since it is impractical to incorporate all of the static properties intothe calculation, certain standardisations are normally adopted:

The axial force refers to the centre of gravity of the beam

Fy = Fz = 0 (2)

Bending takes place about the principal axes

Fyz = 0 (3)

Warping can occur freely in the cross section

Fw = 0 (4)

The torsional moment and the shear forces refer to the centre of shear.

Fyw = Fzw = 0 (5)

Conversely, the conditions in (2) through (5) can be used in determining the centreof gravity, the orientation of the principal axes, the free moduli of warping and thecentre of shear.

The determination of the area moments is simple, and is not described in moredetail. The next paragraph will deal with the more complex calculation of the nor-malized warping function w.

The normal stresses of a bar cross section can be described by means of Swain’sexpression and the normalized warping:

�x � N�A� �

� �My �Iz�Mz �Iyz��Iy �Iz� I2yz�

�·�z � �Mz �Iy�My �Iyz��Iy �Iz� I2yz�

�·�y � Mb

CM��·�w (6)


2−5Version 16.13

In stress analysis, there is no problem in dealing with rotated principal axes. Whenanalysing a frame structure, however, one must start, as a rule, by rotating thecross section coordinate system to coincide with the principal axes. STAR2 doesthis on its own in case of three−dimensional structures. In special cases, AQUAcan also rotate the cross section to coincide with the principal axes. In such casehowever, the local y−axis should then be rotated in SOFiMSHA with the sameamount in the reverse direction.

2.5. Effective Width.

The so−called effective widths are used in literature for modelling the effectswhich derive from the diaphragm action of the plate of a T−beam or a box crosssection. The concept of an equivalent substitute width with constant normal stressnaturally demands different approaches depending on the task at hand (statics,design).

AQUA is able to define the non−effective areas directly by means of polygonalelements. AQUA then stores the cross section values for the total cross sectionas well as for the effective cross section. Static analysis usually refers to the ef-fective parts, whereas prestressing refers to the total cross section. In STAR2,however, this can be explicitly switched one way or the other. Also, when dimen-sioning with AQB, the user can refer to the total cross section at various occa-sions.

The effective widths are not taken into consideration during shear stress calcula-tions due to many consistency reasons.

2.6. Warping and Shear Stresses

In case of warping as well as shear stressing due to torsion and shear force, thecross section no longer remains plane. A deflection w occurring at the cross sec-tion in the longitudinal direction of the bar causes shear stresses.

All the problems of the elasticity theory can be analysed by use of the forcemethod or the displacement method. While the force method is frequently usedin calculations by hand and for non−linear problems, the displacement methodis better suited for processing with the computer. Both procedures are implemen-ted in AQUA for solid cross sections. Certain simplifications of the following equa-tions can be made in case of thin−walled sections, which facilitate a quick solutionfor all tasks. These sections are therefore always analysed by the matrix displace-ment method.


Version 16.132−6

A general formulation for the cross section warping w according to the displace-ment method conforms to the equilibrium condition

G�� 2w�y2

��2w�z2��-

��x�x

(7)

and the boundary condition

�xy �ny�� xz �nz��0 (8)

where the shear stresses are given by

�xy��G��w�y

� z� ��x

�x� (9)

�xz��G��w�z

� y� ��x

�x� (10)

The right side of (7) can be computed for example by (6). Assuming constant nor-mal force and constant cross section properties, one gets:

-��x�x

��Vz �Iz�Vy �IyzIy �Iz�� I2yz

�·�z��Vy �Iy�Vz �IyzIy �Iz� I2yz

�·�y��Mt2

CM�·�w (11)

These equations will be approximated by AQUA either with the Integral equationmethod or the finite element method.

For the Saint Venant’s torsion problem (∂ϑx/∂x=1) the right side of (7) is identicalto zero and the following boundary condition applies:

�w�n

�� z� ny� y�nz (12)


2−7Version 16.13

2.7. Torsional Moment of Inertia.

The torsional moment of inertia according to the displacement method It is de-rived by

It��y2� z2��w�y�2��w�z�

2 dF (13)

As long as AQUA does not solve the differential equation (7), only an estimate ofthe torsional moment of inertia is possible. The last equation shows that the polarmoment of inertia can be substituted for It in case of warp−free cross sections.

It�� Ip�� Iy� Iz (14)

For all cross sections (14) provides an upper limit, which e.g. is about 10% abovethe exact value for a square.

A better approximation was given by Saint Venant:

IT�� A4

�4��2� �Iy� Iz� (15)

This value is exact for circular and elliptical cross sections. For compact solidcross sections this value provides a good approximation.

In case of open sections, however, it is sensible to consider a correction accordingto Wienecke /2/ in consideration of the cross section perimeter, which has beenimplemented in AQUA.

Deviations in rectangular cross sections:

a/b 1/1 2/1 10/1

exact 0.140 0.458 3.13 � b4

Saint Venant 0.152 0.486 3.01

Wienecke 0.124 0.418 3.24

For hollow cross sections with more than 30 percent inner perimeters, an equival-ent hollow cross section based on the external and internal perimeters is used fora more refined estimate. For composite sections this formula (15) is used for eachpartial cross section and the components are added.


Version 16.132−8

2.8. Shear Stresses in Solid Sections.

The calculation of shear stresses for solid sections in AQUA requires that the userspecifies the method to be used and the positions that have to be checked. Theproblem is extremely complicated and can be solved with a variety of methods.This is controlled by the CTRL option STYP:

CTRL STYP 0 force method

CTRL STYP 1 displacement method only for It and location of shear centre(default for concrete and concrete composits)

CTRL STYP 2 displacement method for torsionforce method for shear

CTRL STYP 3 displacement method for torsion and shearshear deformation areas are determined

(default for steel, wood and other composits)

In post−cracking (state II) analysis, AQB always employs the force method withproportional axial force. In case of composite cross sections options 2 and 3should be used with caution. The input of explicit shear sections is required as arule.

2.8.1. Equivalent Hollow Cross SectionsWhile DIN 1045 still allows the calculation of torsional stresses according to stateI, both DIN 4227 and EC2 allow for their calculation on an equivalent hollow crosssection. As long as AQUA does not use the integral equation method, the forcemethod is used in conjunction with the definition of an equivalent hollow crosssection.

2.8.2. Shear CutsThe user normally uses the command CUT to define a so called cut through thesectional geometry where a check of the shear stresses should take place. Eachcut is assigned an identification, which consists of three characters. The cut canbe defined parallel to an axis or as a free form polygon line. Every segment hasits own material number and it will only cut through cross section elements withthe same material number. Gaps between the segments will be closed by means


2−9Version 16.13

of virtual connections. The width of the substitute torsional cross section is avail-able as a special option for the description of equivalent hollow cross sections ofreinforced and prestressed concrete. Two partial cuts are generated for each sec-tion in this case.

If the user does not supply any input, one or two axis−parallel cuts will be createdthrough the centre of gravity. This is generally not sufficient even for a simpleT−Beam, nor for composite sections, where the reference material number of thesection is not necessarily represented at that location. The user will see a warningfor general sections therefore.

CTRL STYP allows the user to control how many of these standard cuts will begenerated (0/1/2).

The cut can dissect the cross section at several locations creating partial cuts.Each partial cut has a direction s and three defined points of interest: beginning(A), middle (M) and end (E):

Shear section

The internal forces perpendicular to the cut M and N act in such way that positiveaxial forces cause tensile stresses across the cut, and positive moments causetensile stresses at the End−Point.

The shear stressing is described primarily by the section moduli of the shearstresses at the three points. Additional values are calculated for the design of linksin reinforced concrete structural elements:

• A mean torsional shear stress which, after being multiplied by the widthof the partial section, must be covered by reinforcement. This correspondsto a section modulus for the shear flow.


Version 16.132−10

• The total cut width, by which the shear stresses due to the shear force mustbe multiplied in order to obtain the shear flow from shear force.

These distinctions are very significant to the definition of equivalent hollow crosssections.

2.8.3. Force MethodThe force method is implemented in AQUA only for ”statically determinate”, i.e.simply connected cross sections. For multiple connected cross sections, the usermust either know the location of zero shear stress or specify the distribution of theshear to the multiple segments of the cut. Since in cracked sections the commonusage is the force method, the distribution values are needed in any case for rein-forced concrete sections. The displacement method allows however to establishreasonable estimates for many cases.

Torsional stress analysis is not elementary even for the force method (stress func-tion with soap film analogy). The resistance areas for the torsional shear stressesare therefore prescribed by two values per section. The first value defines theshear at mid−area (Bredt’s equivalent section). The second value defines the in-crease along the cut:

�m��Mt�WTm��Mt�WTd

The default is one of the following two values, depending on whether the crosssection is a hollow one or an equivalent hollow one:

WTm� 1�2�Ak� b0�

��WTd� 1It�min�b,d�

The sign of the shear stresses is based on the orientation of the cut relative to theshear centre.

The shear force components are calculated by the classic formula

��VI� Sb


2−11Version 16.13

However, each of the four initial values is inadequate in this formula:

• V is only valid for prismatic beams with constant normal force

• I has to be generalized with Swains formula

• For S the separated part of the cross section is not known for multiple con-nected sections.

• Shear stress does not need to be constant across the width b

The separated part of the cross section is based on the positive face the one tothe left of the cut’s direction on the positive side. During this calculation any miss-ing partial sections are automatically filled in. It is therefore extremely importantto input the sections correctly, and especially to maintain their sequence.

For special cases, such as dowel outline joints, deductible areas, equivalent hol-low cross sections, multiply connected cross sections etc., the component of theshear force for each partial cut can be provided by a factor.

Multiply connected cross section types require special considerations:

Shear sections in hollow cross section

Similarly difficult is the processing of cross sections consisting of several poly-gons, either inner perimeters or composite cross sections, not dissected by thepolygonal shear cut. In such cases AQUA examines all points of the polygon tosee whether they are inside or on the boundary of the already evaluated partialsection. Openings must therefore always be defined according to the polygons


Version 16.132−12

that surround them. In case of composite cross sections it may be helpful to payattention to the cut direction or the sequence of the polygons.

In the definition of cuts across several materials the user must take care that eachsegment of the cut has the correct material number, because a cut will dissectonly parts having the same material number. It makes a difference for the hori-zontal shear in a composite flange if a dowel is before or behind the cut.

Cuts through cross sections with ”open air” between their parts can not be ana-lysed as the section does not hit any elements. A similar problem occurs if a cuthas the wrong material number. This may happen especially with the standardcuts through the centre of gravity.

Problem case

Some additional advice applies to oblique cuts. Since the shear force at an ob-lique cut does not vary significantly compared to the straight cut, however thewidth of the cut does. Since the selection of an inappropriate cut direction can res-ult in the analysis of too small shear stresses.

The stress evaluation with the displacement method always uses the gross sec-tion while the force method may only use the effective part of the section. The lat-ter is the default behaviour. But with CTRL SCUT +8 you may switch to the fullsection if needed.


2−13Version 16.13

2.8.4. Displacement MethodThe analysis with the displacement method employs the integral equationmethod developed by Katz. The cross section contour is discretized into multipleso−called ”boundary elements.” A linear formulation of the warping is made foreach element, and the boundary condition is satisfied by a Galerkin weighted re-sidual.

The number of elements determines the accuracy of the solution. In case of asquare, for instance, the unit lateral warping on all the axes of symmetry is zero.A non−vanishing solution therefore can be obtained only by defining at least fourelements per side. AQUA uses each polygon edge as one element, which canbe further subdivided depending on its size. Duplicate edges are automaticallyremoved. As the results along the edges will vary only linear in all graphics, it isstrongly recommended to use the input value SMAX in POLY to have a coarsesubdivision visible.

Internally a finer subdivision is needed however. Since a finer subdivision in-creases the computational time with a power of three, the subdivision should notbe made too fine. The user can control the mesh size by CTRL SDIV. This indic-ates how big an element may became compared to the largest dimension of thecross section.

CTRL SDIV 0 No subdivisionCTRL SDIV 1 maximum 1/2CTRL SDIV 2 maximum 1/4CTRL SDIV 3 maximum 1/8CTRL SDIV 4 maximum 1/16

etc.

The method computes the shear stresses due to shear force and torsion at allstress points and shear sections. The program also computes the torsional mo-ment of inertia and the shear deformation areas. The description of inner perimet-ers of any shape and at any location is automatically taken into account.

Under no circumstances are the results of this method to be accepted uncritically.It is a numerical approximate method. Local singularities of the shear stresses,such as those at re−entrant corners for example, can generate very high stresses.

The following table shows the convergence of the method using the example ofa square with a side length of 6 m. The torsional moment of inertia and the shearstresses at a centre line near the boundary are shown. Due to the constant formu-


Version 16.132−14

lation of the linearly varying boundary condition, results that are very close to theboundary are relatively inaccurate, while values on the boundary are much better.

The associated shear problem due to shear force can be solved exactly, even withcoarser element subdivision, and it yields resistance 0.04167 and shear deforma-tion area 0.8333 A = 30.0 m2.

SDIV 1 2 3 4 5 exact

Mom.of iner. IT

Warping

tau − Boundary

tau − 3.000 tau − 2.999 tau − 2.990 tau − 2.900

216.0 188.2 183.3 182.4 182.2

0.000 1.542 1.308 1.330 1.319

0.03139 0.0214 0.0220 0.0222 0.0222

0.0456 0.0372 0.0297 0.0258 0.02390.0303 0.0285 0.0252 0.0235 0.02280.0252 0.0255 0.0236 0.0227 0.02230.0197 0.0219 0.0214 0.0212 0.0212

182.2

1.312

0.0222

On the other side the system of equations may become quite large especially forcomposite sections, which leads to very high computation times, as the effortrises with the cube of the problem size.

SMOO

2

36

8

17

19

22

23

2631

36

14

14

11

14

14

11

34

34

31

44

44

41

54

54

51

64

64

61

74

74

71

84

84

81

94

94

91

For this section the cpu time can be dramatically reduced via definition of CTRLSDIV 0 and a sound value of SMAX for the outer polygon, yielding the followingresults:

SDIV/SMAX 0 / − 0 / ca 1/20 B 3 / −

IT [m4]zsmp [mm]

w−max [m2]CPU [sec]

0.5984−4551.276

11

0.3228−55.61.104

13

0.3136−58.01.126

>30 000


2−15Version 16.13

2.9. Shear Stresses in Thin Walled Sections.

The calculation of shear stresses for thin walled sections however is much easier.This is as with a beam analysis compared to a solid continua. I.e. there are closedsolutions possible which do not depend on the subdivision of elements. The the-oretical background has been developed and published by Schade [8].

Therefore AQUA uses the deformation method of the warping function for thesestypes of sections in all cases. The CTRL option STYP has no effects at all, butyou may specify explicit values via SV.

2.10. Plastic forces.

The calculation of fully plastic forces is a very complex task. The single values foreach force component may be evaluated easily, but the interaction of all forcesand moments is a rather extensive numerical problem. With AQUA/AQB youhave the following choices:

• Estimates for typical sections (AQUA−light)Normal force and bending moments can be evaluated precisely. For shearforces Vy the areas will be taken according to the Eurocode including theadditional fillet areas, which is a deviation to the simpler formulas given inDIN 18800 for steel shapes. For Vz the fillets will be ignored. For Mt a moreconservative approximation is done for thin walled sections, while for thicksections, the exact solution given by Bäcklund/Akesson is used.

• Evaluation of plastic forces using the real geometry (AQUA − Full Version)For thin−walled sections, the shear forces may be evaluated rather well(neglecting some plastic shear centre effects). For torsion however, it is dif-ficult in the very general case to distinguish clearly between open andclosed sections and the limiting torque. For thick polygonal sections, a puresum of areas would lead to significantly overestimated values for all shearproblems. AQUA therefore uses the shear deformation area, being up to20 % on the save side. For torsional effects a scaling based on the elastictorsional stress is applied.

• Evaluation of nonlinear interaction values for the real cross section geo-metry (AQB − record NSTR)With this method all prerequisites, like compatibility, yield criteria and equi-librium are fulfilled. However the evaluation is always done for a distinct


Version 16.132−16

force/moment combination. Thus the limiting value has to be found iterat-ively.

2.11. Program LimitsThe following program limits hold:

Materials 999Materials per cross section 31Cross sections 9999Reinforcement layers 10Polygon vertices per polygon 255Shear sections per cross section 255

2.12. Bibliography.[1] Katz,C. (1986)

Self−Adaptive Boundary Elements for the Shear Stress in BeamsBETECH 86, Boundary Element Technology Conference 1986Massachusetts Institute of Technology, Cambridge U.S.A.

[2] Wienecke, U.J. (1985)Zur wirklichkeitsnahen Berechnung von Stahlbeton− undSpannbetonstäben nach einer konsequenten Theorie II.Ordnungunter allgemeiner Belastung.Dissertation Technische Hochschule Darmstadt 1985

[3] Werner,H. (1974)Schiefe Biegung polygonal umrandeter Stahlbeton−QuerschnitteBeton− und Stahlbetonbau 1974 S 92−97

[4] Roik,Carl,Lindner (1972)Biegetorsionsprobleme gerader dünnwandiger StäbeWilhelm Ernst & Sohn, Berlin München Düsseldorf 1972

[5] Roth/Griesshaber (1966)Praktische Berechnung auf Biegung und Torsion beanspruchter Stäbemit dünnwandigen QuerschnittenTeubner, Leipzig.

[6] Bornscheuer, F.W. (1952)Systematische Darstellung des Biege− und Verdrehungvorgangesunter besonderer Berücksichtigung der WölbkrafttorsionDer Stahlbau 21 (1952), S 1−9


2−17Version 16.13

[7] Schade, D. (1969)Zur Wölbkrafttorsion von Stäben mit dünnwandigem QuerschnittIngenieur−Archiv, 38, S 25−34

[8] Schade, D. (1987)Zur Berechnung von Querschnittswerten und Spannungsverteilungenfür Torsion und Profilverformungen von prismatischen Stäben mitdünnwandigen Querschnitten.Z. Flugwiss.Weltraumforschung 11 , 167−173.

[9] Katz, C. (1997)Fließzonentheorie mit Interaktion aller Stabschnittgrößen beiStahltragwerkenDer Stahlbau 66 (1997), S 205−213


Version 16.132−18

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3−1Version 16.13

3 Input Description.

AQUA allows the user to define general cross sections with arbitrary geometryand materials. For simple sections and materials you do not need a special li-cense, but for all sections starting with record SECT you need a license for AQUA.

Before defining a section you have to specify the materials. Materials are ad-dressed by an arbitrary number. Please note, that by keeping track of constructionphases in AQBS, it is assumed that materials with higher material numbers wereadded at a later time.

A standard section is defined by just one input record. All sectional values will becalculated including torsional and shear properties. The maximum componentsfor all stresses are known, but a detailed analysis at different locations within thesection will not take place.

SVAL Sections without geometrySREC Rectangular sections, plates, T−beams and joistsSCIT Circular and annular sections via Diameter / ThicknessTUBE Tubular sectionsPROF Rolled Steel shapesCABL Cable sectionsSECT General section (AQUA licence required)

With AQUA cross sections can be redefined at any time during the processing ofthe project without affecting other defined sections. However if any material defin-ition is made, all existing cross sections are deleted. The distributions of reinforce-ments and stresses are deleted too, unless otherwise specified with CTRL REST.

Freely defined cross sections always start with the record SECT, which specifiesthe cross section number. All subsequent input records describe this one crosssection, which may consist of several partial cross sections (external perimeter,inner perimeter, reinforcement layout etc.). The input for a cross section is con-cluded either by the next SECT record or by two END records.


Version 16.133−2

3.1. Input Language.

The input occurs in a free format with the CADINP input language (see the gen-eral manual SOFiSTiK: ’Basics’).

3.2. Units

SOFiSTiK programs offer the possibility to carry out all input and output of datain engineering units. A number of unit sets are provided for this purpose, whichare preset according to the design code used in the given project. This default canadditionally be changed for each program run separately using the keywordPAGE. More information about unit sets can be found in the general SOFiSTiKmanual, section ’Units’.

Three categories of units are distinguished:m Fixed unit. Input is always required in the specified unit.[mm] Explicit unit. Input defaults to the specified unit. Alternatively, an

explicit assignment of a related unit is possible (eg. 2.5[m] ).[mm]1011 Implicit unit. Implicit units are categorised semantically and

denoted by a corresponding identity number (shown in green).Valid categories referring to the unit ’length’ are, for example,geodetic elevation, section length and thickness. The defaultunit for each category is defined by the currently active (designcode specific) unit set. This input default can be overridden asdescribed above. The specified unit in square bracketscorresponds to the default for unit set 5 (Eurocodes, NORM UNIT 5).

For sections the units for all dimesnions are expected in [mm] in general, the unitsets 0, 3 and 4 expect [m], the Unit−Set 1 [cm]. For reinforcement areas valuesare expected in [cm2], the unit sets 6 and 7 expect [mm2].


3−3Version 16.13

The following unit sets are provided:

0 = Standard units (m, kN, sec with some historic deviations) 1 = German buildings (sections in cm, system in m) 2 = German steel construction, (sections mm,cm2,dm4, system in m) 3 = Bridge construction (like 0 but internal forces in MN instead of kN) 4 = Soil Mechanics (m, kN, sec) 5 = Structural Engineering (sections in mm, system in m) 6 = Metric system (All dimensions in mm, loads in kN) 7 = Mechanical (All dimensions in mm, loads in N) 8 = imperial (US−Units, inch, foot, lbs, kip)

The default unit set (UNIT) of a corresponding design code is described in the re-cord NORM at the respective design code in the tables.


Version 16.133−4

3.3. Input Records.

The following records are defined:

Records Items

CTRL OPT VAL VAL2

NORM

MATE

MAT

MLAY

NMAT

BMAT

HMAT

CONC

STEE

TIMB

MASO

SSLA

MEXT

DC NDC COUN CAT ALT WIND SNOW SEIS

NO E MUE G K GAM GAMA ALFA E90M90 OAL OAF SPM FY FT TYPE TITL

NO E MUE G K GAM GAMA ALFA EYMXY OAL OAF SPM TITL

NO T0 NR0 T1 NR1 T2 NR2 T3 NR3T4 NR4 T5 NR5 T6 NR6 T7 NR7 T8NR8 T9 NR9 TITL

NO TYPE P1 P2 P3 P4 P5 P6 P7P8 P9 P10 P11 P12

NO C CT CRAC YIEL MUE COH DIL GAMBTYPE MREF H

NO TYPE TEMP KXX KYY KZZ KXY KXZ KYZS NSP A B C QMAX TK TITL

NO TYPE FCN FC FCT FCTK EC QC GAMALFA SCM TYPR FCR ECR FBD FFATFCTD FEQR FEQT GMOD KMOD GC GF MUEC TITL

NO TYPE CLAS FY FT FP ES QS GAMALFA SCM EPSY EPST REL1 REL2 R K1 FDYNFYC FTC TMAX GMOD KMOD QS TITL

NO TYPE CLAS EP G E90 QH QH90 GAMALFA SCM FM FT0 FT90 FC0 FC90 FV FVRFVB FM90 OAL OAF KMOD KMO1 KMO2 KMO3 KMO4KDEF TMAX RHO TITL

NO STYP SCLA MCLA E G MUE GAM ALFASCM E90 M90 OAL OAF FCN FC FT FVFHS FTB TITL

EPS SIG TYPE TEMP EPST TS MUET MNRB FCTF

NO EXP TYPE VAL VAL1 VAL2 ... VAL9


3−5Version 16.13

Records Items

BORE

BLAY

BBAX

BBLA

NO X Y Z NX NY NZ ALF TITL

S MN0 ES MUE DES VARI PMAX PMAL CPHI

S1 S2 K0 K1 K2 K3 M0 C0 TANRTAND KSIG D0 D2 CA0 CA2

S1 S2 K0 K1 K2 K3 P0 P1 P2P3 PMA1 PMA2 CL0 CL1 CL2 CL3 SM0 SM2

SVAL

SREC

SCIT

TUBE

CABL

NO MNO A AY AZ IT IY IZ IYZCM YSC ZSC YMIN YMAX ZMIN ZMAX WT WVYWVZ NPL VYPL VZPL MTPL MYPL MZPL BCYZ TITL

NO H B HO BO SO SU ASO ASUMNO MRF RTYP IT SAY SAZ DASO DASU REFBCYZ INCL SPT TITL

NO D T SA SI ASA ASI MNO MRFRTYP DAS TITL

NO D T MNO BC TITL

NO D TYPE INL MNO F K W KETITL


Version 16.133−6

Records Items

SECT

- CS

- SV

- POLY

- - VERT

- CIRC

- NEFF

- CUT

- PANE

- PLAT

- WELD

- PROF

- SPT

- SFLA

- WPAR

- WIND

NO MNO MRF ALPH YM ZM FSYM BTYPBCY BCZ KTZ TITL

NO TITL ATIL

IT AK YSC ZSC CM CMS AY AZ AYZLEVY LEVZ MNO DEFF FACE FACG

TYPE MNO YM ZM DY DZ SMAX EXPREFP REFD REFS

NO Y Z R PHI TYPE EXPREFP REFD REFS

NO Y Z R MNO EXPREFP REFD REFS REFR

TYPE YMIN ZMIN YMAX ZMAX MNO ALPHREFI RFDI RFSI REFA RFDA RFSA

NO YB ZB YE ZE NS MS WTM WTDMNO MRF LAY ASUP OUT TYPE VYFK VZFKINCL BMAX BRED BCT MUE SXE TANAREFA RFDA RFSA REFE RFDE REFS

NO YB ZB YE ZE T MNOREFA RFDA RFSA REFE RFDE RFSE R PHIOUT FIXB FIXE TYPEAS ASMA LAY MRF TORS DAS A

NO YB ZB YE ZE T MNOREFA RFDA RFSA REFE RFDE RFSE R PHIOUT FIXB FIXE TYPE

NO YB ZB YE ZE T MNOREFA RFDA RFSA REFE RFDE RFSE

NO TYPE Z1 Z2 Z3 MNO ALPH YM ZMREFP REFD REFS REFR DTYP SYM REF MREFVD VB VS VT VR1 VR2 VB2 VT2CW BCYZ WU1 WU2 WU3

NO Y Z WTY WTZ WVY WVZ SIGY TEFFCDYN SIGC TAUC MNO FIX REFP REFD REFS

NO U F S SH FP TYPE LEV TITL

CS KR ICE TRAF YMIN YMAX ZMIN ZMAX

ALPH CWY CWZ CWT REF CLAT S AG


3−7Version 16.13

Records Items

- RF

- LRF

- CRF

- CURF

NO Y Z AS ASMA LAY MRF TORS DAR SIG TEMP REFP REFD REFS

NO YB ZB YE ZE AS ASMA LAY MRFTORS D A ARREFA RFDA RFSA REFE RFDE RFSE R PHI

NO Y Z R PHI AS ASMA LAY MRFTORS D A AR REFP REFD REFS REFR

H DE AS ASMA LAY MRFTORS D A AR CENT

TVAR

INTE

IMPO

EXPO

NAME VAL SCOP CMNT

NO NS0 NS1 S NREF ICS ... ICS9

MAT SECT FROM

MAT SECT TO PASS

ECHO OPT VAL VAL2


Version 16.133−8

SCITSREC

The records HEAD, END and PAGE are described in the general manualSOFiSTiK: ’Basics’.


3−9Version 16.13

3.4. CTRL − Control of Analysis

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

CTRL

Item Description Unit Default

OPT A literal from the following list:REST Restart options

(like deletion of data at restart)FACE Standard view on section

POS = positive faceNEG = negative faceor numerical value

RFCS Minimum reinforcementfor computingideal cross section values

HMIN max, length of polygon edgesHTOL max. stitch of circular arcsSTYP Method of shear for solid

sectionsSDIV Subdivision for intergral

equation methodSCUT Number of standard shear

sectionsFIXL Max. factor for thickness

step for buckling paneldetection

REFD Control for the input ofreferences

LIT FULL

VALVAL2

The value of the optionAdditional value for the option

−−

**

The CTRL options may be defined at any location within the input data. Howeverif they are intended to be different for individual sections it is mandatory to definethem before the sections intended to use them. Within a reatsrt CTRL REST 3 alldefined options will be effective for all reanalyted sections.

CTRL REST controls what AQUA should do with existing data in the database.As default AQUA will erase everything if materials are defined, and only the min-imum reinforcements, limit stresses and beam stiffnesses if only sections aredefined. This is usually the best choice to avoid unforeseeable results. In some


Version 16.133−10

cases though it is desirable to process these results further. This can take placewithout problems only, if the assignment of the layers and the use of the materialnumbers in the individual cross sections are not changed.

0 delete old values in the database (default)1 keep old values in the database2 Keep all values, even if material is changed, implies a possible reanalysis of the sections. CTRL REST 2 nn will reanalyse section nn. 3 Reanalyse all sections

CTRL FACE defines the standard view on the section. While the physical orienta-tion in space is only specified by the orientation of the local beam coordinate sys-tem, the possible values for graphical views on the section are defined that theliteral POS and all positive numbers define a view on the positive face (i.e. in theinverse direction of the beam or axis) while the literal NEG and all negative valuesdefine a view on the negative face (ie. along the direction of the beam or axis) :

POS y−axis to the left, z−axis downwards (default)NEG y−axis to the right, z−axis downwards1,3 rotation by 0 or 180 degrees (y−axis horizontal)2,4 rotation by 90 or 270 degrees (y−axis vertical)>4 rotated against the default by VAl degrees

CTRL RFCS controls whether minimum reinforcement should be considered inthe calculation of the cross section values:

0 do not consider1 consider for composite sections (default)2 consider for all sections3 consider also effect on dead load+4 do not assign reinforcement to any partial section

HMIN defines a maximum allowed length for linear or circular polygon edges.(Default: no limit)

HTOL defines the maximum allowed stitch (error) of an approximation of a circu-lar arc by a polygon. This is effective on Fillets and arcs. Default: 2[mm].

The meanings of STYP, SDIV and SCUT are explained in paragraph 2.7.

CTRL STYP controls the analysis of shear stresses in solid sections:

0 force method


3−11Version 16.13

1 displacement method only for It and location of shear centre (default for concrete and concrete composits)

2 displacement method for torsion,force method for shear

3 displacement method for torsion and shear, shear deformation areasare determined (default for steel, timber and other composits)

Options 2 and 3 should be used for composite sections, but with caution.

SCUT controls the generation of the two standard cuts parallel to the coordinateaxis and the standard stress points:

SCUT +0 do not generate default shear cuts+1 create main shear cut at gravity center+2 create both default shear cuts at gravity center+8 shear is evaluated according to the force method

for the gross section instead of the effective section.+0*16 do not generated stress points+1*16 corner points with maximum distance (Points 1:4)+2*16 Intersection of principal axis with section (Points 5:8)+4*16 Intersection of principal axis with convex hull (Points 5:8)+128 with original coordinate system instead of principal axes+256 use only z−ordinates (uniaxial bending)

The fineness of the subdivision for the integral equation method is controlled bythe input value CTRL SDIV. This indicates how large an element may be com-pared to the largest dimension of the cross section.

0 No subdivision1 maximum 1/22 maximum 1/43 maximum 1/84 maximum 1/16 (default)

A snap distance (always in m) for the detection of cross section parts connectingtogether can be defined additionally at item VAL2. The value SDIV 4 0.001defines 1 mm, as snap measure.

As the input of references is best done with relative offsets (default: CTRL REFD1), the export however with the actual absolute coordinates, the input CTRLREFD 0 allows to change the default to the definition in absolute coordinates. In


Version 16.133−12

that case it is also allowed to make a reference to an element defined later in theinput stream, but all coordinates will be taken exactly as they have been specified.


3−13Version 16.13

3.5. Materials.

SOFiSTiK supports a large number of different material descriptions. All will beaddressed by a unique material number and should in general be usable every-where. The default for the material type is dependant on the selected design code.

The basic properties are entered via the records:

NORM Selection of a design code or a design code familyMATE General material definition including strengthCONC Concrete materialSTEE Steel and other metallic materialsTIMB Timber/lumber and Fibre materialsMASO Masonry / BrickworkMLAY Layered composite material for QUAD elements

These records are mutually exclusive but may be enhanced by other records:

BMAT Elastic support

NMAT Non−linear material properties for MAT/MATE(ASE/TALPA for QUAD and BRIC elements)

HMAT Material definitions for HYDRA(Thermal or Seepage problems)

SSLA Uniaxial strain−stress law for materialsCONC/STEE/TIMB/MASO

MEXT Special material properties

Input of material is possible in all parts of the program system. However, it is self−evident that not all parameters are used for all types of analysis or system. Eachmaterial has a standard name given by its classification, which might be extendedby the user. If the user wants to replace the standard completely, he has to starthis own text with an exclamation mark (e.g. ’!my own Text’) or to quote it a secondtime (eg. “ ’my own Text’ ”).

Properties of materials must be distinguished according to whether they are prop-erties which are close to the realistic behaviour (e.g. for dynamic calculations) orto which have some lower or upper limit to be multiplied with a safety factor forthe calculation of an ultimate load−bearing capacity. Whereas the safety factorswere formerly assigned more−or−less at random, sometimes to the load andsometimes to the material, more recent regulations (Eurocode) provide a clearer


Version 16.133−14

separation between safety factors for the loads and factors for the material.However, since the material safety factors still depend on the nature of the loador the type of design, it will not be possible to define all safety factors with the ma-terial itself.

SOFiSTiK provides therefore the definition of:

• Properties and safety factors for the standard design

• Mean values or calculation values and safety factors for nonlinear service-ability and deformation analysis

If some design codes (DIN 18800, DIN 1045−1) apply additional safety−factorsto the mean values, this may be defined with the stress−strain relation via SSLA.The safety factor defined with the material will thus be used only for the full plasticforces in AQUA.

Note: The following pages are valid in all details only for AQUA, for other pro-grams (SOFiMSHB) deviations are possible due to older versions with missingor changed items.

Note: Hints for material properties of strange materials may be found on the inter-net at www.azom.com (The A to Z of Materials).


3−15Version 16.13

3.6. NORM − Default Design Code

ÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖ

NORM


DC Design code familyEN EurocodesDIN German StandardsOEN Austrian StandardsSIA Swiss StandardsAS Australian StandardBS British StandardIS Indian StandardsJS Japanese StandardUS US Standards (ACI etc.)GB Chinese Building CodesNF French StandardsI Italian StandardsE Spanish StandardsS Swedish StandardsDS Danish StandardsNS Norwegian StandardsSNIP Russian StandardsNZS New Zealand StandardsET Egypt Building CodesMSZ Hungarian StandardsSFS Finnish StandardsNEN Netherlands StandardsNBR Brazilian StandardNBN Belgian Standards

LIT EN

NDC Designation of a specific design code Lit16 −


Version 16.133−16

Item DefaultUnitDescription

COUN Country code for boxed values within EN00 General ENFR / F / 33 FranceES / E / 34 Spain IT / I / 39 Italy CH / 41 SwitzerlandAT / A / 43 AustriaUK / 44 Great BritainDE / D / 49 Germanyor any other valid TLD

− *

CATALTWINDSNOWSEISWCAT

Category or ClassAltitude above sea levelWind zoneSnow zoneSeismic zoneTerrain category for wind

Lit4m

Lit4Lit4Lit4Lit4

−/!0.0****

UNITLANG

Selection of a set of unitsSelection of output language

−−

**

Many defaults for materials, superposition and design are selected according tothe selected design code and an optional country code and all the other data pro-vided with this record. It is therefore strongly recommended to specify this datawith the beginning of the project.

A redefinition of the design code after the definition of actions or load caseshave been defined or the editing of the INI−File to include “missing” ma-terials does not comply with the provisions of SOFiSTiK for a proper use ofthe software.

It is possible to redefine the design code NORM temporarily (eg. concrete / steeldesign) if the parameters of the loading definitions remain the same, but as thishas some special risques, the user should use this option very thoroughly.

Although there are still explicit code fragments in the software unavoidable, manyof the defaults are specified in so called INI−Files located in the SOFiSTiK direc-tory. The name of the matching INI−file is derived from the given data asDC_NDC.INI.


3−17Version 16.13

Some properties (e.g. Eurocode) are dependant on national variants (boxed va-lues). Corresponding INI−files to EN 1992−2004 and EN 1993−2005 and thecountry code may be used to select those values, as far as we have got noticeof them. The country code for example is valid for deviations in Hong Kong to theBritish Standard or similar.

Some codes require or allow the selection of a category or class. This can thenbe specified with CAT. The possible items are given in the INI−File. In the caseof a subsequent modification of these classes or categories the inputswhich depends on the design code have to be checked and adapted if ne-cessary.

The extend to which the specified altitude, wind/snow or earthquake zone defini-tions are accounted for is described in the program manuals of the modules usingthose values. The user should never assume that all regulations of the designcodes are automatically fulfilled when selecting such a value. The possible itemsand defaults are given in the matching INI−File. The resultant values which resultfrom the altitude or the wind/snow/earthquake zones have to be checked in thecorresponding programs in the case of a subsequent modification. E.g. for somdesign codes the combination coefficients of the snow depend on the altitude. Inthe case of the modification these combination coefficients have to be adapt bythe user if necessary.

If the user wants to suppress such a value completely he may specify it with“NONE”.

The items UNIT and LANG will be processed only in AQUA or TEMPLATE. Witha definition of UNIT a set of units will be selected globally for all input and outputdata in all other modules. The default is specified in the INI−file. The item LANGwill define the language for all results. The default is depending on the selectedinput language.

Definitions with record PAGE will be active only within the current module.


Version 16.133−18

The following design codes are available as INI−Files and/or special programcode has been created to cope with special regulations. The marks A, B and Cindicate if this code has been implemented in AQB, BEMESS and the SOFis Formore detailed information, especially which provisions of the codes have beenimplemented, please check the manuals and the HTM−files of the design pro-grams. In many cases it is possible to add some clauses within short time withinthe program or with CADINP.

EN − Eurocodes

Description UNIT Design

EN 1992−2004 EN 1992−1 (2004)CAT AN/AP Building construction

Table 7.1N EN 1992−1−1CAT B,C,D Bridges

5 A,B

EN 1993−2005 EN 1993−1 (2005)CAT A Building constructionCAT B,C,D Bridges

5 A

EN 1994−2004 EN 1994−1 (2004)CAT A Building constructionCAT B,C,D Bridges

5 A

EN 1995−2004 EN 1995−1 (2004) 5 A

EN 1996−2005 EN 1996−1 (2005) 5 A

EN 1997−2004 EN 1997−1 (2004) 5 A

EN 1999−2007 EN 1999−1 (2007) 5 A

EN 1992−1991 EN 1992−1 (1991) 5 A,B,C


3−19Version 16.13

DIN − Deutsche Norm


DIN EN1992−2004 DIN EN 1992−1−1/NA:2011DIN EN 1992−2/NA:2011CAT AN/AP/AV Hochbau Tabelle7.1

DECAT B,C,D Brückenbau

5 A,B

DIN EN1993−2005 DIN EN 1993−1−1/NA:2010−12CAT A HochbauCAT B,C,D Brückenbau

5 A

DIN 1045−2008 DIN 1045−1 (2008)CAT −/A/B/C/D/E/F (Tab. 18)

Klassifizierung von Nachweis−bedingungen

0 A,B,C

DIN FB102−2009 DIN Fachbericht 102 (2009)CAT A/B/C/D/E (Tab. 4.118)


0 A,B

DIN FB103 DIN Fachbericht 103 (2003) 2 A

DIN FB 104 DIN Fachbericht 104 (2003)CAT A/B/C/D/E (Tab. 4.118 des FB

102), Klassifizierung vonNachweisbedingungen

0 A

DIN 18800 Stahlbau (Nov. 2008)CAT A/B

A voreingestellte Über−lagerung DIN 18800

B voreingestellte Über−lagerung DIN 1055−100

2 A

DIN 1052−2008 Holzbau (2008) 0 A

DIN 1045−1 DIN 1045−1 (2001)CAT −/A/B/C/D/E/F (Tab. 18)


0 A,B,C


Version 16.133−20

DIN FB 102−2003 DIN Fachbericht 102 (2003)CAT A/B/C/D/E (Tab. 4.118)


0 A,B

DIN 1045 Alte Norm (1988)DAfStb hochfest.Beton (1995)

0 A,B,CA

DIN 1052 Holzbau (1988) 0 A

DIN 1054 Grundbau (2005) 0

DIN 4227 Alte Spannbetonnorm + Anhang A1(1995)

0 A

DIN 4228 Betonmaste (1990) 0 A

DIN 18800−1990 Stahlbau (1990) 2 A

OEN − Österreichische Norm


OEN EN1992−2004 OENORM B 1992−1 (2011)OENORM B 1992−2 (2008)CAT AN/AP/AV Hochbau Tabelle 4

B 1992−1−1CAT B,C,D Brückenbau B 1992−2

5 A,B

OEN EN1993−2005 OENORM B 1993−1−1 (2007)CAT A Hochbau CAT B,C,D Brückenbau

5 A

OEN 4700 Stahlbeton OENORM B 4700 (2001) 0 A,B,C

OEN 4750 Spannbeton OENORM B 4750(2000)

0 A

OEN 4300 Stahl OENORM B 4300 (1994) 0 A

For the old design codes OEN 4200, OEN 4250, OEN 4253 no INI files exist. Theprogram AQB is so programmed that the appropriate design is done with inputof the design code. As materials BOE is input for concrete and BSOE for steel.


3−21Version 16.13

SIA − Schweizer Norm


SIA 262 Schweizer Betonbaunorm (2003) 0 A,B

SIA 263 Schweizer Stahlbaunorm (2003) 2 A

SIA 265 Schweizer Holzbaunorm (2003) 0 A

SIA 162 Schweizer Stahlbetonnorm (1989) 0 A

BS − British Standard


BS EN1992−2004 NA to BS EN 1992−1−1:2004 (2005)CAT AN/AP Building construction

Table 7.1N EN 1992−1−1CAT B,C,D Bridges

6 A,B

BS 8110 British Standard Concrete (1997) 6 A,B

BS 5400 British Standard Concrete Bridge(1990)CAT 0 without PrestressCAT 1/2/3 Prestress for Class 1/2/3

6 A

BS 5950 British Standard Steelwork (2001) 6 A


Version 16.133−22

US − American Standards and Unified Building Code


US ACI−318−08 American Standard ACI / UBC (2008) 0 A,B

US ACI−318−02 American Standard ACI / UBC (2002)incl. ACI−318−05

0 A,B

US ACI−318−99 American Standard ACI / UBC (1999) 0 A

US AASHTO−2010 American Highway (2010) 0 A



US AISC−2005 American Standard AISC (Steel)2005

0 A

US AISC American Standard AISC (Steel)1998

0 A

SNIP − Russian Standards


SNIP 52101 SP 52−101−2003 (2004) (Concrete) 0 A,B

SNIP 20301 SNIP II 03.01 − 84 (89) (Concrete) 0 A,B

SNIP 22381 SNIP II 23.81 (89) (Steel) 2 A

SNIP RK50333 SNIP RK 5.03−33−2005 (Concrete)Kasakhstan

0 A

IS − Indian Standards


IS 456 Indian Standard (2000) (Concrete) 6 A

IS IRC18 Indian Roads CongressPrestressed Road Bridges

6 A

IS IRC21 Indian Roads Congress RoadBridges

6 A

IS IRC112 Indian Roads Congress: Code ofPractice for Concrete Road Bridges(2011)

6


3−23Version 16.13

AS − Australian Standards


AS 3600 Concrete Structures (2009) 6 A,B

AS 4100 Structural Steel (1998) 6 A

AS 5100 Bridge Design (2004) 6 A

E − Instrucciones espaniola


E EHE Instrucion de hormigón estructuralNivel de control de ejecución:EHE NormalEHE_INTENSIO IntensioEHE_REDUCIDO Reducido

0 A,B

I − Decreto Ministeriale Italiane


I DM−2008 Decretto Ministeriale 2008CAT A1 Costruzioni CiviliCAT A2/A3 Ponti

0 A,B

I DM−2005 Decretto Ministeriale 2005 0 A,B

I DM−96 Decretto Ministeriale 9. gennaio1996:Parte I: Cemento armato normale

e precompressoParte II: AcciaioParte III: Manufatti prefabbricati

prodottiParte IV: Costruzioni composte d

elemeti in metalliParte V: Per travi composte

“acciaio − calcestruzzo”

0 A,B,C

I EC Decretto Ministeriale 9. gennaio1996:Parte VIII: Eurocode

0 A,B,C


Version 16.133−24

Note for I EC:This will select EC as design code with a Country−Code I (39) and additionallyintroduce the materials of the Italian decreto (CAN, CAP, FEB etc.).

NF − AFNOR Association francaise de normalisation


NF EN1992−2004 Annexe Nationale á la NF EN1992−1−1/−2 CAT AN/AP Bâtiment Tableau

7.1NF NF EN 1992−1−1/NA

CAT B,C,D Ponts

5 A,B

NF BAEL Règle techniques de conception et decalcul des ouvrages et constructionen beton armé suivant la methodedes états limites.BAEL−91 revisées 99

0 A,B


3−25Version 16.13

S − Svenska Boverkets Konstruktionsregler (BKR)


S EN1992−2004 National Annex to Eurocode 2SS−EN 1992−1−1:2004/NA:2009, SS−EN 1992−2:2005/NA:2009CAT A1 byggnader & säkerhets−

klass 1A2 byggnader & säkerhets−

klass 2A3 byggnader & säkerhets−

klass 3B1 vegbruer & säkerhets−



klass 3C1 gangbruer & säkerhets−



klass 3D1 jernbanebruer &

säkerhetsklass 1D2 jernbanebruer &

säkerhetsklass 2D3 jernbanebruer &

säkerhetsklass 3

5 A,B

S BBK−04 Boverkets Handbok om Betong−konstruktioner CAT 1/2/3 (Säkerhetsklass låg/normal/hög)

0 A,B

S BBK−94 Boverkets Handbok om Betong−konstruktioner CAT 1/2/3 (Säkerhetsklass låg/normal/hög)

0 A,B

S BRO−2004 Vägverket BRO 2004 0 A


Version 16.133−26

DS − Danish Standard


DS EN1992−2004 National Annex to Eurocode 2EN 1992−1−1 DK NA:2007CAT LE low safety & extended

controlNE normal safety &

extended controlHE high safety & extended

controlLN low safety & normal

controlNN normal safety & normal

control (default)HN high safety & normal

controlLR low safety & reduced

controlNR normal safety & reduced

controlHR high safety & reduced

control− safety acc. to EN 1990 DK NA:2007consequences classes− control acc. to EN 1992−1−1 DKNA:2007 inspection level

5 A,B


3−27Version 16.13

DS 411 Norm for betonkonstruktionerCAT LE low safety & extended









control

0 A,B

DS 411−bro Norm for betonkonstruktioner Default for superpositions for bridges

3 A,B


Version 16.133−28

NS − Norsk Standard


NS EN1992−2004 National Annex to Eurocode 2NS−EN 1992−1−1:2004/NA:2008, NS−EN 1992−2:2005/NA:2010CAT A1 bygninger & pålitelighets−

klasse 1A2 bygninger & pålitelighets−



klasse 4B vebruer (pålitelighets−

klasse 3)C gangbruer (pålitelighets−

klasse 3)D jernbanebruer (pålitelig−

hetsklasse 3)

5 A,B

NS 3472 Prosjektering av StålkonstruksjonerCAT 1/2/3/4 (Pålitelighetsklasse)

Liten / Middels / Stor / Saerlig stor

0 A

NS 3473 Prosjektering av Betongkonstruks−jonerCAT 1/2/3/4 (Pålitelighetsklasse)

Liten / Middels / Stor / Saerligstor

0 A


3−29Version 16.13

SFS − Finnish Standard


SFS EN1992−2004 National Annex to Eurocode 2SFS−EN 1992−1−1 NA:2007CAT LE low safety & extended









control− safety acc. to SFS−EN 1990 NAconsequences classes− control acc. to SFS−EN 1992−1−1NA:2007 inspection level

5 A,B

SFS TA1992−2004 National Annex to Eurocode 2 forbridges onlyCAT B,C,D,E Bridges

5 A

NEN − Netherlands Standard


NEN EN1992−2004 NEN−EN 1992−1−1:2005/NB:2007(EN 1992−1(2004))CAT AN/AP Building construction

Table 7.1N EN 1992−1−1

CAT B,C,D Bridges

5 A,B


Version 16.133−30

NBN − Belgian Standard


NBN EN1992−2004 NBN EN 1992−1−1 ANB:2010CAT AN1−AN3/AP1−AP3

Building constructionTable 7.1N EN 1992−1−1

CAT B1−B3,C1C3,D1−D3Bridges

5 A,B

MSZ − Magyar Szabvány


MSZ UT414 Code of Roadbridges 0 A,B

NZS − New Zealand Standards


NZS 3101 Concrete Structures Standard (1995) 6 A,B

ET − Egypt Reinforced Concrete Design Code


ET RC−2001 Based on description “Reinforced Concrete DesignHandbook” Prof.Dr.Shaker El−Behairy, AinShams Univers.

0 A,B

GB − Chinese Standard


GB 50010 Chinese Standard for ConcreteStructures (2002)

0 A

JS − Japan Standard


JS JRA Japan Road Association Standard(2002)

0 A


3−31Version 16.13

NBR − Brazilian Standard


NBR 6118−2003 Norma Brasileira, Projeto de estrutu-ras de concreto − Procedimento CAT A EdifíciosCAT B Pontes rodoviáriasCAT C Passarelas de pedestresCAT D Pontes ferroviárias

5 A


Version 16.133−32

3.7. MATE − Material Properties

ÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖ

MATE


NO

EMUEGKGAMGAMAALFA

Material number

Elastic modulusPoisson’s ratio (between 0 and 0.49)Shear modulusBulk modulusSpecific weightSpecific weight under buoyancyThermal expansion coefficient

−

MPa−

MPaMPa

kN/m3

kN/m3

1/°K

1

****

25*

E−5

E90M90OAL

OAF

SPMFYFT

TYPETITL

Anisotropic elastic modulusAnisotropic poisson's ratioMeridian angle of anisotropyabout the local x axisDescent angle of anisotropyabout the local x axisMaterial safety factorDesign strength of materialUltimate strength of material

Material type for default valuesMaterial name

kN/m3

−deg

deg

−MPaMPa

LITLit32

EMUE

0

0

1.0−−

−−

Materials which can be used for SVAL or QUAD and BRIC elements may bedefined with the record MATE. The number of the material must not be used forother materials.

