Krasta Manual English

Kühne BSB GmbH, DE 64295 Darmstadt, Mina-Rees-Straße 5A, Tel:+49-(0)6151/397690-0, Fax: -200

KRASTA Program for statical and modal

analysis of spatial frames

MANUAL

KRASTA 9.6 Manual Contents iii

Contents

1 KRASTA ............................................................................................................................................... 1

1.1 POSSIBILITIES AND FIELDS OF USAGE OF KRASTA ............................................................................ 3 1.2 CACLULATION ACCORDING TO THEORY 2

ND ORDER ............................................................................. 3

1.3 LOADS AND PREDISPLACEMENTS ...................................................................................................... 3 1.4 MASS DISTRIBUTION ........................................................................................................................ 3 1.5 PAS ................................................................................................................................................ 3 1.6 STAB88 / NODYA .......................................................................................................................... 3

2 LEGAL ISSUES.................................................................................................................................... 5

2.1 LICENSE AGREEMENT ....................................................................................................................... 5 2.2 LIABILITY ......................................................................................................................................... 6

3 INSTALLATION.................................................................................................................................... 7

3.1 KRASTA ........................................................................................................................................ 7 3.1.1 Obtaining the latest KRASTA Version .................................................................................... 7 3.1.2 Start of Installation .................................................................................................................. 7 3.1.3 Determine directory for manager system and temporary files ............................................... 7 3.1.4 First start of KRASTA ............................................................................................................. 8 3.1.5 Closing KRASTA .................................................................................................................... 9

3.2 LICENCE FILES ............................................................................................................................... 10 3.2.1 Naming extension and location of the Licence File .............................................................. 10 3.2.2 How to check your Licence File ........................................................................................... 10 3.2.3 Changes to the Licence File ................................................................................................. 10 3.2.4 Protection against misuse .................................................................................................... 10

4 BASICS IN PROGRAM USAGE ........................................................................................................ 11

4.1 USER SETTING AND SETUP ............................................................................................................. 13 4.1.1 The KRASTA-Manager ........................................................................................................ 13 4.1.2 The User Profile ................................................................................................................... 13

4.2 KRASTA BASICS .......................................................................................................................... 15 4.2.1 Main Window ........................................................................................................................ 15 4.2.2 Left mouse button ................................................................................................................. 18 4.2.3 Middle mouse button / mouse wheel .................................................................................... 18 4.2.4 Right mouse button .............................................................................................................. 18 4.2.5 Orbit-Mode ........................................................................................................................... 19 4.2.6 Hotkeys................................................................................................................................. 20 4.2.7 KRASTA Objects .................................................................................................................. 20 4.2.8 Single Object Selection ........................................................................................................ 21 4.2.9 Multiple Object Selection ...................................................................................................... 22 4.2.10 OK and Cancel ..................................................................................................................... 22 4.2.11 Saving of texts and pictures ................................................................................................. 22 4.2.12 Input Controls ....................................................................................................................... 22

4.3 HANDLING OF KRASTA SYSTEMS ................................................................................................... 25 4.3.1 Purge System ....................................................................................................................... 25 4.3.2 KRASTA archives ................................................................................................................. 25

4.4 SELECTION OF BEAMS AND NODES ................................................................................................. 27 4.4.1 Current Selection .................................................................................................................. 27 4.4.2 Selection Mode ..................................................................................................................... 27 4.4.3 Changing the current selection, graphically interactive ........................................................ 27 4.4.4 Changing the current selection, in respect to beam or node properties .............................. 28

4.5 VIEW, DISPLAY, PROJECTION ......................................................................................................... 29 4.5.1 Display Subset ..................................................................................................................... 29

4.6 COLORS AND CAPTIONS ................................................................................................................. 31 4.6.1 Colors ................................................................................................................................... 31 4.6.2 Captions ............................................................................................................................... 31 4.6.3 Text and symbol sizes .......................................................................................................... 32

iv Contents KRASTA 9.6 Manual

4.7 PRINTING ....................................................................................................................................... 33 4.8 PAGE LAYOUT ................................................................................................................................ 34 4.9 OPTIONS........................................................................................................................................ 35

4.9.1 Units ...................................................................................................................................... 35 4.9.2 Languages ............................................................................................................................ 35 4.9.3 User ...................................................................................................................................... 35 4.9.4 Automatic save ..................................................................................................................... 35

5 MODELLING ....................................................................................................................................... 37

5.1 COORDINATE SYSTEMS .................................................................................................................. 39 5.1.1 Inertial System ...................................................................................................................... 39 5.1.2 Subsystem Coordinate System ............................................................................................ 39 5.1.3 Beam Coordinate System ..................................................................................................... 39 5.1.4 Principal Axes Coordinate System ....................................................................................... 40

5.2 BEAMS AND NODES ........................................................................................................................ 41 5.2.1 Beam and Node Name ......................................................................................................... 41 5.2.2 Beam Properties ................................................................................................................... 42 5.2.3 Node Properties .................................................................................................................... 45

5.3 CONSTRUCTION ............................................................................................................................. 47 5.3.1 Split Beam ............................................................................................................................ 47 5.3.2 Reverse Beams .................................................................................................................... 48 5.3.3 Translation, Stretching, Copying and Mirroring .................................................................... 48 5.3.4 Rounding .............................................................................................................................. 49 5.3.5 Check for double beams or nodes ....................................................................................... 49

5.4 CROSS SECTIONS .......................................................................................................................... 51 5.4.1 Points for Proof of Stresses .................................................................................................. 51 5.4.2 Direct Input Cross Section .................................................................................................... 52 5.4.3 Partial Rigid Cross Sections ................................................................................................. 52 5.4.4 Thin-Walled Cross Sections ................................................................................................. 54 5.4.5 Parametric Cross Sections ................................................................................................... 55 5.4.6 Standard Cross Sections ...................................................................................................... 66 5.4.7 Import Cross Sections .......................................................................................................... 66 5.4.8 Plot Cross Sections .............................................................................................................. 66 5.4.9 Clean Up Cross Sections ..................................................................................................... 66

5.5 MATERIAL ...................................................................................................................................... 67 5.5.1 Clean Up Materials ............................................................................................................... 67

5.6 LISTS ............................................................................................................................................. 69 5.6.1 Simple Beam or Node Lists .................................................................................................. 69 5.6.2 Other simple lists .................................................................................................................. 69 5.6.3 Composition Lists ................................................................................................................. 70 5.6.4 Filter Lists ............................................................................................................................. 70 5.6.5 Clean Up of Lists .................................................................................................................. 70

5.7 MASS CASES ................................................................................................................................. 71 5.7.1 Permanent Mass .................................................................................................................. 71 5.7.2 Basic Mass Cases (BMC) ..................................................................................................... 71 5.7.3 Combination Mass Cases (CMC) ......................................................................................... 74 5.7.4 Situation Dependent Mass Case (SMC) .............................................................................. 74 5.7.5 Sum of Masses ..................................................................................................................... 74

5.8 LOAD CASES .................................................................................................................................. 75 5.8.1 Basic Load Case (BLC) ........................................................................................................ 75 5.8.2 Combination Load Case (CLC) ............................................................................................ 80 5.8.3 Situation Dependent Load Case (SLC) ................................................................................ 80 5.8.4 Load Case 2

nd Order Theory (TH2) ...................................................................................... 80

5.8.5 Geometrical nonlinear Load Case (S88) .............................................................................. 81 5.8.6 Logic Load Case (LLC) ......................................................................................................... 81 5.8.7 Nonlinear Logic Load Case .................................................................................................. 82

5.9 SITUATION DEPENDENT LOAD AND MASS CASES ............................................................................. 83 5.10 LOAD EVENTS ............................................................................................................................ 85 5.11 LOAD SEQUENCES ...................................................................................................................... 87 5.12 DESIGN SPECTRA ....................................................................................................................... 89

KRASTA 9.6 Manual Contents v

5.13 CONSTRAINT CONDITIONS .......................................................................................................... 91 5.13.1 Types of Constraint Conditions ............................................................................................ 91 5.13.2 Consideration in Display and Results .................................................................................. 92 5.13.3 Example: Constraint Conditions ........................................................................................... 92 5.13.4 Sensor degrees of freedom and “optimised coupling” ......................................................... 96 5.13.5 Assistant for Constraint Conditions ...................................................................................... 98 5.13.6 Buffer for Constraint Conditions ......................................................................................... 101 5.13.7 Error Bounds ...................................................................................................................... 102 5.13.8 Compatibility with KRASTA 9.3 and prior ........................................................................... 102

5.14 SUBSYSTEMS ........................................................................................................................... 103 5.14.1 Hierarchy, Organization ...................................................................................................... 103 5.14.2 Import Subsystems ............................................................................................................. 103 5.14.3 Simplified orientation after copy or import .......................................................................... 105 5.14.4 Geometrical Orientation of a Subsystem ........................................................................... 105 5.14.5 Current Subsystem ............................................................................................................. 105 5.14.6 Beams and Nodes of a Subsystem .................................................................................... 105 5.14.7 Beams between subsystems ............................................................................................. 105 5.14.8 Split off Marked Nodes as New Subsystem ....................................................................... 106 5.14.9 Melt a subsystem ............................................................................................................... 106

5.15 CONNECTIONS AND CONTACTS ................................................................................................. 107 5.15.1 Structural Build-Up ............................................................................................................. 107 5.15.2 Means for the orientation of the structure .......................................................................... 107 5.15.3 Example for a subsystem structure .................................................................................... 109 5.15.4 Examples for Contacts ....................................................................................................... 111 5.15.5 Connection ......................................................................................................................... 112 5.15.6 Contact ............................................................................................................................... 113 5.15.7 Error messages (Contact) during connection of subsystems ............................................ 113

5.16 ORIENTATION ........................................................................................................................... 115 5.16.1 Basic Orientation ................................................................................................................ 115 5.16.2 Relative Orientation ............................................................................................................ 116 5.16.3 Orientation Modification...................................................................................................... 117 5.16.4 Methods of orientation ........................................................................................................ 117 5.16.5 Notifications during the execution of orientations .............................................................. 118

5.17 KINEMATICS ............................................................................................................................. 119 5.17.1 Dialog: Kinematic ............................................................................................................... 120 5.17.2 Error messages (Kinematic) ............................................................................................... 123 5.17.3 Example: (Kinematic) ......................................................................................................... 124 5.17.4 Further possibilities to model kinematic displacements ..................................................... 126

5.18 SITUATION ............................................................................................................................... 127 5.18.1 Methods of situations ......................................................................................................... 127 5.18.2 Dialog “Situation” ................................................................................................................ 128 5.18.3 The situation “$uncertain”................................................................................................... 128 5.18.4 Create situations for orientations ....................................................................................... 129

6 CALCULATION ................................................................................................................................ 131

6.1 CALCULATION SUITE .................................................................................................................... 133 6.1.1 Available solvers and computation theories ....................................................................... 133 6.1.2 Methods of calculation suites ............................................................................................. 133 6.1.3 The default calculation suites „PAS linear“ and „PAS ThII” ............................................... 134 6.1.4 Dialog: Calculation Suite .................................................................................................... 134 6.1.5 Calculate specific Results .................................................................................................. 136

6.2 CALCULATION ACCORDING 2ND

ORDER THEORY ............................................................................. 137 6.2.1 2

nd Order Theory, Basics .................................................................................................... 137

6.2.2 Th. II, Modelling techniques ............................................................................................... 137 6.3 SITUATION-INDEPENDENT CALCULATION ........................................................................................ 139 6.4 CONTENT OF THE RESULT FILE ...................................................................................................... 141 6.5 PROCESS SOLVER INPUT FILES .................................................................................................... 143 6.6 CALCULATION LOG ....................................................................................................................... 145 6.7 PAS ERROR MESSAGES ............................................................................................................... 147

6.7.1 Error/Warning Nr. 229 ........................................................................................................ 147

vi Contents KRASTA 9.6 Manual

6.7.2 Error/Warning Nr. 451 ........................................................................................................ 147 6.7.3 Error/Warning Nr. 453 ........................................................................................................ 150 6.7.4 Error/Warning Nr. 455 ........................................................................................................ 152

6.8 MODAL ANALYSIS ......................................................................................................................... 155

7 ANALYSIS AND DOCUMENTATION .............................................................................................. 157

7.1 PROOFS ...................................................................................................................................... 159 7.1.1 Proof of fatigue based on damage accumulation ............................................................... 161 7.1.2 Proof of Fatigue acc. DIN 15018 ........................................................................................ 165 7.1.3 Proof of Fatigue acc. DIN 22261 ........................................................................................ 167 7.1.4 Proof of Fatigue according to DIN CEN/TS 13001-3-1:2005-03 ........................................ 169 7.1.5 Proof of Fatigue according to prEN 13001-3-1:2009 ......................................................... 175 7.1.6 Common information to proof of fatigue according to EN 13001-3 .................................... 181 7.1.7 Proof of Fatigue according to EN 1993-1-9:2005 (EC 3) ................................................... 185 7.1.8 Proof of Fatigue acc. FEM 1.001 ........................................................................................ 193 7.1.9 Proof of Fatigue acc. ISO 5049-1 ....................................................................................... 195 7.1.10 Proof of Fatigue according to DASt-Ri 011 ........................................................................ 197 7.1.11 Proof of Fatigue acc. AS 4100:1998 .................................................................................. 199 7.1.12 Proof of Stresses el.-el. acc. DIN 18800:1990-11 .............................................................. 207 7.1.13 Proof of Stresses, Buckling acc. DIN 4114-1:1952-07 (Omega-Method) .......................... 209

7.2 RESULTS ..................................................................................................................................... 211 7.2.1 Delta Stress Results ........................................................................................................... 213

7.3 PROOF- / RESULT-CONTROL-SETS ............................................................................................... 215 7.3.1 Options for search of extreme values ................................................................................. 215 7.3.2 Evaluation ........................................................................................................................... 216 7.3.3 Output ................................................................................................................................. 216 7.3.4 Evaluation Pattern .............................................................................................................. 217 7.3.5 Details of Output ................................................................................................................. 220

7.4 OUTPUT FORMAT ......................................................................................................................... 221 7.5 PALETTES .................................................................................................................................... 222 7.6 SYSTEM DOCUMENTATION ............................................................................................................ 223

7.6.1 Textual Documentation ....................................................................................................... 223 7.6.2 Graphical Output ................................................................................................................ 223

8 BRIEF INFORMATION FOR REVIEW ............................................................................................. 225

8.1 GENERAL ..................................................................................................................................... 225 8.2 COORDINATE SYSTEMS ................................................................................................................ 226 8.3 PROPERTIES OF BEAMS ................................................................................................................ 228

8.3.1 Beam Spring ....................................................................................................................... 228 8.3.2 Joints .................................................................................................................................. 228 8.3.3 Material ............................................................................................................................... 228 8.3.4 Force Conditions ................................................................................................................ 228 8.3.5 Beam Buckling Data ........................................................................................................... 228

8.4 PROPERTIES OF NODES ............................................................................................................... 228 8.4.1 Support Conditions ............................................................................................................. 228

8.5 CROSS SECTION .......................................................................................................................... 229 8.6 MASS CASES ............................................................................................................................... 231 8.7 LOAD CASES ................................................................................................................................ 232 8.8 RESULTS ..................................................................................................................................... 234 8.9 SIGN DEFINITION OF INNER FORCES AND STRESSES ........................................................................ 234

9 INDEX ............................................................................................................................................... 235

KRASTA 9.6 Manual KRASTA 1

1 KRASTA KRASTA is a program system for structural and modal analysis of spatial framework in the fields of material handling and general steel engineering. Structures or parts of it can be moved in different configurations for calculation. Results from several positions can be evaluated together.