With the definition of a literal at TYPE from the following list, default values willbe selected:

GLAS, ESG Floatglass, toughened safety glasVSGh, VSGv laminated (horiz./vertical usage), TVG semi−tempered glasCu, Pb, Mg, W, Zn Copper, Lead, Magnesia, Wolfram, ZincBRAS, BRON brass, bronce


3−33Version 16.13

CLAY, SAND clay, sandROC1, ROC2 crystal rock, sediment rockROC3, ROC4 light sediments, porous rock

BRIC, SLBR, CLIN brick, sand−lime−brick, clincerIGYP, GYPS isolat. gypsum, standard gypsum plasterMOGY, MOCH, MOCE gypsum/chalc/cement mortar

ASPH, BITU Asphalt, BitumenCARP, WOOL Carpet, Felt/WoolCORK, LINO Cork, Linoleum

EPOX, PHEN, PEST Epoxid−, Phenol−, Polyester resinACRY, PC, PTFE Acryl, Polycarbonat, PolytetrafluorethylenPVC, PMMA Polyvinylchlorid, PolymethylmethakrylatPOM, PA Polyazetat, Polyamid/NylonPEHD. PELD Polyethylen high/low densityPS. PP, PUR Polystyrol, Polypropylen, PolyurethanRUBB, NEOP, EBON Rubber, Neopren, EbonitEPDM, PSUL, BUTA Ethylen−Propylenedien,Polysulfid,ButadienSI, SILA Silicone, Silica FOAM, FOAS, FOAU foamed rubber, silicone, urethanFOAC, FOAR, FOAE foamed PVC, PUR, PE

The mechanical properties of those materials are not always known with a distinctvalue or even suitable for a linear material descripotion at all!

Further TYPE may be used to preset fluid material constants for:

AIR Air (1 bar, 20 deg Celsius)H2O Water (1 bar, 10 deg. Celsius)CO2, O, N Carbondioxid, Oxygen, NitrogenAR, KR, XE, SF6 Argon, Krypton, Xenon, Sulfurhexafluorid

where MUE is the kinematic viscosity ν [m2/sec].


Version 16.133−34

Sometimes it is more convenient to define the elastic constants by other valuesthan the Elasticity modulus, the Shear modulus and the Poisson ratio. You maytransform your values by the following formulas:

E Elastic modulusEs subgrade modulus (horizontally constrained)K Bulk modulusG Shear modulusμ Poisson’s ratio

K� E3(1� 2�)

G� E2(1��)

E� 9·K·G(3K�G)

�� 3K� 2G6K� 2G

Es�E��1��

(1��)(1�2�)

G� 3·K·E9·K�E

G� 3·K·(1� 2�)2·(1��)

If not specified, missing values will be calculated according to these formulas. Itis, however, possible to define non−consistent constants. If no values are given,E defaults to 30000 MPa and MUE to 0.2.

Orthotropy may be defined via material and thickness of QUAD elements. (seerecord QUAD in SOFiMSHA and manuals to ASE, SEPP and TALPA).

The material law of a transversal orthotropy according to Lechnitzky has one dir-ection that has different properties, while the description in the plane perpendicu-lar to this direction remains isotropic. This covers most practical problems like tim-ber and rock. Unfortunately the designation of the general material constants fortimber materials is not compatible with that convention, so we strongly recom-mend to use TIMB for the description of timber materials.

The principal values E and � are related to the isotropic plane, while E90 (MATstill old literal EY) acts normal to that plane and μ90 and G90 (attention: input para-meter G) describe the transverse straining behaviour between normal directionand isotropic plane. With z being the normal direction we have:

�x� �xE��·

�yE��90·

�zE90


3−35Version 16.13

�y��yE��·�x

E��90·

�zE90

�z� �zE90

��*90·

(�x��y)E

�*90� �90·

EE90

It should be noted, that poisson’s ratios μ90 and μ90* are no longer limited by an

upper bound of 0.5 (this would hold for the isotropic case). According to theformula given above, their relation is determined by the ratio of the elasticity mod-uli; this preserves symmetry of the stress strain matrix, which is required to fulfillelemental equilibrium.

The order of the indices of stress and strain components for subsequent equa-tions is defined as:

[ x y z xy xz yz ] general three−dimensional case[ x y xy z ] plane stain condition, axial symmetry[ x y xy ] plane stress

With axial symmetry x denotes the axis of rotation while y represents the radialand z the tangential direction.

Furthermore holds:

E1�E , E2�E90 , �1� � , �2� �90 , G1�E1

2�1� �1� , G2�G

General three−dimensional case: The three−dimensional material matrix is obtained by inversion of the strainstress relations and reads (z being the direction normal to the isotropic plane):

D�

��

�

�

E1�1� n��2

2�1� �1

� �m

E1��1� n� �2

2�1��1

� �m

E1��2m

0

0

0

�E1��1� n � �2

2�1��1

� �m

�E1�1� n� �2

2�1� �1

� �m

E1��2m

0

0

0

E1��2m

E1��2m

�E2�1��1

m0

0

0

0

0

0

�G1�

0

0

0

0

0

0

G2

0

0

0

0

0

0

�G2

��

�

�


Version 16.133−36

n�E1E2

, m� 1� �1� 2� n��22

Plane strain conditions: Here we have in difference to the three−dimensional case, the y direction definedas normal to the isotropic plane. The reduced material stiffness matrix yields:

D�

��

�

�

E1�1� n��2

2�1��1

� �m

E1��2m

0

E1��1� n� �2

2�1��1

� �m

E1 ��2m

E2�1� �1

m0

E1 ��2m

0

0

G2

0

��

�

�

n�E1E2

, m� 1� �1� 2� n��22

Plane stress conditions: Here we have in difference to the three−dimensional case, the y direction definedas normal to the isotropic plane. The material stiffness matrix is obtained via inver-sion of the reduced three−dimensional strain−stress matrix and reads:

D��

�

�

E1

1� n��22

E1 ��2

1� n��22

0

E1� �2

1� n ��22

E2

1� n ��22

0

0

0

G2

��

�

�

, n�E1E2

Axial symmetry: A general case of anisotropy does not need to be considered since axial sym-metry would be impossible to achieve under such circumstances. A case of in-terest in practice is that of a stratified material in which the rotational axis x is nor-mal to the plane of isotropy. For such a case the material stiffness matrix reads:

D�A�

��

�

�

1��21

n

�2�1��1

�

0

�2�1��1

�

�2�1� �1

�

�1� n�22�

0

�1� n�22

0

0

G90A

0

�2�1��1

�

�1� n�22

0

1� n�22

��

�

�


3−37Version 16.13

A�E2 � n

�1� �1� �m

, n�E1E2

, m� 1� �1� 2� n��22

Skew orthotropy:Consideration of ’skew’ orthotropy is also possible. In geological terms, the three−dimensional orientation of the isotropic plane is defined by means of the meridianand descent angle. They describe the deviation of the steepest descent to thenorth direction and the inclination of the layers. Mathematically, the angles areequivalent to the first and third of the Eulerian angles. The transformation isdefined by two rotations, the north axis (N) corresponding to the element y−direc-tion and the G−axis corresponding to the element z−direction. Axes K, N and Gform a right handed Cartesian coordinate system.

The transformation is defined as follows:

1. Rotation of axes K and N by meridian angle OAL about G−axis

2. Subsequent tilting of the rotated system (K’, N’, G’=G) by descentangle OAF about axis K’.

Apart from 3D continuum elements these transformation rules apply to shells andplates, as well.

For planar systems (TALPA) the value OAL defines the slope of the stratification,i.e. the angle between the element x−direction and the stratification direction. In-put for OAF is not evaluated for the plane case.

For axial symmetry input of OAF and OAL is not evaluated (see above: axial sym-metry).


Version 16.133−38

3.8. MAT − General Material Properties


MAT


NO

EMUEGKGAMGAMAALFA

Material number

Elastic modulusPoisson’s ratio (between 0 and 0.49)Shear modulusBulk modulusSpecific weightSpecific weight under buoyancyThermal expansion coefficient

−

kN/m2

−kN/m2

kN/m2

kN/m3

kN/m3

1/°K

1

*0.2**

25*

E−5

EYMXYOAL

OAF

SPM

TITL

Anisotropic elastic modulus EyAnisotropic poisson’s ratio m−xyMeridian angle of anisotropyabout the local x axisDescent angle of anisotropyabout the local x axisMaterial safety factor

Material name

kN/m2

−deg

deg

−

Lit32

EMUE

0

0

1.0

−

Materials which can be used for SVAL or QUAD and BRIC elements may bedefined with the record MAT and MATE. The number of the material must not beused for other materials.

The differences between the two records are mainly the used dimensions. MATEis analogue to CONC,STEE etc. (MPa) and has additional strength values, whileMAT uses (kN/m2) analogue to NMAT. MAT has older item names for the ortho-tropic parameters.


3−39Version 16.13

3.9. MLAY − Layered Material


MLAY


NOT0NO0T1NO1...T9NO9TITL

Number of composite materialThickness of first layerMaterial number of first layerThickness of second layerMaterial number of second layer

Thickness of 9th layerMaterial number of 9th layerMaterial Designation

−*−*−

*−

Lit32

1!!!!

−−−

With MLAY you may define for QUAD elements a composite layered material withup to 10 layers. Each layer may be defined with a positive absolute thickness ora negative relative one. The total thickness of the element will be calibrated to thesum of the thicknesses of the material definition. If some layers have negativethickness only these layers will be adapted. Otherwise a uniform scaling will takeplace.

If you have a sandwich element with two outer laminates with a given thicknessfor example:

MLAY 1 0.02 1 $$ upper laminate -1.00 2 $$ interior laminate 0.02 1 $$ lower laminate

then this data will be applied to match two QUAD elements with a total thicknessof 0.10 or 0.15 as follows:

MLAY 1 0.02 1 $$ upper laminate 0.06 2 $$ interior laminate if 0.10 total thickness 0.02 1 $$ untere Deckschicht

MLAY 1 0.02 1 $$ upper laminate 0.11 2 $$ interior laminate if 0.15 total thickness 0.02 1 $$ lower laminate

For non−linear calculations a material definition with mean values is stored.


Version 16.133−40

3.10. NMAT − Non−linear Material


NMAT


NOTYPE

Material numberKind of material law

LINE Linear materialVMIS von Mise law, optional

viscoplastic extensionDRUC Drucker−Prager law, optional

viscoplastic extensionMOHR Mohr Coulomb lawGRAN Granular hardeningSWEL SwellingFAUL Faults in rock materialROCK Rock materialMISE Mise / Drucker Prager lawGUDE Gudehus lawLADE Lade lawMEMB Textile membraneUSP1 to USP8 and USD1 to USD8

reserved for user defined materialmodels

−LIT

1!

P1P2P3P4...P12

1st parameter of material law2nd parameter of material law3rd parameter of material law4th parameter of material law

...12th parameter of material law

****

*

−−−−

−

The types of the implemented material laws and the meaning of their parameterscan be found in the following pages.

In a linear analysis the yield function for the non−linear material is merelyevaluated and output. This enables an estimation of the non−linear regions for asubsequent non−linear analysis.

If TYPE LINE is given, the material remains linear.


3−41Version 16.13

3.10.1. Invariants of the Stress TensorFor the present chapter, as long as not specified differently, the followingconventions hold:

I1�� x��y��z

Deviatoric stress tensor:

sx�� x�I13

sy�� y�I13

sz�� z�I13

J2��12(sx

2� sy2� sz

2)� �xy2� �yz

2� �xz2

J3�� sxsysz� 2�xy�yz�xz� sx�yz2� sy�xz

2� sz�xy2

��13sin�1�

�

�� 3 3� J3

2J232

��

�; ��

6� ��

6

3.10.2. Material ParametersNon−linear material parameters have to be selected very carefully. Especially forsoil and rock mechanics the values of the site have to be used, at least for the finaldesign. There are some values available in literature (e.g. EC7, DIN 1055 part2, EAU), but these values are hardly usable for a non−linear FEM analysis. If wecite some of the values here, we deny any responsibilities for the correct selectionof values for any current project.

Angle of friction:The angle of friction is zero for most fine grained cohesive soils under undrainedconditions. Friction angles larger than 40 degrees are encountered rarely.

Note: A slope without cohesion world cannot be steeper than the material’sultimate friction angle.

Cohesion:The cohesion as well as the friction have to be clearly distinguished for drained


Version 16.133−42

and undrained conditions. For fine grained soils a pore pressure is created forsudden loading which decreases the possible friction considerably. As timepasses, the water will leave the soil, the friction increases, but the cohesion willbe reduced by a factor up to 10.

Dilatancy:Dilatancy denotes the plastic deformation behavior of a material sample, thecorresponding quantity is the dilatancy angle:

• � 0 plastic deformation associated with reduction of material volume (compaction)

• � 0 volume−neutral plastic deformation (holds, e.g., for steel)

• � 0 plastic deformation associated with volume increase

For soil materials, the plastic deformation behavior depends on the material’seffective density, which in turn changes with the material’s loading state −therefore, the dilatancy angle is in fact not a constant quantity. This coherence isdescribed by the well−established stress dilatancy theory (Rowe 1962), whichlinks the mobilized dilatancy angle to the actual shear straining level, the latterbeing characterized by the mobilized friction angle (cf. section NMAT HardeningPlasticity Soil Model − GRAN).

Classical elasto−plastic material models (e.g. MOHR, DRUC) adopt a constantdilatancy angle. If the dilatancy has considerable effects (e.g. due to arch action)the predominant loading situation should be assessed carefully. As a coarse ruleof thumb, for dense soils a value of +ϕ/2, for middle dense soils a value of 0.0and for loose soils a value of −ϕ/2 can be adopted.

In contrast, the advanced theoretical setting of the Hardening Plasticity Soilmodel directly incorporates a loading state dependent variation of the dilatancyangle according to the above mentioned stress dilatancy theory (cf. sectionNMAT Hardening Plasticity Soil Model − GRAN).

Uniaxial Tensile StrengthAs tensile stresses are not allowed in soils in general, a tension cut off will beapplied for most soils. However, it might be advisable to define a small uniaxialtensile strength for numerical reasons. e.g. if the soils becomes stress free at thesurface.

Characteristic values:DIN 1054−100 Appendix A gives characteristic values for soils as follows:


3−43Version 16.13

Soil type DesignationDIN 18196

Density Weightwet

[kN/m3]

Weightbuoan. [kN/m3]

cal ϕ'

Sand, low siltysand, gravelysand, uniform orpoorly graded

SE as wellas SU withU<6

loose mid.densedense

17.018.019.0

9.010.011.0

30.0 °32.5 °35.0 °

Gravel, Boulder,stones with smallsand content,uniform or poorlygraded

GE loose mid.densedense

17.018.019.0

9.010.011.0

32.0 °36.0 °40.0 °

Sand, Gravely-Sand, Gravel, wellgraded

SW, SI, SU,GW, GIwith6<U<15


18.019.020.0

10.011.012.0

30.0 °34.0 °38.0 °

Sand, Gravely-Sand, Gravel, wellgraded

SW, SI, SU,GW, GIwith U>15,as well asGU


18.020.022.0

10.012.014.0

30.0 °34.0 °38.0 °

Saturated weight = weight buoyancy + 10.0


Version 16.133−44

Soil type Designation DIN18196

Condition

Weight cal ϕ' ck'[kN/m2]

cuk[kN/m2]

Anorganic finegrained cohesivesoils with highplasticity(wL > 50%)

TA softstiffhard

18.019.020.0

***

***

***

Anorganic finegrained cohesivesoils withintermediateplasticity(50% > wL > 35%)

TM andUM

softstiffhard

19.019.520.5

20 °20 °20 °

0 510

52560

Anorganic finegrained cohesivesoils with lowplasticity(wL < 35%)

TL andUL

softstiffhard

20.020.521.0

27 °27 °27 °

0 510

52560

organic Clayorganic Silt

OT andOU

softstiff

14.017.0

* * 515

Peats withoutpreloadingPeats withmoderatepreloading

HN andHZ

11.0

13.0

*

*

*

*

5

20

Weight with buoyancy = weight - 10.0*) only based on tests

3.10.3. Non−linear State Variables (hardening parameters)General non−linear material laws are normally influenced by the loading history.Therefore, for every load step material point state−variables are stored to the database, that can be visualized with WinGRAF during post−processing.Subsequently, the meaning of the stored values is shortly explained.

Plastification number

Value of the corresponding yield function for the uncorrected (=linearelastic) stress state, possibly scaled to stress units. If >0 the materialundergoes plastification. The value is computed for each loading step


3−45Version 16.13

anew. Therefore, regions that possibly have plastified previously, stillcan get values <0 in a subsequent loading step. For GRAN the valueof the MOHR yield function is computed, here.

For the ’Hardening Plasticity Soil’ (GRAN) material model, theplastification number is an identifier that holds more detailedinformation about the current state of loading (see section ’HardeningPlasticity Soil Model’) − instead of storing the current value of the yieldfunction, only.

Deviatoric hardening variable

Effective plastic strain (scalar value), accumulated fromcorresponding strain rates. It reflects the volume neutral (shearing)portion of the plastic deformation.

�.

p,dev�23� �

.p,xx

2 � �.p,yy

2 � �.p,zz

2 � 12��. p,xy2 � �

.

p,yz2 � �

.

p,xz2��

Volumetric hardening variable

Effective plastic strain (scalar value), accumulated value fromcorresponding strain rates.

�.p,v� �

.p,xx� �

.p,yy� �

.p,zz

Mobilized friction angle m

Measures the degree of shearing strain based on the Mohr−Coulombcriterion. Computed according to:

sin m� ��1��32ccot ��1��3

Utilization level

Ratio u� m� inp� 1, where the material input parameter inp

marks the maximum (ultimate) friction angle.

3.10.4. Material Law VMISElastoplastic material according to van MISE with associated flow rule andoptional viscoplastic extension.

f�� 3� J2� �p1� 0


Version 16.133−46

Application range:

Metals and other materials without friction. Simulation of creep effects.

Parameters:

Description Unit Default

P1 Yield stress [kN/m2] !

P2 Hardening modulus (tangent modulus) [kN/m2] 0.0

P10 Type of creep law (overstress function) (0=no viscous effects, pure elasto-plastic)

[-] 0

P11 Creep parameter, exponent m >= 1.0 [-] 1.0

P12 Viscosity η >= 0.0 [kNs/m2] 0.0

Formulation of the viscoplastic material behaviour is based on the Perzynamodel. Accordingly, the viscoplastic strains are defined by

��vp �t0

t

�. vp d�

�t0

t

�.

�g��,�� d�

�t0

t ��f ��,�� g

��,�� d�

In case of an associative flow−rule (e.g. von Mise material) the plastic potentialg equals the yield function. The overstress function � reads

��f(�, �)

m

�0

��,� f� 0

��,� f� 0

This frequently used form can be calibrated to reproduce a wide range of time−dependent material phenomena adequately.

Reference:

M.A.ChrisfieldNon−linear Finite Element Analysis of Solids and Structures. Vol. I.Essentials. Chapter 14. Wiley & Sons (1991)


3−47Version 16.13

M.A.ChrisfieldNon−linear Finite Element Analysis of Solids and Structures. AdvancedTopics. Vol. 2, chapter 6. Wiley & Sons (1997)

O.C. Zienkiewicz and R.L. Taylor (1991)The Finite Element Method, volume 2.McGraw Hill, London.

O.C. Zienkiewicz and I.C. Cormeau (1974)Visco−Plasticity − Plasticity and Creep in Elastic Solids − a UnifiedNumerical Solution Approach.In International Journal for Numerical Methods in Engineering, volume8, pages 821−845.

3.10.5. Material Law DRUCElastoplastic material with a conical yield surface according to DRUCKER/PRAGER and an optionally non−associated flow rule. The model is extended bymeans of a spherical compression cap and plane tension limits. Formulation ofyield condition and plastic potential using stress invariants:

f��2sin

3� �3� sin �� I1� J2� ��

6ccos

3� �3� sin �� 0

g�� 2sin�3� �3� sin��

� I1� J2�

This formulation describes a cone in principal stress space that either embracesthe MOHR yield surface (− sign) or is inlying and tangent to it (+ sign).

For description of the material’s viscoplastic extension see NMAT VMIS.

Application range:

Soil and rock with friction and/ or cohesion. Modelling of time−dependenteffects (e.g. short term strength)

Parameters:


P1 Friction angle ϕ(< 0 inner cone, >= 0 outer cone)

[°] 0.0

P2 Cohesion c [kN/m2] 0.0


Version 16.133−48

P3 Tensile strength βt [kN/m2] 0.0

P4 Dilatancy angle ν [°] 0.0

P5 unused [kN/m2] -

P6 Plastic ultimate strain εu [0/00] 0.0

P7 Ultimate friction angle ϕu [°] P1

P8 Ultimate cohesion cu [kN/m2] P2


[-] 0


P12 Viskosity η >= 0.0 [kNs/m2] 0.0

Reference:

M.A.ChrisfieldNon−linear Finite Element Analysis of Solids and Structures. AdvancedTopics. Vol. II. Chapter 14. Wiley & Sons (1997)

O.C.Zienkiewicz,G.N.Pande Some Useful Forms of Isotropic Yield Surfaces for Soil and RockMechanics. Chapter 5 in Finite Elements in Geomechanics(G.Gudehus ed.) Wiley & Sons (1977)

3.10.6. Material Law MOHRElastoplastic material with a prismatic yield surface according to MOHR−COULOMB and a non−associated flow rule. The model is extended by means ofplane tension limits. Formulation of yield condition and plastic potential usingstress invariants:

f��13I1 sin � J2� (cos� sin sin

3�)� ccos � 0

g�� 2sin�3� �3� sin��

� I1� J2�

with:

Application range: soil and rock with friction and/ or cohesion


3−49Version 16.13

Parameters:


P1 Friction angle ϕ [°] 0.0


P3 Tensile strength βt [kN/m2] 0.0

P4 Dilatancy angle ν [°] 0.0

P5 unsused [kN/m2] -

P6 Plastic ultimate strain εu [0/00] 0.0

P7 Ultimate friction angle ϕu [°] P1

P8 Ultimate cohesion cu [kN/m2] P2


[-] 0


P12 Viskosity η >= 0.0 [kNs/m2] 0.0

Special comments:

The following expressions are better suited for checking the yield criterion:

f� �I�1� sin 1� sin

��III�2ccos 1� sin

For description of the material’s viscoplastic extension see NMAT VMIS.

Reference:


M.A.ChrisfieldNon−linear Finite Element Analysis of Solids and Structures. AdvancedTopics. Vol. 2, chapter 6. Wiley & Sons (1997)

O.C. Zienkiewicz and R.L. Taylor (1991)The Finite Element Method, volume 2.McGraw Hill, London.


Version 16.133−50

O.C. Zienkiewicz and I.C. Cormeau (1974)Visco−Plasticity − Plasticity and Creep in Elastic Solids − a UnifiedNumerical Solution Approach.In International Journal for Numerical Methods in Engineering, volume8, pages 821−845.

3.10.7. Hardening Plasticity Soil Model − GRANExtended elastoplastic material with an optimized hardening rule (single anddouble hardening) for soil materials.

Application range: realistic stiffness and hardening behavior of soil, settlementanalysis

Parameters:


P1 Friction angle ϕ [°] 0.0


P3 Tensile strength ft [kN/m2] 0.0

P4 Dilatancy angle ψ [°] 0.0

P5 Stiffness modulus Es,ref (GRAN-extended) [kN/m2] *

P6 lateral earth pressure coefficient k0(GRAN-extended)

[-] 1-sinϕ

P9 Modulus for primary loading E50,ref [kN/m2] !

P10 Exponent m >= 0 [-] 0.7

P11 Failure factor 0.5 < Rf < 1.0 [-] 0.9

P12 Reference pressure pref [kN/m2] 100.0

The extended version of the GRAN−model (two−surface model, doublehardening) is activated by specification of the oedometric stiffness modulus Es,ref(P5) − only in this case the lateral earth pressure coefficient k0 (P6) takes effect.In case no input of Es,ref is provided, the basis version of the GRAN materialmodel (single−surface model, single hardening) is adopted.

The hardening rule is based on the hyperbolic stress−strain relationshipproposed by KONDNER/ZELASKO, which was derived from triaxial testing.Hardening is limited by the material’s strength, represented by the classic MOHR/COULOMB failure criterion. Additionally, the model accounts for the stressdependent stiffness according to equations (4−6). A further essential feature is


3−51Version 16.13

the model’s ability to capture the loading state and can therefore automaticallyaccount for the different stiffness in primary loading and un−/reloading paths.

In the subsequent notation, compression and contraction are defined asnegative; for the principal stresses the relation �1� �2� �3 holds. Accordingly,for the triaxial state index 3 denotes the axial and index 1 the lateral direction.

Summary of essential features:

• deviatoric hardening based on the hyperbolic stress−strain relationshipaccording to KONDNDER/ZELASKO=> plastic straining prior to reaching shear strength

parameter: E50,ref; Rf

• MOHR/COULOMB failure criterion

parameter: ϕ; c

• optional accounting of dilatant behaviour (non−associated flow)

parameter: ψ

• stress dependent stiffness

parameter: m; pref

• loading dependent stiffness=> differentiation between primary loading and un−/reloading

parameter: Eur; μ (elastic, from MAT/MATE record)

• optional limitation of tensile stress (tension cut−off)

parameter: ft;


Version 16.133−52

The extended version (GRAN−extended) enhances the model by an additionalhardening two−parameter cap surface. An appropriate calibration of the cap’shardening and shape parameters is done automatically, based on the input ofphysically sound input parameters − and, hence, allows for

• a realistic modelling of the contractant behaviour and stiffness duringprimary compression (oedometric testing)=> plastic straining

• preservation of a realistic stress ratio

k0��lateral�axial

, e.g. according to Jaky as k0� 1� sin

parameter: Es,ref; k0; (m; pref)


3−53Version 16.13

Strength and hardening properties:

According to Kondner, the stress−strain behaviour of granular soil under triaxialconditions can be approximated well by a hyperbolic relation.

q� �1��3�� 3

b�a� �3(1)

where

1b�Ei� 2�E50 (2)

1a� qa�

qfRf

(3)

Stress dependent stiffness:

Granular materials show a stiffness behaviour that is dependent on the stressstate (and the compactness of the packing). Extending the approach from (Ohde1939, 1951) − which was derived from oedometric testing − by cohesive termsthe oedometric modulus’ magnitude depends on the effective axial stress stateaccording to:


Version 16.133−54

Es�Es,ref��

�|�3| � sin � c � cos

pref � sin � c � cos �

!

m

, (4)

Parameter m generally varies between 0.4 and 0.75.

In contrast to oedometric test conditions, lateral expansion is not constrainedunder triaxial conditions. Due to the changed boundary conditions the triaxialmodulus’ stiffness E50 deviates from the stiffness modulus. E50 is defined assecant stiffness that corresponds to a 50−percent mobilisation of the maximumshear capacity (figure 1). Choosing the smaller compressive stress �1 asreference stress, a relation anlogous to equation (4) can be established for thestiffness evolution of the triaxial modulus E50 (Kondner & Zelasko 1963, Duncan& Chang 1970), which is then used in the model equations (1) to (3).

E50�E50,ref��

�|�1| � sin � c � cos


!

m

, (5)

An analogous approach for the elastic un−/reloading stiffness yields:

Eur�Eur,ref��

�|�1| � sin � c � cos


!

m

, (6)

From empirical observations E50,ref"Es,ref

Plastic volumetric strain (triaxial stress states):

Like other plasticity models, the Granular−Hardening model incorporates arelationship between activated plastic shear strains �p and corresponding plasticvolumetric strains �p,v. The according flow rule in rate form reads


3−55Version 16.13

�.p,v� �

.p� sinm (7)

For the Granular−Hardening model, the so−called mobilized dilatancy angle m

is defined from the well−established stress dilatancy theory (Rowe 1962) as

sinm� sin m� sin cs

1� sin m� sin cs(8)

(since TALPA v23.36 / ASE v14.57). Therein, the critical state friction angle cs

marks the transition between contractive (small stress ratios with m� cs) anddilatant (higher stress ratios with m� cs) plastic flow. The mobilized frictionangle m in equation (8) is computed according to

sin m� ��1��32ccot ��1��3

(9)

At failure, when m� , also the dilatancy angle reaches its final valuem�. Accordingly, from equation (8) the critical state friction angle can bederived as

sin cs�sin � sin1� sin � sin

(10)

SOFiSTiK performs the computation of the critical state friction angle cs

automatically on basis of the user specification for the final angles and .Consideration of a constant dilatancy angle m�, i.e., the deactivation ofrelationship (8) can optionally be requested by specifying CTRL MSTE EMAX 0(ASE: CTRL MSTE W4 0) in the corresponding TALPA / ASE run.

Nonlinear state variables:

Plastification number

Identifier for the current material state of loading:

0 elastic +2 deviatoric hardening+4 volumetric hardening (cap)+8 material failure (Mohr−Coulomb)

Example: For the current loading stage, a material point experienceshardening in both ’directions’ and finally reaches the failure limit. Thecorresponding value of the identifier amounts to 14=2+4+8.


Version 16.133−56

Deviatoric hardening variable

According to section 3.10.3. Non−linear State Variables.

Volumetric hardening variable

According to section 3.10.3. Non−linear State Variables.

Mobilized friction angle m

Measures the degree of shearing strain based on the Mohr−Coulomb criterion.Computed according to equation (9).

Utilization level

Ratio u� m� inp� 1, where inp is the maximum (ultimate) friction angle

provided as material input parameter.

Isotropic pre−consolidation stress

Hydrostatic stress pc marking the highest state of compression that wasreached in loading history (cap); the hydrostatic stress being definedas p��x��y��z��3.

Mobilized dilatancy angle m

Used dilatancy angle for the current loading stage. Computed according toequation (9), if dilatancy theory is activated. Otherwise equal tomaterial input parameter: m�.

Special comments:

The model can easily be calibrated according to triaxial/oedometric test data.Therefore, deformation behaviour of the material prior to failure can be capturedwith a good accuracy. This feature, combined with the consideration of specificstiffnesses for primary and un−/reloading, respectively, constitutes a significantprogress when compared to the behaviour of classic elasto−plastic soil materialmodels. Consequently, GRAN is particularly suited for tasks that require moreprecise settlement predictions.

If no precise data is available, then the following estimations may be used for anapproximation of the properties of normally consolidated soil:

pref� 100kPa


3−57Version 16.13

m� 0.4###0.7

Rf� 0.7###0.9

E50,ref"Es,ref

Eur,ref� 3�E50,ref

As a consequence of the GRAN hardening plasticity formulation, Poisson’s ratioMUE ( MAT/MATE ) should be chosen to mimic the elastic loading behavior (i.e.unloading, reloading) of the soil skeleton, only. The actual evolution of lateralstresses during primary loading is controlled by the hardening plasticityformulation itself. Therefore − as opposed to common practice with elastic−idealplastic material models, where calibration for primary loading behavior oftenresults in values MUE>>0.3 − for the hardening plasticity formulation suitablevalues of MUE are significantly lower, usually in the range from 0.2 to 0.3. Forhigher values, the development of volumetric strains is prone to be overestimated(also at the cost of model performance).

Reference:

Kondner, R.L.: Zelasko, J.S. (1963): A hyperbolic stress strain relationfor sands, Proc. 2nd Pan. Am. I−COSFE Brazil 1, 289−394

Schanz, T. (1998): Zur Modellierung des mechanischen Verhaltens vonReibungsmaterialien, Habilitationsschrift, Institut für Geotechnik derUniversität Stuttgart

Duncan, J.M.: Chang, C.Y. (1970): Nonlinear analysis of stress andstrain in soil, J. Soil Mech. Found. Div. ASCE 96, 1629−1653

Desai, C.S.: Christian, J.T. (1973): Numerical Methods in GeotechnicalEngineering, Chapter 2, McGraw−Hill Book Company

3.10.8. Material Law SWELAdditional parameters for swelling soils

Application range: Swelling of soils due to stress disturbance (unloading)

Relationship between stress and swelling strains of the final state:


Version 16.133−58

�qi$�� p1�

��

��

�

�

�

0�� i� �0i

log10� �i�0i��0i� �i�� p2

log10��c�0i��p2� �i

i��1..3

�i = principal normal stresses�0i = equilibrium state of stress wrt swelling (initial condition),

transformed to the direction of the principal normalstresses �i

Parameters:


P1 Swelling modulus Kq [o/oo] 3.3

P2 Swelling limit stress (absolute value)|σc| > 0(magnitude of smallest compressive stressbelow which no further increase ofswelling occurs)

[kN/m2] 10.0

P3 Historical swelling equilibrium stress(absolute value) from oedometer testing|σ0,hist| > |σc|

[kN/m2] 2000.0

P4 Viscous extension: retardation time η >=0.0

[h] 0.0

Special comments:

Swelling of soils is a complex phemomena that is influenced by various factors.There are two swelling mechanisms of practical importance that can bedistinguished − for both processes the presence of (pore−) water is a commonprerequisite. The first mechanism is termed as the “osmotic swelling” of clayminerals, which basically is initiated by unloading of clayey sedimentary rock. Thesecond mechanism takes place in sulphate−laden rock with anhydride content.In this case the swelling effects are due to the chemical transformation ofanhydride to gypsum− which goes along with a large increase in volume (61%).

For both described mechanisms a principal dependency between the increasein volume, caused by swelling, and the state of stress was observed both inlaboratory and in in−situ experiments. The formula employed represents a


3−59Version 16.13

generalization of the 1−dimensional stress−strain relationship that HUDER andAMBERG derived from oedometer tests for the final state. Here the timedependent evolution of the swelling process is not considered.

The equilibrium stress state with respect to swelling �0 is defined by means of theGRP record. For this we use the option PLQ in order to reference a (previouslycalculated) load case as “primary state for swelling”. This state is regarded as anequilibrium state with respect to swelling (normally in−situ soil prior toconstruction work). I.e. swelling strain increments caused by an eventual“unloading” from the historical equilibrium state �0,hist to this new “primary state”�0 have already occurred. Swelling strain increments in the course ofconstruction work are only due to unloading related to the new “primary state forswelling” �0:

��qi$� �� q

i,tot�� q

i,hist

��%� p1� log� �i�0,hist�&�%�p1� log� �0i

�0,hist�&

�� p1��log� �i�0i�


Version 16.133−60

The constitutive equation reproduced above is limited to the final (stationary)state, i.e. it relates the evolved swelling strains to the stress state that is presentat time t�$. To account for time dependent behaviour, the relation is extendedto the time scale by a formal viscous approach. Correspondingly, the rate ofswelling strains is defined as

�. q� �q$�� q

�

with the retardation time � as a viscosity parameter and �q denoting the swellingstrains that have developed at the considered time t. In rheological terms thisapproach can be interpreted as a parallel coupling of a ’swelling’ and a dashpotdevice.

The time dependent response can be calibrated via the retardation time � (P4)− the greater � the more accentuated is the retardation in the evolution of swellingstrains. For �� 0 the response is instantaneous, identical with the non−viscous(instationary) case. Furthermore, for t'$ the model’s response converges tothe instationary solution − independent of the adjusted retardation time �. Thisproperty enables application of the viscous model also for stabilisation of thesolution process, even if one is not explicitly interested in modelling time effects.

The SWEL record is specified in addition to a linear elastic or elastoplastic basicmaterial.

Anisotropy is not possible with this model.

Reference:

P.Wittke−Gattermann Verfahren zur Berechnung von Tunnels in quellfähigem Gebirge undKalibrierung an einem Versuchsbauwerk. Dissertation RWTH−Aachen, Verlag Glückauf 1998

W.Wittke Grundlagen für die Bemessung und Ausführung von Tunnels inquellendem Gebirge und ihre Anwendung beim Bau der Wendeschleifeder S−Bahn Stuttgart. Veröffentlichungen des Institutes für Grundbau, Bodenmechanik,Felsmechanik und Verkehrswasserbau der RWTH−Aachen 1978


3−61Version 16.13

W.Wittke, P.RisslerBemessung der Auskleidung von Hohlräumen in quellendem Gebirgenach der Finite Element Methode. Veröffentlichungen des Institutes für Grundbau, Bodenmechanik,Felsmechanik und Verkehrswasserbau der RWTH−Aachen 1976, Heft2, 7−46

Nichtlineare Stoffgleichungen für Böden und ihre Verwendung bei dernumerischen Analyse von Grundbauaufgaben. Mitteilungen Heft 10des Baugrund−Instituts Stuttgart (1979)

3.10.9. Material Law FAULDiscrete shear surfaces (crevice planes)

f1 = tan ϕ ⋅ σ − c + τ < 0

g1 = tan ν ⋅ σ + τ

f2 = σ − βz < 0

g2 = f2

Application range:

Additional discrete faults to a given base rock material.

Parameters:


P1 Crevice friction angle ϕ [°] 0.0

P2 Crevice cohesion c [kN/m2] 0.0

P3 Crevice strength ftu [kN/m2] 0.0

P4 Crevice dilataion angle ν [°] 0.0

P5 Meridian angle of crevice plane (OAL) [°] (*)

P6 Descent angle of crevice plane (OAF) [°] (*)

P9 Tensile fracture energy Gf [kNm/m2] 0.0

Special comments:

This material law may be specified up to three times in addition to the material lawof the base material (elastic, MOHR, DRUC). This allows for the consideration of


Version 16.133−62

different distinct fault directions. Increasing the number of specified shear planesper material, also increases the number of possible equilibrium states for amaterial point − this may possibly affect the stability of the overall equilibriumiteration process.

Specification of meridian angle OAL and descent angle OAF follows theinstructions given in the descriptions for input records MAT/MATE. For planarsystems the value OAL directly defines the slope of the stratification, i.e. the anglebetween the local x direction and the global X direction. Input for OAF is notevaluated for the plane case.

For P9>0 a scalar damage model with exponential softening of the tensilestrength is applied. The softening obeys

ft� ftu�exp��w � ftu

Gf� !

where w denotes the crack opening. In this context, the tensile fracture energyGf represents an objective material parameter. In order to minimize discretizationdependent spurious side effects, a characteristic element size is incorporated intothe softening formulation. This requires, however, a sufficiently fine finite elementdiscretization in the corresponding system domains.

In case of P9=0 a tension cut−off with respect to ftu without consideration ofsoftening is executed.

3.10.10. Material Law ROCKElastoplastic material with oriented shear surfaces

f1 = tan (p1) ⋅ σ − p2 + τ < 0

g1 = tan (p4) ⋅ σ + τ

f2 = σ − p3 < 0

g2 = f2 (Kluftfläche/Fault)

f3 = tan (p6) ⋅ σ − p7 + τ < 0

g3 = tan (p9) ⋅ σ + τ

f4 = σI − p8 < 0

g4 = f4 (Felsmaterial/Rock)


3−63Version 16.13

Application range:

Plane strain conditions and anisotropic material

Parameters: Default values:

P1 = Crevice friction angle ϕ [degrees] (0.)P2 = Crevice cohesion c [kN/m2] (0.)P3 = Crevice tensile strength β−z [kN/m2] (0.)P4 = Crevice dilatancy angle ν [degrees] (0.)P5 = Angle of crevice direction [degrees] (*)

with respect to x axis (0−180)P6 = Rock friction angle ϕ [degrees] (0.)P7 = Rock cohesion c [kN/m2] (0.)P8 = Rock tensile strength β−z [kN/m2] (0.)P9 = Rock dilatancy angle ν [degrees] (0.)

Special comments:

This law ignores the effect of the third principal stress acting perpendicularly tothe model. One can, however, specify the strength of the rock as well as thestrength of the sliding surfaces, which are defined by the angle P5 (default valueis that of an anisotropic material). The flow rule of the shear failure is non−associated if P4 is different from P1.

Any of the two limits can be deactivated in special cases by specifying ϕ = c = 0.0.

Reference:

W.Wunderlich,H.Cramer,H.K.Kutter,W.Rahn Finite Element Modelle für die Beschreibung von Fels Mitteilung Nr.81−10 des Instituts für konstruktiven Ingenieurbau der Ruhr UniversitätBochum, 1981.

3.10.11. Material Law MISEElastoplastic material according to van MISE or DRUCKER−PRAGER withassociated flow rule.

f�� p2 � I1� J2� � p1

3�� 0

Application range:

Metals and other materials without friction (module ASE, 3D solidelements)


Version 16.133−64

Parameters:

P1 = Comparison stress [kN/m2]P2 = Friction parameter [−]P3 = Hardening module [kN/m2]P4 = Tensile strength β−z [kN/m2]P5 = Compressive strength (cap) β−c [kN/m2]

Several substitutes for P1 and P2 can be used for the calculation of commonparameters in soil mechanics. Commonly used e.g. is the compression cone:

P1�6ccos 3� sin

P2�2sin

3� (3� sin )

The values for the internal cone are better suited for plane strain conditions:

P1�6ccos 3� sin

P2�2sin

3� (3� sin )

If the Drucker−Prager criterion is used for modelling concrete behaviour, then ingeneral uniaxial compressive strength ( fc ) and/or tensile strength ( ft ) areprovided rather than cohesion and friction angle. Presuming, that also the tensilestrength is captured with the Drucker−Prager yield surface, i.e. no explicit tensilestrength is provided via parameter P4, the model can be calibrated by means of:

P1� 2�(fc( � ft(fc(� ft

P2� 13��(fc(� ft(fc(� ft

Parameter P4 extends the model by an explicit tension limit, often referred to asRankine criterion.

By specification of parameter P5 the model can optionally be extended by aspherical cap (in principal stress space) that limits the volumetric compressivestress to a maximum value. This can be meaningful in particular for mainlyhydrostatic compression. The cap is defined by:

f�� 12 � �2

2 � �32� � P5

2 � P52 � P5

2� � 0

Reference:



3−65Version 16.13

M.A.ChrisfieldNon−linear Finite Element Analysis of Solids and Structures. AdvancedTopics. Vol. II. Chapter 6. Wiley & Sons (1997)

3.10.12. Material Law GUDEElastoplastic material in its extended form according to Gudehus with non−associated flow rule.

f = q2 − c7 p2 + c6 p − c5 < 0

g = q2 − c9 p2 + c8 p

with:

p = (σx + σy + σz)/3 γ = (3−sinϕ)/(3+sinϕ)

q�� 12��1� � J2

� ��1� �3 3� � J32� J2

��

c5 = (12c2cos2ϕ)/A ; A = (3−sin ϕ)2

c6 = (24c cosϕ sinϕ)/A

c7 = (12 sin2ϕ)/A

c8 = (24c cosϕ sinν)/B ; B = (3−sin ϕ)(3−sinν)

c9 = (12 sinνsinϕ)/B

Application range: soil and rock with friction and cohesion (module ASE, 3D solidelements)


P1 = friction angle ϕ [degrees] (0.)P2 = cohesion c [kN/m2] (0.)P3 = tensile strength β−z [kN/m2] (0.)P4 = dilatatancy angle ν [degrees] (0.)P5 = compressive strength (cap) β−c [kN/m2] (−) P6 = plastic ultimate strain εu [o/oo] (0.)P7 = ultimate friction angle ϕu [grad] (P1)P8 = ultimate cohesion cu [kN/m2] (P2)


Version 16.133−66

Special comments:

This law is capable of describing a multitude of plane or curved yield surfaces. Forγ =1 a circle in the deviatoric plane is obtained. The dilatation angle is usually seteither to zero or equal to the friction angle.


f�� 12 � �2

2 � �32� � P5

2 � P52 � P5

2� � 0

Reference:

W.Wunderlich, H.Cramer, H.K.Kutter, W.Rahn Finite Element Modelle für die Beschreibung von Fels Mitteilung 81−10des Instituts für konstr.Ingenieurbau der Ruhr Universität Bochum,1981

3.10.13. Material Law LADEElastoplastic material according to LADE with non−associated flow rule.

f�� I13��

�

�27� p1��pa

I1��m�

!� I3� 0

g�� I13��

�

�27� p4��pa

I1��m�

!� I3

with

pa = 103.32 kN/m2 = atmospheric air pressure

I1��1�P3�� 2�P3

�� 3�P3�

I3��1�P3� � ��2�P3

� � ��3�P3�

Application range: all materials with friction including rock and concrete (moduleASE, 3D solid elements)


3−67Version 16.13


P1 = Parameter ”η” (−)P2 = Exponent ”m” (−)P3 = Uniaxial tensile strength [kN/m2] (0.)P4 = Parameter ”η” for flow rule (−)P5 = Compressive strength (cap) βc [kN/m2] (−)P6 = Plastic ultimate strain εu [o/oo] (0.)P7 = Ultimate Parameter ”η” (P1)P8 = Ultimate Exponent ”m” (P2)

Special comments:

Material LADE has shown very good compliance between analytical andexperimental results. In practice therefore, the parameters can be taken fromexperiments on the material’s strength. The law at hand can also describeconcrete or ceramics. A simple comparison with the material parameters of theMohr−Coulomb law can be made only if the invariant I1 is known.

Due to the non−physical parameters the calibration of the LADE yield functionmight not seem straight forward at first sight. For this reason, the basic procedurefor a material with known uniaxial tensile and compressive strength (e.g.concrete) is described in the following. Of particular interest is the section of thethree−dimensional yield surface with one of the principal planes (−> “KupferCurve”).

Parameter P2 (exponent) affects the curvature (convexity) of the yield surfacetowards the hydrostatic axis − the larger P2 the stronger the curvature. In thismanner P2 determines the shape of the intersection curve. For most types ofconcrete a value of P2 between 1.0 and 2.0 is reasonable.

Using the known quantities of uniaxial tensile and compressive strength and thechosen parameter P2, P1 can now be determined from the condition: For thestress state corresponding to the uniaxial compressive stress limit the yieldcondition must be fulfilled.

We rewrite the yield function as:

P1��I31

I3�27�

!��(I1(pa� !

m

The considered stress state is defined by (translated reference system):


Version 16.133−68

�I�� II�� ft

�III��ft� fc�

I1�� I��II��III , I3�� I��II��III

Where ft�� P3� and fc are the magnitudes of the uniaxial tensile and

compressive strength, respectively, I1 and I3 the required invariants for thisstress state. Substituing into the rewritten yield function yields the yet unknownparameter P1.

The following table contains exemplary parameters for selected concrete types,derived from the procedure described above (classification according to EC2,Ultimate Limit State).

Strengthclass

fcd[kN/m2]

P3 (fctk;0.05)[kN/m2]

P2[-]

P1[-]

C20/25 13333 1500 1.0 24669.11

1.5 324095.87

C30/37 20000 2000 1.0 43466.02

1.5 689515.99

C40/50 26667 2500 1.0 63426.77

1.5 1153410.57

C50/60 33333 2900 1.0 88162.15

1.5 1778218.62


f�� 12 � �2

2 � �32� � P5

2 � P52 � P5

2� � 0

Reference:

P.V.LadeFailure Criterion for Frictional Materials in Mechanics of EngineeringMaterials, Chap 20 (C.s.Desai,R.H.Gallagher ed.) Wiley & Sons (1984)


3−69Version 16.13

3.10.14. Material Law MEMBParameters for textile membranes

P1 Maximum yielding force in kN/mdefault: − no yielding for tension

P2 Factor for compression stiffness0.0 no compressive stress possible1.0 full compressive stress possible0.1 intermediate values for scaling the elasticity modulus

3.10.15. User Defined Material LawsParameters for user−defined material laws (USP1..USP8 und USD1..USD8)

For the advanced user the modules TALPA (for QUAD−elements) and ASE (forBRIC−elements) offer the possibility to plug in self−developed non−linearmaterial models via an interface (currently only for WINDOWS−OS). Thefollowing paragraphs describe the interface in detail.

The user−defined material models have to be provided in a Dynamic Link Library(DLL) with arbitrary name. The variable SOFISTIK_USERMATDLL must be setwith the name of this DLL. This can either be done by specification of

SET SOFISTIK_USERMATDLL=my_material

at the CMD−command prompt or via adding the entry

SOFISTIK_USERMATDLL=my_material

into the SOFISTIK.DEF file. In both cases the user defined material models, inthe DLL my_material.dll, are loaded at run−time. The interface routine itselfreads:

The parameter list consists of:

NMAT3D_USD( Ss, SsPrim, deltaSn, SnIe, StateV, Mtype, ParMat, ElcMat, D, C, Ctrl, deltaTime, iNonl,

iUpd, iErr, NrEl, iGP )


Version 16.133−70

Input parameters:

Parameter Dim Type Description

Ss 6 Double Elastic stress tensor (trial stress)[xx,yy,zz,xy,xz,yz]

SsPrim 6 Double Stress tensor primary state[xx,yy,zz,xy,xz,yz]

deltaSn 6 Double Strain increment related to primary state[xx,yy,zz,xy,xz,yz]

SnIe 6 Double not used

StateV 10 Double State variables

Mtype 1 Integer Identifier for material typeUSP1-USP8 -> 101-108USD1-USD8 -> 109-116

ParMat 12 Double Non-linear material parameters P1-P12

ElcMat 16 Double Elastic material constants from record001/No:1, @1-@14 (where appropriatemultiplied with factor of stiffnessFACS!). Additionally FACS at pos 15 and,as the case may be thickness of QUAD-element at pos 16.

D (6,6) Double Elastic material stiffness matrix

C (6,6) Double Elastic compliance

Ctrl 5 Single Control values from CTRL MSTE- record

deltaTime 1 Double not used

NrEl 1 Integer Element number

iGP 1 Integer Identifier for Gauss-Point


3−71Version 16.13

Return values:

Parameter Dim Type Description

Ss 6 Double Updated stress tensor [xx,yy,zz,xy,xz,yz]

SnIe 6 Double not used

StateV 10 Double Updated state variables

D (6,6) Double Updated (tangential) material stiffnessmatrix

iNonl 1 Integer =0 for linear-elastic response=1 for non-linear response

iUpd 1 Integer =0 no update of stiffness matrix=1 update of stiffness matrix (only

ASE)

iErr 1 Integer Error indicator=0 no error=1 error -> program terminates=-99 no user defined material model

provided -> program terminates


Version 16.133−72

3.11. BMAT − Elastic Support / Interface


BMAT


NO Material number − 1

CCTCRACYIELMUECOHDILGAMB

Elastic constant normal to surfaceElastic constant tangential to surfaceMaximum tensile stress of interfaceMaximum stress of interfaceFriction coefficient of interfaceCohesion of interfaceDilatancy coefficientEquivalent mass distribution

kN/m3

kN/m3

kN/m2

kN/m2

−kN/m2

−

t/m2

0.0.0.−−−0.0

TYPE

MREFH

ReferencePESS Plane stress conditionPAIN Plane strain conditionHALF Circular disk at halfspaceCIRC Circular hole in infinite diskSPHE Sperical hole in infinite spaceNONE no reference

Number of a reference materialReference dimension (thickness/radius)

LIT

−m

−

NO!

The bedding approach works according to the subgrade modulus theory (Winkler,Zimmermann/Pasternak). It facilitates the definition of elastic supports by an en-gineering trick which, among others, ignores the shear deformations of the sup-porting medium. The bedding effect may be attached to beam or plate elements,but in general it will be used as an own element. (see SPRI, BOUN, BEAM orQUAD and the more general description of BORE profiles)

The determination of a reasonable value for the foundation modulus oftenpresents considerable difficulty, since this value depends not only on the materialparameters but also on the geometry and the loading. One must always keep thisdependance in mind, when assessing the accuracy of the results of an analysisusing this theory.