The idea for KRASTA was born in 1973 at the Fach-gebiet Fördertechnik und Lasthebemaschinen (Institute for Material Handling and lifting appliances) of the Technische Hochschule Darmstadt, Prof. Dr.-Ing. R. Neugebauer. The program has been developed at the institute in cooperation with the industry first of all for mainframe- and minicomputers. The work has been supported by the Fachgemeinschaft Fördertechnik im VDMA (Verband Deutscher Maschinen- und Anlagenbau e.V.) and FKM (Forschungskuratorium Maschinenbau). Since 1980 the program is used in the industry. In 1987 the program was ported to PC under DOS.

Since 1990 the graphical-interactive in- and output was developed. The idea to this was brought in by the Lehrstuhl für Fördertechnik und Maschinenelemente of the RU Bochum, Prof. Dr.-Ing. G. Wagner.

Since 1991 further development, maintenance and sale are done by Kühne BSB GmbH.

The program system was ported to Windows in 1995.

Program authors:

Holger Ackermann Georg Kohlhas Michael Kühne Alfried Lautermann Hans Lautner Frank Meier-Dörnberg Gerhard Wagner and others

PAS III, developed parallel to KRASTA at the Institut für Statik und Stahlbau of the TH Darmstadt, Prof. Dr.-Ing. H. Ebel, respectively version PAS IV, enhanced by Kühne BSB, is used as solver.

As an alternative to PAS the program STAB88, developed by the Lehrstuhl für Förderwesen of the TU München, can be used.

© 2013 Kühne BSB GmbH

KRASTA 9.6 Manual KRASTA 3

1.1 Possibilities and fields of usage of KRASTA

KRASTA is a program system for structural and modal analysis in the fields of general steel engineering, material handling and plant manufacturing. The structural model is created graphical interactive by means of beam elements and nodes.

The calculation continues up to the proof of stresses and fatigue. The proof of stresses can be made independent of standards or according to DIN 18800, the proof of fatigue can be made according several standards e.g. DIN 15018, DIN 22261 and EN 1993-1-9 (EC3) incl. damage accumulation.

The nominal stresses are determined on the base of technical bending theory of the beam and the St. Venant torsion theory.

1.2 Caclulation according to theory 2nd order

For a calculation according to theory 2nd order, partial safety coefficients and predisplacements can be considered.

1.3 Loads and predisplacements

Loads and predisplacements (concentrated, evenly distributed or trapezoidal) can act on parts of a beam or on the complete beam.

1.4 Mass Distribution

The mass distribution can be described exactly. Loads resulting from translational or rotational accelerations or rotational velocities are generated automatically on the base of the mass distribution.

Structures or parts of it can be brought to different positions for calculation. The results from different positions can be evaluated together.

1.5 PAS

PAS theoretical foundation

The program PAS°III or PAS°IV used as solver has the following theoretical foundation.

For the single beam the differential equation system (DES) is solved according to the technical beam bending theory. As the inhomogeneous DES is solved loads and predisplacements can be placed inside the beams without definition of intermediate nodes.

The calculation may be according to theory 1st or 2

nd order. The equilibrium is calculated in the deformed

state.

Theory 2nd order iterates over the normal force of the beam.

The buckling load (Eigen value) can be determined iteratively.

PAS contains a theory of small displacements which means that the plan of displacement is built linear.

Partial rigid cross sections

Each of the 6 cross section values (area, shear areas, bending- and torsional inertia moments) can be set rigid or elastic. Elasticity equations for rigid values are replaced by equilibrium conditions. Structures that show great differences in elasticity or regions that cannot be modelled by beams, can be modelled in this way so that the global flow of forces can be determined correctly without numerical difficulties in solving the equations.

1.6 STAB88 / NODYA

The optional solver program STAB88 is a finite element program with geometrical nonlinear calculation of beam -, bar - and rope structures.

KRASTA 9.6 Manual Legal Issues 5

2 Legal Issues

2.1 License agreement

1. The license agreement exists between the end user as licensee and the company Kühne BSB GmbH.

2. Concession of a license. The license agreement gives you the right to install and to use a copy of the program KRASTA on your computer (single user license). In case you have several licenses of KRASTA you are allowed to install it on as many computers as licenses exist. If you have a network license there is no numerical limitation of computers on which the program is installed in one location. If the program is supplied with a dongle it may be installed on several computers.

3. The program is property of the company Kühne BSB GmbH and it is protected by copyright. Copying of the program or the manual without written permission is prohibited. The licensee is authorized to make a backup of the original data media for his own use (exception see 5.).

4. The program must not be leased or hired. However there is the possibility to definitely transfer the license to a third party. The license can be transferred only if this contract is accepted by the new licensee. All available program versions as well as all manuals have to be passed on to the new licensee, no copy is allowed to remain with the person who transfers the license. Decompilation and disassembly of the program is not allowed.

5. If a user wants to install a version that is not provided with a dongle on other computers for testing or does he want to copy the manual in parts or in total a written permission of the company Kühne BSB GmbH is required.

6 Legal Issues KRASTA 9.6 Manual

2.2 Liability

The company Kühne BSB GmbH takes no liability for secondary damages which are caused by using the program.

The responsibility for the correctness of the results is exclusively up to the user.

Should you have any questions about this contract, please contact the company Kühne BSB GmbH at the following address:

Kühne BSB GmbH Mina-Rees-Straße 5A DE 64295 Darmstadt

Phone Fax

Hotline

+49 (0) 6151 397690-0 +49 (0) 6151 397690-200 +49 (0) 6151 397690-222

KRASTA, KRACAD, KRAMOD

Copyright 1991-2013 Kühne BSB GmbH. All rights reserved.

KRASTA and KRACAD are registered trademarks.

AutoCAD is a registered US-trademark of Autodesk, Inc.; MS-DOS, Windows are registered trademarks of Microsoft

Corporation.

KRASTA 9.6 Manual Installation 7

3 Installation

3.1 KRASTA

KRASTA can be installed at present under the following different operating systems:

Windows 8, Windows 7, Windows Vista

Windows NT, Windows 2000, Windows XP

Should any problems occur during the installation or later our hotline will be available for help.

3.1.1 Obtaining the latest KRASTA Version

KRASTA customers with an active maintenance agreement may access the “Customer’s area” under www.krasta.de after login with their credentials (Username and Password):

In the customer’s area the latest KRASTA version and according release notes are available for download.

To use all licensed feature of KRASTA, you additionally may need a licence file and a dongle “Sentinel Driver”. The licence file will usually be send via e-mail from our support if needed. The handling of the licence files is described in chapter "Licence Files (p.10)". The latest “Sentinel Driver” can be found on the manufacturer’s website.

3.1.2 Start of Installation

The actual installation is done by running the installation program1 (e.g. "krasta_960_full.exe").

After the confirmations of security warnings and the question of the installation language, the complete

KRASTA version info is shown. (e.g. "KRASTA 9.6.0.4240"). Please follow the instructions and

questions.

By default, KRASTA is stored in a directory like “C:\Program Files\KUEHNE_BSB\KRASTA_9.6\".

This directory is known as the "KRASTA root directory”

Within this directory the executables are stored to subdirectory „BIN“, the cross section library to sub-

directory „LIB“ and the program documentation to subdirectory „MANUAL“.

3.1.3 Determine directory for manager system and temporary files

KRASTA automatically creates files to store the user settings. By default, these files are stored into the KRASTA root directory and are named with the prefix “MANAGER”.

1 Respectively, when installing from CD: Inserting the CD and automatically or manually run "start.exe".

There: "KRASTA 9.6" runs the actual installation program.

http://www.krasta.de/en/start

https://www.safenet-inc.com/support-downloads/sentinel-drivers/

8 Installation KRASTA 9.6 Manual

You can however choose other locations and/or file names for those files in KRASTA. This allows for multiple user access to a shared manager system. KRASTA users must have write permission to this file.

KRASTA automatically stores temporary files within the actual windows temp directory in a separate

subdirectory „KRASTA“.

You can choose another position for this too. Access to this directory should be as fast as possible, therefore, it should be located on the local hard drive and should be locally accessed, too. KRASTA users must have write permission for this directory.

3.1.4 First start of KRASTA

When launched for the first time, KRASTA will detect the fact that some information is still missing and will ask for it.

A dialogue window will appear for the selection of the language, which should be used by KRASTA by default. Later (and for individual projects), it is possible to select another language at any time.

KRASTA Start Window

In the first window to appear the name of the user has to be selected and possibly an according password entered.

At the very first start, KRASTA will select name “Anwender“ as the default (German) name for a user. Accept this once and change it afterwards to your preference.

KRASTA 9.6 Manual Installation 9

KRASTA Main Window

After the selection of a user the main window of KRASTA appears.

The main window of KRASTA includes the following elements:

Main menu

Tool bar

Status bar

Working area

Object tree

Information window

KRASTA generally opens a new, empty system auto-matically when started.

You can select an existing system, by selecting a directory, which contains KRASTA systems.

There, you can select a system (e.g. test.kr2), to open it click “Open” or double-click the system name.

3.1.5 Closing KRASTA

You can close KRASTA by using the submenu item „Close“ in the main menu item “File”.

10 Installation KRASTA 9.6 Manual

3.2 Licence Files

Starting with KRASTA 9.3 some special program features (e.g. regarding Network/Dongle or Basic/Fatigue/Full version) are activated by an individual Licence-File.

In order to be able to use all licensed KRASTA features, customers with network and/or customers with full version must have an appropriate Licence File.

The license files contain information in coded form. Apart from an individual identification for the identification of the licensee, further information to enable individual features of KRASTA are also contained in this file.

3.2.1 Naming extension and location of the Licence File

The KRASTA Licence File has the file extension “*.liz.

In order to enable KRASTA to find the licence file it must be located in the same directory as the program executable (“KRASTA.EXE”). If the appropriate default settings were assumed during the installation of

KRASTA, this then should be “C:\Program Files\Kuehne_BSB\KRASTA_9.6\BIN” or similar.

Make sure that multiple Licence Files are not present at the same time. KRASTA will always analyze the first licence file found

3.2.2 How to check your Licence File

You are able to check your currently licensed KRASTA features at any time through the KRASTA menu item menu item “Info...”.

3.2.3 Changes to the Licence File

Changes to the license file, e.g. the individual identification used by KRASTA, can be done by us at any time.

Please contact our support:

Email: [email protected]

Phone: +49 (0) 6151 / 397690 – 222

Fax: +49 (0) 6151 / 397690 – 200

3.2.4 Protection against misuse

Secure the Licence File (in particular in network environments) against misuse and unauthorized third party access.

mailto:[email protected]

KRASTA 9.6 Manual Basics in Program Usage 11

4 Basics in Program Usage The following chapter describes usage of KRASTA itself and handling KRASTA systems. Items regarding configuration, basic usage concepts and some special controls are covered.


4.1 User Setting and Setup

KRASTA may be used by single users or work groups that are manager by KRASTA themselves. A special user, the manager, is responsible for the organization of users and data.

Every user has a user profile, which, among other preferences, defines the dialog and output language of KRASTA.

Users are data-technical "objects" and they can be generated, copied, edited and deleted.

4.1.1 The KRASTA-Manager

If functions are called, that are only allowed for the "Manager", the program asks for the manager password. After input of this password the user is authorized as Manager until the end of the current KRASTA session.

4.1.2 The User Profile

In the user profile the dialog- and output language as well as the physical units can be set.

The user profile is organized hierarchically:

By this means settings with higher priority overwrite lower ones.

4.1.2.1 In- and Output Units:

length : m, cm, dm, mm, in, ft

force : N, kN, pond, kp, Mp, lbs, Dyn, daN, MN

mass : kg, t, g, lbs

time : sec, min, h

temperature : centigrade, Fahrenheit

angle : rad, Grad, gon, rev., mrad

fraction : part, percent, per mill

In the database all data is saved in SI-units. The units used for in- and output can be changed at any time.

4.1.2.2 In- and Output Language

Texts for dialog and textual output are saved in a file and may be translated into other languages. German and English language databases are delivered with the program system. The user can specify which languages he wants to use for dialog and output separately.

default settings by KRASTA

settings by the KRASTA-manager

settings by the user

fixed settings in the system

temp. settings in the system

increasing priority


4.2 KRASTA Basics

In the following chapter, KRASTA basics and common usage pattern are covered.

4.2.1 Main Window

The main screen of KRASTA provides the following items:

Titlebar, here you see the topical system name with path.

Working Area - In the working area you see the display of the entered structure, loads, masses, inner forces, deformation and stresses as well as the selection of beams and nodes.

Object Tree, here all objects of the current model are displayed in a tree structure.

Information Window, here information concerning the picture is displayed.

Status Line, here you see topical settings and prompts.

Toolbar, here you see different tools for information and display.

Main Menu - gives the user access to all functions of the program.

KRASTA Main Window

16 Basics in Program Usage KRASTA 9.6 Manual

4.2.1.1 Working Area

In the working area the structure, cross sections, loads, masses, inner forces, deformation and stresses are displayed.

Using the mouse you can select (p.27) subsystems, beams, and nodes.

Viewing direction, size and center can be changed directly by mouse in the so-called "Orbit-Mode (p.19)”. Additionally, you can use the scroll-bars to scroll the view or use the toolbar to zoom or to vary the view direction stepwise.

Window: Working Area


4.2.1.2 Object Tree

On the left side of the screen all objects of the current system are displayed in a tree view.

Window: Object Tree

By clicking on the plus sign in front of the object name or by double clicking the name itself, further levels below this point can be displayed.

For reasons of improved readability load cases, mass cases and list are divided into sub topics.

Pressing the right mouse button in the tree view brings up a context menu that offers the options that are usually connected with that type of object.

In addition it is possible for some types of objects to pull them via drag and drop onto the working area.

The results depend on the object type:

Display and Projection Settings are applied to the current display

Mass Cases turn on mass case display for the selected mass case

Load Cases switch load dependent displays (load, bending line, inner forces) to the current load case, if such a display is active; else it turns on load display.

Beam or Node Lists are used as under the menu item "selection by list“

Cross Sections and Materials are assigned to the currently selected beams

The dividing line between object tree and working area can be moved left or right.

By pressing the button Minimize Tree the tree is reduced to the main level.

User Defined Folder in Object Tree

Below the most object types in the object tree, it is possible to use user defined folder to further sub-divide the object groups.

By the context menu of the respective object group, user defined folder can be created, edited or dissolved:

New Folder… Creates a new folder and opens the folder edit dialog.

Edit Folder… Opens the folder edit dialog of a already existent folder.

Dissolve Folder Removes the folder and reinsert the contained objects in superior object group.

Each KRASTA object is represented exactly once in the object tree, never simultaneously in multiple folders.


4.2.1.3 Information Window

In a window situated between working area and status line, information concerning the currently displayed graphics (description of display, scaling factor for figures, load and mass totals) is shown.

In the information window shown totals only consider the currently displayed subset, not the entire system. In case thereby the totals may incomplete, i.e. not all loaded objects are currently displayed, this is indicated by the note "partial summation".

Window: Information

The dividing line between information window and working area can be moved up or. This may also be used to adjust the aspect ratio of the display for output.

4.2.1.4 Items of the Status Line

In the status line selected units, beam and node selection state and current time is displayed.

Additionally prompts for input in dialogs and information about the menu items are displayed. For operations which may take some time a progress bar is shown.

4.2.2 Left mouse button

In the working area is possible to select or deselect beams and nodes by the left mouse button. Details can be found in Section “Selection of Beams and Nodes (p.27)”.

If the left mouse button is pressed down in “Orbit-Mode (p.19)”, the view direction is changed.

4.2.3 Middle mouse button / mouse wheel

In the working area a menu to control selection modes is opened by pressing the middle mouse button / the mouse wheel.

Turning the mouse wheel, if not set otherwise in the orbit-settings (p.19), the view size is changed (zoomend). By zooming by the mouse wheel, the model location under the mouse cursor stay fixed.

If the middle mouse button / mouse wheel is pressed down in “Orbit-Mode (p.19)”, the view is rotated around the viewing axis.

4.2.4 Right mouse button

In the working area you can pop up a menu by clicking the right mouse button.

If you click the right mouse button in the working area, the menu contains items to Zoom the view, to change the displayed Subset and to Copy the current view into the clipboard (in meta file and in bitmap format).

If the mouse points to a beam or node additional menu items Edit Beam and Edit Node appear for the individual beams or nodes.

If the right mouse button is pressed down in “Orbit-Mode (p.19)”, the view is moved (panned).


4.2.5 Orbit-Mode

In “Orbit-Mode” it is possible to quickly change

view direction (left mouse button to roll around lateral axis),

vertical axis (middle mouse button to rotate around view axis),

view size (roll mouse wheel to zoom) or

view center (right mouse button to pan).

If the “Orbit-Mode” is active (p.19), then the current center of rotation is displayed and a small orbit

symbol is attached to the mouse cursor ( ).

Orbit - Center of Rotation

The current center of rotation is determined at the time the Orbit-Mode is activated. The (yet only available) type of determination of center of rotation is “Mouse Position”. By this method the spatial center of the node points displayed near to the actual mouse position is used as center of rotation.

4.2.5.1 Orbit-Settings

Dialog: Orbit-Settings

The menu item “Option | Orbit-Settings…” opens den configuration dialog shown above.

Orbit - Activations

Available are the following methods of activation:

Via Context menu: In the context menu of the working area a menu item “Orbit” is available. By this type of activation the Orbit-Mode is deactivated by a click with the right mouse button. There-fore the usual context menu is unavailable in Orbit-Mode.

Key for activation / deactivation: The Orbit Mode is activated by pressing down and de-activeted by releasing the chosen Key.

Orbit – Center of Rotation

The indication of the current center of rotation can be controlled. The (yet only available) type of determi-nation of the center of rotation is “Mouse Position”. By this method the spatial center of the node points displayed near to the actual mouse position is used as center of rotation.

Sensitivity / Direction

These parameters are used to scale the speed of movement. The sign switched the direction of the movement


4.2.6 Hotkeys

Beside the standard windows behavior to select menu items via keyboard by pressing [ALT]-Key and an underlined letter of the menu item, KRASTA offers the following short cut keys for common actions additionally:

CTRL+N open new (empty) model

CTRL+O open existing model

CTRL+S save model

CTRL+P print

CTRL+R refresh display

STRG+Q quit KRASTA

4.2.7 KRASTA Objects

The expression "object" as used in this text means things like beams, nodes, load cases or cross sections as well as users, page layouts etc. All such objects have a Name, a Comment and Information about creation and modification date.

Using the relevant menu item the user can create such objects New, Edit them, Copy existing ones or Delete them. Objects of most types may also be Imported from other systems and stored in Lists (p.69). A list is also an object.

4.2.7.1 Name

For all objects, e.g. beams, nodes, load cases, cross sections, etc. a Name is used, under which this object is managed. The name can consist of up to 16 letters and 4 figures.

The program proposes a standard name for a new object. It consists of the standard name part for the type of object and a number.

4.2.7.2 Comment

For all objects a Comment can be entered in addition to the name. Here further explanations may be specified, to make the function of parts of the system clearer.

4.2.7.3 Information

For each object the system stores the date and the time of the creation and the date and time of the last modification. This data can be reviewed by clicking the button Information.

4.2.7.4 Create an Object

On creation of a new object KRASTA creates a standard object of the respective type with standard attributes and calls the relevant dialog to edit this type of object.

KRASTA proposes a unique name for the new object consisting of the standard name of the specific object and a number, that is automatically incremented.

In some cases the menu item New is followed by a submenu for the specification of the subtype of object to create.

4.2.7.5 Edit an Object

The menu item Edit calls the corresponding object dialog for the chosen object.

Example: Edit an Object

After the selection of the menu item Edit in the main menu item load case, a selection box appears where all existing load cases are listed. After selecting a load case and confirming by pressing OK or double clicking, the corresponding load case is opened for editing.


4.2.7.6 Copy an Object

The menu item Copy copies an object and calls the corresponding object dialog for the copy.

Example: Copy an Object

Click main menu item load case and then Copy. A selection box appears, where all existing load cases are listed. After selecting a load case and confirming by pressing OK or by a double clicking, the corresponding load case is copied into a new load case. This new load case is opened for edition.

4.2.7.7 Delete an Object

With the menu item Delete you can delete an existing load case, mass case, cross section etc.

Example: Delete an Object

After clicking Delete in the main menu item load case a multiple object selection appears, where all existing load cases are listed on the left. After selecting the desired load cases (bringing them to the right side) and confirming by clicking OK the load cases are deleted.

4.2.7.8 Import an Object

Objects can be imported from other KRASTA systems.

To import an object, the system from which to import has to be selected first.

In the next step the desired objects can be selected in a multiple object selection dialog.

If the names of imported objects conflict with already existing ones, the number part of the name is automatically incremented for the imported objects.

4.2.7.9 Object Lists

Object lists are used to manage a group of objects of one type. They can be used for example to describe a list of nodes that carry a specific load.

Lists (p.69) are KRASTA objects and have a name and a comment.

Usage of a list in other objects is registered. If a list is no longer used, KRASTA asks the user if it should delete the specific list.

Lists can be created new, copied, edited or deleted.

Multiple object selections are usually used to edit simple object lists. On the right side the selected objects are shown, on the left the unselected ones.

Beam and node lists use special dialogs to graphically interactive select the object on the screen.

In addition to Simple Lists of objects, in which individual objects are explicitly listed, there are so-called Filter (p.70)- and Composition-Lists, (p.70) whose contents follow an individually defined rule.

4.2.8 Single Object Selection

When it is necessary to select one object out of a list of objects this often can be done with the dialog Selection. By marking and clicking the button OK or by double clicking on the corresponding list entry an object can be selected. In most cases the dialog caption shows the purpose of the selection.


4.2.9 Multiple Object Selection

Several objects out of a list of objects can be selected in the dialog object selection. The caption shows the purpose of this selection. The available objects are listed on the left. The selected objects are shown on the right.

An object can be selected by marking on the left and clicking the button Add or by double clicking on the left. The button “All >“ moves all objects to the right.

An object can be removed by marking on the right and by clicking the button Delete or by double clicking in the right field. The button “< All” moves all objects to the left.

The objects can be sorted alphabetical or according to other eligible criteria.

4.2.10 OK and Cancel

All input dialogs can be shut down by OK or Cancel, clicking the button OK stores the input, clicking Cancel leaves the object as is.

4.2.11 Saving of texts and pictures

Saving picture or text is done in similar manner.

Saving a plot file

Besides Name and Comment a Position Number can be given to the text that is to be saved. KRASTA needs a page layout (p.34).

The file name for the file can be input directly or selected by pressing Browse.

Checking Minimal Text Only leads to a plot text that does not contain load, mass or support force sums.

By activated option “Automatic trimming”, KRASTA is choosing a minimal frame to plot the currently displayed picture. The button Select Picture Details allows to select a smaller frame of the picture to be saved.

By clicking the button Print the picture is printed directly to the currently configured printer (p.33) without keeping a plot file.

Saving a text

There are the same items for saving a text as for saving a plot except for the button Select Picture Details.

A text or a plot file represents one or more output pages which may later be printed via the printing dialog (p.33).

By clicking the button Print the text is printed directly to the currently configured printer (p.33) without keeping a text file.

4.2.12 Input Controls

In KRASTA dialogs often have input controls with specialized properties e.g. for simplified entering of points or vectors, to autoamtically adjust values in regard of physical units or for “in place” calculation of simple math expressions.


4.2.12.1 Input of points and vectors

It is necessary to define a point or a vector at several places in the program.

The input can be made by setting the coordinates via keyboard into the corresponding input fields or by graphical selection.

Input of point coordinates

To select point coordinates graphically you can click the button Graphical Selection. In the following you can select a node in the working area of which the coordinates are set as point coordinates.

It is also possible to place the cursor in an input control of a component (x, y, z) and click a node afterward. This only copies the corresponding component of the node.

Input of a vector

To select a vector graphically you can click the button Graphical Selection. In the following you can to select two nodes in the working area; the difference of the node coordinates is set as the vector.

It is also possible to place the cursor in an input control of a component (x, y, z) of the vector and click two nodes afterwards. This only copies the corresponding component of the vector.

4.2.12.2 Display of physical units

All numerical input lines have their current physical units displayed next to the input field.

4.2.12.3 Input of numerical values

While entering numerical values, one can use either decimal points or commas to divide the fraction from the integer part (required for input on the german numeric keypad). The output is displayed with a decimal point only.

In addition calculations may be made on the input line. Expressions can be used that contain "+", "-", "*", "/", "(", ")", "**"(exponentiation) "sqrt"(square root), "sin", "cos" und "tan". Trigonometric functions always expect degrees as input.


4.3 Handling of KRASTA systems

The term “KRASTA system” refers to all data stored under a specific system name, e.g. construction, evaluation logic, calculation results, proofs and plots. All these data are stored in seperate files. The file names are made up of system name and different suffixes. As a kind of handle to all of these files, one file with suffix “.kr2” is used.

With KRASTA you are able to create new, open, save, or delete KRASTA systems. As usual, the menu items for these purposes you can find at the main menu item File. There, additionally a list of recently edited systems is offered to open.

4.3.1 Purge System

KRASTA systems may purged in various steps to save disk space. The files which store the selected data will be deleted.

Dialog: Purge System

The following options can be selected to purge:

Solver log-file (p.145)

Inner forces and node displacements (p.141)

Textual output files

Graphical output files

Solver input data (p.143)

Undo Files

The selected files (or the files representing the selected data) will be deleted by clicking OK.

To purge the current system is default. By clicking the Browse button you can purge any other system instead.

4.3.2 KRASTA archives

To save individual development stages of a KRASTA system, it is sufficient to create a so called KRASTA archive. It is compact, if so complete and unambiguous named.

As archive format, the widely-used ZIP-format is used.

Archive / Dearchive

In “Save and archive” some details are queried in the dialog “Put KRASTA systems into archives”, before, if necessary, the current changes of the KRASTA system are stored and the KRASTA system is archived.

After choosing the archives in “Unpack and open” the compressed KRASTA-System is extracted and the system opened. If necessary a further inquiry takes place whether an existing system of same name is to be overwritten or not.

The KRASTA System is archived under its original name, but in general, the name of the archive is individualized by e.g. a time stamp.


Dialog: Put KRASTA System into archives

put system into: Shows the name of the archive, as it results from the specifications in the zip file.

Zip File Name: Specifies the name and location of the archive. It is possible to add automatically Date, Time and an individual Add-On to the archive name. Thus, archives have clear individual and informative names.

In addition: Specifies the contents of the archive in addition to the actual core data of a KRASTA system, which is archived by default, some additional data can be selected for archiving.

The input shown in the dialog here corresponds to the default settings plus an add-on “V01” for the archiving of a KRASTA system named “Gantry Crane”.

AutoBack.zip

A special form of the KRASTA archive is an automated backup when saving. Each time the system is saved; the “Auto-Backup” will be created or overwritten.

This ensures that the most important information of a KRASTA system is stored compressed in a file. This file allows to handle a KRASTA system easily with conventional backup strategies and to save it completely and consistently in itself.

Only the most crucial data, e.g. no computation results, are stored into the archives.


4.4 Selection of Beams and Nodes

4.4.1 Current Selection

At any time a “Current Selection” exists of beams and, independently from that, of nodes, which contains the currently selected beams or nodes respectively.

The selection of beams or nodes is modifiable in many ways. On way is graphically interactive by selecting single or multiple beams or nodes by picking with the mouse, another way by selecting existing lists or by selecting specific beam or node properties (menu item Selection)

If a selection acts additive or subtractive to the current selection is controlled by the Selection Mode (p.27).

4.4.2 Selection Mode

Single or multiple beams resp. nodes can be

selected, i.e. be added to the selection,

deselected, i.e. subtracted from the selection, or

inverted, i.e. selected be deselected and deselected be selected.

These selection modes are applied all same kind for graphical interactive, for selection in respect to properties and for selection of an existent list.

4.4.3 Changing the current selection, graphically interactive

The selection is done with the left mouse button by clicking single objects or by drawing a rectangular area.

Always, there are

only beams or

only nodes selected.

But by choice

single beams or nodes,

subsystems

subsystem branches or

all.


When selecting "subsystems", "subsystem branches" or "all", not the single beams or nodes are selected, but the entire subsystem. This difference is important for simple beam and node lists, as this selection state is adopted exactly in the list. Nodes and beams which are added to subsystems subsequently are automatically included in the beam list if the subsystem is included in the list.

The current selection state is shown in a status line in the bottom right corner. It is differentiated between beams and nodes in general and single beams or nodes, subsystems and subsystem branches.