The subgrade parameters C and CT will be used for bedding of QUAD elementsor for the description of support or interface conditions. A QUAD element of a slabfoundation will thus have a concrete material and via BMAT the soil properties at-


3−73Version 16.13

tached to the same material number. The value C is than acting in the main direc-tion perpendicular to the QUAD surface in the local z−direction, while CT is actingin any shear direction in the QUAD plane.

If subgrade parameters are assigned to the material of a geometric edge (GLN),spring elements will be generated along that edge based on the width and the dis-tance of the support nodes.

Instead of a direct value you may select a reference material and a reference di-mension for some cases with constant pressure [1]:

• Planar layer with horizontal constraints e.g. for modelling elastic supportby columns and supporting walls (plane stress condition):

Cs� EH� 1(1��)(1��)

Ct� EH� 12(1��)

• Planar layer with horizontal constraints for settlements of soil strata (planestrain condition):

Cs� EH� (1��)(1��)(1�2�)

Ct� EH� 1(1��)

• Equivalent circular disk with radius R on an infinite halfspace:

Cs�ER� 2�(1��)(1��)

• Circular hole in unfinite disk with plane strain conditions (bedded pipes orpiles):

Cs�ER� 1(1��)(1�2�)

Ct�Cs

• Spherical hole with radius R in infinite 3D elastic continua:

Cs�ER� 2(1��)

Ct�Cs

Including a dilatancy factor describing the normal strain induced by shear deform-ations, we have for the stresses the following equations:

��Cs� (un�DIL�ut)��Ct�ut


Version 16.133−74

Non−linear effects are controlled by CRAC, YIEL, MUE and COH:

Cracking: Upon reaching the failure stress, the interface fails in boththe axial and the lateral direction. The failure load is al-ways a tensile stress. If the bedding reaction is applied toa QUAD element, a deformation in the direction of the lo-cal z−axis will create compressive (negative) stresses.

Yield load: Upon reaching the yield stress, the principal deformationcomponent of the interface increases without an increaseof the stress.

Friction/cohesion: Defining a friction and/or a cohesion coefficient, the lat-eral shear stress can not become larger than:

Friction coefficient * normal stress + Cohesion

Please note, that before reaching this limit the stiff−nessCT will produce the shear stress only if a deformation ispresent.

If the principal interface has failed (CRAC), then the lateral bedding acts only if0.0 has been entered for both friction− coefficient and cohesion.

The non−linear effects can only be taken into account by a non−linear analysis.The friction is an effect of the lateral bedding, while all other effects act upon theprincipal direction.

[1] Katz, C., Werner, H. (1982)Implementation of nonlinear boundary conditions in Finite ElementAnalysisComputers & Structures Vol. 15 No. 3 pp. 299−304


3−75Version 16.13

3.12. HMAT − Material Constants HYDRA


HMAT


NOTYPE

Material numberType of material law

DARC Darcy (linear)FORC ForchheimerMISS MißbachFOUR Fourier (linear)EC Concrete/Steel/AluminiumJONA Jonasson hydrationHSCM ”Shrinkage−Core” modelWESC Danish model acc. to WescheFVOL isotrope stress factors FSIN anisotrope stress factorsFSIT anisotrope stress factors

−LIT

!*

TEMP Temperature or pore pressure level grad/kPa 0

KXXKYYKZZKXYKXZKYZS

NSP

Isotrope permeability or conductivityor anisotrope permeability/conductivity or parameters A, B (Forchheimer), or parameters C,M (Mißbach)

Specific Capacity/Storage coefficient

effective porosity or moisture grade for EC4C

m/secW/Km

****

1/mJ/Km3

−

0.KXXKXX

0.0.0.0.

0.

ABCQMAXTK

Constant a for JONA / HSCM / WESCConstant b for JONA / WESCConstant c for WESCMaximum heat quantity for hydratationReference time

−−−

kJ/m3

h

***0.15

TITL Designation of material Lit32 −


Version 16.133−76

Material properties have to be selected according to literature or experimentaldata. But some rough estimates (without warranty) are given here.

For any material there might be up to 15 different sets of materials for differenttemperatures [° Celsius] or pore water pressures [kPa = kN/m2]. With a nonlinearanalysis the material values will then be interpolated between those values.

Within HYDRA the user has the possibility to define material properties for the ele-ments either via a given material number (engineering constructions) or via thenodes (element material number = 0), especially for ground water models. Bothmethods may be used together within the same system.

3.12.1. Hydraulic ParametersHydraulic permeabilities (acc. Dyck, Peschke):

Type of soil k [m/sec]

Sandy gravelGravelly sandMedium sandSilty sandSandy siltSilty clayClay

3·10-3 ... 5·10-4

1·10-3 ... 2·10-4

4·10-4 ... 1·10-4

2·10-4 ... 1·10-5

5·10-5 ... 1·10-6

5·10-6 ... 1·10-8

≈ 10-8

Positive pressures represent saturated flow regions while negative values de-scribe unsaturated soils. Conductivities and Capacities will be interpolated. Freesurface problems also use a variation of the porosity to account for the effectivecapacity of the free surface.

Material values may be defined isotropic or anistropic depending on a stress statefrom the database. This is performed by additional data given with the same ma-terial number and the types FVOL, FSIN or FSIT. The difference between FSINand FSIT is given by the fact that FSIN modifies the values across the crack, whileFSIT does this perpendicular to the crack. It is recommended to use a linear stressfield for that purpose and not a plasticity field.


3−77Version 16.13

3.12.2. Heat Conduction.Thermal properties (S = specific capacity*Weight):

Material Conductivity� [W/Km]

Capacityc [J/kgK]

Elongationcoeff. [-]

Emission rate � [-]

P.concreteLW concreteconcretebrickworkinsulations

SteelcopperAluminium

Timber

Water

0.14 ... 1.200.70 ... 1.201.60 ... 2.100.50 ... 1.300.020 ... 0.090

50380200

0.13 ... 0.20

0.58

105010501050950850

850850850

2500

4187

(S = c·ρ)

1.0·10-5

1.2·10-5

1.6·10-5

2.4·10-5

-

0.18·10-3

0.93-

0.06 … 0.670.04 … 0.780.05 … 0.30

With the definition of a literal at TYPE (default as specified with MATE) from thefollowing list, default values will be selected according EN 12524:

AIR Air (1 bar, 20 deg Celsius)H2O Water (1 bar, 10 deg. Celsius)CO2, O, N Carbondioxid, Oxygen, NitrogenAR, KR, XE, SF6 Argon, Krypton, Xenon, Sulfurhexafluorid

GLAS, ESG Floatglass, toughened safety glasVSGh, VSGv laminated (horiz./vertical usage), TVG semi−tempered glasCu, Pb, Mg, W, Zn Copper, Lead, Magnesia, Wolfram, ZincBRAS, BRON brass, bronce

CLAY, SAND clay, sandROC1, ROC2 crystal rock, sediment rockROC3, ROC4 light sediments, porous rock

BRIC, SLBR, CLIN brick, sand−lime−brick, clincerIGYP, GYPS isolat. gypsum, standard gypsum plasterMOGY, MOCH, MOCE gypsum/chalc/cement mortar

ASPH, BITU Asphalt, Bitumen


Version 16.133−78

CARP, WOOL Carpet, Felt/WoolCORK, LINO Cork, Linoleum

EPOX, PHEN, PEST Epoxid−, Phenol−, Polyester resinACRY, PC, PTFE Acryl, Polycarbonat, PolytetrafluorethylenPVC, PMMA Polyvinylchlorid, PolymethylmethakrylatPOM, PA Polyazetat, Polyamid/NylonPEHD. PELD Polyethylen high/low densityPS. PP, PUR Polystyrol, Polypropylen, PolyurethanRUBB, NEOP, EBON Rubber, Neopren, EbonitEPDM, PSUL, BUTA Ethylen−Propylenedien,Polysulfid,ButadienSI, SILA Silicone, Silica FOAM, FOAS, FOAU foamed rubber, silicone, urethanFOAC, FOAR, FOAE foamed PVC, PUR, PE

The type EC and the moisture ratio NSP will select the non linear properties de-pending on the material type available in the database (concrete, light−weightconcrete, structural steel and aluminium and timber) according to EN. With expli-cit definition of a TEMP−value it is possible to create and modify tabulated values.The types EC4C and EC4S allow a direct approach without a material definitionin the database.


3−79Version 16.13

k [W/m/K]

[ C]

1200

.00

1100

.00

1000

.00

900.

00

800.

00

700.

00

600.

00

500.

00

400.

00

300.

00

200.

00

100.

00

0.00

1.80

1.60

1.40

1.20

1.00

0.800

0.600

0.400

0.200

0.0

S [kJ/m3/K]

[ C]

1200

.00

1100

.00

1000

.00

900.

00

800.

00

700.

00

600.

00

500.

00

400.

00

300.

00

200.

00

100.

00

0.00

4500

4000

3500

3000

2500

2000

1500

1000

500

0.0

Conductivity and Capacity of ConcreteThe thermal conductivity of the concrete is given by an upper (A=1.0) and a lower(A=0.0) limit. The special effect for S is the evaporation of pore water.

k [W/m/K]

[ C]

1200

.00

1100

.00

1000

.00

900.

00

800.

00

700.

00

600.

00

500.

00

400.

00

300.

00

200.

00

100.

00

0.00

50.0

45.0

40.0

35.0

30.0

25.0

20.0

15.0

10.0

5.000.0

S [kJ/m3/K]

[ C]12

00.0

0

1100

.00

1000

.00

900.

00

800.

00

700.

00

600.

00

500.

00

400.

00

300.

00

200.

00

100.

00

0.00

18000

16000

14000

12000

10000

8000

6000

4000

2000

0.0

Conductivity and Capacity of Structural Steel

k [W/m/K]

[ C]

1200

.00

1100

.00

1000

.00

900.

00

800.

00

700.

00

600.

00

500.

00

400.

00

300.

00

200.

00

100.

00

0.00

1.501.401.301.201.101.00

0.9000.8000.7000.6000.5000.4000.3000.2000.100

S [kJ/m3/K][ C]

1200

.00

1100

.00

1000

.00

900.

00

800.

00

700.

00

600.

00

500.

00

400.

00

300.

00

200.

00

100.

00

0.00

7.006.506.005.505.004.504.003.503.002.502.001.501.00

0.500

Conductivity and Capacity of Timber


Version 16.133−80

3.12.3. Hydration of ConcreteFor the hydration of concrete it is required to know the maximum heat releaseQMAX, a function for the effective age of concrete (see HYDRA CTRL TEFF) anda formula for the hydration degree α governing all other properties. There are nu-merous possibilities with different parameters. All of them have in common:

TEMP Eine Referenztemperatur [°C] 10QMAX The maximum heat quantity [kJ/m3] !TK The reference time τk [h] 15S The exponent for maturity function acc. Saul 1.00

TYPE JONAFunction of Jonasson, an extension to the Byfors definition:

�� exp��

��b � ·�� ln�1� �w

�k��

a

�

!Examples of those constants a,b and τk can be found in Appendix A of Heft 512of the German DAfStB, printed with the input record HMAT but the general ruleis that you need tests! Unfortunately there are publications with exchanged para-meters a and b.

A,B Parameters a and b [−} −1.15,−1.00

The values have to be determined from experiments, values for the total heat inthe literature are often defined in [kJ/kg] . However the following values might givea rough idea:

TYPE HSCM“Shrinkage−Core” model:

��a � ·��w� �k�

�1� a � ·��w� �k��w� �k

τk is a period with very low chemical reaction, named d in the original formula. Val-ues for a mass concrete are given by Dussinger:

τk = 2.88 [h]a = 0.029 [1/h]

TYPE WESCDanish model according to Wesche:


3−81Version 16.13

�� exp��

��

��k��w� !

b

��

!

�� fcc(t)�fcc(28d)�

� a�·�exp�c�·�t�0.55��c� c1�·�w0

�z

The water cement ratio w0/z has to be incorporated in the input value c. Pleasenote that parameter a is used in the original with two different meanings. The fol-lowing parameters for the Wesche model can be found in the literature.

Values for a mass concrete (Z 35L) are given by Dussinger:

τk = 24.87 [h]b = 0.84 [−]w0/z = 0.68 [−]a = 1.63 [−]c1 = −4.4 [−] => c = −4.4 � 0.68 = − 2.99

Hint: If the maturity function according to Saul is used, the exponent s there mightbe specified with item S.


Version 16.133−82

3.13. CONC − Properties of Concrete


CONC


NOTYPE

Material number (1−999)Type of concrete:

C, LC regular / light−weightfor more types see following remarks

−LIT

1*

FCN Nominal strength class (fck/fcwk/fc’ etc.) N/mm2 *

FCFCTFCTKECMUEGAMALFASCMTYPR

FCRECRFBDFFATFCTDFEQRFEQTGMODKMODRHOGCGFMUECTITL

Compressiv strength of concreteTensile strength of concreteLower fractile strength valueElastic modulusPoisson’s ratio or shear modulusUnit weightThermal expansion coefficientTypical material safety factorType of service state line

LINE = constant elastic modulus A,B C = shorttime lines (Eurocode2)

Strength for non−linear analysisElastic modulus for servicabilityDesign bond strengthFatigue strengthDesign tensile strengthEquiv. tensile strength after crackingUltimate tensile strengthShear modulusBulk modulusDensityEnergy at break for compressive failureEnergy at break for tensile failureFriction in cracksMaterial name

N/mm2

N/mm2

N/mm2

N/mm2

−kN/m3

1/°K−

LIT

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

kg/m3

N/mmN/mm

−Lit32

****

0.225

1E−5**

****

0.0FCTDFEQR

*******


3−83Version 16.13

3.13.1. Eurocode / DIN 1045−1 / OEN B 4700According to Eurocode EN 1992 and other design codes derived from that the fol-lowing types are available:

C = regular concreteLC = light−weight concrete

The cylindrical strength is always to be input for FCN. The possible values aregiven in table 3.1 and 3.2 of EN, resp. table 9 and 10 of DIN 1045−1 resp. table4 of OEN B 4700 and not repeated here in detail. The default value is 20.

FCN = fck 12 16 20 25 30 35 40 45 50

fck,cube 15 20 25 30 37 45 50 55 60

FCN 55 60 70 80 90 100

fck,cube 67 75 85 95 105 115

Some properties are dependent on so called boxed values or other national re-gulations. The definition of NORM COUN is used to select those boxed values.As OEN and DIN 1045−1 differ considerably from the EC 2, you should useNORM to select the proper design code family.

The default values for strength and elastic modulus are derived as follows:

FC = 0.85 ⋅ fck

FCT = 0.3 ⋅ fck 2/3 (fck < 55)= 2.12 ln((fck+8)/10+1) (fck > 55)

EC = 9500 ( fck + 8 ) 0.3 (EN 1992 −1992)EC = 22000 ( fcm /10 ) 0.3 (EN 1992 −2004)

FBD = 2.25 ⋅ fct,0.05/γ (Tbl. 5.3.)

The coefficients αcc and αlc for the long term strength effects are defined in thenational annexes. The Eurocode suggests values between 0.8 and 1.0 and rec-ommends as default the value of 1.0. However SOFiSTiK uses a default on thesafe side of 0.85, if not specified explicitly in the INI−file according to the nationalannex. An explicit definition of FC = αcc�FCN is possible of cause. However, forthe fatigue, bond or tensile strength values all corrective factors and the safetyshould be included in the input data.


Version 16.133−84

For the elasticity modules we have to distinguish between a secant modulus Ecm(Input value EC of this record) for elastic deformations, especially constrainingforces and a tangential modulus Ec0,28 = 1.05 Ecm or Ec0,28 = Ecm / αi , used forcreep and nonlinear analysis (input item ECR) where Heft 525 of DAfStb chapter9.1 provides:

αi = 0.8 + 0.2 fcm / 88 < 1.0

For light−weight concrete (LC) according to EC2−4, the elasticity module ECmust be defined either explicitly or by means of GAM. For GAM also the densityclass is accepted and GAM and EC will then be defined appropriately. For thedensity ρ in kg/m3 we have ρ = (γ−1.5)⋅100

Ecml = Ecm ⋅ ( ρ/2200 ) 2

For light−weight concrete, the tensile strength and bond values and limit strainswill be scaled by a factor η1. For the ultimate limit stress strain law the bilinearversion is selected. The different coefficients for natural sand and othercomponents are selected by AQUA automatically based on the defined weightand strength.

The fatigue strength may be specified with item FFAT. The formula given in DIN1045−1 (124) is as follows:

fcd,fat� �cc(t0)· fcd ·��1� fck

250� !

�cc(t0)� e0.2(1� 28�t0� )

For detailed analysis of concrete according to appendix 1 you need to know thekind of cement. You may specify this by appending a literal to the concrete grade

N normal cement (α = 0.0)S slow hardening cement (α = −1.0)R fast hardening / high strength cement (α = +1.0)

In case of a fire design it is required to distinguish between quartzitic and calca-reous aggregates. For the second case an additonal character C may be ap-pended to the cement type: NC, SC and RC.

The usual stress−strain curve of the C types is the parabolic−rectangular stress−strain diagram of Eurocode 2 / DIN 1045 / OeNORM B 4200 / SIA 162. For non−linear analysis or deformation analysis, there are other types A/B available, fol-lowing the expression:


3−85Version 16.13

�fc� k·n� n2

1� (k�2)·n

with

n = ε / εc1

k = Ec0 ⋅ εc1/fc

For fc the value fck+8 is used for the curves A and B . The maximum strain is li-mited according to the strength. The B line does not possess a descendingbranch, and it is thus possibly more stable numerically. The C line has its stressvalues even for very large strains and will be the most robust case.

The safety factors SCM are preset to 1.5 (in Italy to 1.6). However, they shouldbe selected at the design explicitly, because they are dependent on the loadingcombinations. For concrete with high strength the factor will be increased by γ’,which will be incorporated in the strain−stress laws immediately, to allow a globalsafety factor to be used for the design.

For non−linear analysis with a unified safety factor according to DIN 1045−1 thestrength of the concrete will be reduced to a value of 0.85αfck, while those of thereinforcements will be raised. These non linear analysis stress−strain laws aregenerated automatically.

For steel fibre concrete according to DBV−Merkblatt (Oct. 2001, § 4.2) it is al-lowed to use higher concrete tensile bending strength values for elements notthicker than 60 cm. If desired the user has to enter that value of FCTD explicitly.(with a factor of 1.6−d). However only if a value is given for FCTD FEQR or FEQTthe tensile strength of the concrete is applied for the design and nonlinear analy-sis. Values are defined as follows:

FCTD = f,ctd = f,ctk,fi ⋅ αfc / γf

ctFEQR = feq,ctd,i = feq,ctk,i ⋅ αf

c ⋅ αsys / γfct

FEQT = feq,ctd,ii = feq,ctk,ii ⋅ αfc ⋅ αsys / γf

ct

αfc = 0.85 (C) / 0.75 (LC)

αsys = 1.0 ⇒ 0.8 (d = 15 ⇒ 60 cm, Bild 4.1)γf

ct = 1.25 (> F0.6)

With these values the stress strain laws according to pictures 4.2 or 4.3. of theDBV paper are created.

The increased saftey factor according 2.4.2.5 EN 1992 (2004) for cast in placepiles with kf = 1.1 has to be specified by the user explicitly.


Version 16.133−86

3.13.2. DIN 1045 old / DIN 4227 / DIN 18806:

The old DIN can be addressed with:

B = regular concrete (DIN)LB = light−weight concrete (DIN)SB = pre−stressed concrete (DIN)

The default FCN is 25 for B and LB, and 45 for SB. FCT is defined by:

FCT = 0.25 ⋅ FCN 2/3

Defaults in accordance with old DIN 1045 / DIN 4227 / DIN 18806:

FCN 10 15 25 35 45 55

FC:B (DIN 1045)B (DIN 4227)FBD:B (DIN 1045)EC

7−−

22000

10.5−

1.426000

17.515.0

1.830000

2321

2.234000

2727

2.637000

3033

3.039000

as well as the following high−strength concretes:

FCN 65 75 85 95 105 115

FCEC

40.040500

45.042000

50.043000

55.044000

60.044500

64.045000

The elastic modulus or the weight has to be specified in case of light−weight con-crete. However, the density class according to DIN 4219 (1.0 − 2.0) may be inputfor item GAM. The default for GAM and EC then complies with DIN 1055. A bili-near stress−strain curve is usually employed for light−weight concrete.

For detailed analysis of creep and shrinkage according to DIN 4227 you need thekind of cement and the consistency. You may specify this by appending a Literalto the class of concrete


3−87Version 16.13

KS Normal cement (Z35 F/Z 45F) consistency stiffKP Normal cement (Z35 F/Z 45F) consistency plasticKR Normal cement (Z35 F/Z 45F) consistency softSL slow hardening cement (Z 25, Z35L / Z45L) / stiffPL slow hardening cement (Z 25, Z35L / Z45L) / plasticRL slow hardening cement (Z 25, Z35L / Z45L) / softSR very fast hardening cement (Z 55) / stiffPR very fast hardening cement (Z 55) / plasticRR very fast hardening cement (Z 55) / soft

DIN 4227 has some contradictions about the bond stress. Chapter 13 gives va-lues which correspond quite well to the ratios given in table 7 of appendix A1. Butthese values do not match those given at DIN 1045 Table 19. Thus we have de-cided to enlarge the FBD values for concrete SB by a factor of 1.43. With thatamendment the value may be used for the bond design according to chapt. 13of DIN 4227.

For standard concrete a parabola−rectangular stress−strain diagram will be se-lected according to Eurocode EC2 / DIN 1045 / ÖNORM B4700 / SIA 162. SCMwill default to 1.00. If you analyse composite sections you might want to changethe value. High strength concrete will have lesser ultimate strains.

3.13.3. ÖNORM B 4700 / B 4750Although the OENORM B 4700 calls itself close to Eurocode, it deviates just withthe classification of concrete based on the cubic strength instead of the cylindricalstrength. As the designation is C resp. LC the user has to select the option NORMOEN.

B = regular concrete based on cube strength (ÖNORM 4700)LB = light−weight concrete on cube strength (ÖNORM 4700)C = regular concrete on cylindrical strength (ÖNORM 4700)LC = light−weight concrete, cylindrical strength (ÖNORM 4700)

The default FCN is 25 resp. 20.

Defaults in accordance with OeNORM B 4700:

FCN 20.0 25.0 30.0 40.0 50.0 60.0

FCFCTEC

15.01.9

27500

18.82.2

29000

22.52.6

30500

30.03.0

32500

37.53.5

35000

45.04.1

37000


Version 16.133−88

SCM is preset to 1.5, FCTK to 0.7⋅FCT.

3.13.4. Swiss Standard SIAThe SIA 262 (2003) is very similar to the Eurocodes, but there are numerous devi-ations (E−Modulus, bond strength, stress−strain law). As type we have therefore:

C = cylindrical strength of regular concrete (SIA 262)LC = cylindrical strength of light−weight concrete (SIA 262)

The elastic moduli are calculated based on the mean strength. For light−weightconcrete the values are corrected depending on the specific weight. The defaultstress−strain diagram is always according to the deformation stress strain law ofEC−2, even for the design. SCM will be preset with 1.5.

FCN = fck 12 16 20 25 30 35 40 45 50

fck,cube C 15 20 25 30 37 45 50 55 60

fck,cube LC 13 18 22 28 33 38 44 50 55

According to the old SIA 162 (1989) as type we have

SIAB = cube strength of regular concrete (SIA 162)SIAL = cube strength of light−weight concrete (SIA 162)

The elastic moduli are the mean values from Figure 31 in Section 5.18 of SIA. Halfof the elasticity moduli are used for light−weight concrete. The default stress−strain diagram is the parabolic−rectangular one in accordance with Eurocode 2/ DIN 1045 / OeNORM B 4200 / SIA 162. SCM will be preset with 1.2.

FCN 20.0 25.0 30.0 35.0 40.0 45.0

FCN−minFCFCTEC

10.06.52.0

29000

15.010.02.0

31000

20.013.02.0

33500

25.016.02.5

35000

30.019.52.5

36000

30.023.02.5

37000


3−89Version 16.13

3.13.5. French BAEL−99

The “Association francaise de normalisation” has published with the BAEL 91(Règle techniques de conception et de calcul des ouvrages et construction enbeton armé suivant la methode des états limites) a design code with similar re-gulations as the Eurocode but also with some deviations in several points. Wehave implemented the revision of 1999.

This code allows a characteristic strength of the concrete depending on the ageof the concrete and a calculation strength depending on the duration of the load-ing tl, to be defined by the user explicitly. Further we have:

FC = 0.85/θ ⋅ fckθ = 1.00 (tl > 24 h)θ = 0.90 (24h > tl > 1 h)θ = 0.85 (1h > tl)

FCT = 0.6 + 0.06 ⋅ fck (fck < 60)= 0.275 ⋅ fck 2/3 (fck > 60)

EC = 11000 ⋅ fck1/3

FBD = 0.60 ⋅ ψs2 ⋅ fct,0.05/γ ; ψs = 1.5

High strength concrete up to 80 is defined in appendix F. These have modifiedstress−strain−laws.

There is also a class DUCT for the UHPRFC Ductal FM. For the stress strain lawthe values GF is taken as w0.3/lc.

3.13.6. Spanish EHEThe Spanish EHE (Instrucción de hormigón estructural) is very similar to the Eu-rocode. Deviations are mainly in the designations, the elastic modulus and in thedesign algorithms itself.

HA = Hormigón masa/armado 20, 25, 30, 35, 40, 45, 50HP = Hormigón pretensado 25, 30, 35, 40, 45, 50


Version 16.133−90

3.13.7. Swedish BBKThe Swedish BBK has rather complex provisions for the safety factors, which areinfluenced by the safety class (see NORM) and are different for the elasticity mo-dulus and the strength. The following types are available for the 94−Release.

K = 16, 20, 25, 30, 35, 40, 45, 50, 55, 60, 70, 80LK = 8, 12, 16, 20, 25, 30, 35, 40, 45, 50, 55, 60, 70, 80

The new release (2004) uses now the designations according to the EC, butkeeps the safety concept of the old BBK. Then we have:

C = 16, 20, 25, 28, 30, 35, 40, 45, 50, 54, 55, 58, 60LC = 8, 12, 16, 20, 25, 30, 35, 40, 45, 50, 55, 60

As the BBK does not state any details about the transition zone in the work law,the user has the possibility to influence with FCR between 0.6FCK and 1.0FCKthe shape of this curve.

3.13.8. Danish DS 411The Swedish BBK has very complex provisions for the safety factors, which areinfluenced by the safety class (see NORM). The following types are available:

C = 16, 20, 25, 30, 35, 40, 45, 50, 55, 60

For E−modulus and tensile strength specific formulas are provided in the designcodes. For the design it is allowed to use a rectangular stress block, but the defaultis the Parabula−Rectangle−Diagram.

3.13.9. Norwegian NS 3473The classification of the Norwegian concretes NS is based on the cylindricalstrength. Avilable values are 20 / 25 / 30 / 35 /45 / 55 / 65 / 75 / 85 / 95. For Light-weight concrete (LNS) the highest strength class is 75.

3.13.10. Italian design codesThe design code “Decreto Ministeriale Italiane” published in 1996 as well as the2005 version of the “Norme Tecniche” classifies the concrete based on the cubicstrength Rck. Even the Version of 2008 favours this type of strength.


3−91Version 16.13

CAN = 2008 regular concrete with cube strength fwk (γ=1.50)CAL = 2008 light weight concrete with cylindrical strength fck (γ=1.50)CAN = 2005 regular concrete with cube strength Rck (γ=1.90)CAN = 1996 regular concrete with cube strength Rck (γ=1.60)CAP = 1996 prestressed concrete with cube strength Rck (γ=1.50)

The default values for design strength and elastic modulus are as follows:

FC = 0.83⋅0.85⋅Rck (1996) = 0.85 ⋅ fck (2008)

FCT = 0.27 ⋅ Rck 2/3 (1996) = 0.30 ⋅ fck 2/3 (2008)

EC = 5700 ⋅ Rck 1/2 (1996) = 22000 ⋅ ( fcm/10) 0.3 (2008)

FBD = 2.25 ⋅ fct,0.05 / γ

3.13.11. Hungarian design codesThe classification of the Hungarian design codes is based on the cylindricalstrength. Avilable values are 16 / 20 / 25 / 30 / 35 / 40 / 45 / 50 / 55.

3.13.12. British Standard BS 8110As type we have:

BS = normal weight concrete BS 8110

The nominal strength FCN is the cube strength. The design strength is obtainedby

FC = 0.67 FCN

British Standard employ a parabolic rectangle curve, starting from a design cubestrength β = FC/0.67 with 0.24 √β strain at full plasticity and an initial stiffnessof 5.5 √β according to Figure 2.1. The safety factor SCM is preset to 1.5. Thebond strength will be set to the non−physical maximum value for table 3.28 of BS8110 of √fc.

For Hong Kong slight modifications to British Standards are selected with thecountry code 852. The initial stiffness will then be 5.0 √β.


Version 16.133−92

3.13.13. American concrete institute ACI 318MAs class we have the specified compressive strength fc’ in MPa:

ACI = normal weight concrete ACI 318M

The test values of the cylindrical strength have to exceed the class value by a cer-tain amount based on the standard deviation. Chapter 5.3 specifies default va-lues for this required distance as 7.0, 8.5 and 10.0 MPa for class values of fc’ upto 21, until 35 and above.

As the value of fc�� should not exceed the value of 25/3 MPa in general and differ-ent reductions have to be applied for lightweight concrete, we use the tensilestress to define the value of fc�� . The modulus of rupture fr is the upper fractilevalue of the tension strength. ACI 9.5.2.3 defines:

fr � 0.75 * fc�� 0.75 * 25�3

or for lightweight concrete:

fr � 0.70 * min( fc�� , 1.8 * fct�m)

fr � 0.70 * 0.75 * fc��

The ratio of the fractiles is thus 1.26. The mean value fct−m will be preset to0.5 * fc�� . All other values will be derived from this value by a factor. If needed thelower fractile may be given, which will then set the upper value. But this value isonly used for those cases where explicitly the value fr is used within a formula.

The bond strength will be set to the non−physical maximum value for chapter 12.2of ACI 318 to a value of √fc.

3.13.14. Brasilian NBR 6118−2003As class we have NBR or C, where the used cement type is appended to thestrength class:

NBR 25 (for Cement Classes CP I and CP II)NBR 25L (for Cement Classes CP III and CP IV)NBR 25R (for Cement Classes CP V−ARI)

The modulus of elasticity is given by Eci = 5600�fck1/2 and Ecs = 0.85Eci. The

design curve is a Parabola−Rectangle with 0.85�fcd, as tensile strength we have


3−93Version 16.13

fct,m = 0.3�fck2/3; fct,kinf = 0.7�fct,m; fct,sup = 1.3�fct,m. Bond strength fbd =

η1�η2�η3�fctk,inf/γc ; η1=2.25.

3.13.15. Australian AS 3600 and New Zealand NZS 3101TYPE AS or TYPE NZS selects the respective standard. The characteristic com-pressive strength (i.e. 20, 25,32, 40, 50 or 65 MPa) can be entered using FCN(e.g. CONC TYPE AS FCN 50). Only selected material parameters are currentlypre−defined explicitly for AS and NZS standards. The modulus of elasticity is afunction of the mean strength value which is not provided in these design codes.Therefore the modulus of elasticity is estimated similar to the EC.

3.13.16. Japanese StandardsJapan has few official standards. As type we have the values from the books ofthe Japan Road Association (2002):

JIS = Japan concrete

The nominal strength FCN (21 to 60) as well as the elasticity and shear modulusare given in table 3.3.3 (JRA). The design strength is 0.85 fcn.

3.13.17. Chinese StandardsAccording to GB 50010−2002 we have:

GB = Standard and high strength concrete

The nominal strength FCN (15 to 80) and the the design strength are taken fromtable 4.1.3./4. Youngs modulus is derived from 4.1.5.

3.13.18. Indian Standards IS / IRCAs type we have:

M = Generic type for all design codesIS = Indian Standards IS 456 (10 bis 80)IRC = Indian Roads Congress IRC 21 (15 bis 60)

With the IRC 112 a complety new design code has been released, which is stron-gly related to the Eurocode EN 1992. The nominal strength FCN is now the cy-lindrical strength. However there are a lot of deviations in the coefficients, whichare not all described here. For example the mean strength fcm is defined asfck+10 and the tensile strength is about 13% less. More details may be found inthe chapter for the Eurocode.


Version 16.133−94

The nominal strength FCN is the cube strength in the IS 456 / IRC 21. The designstrength there is obtained by

FC = 0.67 FCN

The elasticity modulus is preset according to IS to 5000 * fck� , for IRC according

to table 9. For the Indish Standards the default is the “limit state method” whichuses a standard parabola rectangle diagram. The working stress method ((IRCresp. Annex B of IS 456) may be selected via the type CE. The mean tensilestrength is preset to 0.7 * fck

� , the safety factor SCM to 1.5. The bond strengthwill be set according to chapter 26.2.1.1. of IS 456.

3.13.19. Egyptian Standard ET RC−2001As type we have:

CET Standard concrete of the quality 15,20,25,30

where SCM = 1.5GAM = 24.0

EC = 4400. * fck�FC = 0.67 ∗ fck

FCT = 0.8 * fck�FCTK = 0.6 * fck�95% fctk = 1.0 * fck�FBD = 0.3 * fck�1.5�

3.13.20. Russian Standard SNIPThis design code has a wide range of classifications. Thus the user has to entersome specific values in some cases. Especially the safety factors for the loadsare depending on the environmental conditions and are not to be defined with thematerial here.

SNIP Concrete with compressive strength class 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60as well for old SNIP 2.03.01 with possible appendicesto the class value: T thermal treatment


3−95Version 16.13

TW thermal treatment in Autoclave A fine granular concrete group A (grain > 2.0) AT thermal treatment fine granular group A B fine granular concrete group B (grain < 2.0) BT thermal treatment fine granular group B W fine granular in Autoclave

LSNI Light weight concrete with compressive strength classthe property “porous” may be selected by appendinga letter “P” to the class value.

The compressive and tensile strength is selected according to tables 5.1−5.3.The elasticity modulus is taken from table 5.4.

3.13.21. Linear Elastic ConcreteA linear elastic material without tensile stresses is specified for CE. This can beused for analysis of stress distributions of foundations or older design codes withthe working stress method. FC is the allowed compressive stress in those cases.The modulus of this stress strain law should be less than EC in general and maybe specified with Item ECR. Values less than 100 are treated as explicit modularratio m = Es/Ec.


Version 16.133−96


3−97Version 16.13

3.14. STEE − Properties of Metals


STEE


NOTYPE

CLAS

Material number (1−999)Type of the material

S / Y Reinf./prestr. steel ECBST/PST Reinf./prestr. steel DINS Structural steel EC/DINAL,AC,AW Aluminium alloymore types see comments

Steel class or quality

−LIT

*

1*

*

FYFTFPESMUEGAMALFA

SCM

Yield strength (f0.01 or f0.02)Tensile strengthElastic limitElastic modulusPoisson’s ratioUnit weightThermal expansion coefficient

Default for AL:Typical material safety factor

N/mm2

N/mm2

N/mm2

N/mm2

−kN/m3

1/°K

****

0.3*

1.2E−52.38E−5

*

EPSYEPSTREL1REL2RK1FDYNFYCFTCTMAXGMODKMODQSTITL

Permanent strain at yield strengthUltimate strainCoefficient of relaxation (0.70 βΖ)Coefficient of relaxation (0.55 βΖ)Relative bond strengthBond coefficient for crack width EC2Allowed stress rangeCompressive yield strength (f0.02)Compressive strengthMaximum plate thicknessShear modulusBulk modulusPoisson ratio / shear modulus (obsoleted)Material name

o/ooo/oo%

LIT / %−−

N/mm2

N/mm2

N/mm2

mmN/mm2

N/mm2

*Lit32

***0 ***

FYFT*****


Version 16.133−98

There are some, but not very rigorous checks about the usage. While structuralsteel types (e.g. S 235, ST, AL etc) can be used only for cross sections, prestres-sing steel is only allowed for reinforcements, cables and tendons.

3.14.1. Structural Steel

FY FT EPST FP EPSY ES GAM

Eurocode:EN 1993−1−1Tab. 3.1* S 235

S 275S 355S 450S 275NS 355NS 420NS 460NS 275MS 355MS 420MS 460MS 235WS 355WS 460Q

t < 40 mm235 360 − − − 210000 78.5275 430 − − − 210000 78.5355 510 − − − 210000 78.5440 550 − − − 210000 78.5275 390 − − − 210000 78.5355 490 − − − 210000 78.5420 520 − − − 210000 78.5460 540 − − − 210000 78.5275 370 − − − 210000 78.5355 470 − − − 210000 78.5420 520 − − − 210000 78.5460 540 − − − 210000 78.5235 360 − − − 210000 78.5355 510 − − − 210000 78.5460 570 − − − 210000 78.5


3−99Version 16.13


Eurocode:EN 1993−1−1Tab. 3.1

S 235TS 275TS 355TS 450TS 275NTS 355NTS 420NTS 460NTS 275MTS 355MTS 420MTS 460MTS 235WTS 355WTS 460QT

40 < t < 80 mm215 360 − − − 210000 78.5255 410 − − − 210000 78.5335 470 − − − 210000 78.5410 550 − − − 210000 78.5255 370 − − − 210000 78.5335 470 − − − 210000 78.5390 520 − − − 210000 78.5430 540 − − − 210000 78.5255 360 − − − 210000 78.5335 450 − − − 210000 78.5390 500 − − − 210000 78.5430 530 − − − 210000 78.5215 340 − − − 210000 78.5335 490 − − − 210000 78.5440 550 − − − 210000 78.5

Eurocode:EN 10025−6

S 500QS 550QS 620QS 690QS 890QS 960Q

TMAX ...*) *) − − − 210000 78.5*) *) − − − 210000 78.5*) *) − − − 210000 78.5*) *) − − − 210000 78.5*) *) − − − 210000 78.5*) *) − − − 210000 78.5

*) Material values in dependence on the defined max. thickness TMAX

For structural steel that should get the material values of the product standard EN10025−2 till −6 the plate thickness TMAX has to be input. E.g. the input

STEE 1 S 355 TMAX 80

STEE 2 S 355M TMAX 100

defines in the first case the limit values of the stiffnesses for the structural steelof the quality 355 according to EN 10025−2 for the plate thickness of 63 mm <t � 80 mm und in the second case the limit values of the stiffnesses for the structu-ral steel of the quality 355M according to EN 10025−3 for the plate thickness of


Version 16.133−100

80 mm < t � 100 mm.

Note: In the National Annexes the material values may be specified differently.


DIN:ST 33ST 37ST 52

* S 235S 275S 355S 460

S 235S 275S 355

* GU 52GU 17GU 20GU 200GU 240GU 400

190 330 − − − 210000 78.5240 370 − − − 210000 78.5360 520 − − − 210000 78.5

TMAX 40 (t < 40 mm):240 360 − − − 210000 78.5275 430 − − − 210000 78.5360 510 − − − 210000 78.5460 600 − − − 210000 78.5

TMAX 80 / 100 (40 < t < 80 / 100 mm):215 340 − − − 210000 78.5255 410 − − − 210000 78.5335 490 − − − 210000 78.5

260 520 − − − 100000 72.5240 370 − − − 210000 72.5300 500 − − − 210000 72.5200 380 − − − 210000 72.5240 450 − − − 210000 72.5250 390 − − − 169000 72.5

OENORM:ST 44ST 55

285 430 − 230 −.2 206000 78.5355 540 − 285 −.2 206000 78.5

SIA:* S 235

S 275S 355S 460

S 235S 275S 355S 460

TMAX 40 (t < 40 mm):235 360 − − − 210000 78.5275 430 − − − 210000 78.5355 510 − − − 210000 78.5460 550 − − − 210000 78.5

TMAX 100 (40 < t < 100 mm):215 340 − − − 210000 78.5255 410 − − − 210000 78.5335 490 − − − 210000 78.5430 530 − − − 210000 78.5


3−101Version 16.13


BritishStandard:

BS 275BS 355BS 460

BS 275BS 355

*BS 460

BS 275BS 355BS 460

BS 275BS 355BS 460

BS 275BS 355BS 460

BS 275BS 355

TMAX 16 (t < 16 mm):275 430 − 205000 78.5355 500 − − − 205000 78.5460 550 − − − 205000 78.5

TMAX 40 (16 < t < 40 mm):265 430 − 205000 78.5345 500 − − − 205000 78.5440 550 − − − 205000 78.5

TMAX 63 (40 < t < 63 mm):255 430 − 205000 78.5335 500 − − − 205000 78.5430 550 − − − 205000 78.5

TMAX 80 (63 < t < 80 mm):245 430 − 205000 78.5325 500 − − − 205000 78.5410 550 − − − 205000 78.5

TMAX 100 (80 < t < 100 mm):235 430 − 205000 78.5315 500 − − − 205000 78.5400 550 − − − 205000 78.5

TMAX 150 (100 < t < 150 mm):225 430 − 205000 78.5295 500 − − − 205000 78.5

EA:EA 37EA 42EA 52

235 360 − − − 210000 78.5275 430 − − − 210000 78.5355 510 − − − 210000 78.5


Version 16.133−102


BSKBSK235BSK275BSK355BSK355NBSK355MBSK420BSK460

BSK235BSK275BSK355BSK355NBSK355MBSK420BSK460

BSK275BSK355BSK355NBSK355MBSK420BSK460

BSK275BSK355BSK355N

BSK235BSK275BSK355BSK355N

TMAX 16 (t < 16 mm):235 340 − 210000 78.5275 410 − 210000 78.5355 490 − − − 210000 78.5355 470 − − − 210000 78.5355 450 − − − 210000 78.5420 500 − − − 210000 78.5460 530 − − − 210000 78.5

TMAX 40 (16 < t < 40 mm):225 340 − 210000 78.5265 410 − 210000 78.5345 490 − − − 210000 78.5345 470 − − − 210000 78.5345 450 − − − 210000 78.5400 500 − − − 210000 78.5440 530 − − − 210000 78.5

TMAX 63 (40 < t < 63 mm):255 410 − 210000 78.5335 490 − − − 210000 78.5335 470 − − − 210000 78.5335 450 − − − 210000 78.5420 500 − − − 210000 78.5430 530 − − − 210000 78.5

TMAX 80 (63 < t < 80 mm):245 410 − 210000 78.5325 490 − − − 210000 78.5325 470 − − − 210000 78.5

TMAX 100 (80 < t < 100 mm):215 340 − 210000 78.5235 410 − 210000 78.5315 490 − − − 210000 78.5315 470 − − − 210000 78.5


3−103Version 16.13


BSKBSK460QBSK500QBSK550QBSK620QBSK690Q

BSK460QBSK500QBSK550QBSK620QBSK690Q

TMAX 50 (t < 50 mm):460 550 − − − 210000 78.5500 590 − 210000 78.5550 640 − − − 210000 78.5620 700 − − − 210000 78.5690 770 − − − 210000 78.5

TMAX 100 (50 < t < 100 mm):440 550 − − − 210000 78.5480 590 − 210000 78.5530 640 − − − 210000 78.5580 700 − − − 210000 78.5650 760 − − − 210000 78.5

NSNS 235NS 275NS 275NNS 275MNS 355NS 355NNS 355MNS 420NNS 420MNS 460NNS 460MNS 460Q

NS 235NS 275NS 275NNS 275MNS 355NS 355NNS 355MNS 420NNS 420MNS 460NNS 460MNS 460Q

TMAX 40 (t < 40 mm):235 360 − 210000 78.5275 430 − 210000 78.5275 390 − 210000 78.5275 380 − 210000 78.5355 510 − − − 210000 78.5355 490 − − − 210000 78.5355 470 − − − 210000 78.5420 540 − − − 210000 78.5420 520 − − − 210000 78.5460 570 − − − 210000 78.5460 550 − − − 210000 78.5460 570 − − − 210000 78.5

TMAX 80 (40 < t < 80 mm):215 340 − 210000 78.5255 410 − 210000 78.5235 370 − 210000 78.5255 360 − 210000 78.5335 490 − − − 210000 78.5335 470 − − − 210000 78.5335 450 − − − 210000 78.5390 520 − − − 210000 78.5390 500 − − − 210000 78.5430 550 − − − 210000 78.5430 530 − − − 210000 78.5440 550 − − − 210000 78.5


Version 16.133−104


DM−96:FEI 360FEI 430FEI 510

FEI 360FEI 430FEI 510

FEG 400FEG 430FEG 520

TMAX 40 (t < 40 mm)235 360 − − − 206000 78.5275 430 − − − 206000 78.5355 510 − − − 206000 78.5

TMAX 63,80,100 (t > 40 mm):210 340 − − − 206000 78.5250 410 − − − 206000 78.5315 490 − − − 206000 78.5

TMAX 40 (t < 40 mm):180 − − − 206000 78.5225 − − − 206000 78.5255 − − − 206000 78.5

MSZ:S 37S 45S 52

230 370 − 200 − 206000 78.5290 450 − 240 − 206000 78.5350 520 − 280 − 206000 78.5

AISC/ASTM;A 36A 42A 50A 53A 290A 345A 415A 450A 500AA 500BA 500CA 500DA 514A 517A 242A 588A 992A 70WA 100W

200000 78.5250 400290 415345 450240 415290 415345 450415 520450 550230 310290 400315 425250 400689 758 (TMAX 63,152 mm)689 793 (TMAX 63,152 mm)340 480 (COR−TEN, TMAX 19,25,102 mm)340 480 (COR−TEN, TMAX 4,6,8 mm)345 450485 586690 760


3−105Version 16.13


ABNT:NBR 250NBR 350NBR 415

250 400 205000 78.5350 450 205000 78.5415 520 205000 78.5

Australian:AS 400AS 400AS 350

*AS 350AS 350AS 300AS 300AS 300AS 250AS 250AS 250

AS 400AS 400AS 400AS 350

*AS 350AS 350AS 300AS 300AS 300AS 250AS 250

Flats and Sections:400 520 TMAX 17 (0 mm < t < 17 mm)380 520 TMAX 100 (17 mm < t < 100 mm)360 480 TMAX 11 (0 mm < t < 11 mm)340 480 TMAX 40 (11 mm < t < 40 mm)330 480 TMAX 100 (40 mm < t < 100 mm)320 440 TMAX 11 (0 mm < t < 11 mm)300 440 TMAX 17 (11 mm < t < 17 mm)280 440 TMAX >17 (17 mm < t)260 410 TMAX 11 (0 mm < t < 11 mm)250 410 TMAX 40 (11 mm < t < 40 mm)230 410 TMAX >40 (40 mm < t)

Hexagons, Rounds and Squares:400 520 TMAX 50 (0 mm < t < 50 mm)380 520 TMAX 100 (50 mm < t < 100 mm)360 520 TMAX >100 (100 mm < t)340 480 TMAX 50 (0 mm < t < 50 mm)330 480 TMAX 100 (50 mm < t < 100 mm)320 480 TMAX >100 (100 mm < t)300 440 TMAX 50 (0 mm < t < 50 mm)290 440 TMAX 100 (50 mm < t < 100 mm)280 440 TMAX >100 (100 mm < t)250 410 TMAX 50 (0 mm < t < 50 mm)230 410 TMAX >50 (50 mm < t)


Version 16.133−106


JISJIS 400

400

JIS 490490

JIS 520520520

JIS 570570570

235 400 TMAX 40 (t � 400 mm) 200000 77.0215 400 TMAX 100 (40 mm < t � 100 mm)

(SS 400, SM 400 and SMA 400W identical)315 490 TMAX 40 200000 77.0295 490 TMAX 100 ( 40 mm < t � 100 mm)355 520 TMAX 40 200000 77.0335 520 TMAX 75 (40 mm < t � 75 mm)325 520 TMAX 100 75 mm < t �100 mm

(SM 520, SM 490Y and SMA 490W identical)450 520 TMAX 40 200000 77.0430 530 TMAX 75 (40 mm < t � 75 mm)420 530 TMAX 100 (75 mm < t � 100 mm)

IS/IRCIS 250 250 250 − − − 211000 77.0

GBQ 235

235235235

345345345345

390390390390

420420420420

GB 50017−2003215 360 TMAX 16 210000 78.5205 TMAX 40 (16 mm < t < 40 mm)200 TMAX 60 (40 mm < t < 60 mm)190 TMAX 100 (60 mm < t < 100 mm)

310 490 TMAX 16 210000 78.5295 TMAX 35 (16 mm < t < 35 mm)265 TMAX 50 (35 mm < t < 50 mm)250 TMAX 100 (50 mm < t < 100 mm)




3−107Version 16.13


SNIPC 235

235245245255255275275285285345345345345345K375375390440440590

SP 52−102 (Table B.5) / SNIP II−23−81, 2 (Table 51)230 350 TMAX 20 206000 78.5220 350 TMAX 40 (20 mm < t � 40 mm)240 360 TMAX 20 206000 78.5230 360 TMAX 30 (20 mm < t � 30 mm240 360 TMAX 20 206000 78.5230 360 TMAX 40 (20 mm < t � 40 mm)270 370 TMAX 10 206000 78.5260 360 TMAX 20 (10 mm < t � 20 mm)270 380 TMAX 10 206000 78.5260 370 TMAX 20 (10 mm < t � 20 mm)315 460 TMAX 20 206000 78.5305 450 TMAX 40 (20 mm < t � 40 mm)280 440 TMAX 80 (40 mm < t � 80 mm)260 420 TMAX 100 (80 mm < t � 100 mm)335 460 TMAX 10 (4 < t � 10 mm) 206000 78.5345 480 TMAX 20 206000 78.5325 470 TMAX 40 (20 mm < t � 40 mm)380 525 TMAX 50 (4 < t � 50 mm) 206000 78.5430 575 TMAX 30 (4 < t � 30 mm) 206000 78.5400 555 TMAX 50 (30 mm < t � 50 mm)575 670 TMAX 40 (10 < t � 40 mm) 206000 78.5

The specifications which are a part of the steel quality and are printed in italics(e.g. T, T8, 4) describe the thicknesses. They have to be input by the user onlyin the case of a CADINP input.

The strength values especially for the high strength steels may vary dependingon the manufacturer and the alloy considerably, a check of the assumed valuesagainst the actual values is strongly recommended.

The maximum allowed plate thickness may be specified via TMAX, reducing thestrength values according to the design codes. As different strength values withinthe section may lead to consistency problems for some design tasks, we allowonly for a unified approach based on the maximum thickness. It will be checkedduring the generation of sections. For many grades one may append an identifierfor a maximum plate thickness for a direct definition.

Attention: The maximum thickness will be also used to control if the design of acomposite section with DESI in AQB will allow compressive strains beyond theyield limit. For sections of classes 3 and 4, this limit will be observed by default.


Version 16.133−108

For sections of class 1 or 2, the strain becomes unlimited by definition of TMAX0.0.

The safety factor SCM is preset to 1.1 for most structural steel materials. Thesafety factor becomes effective immediately for the calculation of the full plasticinternal forces of steel and composite sections.