If subsystems are selected and according single beams or nodes are to be unselected, the selection state of the subsystem is transferred to the single nodes and beams and then the subsystem and the single objects are unselected. There is no selection state "whole subsystem without beam <xyz>".


4.4.4 Changing the current selection, in respect to beam or node properties

The current selection may change in respect to specific beam or node properties. At first a property type is chosen, KRASTA then offers a choice of all varieties present in the system.

All beams or nodes with the specified property are selected.



4.5 View, Display, Projection

The way how structural details or results are shown can be controlled in detail in many aspects, which can be stored for a quick reuse later. KRASTA here distinguishes between projections and display settings.

Projection Settings

Projection settings define from which spatial direction the model is shown.

In newly created KRASTA systems the projections setting “Dimetrie”, a diagonal view is available by default.

Display Settings

Defines extent and details of structural and result views.

In newly created KRASTA systems the display setting “Minimal” that shows beams and nodes is available by default.

4.5.1 Display Subset

KRASTA is able to switch between displaying the whole structure or a subset of beams and nodes. Therefore four menu items below main menu item “View” and at the context menu of the plot area are available:

Display Subset

Only the currently selected nodes and beams are shown as a subset. Unselected nodes of selected beams remain in the subset while unselected beams with selected nodes are removed from the subset.

Hide Subset

The currently selected nodes and beams are removed ffom the display subset.

Expand Subset

The subset is expanded at it edges by one beam and according node.

Display Everything

The whole structure is displayed. Beams and nodes of the previous subset are selected.


4.6 Colors and Captions

The settings of screen colors and text sizes reside at the main menu item View

4.6.1 Colors

The user (p.35) can set individual colors to be used by KRASTA.

You can reset the colors to default by the button Standard Colors.

Dialog: Colors

You find a button next to each color box for changing the color display.

4.6.2 Captions

You can define the header text of plot and text pages. Project Name, System Text and User Text can be set by the user, the Company Text can only be changed by the manager.

Dialog: Captions

The Project Name, System Text and Comment (white) is stored by the system. The User Text (blue) is stored individually for the current user. The Company Text is stored globally into the manager system and common to all users.


4.6.3 Text and symbol sizes

Dialog: Text and Graphic Sizes

In the dialog you can make the following settings:

The relative size of texts, node boxes, beam arrows and joints on the screen or printer resp. "1" is about 1.5% of the picture diagonal.

The relative distance to the margin

The pick sensitivity radius in pixel

The thickness of lines [approximately in mm]

In multiplication to the above (common) text size factor the field Text Sizes provides particular text size factors.


4.7 Printing

You can print out text and plot files with the menu item Print.

For printing, you can find and select your previously saved Text- and Plot-Files of this system in the according list boxes. You can also print out (ANSI text) files, which are not created by KRASTA.

Dialog: Printing

For the selected text or plot files the page layout is shown which was selected during creation of the file.

Plots can be output in normal (position as on the screen), rotated or optimal adapted in the existing frame.

Text or plot files can be added to the output files by clicking the button Add or by double click.

A preview of the text or plot files can be shown in an individual window by clicking the button Display.

You can select text and plot files and delete them by clicking the button Delete.

Selected files for printing can be marked and removed from the list „Files to Print“ by clicking the button Remove.

For the files which are to be printed a Start page number can be committed. Then the files are printed continuously with page numbers in that order as they are in the list.

You can enter a chapter heading and/or number for the files which are to print at Chapter.

You can change the printer settings by clicking the button Printer Setup.

The appropriate Windows standard dialog appears.


4.8 Page Layout

You can define Page Layouts for text and plot prints.

Page Partitioning

The user can set the following parameters:

Number of header and footer lines

Margins left, right, top and bottom

Font size of header and footer lines

Font size of text/plot area

Width of the frame lines

The sheet is partitioned as shown.

There is a different size of printable area on the sheet dependent on the used printer and printer driver.

Dialog: Page Layout

You can set the margins for left, right, top and below in millimeters. The distance to the margins always relate to the printable area.

Additionally you can define header and/or footer lines within the frame. The size of the head or bottom lines is dependent on the used font size (default: font size 10 point).

The area, where pictures or texts can be displayed, result from the frame minus the header and footer area.

The number of lines and columns which can be displayed on the sheet (default: font size 10 point) are dependent on the used text font.

This number of lines is calculated by the program to fit within the margins, considering the font size and number of header and footer lines and the currently set standard printer.

Paper Size

Header Lines

Printable Area

Frame

Plot Area

Right Margin

Left Margin

Top Margin

Footer Bottom Margin


4.9 Options

In the main menu item “Option” different settings can be made.

4.9.1 Units

The units can be set individually in Global (green), For current User (blue) and For current System (white) (see User Setting and Setup (p.13)). The Global unit settings are used if no other values are set.

Setting an arrow (->) instead of the dimension, the dimension of the unit is taken over from the column which stands right beside it.

Dialog: Units

4.9.2 Languages

Languages can be set for the current system (white) and/or User (blue) separately for screen Dialogs and textual Output individually.

If an arrow (->) is selected instead of a language, the language selected on the right is used.

Dialog: Languages

4.9.3 User

Users can be created, edited, copied or deleted. Changing of the user setting (p.13) can only be done by the KRASTA-manager. The manager has to authorize before manipulating users by his Manager Password.

4.9.4 Automatic save

KRASTA is able to automatically save or remind the user saving in certain intervals.

For further information see chapter KRASTA-Archives (p.25).

KRASTA 9.6 Manual Modelling 37

5 Modelling This chapter contains all topics in regard of the formulation of the physical model.


5.1 Coordinate Systems

KRASTA provides 4 coordinate systems:

Inertial System (p.39)

Subsystem Coordinate System (p.39)

Beam Coordinate System (p.39)

Principal Axes Coordinate System (p.40)

5.1.1 Inertial System

The inertial system (IN-CS) is the fixed global cartesian coordinate system.

5.1.2 Subsystem Coordinate System

Each subsystem has its own subsystem coordinate system (SS-CS), in which the according objects are defined. In the KRASTA-basic version the SS-CS is equivalent to the IN-CS.

5.1.3 Beam Coordinate System

For each beam a beam coordinate system (BM-CS) (x0, y0, z0) is defined. The SS-CS is defined by the start of the beam, the end of the beam and an auxiliary vector. Cross sections are defined in the BM-CS.

The x0 points from beam start to the beam end.

The positive local x0 axis and the auxiliary vector define the plane in which the local y0 axis lies.

40 Modelling KRASTA 9.6 Manual

The definition of the local beam coordinate system can be described as follows:

The local x0-axis is defined by start and end node of the beam.

An auxiliary vector, described in subsystem coordinates, is input to the set the other local axes.

The cross product of x0 and auxiliary vector gives the local z0- axis.

The cross product of z0 and x0 gives the local y0- axis.

Section banks are set according to the convention positive inner forces point into positive coordinate direction at the end of the beam (positive section bank).

At the start of the beam positive inner forces point into negative coordinate directions (negative section bank).

During input of objects and attributes the user may choose among different coordinate systems. Beam loads, for example, may be input in IN-, SS- or BM-CS.

5.1.4 Principal Axes Coordinate System

The principal axes coordinate system (PA-CS) is rotated by a principal axis angle against the BM-CS.

At double or single symmetrical cross sections the PA-CS corresponds to the BM-CS. Inner forces and beam deformations are given in principal axes.

Cross sections are described in the local y0, z0 plane. If cross sections have principal axis angles different to 0°, the local beam axes are transformed into the principal axes for the solver input file.


5.2 Beams and Nodes

The structure consists of beams, which have six degrees of freedom at each end. They can transmit normal forces, shear forces as well as bending and torsional moments.

A beam is determined by a start and an end node.

At one node several beams may start or end.

Beams are physically connected with each other by assignment of identical nodes.

Beams and nodes can be given beam properties or node properties respectively.

Nodes are described in a spatial cartesian coordinate system.

Beams and nodes are associated with just one, their subsystem.

In this chapter the individual properties of beams and nodes are described.

The description of how to compose a structure (p.47), handling of subsystems (p.103), mass cases (p.71) or load cases (p.75) is given in further chapters.

Beams and nodes are KRASTA objects (p.20) and have a name and a comment.

The beam and node properties can be edited individually for a certain beam or node by the appropriate edit dialog.

Additionally, most beam and node properties can be changed for all beams and nodes of the “Current Selection” at once. The corresponding menu items can be found below the main menu item ”Property”.

5.2.1 Beam and Node Name

The name is unique in the subsystem, but possible repeated in another subsystem. A global unique identifier is given with the combination with its subsystem name.

Beams and nodes, as well as all KRASTA objects, may be renamed at every time.

Dialog: Name Assignment


5.2.2 Beam Properties

Beams can have the following properties:

Name (p.41) and Comment

Springs (p.42)

Joints (p.42)

Force Conditions (p.42)

Auxiliary Vector (p.43)

Material (p.43)

Cross Sections (p.43)

Beam Masses (p.43)

Beam Mass Factors (p.43)

Section Points (p.44)

Beam Buckling Data (p.44)

5.2.2.1 Beam Springs

The connection between beam and node is rigid by default. Springs may be used to define elasticity between beam and node.

5.2.2.2 Joints

Beam joints provide translational and rotational degrees of freedom between beam end and node.

Beam joints are beam properties, they are defined in the beam coordinate system of the beam.

If the beam coordinate system does not correspond with the desired directions of the joint axes a short (rigid) beam with the desired local axes can to be created.

Joints at the beams 1 and 2 in the left part of the figure do not result in rotational degree of freedom around the dashed axis, but joints at the auxiliary beams 7 and 8 do.

5.2.2.3 Force Conditions

For elements that can only transmit forces that are higher or lower than a certain value, force conditions can be defined. They behave like an ideal elastic-plastic material.

Typical applications for such elements are ropes that only transmit tension, wheels and legs, that only transmit pressure or hydraulic buffers that only transmit a limit force.

A more general form of force conditions, e.g. across multiple beams, can be formulated via Constraint Conditions (p.91).

Caution: These elements can only be used with linear theory!


5.2.2.4 Auxiliary Vector

The auxiliary vector describes the orientation of the beam coordinate system. The usage of the auxiliary vector is described in the chapter coordinate systems (p.39). All components of the auxiliary vector are initially zero.

For the H-section girder in the following figure several possibilities for the position of the inertial coordinate system are represented together with the corresponding auxiliary vector definition.

5.2.2.5 Material

KRASTA allows the definition of different materials like steel or aluminum by the input of specific material properties.

For proofs a material may need to be classified according to a standard.

5.2.2.6 Cross Sections

KRASTA provides four different types of cross sections:

Thin-Walled Cross Sections (p.54)

Direct Input Cross Sections (p.52)

Standard Cross Sections (p.66)

Parametric Cross Sections (p.55)

Please refer to chapter Cross Sections (p.51) for details.

5.2.2.7 Beam Masses

Concentrated or distributed beam masses which are stored as "Permanent Mass" (p.71) with the beams can be applied to any location on the beams. A beam can have several beam masses.

5.2.2.8 Beam Mass Factors

The "constant" beam net mass, calculated from the cross section area and material density, can be modified by the input of a beam mass factor.

The overall mass distribution can be adapted to given material lists by the usage of beam mass factors, beam masses and node masses. With the mass distribution described in that way, all acceleration (inertia) loads (including dead weight) can be generated easily.


5.2.2.9 Section Points

By default inner forces and beam displacements are calculated at the start and the end of beams only.

Additional section points can be defined in order to evaluate inner forces and stresses for specific locations along the beam.

5.2.2.10 Beam Buckling Data

Beam Buckling Data define beam buckling properties of an individual beam. They are used in proofs of buckling (e.g. acc. DIN 4114 (Omega-Method)).

The Beam Buckling Data is defined for each principle axis separately by the user.

Slenderness

If required, KRASTA evaluates the actual beam slenderness for each principle axis separately, based on the directly or indirectly defined beam buckling length and cross section properties and or :

√ ⁄

√ ⁄

For conical beams the smaller of the inertia radii associated to the end cross sections is used, seperately for each principle axis ( ). This results in a save upper approximation of the

slenderness of a conical beam.

Dialog: Beam Buckling Data

Separately for each principle axis, the following options to specify the beam buckling length are available:

Specification of a buckling length coefficent

Specification of a buckling length .

The values of buckling length and buckling length coefficent are both stored independently from each other.

If a buckling coefficient is specified for a principle axis then KRASTA determines the according

buckling length based on the current beam length .

The beam length is defined as the distance between start and end node of a beam. Therefore, the beam length may differ from the net length of the buckling beam / of the buckling problem.

If beam buckling data is edited for multiple beams at once, the already associated beam buckling data is not shown in the dialog. In this case it is possible to keep the data unchanged or to delete the data separately for each axis.


5.2.3 Node Properties

Nodes can have the following properties:

Name (p.41) and Comment

Node Masses (p.45)

Support Conditions (Joints/Springs) (p.45)

Displacement Conditions (p.45)

5.2.3.1 Node Masses

Node masses can be assigned to the nodes. These masses are stored as "permanent mass" with the nodes.

5.2.3.2 Support Conditions (Joints/Springs)

Each individual degree of freedom can be defined as rigid, jointed or can be given a spring rate.

5.2.3.3 Displacement Conditions

For nodes with displacement conditions, KRASTA automatically determines the outer reaction forces necessary to meet the conditions. These reaction forces are displayed and documented as ordinary support forces.

If limit displacements are specified, there is no reaction if the limit is already kept.

Dialog: Displacement Conditions

Displacement Conditions are always defined in the global inertial coordinate system. The following types are available: “Lower limit”, “Upper limit”, “Target” and “unchanged”.

Caution: Displacement conditions can only be used with linear theory!


5.3 Construction

The term “construction” refers to the various steps to create and modify the structure made of nodes and beams.

These steps are

creating, editing or deleting nodes or beams,

translation, stretching, copying and mirroring of nodes and enclosed beams

spliting and reversing beams

checking for double nodes and beams

5.3.1 Split Beam

The splitting options defined in the dialog are applied to all currently selected beams.

Beams can be split in two or more beams at one or more (split-) points. For each point a new node and a new beam is created automatically. The new nodes and beams get node and beam properties automatically to form a statically equivalent system. Note: Loads and Masses may not be transformed in a proper way and may be adjusted manually.

Beams can be split in different ways:

Number of points: The beam is split into equidistant sections.

Equidistant: Sections with the given length are split off the beam, beginning at the start (or end) of the beam. The last section may be shorter than the given length.

Single point absolute: The section, where the beam is to be divided, is defined by an absolute distance from the start (or end) of the beam.

Single point relative: The section, where the beam is to be divided, is defined by a relative distance from the start (or end) of the beam.

At Plane: The beam is divided at the intersection with a defined plane.

Dialog: Split Beams

To split beams at a plane, the Coordinate System has to be selected first. The inertial system (p.39) or the subsystem coordinate system (p.39) may be selected to define a point and a normal vector.


A point in the plane is to be defined. The coordinates of the point can be entered via keyboard or by a Graphical Selection of a node.

Then a normal vector is entered, which is perpendicular to the plane. This vector can be entered via keyboard or by a Graphical Selection of two nodes.

All selected beams, which are intersected by the defined plane, are divided at the intersection points.

5.3.2 Reverse Beams

Reversing Beams allows to change the beam orientation without changing the static properties. In this sense it is complete to swap begin and end node and swap all beam properties in regard to the new beam orientation as well. To handle nonsymmetric cross sections or cross sections with an angle of principle axes different from 0° the auxiliary vectors and cross sections have to be readjusted by the user properly.

Dialog: Reverse Beam

5.3.3 Translation, Stretching, Copying and Mirroring

Translating, stretching, copiing or mirroring parts of the structure is done in a very similar manner.

The current selection of nodes specifies the substructure to be copied or to translated.

Geometrical Specifications

A translation is defined by a distance vector.

A rotation is defined by an axis and an angle.

A mirror plane is defined by a locational point and a normal vector perpendicular to that plane.

A “stretch” is defined by an origin, a direction and a stretch factor.

Move

For moving a structure you may select

If coincident objects should be merged. Objects in identical locations will be merged by deleting the newer object (refer “Merging (p.49)”).

Copy

For copiing a structure you may select

If (and for which) nodes a new beam shall be created between master and copy.



Mirroring

For copiing a structure you may select

If (and for which) nodes a new beam shall be created between master and copy.


Which beam axis (for the purpose of right-handed coordinates) should not be mirrored.

Since the beam coordinate system must always remain right handed, not all of the three beam axes can be mirrored. If the longitudinal beam axis is not mirrored, an additionally choice is available, if physical characteristics should be adapted. If the longitudinal beam axis is not mirrored but physical characteristics should be adapted, this is similar to a beam reversal without switching start and end nodes.

Stretching

The distance to the origin, projected in the direction of stretch is scaled by the factor. Consequently, scaling by zero is Projecting the structure into the plane.

Scaling

To scale a substructure by a certain factor, three sequel stretches have to be done in each of the three spatial directions

Insert new objects into lists

After copying, mirroring and splitting a dialog “Insert new objects into lists” occurs if necessary.

KRASTA examines in which beam and/or node lists the master objects are included. KRASTA offers to select to which lists the copies shall be added.

5.3.4 Rounding

Allows to round the Coordinates and Aux.-Vector components of currently selected nodes and beams to the defined precision.

Dialog: Rounding

5.3.5 Check for double beams or nodes

Multiple nodes and/or beams can be defined at the same location. Beams or nodes at the same location are not connected in respect to the static system, as long as this is not explicitly defined.

KRASTA can check for coincident beams and/or nodes. If found, KRASTA offers to merge coincident nodes and selects coincident beams.

Merging

Merging is done in regard to structural interconnection, but not in regard to masses or loads.

Caution: By discarding nodes all mass and/or loads applied to them are omitted.


5.4 Cross Sections

In KRASTA four different types of cross sections are available:

Direct Input (p.52), also Partial Rigid Cross Sections (p.52)

Thin Walled Cross Sections (p.54)

Parametric Cross Sections (p.55)

Standard Cross Sections (p.66)

Cross Sections can be provided in libraries from where they can be inported.

For common standard cross sections, libraries are provided.

5.4.1 Points for Proof of Stresses

Points for proof of stresses define locations within cross sections for which KRASTA calculates stresses. These points are already defined for parametric and thin-walled cross sections. For direct input cross sections points for proof of stresses may be defined manually.

Classification

Where appropriate, the stresses are taken into account according to specific proofs. Additional classifications according to standards may be required. Example: Proof of fatigue according DIN 15018 (p.165).

Selection

Point for proof of stresses can be selected (active) or not selected (inactive). Only selected (active) points for proof of stresses are taken into account by proofs or results.

Structural Thickness

For some proofs direct input cross sections require a thickness to be defined for the points for proof of stresses. Example: Proof of Stresses elast.-elast. according DIN 18800 (p.207). If no thickness is specified KRASTA assumes the best case for thickness dependend values.

Welding seams

Points for proof of stresses can be specified to represent a longitudinal welding seam. This information will be considered at proof of fatigue according DIN 15018, for example.

Scope

All attributes of points for proof of stresses (e.g. notch cases) are effective for all beams with this cross section and at all section points of these beams. If on single points other attributes are to be used, a copy of the cross section can be used and modified as desired.


5.4.2 Direct Input Cross Section

Dialog: Cross Section - Direct Input

Six cross section values can be input::

Ax Cross sectional area

Ay Shear area

Az Shear area

Ix Polar area moment of inertia

Iy area moment of inertia around y-axis

Iz area moment of inertia around z-axis

Optionally it is possible to specify points for proof of stresses (yp, zp) and their unit stresses, which will be used in proof of stresses.

It is possible to specify one or more section values as rigid, see Partial Rigid Cross Sections (p.52).

5.4.3 Partial Rigid Cross Sections

(Partial) rigid cross sections are cross sections, with one or more rigid cross section values.

A checkmark indicates the corresponding cross section property as rigid. Note: Even rigid cross sections have a weight calculated by

For example, fully rigid direct input cross sections can be used for auxiliary beams at excentric connections or to meet correct load and mass points.

Beams representing ropes usually have a partial rigid cross section with elastic cross sectional area only and rigid other cross section values. Additionally the beams may have joints at the ends in order to transfer normal forces only.

Notes on using rigid cross sections

When using (partial) rigid cross section be careful not to limit elastic deformations of adjacent elastic cross sections. This can lead to a stiffness bandwidth within the structure that may result in numerical problems during calculation. There are no warnings in this matter.


Example: Use of rigid cross sections

The mass of a control cabin shall be applied in the correct location (Fig. “Cabin”).

For this purpose a rigid set of beams is modelled at the platform consisting of a bracing in the platform and a rigid beam from the center of the bracing to the approprate height (Fig: “rigid bracing”),

The rigid bracings prevent elastic deformation of adjacent elastic beams. This region of very high stiffness may attract inner forces massively higher than the applied loads. In regions of “normal” stiffness the numerical percision may then some percent of the applied loads. A symptom may be a significant difference between applied loads and according support reactions.

It is better to add joints that way that the angles within the rigid bracing can vary freely (Fig.: “joints”). Adjacent beams may distort and the inner forces are about the magnitude of applied loads.

Fig. „Cabin“

Cabin

Fig. „rigid bracing“

rigid bracing

no distortion possible

Fig. „joints“ possible distortion


5.4.4 Thin-Walled Cross Sections

For thin-walled cross sections the plate thickness has to be small in comparison to the dimension of the cross sections.

The thin-walled cross section has to be decomposed into individual parts before input. The input of the parts is done in the beam coordinate system. The number of cells is not limited.

The length of the parts can be input or calculated, if the start and end point of the part in question are defined by other parts. The plate thickness and optionally a point area have to be given.

Dialog: Structural Input of thin-walled Cross Sections

Point areas can be used to replace cross section parts which are small in comparison to the total dimension. In this way rolled radii, welds or stiffeners for example can be input as point areas. For the point areas only the Steiner-parts only are taken into consideration for the determination of moments of inertia.

The following basic cross section properties are calculated from the input:

Areas and moments of inertia

Center of gravity, center of shear forces, principal axis angle

Unit stresses as a result of bending, shear and torsion in the plate centerline

Unit warp coefficients and normal shear forces

Shear forces per plate to carry partial inner forces

It is possible to define conical beams by assignment of two geometric similar thin-walled cross sections to start and end of a beam. The unit stresses are determined for any beam section points by interpolation of the existing cross section geometry.


5.4.5 Parametric Cross Sections

Parametric cross sections are described by a limited number of geometrical parameters.

The cross section values and the unit stresses are calculated as a function of the parameters.

5.4.5.1 Calculation formulas

Cross sectional area

The area is directly calculated from the cross sectional dimension. The cross sectional area is used for the calculation of the cross sectional weight.

Shear Areas

The shear areas are calculated using the factor .

with

∫ (

)

Statical Moment

∫

∫

Center of Gravity

The center of gravity is calculated relative to the input coordinate system.

Center of Shear Forces

The center of shear forces is calculated relative to the input coordinate system.

Torsional Moment of Inertia


∮

(2nd

Bredt Formula)

For thin-walled open cross sections (H, C and L-Sections) the Bredt Formula extends to:

∑

For determination of IT a correction factor is used for thin-walled sections. The exact value is shown in the description of the specific cross sections.

Moments of Inertia

The moments of inertia are calculated with the help of the Steiner Theorem, radii are considered with their moment of inertia and the Steiner part. More complicated cross sections are decomposed into partial cross sections, for which the individual moments of inertia are calculated and combined.

∫

∫

∫

For asymmetric cross sections (L-Sections) the principal axis angle and the moments of inertia about the principal axes are calculated.

Principal Axis Angle:

The principal axis angle defines the rotation of the principal axes against the beam coordinate system.

Moments of Inertia about the Principal Axes:

The moments of inertia about the principal axes follow are determined as follows:

( )

( )

( )

( )

Torsional Moment of Resistance

The torsional moment of resistance for St. Vernant torsion is calculated according to the Bredt Formula.

(1st Bredt Formula)

For thin-walled sections

∑

Bending Moment of Resistance

The bending moment of resistance is calculated from the moment of inertia and the distance of the section center line to the outmost edge.

Normal Stresses as a result of Normal Force

The stresses as a result of normal force are calculated from the force acting in longitudinal direction of the beam and the cross sectional area.


Bending Stresses

The bending stresses are calculated from the bending moment and the bending moment of resistance.

Torsional Shear Stresses

The torsional shear stresses are calculated from the torsional moment and the torsional moment of resistance.

Shear Force induced Shear Stresses

The shear force induced shear stresses are calculated from the shear force, the statical moment, the moment of inertia and the thickness according to the "Dowel" Formula.

Sign definition:

At open cross sections the shear stresses resulting from torsion and shear forces are positive in positive beam coordinate direction, at closed cross sections (tube and rectangular tube) in mathematical positive direction of rotation.

Plastic Moment of Resistance

The plastic moment of resistance is determined to the double of the statical moment.


5.4.5.2 Types of Parametric Cross Sections

In KRASTA at the following parametric cross sections are available:

H-Section (p.59)

C-Section (p.60)

L-Section (p.61)

Rectangular Tube (p.62)

Rectangle Section (p.63)

Round Section (p.64)

Circular Tube (p.65)


H-Section

Input parameters for the H-Section:

Width b

Height h

Flange thickness tg

Web thickness ts

Rounding radius r

All cross sectional values except the shear areas and torsional moment of inertia are calculated exactly for the shown H-Section (equivalent to IPE or HE). The cross sectional values for "old-style" H-Sections (sloping flanges) can be approximately calculated with this model.

The shear areas and are determined according to thin-walled theory.

The torsional moment of inertia is calculated with the formula for St. Venant torsion for thin-walled cross

sections. The formula is extended with a factor for consideration of the radii.

(

( ) ) , , {

For the H-Section 11 points for proof of stresses are available.


C-Section

Input parameters for the C-Section:

Width b

Height h

Flange thickness tg

Web thickness ts

Rounding radius r

All cross sectional values except the shear areas and the torsional moment of inertia are calculated exactly for the shown C-Section (equivalent to UAP). The cross sectional values for simple C-Sections (sloping flanges) can be calculated approximately with this model.


The torsional moment of inertia is calculated with the formula for St. Venant’s torsion for thin-walled

composed cross sections. The formula is extended with a factor for consideration of the radii.

(

)

For the C-Section 9 points for proof of stresses are available.


L-Section

Input parameters for the L-Section:

Height a

Width b

Thickness s

Rounding radius r1

Rounding radius r2

The shear areas for the L-Section are simplified determined to the area of the flanges.

The values for the moments of inertia and the moments of resistance are output in the principal axes coordinate system.

For the L-Section 3 points for proof of stresses are available.


Rectangular Tube

Input parameters for the rectangular tube:

Width b

Height a

Thickness t

Rounding radius r


For the rectangular tube 8 points for proof of stresses are available.


Rectangle Section

Input parameters for the rectangle section:

Width b

Height h

The shear areas are calculated from the cross sectional area using a correction factor.

For the torsional moment of inertia and the torsional moment of resistance the following approximation equations are used:

[

(

)

]

[

(

)

]

[

(

)

]

[

(

)

]

For the rectangle section 9 points for proof of stresses are available.


Round Section

Input parameter for the round section:

Diameter d

The shear area is calculated from the cross sectional area using a correction factor.

The unit stresses resulting form shear force are calculated according to the formula:

The number of points for proof of stresses is variable for the round section.


Circular Tube

Input parameters for the circular tube:

Diameter d

Wall thickness t

The shear areas are calculated from the cross sectional area using a correction factor.

with (

)

The number of points for proof of stresses on the tube is variable.


5.4.6 Standard Cross Sections

Standard cross sections like e.g. H, L and C sections are standardized cross sections where cross sectional values are directly taken from manufacturers lists. Additional values are calculated according to the corresponding parametric cross sections.

5.4.7 Import Cross Sections

A cross section, as all other KRASTA Objects (p.20) can be imported from other KRASTA systems or from KRASTA standard cross section libraries.

If the user selects Other KRASTA system, a dialog appears to select the system to import from. If you open a system for import, a multiple selection appears, listing all available cross sections on the left hand. On confirmation, all cross sections shown on the right hand will be imported.

5.4.8 Plot Cross Sections

To print (p.33) cross section plots, the menu item “Cross Section | Plot…” is available. A Multi-Selection-Dialog (p.22) is opened, listing all currently defined cross sections.

For each selected cross section, a Plot-File is created. The plot file contains the graphical representation and additionally common cross sections data as name, section values, principle axis angle and center of shear forces.

A detailed list of all cross sections properties is available by “Text Documentations (p.223)”.

5.4.9 Clean Up Cross Sections

A way to clean up the system of currently unused cross sections (or to list such) is available by the menu item “Cross Section | Clean up…”. A Multi-Selection-Dialog (p.22) is opened, listing all currently unused cross sections.


5.5 Material

KRASTA allows the definition of different materials like steel or aluminum by the input of specific material properties.

A material needs a classification according to each standard, with which it is to be used.

Dialog: Material

The following material characteristics have to be entered in the current selected units:

Elasticity Modulus

Shear Modulus

Density

Thermal Expansion coefficient

The following values are optional:

Yield Point

Tensile Strength

Classification

In the Classification field you can select a Classification in the scope of several Standards. The list of available classifications depends on the standard you have selected. Use the button Add > to add the current classification on the left hand to the list of Chosen classifications. The button < Remove to remove the selected one from the list.

5.5.1 Clean Up Materials

A way to clean up the system of currently unused cross sections (or to list such) is available by the menu item “Material | Clean up…”. A Multi-Selection-Dialog (p.22) is opened, listing all currently unused materials.