For the Russian design steel the defaults are provided according to the controlprocedure GOST 27771 (γ = 1.025). These values are almost identical to thoseof the old SNIP, however the latter document provides higher values for thinnerelements and in some cases for rolled steel in a separate column. All these exten-sions have to be specified by the user explicitly.

For the hungarian MSZ the default values are not valid for all possible derivativesof the material. Further the strength to be used for the design is given as FP asa rounded value obtained from FY and a saftey factor depending on the strengthitself.


3−109Version 16.13

3.14.2. Aluminium alloy

FY FT EPST BC np TMAX

AWP 3004AWP 3005AWP 3103AWP 5005AWP 5052AWP 5049AWP 5454AWP 5754AWP 5083AWP 6061T4AWP 6061T6AWP 6082T4AWP 6082T6AWP 7020T6AWP 8011

AW 6060T5AW 6060T6AW 6060TXAW 6060DTAW 6061T4AW 6061T6AW 6063T5AW 6063T6AW 6063TXAW 6063DTAW 6005T6AW 6106T6AW 6082T4AW 6082T5AW 6082T6AW 6082ERAW 6082DTAW 7020T6AW 7020DT

180. 220 10 B 23 6.0150. 170 10 B 38 6.0120. 140 20 B 31 25.095. 125 20 B 25 12.5

160. 210 40 B 17 40.0190. 240 30 B 20 25.0220. 270 20 B 22 25.0

190. 240 30 B 20 25.0250. 305 30 B 22 40.0 110. 250 120 A 23 12.5 240. 290 60 B 23 12.5 / 80.0 110. 205 120 A 25 12.5 240. 295 60 B 25 6.0 / 12.5 /100.0280. 350 90 A 19 12.5 110. 125 20 B 37 12.5

120. 160 80 B 14 5.0 / 25.0140. 170 80 A 16 15.0150. 195 80 A 18 3.0 / 25.0160. 215 120 A 20 20.0110. 180 120 B 8 25.0240. 260 80 A 55 20.0110. 160 70 B 13 3.0 / 25.0160. 195 80 A 24 25.0180. 225 80 A 21 10.0 / 25.0190. 220 100 A 31 20.0200. 250 80 A 20 5.0 / 10.0 / 25.0200. 250 80 A 20 10.0110. 205 140 B 8 25.0230. 270 80 B 28 25.0260. 310 100 A 25 5.0 / 15.0240. 295 100 A 17 15.0 / 40.0240. 310 100 A 17 5.0 / 20.0275. 350 100 A 19 15.0 / 40.0280. 350 100 A 18 20.0


Version 16.133−110

FY FT EPST BC np TMAX

EurocodeAC 42100AC 42200AC 43000AC 43300AC 44200AC 51300

DIN:AL 18AL 20AL 22AL 25AL 27AL 28AL 31AL 35

147. 203 20.168. 224 15. 63. 126 12.5147. 203 20. 56. 119 30. 70. 126 20.

FY FT EPST FP EPSY TMAX80 180 − 60.0 * −

100 200 − 88.0 * −160 215 144.5 * −180 250 − 144.5 * 5.0140 270 − 110.5 * −210 275 − 168.0 *230 310 − 229.5 * 20.0290 350 − 246.5 * 30.0

EC 9 and the new DIN 4113 (2002) use the American system for classification ofaluminium alloys. As there are more than 300 different materials available, withsignificant differences of properties, the user should check the thickness limit andstrength parameters thoroughly. For the default values the following scheme hasbeen used:

• For plates we use the type AWP to distinguish them properly from the pro-file and tubes. For untreated alloys only the number of the alloy is necessa-ry.

• For tubes and profiles the type AW is used and either ER or DT (drawn tu-bes) or the important criteria of the heat treatment as T4, T5, T6 or TX forT66 has to be appended to the alloy as characters.

• For the castings the case of a cocille and temper F or T6 has been selectedas default.

As the reduction of the strength in the HAZ is depending on the welding processand the thickness, the user has to define a separte Materialnumber for those re-gions with a explicitly reduced values for FY and FT.

DIN 4113 requires the stress for Aluminium to be reduced for creep effects ac-cording to chapter 6.3 with a factor c between 0.8 and 1.0. As the exact evaluation


3−111Version 16.13

would be rather complex, this is accounted for by the global factor of safety 1/c.The default on the safe side is a value of 1.25. Better values have to be specifiedexplicitly by the user.

A reduction for generally higher temperatures has to be specified explicitly, butthe reduction for the fire case is available via the stress strain law.

The values ES and GAM are for all classes with 70000 [MPa] and 28.0 [kN/m3]preset, the values FP and EPSY are selected according to the data of table 10of the DIN 4113.


Version 16.133−112

3.14.3. Reinforcing and Prestressing Steel

FY FT EPST FP EPSY ES GAM REL1

Eurocode:S 220AS 220BS 220CS 450AS 450BS 450CS 500AS 500BS 500CS 550BS 600BY 1100Y 1030Y 1230Y 1450CY 1570CY 1670CY 1770CY 1860CY 1770Y 1860Y 1960Y 2060Y 2160Y 1700Y 1820

220 220 25 − −. 200000 78.5220 220 50 − −. 200000 78.5220 220 75 − −. 200000 78.5450 486 25 − −. 200000 78.5450 486 50 − −. 200000 78.5450 486 75 − −. 200000 78.5500 550 25 − −. 200000 78.5500 550 50 − −. 200000 78.5500 550 75 − −. 200000 78.5550 620 50 − − 200000 78.5600 670 50 − − 200000 78.5900 1100 3.5 − − 205000 78.5 ECL3835 1030 3.5 − − 205000 78.5 ECL3

1080 1230 3.5 − − 205000 78.5 ECL31100 1450 6.0 − − 130000 78.5 ECL11300 1570 6.0 − − 205000 78.5 ECL11385 1670 6.0 − − 205000 78.5 ECL11470 1770 6.0 − − 205000 78.5 ECL11545 1860 6.0 − − 205000 78.5 ECL11520 1770 6.0 − − 195000 78.5 ECL11600 1860 6.0 − − 195000 78.5 ECL11685 1960 6.0 − − 195000 78.5 ECL11600 2060 6.0 − − 195000 78.5 ECL11770 2160 6.0 − − 195000 78.5 ECL11460 1700 6.0 − − 195000 78.5 ECL11565 1820 6.0 − − 195000 78.5 ECL1


3−113Version 16.13


DIN:BST 220BST 420BST 500PST 835PST 1080PST 1100PST 1375PST 1420PST 1470PST 1570

220 340 − − −.2 210000 78.5420 500 − − −.2 210000 78.5500 550 − − −.2 210000 78.5835 1030 7 735 −.2 205000 78.5 3.3

1080 1230 6 950 −.2 205000 78.5 3.31100 1450 6 − − 130000 78.5 7.51375 1570 6 1150 −.2 205000 78.5 7.51420 1570 6 1220 −.2 205000 78.5 2.01470 1670 6 1250 −.2 205000 78.5 7.51570 1770 6 1300 −.2 195000 78.5 7.5

OENORM:BSOE 240BSOE 420BSOE 500BSOE 550BSOE 600PSOE 835PSOE 1080PSOE 1375PSOE 1420PSOE 1470PSOE 1570

240 360 17 − .4 210000 78.5420 500 10 − .4 210000 78.5500 550 10 − .4 210000 78.5550 620 10 − .4 210000 78.5600 670 10 − .4 210000 78.5835 1030 7 − −.2 205000 78.5 3.3

1080 1230 6 − −.2 205000 78.5 3.31375 1570 6 − −.2 205000 78.5 7.51420 1570 6 − −.2 205000 78.5 2.01470 1670 6 − −.2 205000 78.5 7.51570 1770 6 − −.2 195000 78.5 7.5

SIA:B 500AB 500BB 450CY 1030Y 1100Y 1230Y 1570Y 1670Y 1770Y 1860

500 525 20 − − 205000 78.5500 540 45 − − 205000 78.5450 520 65 − − 205000 78.5830 1030 20 − − 205000 78.5 4.0900 1100 20 − − 205000 78.5 4.0

1080 1230 20 − − 205000 78.5 4.01300 1570 20 − − 205000 78.5 4.01440 1670 20 − − 205000 78.5 4.01520 1770 20 − − 195000 78.5 2.51600 1860 20 − − 195000 78.5 2.5


Version 16.133−114


BBK−94:KS 26KS 40

40D40DD

KS 50KS 60

60DKS 500BBK−04:KS 260KS 500KS 600KSY 1030KSY 1670KSY 1770KSY 1860KSY 2060

∅270 − − − 200000 78.5 <32370 − − − 200000 78.5 <32390 − − − 200000 78.5 <25410 − − − 200000 78.5 <16510 − 30 − −.2 200000 78.5 <12590 − − − 200000 78.5 <16620 − − − 200000 78.5 <25500 − 50 − − 200000 78.5 <32

260 − 50 − − 200000 78.5 <32500 − 50 − − 200000 78.5 <32600 − 50 − − 200000 78.5 <32835 1030 35 − − 205000 77.0 4.0

1470 1670 35 − − 205000 77.0 4.01500 1770 35 − − 205000 77.0 4.01650 1860 35 − − 205000 77.0 4.01790 2060 35 − − 205000 77.0 4.0

DS−411:BDS 410BDS 500BDS 550

∅410 − − − 200000 78.5 <32500 − − − 200000 78.5 <32550 − − − 200000 78.5 <32

NS−3473:BNS 500

∅500 − − − 200000 78.5 <32

BAEL−99:FEE 215FEE 235FEE 400FEE 500

215 215 − − 200000 78.5235 235 − − 200000 78.5400 400 − − 200000 78.5500 500 − − 200000 78.5


3−115Version 16.13


DM−96:FEB 22FEB 32FEB 38FEB 44FEB 39Norme−2005FEB 450Norme−2008FEB 450AFEB 450C

215 335 − − 200000 78.5315 490 − − 200000 78.5375 450 − − 200000 78.5440 540 − − 200000 78.5390 440 − − 200000 78.5

450 540 − − 200000 78.5

450 540 22.5 − − 200000 78.5450 540 67.5 − − 200000 78.5

MSZ:B 240BB 360BB 500BY 1030Y 1230Y 1670Y 1770Y 1860

240 380 210 − 200000 78.5360 500 310 − 200000 78.5500 600 420 − 200000 78.5830 1030 720 − 195000 78.5

1080 1230 920 − 195000 78.51435 1670 1230 − 195000 78.51520 1770 1320 − 195000 78.51580 1860 1375 − 195000 78.5

EHE:B 400B 500Y 1570Y 1670Y 1770Y 1860Y 1960Y 2060

400 440 50 − − 200000 78.5500 550 50 − − 200000 78.5

1340 1570 35 − − 205000 78.51420 1670 35 − − 205000 78.5 2.01500 1770 35 − − 205000 78.5 2.01580 1860 35 − − 205000 78.5 2.01670 1960 35 − − 195000 78.5 2.01750 2060 35 − − 195000 78.5 2.0


Version 16.133−116


BritishStandard:SBS 250SBS 460SBS 500PSBS 1570PSBS 1620PSBS 1670PSBS 1720PSBS 1770PSBS 1860

250 250 − − 200000 78.5460 460 − − 200000 78.5500 500 − − 200000 78.5

1256 1570 −5 − − 205000 78.5 8.01296 1620 −5 − − 205000 78.5 8.01336 1670 −5 − − 205000 78.5 8.01376 1720 −5 − − 205000 78.5 8.01416 1770 −5 − − 205000 78.5 8.01488 1860 −5 − − 205000 78.5 8.0

ACI/AASHTO:SACI 40SACI 50SACI 60SACI 65SACI 70SACI 75SACI 80PSAC 160PSAC 250PSAC 270

280 420 − − 200000 78.5350 560 − − 200000 78.5420 620 − − 200000 78.5460 460 − − 200000 78.5490 560 − − 200000 78.5520 690 − − 200000 78.5550 725 − − 200000 78.5

1100 1250 − − 207000 78.5 2.01730 1730 − − 197000 78.5 8.01860 1860 − − 197000 78.5 8.0


3−117Version 16.13


NBRCP 25CP 40CP 50CP 60CA 85CA 150RNCA 150RBCA 160RNCA 160RBCA 170RNCA 170RBCA 175RNCA 175RBCA 180RNCA 190RNCA 190RB

250 300 − − 210000 78.5400 440 − − 210000 78.5500 550 − − 210000 78.5600 660 − − 210000 78.5850 1050 − − 200000 78.5

1280 1500 6.0 − −2 195000 78.5 7.51350 1500 6.0 − −2 195000 78.5 3.01360 1600 5.0 − −2 195000 78.5 5.01440 1600 5.0 − −2 195000 78.5 2.01490 1700 5.0 − −2 195000 78.5 5.01580 1700 5.0 − −2 195000 78.5 2.01490 1755 3.5 − −2 185000 78.5 7.01580 1755 3.5 − −2 185000 78.5 2.51530 1800 3.5 − −2 185000 78.5 7.01610 1900 3.5 − −2 185000 78.5 7.01710 1900 3.5 − −2 185000 78.5 2.5

IS/IRC:SIS 240SIS 415SIS 500PSIS 800PSIS 1050PSIS 1350PSIS 1500PSIS 1600

240 240 − − 200000 78.5415 415 − − 200000 78.5500 500 − − 200000 78.5800 1000 7 800 −.5 200000 78.5 2.5

1050 1250 6 1000 −.5 200000 78.5 2.51350 1650 6 1320 −.5 200000 78.5 8.01500 1800 6 1440 −.5 200000 78.5 8.01600 1900 6 1520 −.5 195000 78.5 8.0

GB:SGB 235SGB 335SGB 400PSGB 1470PSGB 1570PSGB 1670PSGB 1770PSGB1570SPSGB1720SPSGB1860S

FY FY’ FT210 235 − − 210000 78.5300 335 − − 200000 78.5360 400 − − 200000 78.5

1040 400 1470 − − 210000 78.5 5.01110 410 1570 − − 205000 78.5 5.01180 410 1670 − − 205000 78.5 5.01250 410 1770 − − 205000 78.5 5.01110 390 1570 − − 195000 78.5 5.01220 390 1720 − − 195000 78.5 5.01320 390 1860 − − 195000 78.5 5.0


Version 16.133−118


GBJ:SGB ISGB IISGB IVPSGB IV

235 235 − − 210000 78.5 8.0335 335 − − 210000 78.5 2.5380 835 − − 190000 78.5 5.0751 835 − − 190000 78.5 5.0

AS/NZS:SAS 250SAS 400SAS 450SAS 500PAS 1030PAS 1670PAS 1700PAS 1790PAS 1830PAS 1870

250 250 − − 200000 78.5400 400 − − 200000 78.5450 450 − − 200000 78.5500 500 − − 200000 78.5840 1030 − − 200000 78.5 3.0

1340 1670 − − 205000 78.5 1.01360 1700 − − 205000 78.5 1.01468 1790 − − 195000 78.5 2.01500 1830 − − 195000 78.5 2.01533 1870 − − 195000 78.5 2.0

JIS:SJS 235SJS 295SJS 345SJS 390PSJS 930PSJS 1030PSJS 1080PSJS 1180PSJS 1420PSJS 1470PSJS 1520PSJS 1620PSJS 1720PSJS 1860

235 380 − − 200000 77.0295 440 − − 200000 77.0345 490 − − 200000 77.0390 560 − − 200000 77.0

0.80ft 930 − − 200000 77.00.80ft 1030 − − 200000 77.00.80ft 1080 − − 200000 77.00.80ft 1180 − − 200000 77.00.93ft 1420 0.84ft 15 200000 77.00.93ft 1470 0.84ft 15 200000 77.00.93ft 1520 0.84ft 15 200000 77.00.93ft 1620 0.84ft 15 200000 77.00.93ft 1720 0.84ft 15 200000 77.00.93ft 1860 0.84ft 15 200000 77.0


3−119Version 16.13


ET RC−2001SET 350SET 450SET 520SET 520MSET 600

TMAX350 240 350 200000 78.5 40.450 280 450 200000 78.5 40.520 360 520 200000 78.5 36.520 450 520 200000 78.5 −600 400 600 200000 78.5 36.

SP52−101−2003SNIA 240SNIA 300SNIA 400SNIA 500SNIB 500

RK 5.03−33− 2005SNIA 600SNIA 800SNIA 1000

SNIP2.03.01:SNIA ISNIA IISNIA IIISNIA IVSNIA VSNIA VISNIA VIISNIB ISNIB 1000SNIB 1100SNIB 1200SNIB 1300SNIB 1400SNIB 1500

FY FT FP FYC ES GAM γs

235 400 190 235 − 200000 78.5 1.10300 500 235 300 − 200000 78.5 1.10400 500 320 400 − 200000 78.5 1.13500 600 345 460 − 200000 78.5 1.15410 500 290 360 − 200000 78.5 1.20

600 800 360 540 − 200000 78.5 1.15800 1000 360 575 − 200000 78.5 1.15

1000 1000 360 600 − 200000 78.5 1.20

225 235 175 225 − 210000 78.5 1.05280 295 225 280 − 210000 78.5 1.05365 390 290 365 − 200000 78.5 1.10510 590 405 450 − 190000 78.5 1.15680 788 545 500 − 190000 78.5 1.15815 980 650 500 − 190000 78.5 1.20980 1175 785 500 − 190000 78.5 1.20410 1000 290 375 − 170000 78.5 1.20850 1000 680 500 − 200000 78.5 1.20915 1100 730 500 − 200000 78.5 1.20

1000 1200 785 500 − 200000 78.5 1.201050 1300 835 500 − 200000 78.5 1.201170 1400 940 500 − 200000 78.5 1.201250 1500 1000 500 − 200000 78.5 1.20

For the steel type BST you may attach to the grade two extra characters switchingto new DIN 1045−1:


Version 16.133−120

SA Reinforcing bars with standard ductilitySB Reinforcing bars with high ductilityMA Reinforcing bar mats with standard ductilityMB Reinforcing bar mats with high ductility

The safety factor SCM is preset for most reinforcing and prestressing steels to1.15 and 1.05 (BS) respectively. The safety factor becomes effective immediatelyfor the calculation of the full plastic internal forces of steel and composite sections.

For non−linear analysis with a constant safety factor according to DIN 1045−1 thestrength of the concrete will be reduced, while those of the steel will be raised. Forthis a special serviceability stress−strain law is generated with a safety factor of1.3.

The Russian SNIP has a reduced strength for shear links and inclined bars. Thisvalue is taken from the value FP. In the very general case, it might be necessaryto use a separate material with a reduced strength.

For the hungarian MSZ the defualt values are not valid for all possible derivativesof the material. Further the strength to be used for the design is given as FP asa rounded value by the minimum from FY/1.15 and FT/1.3.

Attention:Some material parameters may depend on other parameters not known to theprogram. E.g. the dynamic stress range of the reinforcements is not only depend-ing on the diameter TMAX of the bars but also on the curvature and the type ofthe material of the duct (steel, plastic). In all those cases it is necessary to usedifferent material numbers and to specify the deviating values explicitly.


3−121Version 16.13

3.14.4. Relaxation

Relaxation of tendons is implemented in AQUA/AQB as a product. While the timefactor is specified in AQB, AQUA defines the stress dependant factor for the refer-ence time of 1000 h. This may be accomplished either by a linear relation estab-lished by two values at 0.55⋅fpk and 0.70⋅fpk or via selected literals for item REL2as quadratic function according to CEB / EN1992 or the general function accord-ing to BPEL annexe 2 or AS 3600.

Literal 0.60⋅fpk 0.70⋅fpk 0.80⋅fpk

CEB1

CEB2

CEB3

4.00 %

1.00 %

2.00 %

8.00 %

2.00 %

4.00 %

12.00 %

5.00 %

6.67 %

CEB model code 1990

normal

improved

bars

ENC1

ENC2

ENC3

5.39�ρ1000�e6.7μ(t/1000)0.75(1−μ)10−5

0.66�ρ1000�e.9.1μ(t/1000)0.75(1−μ)10−5

1.98�ρ1000�e8.0μ(t/1000)0.75(1−μ)10−5

Euronorm EN 1992 (2004)

ordinary (ρ1000 = 8.0)

low relaxation(ρ1000 = 2.5)

bars (ρ1000 = 4.0)

ECL1

ECL2

ECL3

4.50 %

1.00 %

1.50 %

8.00 %

2.50 %

4.00 %

12.00 %

4.50 %

7.00 %

Eurocode EC 2 < 2004

ordinary

low relaxation

bars

RN

TBR

Annexe 2 8.00 %

2.50 %

Annexe 2

BPEL 91

relaxation normale

très basse relaxation

AS

1.00 %

2.00 %

3.00 %

AS 3600/5100

Rb (Chapter 6.3.4)

IRCIRCL

5.00 %

2.50 %

IRC 112


Version 16.133−122

3.14.5. Bond Properties

The bond properties are specified highly different within the codes. They dependboth on the concrete and the steel properties. When defining the concrete themaximum bond stress for optimal bond properties is specified. The value R de-fines then the relative bond strength for this steel as specified in:

Tab. 7 DIN 4227 A1 ( R = 0.3 ÷ 0.9)

Tab. 15 DIN 1045−1 ( R = 0.3 ÷ 0.8) / Tab. 4.115 DIN−FB−102

Tab 5.3 chap. 5.2.2.2. EC 2 (R = 0.7 ÷ 1.0)

§ 9.3.1 GB 50010 (R = α/0.14 = 0.737 ÷ 1.077)

If different bond properties should be applied, different materials have to be speci-fied. The bond value is needed for

• Crack width

• Limitation of stress increase for tendons

Depending on which effect is more severe, you might have to choose betweendifferent code factors for this value. Please see also remarks for FBD in recordCONC.

The second coefficient is used for those design codes using special values notdeductable from the relative bond coefficients alone. This is especially the Euro-code, but also the russian SNIP:

§ 4.14 SNIP 2.03.01 ( K1 := η = 1.0 ÷ 1.4)§ 7.2.12 SP 52−101 ( K1 := ϕ2 = 0.5 ÷ 0.8)

The defaults are given in principal in the following table. However, there are somedeviations depending on the design code and the strength possible:

R K1

Reinforcing steelPrestressing steel

1.00.75

0.81.6


3−123Version 16.13

3.14.6. Stress−Strain Relations

The stress−strain law may have up to 4 segments:

• Up to the proportional limit (FP/ES,FP)

• Up to the yield limit (EPSY,FY)EPSY may be defined absolute (positive) or relative to the strain limit(negative)

• Up to the tensile strength (EPST,FT)

• Constant to the nearly infinity (1000 o/oo)

Depending on the steel type and grade the values EPSY and EPST as well asFP will be preset. With explicit definitions you may suppress:

• If FP is not lesser than FY the first part will be omitted.

• If EPST is not greater than EPSY the third part will be omitted.

More general stress−strain laws are specified via record SSLA.

In general the stress−strain laws are identical for serviceability and ultimate limitdesign. However, for reinforcing steel according to EC2 and DIN 1045−1 there arenumerous explicit changes.

As the safety factor concept will not generate an affine curve for the ultimate state,the safety factor will be applied immediately.

Although the tensile strength for reinforcement steel with standard ductility will bereached at 25 o/oo, it is not allowed to use this in the design according to DIN1045−1. The stress strain laws for design and non linear analysis differ thereforefor those materials.


Version 16.133−124


3−125Version 16.13

3.15. TIMB − Timber and Fibre Materials


TIMB


NOTYPE

CLAS

Material number (1−999)Type of material

see following tableQuality class / Strength

type of matrix for compound fibres

−LIT

−

1*

*

EPGE90QHQH90GAMALFASCMFMFT0FT90FC0FC90FVFVRFVBFM90G90OALOAF

Elastic modulus parallel to fibreShear modulusElastic modulus normal to fibrePoisson’s ratio yz (polywood panels)Poisson’s ratio xy / xz (solid wood)Unit weightTemperature elongation coefficientMaterial safety factorBending strengthTensile strength parallel to the fibreTensile strength normal to the fibreCompressive strength parallel to fibresCompressive strength normal to fibresShear strength at center (shear force)Shear strength at the edge (torsion)Shear strength for plate bendingBending strength normal to fibresShear modulus for plate bendingMeridian angle of anisotropyDescent angle of anisotropy

N/mm2

N/mm2

N/mm2

−−

kN/m3

1/°K−

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

degreedegree

******

0.01.3/*

**********

0.00.0


Version 16.133−126


KMODKMO1KMO2KMO3KMO4KDEFTMAXRHO

Strength modification permanent loadingor long term loadingor middle term loadingor short term loadingor very short term loadingmodification for long term deflectionsmaximum thickness for platescharacteristic density

−−−−−−

mmkg/m3

********

TITL Material designation Lit32 *

TIMB allows the definition of all materials with a preferred fibre orientation. Astype you have the timber classes of Eurocode, respective DIN, OENORM andSIA and the German compound fibre types. As the EN 1995 does not specify anystrength values, those values have to be specified for all other countries explicitly.

With the EN 1995 (EC5) and the derived design codes correction factors kmodhave been introduced for the permissible stresses and kdef for the deformations.The distinct value is depending not only on the material but also on the serviceclass and the duration of the loading. The following table shows the values forsolid timber, however there are much more values available within the programand the user may change theses values explicitly.

Class of load durationService Class

1 2 3permanent 0.60 0.60 0.50long term 0.70 0.70 0.55medium term 0.80 0.80 0.65short term 0.90 0.90 0.70very short term 1.10 1.10 0.90k-def 0.60 0.80 2.00

The service class may be either specified in general with the definition of thedesign code NORM or be appended to the class definition with a colon. The inputof TIMB C 30:2 selects a solid soft wood of strength class 30 and the service class2.

Types and defaults:


3−127Version 16.13

TYPE CLAS Explanation

C

D

GL

PLY

PART

OSB

FIB

14 / 16 / 18 / 20 / 22 / 24 / 27 / 30 / 35 / 40 / 45 / 50

30 / 35 / 40 / 50 / 60 / 70

24 / 28 / 32 / 36

24c / 28c / 32c / 36c

25 / 40 / 50 / 60

1 / 4 / 5 / 6 / 7

2 / 3 / 4

HB MHB MDF SB

DIN 1052-2004:Solid soft woodTab. F5

Solid hard woodTab. F7

homog. laminated timber Tab.F9

combined laminated timber Tab.F9

Plywood Tab. F11/F12

Particle board,Tab. F15/F16/F17/F18

OSB, Tab. F13/F14

Hardboard Fibre boardMedium hardboardMedium densitySoft Fibre board

C

D

GL

20 / 24 / 27 / 35 / 45

30

24 / 28 / 36

24k / 28k / 36k

SIA 265:Solid soft wood, Tab. 6

Solid hard wood (Beech / Oak)

homog. laminated timber Tab. 7combined laminated timber Tab. 7


Version 16.133−128

TYPE CLAS Explanation

S

MS

BS

NA

BS

LA/LB/LC

FTK/L/BE

7 / 10 / 13

10 / 13 / 17

11 / 14 / 16 / 18

1 / 2 / 3

1 / 2

DIN 1052 A-1Timber, Sorted acc. DIN 4076

Timber, Sorted acc. DIN 4076

glued laminated timber

DIN 1052 oldSoft wood

glued laminated timber

Hard wood

ÖNORM B3001spruce,fir,pine / larchbeech,oak

GFK/CFK/SFK

EPUPVE

Values strongly dependon fibre properties!40000 / 5000 12.530000 / 4500 12.520000 / 3500 10.7

Glas-/Carbon-/Synthetic-compound fibre materialsEpoxid resinUnsaturised poliester resinVinil ester resin

There are many composite materials in timber constructions. Although a precisetreating is possible with composite sections or MLAY, the design codes provideequivalent materials for that purpose. As the strength is no strongly dependanton the thickness of the construction part, the definition of that value with TMAXis mandatory.

The description of a transverse orthotropy material law has one direction that hasdifferent properties (fibre direction), while the description in the plane perpendicu-lar to this remains isotropic. The law defined with TIMB is formal equivalent,however not identical with that defined via MATE.

If x is chosen as this special direction it holds:

�x� �xE��90·

(�y��z)E90

�y��yE90

��· �zE90

��*90·

�xE

�z� �zE90

��·�yE90

��*90·

�xE


3−129Version 16.13

�*90� �90·

EE90

It should be noticed, that the poisson’s ratios μ90 and μ90* are no longer bound

to 0.5 and are strongly connected to the ratio of the elasticity moduli, as the result-ing stress−strain matrix has to be symmetric.

The order of the indices of stress and strain components notation is defined asfollows:

[ x y z xy xz yz ] general three−dimensional case[ x y xy z ] plane strain condition, axial symmetry[ x y xy ] plane stress

For the axial symmetric case x denotes the axis of rotation while y represents theradial and z the tangential direction.

Furthermore holds:

E1�E90 , E2�E , �1� �90 , �2� � , G1�G90 , G2�G

General three−dimensional case: The three−dimensional material stiffness matrix is obtained by inversion of thestrain−stress matrix and reads (z being the direction normal to the isotropic plane= fibre direction):

D�

��

�

�

E1�1� n��2

2�1� �1

� �m

E1��1� n� �2

2�1��1

� �m

E1��2m

0

0

0

�E1��1� n � �2

2�1��1

� �m

�E1�1� n� �2

2�1� �1

� �m

E1��2m

0

0

0

E1��2m

E1��2m

�E2�1��1

m0

0

0

0

0

0

�G1�

0

0

0

0

0

0

G2

0

0

0

0

0

0

�G2

��

�

�

n�E1E2

, m� 1� �1� 2� n��22

Plane strain conditions: The x direction is defined as the fibre direction (=normal to the isotropic plane).The reduced stress−strain matrix yields:


Version 16.133−130

D�

��

�

�

E2�1��1

m

E1��2m

0

E1��1� n� �2

2�1��1

� �m

E1��2m

E1�1� n� �2

2�1� �1

� �m0

E1��2m

0

0

G2

0

��

�

�

n�E1E2

, m� 1� �1� 2� n��22

Plane stress conditions: The x direction is defined as the fibre direction (=normal to the isotropic plane).The material stiffness matrix is obtained via inversion of the reduced strain−stress matrix and reads:

D��

�

�

E2

1� n��22

E1 ��2

1� n��22

0

E1� �2

1� n ��22

E1

1� n ��22

0

0

0

G2

��

�

�

, n�E1E2

Axial symmetry: The general case of anisotropy does not need to be considered since axial sym-metry would be impossible to achieve under such circumstances. A case of in-terest in practice is that of the fibre direction parallel to the rotational axis x, i.e.the x direction is normal to the plane of isotropy. For such a case the materialstiffness matrix reads:

D�A�

��

�

�

1��21

n

�2�1��1

�

0

�2�1��1

�

�2�1� �1

�

�1� n�22�

0

�1� n�22

0

0

G90A

0

�2�1��1

�

�1� n�22

0

1� n�22

��

�

�

A�E2 � n

�1� �1� �m

, n�E1E2

, m� 1� �1� 2� n��22


3−131Version 16.13

Definition of fibre direction:Depending on the element type we have slightly different orientations of ortho-tropy:

For beams the fibre direction is identical with that of the beam axis.

For planar systems (TALPA) the value OAF is the angle between the fibre direc-tion and the element x−direction. The values E90 and μ90 then hold within the iso-tropic plane whose normal is given by the (skew) fibre direction.

For shells and plates it might be possible (eg. plywood) that there are fibres in bothx and y direction. The anisotropy effects thus reduces to different shear modulifor in plane membrane shear (Gm=0.5E90/(1+μ)) and the transverse shear forcedirections (G). This may be accomplished either with an explicit definition E90 ==E or with a layered material (MLAY). For the case of vertical boards tied together,you may use the orthotropy factors of thickness description (−> QUIAD) or usea 3D model.

In three−dimensional systems (continuum elements) the default fibre direction isthe element z−direction. Other fibre directions can be specified by defining thethree−dimensional orientation of the isotropic plane (=plane, whose normal direc-tion is the fibre direction) via meridian and descent angle, known from geology(compare MATE).


Version 16.133−132

3.16. MASO − Masonry / Brickwork


MASO


NOSTYP

SCLAMCLA

Material number (1−999)Type of brick stone

SB Standard solid BrickLS Limestone BrickLC Lightweight concreteC concreteCC cellular concreteBS British Standard 5628−1BS−2 Britisch Standard 5628−2

Strength of brick stoneGroup or strength of mortar

i,ii,iia,iii,iiia Standard mortarDM Thin bed mortarLM21,LM36 Light mortarnumerical Qualified mortar

−LIT

N/mm2

LIT

N/mm2

1SB

**

EGMUEGAMALFASCME90M90OALOAFFCNFCFTFVFHSFTB

Elastic modulusShear modulusPoisson’s ratioUnit weightTemperature elongation coefficientMaterial safety factorElastic modulus in lateral directionPoisson’s ratio in lateral directionMeridian angle of anisotropyDescent angle of anisotropyNominal strength σo

Compressive strengthTensile strengthShear strengthAdhesional shear strength βHS=2σoHS

Brick tensile strength βRZ

N/mm2

N/mm2

−kN/m3

1/°K−

N/mm2

−degreedegreeN/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

*****

2.5**

0.00.0*

σo/0.35****

TITL Material name Lit32 *


3−133Version 16.13

As there are not yet any specific design routines, the parameters follow DIN1996−1−1 (EC6). According to DIN 1053−1 you should use a value of 2.5 for SCMand 2.67 for FC.

For masonry according to BS 5628−1 the group identifier A to D has to be includedas a prefix to the stone class. You may then select the mortar designations I toIV. FT is the tensile strength for bending according Table 3 “parallel to bed joints”,FV is the vertical shear strength according pict. 2 and clause (25, part 2), FHS isthe basic shear value according clause 25 part 1, FTB is the bending tensilestrength according Table 3 “perpendicular to bed joints”. FT and FTB vary consid-erably and should therefore be specified.


Version 16.133−134

3.17. SSLA − Stress−Strain Curves


SSLA


EPS

SIG

TYPE

TEMPEPST

Strain valueor type of state in a header record

SERV ServiceabilityULTI Ulimate LimitCALC Calculatoric Mean values

Stress valueor safety factor in Header recordType of vertex

POL discontinous slopeSPL continuous slopeLIM no extensionEXT extension to infinite strains

Temperature levelModification of total length

SHIFT Shift of the stress−straincurve about the thermallength modification

o/ooLIT

N/mm2

LIT

gradLIT

−

−

POL

0−

TS

MUETMNRBFCTF

Tension Stiffening for ReinforcementI Initial crackII Completed crack patternI_S I for short time loadingII_S II for short time loadingI_F I, first crack at fctk,0.05 I_FS I_S first crack at fctk,0.05

Reinforcement ratio As/AbeffMaterial number of the concreteFactor for tensil concrete strength fctm

LIT

−−−

−

−1

1.0

Stress−strain curves are generally used for design or non−linear sectionalanalysis in AQB / STAR2 / ASE. If the default stress−strain curves are not applica-ble, stress−strain curves must be defined immediately after the input of thematerial. Three different stress−strain diagrams can be specified for the checks


3−135Version 16.13

of the ultimate state, the serviceability state and for a non−linear analysis, eachset may have multiple temperature levels, to be defined in ascending order.

A stress−strain curve starts with one of the possible headers:

SSLA SERV safety_factor [LIM/EXT] [TEMP tempval]SSLA ULTI safety_factor [LIM/EXT] [TEMP tempval]SSLA CALC safety_factor [LIM/EXT] [TEMP tempval]

The safety factors are predefined as specified with the material, but may bechanged if needed. In particular it is possible to modify a standard stress−strainlaw with an own safety factor, by defining a header record only. The design codesuse the safety factors quite differently, some materials will be divided by the safetyfactor in total, others reduce only the maximum stress value and keep theelasticity modulus. A positive safety factor will select the first case, while anegative value will select the second one. For the standard design tasks thematerial safety factors are chosen by AQB depending on the loading conditionand design code.

The stress−strain curve follows. Each consists of several data points in anordered sequence. For each data point it is specified whether it should behaveas a vertex (linear polygon line) or it should be part of a smooth curve (quadraticor cubic parabola).

The user must make sure that a sufficiently large strain range gets covered andthat the zero point constitutes a data point of its own. Strains outside the definedrange will have for TYPE EXT the last defined stress value and will use thetangent at the last point, provided this has a positive elasticity module. If the TYPEis specified as LIM, stresses outside the defined range will become zero, whichhowever lead to trouble in numerical behaviour of non−linear iterations. On theother hand the stresses outside the defined range are extrapolated by an inputof TYPE EXT. Default is EXT, however for ultimate limit state of concrete it is LIM.


Version 16.133−136

For concrete without explicit data points it is possible to define with EPST a factorfor the strains. This may be used to account for creep effects as specified in theEN 1992 with 1+ϕ.

For a fiber or a FE−section the general analysis method will account for tempera-tures according to the Eurocodes EN 1992 to 1999 automatically. However forspecial cases it is also possible to define up to 15 discrete temperature levelsTEMP, to be interpolated. If no explicit strains are specified for one level the stan-dard laws according Eutrocode will be approximated as default

For a zonal method, the section will be subdivided in several zones (polygons)by different material numbers, where every zone has a constant average tempe-rature to be specified for each of these materials with TEMP. One may changethe thermal strain at this temperature with the item EPST. Finally input of the literalSHIFT will shift the stress strain law by this strain, to activate all eigenstressesdirectly.

The contribution of the concrete between the cracks (Tension Stiffening) may betaken into account by a modification of the stress strain law of the concrete or thesteel. With a single record SSLA SERV a modification of the reinforcement stressstrain law for that purpose is possible. However a solution is only possible if theratio of reinforcement is large enough to avoid the complete rupture of thereinforcement, which is equivalent to the requirement that the initial crack stressin the reinforcement must not exceed the yield limit.

The reinforcement ratio MUET is only determined in advance for an annularsection (or those with a similar evenly distributed reinforcement). For all othercases, the design task should adopt the stress strain law accordingly.


3−137Version 16.13

3.18. MEXT − Extra Material Constants


MEXT


NOEXPTYPEVALVAL1VAL2VAL3VAL4VAL5VAL6VAL7VAL8VAL9

Number of materialName of an exposure classType of constantValue of material constantFirst additional material valueSecond additional material valueThird additional material value4th additional material value5th additional material value 6th additional material value7th additional material value8th additional material value9th additional material value

−Lit4LIT**********

1−!−−−−−−−−−−

With MEXT you may define special material values for any type of material. Thevalues may be assigned to different regions (edges) of the material with separatevalues. This is defined by a freely selectable literal EXP. Defaults for those valuesmay be specified in the INI−file. It has to be checked individually to which extendthe defined data is really used in the analysis modules.

The follwong idents for TYPE are allowed:

3.18.1. AIR − Air Contact RatioThe value AIR defines the air contact ratio between 0.0 and 1.0 to be used for thecreep and shrinkage process. Up to 10 values may be defined for the individualconstruction stages.

3.18.2. CNOM − Nominal CoverThe value CNOM defines the nominal cover for reinforcements. This value is de-fined in many design codes based on the exposure class and my be provided wi-thin the INI−files. The full range of tables may become quite lareg however.

3.18.3. CRW − Crack widthThe crackwidth CRW is used for the design of the crackwidth.


Version 16.133−138

3.18.4. KR − Equivalent roughnessWith KR, VAL defines the equivalent roughness according to Table 10.8.1 of EC1 part 2−4, which is especially needed for wind loads on circular sections:

Surface Roughnessk [mm]

Surface Roughnessk [mm]

glass 0.0015 galvanised steel 0.2

polished metal 0.002 spinning concrete 0.2

smooth painting 0.006 cast in situ con-crete

1.0

spray painting 0.02 rust 2.0

blasted steel 0.05 masonry 3.0

cast iron 0.2

Hint: In table 4 of DIN 1055 part 4 slightly larger values are defined for k.

3.18.5. TEMP − Temperature environmentWith type TEMP the temperature environment and the transition conditions aredefined:

VAL The temperature itselfVAL1 The thermal resistance αVAL2 The emmission grade ε for the Boltzmann law


3−139Version 16.13

3.19. BORE − Bore Profile with Beddings


BORE


NO

XYZ

NXNYNZ

ALFTITL

Number of the bore profile

Coordinates of the start point

Direction of the bore profile Default: in gravity direction (since not available in AQUA: NZ=1.0)

Rotation angle of the local axisTitle of the bore profile

−

[m]1001

[m]1001

[m]1001

−−−

degreeLIT32

1

0.00.00.0

***

0.0*

With BORE a bore profile is described defining material layers along an axis theuse of which is different.

• General description of soil mechanic strata (not used within SOFiSTiK atpresent)

• Properties of the constrained soil modulus for the analysis of settlementsor a half space modelling with HASE.

• Soil bedding modulus for the pile elements.These values are derived from the soil modulus above by a multiplicationwith a form factor with typical values between 0.5 and 2.0. More preciselythe soil modulus is transferred to a Winkler bedding constant [kN/m3] bya division with some structural dimension and is then integrated by a multi-plication with the width of the pile section. Please refer to the explanationsof the record BBLA for formulas and examples.


Version 16.133−140

3.20. BLAY − Layer of the Soil Strata

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

BLAY


S

MNOESMUEVARI

DES

PMAXPMALCPHI

Ordinate along the profile axis (depth)

Material number from this ordinateStiffness modulus from this ordinatePoisson’s ratioType of stiffness ES variation within a layer

CONS constantLINE linearPARA parabolic

Increment of ES within a current layer

Max. pressure at pile foot Max. lateral pressureCohesionSoil−Pile friction angle

[m]1001

−[kN/m2]1096

−Lit4

[kN/m2]1096

[kN/m2]1096

[kN/m2]1096

[kN/m2]1096

deg

*

**

CONS

*

****

BLAY is used for the definition of the soil layers of a corresponding BORE profile.This data is then used in program HASE for the determination of the stiffness andresistance properties of soil and piles.

The following example illustrates the functionality of the BLAY command:

BORE NO #nb X #x Y #y Z #zBLAY S #s1 ES #Es1 VARi para PMAX #P1BLAY S #s2 ES #Es2 VARi line DES #dEs2 PMAX #P2BLAY S #s3 ES #Es3 VARi cons PMAX #P3BLAY S #s4


3−141Version 16.13

Figure 3.19a: Distribution of BLAY properties along the BORE axis

Bore profile #nb consist of three soil layers

• First layer L1 starts at the depth #s1 and ends at the next defined depth #s2.L1 is assigned a parabolic stiffness distribution. Since there is no explicitstiffness increase #dEs1 defined, a continuous distribution is realized − theconcluding stiffness value will be equal to the stiffness value of the subse-quently defined BLAY (#Es2).

• Second layer L2 has a linear stiffness distribution. This time, #dEs2 is de-fined, so the concluding stiffness value will be #Es2+#dEs2.

• Third layer L3 has a constant stiffness distribution with the value #Es3.

If there is only one BLAY defined, then the ending depth is by default 999m. If thenumber of BLAY record is larger than 1, the last BLAY defines the ending depthS while the other properties of this BLAY are ignored.

Apart from stiffness modulus ES, all other properties of the BLAY record (MNO,MUE, PMAX, PMAL, C, PHI) are constant within a layer.

Stiffness modulus ES and Poisson’s ration MUE can alternatively be set by refer-ence of a material number, where corresponding elastic material properties aredefined. If within the same BLAY record MNO and ES and/or MUE are defined,the values defined within BLAY have precedence over those defined by materialMNO. If the Poisson’s ratio MUE is defined and larger than 0.0, then ES is inter-preted as the elastic modulus, and a Boussinesq method is used in programHASE (see HASE manual for more details).


Version 16.133−142

By default (no input) the non−linear resistance properties (PMAX, PMAL and C)are switched off, meaning that the x−pile nodal forces are not limited (elastic ana-lysis). As in the default case, the input of a resistance property smaller or equalzero will result in the x−pile contact forces to be unlimited. Any input of the resist-ance properties larger than zero will activate the non−linearities along the x−pile.

PHI is not supported at the moment.

Please note:

• As a prerequisite for a meaningful soil−layer interpolation, all defined boreprofiles (BORE) within a grid must have the same number of layers (BLAY).

• For a consistent input of the BLAY−resistance properties it is required thatwithin a layer of each of the used bore profiles the resistance properties beeither defined or undefined. Otherwise the interpolated properties canhave unpredictable values. In other words, the input where the resistanceproperties within a layer for some bore profiles are defined, while for theothers are not defined, will most likely yield undesired results.


3−143Version 16.13

3.21. BBAX − Axial Beddings


BBAX


S1S2

K0K1K2K3

M0C0TANRTANDKSIGD0D2CA0CA2PMAX

Start parameter (depth)End parameter (depth)

Constant value of pile beddingParabola variationLinear variationQuadratic variation

Load value (e.g. negative skin friction)Maximum skin frictionSoil/pile friction angle coefficient Soil/pile dilatancy angle coefficientLateral pressure coefficientConstant rotational stiffnessLinear rotational stiffnessConstant axial dampingLinear axial dampingMax. pile foot force (Extended Piles, only)

[m]1001

[m]1001

[kN/m2]1096

““

[kN/m]1095

[kN/m]1095

−−−

[kNm]1099

[kNm]1099

[kNsec/m2]1220

[kN]1101

*999.99

0000

00

0.000000

The axial bedding describes the skin friction of the pile in dependence from thedeformation and from the lateral bedding force of the pile. A positive value of theload M0 acts on the pile in the direction of the pile head.

displacement

skin friction

Axial bedding


Version 16.133−144

Further explanations for the axial beddings are contained in the record BBLA.


3−145Version 16.13

3.22. BBLA − Lateral Beddings


BBLA


S1S2

K0K1K2K3

P0P1P2P3

PMA1PMA2

CL0CL1CL2CL3SM0SM2

Start parameter (depth)End parameter (depth)

Constant value of the pile beddingParabola variationLinear variationQuadratic variation

Form factors as variation along the periphery

Maximum compression at S1Maximum compression at S2

Constant lateral dampingParabola variationLinear variationQuadratic variationConstant mass distributionLinear variation of mass distribution

[m]1001

[m]1001

[kN/m2]1096

““

−−−−

[kN/m]1095

[kN/m]1095

[kNsec/m2]1220

““

[t/m]1181

[t/m]1181

*999.99

0000

1111

−−

000000

Elastic supports have many related parameters. Therefore those values are com-bined to special property elements for a geometric line.

All the corresponding GLBA and GLBL records follow the GLN record in the orderdefined by the s ordinate. All data for the s ordinate refer to the parametric systemof coordinates. The default is the global z axis, if the line consists only of a startpoint without geometry segments.

Within a section the bedding is interpolated:

K�K0�K1�� z� z1z2 � z1

�1�2�K2� � z� z1z2� z1

��K3�� z� z1z2 � z1

�2


Version 16.133−146

The pile bedding at the beginning of the section is K0, and the one at its end isK0+K1+K2+K3. The individual values correspond to constant, parabolic, linearand quadratic distributions.

Parts of the bedding

The default value for S1 is the latest S2 value. The initial default is −999.99.

The factors for the variation along the periphery are effective in the four quadrants(angle of 0, 90, 180 and 270 degrees). The angle refers to the local z axis. Forlinear analyses the factor (P0+P2)/2 is used for the principal bending (MY,VZ),while (P1+P3)/2 is used for the transverse bending (MZ,VY).

P2

P1

P0

P3

P2

P1

P0

P3

P2

P1

P0

P3

P2

P1

P0

P3

Distribution of the bedding in transverse direction

The form factor is generated from the fact that the acting bedding force pL perlength is given by the following simplified relation from the deformation uL:

�pL�D � ·�Cl � ·uL�D � · Es

�Deff

� ·�uL


3−147Version 16.13

According DIN we have e.g. Deff = min(D,1.0). For more complex cases wherethe bedding stress is not uniform but more like a cosine, there are of course othervalues possible. Therefore several design codes recommend to use any valuebetween 0.5 and 2.0 to get the most unfavourable results. Thus SOFiSTiK will notchange the prescribed values in any kind.

For the bedding in axial direction a similar form factor may be defined based ona shear modulus instead of the stiffness modulus following the relation:

pA� � � ·�D � ·�Ca� ·�ua� � � ·�D � · Es

2·(1��)·�Deff

� ·�ua

Thus the factors cancel each other in general and it is sufficient to use the stiffnessmodulus Es for the axial bedding as well. In most cases the maximum skin frictionis the more essential part of the relation. However some value has to be specified,otherwise there would be no skin friction at all.

Further there is a a rather sophisticated approach for the interaction of both direc-tions available. The friction has very different causes:

��KSIG� �v�K(x)� �v(x)�TAND�u(x)

��K(x)�u(x) ��TANR� ��C0

The first part of the pressure is described by the vertical earth pressure and thehorizontal pressure coefficient. The second part is given by the elastic constantswhich consist of a stiffness and a dilatation.


Version 16.133−148

3.23. SVAL − Cross Section Values


SVAL


NOMNO

Cross−section numberMaterial number or preferred beamtype

CENT centric beamBEAM excentr. beam (Reference axis)TRUS only truss (no bending)CABL only cables

−−/LIT

11

AAYAZITIYIZIYZCMYSCZSC

Cross section areaShear area for yShear area for zTorsional moment of inertiaMoment of inertia yMoment of inertia zMoment of inertia yzWarping modulusCoordinates of shear centreRelative to the gravity centre

[m2]1012

[m2]1012

[m2]1012

[m4]1014

[m4]1014

[m4]1014

[m4]1014

[m6]1016

[mm]1011

[mm]1011

1.0−−*

A3/12IY0000

YMINYMAXZMINZMAXWTWVYWVZ

Ordinate of the left edge fibreOrdinate of the right edge fibreOrdinate of the top edge fibreOrdinate of the bottom edge fibreShear stress due to Mt = 1.0Shear stress due to Vy = 1.0Shear stress due to Vz = 1.0

[mm]1011

[mm]1011

[mm]1011

[mm]1011

[1/m3]1018

[1/m2]1017

[1/m2]1017

*******

NPLVYPLVZPLMTPLMYPLMZPLBCYZ

Fully plastic axial forceFully plastic shear forceFully plastic shear forceFully plastic torsional momentFully plastic bending momentFully plastic bending momentBuckling strain curve main+lateral

[kN]1101

[kN]1102

[kN]1102

[kNm]1103

[kNm]1104

[kNm]1104

LIT

−−−−−−C

TITL Cross section designation Lit24 −


3−149Version 16.13

This record allows the input of cross sections without the corresponding geomet-ric data, which are necessary of course in detailed stress analysis, yield zone the-ory or reinforced concrete dimensioning. They can be used in the static analysisor simplified checks with full plastic internal forces.

With NO and a Literal for MNO you may also subsequently specify which elementtype should be selected for elements with automatic type selection with that sec-tion. This definition can be redefined at any time for any existing section. All otherinput values will be ignored in that case.

Plastic internal forces may be needed for cross sections with trial values. It is ex-plicitly stated, however, that the use of this input record for dimensioning is by nomeans in accordance with the intentions of the program’s author for a consistentdata input, and the user bears the sole responsibility in this case.