5.6 Lists

Object lists are used to manage a group of objects (p.20) of one type. For example loads can be applied to a list of nodes or a list of beams can be set inactive for a solver run.

Lists are KRASTA Objects (p.20) and have a name and a comment. Lists can be created new, copied, edited or deleted.

The „used by“-box contains the objects (e.g. Load Cases) already using this beam list. If a list is no longer used, KRASTA asks the user if it should delete the specific list.

Below the main menu item “List”, the commands to create beam- or node-lists can be found. List for other objects are located close to the menu items for these objects.

Along with simple lists, which contain single objects, there are composition lists, with which other lists can be related with operators, and filter lists, where the content is created dynamically according to filter criteria.

Additionally to user defined lists, KRASTA knows some generic lists like “$all_nodes” or “$all_beams”.

5.6.1 Simple Beam or Node Lists

Beam or Node Lists creation

If a simple beam or node List is newly created, the dialog to edit beam or node lists is opened. As pre selection, the “Current Selection” (p.27) will be taken over to edit.

Beam or Node Lists editing

By editing a simple beam or node list, the selection specified by the list is made the “Current Selection” and the dialog edit beam or node lists is opened.

Dialog: List

If this dialog is present, the “Current Selection” (p.27) represents the content of the just edited list. The selection can be edited, i.e. changed.

Use Select Model to select the objects of other list.

5.6.2 Other simple lists

Multiple Object Selections (p.22) are usually used to edit simple object Lists except node and beam lists. On the right side the selected objects are shown, on the left the remaining ones.

The sequence [1] of lists can be explicitly set [2]. The sequence is important for executable lists in particular.

In the example dialogue the situations are evaluated in the result set "In Service" in the sequence shown.

Lists of Results or Proofs

It is possible to create lists of result and/or proof control sets (p.215). These lists are executable, i.e. the result resp. proof result sets are computed one after the other in a specified order.

The textual output (p.216) from individual results and proofs are cumulated in single text output. The textual output can be narrowed to the intrinsic result data (minimized output) or fully documented.

[2]

[1]


5.6.3 Composition Lists

Lists and single objects can be composed with composition lists, using the operators "Add", "Subtract" and "Intersect". The composition is performed according to the sequence shown, accordingly, every compostion step uses the result of previous steps. This should be considered when using operators "Subtract" and "Intersect". It is not possible to put parantheses to influence the composition order. Instead, composition lists can be used in composition lists.

The composition is done every time the list is evaluated; it is not just an assistance to generate a fixed list of single objects.

5.6.4 Filter Lists

List contents can be created dynamically with filter lists according to up to three filter criteria. The criteria are related using logical operators "and" and "or".

The criterion “Name” must be mentioned explicitely, as it refers to the base name of objects only. For names a few comparison options are available. By comparison option "begin with", objects will be found if the object name begins with the filter string. For example, by a filter "Name" "begin with" "Susp" all objects with the base name "Suspension” as well as objects with the base name "Susp. Pylon” will be catched.

An extension of a filter criterion by "and" adds a further restriction, "or" opens an alternative. In the above example the beam name has to “begin with” “Susp” and the beam cross-section have to be "HE M 280_" to let the beam be in the list.

The filtering is done every time the list is evaluated; it is not just an assistance to generate a fixed list of single objects.

5.6.5 Clean Up of Lists

A way to clean up the system of currently unused or empty lists (or to list such) is available by the menu item “List | Clean up Lists”.

The following cases are handled separately:

All empty Lists

All unused Lists

List which are empty and unused

For each case, a Multi-Selection-Dialog (p.22) is opened, offering the according lists to delete.


5.7 Mass Cases

Mass cases can be used for modelling fixed, variable or moveable masses placed on the structure.

Mass distributions are usually composed of permanent available masses, masses variable in magnitude (e.g. counter weight, pay load) and moveable masses (e.g. trolley positions).

The net mass distribution of the construction is calculated as the product of cross sectional area and density. Usually the real mass is larger than that. Connections, transverse diaphragms, electrical equipment and further parts are added, which are not included in the statical model. To describe the mass distribution more exactly, beam mass factors can be applied to represent evenly distributed additional masses. For local mass concentrations node- and beam masses (concentrated or distributed) can be defined.

5.7.1 Permanent Mass

The special basic mass case "Permanent Mass" comprises masses which are directly stored for beams and nodes and therefore remain with these objects if they are copied or imported with subsystems [OPTION]. Masses can be applied to beams and nodes in the Property menu or in the beam or node dialog.

Example: Permanent Mass

5.7.2 Basic Mass Cases (BMC)

Basic mass cases containing mass factors and individual masses can be defined for variable or moveable masses or to describe parts of a model that are to be accelerated

Mass factors can be applied to the permanent mass where you can select whether it should be applied on the distributed mass (resulting from sectional area and density) and/or on the beam and node masses.

This mass information is assigned to beam and node lists. On calculation of the mass the permanent mass (beam mass factors, beam masses, node masses) of the given objects in the lists is then multiplied by the respective mass factor. Additional individual masses are added.


Dialog: Basic Mass Case

A basic mass case, as well as all KRASTA Objects (p.20), have a name and a comment.

Additionally, it contains a list of individual mass components of type

Mass Factor,

Beam Mass or

Node Mass.

Each of these mass items is assigned to an individual list of nodes or beams charged by this mass item.


5.7.2.1 Mass Factor

The mass specified in a basic mass case by a mass factor

is in general form:

[ ( ⏟

⏟

)

⏟

]

mit: | | resulting netto beam mass

(distrib.) or (conzentr.) (additionally) mass, specified at beam.

mass factor, specified at beam.

node mass, specified at node.

Herein, the mass items “Mass Distribution”, “Beam Mass” and “Node Mass” can be activated or de-activated individually.

Dialog: Mass Factor

Note: Mass items with type mass factor are assigned to a beam list, and adjacent nodes. Node masses of the end nodes of the beams in the beam list are applied with the factor. To calculate the assigned

node mass

of the bordering nodes, the node masses are considered as equally distributed over

the beams connecting there.

Basic Mass Case: Permanent Mass

The basic mass case “$Permanent Mass” is defined internally as mass factor 1.0 applied to the beam and node mass of all beams and nodes. Thus, the “permanent mass” is the sum of all masses which are assigned to beams and nodes directly.

5.7.2.2 Beam Mass

As a component of a basic mass case (p.71), a list of beams can carry concentrated, uniform or trapezoidal distributed (additionally) masses.

Dialog: Beam Mass


5.7.2.3 Node Mass

As a component of a basic mass case (p.71), a list of nodes can carry concentrated (additionally) masses.

Dialog: Node Mass

5.7.3 Combination Mass Cases (CMC)

Basic mass cases can be supplied with factors and combined to combination mass cases.

Different mass distributions can easily be described by this means. Basic or combination mass cases are used in description of inertia load cases and for the modal analysis. With a consequently mass orientated input all inertia loads can be generated with ease.

Dialog: Combination Mass Case

The assembly of a combination mass case is done analogue to that of combination load cases (p.80).

If selected, the mass case gets the current specified Factor as combination factor. The combination factor can be reassigned to the currently selected mass case.

Combination mass cases are able to contain combination mass cases themselves. To get an overview over all mass cases contained in a combination mass case, the combination mass case can be displayed expanded.

5.7.4 Situation Dependent Mass Case (SMC)

A “Situation Dependent Mass Case” allows to refer to different mass cases in respect to the currently evaluated situation. Individual masses or even individual mass factors can be taken into account for each situation in an explicit and centralized manner.

“Situation Dependent Mass Cases” are similar to “Situation Dependent Load Cases”. Both cases are described together in the chapter “Situation Dependent Mass and Load Cases (p.83)”.

5.7.5 Sum of Masses

The Sum of Masses of a basic or combination load case is shown as a part of the information window (p.18), during textual documentation (p.223) of mass cases or for individual mass cases with the menu item. The total mass and the center of gravity of the currently displayed subset is calculated.

Example: Sum of Masses


5.8 Load Cases

In load cases the loads on the structure resulting from outer forces or predeformations acting on beams and/or nodes is defined.

5.8.1 Basic Load Case (BLC)

A basic load case can consist of directly input loads and/or generated loads. The loads described below can be used with the solver PAS. For STAB88, which supports node loads only, all beam loads are converted automatically into equivalent node loads

Dialog: Basic Load Case

Basic mass cases, as well as all KRASTA objects (p.20), have a name and a comment.

It contains a list of individual load components of type

Beam Load,

Beam Predeformation,

Node Load,

Temperature,

Acceleration,

Wind,

Rope,

Linear Beam Predeformation,

Parabolic Beam Predeformation

Each of these load items is assigned to an individual list of nodes or beams charged by this load item.


5.8.1.1 Beam Loads and Beam Predeformation

It is possible to define concentrated, uniform or trapezoidal distributed beam loads or beam predeformations.

Loads with fixed directions can be described in the inertial (global) coordinate system. Loads that are to be moved with a subsystem or beam, can be described in the subsystem or beam coordinate system. If there are any principal axis angles, loads will automatically be transformed to the principal axes for solver input.

Loads distributed over a length can be projected for spatial beams if desired, where the force or the moment per unit of length is input in the inertial or subsystem coordinate system. The program projects loads according to fig. “Load Projection”. The load is adjusted so that the resultant is constant.

5.8.1.2 Node Loads

Node loads can be input in the according subsystem or in the inertial (global) coordinate system. One node load can consist of up to 6 components.


5.8.1.3 Acceleration Loads

The structure or parts of it can be accelerated translational or rotational and rotated (centrifugal forces). For a translational acceleration the direction of acceleration and its magnitude have to be described. For a rotational acceleration the axis of rotation, the rotational acceleration and/or the angular velocity are to be input.

The acceleration loads are generated from acceleration description and the mass distribution of a mass case.

As a special case of translational acceleration the accel-eration due to gravity is implemented, where only the direction of action of the weight has to be given.

Dialog: Acceleration Load

Here, specification of type, direction, magnitude and which mass to accelerate are made. The specifications may differ depending on the type.

Gravity Load

The Directions of Gravity specifies the direction of the gravity load and the Coordinate System in which the direction is defined. The absolute value of this directional vector is irrelevant.

Translational Acceleration Load

A translational acceleration is specified exactly like gravity acceleration, but it is possible to enter the acceleration magnitude.

Note: KRASTA is toggling the direction of the gravity load vector when switching between “Gravity” and “Translational” in order to keep the load direction.

Rotational Acceleration Load

A rotational acceleration is defined by

The Acceleration, which is the magnitude of the angular acceleration.

The Angular Velocity, which causes centrifugal forces.

The Location of Rotation Axis (Pivot), given by Reference Point and Distance to that point.

The Direction of Rotation Axis (axis direction).

Example: Rotational Acceleration Load


5.8.1.4 Wind Loads

The definition of wind loads is split into two parts, by specifying the wind pressure distribution in a wind (velocity) profile and by specifying beamwise wind resistance coefficients.

The wind profile is the same for all wind load items defined in one basic load case. Even it can be changed in each wind load subdialog.

Wind Profile

Different wind profiles can be defined. You have to input:

Wind direction (IN-CS or SS-CS)

Height ranges with according pressure

Direction of the height range gradation

Dialog: Windprofile

If no distribution profile needs to be specified, a Default Wind Pressure and the Vector of Wind Direction is sufficient.

To specify a profile the direction of the profile and the wind pressure at each altitude range is needed.

The default wind pressure is taken above as well as below individually specified altitude ranges.

Wind resistance

For the wind loads a factor with an according beam list is input. With this factor the resistance coefficient, cross sectional height, wind shadowing, aerodynamic effective length etc. is considered.

Dialog: Wind

Wind load on beams is specified by the Start Value and End Value (for Conical beams) of the dimension (drag coeff. * height) and a Wind Profil.

Wind load on nodes is specified by a wind area .

The wind profile is stored by the basic load case, so all wind loads of one basic load case use the same wind profile.

5.8.1.5 Rope Loads

The rope force and a series of nodes, which the rope shall follow, have to be input. To model a pulley the rope force can be given a different factor between two nodes. This calculation is suitable for 1

st order

theory only, as the course of the rope is modeled by forces with constant load directions.

Dialog: Rope Load

A rope load is defined by the following items:

The Rope Load.

The Pulley Factor, which multiplies the rope load for each part of rope specifically.

The Rope Polygon defined by a sequence of nodes. The route of the rope follows the order of the nodes. You have to select them graphically.

And in case of a Free End of Rope exists:

The Coordinate System, in which the free end of rope is described

The Rope Vector to define the direction of the free end.


5.8.1.6 Temperature Loads

For temperature loads a steady and a different warming at beam upper side and beam underside is possible. From the coefficient of thermal expansion, which is saved in material data and the temperature details, substitute predeformations are applied.

Dialog: Temperature

To edit temperature loads the corresponding dialog offers different sets of items, depending on the selected Temperature Profile along Beam Cross Section.

Commonly available are Start and End distance of the temperature load along the beam in Absolute or Relative beam coordinates probably measured From End.

In case of a Uniform temperature profile additionally only one Temperature(difference) can be entered.

In case of a Trapezoidal temperature profile the dialog offers the following description details:

Temperature at Edge Distance of Upper Side and Lower Side measured across the cross section.

The Direction of Cross Section Gradient to indi-cate in which direction the "upper side" is.

The temperatures and edge distances are used to determine the mean temperature(difference) plus the magnitude of the temperature gradient across the beam section.

The gradient direction vector is an auxiliary vector to determine the gradient direction angle in the cross section plane.

5.8.1.7 Linear Beam Predeformation

This type of load provides pre-distortion of particular beams, e.g. to take into consideration corresponding imperfections. For that purpose the angle and the axis of distortion is defined.

The linear beam predeformation internally consist of two beam predeformations at the start and the end of a beam.

5.8.1.8 Parabolic Beam Predeformation

This type of load provides pre-curvature to particular beams. Similar to the linear one the parabolic beam predeformation is also used to model imperfections.

To define a parabolic beam predeformation the distance and the direction of the apex from the middle

of the beam is used. The distance will be given in relation to the beam length by a fraction ( ⁄ ; e.g. with ).

With regard to universal use, the apex direction does not have to be perpendicular to the respective beam. Via appropriate longitudinal expansion it is possible to locate the "apex" in the requested direction.


5.8.2 Combination Load Case (CLC)

Basic load cases can be combined with partial safety coefficients (factors). These combination load cases can be combined with other combination and basic load cases again. The depth of combination levels is not limited.

Dialog: Combination Load Case

The assembly of a combination load case is done analog to a multi select dialog with an additional factor.

If added the load case gets the current specified Factor as combination factor. The combination factor can also be reassigned to the currently selected load case.

Example: Expanded Combination Load Case

Combination load cases are able to contain combination load cases themselves. To get an overview over all load cases contained in a combination load case, the combination load case can be displayed expanded.

5.8.3 Situation Dependent Load Case (SLC)

A “Situation Dependent Load Case” allows to refer to different load cases in respect to the currently evaluated situation. Individual loads and individual load factors can be taken into account for each situation in an explicit and centralized manner.

“Situation Dependent Load Cases” are similar to “Situation Dependent Mass Cases”. Both cases are described in chapter “Situation Dependent Mass and Load Cases (p.83)”.

5.8.4 Load Case 2nd Order Theory (TH2)

Structures can be calculated according to 2nd order theory (p.137). The equilibrium is formulated in a deformed condition, so that in the differential equation for bending,

the term is considered.

The torsion is considered according to St. Venant theory. Single beam matrices are assembled geometrically linear (Williot plan of displacement). The solution of the equation system is iterated on the normal forces.

Buckling loads can be determined by iterative increments of the loads. The buckling condition is met, if the denominator determination becomes zero.


Load cases 2nd

order theory can be combined with "or" in nonlinear logic load cases (p.82) to ease building load patterns for finding of extreme values (p.215) across all Situations (p.127).

5.8.5 Geometrical nonlinear Load Case (S88)

The program STAB88/NODYA [OPTION] (p.133) allows for geometrically nonlinear calculation of beam structures.

Using this type of load case, individual loads can be gradually applied according to a time function. After each load step the equilibrium between inner and outer forces is improved by an equilibrium iteration. Basic and combination load cases can be multiplied by factors, provided with according time functions and combined to a geometrical nonlinear load case.

5.8.6 Logic Load Case (LLC)

In many cases , especially when many acceleration loads are involved (as often used in material handling), it is not safely possible to tell, which combination of loads leads to the highest stresses in one certain point. Logic load cases can be defined for this purpose.

The following parameters describe a logic load case:

Of the load cases in the logical combination acts "Exactly One", "One or None", "All" or "All Possible Combinations".

Each load case can be given a factor and can possibly be defined to act in positive or negative direction.

The depth of nested logic load cases is not limited.

Dialog: Logic Load Case


Example: Logic Load Case

Wind

Wind "In-operation" can occur in four directions (or may not act at all)

LLC wind_in_operation = [± BLC wind_trans; ± BLC wind_along]; "One or None"

Accelerations by drives

Trolley drives and hoisting unit may operate simultaneously. Crane travelling only occurs, if hoisting unit and trolley drive are not in use.

BLC crane driving, CLC trolley driving, BLC lifting, BLC lowering

LLC hoisting unit = [BLC hoisting; BLC lowering]; "Exactly One"

LLC trolley+hoisting = [±CLC trolley driving; LLC hoisting unit]; "All"

LLC movement = [±BLC crane driving; LLC trolley+hoisting]; "Exactly One"

(Results in 6 possible combinations)

Variant: The crane can travel, while hoisting unit and trolley drive operate. In the last logic load case the option "Exactly One" is replaced by "All":

LLC movement = [±BLC crane driving; LLC trolley+hoisting]; "All"

(Results in 8 possible combinations)

5.8.7 Nonlinear Logic Load Case

Nonlinear load cases can also be arranged in a logic load case.

The nonlinear logic load case corresponds to the logic load case with the restrictions that the included load cases can only be considered with the factor 1, acting in positive direction only, and combined with "Exactly One" or "One or None".


5.9 Situation Dependent Load and Mass Cases

Situation dependent load or mass cases allow to refer to different load or mass cases in respect to the currently evaluated situation. (In the further reading, "load case" is synonym to "load or mass case".) A situation dependent load case does not define loads itself, but refers to another load case including an additional factor.

In a situation dependent load case, the correlation between load and situation can be described in an explicit and centralized manner without any impact to the remaining load case pattern. The whole load case pattern can be significantly laid out more clearly, easier to maintain and expand for additional situations.

Example: Situation Dependent Load or Mass Case

A practical application is a luffing crane with a hoist load depending on the outreach. One situation dependent mass case can list all hoist loads individual to the outreach situation. The remaining evaluation pattern stays simple by including situation dependent load cases and remains unaffected by situation and load relations.

A load pattern can be clearly laid out and general structured on the one hand and individual for each situation on the other hand.

Dialog: Situation Dependent Load or Mass Case

Explicitly listed cases

For each considered situation a “case” is defined by a triplet of “Situation or List of Situation”, “Factor” and „Load Case“ and added to the listed cases.

While evaluating a situation dependent load case, KRASTA scans through the sequence of listed cases for an applicable entry for the currently evaluated situation. If a matching entry exists, the referred basic or combination load case multiplied by the load factor is used.

Because a listed case can refer to a situation and to a list of situations as well, eventually a certain situation is referred more than once in the whole list. Nevertheless KRASTA always picks the first matching entry in the sequence of cases. All subsequent matching cases are ignored.

Default Load or Mass Case

The user can opt for three different policies, if no applicable entry is defined in the list of cases:

The evaluation is stopped with a warning message (default)

A zero load case is used

A defined load case is used


5.10 Load Events

The term “load event” is used in KRASTA to refer a particular Load Case (p.75) in a particular Situation (p.127). The KRASTA object “Load Event” gives such a pair of load case and situation a name.

Wherever in KRASTA pairs of load cases and situations are used, they can put together ad hoc or an already known Load Event object can be used.

Load Events are used to

• define Evaluation Pattern (p.217) or Load Sequences (p.87),

• calculate Results,

• plot results or

• document and describe relevant/decisive load events (p.216).

Methods of Load Events

Create New Edit, Copy, Delete

Load Events can be newly created, edited, copied or deleted just like other KRASTA objects (p.20).

Execute The execution of load events can be initiated from the applicable menus or from the editing dialog or by drag’n’drop.

The execution of a load event leads to execution of the associated situation (p.127) and (where applicable) display of the associated load case.

Calculate Provide or (re)calculate result data for the specific Load Event.

See “Calculate specific Results” for Details.

Dialog: Load Event

For new Load Events, the current Situation and (if applicable) the currently displayed load case is used as a preset.

The dialog to edit Load Events offer to

• change the Situation or Load Case,

• execute (p.127) the currently selected situation or

• edit, copy or show the currently selected load case.


5.11 Load sequences

A load sequence is an ordered list of load events, which describes a working cycle or a part of it. It is used by damage accumulation (p.162) based proof fatigues.

Load sequences are regular KRASTA objects with a name and a comment. A certain order of load events is defined, logic load cases cannot be used. Load sequences may be assembled from other (partial) load sequences to create complex work cycles.

When assembling load sequences it is possible

to reuse already defined partial sequences

to use repetitions and modify the sequence order

to consider additional base loads

Dialog: Load Sequence


Load Sequence:

The ordered list of load events may include the following:

Load Event: Object

This kind of load event refers to an existing load event object (p.85).

Load Event: [Situation, Factor * Load Case]

This kind of load event is an ad-hoc combination of particular load case in a particular situation. The loads can be provided with an individual factor.

Sequence:

Already defined load sequences can be used as a partial sequence. The loads can be provided with an individual factor and the partial sequence can be modified in respect due repetition and sequence order.

The following sequence orders are available:

"forward": The partial sequence of events is used in original order.

"reverse": The partial sequence of events is used reversed order.

"forth & back": The partial sequence is extended by the reverse of the partial sequence. The last load of the original partial sequence of events is taken only once.

The number of repetitions is considered for partial sequences. It multiplies the number of load events to be evaluated. Thus, only small repetitions counts (<10) should be used. The number of repetitions within a load sequence is not meant to indicate how often the load sequence will occur within the survival period. This is done by the weighting factor of the load sequence in the design spectrum.

Base Load:

The base load can be used to add a constant load, superimposed to all load events of the load sequence. It is possible to use a situation depended load (p.80) here.

If the list includes partial sequences with their own base load, these base loads are not replaced. The extra base load acts additive.

Example: Load Sequence “PS 15t D->A”

In the above dialog, the load sequence "PS 15t D->A” represents a trolley movement under load. The load case remains the same, but the trolley is moving through multiple situations.

Example: Load Sequence “cycle 15t A<>D”

The load sequence, "cycle 15t A<>D" represents a complete working cycle and is composed of partial sequences.


5.12 Design Spectra

A design spectrum is an unordered set of load sequences (p.87) weighted by the number life time occurrences.

Design spectra are regular KRASTA objects with a name and a comment. They define load spectra for damage accumulation for proofs of fatigue (p.161).

To perform damage accumulation based proofs in KRASTA a design spectrum has to be defined. With this design spectrum the operation during lifetime of the machine is described completely. The design spectrum replaces load group and evaluation pattern (p.217) of “classic” proofs of fatigue.

Dialog: Design Spectrum


5.13 Constraint Conditions

Static systems may have properties not regarded by linear calculation theories. This could be tension elements failing at pressure, bearing play or friction elements. From version 9.4 on those properties can be modelled in KRASTA using constraint conditions.

Constraint conditions are not regarded during a calculation run but afterwards by superposing correction loads with the user defined load pattern. For example pressure on a tension element can be compensated by shortening the tension element (predeformation load generating tension).

Because of the method using superposition of results, it can only be use when superposition is allowed (linear calculations). When performing calculation according to theory 2

nd order (or when using solver

Stab88 or NODYA) constraint conditions are ignored.

In earlier versions of KRASTA force conditions, a subset of constraint conditions, are already available. Constraint conditions exceed the capabilities of force conditions, now including displacement conditions on single beams and nodes and even coupling degrees of freedom.

5.13.1 Types of Constraint Conditions

Constraints in respect to forces, to displacements or any linear combination of both can be imposed to the calculation model. These types of constraint conditions may be defined in KRASTA in various ways.

5.13.1.1 Force Conditions

Force Conditions are beam properties und can be applied to inner forces Fx, Fy, Fz, Mx, My and Mz at begin and end of a beam. Force conditions may have a limit or a target. Targets will always be achieved, limits only when exceeded.

Compensation loads are created automatically using predeformations in constraint degrees of freedom. Predeformations are free of resulting loads having no effect on sums of loads or sums of support forces.

5.13.1.2 Displacement Conditions

Displacement Conditions are node properties und can be applied to nodal displacements Ux, Uy, Uz, Rotx, Roty and Rotz. Displacement conditions may have a limit or a target. Targets will always be achieved, limits only when exceeded.

Compensation loads are created automatically using single forces or moments in constraint degrees of freedom. These compensation loads have resulting loads that are displayed as support forces.

5.13.1.3 General Constraint Conditions

General constraint conditions contain one or more condition component, a limit or target value and eventually user defined compensation load cases. Components consist of a beam or nodal degree of freedom and a combination factor. For each component a compensation load case can be generated automatically in its degree of freedom. The sum of components is restricted by a limit or target value. Targets will always be achieved, limits only when exceeded.

Different degrees of freedom may have different units. The user has to consider units during input of combination factors. Combination factors are not dimensionless in general.

In general constraint conditions the beam degrees of freedom Fx, Fy, Fz, Mx, My, Mz (inner forces) and Ux, Uy, Uz, Rotx, Roty, Rotz (displacements) at beam ends may be selected. Automatically generated compensation load cases for inner forces are predeformations in the constraint degree of freedom. Predeformations are free of resulting loads thus having no effect on sums of loads or sums of support forces. Automatically generated compensation load cases for displacements are single forces or moments in constraint degrees of freedom. These compensation load cases have resulting loads that are displayed as load at the constraint degree of freedom.

As nodal degrees of freedom the displacements Ux, Uy, Uz, Rotx, Roty and Rotz may be selected. Automatically generated compensation load cases are single forces or moments in constraint degrees of freedom. These compensation load cases have resulting loads that are displayed as support forces.


User defined compensation load cases are always displayed as loads.

Dialog: Constraint Conditions

In the group box ”component of constraint condition” (1) a single component is defined or edited. This component has to be added (use button “Add >”) to the list of defined components (3). In group box “constraint condition” (2) the constraint condition is displayed. The sum of defined condition components (3) is restricted by a limit or target value (4). In the group box “user defined compensation load cases” basic load cases can be selected to fulfill the condition. In the left selection box available load cases are displayed, in the right selection box already selected only. The input data is permanently checked. If the input data is not sufficient, a note is displayed in the status line (6).

5.13.2 Consideration in Display and Results

Consideration of constraint conditions (force, displacement and general constraint conditions) on display (graphical output of loads, inner forces, support forces etc.) can be switched on and off as necessary.

This can be done with the button “consider constraint conditions” ( = not considered, = considered) or the similar option in the dialog “display settings”.

Depending on consideration compensation loads are displayed as loads, support forces or are not displayed at all (see also chapter “types of constraint conditions”). Compensation loads are included in sums of loads and sums of support forces when displayed.

Constraint conditions are always considered in results and proofs. In the textual output of permutations at the end of results and proofs the compensation loads and the load factors are shown.

5.13.3 Example: Constraint Conditions

On the basis of the following examples, some practical use cases are illustrated and according specifications by user explained. Where applicable, alternative definitions are compared.

1 2

3

4 5

6


5.13.3.1 Tension element, rope

A tension element cannot bear pressure forces. To avoid pressure forces, the beam is shortened.

Using force condition

In dialog “force conditions” press button “Rope (N>0)” or adjust condition and limit force manually.

Using general constraint condition

In dialog “general constraint condition” input values in group box “component of condition” according to example dialogue shown below. Select a beam and add the component to the list of defined components. As limit choose “>= 0 kN”.

Comparison between force condition and general constraint condition

The results from modelling a tension element using force condition or using general constraint condition are identical. The modelling itself is much quicker using force conditions, especially if you want to define many tension elements. This can be done in a single step. When using general constraint conditions you have to define the conditions for each beam separately.

5.13.3.2 Overload Clutch

An overload clutch can bear a maximum moment. Exceeding this moment will result in rotation of the clutch adverse the adjacent structure. The moment remains at its maximum during and after rotation.

Using force condition

The maximum moment is defined positive as upper limit or negative as lower limit at the correct section of the beam (in example dialog: beam start, momentum about local y-Axis).


Using general constraint condition

In dialog “general constraint condition” input values in group box “component of condition” according to example dialogue shown below. Select a beam and add the component to the list of defined components. As limit choose “absolute value <= limit value unit”. Because of the limit being not zero, the correct unit for the component and for the limit value has to be selected.

Comparison between force condition and general constraint condition

Additionally to the remarks in the last chapter “tension element, rope” force conditions have a massive disadvantage for problems of the overload clutch type: only one limit can be defined (either an upper limit or a lower limit). With general constraint conditions limits can also be defined as absolute values (with limit “<=” only).