If IT is defined as zero, special attention should be paid so that the torsional de-gree of freedom does not lead to undefined rotation capability during the as-sembly of the total static system (Error message: Parts of the system can movefreely.).

The default for IY is equivalent to a rectangular section with a width of 1 m andthe given area A.

In accordance with Saint Venant’s estimate, the default value for the torsional mo-ment of inertia is

)II(4A

Izy

2

4

T +⋅Π⋅=

This value is exact for circular and elliptical sections.

Deviations for a rectangular section:

a/b 1/1 2/1 10/1

exact 0.140 0.458 3.13

approx. 0.152 0.486 3.01

The defaults for ymin up to zmax assume as a first guess a rectangular cross sec-tion and apply then appropriate corrections from the radius of gyration.

The default values for the full plastic internal forces come out of the cross sec-tional area. WT supplies the default for MTPL, while MYPL and MZPL make useof the extreme coordinates ymin through zmax.


Version 16.133−150

All the full plastic internal forces are without safety factor.

In the case of the buckling strain lines the literals 0, A, B, C, D, E are used for thesame curves in the main and the lateral direction and AB, BC and CD for differentcurves.

SVAL can make an identical copy of an already defined cross section by enteringSVAL NEWNO−OLDNO. This serves to accelerate the method, when differentcross section values must be applied later on.

SVAL can also be used for defining a reduced cross section. This can be doneeither by using a negative NO to modify an already defined cross section, or bymaking a copy of an existing cross section by means of a negative MNO. Thevalues A through ZSC are then viewed as factors for the corresponding values,and are thus preset to 1.0. The new cross section has no geometric propertiesany more.

Example:

PROF 1 HEB 300PROF 2 HEB 300SVAL -1 IT 0.5SVAL 3 -2 IT 0.5SECT 4; SV IT -0.5 ; PROF 1 HEB 300

Cross section 1 receives 50% of the torsional moment of inertia. The geometryof the cross section gets erased. Cross section 3 has 50% of the torsional momentof inertia of cross section 2, has no geometry, and is hence identical to cross sec-tion 1. Cross section 2 was not modified. Cross section 4 is a cross section withIT reduced by half and with complete geometry. (Only possible with AQUA)


3−151Version 16.13

3.24. SREC − Rectangle, T−beam, Plate


SREC


NO

HBHOBO

SOSUASOASU

MNO

Cross section number

Total heightWidth for rectangular, T−beamThickness of the plate (upper part)Thickness of the plate (lower part)

Offset of top reinforcementOffset of bottom reinforcementMinimum top reinforcement− layer 2Minimum bottom reinforcement − layer 1

Material number

−

[mm]1011

[mm]1011

[mm]1011

[mm]1011

[mm]1024

[mm]1024

[cm2]1020

[cm2]1020

−

1

−1[m]

00

H/10SO00

*

MRF

RTYP

Material number of reinforcement+1000 ⋅ material link reinforcement

Reinforcement subtypeCORN = single points at cornerCU = perimetric reinforcementSYM = symmetricalASYM = asymmetric two sidedASYT = asymmetric three sidedfor more options see below

−

LIT

*

*

ITAYAZDASODASU

Torsional moment of inertiaShear deformation area for VYShear deformation area for VZDiameter of top reinforcementDiameter of bottom reinforcement

−/m4

−/m2

−/m2

[mm]1023

[mm]1023

−1.0.0.*

DASO


Version 16.133−152


REF

YMZM

Location of zero pointC = gravity centreR/L/M = right / left / middleUR/UL/UM = upper right/left/middleLR/LL/LM = lower right/left/middlePR/PL/PM = plate right/left/middleSC = shear centre

explicit offset of the mid pointexplicit offset of the mid point

LIT

[mm]1011

[mm]1011

C

−−

BCYZINCLSPT

BEFF

Buckling curve selectorInclination of shear linksNumber of stress points

0/ 2/ 4/ 6Width of equivalent hollow section

LITcotLIT

[mm]1011

*00

*

TITL Cross section designation Lit32 *

Depending on the definition of values one of the following section types is gener-ated:

H Plate with implied width of 1 m or width BOH,B Rectangular cross sectionH...BO T−Beam cross section

Following this classification different clauses of the design codes will be appliedto the sections.

When nothing is input for REF, the zero point of the coordinate system of the crosssection is assumed to be at the gravity centre.


3−153Version 16.13

The required dimensions of the cross section can be calculated by AQB. For thistask, B or H can be input negative when only that dimension should be changed.

The full height of the web and the entire plate are used in determining the torsionalmoment of inertia and the torsional shear stresses; for the equivalent hollow crosssection used in computing the torsion reinforcement only the web or only theflange is used, depending on which part is larger. The check of the shear stressdue to shear force takes place at the most unfavourable location (at the height ofthe gravity centre for the web or at the intersection of web and flange). For theinterests of massive constructions the effective torsional moment of inertia canbe reduced by IT. The input of a positive value specifies a value in m4, while a neg-ative value is interpreted as a factor. A value of 0.0 is allowed but may lead to kin-ematic systems.

Shear deformation areas are typically not used for concrete, but are important forsteel and timber. They can be defined, by specifying SAY or SAZ. The input of apositive value specifies a value in m2, while a negative value is interpreted as afactor for the default value of the rectangular cross section and the web or theplate.


Version 16.133−154

The distribution of the reinforcement is controlled with the option RTYP, the dia-meter and some entries for maximum distances between bars of the selected INI−File of the design code. There are four basic options:

Columns:CU layer 0 at all 4 sides (circumferential)SYM layer 0 at upper and lower side, however if the distance

is greater than MaxBarDistanceC (300 mm), same as UCORN layer 0 concentrated in the corners,

bars between according to the selected design codeCORN:n as CORN, but bars in corners with multiplicity of nCSYM layer 0 concentrated in the corners, no bars between

In all cases the diameter will be preset to the smallest allowed value from the INI−File (MinBarDiameterC = 12mm), and the absolute minimum reinforcement ac-cording to the number of bars (minimum 4) with that diameter.

Beams:ASYM two layers at lower (1) and upper (2) side, thus no design

for torsion if distance > MaxBarDistanceT (350 mm).ASYT three layers (1,2,3) at lower, upper and optional at the

sides if distance becomes > MaxBarDistanceT (350 mm).

Die further reinforcement options “without minimum shear links” (appended zero)and “Generate single point reinforcements instead of distributed reinforcementsyield a matrix of possible literals:

Distributed Single Point Distributedno minimum shear

Singel Pointno minimum shear

CU CORN CU0 COR0

SYM CSYM SYM0 CSY0

ASYM CASY ASY0 CAS0

ASYT CAST AST0 CAST

If the reinforcement is desired as single bars, there will be some maximum allow-able distances established in the design codes for columns, bending membersand torsional members. They might trigger additional bars between the corners.To allow for an optimal design procedure however it is possible to define an in-teger factor (1 to 15) for the bars in the corners with an optional appendix. A defini-tion of CORN:3 defines a section where the same bar diameter is concentratedin the corners with a multiplicity of three:


3−155Version 16.13

ÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉ

The bars in the corners will receive a larger equivalent diameter d�√n, unless afurther character S is appended to the input literal.

If the distance of the lower and upper reinforcements is greater than the limit Ma-xBarDistanceT, addititonal reinforcement at the side of the web will be introducedwith layer number 3. As this is mandatory for torsion, you might suppress this byentering a literal ASYM for RTYP or a zero value for IT, but then these sectionswill not be designed for torsion any more. This layer may become partially activefor biaxial bending for the ultimate design.

Further we introduce a reinforcement at the lower side of the plate with layer num-ber 4, if the upper layer is within the topmost quarter of the plate height.

The cover of the reinforcement from the side edge is equal to the minimum coverfrom the upper or lower edge, but not larger than one−fourth of the width.

Please note, that DIN 1045−1 uses the cover of the compressive reinforcement(effective distance − D/2) as a limit for the lever arm during the shear design ofthe cracked section. Thus the diameter has an effect on the shear design,

STB only uses the option SYM for ASO/ASU.

MRF = 0 must be specified for unreinforced cross sections. The input of MRF isnot allowed for steel or wooden cross sections. When MRF is specified to besmaller than 1000, the same material type will be assumed for the link reinforce-ment as is used for the longitudinal one.


Version 16.133−156

3.25. SCIT − Circular and Tube Sections


SCIT


NODTSASIASA

ASI

Cross section numberOuter diameterThickness (0.0 = solid section)Outer reinforcement offsetInner reinforcement offsetOuter reinforcement

(explicit values also in [cm2/m])Inner reinforcement

(omitted if nothing is input)

−[mm]1011

[mm]1011

[mm]1024

[mm]1024

[cm2]1020

[cm2]1020

1–−

T/10SA−

−

MNOMRF

RTYP

DASITAYAZ

Material number of cross sectionMaterial number of reinforcement

+ 1000 ⋅ material of shear linksReinforcement subtype

CU = perimetric reinforcementCU0 = no minimum area for

shear linksDiameter of reinforcementTorsional moment of inertiaShear deformation area for VYShear deformation area for VZ

−−

−

[mm]1023

−/m4

−/m2

−/m2

**

28−1**


Shear deformations are not considered for concrete sections. For all other materi-als they are always included. Values for IT, AY and AZ are either absolute valuesor if defined negativ factors to the theoretical values.

The definition of CTRL RFCS in AQUA is also effective for the SCIT section.

The old record SCIR defines the same section via the radius and should not beused any more.


3−157Version 16.13

T

D

Circular cross section

The distance SI is taken relativ to the inner radius for an annular section, but onthe outer radius for a solid section.


Version 16.133−158

3.26. TUBE − Circular and Annular SteelCross Sections


TUBE


NODT

MNOBC

Cross section numberOuter diameterWall thickness

(0= solid circle)Material number of cross sectionBuckling strain curve

0 (none), a (warm), b (cold) c (solid circle)d (special purpose only)e (old AISC for special purpose)

−[mm][mm]

−LIT

1–0

1a/c


Shear deformations are always considered. Deviations of those values have tobe defined via SCIT or SECT/CIRC/SV or SVAL.


3−159Version 16.13

3.27. CABL − Cable Sections


CABL


NODTYPE

Section numberNominal diameterType of cable section

1x7,1x19,1x37,....1x547DIN number from 3052 to 3071type according ENV DIN 3051 Part 10VVS−1 to VVS−4 full locked coil cablesPfeifer−cables PE/PG/PV−nnnStahlton−cables DINA/HIAM−nnn

−[mm]LIT

1−−

INL

MNO

Type of InlayFE, FEN, FEC = Fiber InlaysSE, SES, SEL = Steel Inlays

Material number of prestressing steel

LIT

−

FE

1

F

K

W

KEREF

Sectional or fill factoror metallic cross section area

Rupture or cable factoror characteristic breaking load

Weight factor (kg/m/mm2) * 100or weight

Loss factor (clamping of endpoints etc.)Reference of factors F/K/W

DIN according to DINEN according to EN

−mm2

−kN*

kg/m−

LIT

*

*

*

1.0*



Version 16.133−160

ÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒ

ÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒÒ

Cables without a type will be taken as a round steel bar. The following cable typesare available:

1x7 DIN 3052 Spiral cable with 7 wires1x19 DIN 3052 Spiral cable with 19 wires

...1x547 DIN 3052 Spiral cable with 547 wires

3052 DIN 3052 Spiral cable 1x73053 DIN 3053 Spiral cable 1x193054 DIN 3054 Spiral cable 1x373055 DIN 3055 Stranded cable 6x73056 DIN 3056 Stranded cable 8x73057 DIN 3057 Strand 6x19 Filler3058 DIN 3058 Strand 6x19 Seale3059 DIN 3059 Strand 6x19 Warrington3060 DIN 3060 Strand 6x193061 DIN 3061 Strand 8x19 Filler3062 DIN 3062 Strand 8x19 Seale3063 DIN 3063 Strand 8x19 Warrington3064 DIN 3064 Strand 6x36 Warrington−Seale3065 DIN 3065 Strand 6x35 Warrington covered3066 DIN 3066 Strand 6x37 Warrington−Seale3067 DIN 3067 Strand 6x36 Warrington−Seale


3−161Version 16.13

3068 DIN 3068 Strand 6x24 Standard3069 DIN 3069 multiple Strand 18x73070 DIN 3070 Flat strand 10x103071 DIN 3071 multiple Strand 36x7

6x7 ENV DIN 3051-10 / Eurocode8x7 ENV DIN 3051-10 / Eurocode6x19 ENV DIN 3051-10 / Eurocode6x19S ENV DIN 3051-10 / Eurocode6x19W ENV DIN 3051-10 / Eurocode6x25F ENV DIN 3051-10 / Eurocode6x36SW ENV DIN 3051-10 / Eurocode8x36SW ENV DIN 3051-10 / Eurocode6x35NW ENV DIN 3051-10 / Eurocode6x19M ENV DIN 3051-10 / Eurocode6x37M ENV DIN 3051-10 / Eurocode17x7 ENV DIN 3051-10 / Eurocode18x7 ENV DIN 3051-10 / Eurocode34x7 ENV DIN 3051-10 / Eurocode36x7 ENV DIN 3051-10 / Eurocode

VVS Pfeifer full locked coil cablesVVS−1 BTS full locked coil cables in opposite/crosslay strandingVVS−1P BTS full locked coil cables in equal lay/compound strandingVVS−2 BTS full locked coil cables in opposite/crosslay strandingVVS−2P BTS full locked coil cables in equal lay/compound strandingVVS−3 BTS full locked coil cables in opposite/crosslay strandingVVS−3P BTS full locked coil cables in equal lay/compound strandingVVS−4 BTS full locked coil cables in opposite/crosslay strandingVVS−4P BTS full locked coil cables in equal lay/compound stranding

PE−nnn Pfeifer cables PE−3 to PE−100 (Y 1450)PG−nnn Pfeifer cables PG−5 to PG−125 (Y 1770 ES 160000)PV−nnn Pfeifer cables PV−40 to PV−2000 (Y 1570 ES 160000)The ultimate forces of the cables are obtained only based on the tensilestrength values given above)

DINA−nn Stahlton cables DINA−13 to DINA−199HIAM−nn Stahlton cables HIAM−56 to HIAM−421

Cable sections differ from circular sections in several reducing factors which arepreselected for the specific design code and the type of inlay:


Version 16.133−162

FE = Fibre inlayFEN = Natural fibre inlayFEC = Chemical fibre inlaySE = Steel inlaySES = Steel cable inlaySEL = Steel strand inlay

In DIN 3051 part 3 the factors are defined as:

Metallic cable section qm� f·d2·�4

Minimum ultimate force Fmin� k·Fr�k·qm·�z

Weight per length G� qm·w

The loss factor ke taking into account the type of fixing of the cable endings isdefined in DIN 18800 for example.

In the Eurocode or DIN 3051 part 10 there are slightly different definitions, whichare also used by the fully locked cables:

metallic cable section A0�C·d2

Minimum ultimate force F0�K·d2·fr

Weight per length M�W·d2

The user has to check all factors in detail, as they depend on the type of anticor-rosive lining and the intended usage (e.g. for cableways). Cable sections mayonly be used for cable elements or automatic elements, which derive their typefrom the cable section type.

ATTENTION:Prestressing steel cables have a different safety factor for concrete and steeeldesign. Please be sure that the value is selected properly or specify the correctvalue with the steel material.The correct modulus of elasticity is not given in the DIN or EN, but has to be takenfrom the manufacturers data. Common values are:

Fully locked cables 160 ± 10 kN/mm2

Spiral cable Galfan EN 12385 160 ± 10 kN/mm2

Spiral cable stainless steel EN 12385 130 ± 10 kN/mm2

Strand ropes 100 ± 10 kN/mm2


3−163Version 16.13

See also: CS INTE SV POLY CIRC PANE PLAT PROF Reinforcement CUT SPT SFLA WIND WPAR

3.28. SECT − Freely defined CrossSections

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

SECT


NOMNOMRF

ALPHYMZM

FSYM

BTYP

BCYBCZKTZ

TITL

Cross section numberMaterial number for cross sectionMaterial number for reinforcement

+ 1000⋅material link reinforcement

Angle of rotationOffset of all cross section ordinates

Suppress rotation of principal axes YES IYZ always set to zeroNO IYZ set to zero when smaller

then 0.001⋅(IY+IZ)

preferred beam typeCENT centric beamBEAM excentr. beam (Reference axis)TRUS only truss (no bending)CABL only cablesCOMP centric compressive memberCOLU excentr. column

Buckling strain curve for y−y axisBuckling strain curve for z−z axisSmall part addition (presently not used)

Cross section designation

−−−

Degrees[mm]1011

[mm]1011

LIT

LIT

LITLIT−

Lit32

11*

000

NO

BEAM

*BCY

*

−


Version 16.133−164


FEM

LTEMT

LTAU

LSIGBNOX

Name of a Data base containing a FEMmesh of the sectionLoad case of a temperature fieldTime value of the temperature field

Loadcase number of the FEM database inwhich the unit shear stress distributions aresaved (for each construction stage 4 loadcases)

Not yet released:Load case number for primary stressesBeam number for primary stressesBeam section for primary stresses

Lit96

−sec

−

−−m

−

−last

9900

−1

0.0

Freely defined cross sections always begin with the record SECT, which definesthe cross section number. All subsequent input records describe this one crosssection, which may consist of several partial cross sections (external outline, in-ner perimeter, reinforcement arrangement etc.). The input for each cross sectionends either by the next SECT record or by the END record.

Freely defined cross sections are divided into three groups (see 1.1):

* solid cross sections * thin−walled cross sections* FE−sections

A coordinate system y − z is established for every SECT definition, the origin ofwhich is in general on the reference axis defined by the two nodes of a beam. Allcoordinate data of the input records which follow a SECT record refer to this co-ordinate system. The directions of the axes are identical to those of the local beamelement and defined in accordance with Chapter 2.1 (y to the left, z downward).The local coordinate axes y’ and z’ of a centric beam are only shifted parallel tothe cross section coordinate system, so that the origin is at the centre of gravityof the cross section.

Prestressing Tendons (AQBS, GEOS) always refer to the input coordinate sys-tem. It may be appropriate to take this into account when selecting the zero point.

If desired, however, it is also possible to rotate the cross section by any angle orinto the direction of the principal axes as well as to translate it (items ALPH, YM


3−165Version 16.13

and ZM). The definition of ALPH will force AQB to do the stress analysis for therotated principal axis system. The input of CTRL AXIS −2 within AQB has thenno effect on this section any more.

On the other hand a definition of FSYM YES will suppress the rotation of the prin-cipal axis completely. This is intended for sections describing only half of a fullsymmetric section, but may have very dangerous effects if applied to general sec-tions. The value of Iyz has considerable effects on deformations and also forceswithin constrained systems. This option enforces also uniaxial bending (Vy=0,Mz=0) within AQB.

With BTYP you may specify your preferred beam element type for that section.This info may be used for the mesh generation and the specifivcation of minimumreinforcements.

For the design of a reinforced concrete cross section with AQB, it is always neces-sary, to specify the location of the intended reinforcement − single, linear, or peri-metric reinforcement− by means of the records RF, LRF, CRF or CURF. Freelydefined cross sections cannot be dimensioned with STB/STBA. MRF defines thematerial number of reinforcement. Only if the link reinforcement has a differentquality of material a combined value is to be entered. Then this combined valuerepresents the default for the records CUT.

ALPH can be used to rotate the cross section about the x axis. A value of 999 forALPH causes a rotation of the cross section in the principal directions by an angleless or equal to 90 degrees. During all rotations, it is not the reference coordinatesystem but the cross section elements that are rotated.

The material number should, in general, be specified by SECT. The declarationof a material number with individual cross section elements is only appropriatefor composite cross sections. In case of composite sections, ideal cross sectionvalues are calculated, based on the material defined in SECT; e.g.:

Ai��A�E�

Eref

There are some other properties controlled by the type of the reference material.For timber and steel shear deformation areas and stresses will be calculated in-cluding also ideal section values, while for concrete the classical concrte designtechniques will be applied.

All cross section elements are addressed with an arbitrarily selected identificationnumber, which has up to four characters in general. In AQB and AQUP you may


Version 16.133−166

specify a mask to select specific elements for the output. You might for examplethen select all elements with a zero at the end.

The buckling strain curve can be input for checks according to DIN 18800 andEC3. The permissible input values are 0 (none), a, b, c or d. Appropriate technicalknowledge is required for making this choice in case of general cross sections.AQUA, however, attempts to model most cases with the following defaults:

strong axis weak axisProfiles without welding joints

Annular and SH−shapes a aU, L and solid circle shapes c cDouble T−shapes h/b>1.2; t≤40mm a b

t>80mm d d others b c

all othersI−strong > 1.67 · I−weak andI−t < 0.50 · I−weak tmax ≤ 40 mm b c tmax > 40 mm c dI−strong < 1.67 · I−weak orI−t > 0.50 · I−weak tmax ≤ 40 mm b b tmax > 40 mm c c

The buckling curve “e” may be input to select the old AISC−curve with the Eulerhyperbola for λ > 0.5 and a quadratic parabola for the plastic region. The safetyfactors have to be large enough for this curve!

Hint:For some records (e.g. TVAR and PROF) it makes a difference if those recordsare defined within a section or separately. A definiton of SECT 0 will allow to ter-minate the current section.


3−167Version 16.13

3.28.1. Parametric SectionsIt is very common, especially in the bridge design, that very similar sections arederived from a template. AQUA will therefore not only allow this parametric ap-proach, but it will also store the parametric information along with the cross sec-tion in the database, in order to allow easy prototyping.

Primary solution for that task are formula expressions to be defined for any co-ordinate or permanent radius (CIRC, CRF) with up to 256 characters in the formof “=formula”. These formulas will be saved with the section and may be reevalu-ated for any section with different values along an axis (see GAX/GAXP) or withexplicit definitions locally with TVAR commands.

The following variables will be predefined for an axis:

#S_ACT The actual distance along the axis#INCR The inclination to the right as arcus#INCL The inclination to the left as arcus#S_XI(x) Array of s−values of the support lines along the axis

#S_XI(2.5) is the S−value in the middle of 2nd and 3rd support

Then we may define coordinates relative to up to three other reference points. Asa reference you may use every stress point, polygon vertex or centre of a circlehaving an explicit identifier. The reference is done via this explicit 4−characteridentifier, treating the specified coordinates as relative to that reference. If CTRLREFD 0 has been specified the coordinates are to be taken as absolut, howevera @ character specified then as prefix to the reference will enforce a relative de-finition which is required for relative references containing formulas. On the otherside for CTRL REFD 1 the @ will switch to the absolute mode just for this definitiononly.

It is also possible to specify the position of the reference point by an axis, for thatcase the reference has to be specified as the ID of that axis with a colon prefix,e.g. “:AX_0”. The local coordinates (y,z) are then given by the 3D−distance to thesame parameter on the reference axis projected in the plane of the section.

If points with multiple identifiers are present, then only the first occurrence of thatpoint is used and the others are neglected. If a reference point is not part of thesection itself, you should use the material number 0 for it. However, you may havean arbitrary number of nested references, i.e. a reference point may use a refer-ence itself. For thin walled elements start and end point may be addressed by areference with an index.


Version 16.133−168

As the references may be used on single points, start points and end points, thefollowing examples use a generic description. Thus REF holds for REFP resp.REFA or REFD.

Case 1: Carthesian References

PTYPT0

PT

PT PTZ

y y

zz

• You may define the coordinates relative to the reference point in absoluteCartesian coordinates y and z (left picture) by specifying:

REF PT0

For a derived instance the relative distance is kept as an absolute valueor taken from the given formula for this type of reference.

• You may define the coordinates relative to two reference points in absolutecartesian coordinates y and z by specifying:

REF PTY PTZ

Now the y−ordinate is taken relative to PTY while the z−ordinate is takenrelative to PTZ. If a reference of only one coordinate is desired the refer-ence of the other coordinate may be specified as ’0000’ relative to the ori-gin of the coordinate system. As shortcut it is also possible to specify onlya single reference with a preceeding > to inherit only the right ordinate yor a ^ for the elevation value (z).

• It is also possible to specify negative references. The coordinates will thenbe used with an alternate sign, allowing easy description of mirroring.Forthe coordinates itself, the double of the coordinate values of the mirroringcenter or line have to be specified. (ynew=2�ymirr−yorg)

REF -PTY Mirroring to a pointREF PTY -PTY Mirroring to the y-axisREF -PTY PTY Mirroring to the z-axis


3−169Version 16.13

Case 2: Polar References

PT0

PTD

PT0

PTD

The point PTD (at item REFD, RFDA or RFDE) defines the direction of the refer-ence relative to the PT0 point− Instead of a point it is also possible to specify thename of a variable or a formula containing the angle of the direction in radians:”=#VARNAME”

The y−coordinate is then measured in the radial direction along, while the z−co-ordinate is perpendicular and positive to the left. The input is done via:

REF PT0 ~PTD absolute coordinatesREF PT0 +PTD affine scaling only along directionREF PT0 *PTD affine sclaing in both directions

For a variant construction the (+) will maintain the ratio of distances in the radialdirection and maintain the value perpendicular to that.

Case 3: Constructional References

PT0

PTDPT3

PT

If three points are given, then the third point may be provided with a prefix oper-ator defining the distance or elevation to be taken from that point and searchingthe corresponding point on the line REF−RFD:

REF PT0 PTD >PT3 Distance (y)REF PT0 PTD ^PT3 Elevation (z)REF PT0 PTD PT3 Perpendicular point

If for the first two cases the third point is specified as the point itself, this will createpoints with the same selected coordinate, which is needed for example for pointswith a fixed distance, but a height depending on the cross inclination.


Version 16.133−170

For a circle you may specify an additional point. The distance of this point to thecentre will then specify the radius of the circle. For steel shapes the angle of ori-entation is used in a similar way.

REF .... REFR PTR

Examples showing most of these features are given with AQUA31.DAT toAQUA33.DAT in the example directory AQUA.DAT.

3.28.2. Import of FE−SectionsFor advanced design tasks like a hot design it is not sufficient to describe the sec-tion just by its outer contour. For such cases it is possible to import a plane FiniteElement mesh from a secondary database into a section. The secondary data-base will contain in general also temperature distribution fields. A spatial definedsection will be projected automatically into the best fitting global coordinate plane.

The section will be converted to single integration points given by the center ofall QUAD elements. These may be imported group wise with POLY to specify anyconstruction sequences or in total if no such definition is made.

As this feature allows the evaluation of all sectional values for any type of section(e.g. secondary torsion for a solid section) it is the most general type of sectiondefinition. All additional elements (Stress points, reinforcements, shear cuts) aredefined as usual.

With the definition of LTAU the unit warping and the shear stress distributions willbe saved to the original database. So it becomes possible to view those resultswith WING/WINGRAF.


3−171Version 16.13

See also: SECT

3.29. CS − Construction StagesÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

CS


NO

TITL

ATIL

First active number in construction sequence

Title of construction stage

Last active numberin construction sequence

−

LIT32

−

*

−

−

With CS you may specify a cross section for (up to 9) construction stages. All ele-ments following this record will be added within that stage. The current construc-tion stage will also contain all the elements of the previous construction stages.

If part of the section is active only temporarily, a value for ATILmay be specified.This is then the last construction stage where this part is active. The CS−stagerecords have to be given in monotonic ascending sequence of NO, but for thiscase multiple records with the smae NO value may be given. However the desig-nation should be given with the first record of such a CS block.

ÑÑÑÑÑÑÑÑÑÑÑÑÑÑ

ÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑ

ÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏ

10 20 22 24 30 ∞21 40

ÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏ

The picture above defines a general construction process. As phase 21 has noimpact on the section itself it does not need to be defined. The same holds for anyother construction phase like prestress stages. The input scheme in general isgiven by:

CS 10 ; black section partsCS 20 ATIL 20 ; red section partsCS 22 ATIL 22 ; blue section partsCS 24 ATIL 39 ; black section partsCS 30 ; green section parts


Version 16.133−172

This will generate 6 construction stages::

NO is the total section for the final phases starting from 40NO.1 is the first construction stage for Phases 10−19NO.2 is the second construction stage for phases 20−21NO.3 is the third construction stage for phases 22−23NO.4 is the fourth construction stage for phases 24−29NO.5 is the fifth construction stage for phases 30−39

The defintions of ATIL for phases 20 and 22 will be extended automatically to thenext defined construction stage, only for phase 24 the end value has to be speci-fied explicitly. The transition to the final stage may be defined either by an explicitconstruction stage 40 or by the latest removal of any other phase. There is nogeneration of intermediat values, a CS 20 ATIL 33 will not generate a constructionstage at 34.

The construction stages are assigned to the individual elements with the groupdefinition of the analysis program, a construction stage number defined there isinserted between the defined numbers here. The number NO will be incrementedby default. You may want to use larger gaps to allow prestressing stages to bemixed in. With the construction stages defined in AQUA as 10, 20 and 30 the se-lection of stage 25 would use the 20−section and all tendons up to stage 25.

For every construction stage it is also possible to specify with SV for every mater-ial a factor for the elasticity and the shear modulus after the CS record.


3−173Version 16.13

See also: SECT

3.30. SV − Additional Cross SectionProperties


SV


ITAK

YSCZSC

CMCMS

AYAZAYZ

LEVYLEVZ

Torsional moment of inertiaArea of Bredt’s box

Coordinates of the shear center in thereference coordinate system

Warping modulusWarping shear modulus

Shear deformation area yShear deformation area zShear deformation area yz

Minimum lever arm for VYMinimum lever arm for VZ

[m4]1014

[m2]1012

LIT/*LIT/*

[m6]1016

[m4]1014

[m2]1012[m2]1012

[m2]1012

[mm]1011

[mm]1011

−1.0*

**

**

***

−−

MNODEFFFACEFACG

Material number for the following optioneffective thickness of sectional partFactor E−modulus for construction stageFactor G−modulus for construction stage

−[mm]1011

−−

*2A/U1.0

FACE

In general, these cross section properties will be computed automatically. Youonly have to specify explicit deviations.

AK defines the area of the equivalent hollow cross section according to Bredt.This value is used for determining the longitudinal reinforcement and the link rein-forcement due to torsion. However, in general AK should be defined implicitly byspecifying the torsion resisting reinforcements.

An absolute value (0. or positive) can be input for IT. If a negative value is input,the moment of inertia computed by the program is multiplied by a factor. The value−0.5, for example, results in a cross section with 50 percent of the torsional mo-ment of inertia.


Version 16.133−174

YSC and ZSC can define a mandatory centre of rotation or, in case of only onevalue, a restraining plane. The literal ’S’ can be used in both cases to set this ordi-nate to the value of the center of gravity.

AY and AZ are not set for solid cross sections of concrete (CTRL STYP 0/1). Ifyou want to use them, then CTRL STYP 3 should be entered. If shear deforma-tions are not to be taken into account, despite a detailed shear stress evaluation,AY, AZ , AYZ and CMS should be set to ”0.”

For shear force dimensioning in state II, minimum lever arms can be specifiedwith LEVY and LEVZ, in order to obtain more economical results (e.g. 0.90d) orcover extreme cases (e.g. moment=0). Positive values are absolute, negativevalues are relative to the height or width of the section.

For the analysis of creep and shrinkage effects an effective depth deff is required.This value is defined by the area of the section A and the length of the peripheryU which has air contact by the formula 2A/U. The air contact ratio may be definedfor the vertices of a polygon and for circles. If not otherwise stated, outer peripher-ies will have a ratio of 1.0 and inner peripheries of 0.0. However you may specifythe value for every material within a section via record SV explicitly.

For construction stages it is possible to define with SV MNO two factors for theelasticity and the shear modulus. They will be mainly used for the evaluation ofthe sectional values. A consistent treating in AQB for all effects is still under in-vestigation.


3−175Version 16.13

See also: SECT CIRC VERT CUT SPT

3.31. POLY − Polygonal Cross−SectionElement / Blockout


POLY


TYPE

MNO

Type of polygonO Outer perimeterI Inner perimeter (obsolete)OPY,OPZ Outer perimeter

symmetric w.r.t y/z−axisRECT centric rectangle

width/height DY/DZREC+ positive rectangle

(eccentric position below)REC− negative rectangle

(eccentric position above)GRP Group of a FE−Mesh

selected with SECT FEM

Material number (composite sections)0 = hole

LIT

−

O

(SECT)

YMZMDYDZSMAXEXP

Differential coordinates of the polygon inthe reference coordinate systemSize of the rectangle definitions

Maximum edge length of polygonLiteral of exposure class

[mm]1011

[mm]1011

[mm]1011

[mm]1011

[mm]1011

Lit4

00!!−−

REFPREFD

REFS

Default reference point for all verticesDefault reference direction for all verticesDefault reference of initial coordinates fortemplates

LIT4LIT4

LIT4

−−

−

Unless a REC*−type has been selected, the record POLY must be followed bythe input of the polygon vertices with VERT . The sequence of the polygon (clock-wise or counter−clockwise) has no effect. The polygon will be closed by the pro-


Version 16.133−176

gram automatically. In case of symmetry, the polygon is extended by mirroring be-fore being closed.

A hole is automatically created when polygons or circles overlap, a true hole isthus defined by a polygon or circle with material number 0. The definition of a spe-cial inner polygon with the same material number or the formerly common methodof combining several polygons (outer perimeter and inner perimeters) into onesingle polygon by making two passes along the same edge should normally beavoided.

The input of YM and ZM causes a corresponding shift of the given polygon. Thecoordinates of VERT or DVER refer then to the shifted (by YM, ZM) coordinatesystem. The symmetry data also refers to the shifted coordinate system. Thus,for example, similar openings can be generated easily.

A rectangle can easily be defined by means of a special type. These define a rect-angle with sides DY and DZ, with its centre or upper or lower midside point at thecoordinates YM,ZM.

AQUA stores the shear stress only for polygon or stress points. If you want to seesmooth shear stress distributions with AQUP it is mandatory to subdivide thepolygon edges. This can be done most easily with a value SMAX. As an alternateway we have the value PHI at VERT, but this requires to define additional verticesat the symmetry axis to allow a subdivision of the closing edges. For theREC*−types SMAX is preset to DZ/4.

The exposition class EXP allows the definition of special materialparameters(MEXT) to individual poygon edges. The value specified here becomes thedefault for that polygon.

For all references it is possible to select a third item (REFS). This will define thestarting coordinates for all successive references to be taken from the relative po-sition of the axis with that name to the central reference. The coordinates them-selves have to be given with the initial definitions as absolute reference to the ori-gin. This feature allows to define references to points to be entered later in theinput deck when specifying the 3rd reference with ”NULL”.


3−177Version 16.13

See also: SECT POLY parametric sections

3.32. VERT − Polygon Vertices inAbsolute Coordinates


VERT


NO

YZ

RPHI

TYPE

EXP

Designation of the polygon vertex

Coordinates of the polygon vertexrelative to YM, ZM

RadiusMaximum sector angle

Type of vertexO Outer perimeterTP Intersection of tangents

Literal of exposure class /Degree of air contact (0.0 to 1.0)from that point

Lit4

[mm]1011

[mm]1011

[mm]1011

Degrees

LIT

Lit4

*

00

−*

*

*

REFPREFDREFS

Reference pointReference direction pointReference initial coordinates for templates(see also POLY)

Lit8Lit8Lit8

***

NO is used for identification during any output of stresses. If nothing is input,AQUA generates internal numbers in sequence.

The distances between adjacent polygon vertices must be at least 0.0001 m. Thepolygon is defined by the sequence of the vertices, not by their numbers. Thenumber of points is limited to 255 per polygon.

If a radius is specified, there are two possibilities:

• for tangential points a fillet is created at that vertex with the given radius.If the radius is defined negative, a chamfer is created instead with the valueof R used as a distance along the edges.

• for other cases additional points are inserted between this and the previ-ously defined vertex in order to simulate a circular arc with an angle < 180


Version 16.133−178

degree. The aperture angle is defined by CTRL HMIN/HTOL. If R is posi-tive, the area of the polygon will be increased. With an explicit definition of PHI however, explicit vertices will be gene-rated. In that case the sign of PHI will define the orientation of the arc.

Non effective areas can be defined by means of NEFF−areas, where parts of thepolygons within those areas become non effective for selected forces by the inter-nal introduction of deductional polygons.

The old method of short cuts within the polygon definition sohould not be used anymore. There non effective points are specified either with the definition of NEFFor INEF for the TYPE of the vertex or by giving values for YEFF or ZEFF to intro-duce additional vertices at these limits automatically.

The sectional values of the total sections are only used for the calculation of thearea as well as the torsional stress and the integral equation solution. All geo-metrical moments of inertia are computed based on the effective parts only (referto the AQB manual). It is to be noted that the effective width is actually dependenton the load case and the on the purpose of design.

The exposition class EXP allows the definition of special materialparameters(MEXT) to individual poygon edges. For the degree of air contact the geometricmean value is used. i.e. if one of the two vertices of an edge has the degree 0.0,the total edge will have this value.


3−179Version 16.13


3.33. CIRC − Circular Cross SectionElements


CIRC


NO

YZ

R

MNO

EXP

Designation of the circular element

Coordinates of the centre point in thereference coordinate system

Radius of the circle(negative = inner perimeter, obsoleted)

Material number (composite sections)0 hole

Literal of exposure class /Degree of air contact (0.0 to 1.0)

Lit4

[mm]1011

[mm]1011

[mm]1011

−

Lit4

*

00

−

(SECT)

−

REFPREFDREFS

REFR

Reference pointReference direction pointReference initial coordinates for templates(see also POLY)Reference radius point

Lit8Lit8Lit8

Lit8

−−−

−

Internal sequential numbering takes place when nothing is input for NO. NO canbe selected arbitrarily.

When CIRC is defined for an inner perimeter, the material number must be thesame as that of the element in which the inner perimeter lies.


Version 16.133−180


3−181Version 16.13

See also: SECT POLY CIRC parametric sections

3.34. CUT − Shear and Partial SectionsÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

CUT


NOYBZBYEZE

Designation of shear or partial sectionOrdinates of the cut segment

Lit3[mm]1011

[mm]1011

[mm]1011

[mm]1011

!****

NSMSWTMWTD

Normal forces perpendicular to sectionMoment perpendicular to sectionTorsional resistance for the centreAdditional resistance for the edges

[kN/m]1111

[kNm/m]1112

[1/m3]1018

[1/m3]1018

0.0.**

MNOMRFLAYASUP

Material number of the sectionMaterial no of shear reinforcementShear reinforcement layerMinimum shear reinforcement

−−−*

(SECT)(SV)

1*

OUT Output optionsNONE no output orM,A,E,MA,ME,AE,MAE

LIT MAE

TYPE Type of section (see remarks) LIT *

VYFKVZFK

Partial factor for shear force VYPartial factor for shear force VZ

−−

**

INCLBMAXBREDCINTMUE

Inclination of links w.r.t. bar axisWidth of the equivalent hollow sectionDeductible width due to hollow pipes etc.Roughness coefficient of construct. jointFriction coefficient of construct. joint

Degree*/LIT

[mm]1011

−−

90*0.**


Version 16.133−182


SXETANA

“crack spacing parameter” für AASHTOMinimum inclination of truss diagonal

*−

0−

REFARFDARFSA

REFERFDERFSE

Reference point for start pointReference direction point for start pointReference initial coordinates for templatesfor start point (see also POLY)Reference point for end pointReference direction point for end pointReference initial coordinates for templatesfor end point (see also POLY)

Lit8Lit8Lit8

Lit8Lit8Lit8

−−−

−−−


3−183Version 16.13

With a CUT one specifies a part of the section to be used for shear design and/orthe minimum reinforcement or crack width of a partial section. The input of shearsections is necessary for the checking of shear stresses in concrete cross sec-tions. Without input for CUT, up to two axis parallel sections are defined throughthe gravity centre (see CTRL STYP). As these do not necessarily pass throughthe smallest width of the tensile zone, a warning is issued when the user enterscomplicated polygons without shear sections.

The TYPE of the cut defines some important properties for the design. The follow-ing values are available:

• ACT Only for the crack width design

• WEB Web of a cross sectionWRED Web with reduced allowed strengthAWEB WEB + Partial area for crack widthAWRE WRED + Partial area for crack width

• FLAN Flange of a cross sectionFFUL Flange with enhanced strength allowanceAFLA FLAN + Partial area for crack widthAFFU FFUL + Partial area for crack width

• JOIN Construction jointINDE indented shear jointROUG rough shear jointEVEN even shear jointSMOO smooth (very even) shear jointThe coefficients CINT and MUE are defined in EN 1992 or DIN 1045−1(2008). For design according to the old DIN 1045−1 (ch.10.3.6) the valueCINT has to be specified with the value of βct > 1.

• SLAB For special cases (e.g. hollow plates) it is possible todesign a cut of any section like a plate.

In general the definition of WRED / FLAN is expected to describe structured sec-tions, while WEB / FFUL is defining a compact section.

For DIN 1045 (1978) this info is used to allow the shear region 3. However in thiscase, the requested minimum height of 30 cm may override a definition here.

AASHTO 2005 distinguishes for the shear design (5.8.3.) between two alternatesdepending on the presence of sufficient minimum shear reinforcement. If less


Version 16.133−184

minimum reinforcement should be provided, a “crack spacing parameter” has tobe specified depending on the maximum aggregate size ag [mm] and a maximumdistance between longitudinal crack reinforcements sx :

sxe� sx�· 35�ag�16

�� 2000�mm

The definition of the sign of the section, its internal forces and torsional resis-tances can be seen in the following figure. The sign of INCL applies to a rotationfrom the bar axis towards the normal direction n.

Shear cut

A cut can be defined parallel to the axis by the input of YB or ZB only. In such casesthe literal S can be used for describing the location of the centre of gravity. How-ever, the cut can also be defined by the input of two points (YB,ZB) and (YE,ZE).In this case the intersection points with the section periphery outside the definedcut line are not taken into account.

If several cuts with the same number are defined in immediate succession, thepolygon line defined by them is used as a cut. Missing intermediate segments arefilled in automatically.

Additionally for each edge, not only special torsional resistances can be definedfor each edge, but a proportional factor for the shear force as well. This makesit possible to describe outer dowel joints, reduced web widths, and cuts in multiplyconnected sections. These factors specify the portion of the total shear force V·S/Iapplied to the partial cut. The integral equation algorithm (CTRL STYP 3) will es-tablish these factors based on the integrals of the shear stress along the cutsautomatically.


3−185Version 16.13

BMAX defines whether an equivalent hollow cross section should be used (e.g.for reinforced concrete cross sections). If the cut width is greater than BMAX, thefound cuts are automatically subdivided into two partial cuts, each of them pro-cessing the external width of the equivalent hollow cross section. The width canbe defined directly in m, but two literals can be defined too:

EC2 The substitute width A/U in accordance with EC2 is used.

DIN An inscribed circle is estimated due to the area and the moment ofinertia. A sixth of the diameter is used.

The default value of BMAX for steel or wooden sections and multiple cuts fromseveral CUT records is 999. (no consideration), and for all other cuts EC2 or DINdepending on the material type. An increase in this value results in a smallerequivalent cross section, thus leading to greater shear reinforcement but smallershear stress. Design of the shear reinforcement only takes place for cuts whena genuine or an equivalent hollow cross section has been defined.

The following defaults apply for WTM and WTD: If the cross section has inner per-imeters, or an equivalent hollow cross section has been defined by means ofBMAX, then a closed cross section is assumed. WTM is then computed basedon Bredt’s area as 1./(2.·AK·b), and WTD is assumed zero. If neither of theseconditions is satisfied, WTM is assumed zero, WTD is set equal to b−min/IT andthe middle output point is omitted.

For precise calculations in accordance with the theory of elasticity, the shearstress values can be stipulated by hand or be computed by means of the integralequation method (CTRL STYP 2 / 3).

The effective width for the shear force can be reduced by BRED. This is appropri-ate, for example, when ungrouted ducts weaken the web and the width must bereduced accordingly.

The forces N and M perpendicular to the cut are only used to describe the stress.There will be no design for bending and normal force with the links as reinforce-ment. Thus a tensile force may lower the required link area while the total steelarea becomes higher.

Attention!In cracked state the reinforcement is used in the shear checks only when it is situ-ated inside the separated polygon. In particular, a partial area without reinforce-ment leads to a shear stress 0.0 if it is in the tensile zone! Therefore we use a mini-mum shear stress which is taken from the uncracked state and a reduction factorbased on the lever arms.


Version 16.133−186

The individual segments of one cut are treated separately during the design. Thefollowing rules apply for the extreme values of reinforcement of all shear cuts,which are stored separately for each rank of links:

• Simple cuts with the same link rank enter the end result with the largestvalue.

• Multiple segments, equivalent hollow cross sections or polygon cuts withn checking locations with the same link rank enter the results with n timesthe maximum. This assures, that the total reinforcement is computed bysuperposition of the shear and torsion components as required by old DIN.

• Multiple or polygon cuts with checking locations having different link ranksenter the results separately for each rank with the corresponding multipleof the maximum. Different link ranks should thus always be used when dif-ferent reinforcement is to be placed in the individual parts of the cut.

The minimum reinforcements ASUP may be specified with a positive value whichis referred to the length or with a negative value which is referred to the length andthe width of the cut as specified in most design codes. If not defined, the defaultaccording to the design code will be selected. If ASUP is defined as zero, it willbe tried not to use any shear links (slabs and beams of minor importance). Aspecial minimum reinforcement according DIN 1045−1 13.2.3 (5) as “articulatedsections with pretensioned tensile flanges” requires the definition of Literal ’PFLA’for ASUP.

Shear in composite cross sections

Special attention should be paid when making shear cuts through compositecross sections. First, it holds generally that a shear cut should cut through partswith the same material number. In case a segment cuts through several materials,one should input several cuts with the same number but different materialnumbers.

It is additionally checked for all cross section elements with other materialnumbers whether they are attached or inside any already separated cross sectionpart. In such a case they contribute to the static moment as long as they are nottouched or divided by the cut.

Most cases are handled correctly by this method, yet the results of the programfor composite cross sections should always be critically checked.


3−187Version 16.13

See also: SECT SPT parametric sections Reinforcement

3.35. PANE − Thin−Walled Cross SectionElement


PANE


NO

YBZBYEZETMNO

Designation of the panel element

Coordinates of start point* Default: YE,ZE of the last elementCoordinates of the end point

Panel thicknessMaterial number (composite sections)

Lit4

[mm]1011

[mm]1011

[mm]1011

[mm]1011

[mm]1011

−

*

(YE)(YA)YBZB−

(SECT)

REFARFDARFSA

REFERFDERFSE


Lit8Lit8Lit8

Lit8Lit8Lit8

−−−

−−−

RPHI


mmdegree

−15

OUT Output pointNONE no output orM,A,E,MA,ME,AE,MAE or NONE

LIT MAE


Version 16.133−188


FIXBFIXETYPE

Location of clamped edge from start Location of clamped edge from endSpecial Options

NEFF not effective NCHK no stress check to be appliedNNCH both options

**

LIT

**−

ASASMALAYMRFTORS

DASA

reinforcement positive in cm2/m negative in cm2

Material number of reinforcementTorsional action (see Reinforcement)

PASS / ACTI / ADDIDiameter for crack widthDistance between the bars

[cm2/m]1021

[cm2]1020

LIT−

LIT

[mm]1023

[mm]1011

−−0

(SECT)ACTI

−1[m]

Thin−walled cross section element

Uniform normal and shear stresses are generally assumed across the thicknessof thin−walled elements. Therefore the moment of inertia about the longitudinalaxis (B−E) is zero. The shear stresses due to torsion, however, are distributed lin-early across the thickness. The thickness is considered likewise for the maximumstress. A mixture of the cross section elements POLY or CIRC inside a cross sec-tion is not permitted.

The transmission of shear is only possible at interconnected elements. The pro-gram does not recognise any penetrations of thin− walled elements. In the de-termination of shear stresses, elements are considered to be connected witheach other when their coordinates are no further than 1 mm apart.


3−189Version 16.13

If NO is not specified, then an internal sequential numbering will take place. OUTspecifies for which points (Middle M,Beginning A,End E) results are requested.(See AQUA, AQB)

If a radius is specified, additional straight elements are generated in order to simu-late a circular arc (180� maximum). The aperture angle is defined as less than PHIper segment (Default defined by CTRL HMIN/HTOL). The orientation of the arcis defined by the sign of PHI respective R. Positive values describe an arc rotatingabout the positive x−axis.

For a buckling design it is necessary to define the boundary conditions (free,built−in) and to combine several plates to an integral field. To allow this we havethe convention that plates will be combined if

− they meet in the same plane − do not deviate in thickness more than a factor of 1.25 (may be changed with CTRL FIXL) − deviate in their identification only within the 4th character − do not have stiffeners at the end points

As stiffener we declare all plates intersecting with an angle greater than 45 de-grees. The length of the plate has no influence. A stiffener will move the locationof the built−in face by the projection of its thickness to the inner of the plate.

The user may define the built−in face with an explicit value measured from thebeginning or the end respectively. Negative values will describe a free end, whilevalues larger than the length of the element will disable the buckling design.


Version 16.133−190

See also: SECT WELD PROF SPT parametric sections

3.36. PLAT − Thin−Walled Cross SectionElement

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

PLAT


NO

YBZB

YEZE

TMNO

Number of the plate element

Coordinates of the beginning point in thereference coordinate system* Default: YE,ZE of the last elementCoordinates of the end point in thereference coordinate system

Plate thicknessMaterial number (composite sections)

Lit4

[mm]1011

[mm]1011

[mm]1011

[mm]1011

[mm]1011

−

*

**

YBZB

−(SECT)

REFARFDARFSA

REFERFDERFSE


Lit8Lit8Lit8

Lit8Lit8Lit8

−−−

−−−

RPHI


[mm]1011

degree−15

OUT Output pointNONE no output orM,A,E,MA,ME,AE,MAE

LIT MAE

FIXBFIXETYPE

Location of clamped edge from start Location of clamped edge from end Special Options

NEFF not effective NCHK no stress check to be appliedNNCH both options

**

LIT

**−

Uniform normal and shear stresses are generally assumed across the thicknessof thin−walled elements. Therefore the moment of inertia about the longitudinal


3−191Version 16.13

axis (A−E) is zero. The shear stresses due to torsion, however, are distributed lin-early across the thickness. The thickness is considered likewise for the maximumstress. A mixture is permitted only with section elements PROF or WELD, butPROF must be defined as thin−walled.

The transmission of shear is only possible at interconnected elements. The pro-gram does not recognise any penetrations of thin− walled elements. In the de-termination of shear stresses, elements are considered to be connected witheach other when their coordinates are no further than 1 mm apart.

If NO is not specified, then an internal sequential numbering takes place. OUTspecifies for which points (Middle M, Beginning A, End E) results are requested.(See AQUA, AQB)

If a radius is specified, additional straight elements are generated in order to simu-late a circular arc (180� maximum). The aperture angle is defined as less than PHIper segment (Default defined by CTRL HMIN/HTOL). The orientation of the arcis defined by the sign of PHI respective R. Positive values describe an arc rotatingabout the positive x−axis.

Thin−walled cross section element

For a buckling design it is necessary to define the boundary conditions (free,built−in) and to combine several plates to an integral field. To allow this we havethe convention that plates will be combined if

− they meet in the same plane − do not deviate in thickness more than a factor of 1.25 (may be changed with CTRL FIXL) − deviate in their identification only within the 4th character − do not have stiffeners at the end points


Version 16.133−192

As stiffener we declare all plates intersecting with an angle greater than 45 de-grees. The length of the plate has no influence. A stiffener will move the locationof the built−in face by the projection of its thickness to the inner of the plate.

The user may define the built−in face with an explicit value measured from thebeginning or the end respectively. Negative values will describe a free end, whilevalues larger than the length of the element will disable the buckling design.


3−193Version 16.13

See also: SECT PANE PLAT PROF

3.37. WELD − Welded Shear Connection


WELD


NO

YBZB

YEZE

TMNO

Designation of the element

Coordinates of the beginning point in thereference coordinate system* Default: YE,ZE of the last elementCoordinates of the end point in thereference coordinate system

Effective thicknessMaterial number (composite sections)

Lit4

[mm]1011

[mm]1011

[mm]1011

[mm]1011

[mm]1011

−

*

**

YBZB

−(SECT)

REFARFDARFSA

REFERFDERFSE


Lit8Lit8Lit8

Lit8Lit8Lit8

−−−

−−−

This element connects thin−walled section elements PLAT and PROF shear−re-sistant, without influencing the section values for bending and normal force. Thusone can describe:

− Longitudinal seams of welded joints (T>0)− Buckling fields of thin−walled sections (T>0)− Shear bonds in composite sections (T<0)− Trussed walls (T<0)

For real welds the equivalent seam thickness is to be used for T. The element isthen used for the determination of the shear stresses in welds. The use of aspecial material number, which is not used otherwise within the section is not al-lowed.


Version 16.133−194

For bracing walls the effective thickness T is given through the shear stiffness Sid of the frame divided by the product of the WELD−shear modulus and the length of the shear connection in the section plane. T = Sid/(G�L)

If NO is not specified, an internal sequential numbering takes place.

The coordinates of the end points must be placed exactly within 1 mm (or snapdefined by CTRL SDIV) to the end points of the corresponding elements.

Modelling of longitudinal weld


3−195Version 16.13

See also: SECT PLAT WELD SPT parametric sections

3.38. PROF − Rolled Steel ShapesÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

PROF


NOTYPEZ1Z2Z3MNO

Number of the shape / sectionProfile type (see next page)Identifier of shapeAdditional identifier of shapeAdditional identifier of shapeMaterial number of shape

Lit4LIT***−

*IPE

*−−

(SECT)

ALPHYMZMREFPREFDREFS

REFR

Angle of rotation about reference pointCoordinates of reference point

Reference point for total shapePolar direction of reference pointReference initial coordinates for templates(see also POLY)Reference point for rotation

Degrees[mm]1011

[mm]1011

Lit8Lit8Lit8

Lit4

000−−−

−

DTYP RepresentationT thin−walledS solid (thick) cross sectionTP T positive z ordinates only SP S positive z ordinates only

(bisected shapes not for L,T,Zand SH profiles)

TABT thin−walled (light version)TABS solid (light version)TATP TP (light version)TASP SP (light version)

− S

SYM Symmetric optiono−o Central symmetry to originy−y Axial symmetry to y axisz−z Axial symmetry to z axisQUAD Three times mirroring

LIT −


Version 16.133−196


REF

MATI

Location of shape‘s reference pointS Gravity centerSC Shear centerUR/UL/UM top right/left/middleR /L /M right/left/middleLR/LL/LM lower right/left/middle

Material of a filling for hollow sections

LIT

−

*

0

VDVBVSVTVR1VR2VB2VT2

Explicit definition of heightExplicit definition of widthExplicit definition of web thicknessExplicit definition of flange thicknessExplicit definition of root radiusExplicit definition of root radiusExplicit defnition of lower widthExplicit lower flange thickness(dimensions are in units, which arestipulated by the profile type)

********

−−−−−−−−

CW

BCYZ

Wind coefficientsDIN detailed distribution of DINEC simplified values of Eurocode

Explicit definition for a buckling stresscurve (see record SECT)

LIT

LIT

*

*

Record PROF may be entered without a preceding SECT. In that case a sectionwith the given shape−number NO will be generated. If no AQUA licence is avail-able or if selected explicitly via DTYP a section with simplified sectional propertiesis generated (AQUA−light−version). This is in particular valid for:

Torsional inertia, shear deformation areas and warping torsionno detailed comparative stresses.

The actual list of shapes can be printed by an incomplete input. If nothing is se-lected you will get a list of possible shapes, if you have selected a shape type youwill get the list of all shapes of that type, if you have selected only partial identifiersyou will get the set of matching shapes.


3−197Version 16.13

List of tabulated European shapes: Example

I Double T−Beam with inclined flanges I 300DIN 1025 Blatt 1 I 80 to I 600

IPE Double T−Beam with parallel flanges IPE 270DIN 1025 Blatt 5 IPE 80 bis IPE 600

HE European shapes with parallel flanges HE 300 MHE 300 BHE 400 299

HEAA extra light version HEAA 200HEA wide double T−Beams, light version HEA 300HEB wide double T−Beams, normal version HEB 200HEM wide double T−Beams, heavy version HEM 600HSL extra light type HSL 100HD wide column shapes HD 320 97.6HL special large sizes HL 1000 AAHP wide shapes with uniform thickness HP 220 57.2

U Channels with inclined flange (DIN 1026) U 300UPE Channels with parallel flanges UPE 100UAP Channels of Arbed Saarstahl UAP 200T T−shapes with inclined web/flange T 80TB T−shapes heavy version TB 60Z Z−shape acc. to DIN 1027 Z 100L hot formed L−shapes, all identifiers allowed

thickness at second position: L 20 3thickness at third position: L 90 60 8

CDL cold formed L−shapes, all identifiers allowedSH hot formed hollow sections (EN 10210−2)SHC cold formed hollow sections (EN 10219−2)

all identifiers width x height (20 to 600)thickness at third positionHint: there are various variations with different radiiif needed please specify VR1 and VR2

BAR Round bars according EN 10060 BAR 100WARM Hot manufactured tubes (EN 10210) WARM 711 8.0COLD Cold manufactured tubes (EN 10219) COLD 711 8.0CDS Cold manufactured shapes (EN 10162) CDS 100 80 6


Version 16.133−198

List of other international tabulated shapes: Example

UB Universal Beam Section of British Steel 3 IdentifiersUC Universal Column Section of British Steel 3 IdentifiersUBP Universal Bearing Pile 3 IdentifiersRSJ Joists 3 Identifiers

W American W−Shape of AISC 2 IdentifiersWT halfed W−shapeM American M−Shape of AISC 2 IdentifiersMT halfed M−shapeS American S−Shape of AISC 2 IdentifiersST halfed S−shapeHPus American HP−Shape of AISC 2 IdentifiersC_us American Channels of AISC 2 IdentifiersMCus AISC Miscellaneous Channels of AISC 2 IdentifiersL_us American angles of AISC 3 IdentifiersPIPE American pipes standard / extra / double 2 Identifiers

JIS Japanese shapes 3 IdentifiersMBis Indian MB − shape 1 (2) IdentifiersHBis Indian ISHB − shape 1 IdentifierMCis Indian MC − shape 1 IdentifierL_is Indian angle − shape 3 Identifiers

Shapes according to Australian / New Zealand AS / NZS 4600UBas UB shapes 2 valuesUCas UC shapes 2 valuesUBPas UBP shapes 2 valuesPFCas PFC shapes 1 valuesL_as EA and UA shapes 2 or 3 values

Specify thickness as actual value!SHas SHS and RHS shapes 3 valuesCCas CC shapes (cold formed) 3 valuesCAas CA shapes (cold formed) 3 values


3−199Version 16.13

GOST Russian I−Shapes (GOST 8239) GOST 30Parallel Bending−Shape (GOST 26020) GOST 12 B 2Parallel Column Shape (GOST 26020) GOST 30 K 3Parallel high strength shape (GOST 26020) GOST 45 S 2

U_gost Russian U−Shape (GOST 8240) U_GO 30Parallel U−Shape (GOST 8240) U_GO 30 P

L_gost Russian L−Shape (GOST 8509/8510) L_GO 60 60 8

List of sheet pile shapes: Example(See SYM to define singel pile or wall)

LARS Larssen−U−shapes from Hoesch LARS 603AU Arbed / Arcelor U shapes AU 17PAL Arcelor cold deformed U−shapes PAL 31 40PAU Arcelor cold deformed U−shapes PAU 24 50PU U−Shapes PU 12

L 3S / JSP 3

HOES Hoesch Z−Shapes HOES 1705AZ Arbed Z−Shapes AZ 28PAZ Arcelor cold deformed Z−Shapes PAZ 55 70PZ SkylineSteel Z−Shapes PZ 35

Profiles are primarily tabulated geometric types. Exotic shapes may be definedvia explicit values VD to VR2. But you have to specify a basic type of the shapeand the normally required identifiers in any case. If you select non tabulated ident-ifiers (e.g. HEM 172), all explicit dimension values have to be specified.

Cold formed shapes (CDL) may be defined as U, Z, C or OMEGA shapes by defin-ing the values of the width B and/or the grps T positive or negative:


Version 16.133−200

This input always defines polygons or thin−walled section elements and not anyfixed cross section properties. Therefore the analysis of thin−walled section typesis performed with small deviations from the tabulated cross section values. Fortorsional values with very thin shapes with significant fillets, more severe devi-ations may occur. The default for DTYP is changed to T, if beforehand a thinwalled element in that cross section has been defined. If the profile is included(oartly or complete) in concrete (also core concrete) a hole in the surrounding con-crete is created automatically unless MREF is specified with zero.

If NO is not specified, internal sequential numbering takes place.

By default profiles are oriented with their legs in the direction of the y and z coordi-nate axes, so that the y axis shows the larger moment of inertia. Channels (U−Profiles) are oriented with their opening to the right. Angles (L−Profiles) stand likethe letter L (height Z1, width Z2, but the values can be interchanged). ALPH canrotate the cross section about the x axis.

When nothing is input for REF, the reference point of the shape (YM,ZM) is lo-cated at the gravity centre for double T and SH−shapes, left outside at mid−heightfor Channels, bottom left outside for Angles and top middle for T−shapes. Thecoordinates of these reference points and the angle of rotation may be definedwith reference to other points, but the shape and its size itself may of course notbe influenced by other reference points of.

Standard orientation of shapes

The shapes can be coupled with other cross section elements, but then the typeof element must match. Thus thin walled elements (PANE, PLAT, WELD) may becombined only with DTYP D profiles, while thickwalled elements are allowed withDTYP V profiles, overlapping definitions with other materials will generateautomatic holes. And it must be kept in mind that the transfer of shear forces for


3−201Version 16.13

thin walled profiles is only possible at ends, vertices, or at the centre point (DoubleT and Channels). In case of solid cross sections the edges must lie exactly on topof each other. As can be seen in the following example, the bisected shapes musttherefore be positioned on the outer edge of the other profile’s web.

Transmission of shear

Examples of Thin−walled Profiles:

a) Cross girder made out of 4 bisected HEB 400:

SECT 1PROF 101 HEB 400 ALPH 0 DTYP T 102 HEB 400 ALPH 90 DTYP T

b) Cross girder made out of 2 bisected HEA 300:


Version 16.133−202

SECT 1PROF 101 HEA 300 ZM -145 DTYP TP ALPH 180.

102 HEA 300 ZM 145 DTYP TPWELD 200 150 -7 150 7 14

200 -150 -7 -150 7 =

c) 2 216/3.6 pipes with strengthening of 4 mm:

SECT 1PLAT 101 120 -106.2 120 106.2 3.6 R -106.2

101 120 106.2 120 -106.2 3.6 R -106.2102 -120 -106.2 -120 106.2 3.6 R -106.2102 -120 106.2 -120 -106.2 3.6 R -106.2

PLAT 201 120 -110 -120 -110 4.0202 120 110 -120 110 =

$ connectionsWELD 300 120 110 120 106.2 6.0

300 -120 110 -120 106.2 =300 120 -110 120 -106.2 =300 -120 -110 -120 -106.2 =

Double pipe cross section


3−203Version 16.13

For the combination of solid polygon items, one has to check that the polygoncomponents are perfectly aligned with each other along their edges, so that theshear connection can be identified. For the definition of the following section onehas to stipulate the exact coordinates and the exact height of the second dividedHEM 1000:

SMOO

102

103

104

105

106

112

113

114

122

123

124

132

133

134

142

143

144

152

153

154

162

163

164

SECT 2 TITLE 'Double Cross'PROF 10 HEM 1000 ALPH 0 YM 0.0 ZM 0.0 DTYP S PROF 11 HEM 1000 ALPH 90 YM +10.5 ZM 0.0 DTYP SP VD 1008-21PROF 12 HEM 1000 ALPH 270 YM -10.5 ZM 0.0 DTYP SP VD 1008-21PROF 13 HEM 500 ALPH 0 YM 0.0 ZM -504.0 DTYP SP PROF 14 HEM 500 ALPH 180 YM 0.0 ZM 504.0 DTYP SP PROF 15 HEM 500 ALPH 90 YM 504.0 ZM 0.0 DTYP SP PROF 16 HEM 500 ALPH -90 YM -504.0 ZM 0.0 DTYP SP

A defined profile is mirrored three times with SYM QUAD. With the input

PROF 101 L 50 50 8 YM 10 ZM 10 DTYP T SYM QUAD

following cross section combined from the profiles L 50x50x8 results.


Version 16.133−204

Remarks for the sheet piles:The geometry of the shapes can be modelled only roughly. The most importantdata is the weight of a single pile Z3 in kg/m and a few more dimensions. AQUAwill create the locks as equivalent solid sections such that the total area (basedon a weight of 7850 kg/m3) is achieved. Input of R1 is the half diameter of the lock(U−shapes only), R2 is the angle of the web against the horizontal length of thewall and B2 may be used to specify the width of the “upper” flanges.

For the sheet piles the input for SYM defines:none single pilez−z Wall with 1 m width (locks not fixed)o−o Wall with 1 m width (locks are fixed, only for U shapes)


3−205Version 16.13


3.39. SPT − Points for StressesÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

SPT


NO

YZ

WTYWTZWVYWVZSIGY

TEFFCDYNSIGCTAUCMNO

FIX

Designation of the point

Coordinates of the point in the reference coordinate system

Torsional stress tau−xy due to Mt=1Torsional stress tau−xz due to Mt=1Shear stress tau−xy due to Vy=1Shear stress tau−xz due to Vz=1Stress in transverse direction

Effective thicknessNotch and loading typeallowed stress range σ−d(−1)allowed stress range τ−d(−1)Material number for composite sections(= 0 if it is a pure reference point)Degree of restraint for b/t check

Lit4

[mm]1011

[mm]1011

[1/m3]1018

[1/m3]1018

[1/m2]1017

[1/m2]1017

[MPa]1092

[mm]1011

LIT[MPa]1092

[MPa]1092−

−

*

00

−−−−−

*−*

σ/√3(SECT)

−

REFPREFDREFS


Lit8Lit8Lit8

−−−

Additional output points for normal and shear stresses or arbitrary referencepoints may be defined with SPT. The design for fatigue is only possible with thosepoints. A stress point will create its own stress results in the database visible withWinGRAF along a beam or may be addressed in MAXIMA for the superpositionof stresses at that point. For most cases the evaluation of maximum stressesmight be sufficiently performed with all polygon vertices and the intermediatepoints of the thin walled elements.

The normal stresses can be calculated from the X and Y coordinates usingSwain’s formula.


Version 16.133−206

The shear stresses are calculated by the following expressions:

�xy��Mt�Wty�Vy�Wvy

�xz��Mt�Wtz�Vz�Wvz

�� 2xy � �2xz��The stress coefficients will be determined completely for thin walled sections if thestress point is within a sectional element. If the Integral equations are active forthe shear stress (CTRL STYP 3) you will get unit shear stress for all polygon ver-tices and stress points inside a polygon. For some design tasks an effective widthis needed, which will only be provided automatically for thin walled sections.

For the fatigue design according to DIN 15018/4132 you may also specify literalsfor item CDYN indicating the working conditions and notch types (B1W0 to B6K4)as well as explicit allowed stress values SIGC and TAUC.

For the fatigue design according to DS 804 / DS 805 the notch groups (WI, WIIor WIII as well as KII, KII, KIV, KV, KVI, KVII, KIIX(!), KIX and KX) may be selected.SIGC and TAUC are as stress sways the double value of those of the first row ofthe tables of appendix 6. Precise defaults are available for S 235 and S 355 (DS804), smaller class values will be treated according to the formulas of DS 805.

Specifying only SIGC and TAUC will select the check of the absolute stress rangeas required for solid sections.

For the stress superposition in MAXIMA, the corners and edge−mid points of theencased rectangle will be available for all sections without the need of a SPT de-finition.

For a plate buckling design via a b/t ratio it is necessary to define the effectivethickness TEFF and two stress points with identical identifier describing the endpoints of the plate. With FIX it is defined whether it is a question of a fixed or freeend. A positive value describes a fixed end and a negative one a free end.


3−207Version 16.13

See also: SECT

3.40. NEFF − Non effective partsÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

NEFF


TYPE Not effective for (any combination from:)N Normal forceY,MZ y−ord. = secondary bending MzZ,MY z−ord. = primary bending MyV no interpolated vertices

Lit4 YZN

YMINZMINYMAXZMAX

MNOWIDTNO

Corner points of a rectangular window

Material number (no definition = all)Thickness of rectangleDesignation of the non effective part

[mm]1011

[mm]1011

[mm]1011

[mm]1011

−[mm]1011

Lit4

−9999−9999+9999+9999

−−1

REFIRFDIRFSI

REFARFDARFSA

References for the point(YMIN,ZMIN)

References for the point(YMAX,ZMAX)

Lit4Lit4Lit4

Lit4Lit4Lit4

−−−

−−−

With NEFF it is possible to define parts of polygons or an FE section or a thinwalled section to be non effective for different types of forces or moments. In gen-eral the implemented method will generate multiple deductional areas if the win-dows overlap, so this should be avoided.

For the definition of the NEFF−area it is possible to define the corner points (ymin,zmin) and (ymax,zmax) of a rectangular window or with a specifivcation ofWIDT a rectangle along a line from (ymin,zmin) to (ymax,zmax).

The NEFF window may create additional polygon vertices for the entries and exitspoints. This option may be deactivated with TYPE V. For NEFFs defined withina construction stages this option is always enforced.


Version 16.133−208

See also: SVAL SECT

3.41. SFLA − Forces Work LawsÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

SFLA


NO

U

FS

SHFP

Identification

Displacement [mm], Rotation [mrad],Strain [o/oo] or Curvature [1/km]Force [kN] or Moment [kNm]Stiffness [kN/m] or [kNm/rad]or POL sharp vertex

SPL smooth vertex (Spline)Hardening [kN/m] or [kNm/rad]Proportional Limit [kN] or [kNm]

−

*

**

**

*

!

!−

−−

TYP Type of the line/data pointP Normal force of springPT Shear force of springM Moment of spring

N Normal force serviceabilityVY Shear force Vy serviceabilityVZ Shear force Vz serviceabilityMT Torsional moment serviceabil.

MY Bending moment My servic.MZ Bending moment Mz servic.NU ultimate Normal forceVYU ultimate Shear force VyVZU ultimate Shear force VzMTU ultimate Torsional momentMYU ultimate Bending moment MyMZU ultimate Bending moment Mz

LIT −

TITL Sectional work law designation LIT32 −

With SFLA one may define a direct nonlinear law for forces or moments for beamhinges or springs. These curves consist of up to 20 data points (U,F) interpolatedlinearly or with cubic splines. The so defined curve represents the elasto−plastic


3−209Version 16.13

loading path under monotonic uniaxial loading and therefore marks the boundaryof the elastic domain. For unloading and reloading, a linear elastic path with con-stant stiffness is adopted.

If only a single record is given for any type we have the following special cases:

• for a hinge all values are zero

• for a linear elastic law there is S only

• for a perfect plastic hinge there is F only

• for a bilinear law the values S and F are used

• for a trilinear law the values S, SH, F and FP are usedwhere we have a linear law from 0 to FP with stiffness S, followed by a sec-ond linear branch with the stiffness SH until the maximum value F is re-ached.

For the first point of a line the TYPE has to be indicated, thereafter the last valueis retained as default. The sequence of the input must not mix up data for differentNR values.


Version 16.133−210

See also: SECT POLY PROF WIND

3.42. WPAR − Parameters for WindLoading


WPAR


CS

KR

ICETRAF

YMINYMAXZMINZMAX

Construction stage no

Absolute roughnessdefault according to material (MEXT)

Thickness of ice coverHeight of additional area of wind attack dueto traffic

Explicit dimensions of wind attack area

−

[mm]

[mm]1011

[mm]1011

[mm]1011

[mm]1011

[mm]1011

[mm]1011

0

*

00

****

For the analysis of wind loading you may specify different parameters of the windloading for construction stages. This is mainly the wind attack area due to ice,traffic and building extensions. But in special cases you may even redefine thecomplete set of wind coefficients. The selected CS−number is valid for all consec-utive stages selected in SOFiLOAD with a group.

Currently the roughness is only used for circular sections.


3−211Version 16.13

See also: SECT POLY PROF WPAR

3.43. WIND − Coefficients for WindLoading


WIND


ALPH

CWYCWZCWTREF

Angle for load application (−180≤α≤180)or Type of Derivativa:

H1, H2, H3, H4, A1, A2, A3, A4

Lateral drag coefficientVertical lift coefficientTorsional moment coefficientReference dimension

B always the widthH always the heightBH H for CWY, B for CWZ,

B*H for CWTWB as B but in rotated referenceWH as H but in rotated referenceWBH as BH but in rotated reference

Degrees

−−−

LIT

*

***

BH

CLATSAGVR0V0VR1V1...VR19V19

Transverse driving coefficientStrouhal numberGalloping−Coefficient of EC 1Velocity and Values of the derivativawith up to 20 pairs per record

−−−

m/sec*

m/sec*

m/sec*

0.80.15

*−−−−

−−

The force coefficients are needed for the calculation of wind loads in dependenceof the wind direction. For circular and rectangular sections very detailed valuesare available within the programs. For standard steel shapes default curves aregenerated.

These values have to be stipulated according to an angle sequence. Curves areextended for angles outside the range 0 to 90 or 0 to −180, if they were not defined


Version 16.133−212

explicitly for this range. More than a total of 99 values will not be permittedhowever.

It is especially important to consider the exact definition of the coefficients, be-cause the literature often uses very different coefficients. In wind engineering thegenerally used coordinate system is to align the x−axis in wind direction and thez−axis vertical to the top:

• The angle for load application is the angle against the (lateral) local y−axisof the cross section. 0 degrees correspond to an angle from left to right innegative direction of the y−axis, +90 degrees from below to above in direc-tion of negative z−axis. This definition corresponds to the normal designa-tions. With the normal positive signs of the force coefficients then one re-ceives forces in negative direction.

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

y

z

α = 0°

α > 0°

α < 0°

+ cd

+ cl+ cm

WIND

• The References WB, WH and WBH are similar to their counterpartswithout the W, but the coefficients CWY and CWZ are in wind direction andtransverse upwards as measured in a wind tunnel. They are converted tothe values of the schema mentioned above.


ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

y

z

α > 0°

+ cwy

+ cwz+ cwt

WIND

α < 0°ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

• The coefficients are be to determined from wind−tunnel tests or numericalflow simulations. In order to expand the band width with regard to smallermodifications (e.g. ice arrangement), the flow areas for lateral and verticalflows are usually determined separately. For torsion both dimensions arethen used. Thus is valid:


3−213Version 16.13

py��-q� cwy� �zmax� zmin�

pz��-q� cwz� �ymax� ymin�

mt��-q� cwt� �ymax� ymin� � �zmax� zmin�

plat��-q� clat� �zmax� zmin�

With an input to REF one can also stipulate either the height or the width as refer-ence for all coefficients.

For extended analysis it is also possible to define the Derivativa according toScanlan. For every defined angle up to eight consecutive records with up to 20data pairs may be defined.

FLm� 1

2�U2B��

KH1��U��KH2�

B��U �

��K2H3��K2H4�B��

FMm� 1

2�U2B2��

KA1��U��KA2�

B��U �

��K2A3��K2A4�B��

All values are thus referenced on the total chord width B. When importing datait is strongly advised to check not only the sign of the definitions, but also abouta factor of 2 which might have been used either in the definition of B or with theforces itself.


Version 16.133−214

See also: SECT RF LRF CRF CURF

3.44. Reinforcement.

The reinforcement and its distribution are defined by means of three parameters.

AS is the reinforcement in cm2 or mm2 that must be laidASMA is the maximum reinforcement in cm2 or mm2

LAY is the layer type (F,M,S,Z) and the layer number (0−9)D is the diameter of an individual barA is the distance between the bars

If for a reinforcement a diameter is given, then the value AS is preset to the corres-ponding area (rounded to integer mm2). If AS is also specified, than for the layersof type “F” the value is taken as a factor, while for all others it is taken as absolutevalue. Thus a definition like

AS 4 D 28 LAY F0

is taken as what you expect, i.e. as 4*616 = 2464 mm2. The value ASMA is presetfor those F−layers to the value of AS.

For line−, circular− or circumferential reinforcements there is also an item “A” de-fining the distance of the single reinforcements. Thus the given AS/ASMA valuesare always referred to the distance A. A value of A=0.0 is used for the total areagiven. It should be noted, that A is to be defined in the unit used for the sectiongeometry (m or mm)

Reinforcement with the same layer number is always laid in proportion to the in-put AS−values. Each layer can only be increased to the point where its first rein-forcement reaches its maximum value.

The ratios of the layers to each other are controlled by the layer type. There arelayers with the minimum reinforcement (M0 − M9) and extra layers (Z0−Z9). Thelayer type F may be used instead of M for every individual reinforcement defini-tion. M−layers have minimum reinforcement and, in the absence of any other in-structions, they are laid by at least the specified AS values. On the other hand,Z−layers may be not activated at all. The layer number has no influence on theselection of a particular layer by the dimensioning program. For ideal sectionalvalues only the minimum values of the reinforcements will be used.

If, however, processing in the order of the layer numbers is desired, the layer num-bers S0 − S9 should be used as a special case. S−layers cannot be used in com-


3−215Version 16.13

bination with M/F− or Z−layers. As an exception to this rule, however, a minimumreinforcement can be defined for the lowest layer by M0/F0.

The default layer type is M for 0 and Z for 1 to 9. The input of the layer type forone reinforcement of each layer is sufficient.

In general the absolute value of AS for optional S/Z−layers has no special effect,it is only the relative value within the layer which is important. However the optim-isation method with constraints implemented in AQB may run in numericaltroubles if the relative value between different layers becomes to large (e.g >50).

Each layer is allowed to have only one material number. For the further pro-cessing to be consistent, it is also useful that every one layer lies only in one ma-terial number since only then the right deduction areas or equivalent cross sectionvalues can be determined.

The following principal options are available to the user:

− symmetric reinforcementCompression and tension reinforcement are defined symmetric withrespect to the gravity centre of the cross section and with the samelayer number. Minimum reinforcement requires layer type M.

− non−symmetric reinforcementCompression and tension reinforcement are assigned different layernumbers.

A detailed description of the algorithm for the distribution of layers can be foundin the AQB manual.

Torsional Longitudinal Reinforcement

The keyword TORS and the literal ACTI/ADDI can be used for each reinforce-ment element to indicate that this reinforcement should be used for torsion. Thishas the following effects:

• During dimensioning, the required torsional longitudinal reinforcement iscompared to the total active (ACTI and ADDI) areas divided by the peri-phery length and is then made available with an increase of the involvedlayers. The torsional reinforcement elements do not need to have the samelayer number (e.g. top/bottom). In case of an increase due to torsion,however, each layer is increased as a whole, including reinforcements notactivated for torsion.


Version 16.133−216

• Only the reinforcements designated with ACTI define the equivalentBredt’s box with its area. AQUA establishes itself a reasonable sequenceof the elements and checks the defined area against the cross sectionarea. The result may be checked as shear section “AKT” with AQUP. Ifneeded you may change it with an explicit value with SVAL AK.

The effectiveness of the reinforcement is defined either as linearly distributed re-inforcement directly in cm2/m or in the form of single points with discrete spacing.For the efficiency of the entire box the entire effective reinforcement is distributedabout the entire perimeter. Thus it is the users responsibility to check that the pre-determined distribution is sufficient for the torsional loading.

Crack Widths

The item AR can be used for each reinforcement element in order to introduceadditional properties for checking the crack width. D specifies already the dia-meter for which the crack width must be maintained. AR defines the referencearea for a single check of the crack width, as required for instance by DIN 422710.2 Section 3. Here AR defines the reinforcement ratio μ−z by means of:

�� z��AS� factor�

AR


3−217Version 16.13

See also: SECT LRF CRF CURF Reinforcement

3.45. RF − Single ReinforcementÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

RF


NOYZ

Designation of the reinforcement elementCoordinates of the reinforcement point inthe reference coordinate system

Lit4[mm]1011

[mm]1011

*00

ASASMALAYMRF

ReinforcementMaximum reinforcementLayerMaterialnumber of reinforcement

[cm2]1020

[cm2]1020

LIT−

−−0

(SECT)

TORS Torsional contributionPASS no contributionACTI fully activeADDI partially active,

i.e. active but not defining Akt

LIT PASS

DAR

Diameter for AS and crack widthsReference area for cracked widths

[mm]1023

[m2]1012

−

SIG

TEMP

PrestressStress after creep and shrinkage

Temperature for hot design

[MPa]1092

deg C

0

*

REFPREFDREFS


Lit8Lit8Lit8

−−−

If a temperature field has been selected with SECT FEM, the temperatures TEMPwill be preset with the nodal values closest to the given reinforcement point.


Version 16.133−218

See also: SECT RF CRF CURF Reinforcement

3.46. LRF − Line ReinforcementÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

LRF


NOYBZBYEZE

Designation of the reinforcement lineCoordinates of the beginning point in thereference coordinate systemCoordinates of the end point in thereference coordinate system

Lit4[mm]1011

[mm]1011

[mm]1011

[mm]1011

***

YBZB

AS

ASMALAYMRF

Reinforcement or number of barsfor more details see Reinforcement

Maximum reinforcementLayerMaterial number of reinforcement

[cm2]1020

[cm2]1020

LIT−

−

*(SECT)



LIT PASS

DAAR

Diameter for crack widthsReference length for AS and ASMAReference area for cracked widths

[mm]1023

[mm]1011

[mm]1011

−1.0[m]

−

REFARFDARFSA

REFERFDERFSE


Lit8Lit8Lit8

Lit8Lit8Lit8

−−−

−−−

RPHI

Radius for arrangement in arcAngle for arrangement in arc

[mm]1011

Degrees−

15.


3−219Version 16.13

bb

Line reinforcement

The default for YB and ZB are the last defined values of YE and ZE of the previousline reinforcement.

If a radius is input, then single reinforcement points are defined on the arc (< 180degree) above the defined chord. For each segment the aperture angle is setsmaller than PHI (default from CTRL HMIN/HTOL), the orientation of the arc isdefined by the sign of PHI or R.

The points are always arranged in the middle of the considered sectors. Hence,the beginning and the end point of the arc are not reinforcement points. If an angleof 180 degrees is subdivided into 30−degree segments, the single points lie atangles 15, 45, 75 as well as 105, 135 and 165 degrees.


Version 16.133−220

See also: SECT RF LRF CURF Reinforcement

3.47. CRF − Circular ReinforcementÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

CRF


NOYZRPHI

Designation of the reinforcement circleCoordinates of the center of the circle inthe reference coordinate systemRadius of the reinforcement circleSingle angle

Lit4[mm]1011

[mm]1011

[mm]1011

Degrees

*00−−

AS

ASMALAYMRF


Maximum reinforcementLayerMaterialnumber of reinforcement

[cm2]1020

[cm2]1020

LIT−

−

*(SECT)



LIT PASS

DAAR

Diameter for crack widthsReference length of AS and ASMAReference area for crack widths

[mm]1023

[mm]1011

[mm]1011

−1.0−

RPHI


[mm]1011

Degrees−

15.

REFPREFDREFS

REFR

Reference pointReference direction pointReference initial coordinates for templates(see also POLY)Reference radius point

Lit8Lit8Lit8

Lit4

−−−

−


3−221Version 16.13

When PHI is input, only a single reinforcement point is created at the correspon-ding location. (PHI: 0 = at the z axis, −90 = at the y axis).


Version 16.133−222

See also: SECT RF LRF CRF Reinforcement

3.48. CURF − Perimetric Reinforcement


CURF


HDE

Inset of reinforcement from perimeterMaximum spacing of single reinforcement

cm/mm*

−−

AS

ASMALAYMRF


Maximum reinforcementLayerMaterialnumber of reinforcement

[cm2/m]1021

[cm2]1020

“LIT−

−

−0

(SECT)



LIT PASS

DAAR

Diameter for AS and crack widthsReference length of AS and ASMAReference area for cracked widths

[mm]1023

[mm]1011

[mm]1011

−*−

RPHI


*Degrees

−15.

CENT

EXP

Centring factor

Literal of the exposure classuses CNOM which is defined at MEXT, thedistance is CNOM+D/2+H

−

Lit

1000

−

CURF can be used to define circumferential reinforcement for the last definedpolygon.

If a value is specified for DE, then single reinforcements with equal spacing ≤ DEare laid instead of a line reinforcement. At least one reinforcement bar is placedat each corner, however. The dimension of AS, ASMA and AR is in this case thatof a single point (eg. mm2 or cm2 or m2).


3−223Version 16.13

If A is defined as zero explicitly, then AS and ASMA are the total reinforcementares (eg. mm2 or cm2).

H

Circumferential reinforcement − Polygon

Because it is useful for the design method that the centre of reinforcement coin-cides with the centre of the cross section, AQUA attempts to change the reinforce-ment distribution with a least−square method so that this aim is fulfilled. The sumof the perimetric reinforcement is kept unchanged, however the reinforcementdensities are increased or decreased at the single edges. With CENT 0.0 themethod can be deactivated.


Version 16.133−224

See also: SECT

3.49. TVAR − Template VariablesÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

TVAR


NAME

VAL

SCOP

CMNT

Name of a variable

Value of the variable or expression in theformat “=expression”

Scope of variableIf specified, the varibale will be saved tothe databaseComment to the variable

Lit16

Lit64

−

Lit32

!

!

*

−

SOFiSTiK variables, defined via STO# or LET# are globally valid. For more kom-plex tasks like template section generation, it becomes necessary to define varia-bles valid only within a scope. TVAR allows a very general definition of those va-riables within a freely selectable scope.

TVAR without the definition of a scope saves the value for the current section.Thus the use of this variable becomes possible for template formulas even if thatvariable is not defined globally. Multiple definitions should be used for very specialcases only.

Variables used for a section have a complex hierarchy:

• Highest Rank have variables defined along an axis during interpolationalong the axis.

• Secondary rank have all variables defined in public scopes (0 to 99999),either with CADINP and LET# or with TVAR and an explicit scope.

• Finally for all variables the default−value will become effective, which is thevalue which has been defined at the time when the section has been cre-ated. If no other scope has been used, this will be the value defined withTVAR for the section. These values are saved with the section in the data-base and will be updated with every INTE command.

The name of the variable may be followed by a simple numerical index. For VALit is also allowed to specify a list of up to 8 values, which will be then assigned tothe following indices:


3−225Version 16.13

TVAR INC(0) 0.05 TVAR ALF '=ARC(ATN(+#INC,+1)),ARC(ATN(-#INC,-1))' SCOP 1


Version 16.133−226

See also: SECT

3.50. INTE − Interpolation or Cloning ofSections


INTE


NO

NS0NS1SNREF

ICSICS2...ICS9

Number of new sectionADD Insert a section definitionALL Rebuild all cloned sections

Number of 1st reference sectionNumber of 2nd reference sectionInterpolation or station valueNumber of a beam reference axis

Shift of construction stages

−/LIT

−−/LIT

−−

−−

−

*

−−−−

0*

*

Sections may be interpolated or cloned or inserted in the current section:

• If NO is defined positive a new section will be generated.

• If NO is defined as Literal ADD, an already defined or newly interpolatedsection section will be inserted within the current section definition. This isespecially useful for those cases where sections exist from a general im-port and have to be amended with additional data.

For the elements to be inserted there is:

• Just copy a section definition. For a cross section template cuurently de-fined variables (TVAR) may be evaluated. This method is selected byentering NS0 only. If an identical copy is wanted NS1 may be defined asliteral CLON.

• You may use linear interpolation between two sections having an identicallayout. For this method two cross section numbers and an interpolation fac-tor S (0 for NS0, 1 for NS1) have to be stipulated.

• Last but not least you may extrude a cross section template NS0 with refer-ence points along a general curved axis. This is selected by entering a ref-


3−227Version 16.13

erence number NREF of the beam axis, the common station value S forall the axes and the reference cross section NS0.

With all methods, the construction stage numbers may be canged with a definitionof ICS to ICS9. If only ICS is defined all higher construction stages will be shiftedaccordingly.

You may also work on all sections marked as to be interpolated in the database,by specifying a section number NO as ALL or zero. Depending on the specifica-tion of NREF, all sections along that axis or along all available axis will be treated.When performing this action AQUA will use free section numbers above 100 andabove the cross section template for the new sections. These sections are de-leted and reassigned if this procedure is repeated and will be printed in detail onlyif ECHO SDEF EXTR is given.

AQUA will check the generated sections against duplicates and may use a sec-tion multiple times. A definition of INTE 0 1 will suppress this behaviour.

It is also possible to interpolate typed standard sections. When inserting suchsections, however only the geometric definitions will be inserted into the currentsection.


Version 16.133−228

3.51. IMPO − Import of Data


IMPO


MATSECTFROM

Number of a material ( 0 = all)Number of a section ( 0 = all)Name of a database to read from

−−

Lit48

−0!

With the record IMPO you may import materials and sections from a database tothe current project database. If MAT or SECT are defined negative, then the im-port of materials and cross sections is suppressed respectively.

The import is done before any other input data is treated, an imported sectiontherefore may have a different type of material with the same number. An importof materials will delete all existing materials and sections unless CTRL REST 2has been defined before the IMPO−record.


3−229Version 16.13

3.52. EXPO − Ansi Export of Data


EXPO


MATSECTTOPASS

Number of a material ( 0 = all)Number of a section ( 0 = all)Name of a file to write toPassword of the CDB to be exported

−−

Lit96Lit16

00*−

With the record EXPO you may export the materials and sections in the databaseto an input file for AQUA. This may be useful in special cases. If MAT or SECTis defined negative, then the export of materials and cross sections is deactivatedrespectively.

If the filename is not specified the data will be appended to the most recentlydefined file or a file with the name project_AQU.DAT is generated.

The units of the values will be set to the current setting of UNIE from record PAGE.The language of the new file will be the same as the current CADINP input file.


Version 16.133−230

3.53. ECHO − Extent of Output

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

ECHO


OPT A literal from the following list:MAT Material parametersSNO Saving options at sectionSECT Cross section elementsREFP References of elementsSDEF Cross section values restartSYST System statisticPICT Properties of PicturesIEQ Integral equation methodWIND Wind coefficientsSPRI Spring characteristic curvesBORE Bore profile valuesFULL Select all options

LIT FULL

VAL

VAL2

The extent of the outputOFF nothing computed / outputNO no outputYES regular outputFULL extensive outputEXTR extreme output

Additional value

LIT

−

FULL

−

In case of no ECHO input all options are set to YES (ECHO MAT has NO). Theinput of the option alone is therefore sufficient for increasing the value to FULL.The record name ECHO must be entered for every record.

MATNO Only name of design code and materialsYES Material constantsFULL plus stress−strain curves of materialsEXTR plus default stress strain curves


3−231Version 16.13

The ECHO−options may be defined anywhere in the data record, the last defini-tion will be applied to all sections. However it is possible with a definition of ECHOSNO n1 n2 to remember the currently active values for the print out of sections n1 to n2.

SECTYES Overview of cross section values onlyFULL Plus the most important values for each cross

sectionEXTR Plus the individual elements of the cross section

added15 Printout of the internal generated sectional

elements

REFPNO No printoutFULL For section templates all references of

coordinates are added to the printout

SDEFYES The cross sections which have been input in this

calculation run onlyFULL plus the unmodified cross sections in the data−

baseEXTR plus all interpolated sections

SYSTYES Statistics of total sum of sections and masses in

the system (only available for restart)

PICTNO No pictures to be includedYES Nice pictures with shadingFULL Contours including basis static elementsEXTR Detailed picture including labels

With input VAL2 one may switch from the automaticorientation to an explicit orientation of the sectional coordinate system. For the values from 1 to 4, the y−axis is aligned to the left−hand side, downwards, to the right−hand side, upwards. Other values are taken as rotation angle in degrees.


Version 16.133−232

IEQNO No additional printoutFULL Detailed printout of the analyzed topology of the

section for the integral equation method.

WIND only in connection with ECHO QUERNO No outputYES Values and graphic of the wind coefficients

SPRINO No outputYES Values and graphic of the spring characteristic

curve

BORENO No outputYES Table with the bore profile values


4−1Version 16.13

4 Description of Output.

4.1. Information about the Design Code

The output begins with the information about the used design code:

Default design code is ... The used design code is output here.class The class input at NORM CAT is printed here

(e.g. safety class according to the design code).Altitude above sea levelWind zoneSnow load zoneEarthquake zone

4.2. Material Properties

Only the material numbers with the material designations are printed with the de-fault ECHO MAT NO. The tables of material properties are output with ECHOMAT YES.

General Material PropertiesNo. Material numberYoungs−modulus Elastic modulus for deformation analysis

(DIN 1045−1 Ecm!)Poisson−Ratio Poisson’s ratioShear−modulus Shear modulusCompression modulus Compression modulus Weight Specific weightWeight buoyancy for soil mechanics onlyTemp.elongat.coeff. Temperature elongation coefficientYoung−modulus E−90 Anisotropic elastic modulusPoisson Ratio m−90 Anisotropic Poisson’s ratioNordic angle Meridian angle of anisotropyInclination angle Descent angle of anisotropySafetyfactor Material safetycalc strength fy Design strength ult. strength ft Ultimate strength


Version 16.134−2

Concrete MaterialStrength fc Design strengthNomin. strength fcn Nominal strength (cube or cylinder strength)Tens. strength fctm Middle tensile strength5% t. strength fctk Fractile of tensile strength95% t. strength fctk Fractile of tensile strengthBond strength fbdService strengthFatigue strength

Steel MaterialYield stress fy Yield pointCompr.yield val. fyc Compression yield valueTens. strength ft Tensile strengthCompr.strength fc Compression strengthUltim. plast. strain Ultimate strainrelative bond coeff. Relative bond coefficientEC2 bondcoeff. K1 Bond coefficient K1 from EC2Hardening modulusPropotional limitDynamic stress rangemax. thickness Maximum material thicknessRelaxation at .55ft Relaxation coefficient at 0.55⋅ftRelaxation at .70ft Relaxation coefficient at 0.70⋅ft

Timber MaterialBending strength fm Bending strengthTensile strength ft,0 Tensile strength in fibre directionTensile strength ft,90 Tensile strength vertical to fibre directionCompr.strength fc,0 Compressive strength in fibre directionCompr.strength fc,90 Compressive strength vertical to fibre

directionShear strength fv Shear strengthShear strength fv,T Torsional strength


4−3Version 16.13

Masonry / Brickwork

Compr. strength fc,0 Nominal strengthCompressive strengthTens. strength ft Tensile strengthShear strength fvAdhesional strengthTensile brick strength

Layered Material (MLAY)Layer thickness Layer thickness in mMaterial No. Material number and material designation

Nonlinear Material

Nonlinear accord. van Mises (viskopl.) (NMAT VMIS)Yield stress fyHardening modulusViscosity lawExponent creep lawViscosity

Nonlinear accord. Drucker−Prager (NMAT DRUC)Friction angleCohesionTensile strength ftDilatancy angleCompressive strengthUltim. plast. strain Ultimate plastic strainultimate frict. angle Ultimate friction angleultimate cohesionViscosity lawExponent creep lawViscosity

Nonlinear accord. Mohr−Coulomb(3D) (NMAT MOHR)Friction angleCohesionTensile strength ftDilatancy angle


Version 16.134−4

Compressive strengthUltim. plast. strain Ultimate plastic strainultimate frict. angle Ultimate friction angleultimate cohesion

Nonlinear accord. Granular Hardening (NMAT GRAN)Friction angleCohesionTensile strength ftDilatancy angle Compressive strengthreloading modulusExponentultimate factorReference pressure

Nonlinear accord. Swelling (NMAT SWEL)Swelling isotropic Isotropic swelling moduusmin. stress limitequilibrium stressViscous retardation

Nonlinear accord. Discrete Fault (NMAT FAUL)Fault friction angleFult cohesionFault tens. strength Fault tensile strengthFault dilatationNordic angleInclination angle

Nonlinear accord. Rock/2D−Mohr−Coulomb (NMAT ROCK)Fault friction angleFault cohesionFault tens. strength Fault tensile strengthFault dilatationNordic angleFriction angleCohesionTensile strength ft


4−5Version 16.13

Dilatancy angleCompressive strength

Nonlinear accord. Gudehus (NMAT GUDE)Friction angleCohesionTensile strength ftDilatancy angleCompressive strengthUltim. plast. strain Ultimate plastic strainultimate frict. angle Ultimate friction angleultimate cohesion

Nonlinear accord. Lade (NMAT LADE)Parameter P1Parameter P2Tensile strength ftParameter P4Compressive strengthUltim. plast. strain Ultimate plastic strainParameter P7Parameter P8

Nonlinear accord. Textile−Membrane (NMAT MEMB)Parameter P1Parameter P2

The defined stress−strain curves are output by ECHO MAT FULL. With ECHOMAT EXTR, the standard curves are output as well:

eps (o/oo) Strain in o/oosig−m (MPa) Stress−strain for serviceabilitysig−u (MPa) Stress−strain for ultimate loadsig−r (MPa) Stress−strain for calculated mean valuesE−t (MPa) Tangential elastic modulus at this locationsafetyfactor Material safety

The tangential elastic modulus is given in each case for the following range of thestress−strain curve.


Version 16.134−6

Elastic bedding (record BMAT)No. Material numberCs[kN/m3] Elastic bedding principal directionCt[kN/m3] Elastic bedding transverse directionft[MPa] Tensile strengthfy[MPa] Yield stresstan[−] Friction coefficientc[MPa] Cohesiondil[−] Dilatancy coefficientw[kN/m3] Mass density

Thermal or hydraulic material constants (record HMAT)No. Material numberTEMP Temperature or pore pressure levelS [J/Km3] Specific storage coefficientKxx[W/Km] Permeabilities or conductivitiesKyy[W/Km]Kzz[W/Km]

4.3. Bedding ProfilesIf bedding profiles were entered with the records BORE, BLAY, BBAX, BBLA,then the output of the values is released with ECHO BORE YES. Where the labelsmean the following:

Bore Profile No. Bore profile number with designationX[m] Coordinates of the bore place (start point)Y[m] Z[m] dX[−] Direction of the bore profiledY[−]dZ[−]a[°] Rotation angle of the local axis

S[m] Ordinate along the profile axisMat−Out Material number from this ordinateIBA−Out Construction stage number for excavationMAT−New Material number for back−fillIBA−New Construction stage number for back−fillHW−min[m] Minimum ground water levelHW−max[m] Maximum ground water level


4−7Version 16.13

s[m] Starting and/or ending depthK0−a,K1−a,K2−a, Constants of the foundation profile K3−aM0 Skin friction in kN/mC0 Maximum skin friction in kN/mTANR Soil/pile friction angle in degreesTAND Dilatation angle in degrees KSIG Lateral pressure value

K0−t,K1−t,K2−t, Constants of foundation profile in tangential K3−t direction (lateral) in kN/m2

P0,P1,P2,P3 Factors for circumferential variationPmax Maximum foundation value at starting and

ending depth in kN/m

4.4. Overview of the Cross Section Values and Types

In the usual case (ECHO SECT YES), an overview of all the cross section proper-ties is output at the end of each calculation. Where the abbreviations mean thefollowing:

Cross−section static properties

No Cross section numberMat Material number of the cross sectionMNs Material number of the reinforcementA Cross section areaIt Torsional moment of inertiaAy/Az/Ayz Shear deformation areasIy/Iz/Iyz Area moments of inertiays/zs Coordinates of the gravity centrey−/z−sc Coordinates of the shear centremodulus Elastic and shear moduligam Specific weight

In case a description was defined (which is the default for standard cross sec-tions), then it is appended after each cross section number.

After the calculation of the system a summary of the cross section types can beprinted then via a restart and ECHO SYST YES:


Version 16.134−8

Summary of all sectionsNo. Cross section numberTotal LengthTotal Weightmax. LengthTitle

4.5. Cross Section Properties

If ECHO SECT FULL is defined, a list of additional values is output for eachdefined cross section. (cross section moduli, partial cross section areas, etc.).

Following a repetition of the cross section properties from the overview, the prin-cipal moments of inertia and the locations of the principal axes are output.

Cross section properties are also released separately for each material in thecase of composite sections. For cross sections with effective width, the total crosssectional properties of the unrestricted effective cross section are also released.

In case the materials have safety factors, then some analysis methods requirethat the stiffness to to be reduced by the safety factors. As this would result intotally different values for composite cross sections, an extra table for the designsectional values was introduced.

For the detailed output of cross sections it is important to know, if it refers to a re-start. This is because in such a case only the newly defined cross sections getprinted out. Even in the case, however, one can output all the cross sections withECHO SDEF FULL.

The following data are output in the table of additional cross section properties:

Additional static properties of cross section alfa−T Thermal expansion coefficientymin,ymax Maximum & minimum section coordinateszmin,zmax (relative to the gravity centre)hymin,hzmin Minimum lever arm for shear reinforcementAK Core cross section for computing the

torsional reinforcementAB Concrete cross section area for

reinforcement ratiosMB Material number of the link reinforcementTau−T Maximum shear stress due to


4−9Version 16.13

torsional moment 1Tau−B Maximum shear stress due to

secondary torsional moment MT2=1Tau−Vy Maximum shear stress due to

shear force VY=1Tau−Vz Maximum shear stress due to

shear force VZ=1

The table of cross section values for warping contains:

Sectional values for warpingWmin Minimum value of the unit lateral warping Wmax Maximum value of the unit lateral warping CM Warping modulusCMS Warping shear modulus ASwyy Warping area integral w·y·y ASwzz Warping area integral w·z·z ry Sectional dimension (Iyyy+Iyzz)/Iyy−2ymrz Sectional dimension (Izzz+Iyyz)/Izz−2zm

The table of the effective static properties and table of the design values of crosssection are printed then:

Effective static properties of cross sectionMat Material number of the cross sectionMNs Material number of the reinforcementA Cross section areaIy/Iz/Iyz Area moments of inertiays/zs Coordinates of the gravity centremodulus Elastic and shear moduligam Specific weight

Partial cross sectionsMat Material number of the cross sectionMNs Material number of the reinforcementA Cross section areaIt Torsional moment of inertiaAy/Az/Ayz Shear deformation areasIy/Iz/Iyz Area moments of inertiays/zs Coordinates of the gravity centremodulus Elastic and shear moduligam Specific weight


Version 16.134−10

Design values of cross sectionMat Material number of the cross sectionMNs Material number of the reinforcementA Cross section areaIt Torsional moment of inertiaAy/Az/Ayz Shear deformation areasIy/Iz/Iyz Area moments of inertiays/zs Coordinates of the gravity centrey−/z−sc Coordinates of the shear centremodulus Elastic and shear moduligam Specific weight

The fully plastic internal forces are output for steel or composite sections withSTEE reference.

Design forces and momentsN[kN] Axial forceVy[kN] Shear forcesVz[kN]Mt[kNm] Torsional momentMy[kNm] Bending momentsMz[kNm]y[m] Plastic centre of gravityz[m]BUCK Buckling strain curves y and z axis or

COMB for identification of combinations

The table contains the states:

C characteristic values fully plasticE characteristic values elastic (reaching the yield stress)D design values fully plasticF design values elastic (reaching the design yield stress)

The first line contains the single forces and moments (Points A and B of the inter-action diagram). The plastic forces are followed by the values of point C markedas COMB. (For most composite cross sections point C of the interaction curveis given by double the value of the axial force in point B.)

As long as the tensile and compressive strengths of the material do not match,the values will be denoted with an inverse sign, whereas shear force and torsionalmoments are based only on the other strength.


4−11Version 16.13

If prestressed reinforcement has been defined, the internal forces due toprestress are output.

An additional table includes the output of the design data. The values which areprinted at thet−p, thet−y, thet−z and thet−yz are with masses multiplied momentsof inertia (= rotational masses).

Additional Design DataM Material number (only for composite

sections)periphery−O/−I Outer and inner area deff Effective thickness for creep and shrinkaget−min Minimum plate thickness in mmt−max Maximum plate thickness in mmSMP Weight addition for small parts in percentthet−p Mass moment of inertia ρ⋅(Iy+Iz)=ρ⋅Ipthet−y ρ⋅Iythet−z ρ⋅Izthet−yz ρ⋅Iyz

If reinforcement has been defined, then the output for each layer includes the sumof the input steel areas, the upper and lower limits of the reinforcement, and thegravity centre of the reinforcement.

Reinforcement global valuesLayer Layer numbermS Material number of cross sectionmR Material number of reinforcementarea Sum of the input steel areaslower−A Lower limit of steel areas

= zero for extra positions= minimum value for M−position= maximum value of next lower position in case of sequential position numbering

upper−A Upper limit of steel areasyL Location of gravity centre of the layerzLL−tors Torsional effectiveness

If the position is laid by a factor of 1.0,the accounted torsional reinforcement is


Version 16.134−12

area/L−tors (cm2/m)N−v Statically determinate prestressing axial

forceM−v Statically determinate prestressing moment

4.6. Cross Section Elements

Additionally to the cross section values also the individual elements of the crosssections are printed as well with ECHO SECT FULL. Most descriptions arealready familiar from the input description. If reference points were defined, thenthese references are printed with ECHO REFP FULL in the corresponding tables.

PolygonorPolygon holeId Polygon point numberE Effectiveness (− = not effective)Mat Material numbery Coordinates of the polygonz1/WMy,Mz Inverses of the section moduli for bending

My and Mz (Swain’s formula)1/WT Shear stress due to torsional moment Mt=1.01/WVy,1/WVz Shear stress due to shear force Vy or Vz=1.0

Solid: first row = τxy, second row = τxzThin: first row = 0, second row = τ

WO Unit warpingAir Degree of air contact

Rectangular cross−section/T−beamH/B Height and widthSo/Su Reinforcement distance above/belowAso/u Reinforcement above/belowHo/Bo Height and width aboveB−eff Width of the equivalent hollow section

Circular/annular cross section Ra Outer radiusRi Inner radiusRas Radius of the outer reinforcementRis Radius of the inner reinforcement


4−13Version 16.13

Asa Outer reinforcementAsi Inner reinforcement

Tube/Cable Cable factorsD Nominal diameterT Wall thickness for tubecode Design code of the used cablesstrands Number of strandswire Number of wires per strandw*100 Weight factorf Sectional or fill factork Rupture or cable factorke Loss factor Zmin Failure load

Following table is printed additionally for cables:

Circular elementId DesignationMNo Material numberym Distance of the strand to the overall centre ofzm gravity of the cableR Radius of the strandUa Outer circumference

Rolled steel Profile designationD[mm] Profile heightB[mm] Profile widths[mm] Web thicknesst[mm] Flange thicknessr[mm] Radius transition arch web − flangeyr[mm] Coordinates of the profile reference point zr[mm] within the cross section[grd] Rotation

Cuts for shear designNo Section numberType Type of section

WEB/WRED Web with/without shear region 3

FLAN/FFUL Flange with/without


Version 16.134−14

shear region 3MNo Material number of the partial sectionbeta Parameter of friction in construction jointmue Friction coefficient of construction jointyb/zb Coordinates of the partial sectionye/zeb0 Width of section /

effective width for shear force1/WTM,D Reciprocal torsional stress moduliFVy/z Proportion factors for shear forceNs/Ms Lateral bending internal forcesMRF Material number of the link reinforcementR Layer of the link reinforcementAsSU Minimum link reinforcement

2nd value under AsSU: inclination of linksw.r.t. bar axis in degree

Stress output locations on shear cutsTxt. Point designationMNo Material numbery Coordinates of the pointz1/WT Shear stress due to torsional moment Mt=1.01/WVy,1/WVz Shear stress due to shear force Vy or Vz=1.0


sig−p Stress in transverse directionW0 Unit warping

Construction and Selected Result PointsTxt. Point designationM Material numbery Coordinates of the pointz1/WMy,Mz Inverses of the section moduli for bending

My and Mz (Swain’s formula)1/WT Shear stress due to torsional moment Mt=1.01/WVy,1/WVz Shear stress due to shear force Vy or Vz=1.0



4−15Version 16.13

sig−p Stress in transverse directionW0 Unit warpingsig/tau−d Permissible range of steel stresses or

notch type

Thin elementsorLongitudinal weldId. DesignationMNo Material numberNo Element numbery−B/z−B Coordinates of beginningy−E/z−E Coordinates of endt ThicknessW−B/W−E Unit warping at beginning/endTau−T/B Shear stress due to MT=1.0 or MT2=1.0Tau−Vy/Vz Shear stress due to VY=1.0 or VZ=1.0xF Distance of buckling from end points

dimensionless, in relation to the plate length

Single point reinforcementId. DesignationMNo Material number of reinforcementy Coordinates of the reinforcementzT Temperaturesig PrestressAs Base value or minimum reinforcementAs−max Maximum reinforcementLay Layer numberD DiameterAr Reference area for cracked widths

Distributed reinforcementId. DesignationMNo Material number of reinforcementNo Identification numberya,za Beginning point of the linear reinforcementye,ze End point of the linear reinforcementAs Base value or minimum reinforcementAs−max Maximum reinforcement


Version 16.134−16

Lay Layer numberD DiameterAr Reference area for cracked widths

Circular reinforcementId. DesignationMNo Material number of reinforcementNo Identification numberym,zm Coordinates of reinforcement centreR Radius of the circular reinforcementAs Base value or minimum reinforcementAs−max Maximum reinforcementLay Layer numberD DiameterAr Reference area for cracked widths

4.7. Wind Coefficients

The parameters of wind loading defined in record WPAR are output as follows(ECHO WIND YES):

Areas of wind attackCS Construction stage numberrel.roughnss Relative roughnessiceing Thickness of ice covertraffic Height of additional area of wind attack

due to trafficy−min Dimensions of wind attack areay−maxz−minz−max

The table of wind coefficients is output for steel profiles (record PROF) or in caseof an explicit input with WIND:

Wind coefficients depending on angle of attackalpha Angle for load applicationcw−y Lateral coefficientcw−z Vertical coefficientcw−t Torsional coefficientRef Reference dimension


4−17Version 16.13

c−lat Transverse driving coefficient Strohal Strouhal numbera−gallop Galloping−Coefficient

4.8. Integral Equation Method

The output of the analyzed topology of the cross sections for the integral equationmethod reads:

Detected Geometry of section for Integral equation systemReg Regionedge Boundary numbernode−a Start node node−b End nodeM area numberMNo Material numberConn. Hint to a connecting edgeYA, ZA Coordinates at beginningYE, ZE Coordinates at end

4.9. Spring Characteristic Curves

With SFLA it is possible to define a direct non−linear law for forces or momentsfor every spring. It is printed then with ECHO SPRI YES:

Explicit force deformation ruleNumber Number of the spring characteristic curveu[mm] or [mrad] Displacement or rotation or [o/oo] or [1/km] or strain or curvatureTyp the defined TYPE of the line is printed here


Version 16.134−18

This page intentionally left blank


5−1Version 16.13

5 Examples

The examples of this manual are more to demonstrate variant features. The inputfiles which are explained here are to be found in the installation directorySOFiSTiK in the subdirectory aqua.dat\english. Alternatively you will find theseexamples via the TEDDY menu HELP > EXAMPLES sorted by program nameand language.

For additional help like tutorials, tutorial movies and practical examples pleaserefer to the SOFiSTiK Infoportal (www.sofistik.com/Infoportal).


Version 16.135−2

5.1. Materials.

In a verification dat set aqua0_material.dat a lot of variants of the material defini-tion are present. This data set is not suitable for practical analysis, because weallow only one set of design codes to be selected and any material not within thisfamily will be flagged with a error message. Partial features of this data sethowever might be of general interest.

MAT 13 690000 0.3 GAM 20 TITL 'NONLINEAR TEST MATERIAL'NMAT 13 GUDE 20. 103.5 0. 11. $ GUDEHUS NON ASSOCIATEDNMAT 13 SWEL 5 10 1500.BMAT 13 TYPE PAIN 3 12.0

This definition supplies for a soil material, linear elastic constants, a yield function,swelling properties and elastic bedding constants. It is possible to define theseparameters separately, but a definition of MAT will delete all parameters, whileNMAT GUDE may replace a previously defined NMAT MOHR, but NMATSWEL may be used independently again. It is strongly recommended to controlthe printout to be sure about the current definition of the constants.

CONC 31 C 30S TITL '(Temperature EC 2/4)' SSLA ULTI TEMP 100,300,500,700CONC 32 C 30RS TITL '(Temperature EC 2/4)' SSLA ULTI TEMP 100,300,500,700 SHIF

This defines concrete according to EC2 / EC4 with distinct temperature depend-ant properties from 100 to 700 degree via explicit stress strain laws. The secondcase will shift the curves in such a way, that the zero point of the strain has thecompressive stress induced from the thermal expansion at the selected temper-ature.


5−3Version 16.13

5.2. Standard Sections.

A classified section is created with a single input record. The constraints aboutthe geometry allow the use of special formulas or tabulated values from the literat-ure, but on the other side the general usage is not possible. This is most signific-ant for the definition of steel shapes, which may be defined via 4 different ways(aqua8_shapes.dat).

• classified panels (thinwalled) PROF 31 HEA 300 DTYP TABD

• classified polygon (thick) PROF 32 HEA 300 DTYP TABV

• general Einzelbleche (thinwalled) PROF 35 HEA 300 DTYP D

• general polygon (thick) PROF 36 HEA 300 DTYP V

The summary of the sectional values show the first deviations:

Static properties of cross sectionNo MNo A[cm2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs y/z-sc modules gam

MNs It[cm4] [cm2] [cm4] [mm] [mm] [N/mm2] [kN/m]31 = HE 300 A

1 112.53 70.00 18233.1 0.0 0.0 210000 0.88 85.6 23.46 6300.0 0.0 0.0 81000

32 = HE 300 A 1 112.53 70.00 18261.6 0.0 0.0 210000 0.88 85.6 23.46 6310.1 0.0 0.0 81000

35 = HE 300 A 1 112.53 70.00 18233.1 0.0 0.0 210000 0.88 68.3 23.76 6300.0 0.0 0.0 81000

36 = HE 300 A 1 112.53 76.66 18261.6 0.0 0.0 210000 0.88 84.2 24.33 6310.1 0.0 0.0 81000

The length and thickness of the plates at the fillets have been chosen to matchthe real area and moments of inertia as close as possible ( A = 11300 mm2, Iy= 182600000 mm4, Iz = 63100000 mm4). The value of It is obtained by formulasfrom the literature also accounting for the fillets and match the official value of856000 mm4. The explicit thin walled definition can not reach this value fully, butfor the polygon section this value is obtained depending on the numerical effort.More deviations can be found for the shear and warping sectional values:


Version 16.135−4

Section values for warpingNo Wmin[cm2] Wmax[cm2] CM[cm6] CMS[cm4] ASwyy[cm6] ASwzz[cm6] ry[mm] rz[mm]31 -207.00 207.00 1199772.38 0.0 0.00 0.0032 -207.00 207.00 1199772.38 0.0 0.00 0.0035 -207.00 207.00 1199772.50 13330.8 -0.09 -0.2636 -215.39 215.39 1199772.38 0.0 0.00 0.00

Warping resistance and warping shear resistance are currently only available forthin−walled sections. The warping resistance CM for section 36 is therefore takenfrom the tabulated value, but will not be available for a general section. The differ-ent approaches for the fillets have also an effect on the shear stress. As it is notfair to account for them for the torsional inertia but not for the torsional stress, amodified maximum thickness will be used for the formula Zt=tmax/It.

Design forces and moments(C/E = characteristic plastic/elastic, D=plast.Design, F=elast. Design)

No N[kN] Vy[kN] Vz[kN] Mt[kNm] My[kNm] Mz[kNm] y[mm] z[mm] BUCKC 2700.7 1163.94 516.54 10.34 331.96 153.90 0.0 0.0 B CE 2700.7 777.82 311.00 5.23 301.79 100.80 0.0 0.0D 2455.2 1058.13 469.58 9.40 301.79 139.91 0.0 0.0F 2455.2 707.11 282.73 4.75 274.35 91.64 0.0 0.0

32 C 2700.7 1163.94 516.54 11.28 331.96 153.90 0.0 0.0 B CE 2700.7 777.82 311.00 5.23 302.26 100.96 0.0 0.0D 2455.2 1058.13 469.58 10.26 301.79 139.91 0.0 0.0F 2455.2 707.11 282.73 4.75 274.78 91.78 0.0 0.0

35 C 2700.7 1163.94 395.29 7.56 331.77 151.20 0.0 0.0 B CE 2700.7 775.96 310.69 5.23 317.10 100.80 0.0 0.0D 2455.2 1058.13 359.36 6.88 301.61 137.45 0.0 0.0F 2455.2 705.42 282.45 4.75 288.27 91.64 0.0 0.0

36 C 2700.7 1062.21 337.07 7.23 331.96 153.90 0.0 0.0 B CE 2700.7 750.85 311.00 5.13 302.26 100.96 0.0 0.0D 2455.2 965.64 306.43 6.57 301.79 139.91 0.0 0.0F 2455.2 682.59 282.72 4.67 274.78 91.78 0.0 0.0

For the plastic forces and moments the shear components are critical again. Forthe torsional moment there are good reference values available via the sand hillanalog of Bäcklund/Akesson (1972), for the shear it is possible to assign more orless parts of the area of the section. The values obtained from the program fit quitewell, but for the freely defined sections they are a little bit on the conservative side.

Control value Vy-plas Vz-plas Mt-plasWithout fillets 1058.125 295.519 8.505With fillets 1058.125 469.580 10.209


5−5Version 16.13

5.3. T−Beam with Effective Width.A part of the cross sectional area of a T−beam must become ineffective. Thus thissection is no longer definable via the classified section type:

T−beam

As a comparison the T−beam is defined as a standard cross section with the crosssection number 1. The input (aqua2_tbeam.dat) reads:

PROG AQUAHEAD EXAMPLE 2 T-BEAM WITH EFFECTIVE WIDTHHEAD CROSS SECTION No 1 = T-BEAM AS STANDARDIZED CROSS-SECTIONHEAD CROSS SECTION No 2 = T-BEAM AS GENERAL CROSS-SECTIONNORM DIN 1045-1PAGE UNIO 1 UNII 1ECHO FULLCONC 1 C 45 ; CONC 2 C 30 ; STEE 3 BST 500SA$ SREC 1 100 20 20 100 5 5 10 20 TITL 'T-BEAM STANDARDIZED'$ SECT 2 TITL 'GENERAL T-BEAM'POLY OPZVERT 1 50 0 3 = 20 6 10 = 7 = 100NEFF MY YMIN 40 YMAX 60NEFF MY YMIN -40 YMAX -60CUT 1 ZB S


Version 16.135−6

LRF 1 8 95 -8 95 LAY 1 AS -10 TORS ACTILRF 1 -8 5 8 5 LAY 2 AS -20 TORS ACTI END

This results in the following output:

Cross section No. 1 - T-BEAM STANDARDIZED

Static properties of cross section Mat A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs y/z-sc modules gam NoR It[m4] [m2] [m4] [cm] [cm] [MPa] [kN/m] 1 3.6000E-01 3.142E-02 0.00 0.00 32846 9.00 3 3.786E-03 1.720E-02 0.00 -19.85 13686

Additional static properties of cross section Alfa-T ymin zmin hymin AK MB Tau-T Tau-Vy ymax zmax hzmin AB Tau-B Tau-Vz [1/°K] [cm] [cm] [cm] [m2] [1/m3] [1/m2] 1.0E-05 -50.00 -32.22 2.158E-01 3 3.310E+01 6.977E+00 50.00 67.78 3.600E-01 7.310E+00

Rectangular cross-section/T-beam H/B So/Su Aso/u Ho/Bo B-eff [cm] [cm] [cm2] [cm] [cm] 100.00 3.50 10.00 20.00 7.00 20.00 3.50 20.00 100.00

Additional Design DataM periphery-O/-I deff t-min t-max SMP thet-p thet-y thet-z thet-yz [m2/m] [m2/m] [cm] [cm] [cm] [o/o] [tm2/m] [tm2/m] [tm2/m] [tm2/m] 4.000 18.00 20.00 100.00 0.0 0.122 0.079 0.043

Reinforcement global valuesLayer mS mR area lower-A upper-A yL zL L-tors N-pr M-pr [cm2] [cm2] [cm2] [cm] [cm] [cm] [kN] [kNm] M1 1 3 0.13 20.00 0.00 64.28 10.30 M2 1 3 0.93 10.00 0.00 -28.72 73.68 M3 1 3 1.86 0.00 0.00 17.78 147.35 M4 1 3 0.93 0.00 0.00 -15.72 73.68

Cross section No. 2 - GENERAL T-BEAM

Mat A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs y/z-sc modules gam NoR It[m4] [m2] [m4] [cm] [cm] [MPa] [kN/m] 1 3.6000E-01 3.142E-02 0.00 0.00 32846 9.00 3 4.786E-03 1.720E-02 32.22 12.94 13686


5−7Version 16.13

Additional static properties of cross section Alfa-T ymin zmin hymin AK MB Tau-T Tau-Vy ymax zmax hzmin AB Tau-B Tau-Vz [1/°K] [cm] [cm] [cm] [m2] [1/m3] [1/m2] 1.0E-05 -50.00 -32.22 1.440E-01 3 3.676E+01 50.00 67.78 3.600E-01 7.268E+00

Section values for warping Wmin[m2] Wmax[m2] CM[m6] CMS[m4] ASwyy[m6] ASwzz[m6] ry[cm] rz[cm] -0.0777 0.0777 0.000 0.000 0.000 0.000 0.00 52.39

Effective static properties of cross section Mat A[m2] Iy/Iz/Iyz ys/zs modules gam NoR [m4] [cm] [MPa] [kN/m] 1 3.6000E-01 2.907E-02 0.00 32846 9.00 3 1.720E-02 35.00 13686

Design values of cross section Mat A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs modules gam NoR It[m4] [m2] [m4] [cm] [MPa] [kN/m] 1 3.6000E-01 3.342E-02 0.00 25266 9.00 4.786E-03 1.720E-02 31.11 10528

Additional Design DataM periphery-O/-I deff t-min t-max SMP thet-p thet-y thet-z thet-yz [m2/m] [m2/m] [cm] [cm] [cm] [o/o] [tm2/m] [tm2/m] [tm2/m] [tm2/m] 4.000 18.00 0.0 0.122 0.079 0.043 0.000

Reinforcement global valuesLayer mS mR area lower-A upper-A yL zL L-tors N-pr M-pr [cm2] [cm2] [cm2] [cm] [cm] [cm] [kN] [kNm] Z1 1 3 10.00 0.00 0.00 95.00 70.67 Z2 1 3 20.00 0.00 0.00 5.00 141.33

A first look on the geometry shows that the classified section has created 4 layersof reinforcements, because the height of the web requires a longitudinal rein-forcement at the side if loaded with torsion.

The torsional moment of inertia and the shear stresses for the standard T− beamsare then calculated from the web+plate alone. The more accurate formulation ofcross section 2 results in a slightly higher moment of inertia. By contrast, the polarmoment of inertia 4.8E−2 would be 10 times higher and the Saint−Venant’s estim-ate with 1.1E−2 would be more than twice as big.

If now STYP 0 is input instead of STYP 1 (default) for CTRL, the torsional momentof inertia of the standardized T−beam (cross section) does not changed. On theother hand the torsional moment of inertia of the general T−beam (cross section


Version 16.135−8

2) increases insignificantly. In the case of STYP 1 the values are more accurate:IT = 4.786E−3 and the shear centre zsc= 12.94 cm.

CROSS-SECTION NO 1 T-BEAM STANDARDIZED

Static properties of cross section Mat A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs y/z-sc modules gam NoR It[m4] [m2] [m4] [cm] [cm] [MPa] [kN/m] 1 3.6000E-01 3.142E-02 0.00 0.00 32846 9.00 3 3.786E-03 1.720E-02 0.00 -19.85 13686

Additional static properties of cross section Alfa-T ymin zmin hymin AK MB Tau-T Tau-Vy ymax zmax hzmin AB Tau-B Tau-Vz [1/°K] [cm] [cm] [cm] [m2] [1/m3] [1/m2] 1.0E-05 -50.00 -32.22 2.158E-01 3 3.310E+01 6.977E+00 50.00 67.78 3.600E-01 7.310E+00

CROSS-SECTION NO 2 GENERAL T-BEAM

Mat A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs y/z-sc modules gam NoR It[m4] [m2] [m4] [cm] [cm] [MPa] [kN/m] 1 3.6000E-01 3.142E-02 0.00 0.00 32846 9.00 3 4.957E-03 1.720E-02 32.22 12.63 13686

Additional static properties of cross section Alfa-T ymin zmin hymin AK MB Tau-T Tau-Vy ymax zmax hzmin AB Tau-B Tau-Vz [1/°K] [cm] [cm] [cm] [m2] [1/m3] [1/m2] 1.0E-05 -50.00 -32.22 1.440E-01 3 3.676E+01 50.00 67.78 3.600E-01 7.268E+00

A clear deviation can be seen for the value of TAU−T. The stress in cross section1 is calculated according to the theory of elasticity, whereas a more accurate cal-culation with STYP 2 gives the value of 53.2 for the cross section 2. However, inthe case of the default STYP 1 the displacement method is only used for the tor-isonal moment of inertia and the position of the shear centre. Here the value ofTAU−T only amounts to 70% of the value for STYP 2.


5−9Version 16.13

As a third cross section a principal variation with subsequent in−situ cast concreteis presented here (STYP 1):

PROG AQUAHEAD CROSS SECTION No 3 = T-BEAM AS COMPOSITE CROSS SECTION SECT 4 TITL 'COMPOSITE CROSS-SECTION'POLY OPZ MNO 1VERT 11 10 20 12 10 100CURF 50[mm] D 8 10 TORS ACTI LAY 0 POLY OPZ MNO 2VERT 1 50 0 2 = 20NEFF YMIN 45 ZMIN 0 YMAX 45 ZMAX 20 WIDT 10NEFF YMIN -45 ZMIN 0 YMAX -45 ZMAX 20 WIDT 10 CURF 50[mm] D 8 15 TORS ACTI LAY 1 CUT 1 ZB SEND

The output of the cross section is as follows:

CROSS-SECTION NO 4 COMPOSITE CROSS-SECTION

Static properties of cross section Mat A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs y/z-sc modules gam NoR It[m4] [m2] [m4] [cm] [cm] [MPa] [kN/m] 1 3.3645E-01 3.033E-02 0.00 0.00 32846 9.00 3 4.484E-03 1.491E-02 34.38 13.28 13686

Additional static properties of cross section Alfa-T ymin zmin hymin AK MB Tau-T Tau-Vy ymax zmax hzmin AB Tau-B Tau-Vz [1/°K] [cm] [cm] [cm] [m2] [1/m3] [1/m2] 1.0E-05 -40.00 -34.38 1.341E-01 3 3.730E+01 7.876E-15 40.00 65.62 3.600E-01 7.067E+00

Section values for warping Wmin[m2] Wmax[m2] CM[m6] CMS[m4] ASwyy[m6] ASwzz[m6] ry[cm] rz[cm] -0.0773 0.0773 0.000 0.000 0.000 0.000 0.00 48.58

Partial cross sections Mat A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs modules gam NoR It[m4] [m2] [m4] [cm] [MPa] [kN/m] 1 1.6000E-01 8.533E-03 0.00 32846 4.00 3 2.242E-03 5.333E-04 60.00 13686 2 2.0000E-01 1.716E-01 6.667E-04 0.00 28309 5.00 3 2.601E-03 1.145E-01 1.667E-02 10.00 11796


Version 16.135−10

Effective static properties of cross section Mat A[m2] Iy/Iz/Iyz ys/zs modules gam NoR [m4] [cm] [MPa] [kN/m] 1 3.0197E-01 2.793E-02 0.00 32846 8.00 3 7.897E-03 37.17 13686

Design values of cross section Mat A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs modules gam NoR It[m4] [m2] [m4] [cm] [MPa] [kN/m] 1 2.9790E-01 1.479E-01 2.751E-02 0.00 25266 7.89 4.484E-03 9.873E-02 7.888E-03 36.85 10528

Additional Design DataM periphery-O/-I deff t-min t-max SMP thet-p thet-y thet-z thet-yz [m2/m] [m2/m] [cm] [cm] [cm] [o/o] [tm2/m] [tm2/m] [tm2/m] [tm2/m] 4.400 15.29 0.0 0.122 0.079 0.043 1 2.000 16.00 0.0 0.023 0.021 0.001 2 2.400 16.67 0.0 0.043 0.002 0.042

Reinforcement global valuesLayer mS mR area lower-A upper-A yL zL L-tors N-pr M-pr [cm2] [cm2] [cm2] [cm] [cm] [cm] [kN] [kNm] M0 1 3 8.00 8.00 0.00 60.00 186.80 Z1 2 3 6.67 0.00 0.00 10.00 155.66


5−11Version 16.13

5.4. Polygonal Column Cross Section.

The following cross section is to be described (aqua1_polygon.dat):

Column cross section

A simple definition of the input may be defined with:

PROG AQUAHEAD EXAMPLE REINFORCED CONCRETENORM DIN 1045-1ECHO SECT EXTRECHO FULL EXTRCONC 1 C 20 ; STEE 11 BST 500SASECT 1 TITL 'POLYGON COLUMN SECTION'POLY ; VERT 1 0.000 0.000 2 -0.400 0.000 3 -0.550 -0.315 4 -0.750 -0.315 5 -0.750 -0.630 6 0.000 -0.630RF 101 -0.105 -0.105 55.44 102 -0.320 -0.077 36.96 103 -0.673 -0.392 24.64 104 -0.673 -0.525 36.96 105 -0.105 -0.525 36.96CUT 1 ZB -0.31CUT 2 ZB -0.11CUT 3 YB SCUT 4 YB -0.55END


Version 16.135−12

The printout starts with the materials, followed with an overview of all sectionalvalues. The materials show also some rarely used values. The chosen ECHO−Option shows also all the strain−stress laws of the materials which are availablethreefold for the selected design code DIN 1045−1, having different safety factorsand meaning of the safety factors.

Default design code is DIN 1045-1 (2001) (Germany)

No. 10 C 20/25 (DIN 1045-1)--------------------------------------------------------------------------------Youngs-modulus 24914 [MPa] Safetyfactor 1.50 [-]Poisson-Ratio 0.20 [-] Strength fc 17.00 [MPa]Shear-modulus 10381 [MPa] Nomin. strength fcn 20.00 [MPa]Compression modulus 13841 [MPa] Tens. strength fctm 2.21 [MPa]Weight 25.0 [kN/m3] 5 % t.strength fctk 1.55 [MPa]Weight buoyancy 25.0 [kN/m3] 95 % t.strength fctk 2.87 [MPa]Temp.elongat.coeff. 1.00E-05 [-] Bond strength fbd 2.32 [MPa] Service strength 28.00 [MPa] Fatigue strength 10.43 [MPa]Stress-Strain for serviceability eps[o/oo] sig-m[MPa] E-t[MPa]Is only valid within the defined 0.000 0.00 27405stress range -1.100 -21.50 12242 -2.200 -28.00 0 -3.400 -21.26 -10846 Safetyfactor 1.50Stress-Strain for ultimate load eps[o/oo] sig-u[MPa] E-t[MPa]Is only valid within the defined 0.000 0.00 17000stress range -2.000 -17.00 0 -3.500 -17.00 0 Safetyfactor 1.50Stress-Strain of calc. mean values eps[o/oo] sig-r[MPa] E-t[MPa]Is only valid within the defined 0.000 0.00 27405stress range -1.050 -12.64 4315 -2.100 -14.45 0 -3.500 -12.96 -1804 Safetyfactor 1.30

No. 11 BSt 500 SA (DIN 1045-1)--------------------------------------------------------------------------------Youngs-modulus 200000 [MPa] Safetyfactor 1.15 [-]Poisson-Ratio 0.30 [-] Yield stress fy 500.00 [MPa]Shear-modulus 76923 [MPa] Compr.yield val. fyc 500.00 [MPa]Compression modulus 166667 [MPa] Tens. strength ft 550.00 [MPa]Weight 78.5 [kN/m3] Compr. strength fc 550.00 [MPa]Weight buoyancy 78.5 [kN/m3] Ultim. plast. strain 25.00[o/oo]


5−13Version 16.13

Temp.elongat.coeff. 1.20E-05 [-] relative bond coeff. 1.00 [-]max. thickness 32.00 [mm] EC2 bondcoeff. K1 0.80 [-] Hardening modulus 0.00 [MPa] Proportional limit 500.00 [MPa] Dynamic stress range 195.00 [MPa]Stress-Strain for serviceability eps[o/oo] sig-m[MPa] E-t[MPa]Is also extended beyond the 1000.000 550.00 0defined stress range 25.000 550.00 2222 2.500 500.00 200000 0.000 0.00 200000 -2.500 -500.00 2222 -25.000 -550.00 0 -1000.000 -550.00 0 Safetyfactor 1.15Stress-Strain for ultimate load eps[o/oo] sig-u[MPa] E-t[MPa]Is also extended beyond the 1000.000 456.52 0defined stress range 25.000 456.52 952 2.174 434.78 200000 0.000 0.00 200000 -2.174 -434.78 952 -25.000 -456.52 0 -1000.000 -456.52 0 Safetyfactor ( 1.15)Stress-Strain of calc. mean values eps[o/oo] sig-r[MPa] E-t[MPa]Is also extended beyond the 1000.000 577.50 0defined stress range 25.000 577.50 1236 2.750 550.00 200000 0.000 0.00 200000 -2.750 -550.00 1236 -25.000 -577.50 0 -1000.000 -577.50 0 Safetyfactor 1.30

A listing of the two cross sections follows, since ECHO SECT has been activatedwith option FULL or EXTR. This section has rotated principal axis, or a non van-ishing centrifugal inertia Iyz. It is possible to rotate the section into the principleaxis with a definition at SECT, but this is not necessary for the SOFiSTiK analysissoftware.

Static properties of cross section MNo A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs y/z-sc modules gam MNs It[m4] [m2] [m4] [cm] [cm] [MPa] [kN/m] 10 3.8587E-01 1.180E-02 -32.24 -29.04 24914 9.65 11 1.801E-02 1.571E-02 -35.36 -36.45 10381 4.100E-03

Main axis of inertia rotated at -57.75 [°]Main moments of inertia 1.8297E-02 9.2113E-03 [m4]


Version 16.135−14

Additional static properties of cross section Alfa-T ymin zmin hymin AK MB Tau-T Tau-Vy ymax zmax hzmin AB Tau-B Tau-Vz [cm] [cm] [cm] [m2] [1/m3] [1/m2] 1.0E-05 -42.76 -27.64 2.142E-01 11 1.444E+01 4.007E+00 32.24 35.36 3.859E-01 4.218E+00

Section values for warpingWmin[m2] Wmax[m2] CM[m6] CMS[m4] ASwyy[m6] ASwzz[m6] ry[cm] rz[cm] -0.0353 0.0632 0.000 0.000 0.000 0.000

Design values of cross section MNo A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs modules gam MNs It[m4] [m2] [m4] [cm] [MPa] [kN/m] 10 3.8587E-01 1.180E-02 -32.24 19164 9.65 1.801E-02 1.571E-02 -35.36 7985 4.100E-03

Additional Design DataM periphery-O/-I deff t-min t-max SMP thet-p thet-y thet-z thet-yz [m2/m] [m2/m] [cm] [cm] [cm] [o/o] [tm2/m] [tm2/m] [tm2/m] [tm2/m] 2.644 29.19 0.0 0.688 0.295 0.393 0.102

Reinforcement global valuesLayer mS mR area lower-A upper-A yL zL L-tors N-prM-pr [cm2] [cm2] [cm2] [cm] [cm] [cm] [kN][kNm] 0 10 11 190.96 190.96 -32.98 -29.92

PolygonId. E Mat y z 1/WMy,Mz 1/WT 1/WVy 1/WVz W0 Air [cm] [cm] [1/m3] [1/m3] [1/m2] [1/m2] [m2] [-]1 10 0.00 0.00 25.1135 0.0000 0.0000 0.0000 1.00 -13.9712 0.0000 0.0000 0.00002 10 -40.00 0.00 34.8444 0.0000 0.0000 0.0000 1.00 14.0303 0.0000 0.0000 0.00003 10 -55.00 -31.50 9.1311 0.0000 0.0000 0.0000 1.00 16.8678 0.0000 0.0000 0.00004 10 -75.00 -31.50 13.9966 0.0000 0.0000 0.0000 1.00 30.8685 0.0000 0.0000 0.00005 10 -75.00 -63.00 -15.3658 0.0000 0.0000 0.0000 1.00 23.2054 0.0000 0.0000 0.00006 10 0.00 -63.00 -33.6114 0.0000 0.0000 0.0000 1.00 -29.2974 0.0000 0.0000 0.00001 10 0.00 0.00 25.1135 0.0000 0.0000 0.0000 1.00 -13.9712 0.0000 0.0000 0.0000


5−15Version 16.13

Single point reinforcementId. MNo y[cm] z[cm] T[°C] sig[MPa] As/As-max[cm2] Lay D Ar[m2]101 11 -10.50 -10.50 55.44 0102 11 -32.00 -7.70 36.96 0103 11 -67.30 -39.20 24.64 0104 11 -67.30 -52.50 36.96 0105 11 -10.50 -52.50 36.96 0

Cuts for shear designNo Type MNo yb zb ye ze b0 1/WTM,D FVy/z Ns/Ms MRF AsSU beta mue [cm] [cm] [cm] [cm] [cm] [1/m3] [-] [kN/m] R[cm2/m]1 WEB 10 -31.00 16.16 14.4444 1.000 0.00 11 3.87 54.76 0.0000 1.000 0.00 0 902 WEB 10 -11.00 16.16 14.4444 1.000 0.00 11 3.20 45.24 0.0000 1.000 0.00 0 903 WEB 10 -32.24 16.16 14.4444 1.000 0.00 11 4.46 63.00 0.0000 1.000 0.00 0 904 WEB 10 -55.00 16.16 14.4444 1.000 0.00 11 2.23 31.50 0.0000 1.000 0.00 0 90

Stress output locations on shear cutsTxt. MNo y z 1/WT 1/WVy 1/WVz sig-p W0 [cm] [cm] [1/m3] [1/m2] [1/m2] [MPa] [m2]1A 10 -54.76 -31.00 -14.4444 0.3271 4.2177 0.001 10 -46.68 -31.00 -14.4444 0.3271 4.2177 0.001 10 -8.08 -31.00 14.4444 0.3271 4.2177 0.001E 10 0.00 -31.00 14.4444 0.3271 4.2177 0.002A 10 -45.24 -11.00 -14.4444 0.0415 2.5983 0.002 10 -37.16 -11.00 -14.4444 0.0415 2.5983 0.002 10 -8.08 -11.00 14.4444 0.0415 2.5983 0.002E 10 0.00 -11.00 14.4444 0.0415 2.5983 0.003A 10 -32.24 -63.00 -14.4444 -3.3367 0.1054 0.003 10 -32.24 -54.92 -14.4444 -3.3367 0.1054 0.003 10 -32.24 -8.08 14.4444 -3.3367 0.1054 0.003E 10 -32.24 0.00 14.4444 -3.3367 0.1054 0.004A 10 -55.00 -63.00 -14.4444 -4.0073 -0.6235 0.004 10 -55.00 -54.92 -14.4444 -4.0073 -0.6235 0.004E 10 -55.00 -31.50 -14.4444 -4.0073 -0.6235 0.00

These is surely quite a lot of data. E.g. from the outer periphery the effective thick-ness deff = 29.19 cm is evaluated to be used for creep and shrinkage analysis.

While the evaluation of the area values for normal force and bending momentsis a trivial task, the evaluation of the shear from torsion and bending are open toquite a large range of possible solutions. A detailed analysis of the stress accord-ing to the theory of elasticity is no longer used nowadays for standard concrete,


Version 16.135−16

but may be performed with the option CTRL STYP 3 (eg. for prestressed con-crete). The shear resistance values of the polygon points are only assigned bythis integral equation method. For solid sections the warping resistance is alwayspreset to 0.0.

For the shear design the simple force method with section moduli is used here.But as the width of the tensile zone changes, it is recommended to define morethan just one shear cut at the centre of gravity. If you do not specify CUT−recordsyou will get a warning about this subject. Depending on the forces it might be use-ful to define inclined shear cuts, but for the biaxial shear design of such a section,the only way to get sound results may be the method of distinct struts in 3D.

Also the calculation of a reinforced concrete cross section subjected to torsion isnot an easy or single valued task. Shear stressing always means a check of thecompressive strength of the concrete by means of principal or shear stress limitsas well as a check for the required shear reinforcement. Both values are associ-ated.

The old DIN 1045 required the checking of the torsional shear stresses accordingto the elasticity theory; these can be computed best by the integral equationmethod (CTRL STYP 2 or 3).

By default AQUA always employs the most recent method that uses an equival-ent hollow cross section. While a fixed value for the width is specified by DIN4227, EC2 provides for an upper limit of the width A/U. When the width is reduced,the core cross section is increased leading thus to smaller reinforcement. At thesame time, however, the principal compressive stress becomes larger, so that alower limit is not only set by double the concrete cover but mainly by the principalcompressive stress. The new DIN 1045−1 uses a constant thickness defined bythe position of the longitudinal reinforcement.


5−17Version 16.13

When e.g. a cross section 1x1 m is considered, the following shear stresses areobtained:

Theory of elasticity 4.81 · MtIntegral equation method 4.74 · Mt

Equivalent cross section by DIN 4227 4.61 · MtEquivalent cross section by EC2 3.56 · Mt

Although the required link reinforcement for EC2 is higher because of the smallerAk.

Erroneous input (e.g. BMAX 999 in the record CUT or the torsional reinforcement)may generate unreasonable results for Ak. It is therefore essential that these val-ues are always critically checked.

In the next step the cross section is modified by setting the reinforcement to beeffective totally or partially for torsion with TORS ACTI. Thereby the Bredt’s boxis determined more exact. Although this has no influence on the other results, be-cause the torsional moment of inertia and the shear centre are determined withthe integral equation method.

RF 101 -0.105 -0.105 55.44 TORS ACTI Variant I 102 -0.320 -0.077 36.96 TORS ACTI 103 -0.673 -0.392 24.64 TORS ACTI 104 -0.673 -0.525 36.96 TORS ACTI 105 -0.105 -0.525 36.96 TORS ACTI

orRF 101 -0.105 -0.105 55.44 TORS ACTI Variant II 102 -0.320 -0.077 36.96 TORS PASS 103 -0.673 -0.392 24.64 TORS ACTI 104 -0.673 -0.525 36.96 TORS ACTI 105 -0.105 -0.525 36.96 TORS ACTI

orRF 101 -0.105 -0.105 55.44 TORS ACTI Variant III 102 -0.320 -0.077 36.96 TORS ADDI 103 -0.673 -0.392 24.64 TORS ACTI 104 -0.673 -0.525 36.96 TORS ACTI 105 -0.105 -0.525 36.96 TORS ACTI

orLRF 101 -0.105 -0.105 -0.320 -0.105 50.0 TORS ACTI Variant IV

102 -0.320 -0.105 -0.435 -0.392 50.0 TORS ACTI 103 -0.435 -0.392 -0.645 -0.392 50.0 TORS ACTI 104 -0.645 -0.392 -0.645 -0.525 50.0 TORS ACTI 105 -0.645 -0.525 -0.105 -0.525 50.0 TORS ACTI


Version 16.135−18

106 -0.105 -0.525 -0.105 -0.105 50.0 TORS ACTIor

CURF 2.9 D 12 TORS ACTI Variant V

The following table compares the important values of the different variants:the area Ak of the Bredt’s box. (required reinforcements)the torsional stress modulus Wtthe effectiveness of the torsional reinforcement L−tors defines the factor to convert Asl=mm2/m to absolute mm2.

Var. Ak [m2] 1/Wt [1/m3] L-Tors [cm]

0 0.2142 14.4444 -

I 0.1959 13.8979 181.09

II 0.1571 16.9968 217.92

III 0.1571 16.9968 175.74

IV 0.1500 17.7926 182.72

V 0.2982 19.2241 241.19


5−19Version 16.13

5.5. Polygonal Cross Section with Inner Perimeter.The following cross section (aqua3_bridge.dat) has one inner perimeter as wellas ineffective parts; attention must be paid to the sequence of the polygon verticesfor the internal ineffective areas. The inner perimeter in the following example wasdefined explicitly by means of a polygon with the material number 0. For a correctevaluation of the shear sections, with such an input, special care must be givento the planning of the duplicate edges. More variants to define this section maybe found in the example (aqua30.dat).

Polygonal cross section

Use of the symmetry can be made during the input:

PROG AQUAHEAD CROSS-SECTION WITH EFFECTIVE WIDTHS AND RECESSESNORM DIN 1045PAGE UNII 3 UNIO 3ECHO FULL EXTR ; CTRL STYP 0CONC 1 B 25 ; STEE 2 BST 500SECT 11 TITL 'Hollow Cross Section'POLY OPZVERT 1 3.00 4.00 2 3.50 0.75 3 5.00 0.60 ; 4 7.00 0.40 ; 5 7.00 0.00 6 5.00 0.00 7 0.45 0.00 ; 8 0.00 0.00POLY OPZ MNO 0VERT 9 0.00 0.50 10 0.45 0.50 11 2.75 0.50 PHI 3 12 2.50 3.50 PHI 4 13 0.00 3.50 PHI 3NEFF TYPE YZ YMIN 6.0 ZMIN 0.0 YMAX 6.0 ZMAX 0.6 WIDT 2.0NEFF TYPE YZ YMIN -6.0 ZMIN 0.0 YMAX -6.0 ZMAX 0.6 WIDT 2.0NEFF TYPE YZ YMIN 0.0 ZMIN 0.0 YMAX 0.0 ZMAX 0.5 WIDT 0.9

CUT 1 ZB S


Version 16.135−20

CUT 2 ZB 0.75CUT 3 ZB 3.00CUT 4 YB 2.00CUT 5 YB 0.00CUT 11 YB 2.0 4.5 2.0 3.0 11 YB 2.0 3.0 3.5 3.0CUT 12 YB 1.0 4.5 1.0 3.0 12 YB 1.0 3.0 3.5 3.0CUT 13 YB 0.0 4.5 0.0 3.0 13 YB 2.0 3.0 2.0 4.5 END

The output of the cross section is as follows:

Cross section No. 11 - Hollow section

Static properties of cross section Mat A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs y/z-sc modules gam NoR It[m4] [m2] [m4] [m] [m] [MPa] [kN/m] 1 1.4650E+01 3.068E+01 0.000 0.000 30000 366.25 2 2.787E+01 1.675E+02 1.456 1.169 12500

Additional static properties of cross section Alfa-T ymin zmin hymin AK MB Tau-T Tau-Vy ymax zmax hzmin AB Tau-B Tau-Vz [1/°K] [m] [m] [m] [m2] [1/m3] [1/m2] 1.0E-05 -5.000 -1.456 1.598E+01 2 6.258E-02 2.245E-01 5.000 2.544 1.465E+01 2.216E-01

Effective static properties of cross section Mat A[m2] Iy/Iz/Iyz ys/zs modules gam NoR [m4] [m] [MPa] [kN/m] 1 1.4650E+01 2.678E+01 0.000 30000 366.25 2 9.647E+01 1.673 12500

Design values of cross section Mat A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs modules gam NoR It[m4] [m2] [m4] [m] [MPa] [kN/m] 1 1.4650E+01 3.206E+01 0.000 30000 366.25 2.787E+01 9.647E+01 1.419 12500

Additional Design DataM periphery-O/-I deff t-min t-max SMP thet-p thet-y thet-z thet-yz [m2/m] [m2/m] [m] [m] [m] [o/o] [tm2/m] [tm2/m] [tm2/m] [tm2/m] 34.41 16.52 0.851 0.0 495.548 76.693 418.855 0.000


5−21Version 16.13

PolygonId. E Mat y z 1/WMy,Mz 1/WT 1/WVy 1/WVz W0 exp [m] [m] [1/m3] [1/m3] [1/m2] [1/m2] [m2] [-]1 1 3.000 4.000 0.0829 0.0000 0.0000 0.0000 1.00 -0.0179 0.0000 0.0000 0.00001' 1 -3.000 4.000 0.0829 0.0000 0.0000 0.0000 1.00 0.0179 0.0000 0.0000 0.00002' 1 -3.500 0.750 -0.0230 0.0000 0.0000 0.0000 1.00 0.0209 0.0000 0.0000 0.00003' 1 -5.000 0.600 -0.0279 0.0000 0.0000 0.0000 1.00 0.0298 0.0000 0.0000 0.00004' -* 1 -7.000 0.400 -0.0344 0.0000 0.0000 0.0000 1.00 0.0418 0.0000 0.0000 0.00005' -* 1 -7.000 0.000 -0.0475 0.0000 0.0000 0.0000 1.00 0.0418 0.0000 0.0000 0.00006' 1 -5.000 0.000 -0.0475 0.0000 0.0000 0.0000 1.00 0.0298 0.0000 0.0000 0.00007' 1 -0.450 0.000 -0.0475 0.0000 0.0000 0.0000 1.00 2.69E-3 0.0000 0.0000 0.00008 -* 1 0.000 0.000 -0.0475 0.0000 0.0000 0.0000 1.00 0.0000 0.0000 0.0000 0.00007 1 0.450 0.000 -0.0475 0.0000 0.0000 0.0000 1.00 -2.69E-3 0.0000 0.0000 0.00006 1 5.000 0.000 -0.0475 0.0000 0.0000 0.0000 1.00 -0.0298 0.0000 0.0000 0.00005 -* 1 7.000 0.000 -0.0475 0.0000 0.0000 0.0000 1.00 -0.0418 0.0000 0.0000 0.00004 -* 1 7.000 0.400 -0.0344 0.0000 0.0000 0.0000 1.00 -0.0418 0.0000 0.0000 0.00003 1 5.000 0.600 -0.0279 0.0000 0.0000 0.0000 1.00 -0.0298 0.0000 0.0000 0.00002 1 3.500 0.750 -0.0230 0.0000 0.0000 0.0000 1.00 -0.0209 0.0000 0.0000 0.00001 1 3.000 4.000 0.0829 0.0000 0.0000 0.0000 1.00 -0.0179 0.0000 0.0000 0.0000

Polygon holeId. E Mat y z 1/WMy,Mz 1/WT 1/WVy 1/WVz W0 exp [m] [m] [1/m3] [1/m3] [1/m2] [1/m2] [m2] [-]9 -* 1 0.000 0.500 -0.0312 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0.000010' 1 -0.450 0.500 -0.0312 0.0000 0.0000 0.0000 0.00 2.69E-3 0.0000 0.0000 0.0000 1 -1.217 0.500 -0.0312 0.0000 0.0000 0.0000 0.00 7.26E-3 0.0000 0.0000 0.0000 1 -1.983 0.500 -0.0312 0.0000 0.0000 0.0000 0.00 0.0118 0.0000 0.0000 0.000011' 1 -2.750 0.500 -0.0312 0.0000 0.0000 0.0000 0.00


Version 16.135−22

0.0164 0.0000 0.0000 0.0000 1 -2.688 1.250 -6.71E-3 0.0000 0.0000 0.0000 0.00 0.0160 0.0000 0.0000 0.0000 1 -2.625 2.000 0.0177 0.0000 0.0000 0.0000 0.00 0.0157 0.0000 0.0000 0.0000 1 -2.562 2.750 0.0422 0.0000 0.0000 0.0000 0.00 0.0153 0.0000 0.0000 0.000012' 1 -2.500 3.500 0.0666 0.0000 0.0000 0.0000 0.00 0.0149 0.0000 0.0000 0.0000 1 -1.667 3.500 0.0666 0.0000 0.0000 0.0000 0.00 9.95E-3 0.0000 0.0000 0.0000 1 -0.833 3.500 0.0666 0.0000 0.0000 0.0000 0.00 4.97E-3 0.0000 0.0000 0.000013 1 0.000 3.500 0.0666 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0.0000 1 0.833 3.500 0.0666 0.0000 0.0000 0.0000 0.00 -4.97E-3 0.0000 0.0000 0.0000 1 1.667 3.500 0.0666 0.0000 0.0000 0.0000 0.00 -9.95E-3 0.0000 0.0000 0.000012 1 2.500 3.500 0.0666 0.0000 0.0000 0.0000 0.00 -0.0149 0.0000 0.0000 0.0000 1 2.562 2.750 0.0422 0.0000 0.0000 0.0000 0.00 -0.0153 0.0000 0.0000 0.0000 1 2.625 2.000 0.0177 0.0000 0.0000 0.0000 0.00 -0.0157 0.0000 0.0000 0.0000 1 2.688 1.250 -6.71E-3 0.0000 0.0000 0.0000 0.00 -0.0160 0.0000 0.0000 0.000011 1 2.750 0.500 -0.0312 0.0000 0.0000 0.0000 0.00 -0.0164 0.0000 0.0000 0.0000 1 1.983 0.500 -0.0312 0.0000 0.0000 0.0000 0.00 -0.0118 0.0000 0.0000 0.0000 1 1.217 0.500 -0.0312 0.0000 0.0000 0.0000 0.00 -7.26E-3 0.0000 0.0000 0.000010 1 0.450 0.500 -0.0312 0.0000 0.0000 0.0000 0.00 -2.69E-3 0.0000 0.0000 0.00009 -* 1 0.000 0.500 -0.0312 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0.0000

PolygonId. E Mat y z 1/WMy,Mz 1/WT 1/WVy 1/WVz W0 exp [m] [m] [1/m3] [1/m3] [1/m2] [1/m2] [m2] [-]9 0 0.000 0.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.000010 0 0.450 0.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0 1.217 0.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0 1.983 0.500 0.0000 0.0000 0.0000 0.00


5−23Version 16.13

0.0000 0.0000 0.000011 0 2.750 0.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0 2.688 1.250 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0 2.625 2.000 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0 2.562 2.750 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.000012 0 2.500 3.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0 1.667 3.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0 0.833 3.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.000013 0 0.000 3.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0 -0.833 3.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0 -1.667 3.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.000012' 0 -2.500 3.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0 -2.562 2.750 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0 -2.625 2.000 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0 -2.688 1.250 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.000011' 0 -2.750 0.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0 -1.983 0.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000 0 -1.217 0.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.000010' 0 -0.450 0.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.00009' 0 0.000 0.500 0.0000 0.0000 0.0000 0.00 0.0000 0.0000 0.0000

Cuts for shear design No Type MNo yb zb ye ze b0 1/WTM,D FVy/z Ns/Ms MRF AsSU c mue [m] [m] [m] [m] [m] [1/m3] [-] [kN/m] R [cm2/m]1 WEB 1 1.673 1.412 0.0443 1.000 0.00 2 1.412 0.0000 1.000 0.00 1 902 WEB 1 0.750 1.542 0.0406 1.000 0.00 2 1.542 0.0000 1.000 0.00 1 903 WEB 1 3.000 1.224 0.0511 1.000 0.00 2


Version 16.135−24

1.224 0.0000 1.000 0.00 1 904 WEB 1 2.000 1.000 0.0626 1.000 0.00 2 1.000 0.0000 1.000 0.00 1 905 WEB 1 0.000 1.000 0.0626 1.000 0.00 2 1.000 0.0000 1.000 0.00 1 9011 WEB 1 2.000 4.500 2.000 3.000 0.500 0.0626 0.450 0.00 2 0.500 0.0000 0.450 0.00 1 9011 WEB 1 2.000 3.000 3.500 3.000 0.612 0.0511 0.550 0.00 2 0.612 0.0000 0.550 0.00 1 9012 WEB 1 1.000 4.500 1.000 3.000 0.500 0.0626 0.450 0.00 2 0.500 0.0000 0.450 0.00 1 9012 WEB 1 1.000 3.000 3.500 3.000 0.612 0.0511 0.550 0.00 2 0.612 0.0000 0.550 0.00 1 9013 WEB 1 0.000 4.500 0.000 3.000 0.500 0.0626 0.500 0.00 2 0.500 0.0000 0.500 0.00 1 9013 WEB 1 2.000 3.000 2.000 4.500 0.500 0.0626 0.500 0.00 2 0.500 0.0000 0.500 0.00 1 90

Construction and Selected Result PointsTxt. M y z 1/WMy,Mz 1/WT 1/WVy 1/WVz sig-p W0 sig/tau-d [m] [m] [1/m3] [1/m3] [1/m2] [1/m2] [MPa] [m2] [MPa]BOL 1 3.000 4.000 0.0829 0.0000 0.0000 0.0000 0.00 -0.0179 0.0000 0.0000 0.0000BOR 1 -3.000 4.000 0.0829 0.0000 0.0000 0.0000 0.00 0.0179 0.0000 0.0000 0.0000TOL 1 7.000 0.000 -0.0475 0.0000 0.0000 0.0000 0.00 -0.0418 0.0000 0.0000 0.0000TOR 1 -7.000 0.000 -0.0475 0.0000 0.0000 0.0000 0.00 0.0418 0.0000 0.0000 0.0000

Stress output locations on shear cutsTxt. MNo y z 1/WT 1/WVy 1/WVz sig-p W0 [m] [m] [1/m3] [1/m2] [1/m2] [MPa] [m2]1A 1 -3.358 1.673 -0.0443 2.92E-9 0.2216 0.001 1 -3.005 1.673 -0.0443 2.92E-9 0.2216 0.001E 1 -2.652 1.673 -0.0443 2.92E-9 0.2216 0.001A 1 2.652 1.673 0.0443 2.92E-9 0.2216 0.001 1 3.005 1.673 0.0443 2.92E-9 0.2216 0.001E 1 3.358 1.673 0.0443 2.92E-9 0.2216 0.002A 1 -3.500 0.750 -0.0406 9.62E-9 0.1875 0.002 1 -3.115 0.750 -0.0406 9.62E-9 0.1875 0.002E 1 -2.729 0.750 -0.0406 9.62E-9 0.1875 0.002A 1 2.729 0.750 0.0406 9.62E-9 0.1875 0.002 1 3.115 0.750 0.0406 9.62E-9 0.1875 0.002E 1 3.500 0.750 0.0406 9.62E-9 0.1875 0.003A 1 -3.154 3.000 -0.0511 8.07E-9 0.2210 0.003 1 -2.848 3.000 -0.0511 8.07E-9 0.2210 0.003E 1 -2.542 3.000 -0.0511 8.07E-9 0.2210 0.00


5−25Version 16.13

3A 1 2.542 3.000 0.0511 8.07E-9 0.2210 0.003 1 2.848 3.000 0.0511 8.07E-9 0.2210 0.003E 1 3.154 3.000 0.0511 8.07E-9 0.2210 0.004A 1 2.000 0.000 -0.0626 -0.2038 -0.0349 0.004 1 2.000 0.250 -0.0626 -0.2038 -0.0349 0.004E 1 2.000 0.500 -0.0626 -0.2038 -0.0349 0.004A 1 2.000 3.500 0.0626 -0.2038 -0.0349 0.004 1 2.000 3.750 0.0626 -0.2038 -0.0349 0.004E 1 2.000 4.000 0.0626 -0.2038 -0.0349 0.005A 1 0.000 0.000 -0.0626 -0.2245 -0.0593 0.005 1 0.000 0.250 -0.0626 -0.2245 -0.0593 0.005E 1 0.000 0.500 -0.0626 -0.2245 -0.0593 0.005A 1 0.000 3.500 0.0626 -0.2245 -0.0593 0.005 1 0.000 3.750 0.0626 -0.2245 -0.0593 0.005E 1 0.000 4.000 0.0626 -0.2245 -0.0593 0.0011A 1 2.000 4.000 -0.0626 0.0200 0.0519 0.0011 1 2.000 3.750 -0.0626 0.0200 0.0519 0.0011E 1 2.000 3.500 -0.0626 0.0200 0.0519 0.0011A 1 2.542 3.000 0.0511 0.0200 0.0519 0.0011 1 2.848 3.000 0.0511 0.0200 0.0519 0.0011E 1 3.154 3.000 0.0511 0.0200 0.0519 0.0012A 1 1.000 4.000 -0.0626 0.0270 0.0868 0.0012 1 1.000 3.750 -0.0626 0.0270 0.0868 0.0012E 1 1.000 3.500 -0.0626 0.0270 0.0868 0.0012A 1 2.542 3.000 0.0511 0.0270 0.0868 0.0012 1 2.848 3.000 0.0511 0.0270 0.0868 0.0012E 1 3.154 3.000 0.0511 0.0270 0.0868 0.0013A 1 0.000 4.000 -0.0626 0.0104 0.0776 0.0013 1 0.000 3.750 -0.0626 0.0104 0.0776 0.0013E 1 0.000 3.500 -0.0626 0.0104 0.0776 0.0013A 1 2.000 3.500 0.0626 0.0104 0.0776 0.0013 1 2.000 3.750 0.0626 0.0104 0.0776 0.0013E 1 2.000 4.000 0.0626 0.0104 0.0776 0.00

Section 11 deserves special attention. It consists of two parts. AQUA distributesthe shear on these parts in proportion to the section widths by 0.45 and 0.55(VYFK or VZFK).

In section 3, at the same location, one obtains the value 0.214 of the shear stressdue to Vz. Section 11, however, gives only 0.0505!. This happens because theseparated part is statically indeterminate. There is an additional shear flow goingthrough this section.

This problem can be corrected very easily by a second input. Since the true valueis known, one can modify the factors VZFK, which are computed for the secondsection by:


Version 16.135−26

VZFK = 0.45 · 0.214 / 0.0505 = 1.907

Since the sum of all VZFK must be 1.0, the value −0.907 results for the verticalsection. The following modified input is obtained:

CUT 11 YA 2.0 4.5 2.0 3.0 VZFK -0.907 11 YA 2.0 3.0 3.5 3.0 VZFK 1.907

If one would have made the cut along the symmetry axis of the cross section, thenone could have set the one shear flow to 0.0 and one could have directly input thefollowing:

CUT 11 YA 0.0 4.5 0.0 3.0 VZFK 0.000 11 YA 0.0 3.0 3.5 3.0 VZFK 1.000

Obtaining a known value for VYFK is somewhat more difficult. For this task onecan either employ the integral equation method (STYP 3) or an equivalent thin−walled cross section.

However, this scaling method though fails in state II, if the separated cross sectionpart contains no reinforcement.

As a further reasonable option the cross section is now additionally calculatedwith the integral equation method. Therefore the input is expanded with the record

CTRL STYP 3 ; ECHO IEQ

With this input one receives some slightly different cross section values and shearstresses:

Cross section No. 11 - Hollow section

Static properties of cross section Mat A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs y/z-sc modules gam NoR It[m4] [m2] [m4] [m] [m] [MPa] [kN/m] 1 1.4650E+01 8.947E+00 3.068E+01 0.000 0.000 30000 366.25 2 5.492E+01 3.804E+00 1.675E+02 1.456 1.891 12500

Additional static properties of cross section Alfa-T ymin zmin hymin AK MB Tau-T Tau-Vy ymax zmax hzmin AB Tau-B Tau-Vz [1/°K] [m] [m] [m] [m2] [1/m3] [1/m2] 1.0E-05 -5.000 -1.456 1.598E+01 2 5.594E-02 1.449E-01 5.000 2.544 1.465E+01 2.319E-01


5−27Version 16.13

Section values for warping Wmin[m2] Wmax[m2] CM[m6] CMS[m4] ASwyy[m6] ASwzz[m6] ry[m] rz[m] -4.104 4.101 0.000 0.000 -0.025 -0.004 0.001 -3.435

Effective static properties of cross section Mat A[m2] Iy/Iz/Iyz ys/zs modules gam NoR [m4] [m] [MPa] [kN/m] 1 1.4650E+01 2.678E+01 0.000 30000 366.25 2 9.647E+01 1.673 12500

Design values of cross section Mat A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs modules gam NoR It[m4] [m2] [m4] [m] [MPa] [kN/m] 1 1.4650E+01 8.947E+00 3.206E+01 0.000 30000 366.25 5.492E+01 3.804E+00 9.647E+01 1.419 12500

Additional Design DataM periphery-O/-I deff t-min t-max SMP thet-p thet-y thet-z thet-yz [m2/m] [m2/m] [m] [m] [m] [o/o] [tm2/m] [tm2/m] [tm2/m] [tm2/m] 34.41 16.52 0.851 0.0 495.548 76.693 418.855 0.000

Reinforcement global valuesLayer mS mR area lower-A upper-A yL zL L-tors N-pr M-pr [cm2] [cm2] [cm2] [m] [m] [m] [MN] [MNm] Z1 1 2 55.00 0.00 0.000 3.750 Z2 1 2 55.00 0.00 0.000 3.750

PolygonId. E Mat y z 1/WMy,Mz 1/WT 1/WVy 1/WVz W0 exp [m] [m] [1/m3] [1/m3] [1/m2] [1/m2] [m2] [-]1 1 3.000 4.000 0.0829 -0.0126 0.0126 -0.0277 -1.988 1.00 -0.0179 0.0121 -0.0131 0.0288 1 2.000 4.000 0.0829 -0.0551 0.0999 -0.1453 -1.927 1.00 -0.0119 0.0000 0.0000 0.0000 1 1.000 4.000 0.0829 -0.0559 0.1106 -0.0747 -0.966 1.00 -5.97E-3 0.0000 0.0000 0.0000 1 0.000 4.000 0.0829 -0.0559 0.1136 1.06E-4-2.71E-3 1.00 0.0000 0.0000 0.0000 0.0000 1 -1.000 4.000 0.0829 -0.0559 0.1106 0.0749 0.961 1.00 5.97E-3 0.0000 0.0000 0.0000 1 -2.000 4.000 0.0829 -0.0551 0.0999 0.1455 1.921 1.00 0.0119 0.0000 0.0000 0.00001' 1 -3.000 4.000 0.0829 -0.0126 0.0126 0.0281 1.982 1.00 0.0179 -0.0121 0.0131 0.0284 . . .

First you can see that the torsional moment of inertia is definitely bigger and theshear centre lies now below the centre of gravity. For an open cross section one


Version 16.135−28

would expect a displacement to the side of the main web, thus to the top, but forthis cross section the structural behaviour for torsion is mainly affected by theclosed box. Therefore the shear centre must be in the middle of the box. In theresult one also receives shear stresses at all polygonal points.

A very important point is that the integral equation method calculates more de-tailed shear stress distributions, which leads to higher stresses at reentrantcorners of the section. There are more details about this effect within the dataset.

Cuts for shear design No Type MNo yb zb ye ze b0 1/WTM,D FVy/z Ns/Ms MRF AsSU c mue [m] [m] [m] [m] [m] [1/m3] [-] [kN/m] R [cm2/m]1 WEB 1 1.673 1.412 -0.0330 1.000 0.00 2 1.412 -0.0129 1.000 0.00 1 902 WEB 1 0.750 1.542 -0.0275 0.000 0.00 2 1.542 -6.37E-3 1.000 0.00 1 903 WEB 1 3.000 1.224 -0.0380 1.000 0.00 2 1.224 -0.0100 1.000 0.00 1 904 WEB 1 2.000 1.000 -0.0467 -1.000 0.00 2 1.000 -9.06E-3 1.000 0.00 1 905 WEB 1 0.000 1.000 0.0468 -1.000 0.00 2 1.000 9.11E-3 -1.000 0.00 1 9011 WEB 1 2.000 4.500 2.000 3.000 0.500 -0.0471 3.811 0.00 2 0.500 -7.95E-3 -1.302 0.00 1 9011 WEB 1 2.000 3.000 3.500 3.000 0.612 0.0380 -2.811 0.00 2 0.612 0.0100 2.302 0.00 1 9012 WEB 1 1.000 4.500 1.000 3.000 0.500 -0.0469 3.076 0.00 2 0.500 -9.06E-3 -0.408 0.00 1 9012 WEB 1 1.000 3.000 3.500 3.000 0.612 0.0380 -2.076 0.00 2 0.612 0.0100 1.408 0.00 1 9013 WEB 1 0.000 4.500 0.000 3.000 0.500 -0.0468 9.157 0.00 2 0.500 -9.11E-3 0.001 0.00 1 9013 WEB 1 2.000 3.000 2.000 4.500 0.500 0.0471 -8.157 0.00 2 0.500 7.95E-3 0.999 0.00 1 90

Stress output locations on shear cutsTxt. MNo y z 1/WT 1/WVy 1/WVz sig-p W0 [m] [m] [1/m3] [1/m2] [1/m2] [MPa] [m2]1A 1 -3.358 1.673 -0.0459 0.0339 0.2218 0.00 -0.2121 1 -3.005 1.673 -0.0330 0.0321 0.2204 0.00 -0.4001E 1 -2.652 1.673 -0.0214 0.0359 0.2243 0.00 -0.5361A 1 2.652 1.673 0.0214 -0.0359 0.2244 0.00 0.5301 1 3.005 1.673 0.0330 -0.0321 0.2205 0.00 0.3961E 1 3.358 1.673 0.0459 -0.0339 0.2219 0.00 0.2092A 1 -3.500 0.750 -0.0237 0.0314 0.1314 0.00 -0.9162 1 -3.115 0.750 -0.0275 5.12E-3 0.1736 0.00 -1.5442E 1 -2.729 0.750 -0.0339 -0.0546 0.2318 0.00 -1.914


5−29Version 16.13

2A 1 2.729 0.750 0.0339 0.0546 0.2319 0.00 1.9092 1 3.115 0.750 0.0275 -5.12E-3 0.1737 0.00 1.5412E 1 3.500 0.750 0.0237 -0.0314 0.1314 0.00 0.9143A 1 -3.154 3.000 -0.0481 0.0595 0.2113 0.00 0.7063 1 -2.848 3.000 -0.0380 0.0621 0.2138 0.00 0.9333E 1 -2.542 3.000 -0.0254 0.0580 0.2039 0.00 1.2253A 1 2.542 3.000 0.0254 -0.0580 0.2040 0.00 -1.2333 1 2.848 3.000 0.0380 -0.0621 0.2139 0.00 -0.9383E 1 3.154 3.000 0.0481 -0.0595 0.2115 0.00 -0.7114A 1 2.000 0.000 -0.0558 -0.1328 -0.0826 0.00 2.3564 1 2.000 0.250 -0.0467 -0.1328 -0.0784 0.00 1.8564E 1 2.000 0.500 -0.0361 -0.1285 -0.0788 0.00 1.3564A 1 2.000 3.500 0.0361 -0.0978 0.1313 0.00 -0.9044 1 2.000 3.750 0.0471 -0.1023 0.1509 0.00 -1.4304E 1 2.000 4.000 0.0551 -0.0999 0.1453 0.00 -1.9275A 1 0.000 0.000 -0.0558 -0.1449 -4.73E-5 0.00 -1.06E-35 1 0.000 0.250 -0.0467 -0.1449 -4.64E-5 0.00 -1.16E-35E 1 0.000 0.500 -0.0375 -0.1449 -4.64E-5 0.00 -2.81E-35A 1 0.000 3.500 0.0377 -0.1136 -9.41E-5 0.00 -4.05E-35 1 0.000 3.750 0.0468 -0.1136 -9.41E-5 0.00 -2.61E-35E 1 0.000 4.000 0.0559 -0.1136 -1.06E-4 0.00 -2.71E-311A 1 2.000 4.000 -0.0551 0.0999 -0.1453 0.00 -1.92711 1 2.000 3.750 -0.0471 0.1023 -0.1509 0.00 -1.43011E 1 2.000 3.500 -0.0361 0.0978 -0.1313 0.00 -0.90411A 1 2.542 3.000 0.0254 -0.0580 0.2040 0.00 -1.23311 1 2.848 3.000 0.0380 -0.0621 0.2139 0.00 -0.93811E 1 3.154 3.000 0.0481 -0.0595 0.2115 0.00 -0.71112A 1 1.000 4.000 -0.0559 0.1106 -0.0747 0.00 -0.96612 1 1.000 3.750 -0.0469 0.1106 -0.0748 0.00 -0.71612E 1 1.000 3.500 -0.0377 0.1105 -0.0775 0.00 -0.46712A 1 2.542 3.000 0.0254 -0.0580 0.2040 0.00 -1.23312 1 2.848 3.000 0.0380 -0.0621 0.2139 0.00 -0.93812E 1 3.154 3.000 0.0481 -0.0595 0.2115 0.00 -0.71113A 1 0.000 4.000 -0.0559 0.1136 1.06E-4 0.00 -2.71E-313 1 0.000 3.750 -0.0468 0.1136 9.41E-5 0.00 -2.61E-313E 1 0.000 3.500 -0.0377 0.1136 9.41E-5 0.00 -4.05E-313A 1 2.000 3.500 0.0361 -0.0978 0.1313 0.00 -0.90413 1 2.000 3.750 0.0471 -0.1023 0.1509 0.00 -1.43013E 1 2.000 4.000 0.0551 -0.0999 0.1453 0.00 -1.927


Version 16.135−30

5.6. Polygonal Cross Section with Interpolation

In this example (aqua31_bridge.dat) a similar bridge section is presented,defined via the reference−template with a lot of methods for interpolation for thetransverse inclination and the elevation.

The definition of the section describes all coordinates with reference to three dis-tinct points “upper−middle”, “upper−right” and “lower middle”:

PROG AQUAHEAD CROSS SECTION WITH EFFECTIVE WIDTH AND RECESSES HEAD TEMPLATES FOR INTERPOLATION AND INCLINED TOP DECK NORM DIN 1045 PAGE UNII 3 UNIO 3 ECHO FULL EXTR ; CTRL STYP 0 CONC 1 B 25 ; STEE 2 BST 500$LET#PAR 0,1,2LOOP#1 2 $ 2nd Section needed for InterpolationSECT 11+#1 TITL 'Hollow section'$ LET#PAR(0) 4.00-0.70*#1 $ Total height LET#PAR(1) 3.60+0.80*#1 $ upper width of box LET#PAR(2) 3.50+0.80*#1 $ lower width of box$ SPT OM 0.00 0.00 MNO 0 REFS AXIS $ MAIN AXIS SPT UM 0.00 #par(0) MNO 0 REFS A_UM $ LOWER MIDDLE$ SPT OR #par(1) 0.00 MNO 0 REFP OM INCR $ UPPER RIGHT SPT OL -#par(1) 0.00 MNO 0 REFP OM INCL $ UPPER LEFT SPT UR #par(2) 0.00 MNO 0 REFP UM $ LOWER RIGHT


5−31Version 16.13

SPT UL -#par(2) 0.00 MNO 0 REFP UM $ LOWER LEFT SPT UX 0.00 -0.22 MNO 0 REFP UM $ LOWER CENTRE$POLY OVERT 11 0.00 0.00 REFP UR 12 0.90 0.00 REFP OR +UR 13 5.50 0.60 REFP OM +OR 14 7.50 0.40 REFP OM +OR 15 7.50 0.00 REFP OM +OR 16 5.50 0.00 REFP OM +OR 17 0.45 0.00 REFP OM ~OR 18 0.00 0.00 REFP OM ~OR 19 0.45 0.00 REFP OM ~OL 20 5.50 0.00 REFP OM +OL 21 7.50 0.00 REFP OM +OL 22 7.50 -.40 REFP OM +OL 23 5.50 -.60 REFP OM +OL 24 0.90 0.00 REFP OL +UL 25 0.00 0.00 REFP UL$POLY O MNO 0VERT A1 0.00 0.50 REFP OM ~OR A2 0.45 0.50 REFP OM ~OR A3 2.75 0.50 REFP OM +OR A4 2.50 -.50 REFP UM A5 -2.50 -.50 REFP UM A6 2.75 -.50 REFP OM +OL A7 0.45 -.50 REFP OM ~OL A8 0.00 -.50 REFP OM ~OL $CIRC 100 0.0 -0.3 REFP UM REFR UXCIRC 101 +1.0 -0.3 -0.1 REFP UMCIRC 102 -1.0 -0.3 -0.1 REFP UM$NEFF TYPE YZ YMIN 6.5 ZMIN -1.0 YMAX 6.5 ZMAX 1.0 WIDT 2.0 REFI OM RFDI +ORNEFF TYPE YZ YMIN -6.5 ZMIN -1.0 YMAX -6.5 ZMAX 1.0 WIDT 2.0 REFI OM RFDI -OLNEFF TYPE YZ YMIN 0.0 ZMIN -1.0 YMAX 0.0 ZMAX 1.0 WIDT 0.9 REFI OM RFDI ~OR$RF p1 Y -0.25 -0.25 REFP 11 AS 12.0 LAY 1 TORS ACTIRF p2 Y +0.25 -0.25 REFP 25 AS 12.0 LAY 1 TORS ACTI$LRF 1 YB -0.10 -0.15 REFA 11 $$ YE +0.10 -0.15 REFE 25 AS 1.0 LAY 1 TORS ACTILRF 2 YB -0.10 +0.12 REFA 16 $$ YE +0.10 -0.12 REFE OR -OM AS 1.0 LAY 2 TORS PASSLRF 2 YB +0.10 -0.12 REFA OR -OM $$ YE +0.55 +0.12 REFE OM -OR AS 1.0 LAY 2 TORS ACTILRF 2 YB +0.55 -0.12 REFA OM -OL $$


Version 16.135−32

YE +0.10 +0.12 REFE OL -OM AS 1.0 LAY 2 TORS ACTILRF 2 YB +0.10 +0.12 REFA OL -OM $$ YE +0.10 +0.12 REFE 20 AS 1.0 LAY 2 TORS PASSLRF 3 YB -0.10 -0.15 REFA 11 $$ YE +0.10 -0.12 REFE OR -OM AS 1.0 LAY 3LRF 4 YB +0.10 -0.15 REFA 25 $$ YE +0.10 +0.12 REFE OL -OM AS 1.0 LAY 4$CRF 100 0.0 -0.3 0.12 REFP UM AS 1.13CRF 101 +1.0 -0.3 0.12 REFP UM AS 1.13CRF 102 -1.0 -0.3 0.12 REFP UM AS 1.13$CUT 1 ZB SCUT 2 REFA 24 REFE 12CUT 3 ZB 3.00CUT 4 YB 2.00CUT 5 YB 0.00CUT 11 YB 2.0 0.5 2.0 -1.0 REFA UM REFE UM 11 YB 2.0 -1.0 1.0 -1.0 REFA UM REFE URCUT 12 YB 1.0 0.5 1.0 -1.0 REFA UM REFE UM 12 YB 1.0 -1.0 1.0 -1.0 REFA UM REFE URCUT 13 YB 0.0 0.5 0.0 -1.0 REFA UM REFE UM 13 YB 0.0 -1.0 1.0 -1.0 REFA UM REFE UR$WPAR 0 TRAF 2.500WPAR 1 ICE 0.200WPAR 2 ZMAX 5.200$ENDLOOP

Then one may create other sections via linear interpolation:

$ INTERPOLATION WITH FACTOR INTE 13 11 12 0.5


5−33Version 16.13

Or one may generate for a general curved structure all sections defined by threereference lines:

PROG SOFIMSHCHEAD AXIS IN PLAN VIEW AND ELEVATIONHEAD 3D EXTRUSION WITH INCLINATION AND CHANGE OF WIDTHSYST SPAC GDIR POSZ GDIV 1000GAX 'AXIS' TYPE AXIS GAXA S 0.0 X 0.00 SX 1.0 L 80.0 RA 75 GAXP S 0.0 ALF 10 INCR -0.02 +0.02 GAXP S 80.0 ALF 0 INCR +0.04 -0.02GAX 'A_OR' TYPE BGEO GAXA 0.0 Y 3.60 SX 1.0 L 80.0 RA 71GAX 'A_UM' TYPE BGEO GAXA 0.0 SX 1.0 L 80.0 RA 75 GAXH 0.0 -8.0 40.0 -5.0 R 1600 80.0 -4.0$SPT 100 0.0 0.00 0.00 ; 110 65.00 37.50 0.00SLN 100 100 110 REF AXIS GRP 1 'B' 11 TITL 'CENTER-LINE'CTRL MESH 1 ; CTRL HMIN 10.0 ; CTRL LSUP 1END

PROG AQUAHEAD INTERPOLATE ALL SECTIONSECHO SECTINTE 0 NREF 100END


Version 16.135−34

5.7. Thin−walled Steel Box.

A twin−cell non−symmetric box with different plate thickness’ is examined now(aqua4_thinwalled.dat):

Thin−walled steel box

The input is as follows:

PROG AQUAHEAD THIN-WALLED STEEL BOXNORM DIN 18800PAGE UNII 2 ; ECHO SECT EXTRSTEE 1 S 235SECT 1PLAT 101 -160 000 000 000 16 OUT E $ UPPER FLANGE PLATES 102 000 = 160 = = 103 160 = 560 = = OUT A 104 560 = 610 = =PLAT 202 000 350 160 350 16 $ LOWER FLANGE PLATES 203 160 = 560 = = OUT APLAT 301 000 000 000 350 20 OUT M $ WEB PLATES 302 160 = 160 = 15 OUT M 303 560 = 560 = 10 OUT MSPT ABOV 280 000 CDYN B4W0 WEB 160 170 CDYN 201.9 BELO 280 350 CDYN B4W0 99.9 DS-1 280 350 CDYN WI DS-2 280 350 CDYN WII DS-3 280 350 CDYN WIII DS-4 280 350 CDYN KIII


5−35Version 16.13

EN 280 350 SIGC 71 71/sqr(3)END

All the cross section properties are always calculated for this cross section type.CTRL STYP does not have any effect here. In the table of the cross section prop-erties one can now also find the warping resistance and the warping shear resist-ance, the shear deformation area, as well as the coordinates of the shear centre,which differ to those of the centre of gravity. The torsional moment of inertia of125895.7 cm4 , amounts to 52 percent of the polar moment of inertia. The shearareas are approximately one third of the cross sectional area.

The table of additional cross section properties includes the maximum shearstresses due to unit internal forces. Unit warping and shear stresses are shownfor the panel elements.

Cross section No. 1

Static properties of cross section MNo A[cm2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs y/z-sc modules gam MNs It[cm4] [cm2] [cm4] [mm] [mm] [N/mm2] [kN/m] 1 370.30 175.23 80314.5 218.2 192.6 210000 2.91 125895.7 128.07 163761.3 159.1 171.5 81000 -2798.57 8225.5

Main axis of inertia rotated at -84.42 [°]Main moments of inertia 1.6456E+05 7.9511E+04 [cm4]

Additional static properties of cross section Alfa-T ymin zmin hymin AK MB Tau-T Tau-Vy ymax zmax hzmin AB Tau-B Tau-Vz [mm] [mm] [mm] [cm2] [1/m3] [1/m2] 1.2E-05 -378.2 -167.1 1.900E+03 2.661E+02 6.914E+01 391.8 198.9 1.456E+03 8.798E+01

Section values for warpingWmin[cm2] Wmax[cm2] CM[cm6] CMS[cm4] ASwyy[cm6] ASwzz[cm6] ry[mm] rz[mm] -80.24 194.23 800381.94 5487.6 2073258.62 228479.17

Design values of cross section MNo A[cm2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs modules gam MNs It[cm4] [cm2] [cm4] [mm] [N/mm2] [kN/m] 1 370.30 175.23 80314.5 218.2 190909 2.91 125895.7 128.07 163761.3 159.1 73636 8225.5


Version 16.135−36

Design forces and moments(C/E = characteristic plastic/elastic, D=plast.Design, F=elast. Design) N[kN] Vy[kN] Vz[kN] Mt[kNm] My[kNm] Mz[kNm] y[mm] z[mm] BUCKC 8887.2 2948.64 2182.38 544.12 1209.46 1548.79 163.2 137.7 B BC -463.4 1214.43 0.00 0.0 159.1 COMBC 1573.5 0.00 1612.14 218.2 0.0 COMBE 8887.2 2004.15 1574.93 520.79 950.07 958.17 218.2 159.1D 8079.3 2680.58 1983.99 494.65 1099.51 1407.99 163.2 137.7D -421.3 1104.03 0.00 0.0 159.1 COMBD 1430.5 0.00 1465.58 218.2 0.0 COMBF 8079.3 1821.95 1431.75 473.45 863.70 871.07 218.2 159.1

Additional Design DataM periphery-O/-I deff t-min t-max SMP thet-p thet-y thet-z thet-yz [m2/m] [m2/m] [mm] [mm] [mm] [o/o] [tm2/m] [tm2/m] [tm2/m] [tm2/m] 4.760 15.6 10.0 20.0 0.0 0.192 0.063 0.129 0.006

Thin elementsId. MNo y-B z-B y-E z-E t W-B/W-E Tau-T/B Tau-Vy/z xS [mm] [mm] [mm] [mm] [mm] [cm2] [1/m3] [1/m2]101 1 -160.0 0.0 0.0 0.0 16.0 1.94E+02 1.27E+01 2.77E+01 free -8.02E+01 1.37E+03 2.89E+01 0.12102 1 0.0 0.0 160.0 0.0 16.0 -8.02E+01 1.66E+02 6.24E+01 0.12 -4.59E+01 6.52E+02 -2.72E+01 0.09103 1 160.0 0.0 560.0 0.0 16.0 -4.59E+01 1.74E+02 6.91E+01 0.04 8.03E+01 -1.19E+03 -5.15E+01 0.03104 1 560.0 0.0 610.0 0.0 16.0 8.03E+01 1.27E+01 1.18E+01 0.20 -5.47E+00 -2.34E+02 -1.11E+01 free202 1 0.0 350.0 160.0 350.0 16.0 5.37E+01 -1.66E+02 5.18E+01 0.12 3.05E+01 6.05E+02 4.14E+01 0.09203 1 160.0 350.0 560.0 350.0 16.0 3.05E+01 -1.74E+02 5.95E+01 0.04 -6.81E+01 6.91E+02 4.88E+01 0.03301 1 0.0 0.0 0.0 350.0 20.0 -8.02E+01 -1.39E+02 2.91E+01 0.05 5.37E+01 -6.61E+02 5.86E+01 0.05302 1 160.0 0.0 160.0 350.0 15.0 -4.59E+01 -2.05E+01 -6.63E+00 0.05 3.05E+01 -4.26E+02 7.37E+01 0.05303 1 560.0 0.0 560.0 350.0 10.0 8.03E+01 2.66E+02 -4.42E+01 0.05 -6.81E+01 1.46E+03 8.80E+01 0.05

Construction and Selected Result PointsTxt. M y z 1/WMy,Mz 1/WT 1/WVy 1/WVz sig-p W0 sig/tau-d [mm] [mm] [1/m3] [1/m3] [1/m2] [1/m2] [MPa] [cm2] [MPa]OBEN 1 280.0 0.0 -203.0305 161.3251 67.2679 -27.589 0.0 -8.07 169.7 -47.9217 0.0000 0.0000 0.0000 t = 16.0 B4W0 98.0STEG 1 160.0 170.0 17.2757 0.0000 0.0000 0.0000 0.0 -8.81 201.9 36.4214 -8.5836 -1.3463 73.5698 t = 15.0 expl 116.6UNTE 1 280.0 350.0 235.0100 -161.325 58.9582 20.1523 0.0 0.94 99.9 -25.9195 0.0000 0.0000 0.0000 t = 16.0 B4W0 98.0


5−37Version 16.13

DS-1 1 280.0 350.0 235.0100 -161.325 58.9582 20.1523 0.0 0.94 194.0 -25.9195 0.0000 0.0000 0.0000 t = 16.0 WI 112.0DS-2 1 280.0 350.0 235.0100 -161.325 58.9582 20.1523 0.0 0.94 146.0 -25.9195 0.0000 0.0000 0.0000 t = 16.0 WII 112.0DS-3 1 280.0 350.0 235.0100 -161.325 58.9582 20.1523 0.0 0.94 142.0 -25.9195 0.0000 0.0000 0.0000 t = 16.0 WIII 112.0DS-4 1 280.0 350.0 235.0100 -161.325 58.9582 20.1523 0.0 0.94 163.0 -25.9195 0.0000 0.0000 0.0000 t = 16.0 KIII 129.0EN 1 280.0 350.0 235.0100 -161.325 58.9582 20.1523 0.0 0.94 71.0 -25.9195 0.0000 0.0000 0.0000 t = 16.0DIF 41.0

The full plastic internal forces are output in the first line as individual componentswith and without material safety factor, and the axial force / bending moment com-binations are output in the following lines. The cross section’s design values arereally only of interest for composite cross sections.

The following drawings show the shear stress distribution resulting from torsionalmoment and shear force as well as unit warping.

The input for AQUP is:

PROG AQUPSECT 1 WSIZE LP SPLI 2X2S MT 1.0 ; SECT 1 TAUS VY 1.0 ; SECT 1 TAUS VZ 1.0 ; SECT 1 TAUS MT2 1.0 ; SECT 1 TAU END

Further graphics are created with the given input data.


Version 16.135−38

Shear force and torsion

Warping


5−39Version 16.13

For this section eight stress points have been defined with a specification of theclass and notch−intensity according to DIN 15018. This allows the design for fa-tigue of a dynamic stress range in AQB.

PROG AQBHEAD FATIGUE STRESS CHECKECHO STRE 3+8S 1 1 0 N -300 MY 160 = = = N -300 MY -150 = = = N -50 MY 90STRE K FEND

Stresses [MPa]Beam x[m] NoS LC M A sig- sig+ tau sig-I sig-II sig-v N/Npl* H sig-1- sig-1+ tau-Vz tau-T sig-s dsig-s Q sig-2- sig-2+ tau-Vy tau-T2 sig-W- sig-W+ 1 0.000 1 0 1 A -45.5 33.9 0.0 33.9 -45.5 45.5 0.28 H -41.6 31.7 0.0 0.0 Q -4.3 -12.0 0.0 1 A -47.5 27.0 0.0 27.0 -47.5 47.5 0.26 H 23.3 -45.4 0.0 0.0 Q -11.7 -4.4 0.0 1 A -22.4 22.3 0.0 22.3 -22.4 22.4 0.19 H -20.2 21.1 0.0 0.0 Q 0.8 -3.6 0.0 MIN Vert OBEN -40.6 0.0 0.0 -40.6 19.6 MAX Vert OBEN 22.4 0.0 22.4 0.0 40.6 DIF Vert OBEN 62.9 0.0 22.4 40.6 21.0 FAK Vert OBEN -0.55 1.00 0.00 0.00 0.48 DIN 4132/15018: zul sig-(fak) = 218.9 utilisation 0.185 zul sig+(fak) = 206.9 utilisation 0.108 MIN Vert UNTE -43.4 0.0 0.0 -43.4 19.8 MAX Vert UNTE 29.5 0.0 29.5 0.0 43.4 DIF Vert UNTE 72.9 0.0 29.5 43.4 23.6 FAK Vert UNTE -0.68 1.00 0.00 0.00 0.46 DIN 4132/15018: zul sig-(fak) = 118.9 utilisation 0.365 zul sig+(fak) = 114.5 utilisation 0.258 MIN Vert DS-1 -43.4 0.0 0.0 -43.4 19.8 MAX Vert DS-1 29.5 0.0 29.5 0.0 43.4 DIF Vert DS-1 72.9 0.0 29.5 43.4 23.6 FAK Vert DS-1 -0.68 1.00 0.00 0.00 0.46 DS 804 App. 6 : zul sig-(fak) = 111.3 utilisation 0.389 zul sig+(fak) = 111.3 utilisation 0.265


Version 16.135−40

MIN Vert DS-2 -43.4 0.0 0.0 -43.4 19.8 MAX Vert DS-2 29.5 0.0 29.5 0.0 43.4 DIF Vert DS-2 72.9 0.0 29.5 43.4 23.6 FAK Vert DS-2 -0.68 1.00 0.00 0.00 0.46 DS 804 App. 6 : zul sig-(fak) = 84.9 utilisation 0.511 zul sig+(fak) = 84.5 utilisation 0.349 MIN Vert DS-3 -43.4 0.0 0.0 -43.4 19.8 MAX Vert DS-3 29.5 0.0 29.5 0.0 43.4 DIF Vert DS-3 72.9 0.0 29.5 43.4 23.6 FAK Vert DS-3 -0.68 1.00 0.00 0.00 0.46 DS 804 App. 6 : zul sig-(fak) = 77.2 utilisation 0.562 zul sig+(fak) = 77.7 utilisation 0.379 MIN Vert DS-4 -43.4 0.0 0.0 -43.4 19.8 MAX Vert DS-4 29.5 0.0 29.5 0.0 43.4 DIF Vert DS-4 72.9 0.0 29.5 43.4 23.6 FAK Vert DS-4 -0.68 1.00 0.00 0.00 0.46 DS 804 App. 6 Tab 32: zul sig-(fak) = 91.1 utilisation 0.476 zul sig+(fak) = 91.1 utilisation 0.324 MIN Vert EN -43.4 0.0 0.0 -43.4 19.8 MAX Vert EN 29.5 0.0 29.5 0.0 43.4 DIF Vert EN 72.9 0.0 29.5 43.4 23.6 FAK Vert EN -0.68 1.00 0.00 0.00 0.46 zul delta-sig = 71.0 utilisation 1.026 zul delta-tau = 41.0 utilisation 0.000


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5.8. Composite Section.

The following cross section describes a square steel shape with concrete core(aqua5_composite.dat):

Composite cross section

The steel is defined as a a hollow profile, then the concrete core is inserted.

PROG AQUAHEAD EXAMPLES COMPOSITE SECTIONSNORM DIN 1045ECHO FULLCTRL RFCS 2 ; CTRL STYP 3 ; CTRL SCUT 0CONC 1 B 25 SCM 1.5 ; STEE 2 S 235 ; STEE 3 BST 500SECT 1 2 $ Steel column with concrete centrePOLY OPZ 2 ; VERT 101 0.15 0.15 102 0.15 -0.15POLY IPZ 2 ; VERT 103 0.14 0.14 104 0.14 -0.14POLY OPZ 1 ; VERT 201 0.14 0.14 202 0.14 -0.14CUT 1 YB -0.15 YE -0.14 MNO 2 1 YB -0.14 YE 0.14 MNO 1 MRF 3 1 YB 0.14 YE 0.15 MNO 2 END

The section values are all ideal section values. The values refer to the steel mater-ial, which was defined with the record SECT. The area is calculated as follows:

Ai = Asteel + Aconc·Econc/Esteel =

= 0.0116 + 0.0784·3/21 = 0.0228

One can not use this area as it is for the determination of the dead load, thus theprogram immediately calculates the dead load per unit length.


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γi = ( Asteel·γsteel + Aconc·γconc ) / Ai =

= ( 0.0116·78.5 + 0.0784·25.0 ) = 2.871

With ECHO FULL the material values and the additional static properties of crosssection, the partial cross sections, the design values of cross section and thedesign forces and moments are printed additionally to the static properties ofcross section. Since a composite cross section is concerned, AQUA determinesthe latter for positive and negative moments, because these are different in non−symmetric cross sections.

No. 1 B 25 (DIN 1045)--------------------------------------------------------------------------------Youngs-modulus 30000 [MPa] Safetyfactor 1.50 [-]Poisson-Ratio 0.20 [-] Strength fc 17.50 [MPa]Shear-modulus 12500 [MPa] Nomin. strength fcn 25.00 [MPa]Compression modulus 16667 [MPa] Tens. strength fctm 2.56 [MPa]Weight 25.0 [kN/m3] 5 % t.strength fctk 2.14 [MPa]Weight buoyancy 25.0 [kN/m3] 95 % t.strength fctk 3.08 [MPa]Temp.elongat.coeff. 1.00E-05 [-] Bond strength fbd 1.80 [MPa] Fatigue strength 0.00 [MPa]Stress-Strain for serviceability eps[o/oo] sig-m[MPa] E-t[MPa]Is also extended beyond the 0.000 0.00 30000defined stress range -0.583 -17.50 0 -1000.000 -17.50 0 Safetyfactor 1.50Stress-Strain for ultimate load eps[o/oo] sig-u[MPa] E-t[MPa]Is only valid within the defined 0.000 0.00 17500stress range -2.000 -17.50 0 -3.500 -17.50 0 Safetyfactor 1.50

No. 2 S 235 (DIN 18800)--------------------------------------------------------------------------------Youngs-modulus 210000 [MPa] Safetyfactor 1.10 [-]Poisson-Ratio 0.30 [-] Yield stress fy 240.00 [MPa]Shear-modulus 81000 [MPa] Compr.yield val. fyc 240.00 [MPa]Compression modulus 171821 [MPa] Tens. strength ft 360.00 [MPa]Weight 78.5 [kN/m3] Compr. strength fc 360.00 [MPa]Weight buoyancy 78.5 [kN/m3] Ultim. plast. strain 0.00[o/oo]Temp.elongat.coeff. 1.20E-05 [-] relative bond coeff. 0.00 [-]max. thickness 40.00 [mm] EC2 bondcoeff. K1 0.00 [-] Hardening modulus 0.00 [MPa] Proportional limit 240.00 [MPa] Dynamic stress range 0.00 [MPa]


5−43Version 16.13

Stress-Strain for serviceability eps[o/oo] sig-m[MPa] E-t[MPa]Is also extended beyond the 1000.000 240.00 0defined stress range 1.143 240.00 210000 0.000 0.00 210000 -1.143 -240.00 0 -1000.000 -240.00 0 Safetyfactor 1.10Stress-Strain for ultimate load eps[o/oo] sig-u[MPa] E-t[MPa]Is also extended beyond the 1000.000 240.00 0defined stress range 1.143 240.00 210000 0.000 0.00 210000 -1.143 -240.00 0 -1000.000 -240.00 0 Safetyfactor 1.10

Cross section No. 1

Static properties of cross section MNo A[cm2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs y/z-sc modules gam MNs It[cm4] [cm2] [cm4] [mm] [mm] [N/mm2] [kN/m] 2 228.00 173.99 23596.0 0.0 0.0 210000 2.87 39715.8 173.99 23596.0 0.0 0.0 81000 250.52

Additional static properties of cross section Alfa-T ymin zmin hymin AK MB Tau-T Tau-Vy ymax zmax hzmin AB Tau-B Tau-Vz [mm] [mm] [mm] [cm2] [1/m3] [1/m2] 1.2E-05 -150.0 -150.0 8.947E+02 4.645E+02 1.709E+01 150.0 150.0 7.840E+02 6.751E+01

Section values for warpingWmin[cm2] Wmax[cm2] CM[cm6] CMS[cm4] ASwyy[cm6] ASwzz[cm6] ry[mm] rz[mm] -21.80 22.28 0.00 0.0 294.50 294.50

Partial cross sections MNo A[cm2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs modules gam MNs It[cm4] [cm2] [cm4] [mm] [N/mm2] [kN/m] 2 116.00 50.27 16278.7 0.0 210000 0.91 24414.1 50.27 16278.7 0.0 81000

1 784.00 801.70 51221.3 0.0 30000 1.96 99154.7 801.70 51221.3 0.0 12500


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Design values of cross section MNo A[cm2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs modules gam MNs It[cm4] [cm2] [cm4] [mm] [N/mm2] [kN/m] 2 198.13 141.00 21644.7 0.0 190909 1.56 35635.3 141.00 21644.7 0.0 73636

Design forces and moments(C/E = characteristic plastic/elastic, D=plast.Design, F=elast. Design) N[kN] Vy[kN] Vz[kN] Mt[kNm] My[kNm] Mz[kNm] y[mm] z[mm] BUCKC 2784.0 696.57 696.57 409.27 334.67 334.67 47.3 -47.3 b bC -686.0 759.07 350.90 0.00 0.0 0.0 COMBC -686.0 759.07 0.00 350.90 0.0 0.0 COMBC -4156.0 821.57 821.57 409.27 -334.67 -334.67 -47.3 47.3C -686.0 759.07 -350.90 0.00 0.0 0.0 COMBC -686.0 759.07 0.00 -350.90 0.0 0.0 COMBE 5472.0 1928.70 1928.70 298.32 206.47 206.47 0.0 0.0E -2793.0 1829.47 1829.47 152.68 -206.47 -206.47 0.0 0.0D 2530.9 633.24 633.24 372.07 298.64 298.64 38.1 -38.1D -457.3 674.91 307.36 0.00 0.0 0.0 COMBD -457.3 674.91 0.00 307.36 0.0 0.0 COMBD -3445.6 746.88 746.88 372.07 -298.64 -298.64 -38.1 38.1D -457.3 674.91 -307.36 0.00 0.0 0.0 COMBD -457.3 674.91 0.00 -307.36 0.0 0.0 COMBF 4974.5 1753.37 1753.37 271.20 137.64 137.64 0.0 0.0F -1862.0 1663.16 1663.16 138.80 -137.64 -137.64 0.0 0.0

Additional Design DataM periphery-O/-I deff t-min t-max SMP thet-p thet-y thet-z thet-yz [m2/m] [m2/m] [mm] [mm] [mm] [o/o] [tm2/m] [tm2/m] [tm2/m] [tm2/m] 2.320 1.120 19.7 0.0 0.051 0.026 0.026 2 1.200 1.120 19.3 0.0 0.026 0.013 0.013 1 1.120 140.0 0.0 0.026 0.013 0.013

Although the shear displacement areas are not determined in this example, theplastic shear forces are evaluated.

The above table is a good example of the fact that the elastic forces are not a goodmeasure for the design, this table is a good example. On the one hand the com-pressive force is limited by an early reaching of the yield stress of the steel, andon the other hand the ideal cross section creates an incorrect stress pattern undertension.

If one has to insert a steel shape within a concrete, it is mandatory to define thesteel shape as polygon (DTYP S). AQUA will then find the parts of the concreteto spare automatically. Thus for a two sided fillet of a composite double−T−beam


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this can be easily done by putting the steel shape within the bounding concretepolygon:

SECT 4 2 3 TITL 'STEEL BEAM WITH FILLETS'POLY RECT MNO 1 DY 0.310 0.340PROF 1 HEM 300 DTYP S CUT 1 YB -0.200 YE 0.100 MNO 1 MRF 3 1 YB -0.100 YE 0.000 MNO 1 MRF 3 1 YB -0.020 YE 0.020 MNO 2 1 YB 0.000 YE 0.100 MNO 1 MRF 3 1 YB 0.100 YE 0.200 MNO 1 MRF 3

An other feature for composite sections are construction stages. With the defini-tion of a CS record one may subdivide the sections for this purpose. The usageof the CS−sections is usually defined within a group record.

SECT 8 2 TITL 'COMPOUND WITH CS-DEFINITIONS'CS 10 TITL 'Steel beam'PROF NO TYPE Z1 ZM DTYP REF MNO=2 1 heb 500 190 S UMCS 12 TITL 'In situ concrete'POLY O MNO 1VERT NO Y Z TYPE PHI


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1 1.25 0 O 2 -1.25 0 O 10 3 -1.25 0.19 O 4 1.25 0.19 O 10

Cross-sections static properties No MNo A[m2] Ay/Az/Ayz Iy/Iz/Iyz ys/zs y/z-sc modules gam MNs It[m4] [m2] [m4] [m] [m] [MPa] [kN/m] 8 = COMPOUND WITH CS-DEFINITIONS = HE 500 B = Composit with materials: 2 1 2 9.1721E-02 6.620E-02 3.377E-03 0.000 0.000 210000 13.75 1.002E-03 9.971E-03 3.547E-02 0.185 0.109 81000 8.1 = CS 10 Steel beam 2 2.3864E-02 1.494E-02 1.072E-03 0.000 0.000 210000 1.87 5.434E-06 7.058E-03 1.262E-04 0.440 0.440 81000 8.2 = CS 12 In situ concrete 2 9.1721E-02 6.620E-02 3.377E-03 0.000 0.000 210000 13.75 1.002E-03 9.971E-03 3.547E-02 0.185 0.109 81000

Aqua 1

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Transcript of Aqua 1