5.13.3.3 Friction Element

At contact points between structural members or between one structural member and its support friction

may be important. In beam structures the friction coefficient may be interpreted as maximum ratio between transferable shear force and normal force (pressure):

| |

where shear force at beam end section

normal force at beam end section (negative value, pressure)

As a sum of degrees of freedom it is

| |

This inequation cannot be defined in one general constraint condition because single components cannot be defined as absolute (only the sum on components). The inequation is split into two inequations. Additionally the condition on the normal force (pressure only) is defined:


These three inequations can be modelled using constraint conditions. For the first two of them only general constraint conditions can be used because more than one degree of freedom (component) has to be considered. In both of these conditions a compensation load case must be generated in the shear degree of freedom (as a result only one compensation load case is created which is used in both conditions).

With the following general constraint conditions have to be defined:

Restriction of normal force (tension or pressure) is absolutely necessary to solve the constraint problem. The inequation for an unconstraint normal force is as follows:

| | | |

Replace the absolute shear value, you get

| |

| |

Solution space for a positive normal force:


Solution space for a negative normal force:

When positive and negative normal forces shall be considered and the condition shall be valid all in all, the resulting solution space is the intersection of the two solution spaces shown above. The intersection is reduced to a single point (N=0, V=0). The condition cannot be met for normal forces different from 0.

A friction element capable of transmitting tension and pressure can be modelled using two friction elements with constraint normal forces. These two friction elements can be pressure friction elements arranged as a nipper or one pressure element and one tension element arranged parallel. In any case, two different beams must be used as friction elements.

5.13.4 Sensor degrees of freedom and “optimised coupling”

In which degrees of freedom compensation load cases are applied influences the results. Thus, it is important for compensation load cases to match the real structure that is to be calculated. In the following example the displacements are considerably dependent on the compensation load cases.

A double-span girder (Beams S and S1) with adjacent cantilever (Beam S2) is to be calculated. At the end of the cantilever a single load is applied. Two supports are modelled using additional support beams (Beams DGF1 and DGF2). Various constraint conditions shall be applied on the support beams. In the graphical output the load (turquoise), support forces (red), beam displacements (red and blue border line) and the beam name is displayed.

Basic system without constraint condition

No constraint condition is applied to the support beams. Support forces and beam displacements are as follows:


Sensor and actuator, case 1

Support beam DGF1 is a sensor measuring normal force. Support beam DGF2 is a hydraulic press. The normal force of DGF 2 is adjusted actively to match the normal force of DGF1. At the end of the adjustment, the normal forces in both support beams are the same. In a matching constraint condition, no compensation load is applied to DGF1. In DGF2 a compensation load case is generated automatically.

Sensor and actuator, case 2

Sensor and actuator of case 1 are interchanged. DGF1 is now the active degree of freedom with compensation load case, DGF 2 is a sensor degree of freedom without a compensation load case

Hydraulics with constant hydraulics volume

Beams DGF1 and DGF2 are both hydraulic presses that share a constant hydraulics volume. The plunger areas of both presses are the same size. Two constraint conditions match that state:

- equal normal forces of DGF1 and DGF2 with an automatically generated compensation load case in DGF2

- the sum of elongations of DGF1 and DGF2 is zero, a user defined compensation load case (predeformation, contraction) is applied to DGF1


Optimised coupling

Support beams DGF1 and DGF2 have equal normal forces. One constraint condition with automatically generated compensation load cases for both beams is created. No other condition is defined. In this case, there is only one condition but two compensation load cases. Theoretically there are infinite solutions for this problem. An internal optimisation during solution of constraint conditions assures a unique and repeatable solution. Every constraint problem with more compensation load cases than conditions is solved using an optimisation algorithm and can therefore be called “optimised”. An optimised solution cannot be considered optimal meaning the best solution. The need for optimising a solution can even mean that important conditions are defined falsely or are left (e.g. constant volume of hydraulics or the distinction into sensor and actuator).

5.13.5 Assistant for Constraint Conditions

For certain constraint problems there are assistants assisting input of constraint conditions. Assistants create and manage general constraint conditions. When changing input values of an assistant the managed constraint conditions are updated.

General constraint conditions and compensation loads that are managed by an assistant cannot be altered manually. Managed constraint conditions can be released from an assistant by breaking up an assistant. The assistant will then be deleted.

5.13.5.1 Assistant: Equality

With an assistant “equality” any number of similar degrees of freedom of beams or nodes can be coupled.

For a number of n beams/nodes n-1 constraint conditions are generated. In each constraint condition the chosen degree of freedom of the first beam/node is coupled with the degree of freedom of an other beam/node.

Compensation load cases for inner forces degrees of freedom of beams are predeformations. When choosing option “first beam is sensor only” there is no compensation load case applied to the first


beam in the list. For the other beams compensation load cases are created automatically. With option “optimised compensation” compensation load cases are created for every beam.

Compensation load cases for displacement degrees of freedom of beams and nodes are pairwise forces or moments. There is one compensation load case per generated constraint condition, therefore there is no option “optimised compensation” for displacement degrees of freedom. Caution: Pairwise forces on nodes may have a resulting moment. Pairwise forces on beams may even have resulting forces and moments.

The ratio between the factors defines the ratio of constraint inner forces or displacements.

In the example dialogue it is 1.0*Fx(Beam S 0) = 1.5*Fx(Beam S 7), the normal force of beam S 0 is 1.5 times greater than the normal force in beam S 7

Inner forces and displacements of beams and displacements of nodes can be coupled. Beams and nodes cannot be mixed.

5.13.5.2 Assistant: Hydraulics

With the assistant “hydraulics” normal forces in beams can be coupled.

For a number of n beams n-1 constraint conditions are generated. In each constraint condition the normal force of the first beam is coupled with the normal force of another beam.

The ratio of factors “plunger area” defines the ratio of the plunger areas of the hydraulic presses. The ratio of plunger areas equals the ratio of normal forces.

In the example it is Fx(Beam S 1) / 1.0 = Fx(Beam S) / 2.0 which means that the normal force of beam S is twice the normal force of beam S 1.

When choosing option “first beam is sensor only” there is no compensation load case applied to the first beam in the list. For the other beams compensation load cases are created automatically. With option “optimised compensation” compensation load cases are created for every beam.

The option “constant hydraulics volume” is equal to “first beam is sensor only” with an additional constraint condition on elongations of all beams. The plunger area weighted sum of all elongations results to zero. As compensation load case for this condition a predeformation (contraction) is applied to the first beam in the list. With this option there is no elastic elongation of any hydraulics beam, it is compensated during solution. Thus, the normal stiffness of the beams is irrelevant.


5.13.5.3 Assistant: Rope Polygon

With the assistant “rope polygon” normal forces in beams can be coupled.

For a number of n beams n-1 constraint conditions are generated. In each constraint condition the normal force of the first beam is coupled with the normal force of another beam.

The ratio of factors “reevings” defines the ratio of the reevings of the rope beams. The ratio of reevings equals the ratio of normal forces, i.e. it is inverse to the pulley factor.

In the example it is Fx(Beam S 1) / 1.0 = Fx(Beam S) / 2.0 which means that the normal force of beam S is twice the normal force of beam S 1.

When choosing option “first beam is sensor only” there is no compensation load case applied to the first beam in the list. For the other beams compensation load cases are created automatically.

The option “constant rope length” is equal to “first beam is sensor only” with an additional constraint condition on elongations of all beams. The reevings weighted sum of all elongations results to zero. As compensation load case for this condition a predeformation (contraction) is applied to the first beam in the list. With this option there is no elastic elongation of any rope beam, it is compensated during solution. Thus, the normal stiffness of the beams is irrelevant.

5.13.5.4 Assistant: Friction Element

With the assistant “friction element” normal and shear force at one beam end are coupled. For a description of constraint conditions please see chapter Friction element (p.94).


5.13.5.5 Assistant: Slotted Hole

With the assistant “Slotted Hole” displacements at two beam ends are coupled. The two coupled beams must share a node. Beam 2 must have a local beam axis that is parallel to the chosen degree of freedom of beam 1. The coupled degree of freedom of beam 2 is determined automatically.

The total tolerance is cut into halves for the positive and the negative direction. The compensation load case consists of a single force or moment in each of the two degrees of freedom. The compensation load case has no resulting load. In the coupled degree of freedom of beam one a joint is defined automatically which may not be changed by the user.

5.13.6 Buffer for Constraint Conditions

When a load permutation is evaluated for the first time, the determined compensation loads are stored in a buffer for constraint conditions. For following evaluations of that permutation the compensation loads are taken from that buffer and are not determined again. Repeated evaluations of the same load permutation are significantly faster.

The buffer for constraint conditions is cleared when

force conditions are altered

displacement conditions are altered

beams with force conditions are deleted

nodes with displacement conditions are deleted

general constraint conditions are created, edited or deleted

a calculation suite is executed

the buffered compensation loads are determined using older results than those actually available

the load combination of any permutation has changed (e.g. after editing combination or logic load cases)

KRASTA is restarted

a different KRASTA model is opened

Clearing the buffer is reported in the log window.


5.13.7 Error Bounds

The solution algorithm permits minor exceedance of limits and minor differences to target values. The tolerance is that small that is has no relevant influence on the results.

5.13.8 Compatibility with KRASTA 9.3 and prior

Force conditions with limits (inequalities) are absolutely compatible with every version that supports force conditions. Due to different solution algorithms minor differences may occur between solutions of KRASTA 9.4 and prior versions.

Force conditions with target values (equality), displacement conditions and general constraint conditions are ignored by versions 9.3.x and older. When selecting beams according to beam value “force condition” and during textual documentation of beams target values are interpreted as lower limits.


5.14 Subsystems

KRASTA allows for the subdivision of a structure. This enables the user to create a construction kit of substructures, as e.g. the parts of a tower crane, which can be assembled into different construction phases.

Further, adjustable kinematic systems such as polar kinematics or linear guides in different situations can then be represented as one KRASTA system and can be evaluated across all situations (see section “Situations”).

5.14.1 Hierarchy, Organization

The topological arrangement of subsystems is hierarchical and forms a tree structure. In this hierarchy we talk about parent and child subsystems. The tree hierarchy is independent from the topologigal arrangement of the subsystems in the model strcuture.

If subsystems are to be geometrically oriented or kinematic adjustments several rules have to be followed (see kinematic adjustments of subsystems). Furthermore, it is helpful for the general overview to orient the tree structure according to the model structure.

Each subsystem can be composed of other subsystems and/or beams.

The depth of the subsystem tree is not limited.

As well as all KRASTA objects, subsystems can be newly created, edited, copied, deleted etc. But since the hierarchically structure of subsystems has to been taken into account, this is partly done in a special way.

5.14.1.1 Delete Subsystems

This menu item allows deleting a subsystem. Nodes, beams, connections and contacts using these connections are deleted too.

5.14.1.2 Cut Subsystems

This menu item initializes moving of a subsystem inside the tree. The program retains the name of this subsystem until the next Paste command and then moves the subsystem. The position of subsystems in the tree is independent of their topographical position.

5.14.1.3 Copy Subsystems

This menu item initializes copying of a subsystem inside the tree. The program retains the name of this subsystem until the next Paste command and then copies the subsystem.

5.14.1.4 Paste Subsystems

This menu item completes a copy or move command. Depending on the previous command Cut or Copy, the subsystem is copied or moved under the current subsystem.

5.14.2 Import Subsystems

This menu item allows importing one or more subsystems into the current model. After selecting the model, from which to import, a second tree view appears, showing the subsystems of the other model.


Dialog: Subsystem Import

After selecting a subsystem in this second tree view an pressing the button Add, the corresponding subsystem is copied into the current system as a child of the subsystem that was the current subsystem when initializing the import function.


5.14.3 Simplified orientation after copy or import

After copying or importing a subsystem, KRASTA automatically brings up the subsystem dialog that allows positioning the new subsystem. The outline of the new subsystem is shown in reverse color in the working area.

Screen after copying a subsystem

The subsystem can now be moved by pressing the left mouse button inside this area and moving the mouse while holding the button down.

This can be used to bring the subsystem into a more convenient position for further work. On the other hand KRASTA recognizes if the connection nodes of the moved subsystem get near connection nodes of another subsystem when the mouse button is released. If a connection is found and the number of nodes in the two connections is equal, KRASTA offers to connect them. If this offer is accepted, the program creates a new contact and saves this subsystem with the option "oriented by vector and angles" set.

5.14.4 Geometrical Orientation of a Subsystem

The topmost subsystem is orientated in the inertial system. The displacement and the rotation are initially zero by default, so that this subsystem coordinate system corresponds to the IN-CS. These values as well as the proposed name "root" can be modified.

Each subsystem has its own coordinate system (SS-CS) and it is orientated in his parent subsystem by means of a vector and a rotary matrix (Euler angles). Those orientations are created in several ways (see below).

5.14.5 Current Subsystem

There is always a current subsystem (shown in the right hand combo box control in the button bar). It can be changed by the combo box control or by selecting a subsystem from the tree structure. This is independent from the current selection of beams and nodes.

5.14.6 Beams and Nodes of a Subsystem

Newly created nodes always belong to the current subsystem and there is no off-hand way to transfer them into another subsystem. Newly created beams will belong to the subsystem of it’s end nodes.

5.14.7 Beams between subsystems

A beam cannot be drawn between two nodes in different subsystems.

One has to either create a new node in one subsystem and connect this one by a new connection to the other subsystem or create a new subsystem which contains this beam only.


If one tries to create a beam between two nodes which are in different subsystems, the system inquires automatically whether it is to put in a new subsystem and create the appropriate connections and contacts.

Wizard: Beam as Subsystem

With a set of dialogs the names of the new objects can be set. If the default name is acceptable it is sufficient just to press “next” severeal times. The end node of the new beam is automatically set a “free node”, since the system assumes that the new beam will change its length in different situations (e.g. suspension, hydraulic cylinder etc.).

Example: Suspension between tower and boom

5.14.8 Split off Marked Nodes as New Subsystem

An existing model can be split into subsystems. As a result, the selected nodes are moved into a new subsystem which is a child of the current subsystem. Connections and contacts are created automatically.

Only nodes from the same subsystem can be selected for splitting off at a time.

5.14.9 Melt a subsystem

Melting a subsystem means to delete a subsystem while moving its contents. Beams, nodes and connections are transferred to the parent subsystem. Contacts refering to that subsystem are deleted.


5.15 Connections and Contacts

The objects "connection" and "contact" are used to describe the physical contact of subsystems (p.103).

A connection is a set of nodes within one subsystem.

A contact connects two compatible connections in two different subsystems.

If the relative position of two subsystems is not clear by the two contacts alone, one or two auxiliary vectors can be defined for each contact (see below and examples (p.111)).

KRASTA gives a warning if a distorting transformation matrix results from the geometry of the connections.

5.15.1 Structural Build-Up

A structure can be build up by modelling individual subsystems or by creating individual KRASTA systems and eventually compose them (see further down for the example of a tower crane).

Subsystems from other KRASTA systems can be imported into the current system. The new subsystem can then be geometrically oriented after its import. This can be achieved by either entering the coordinates directly or dragging the subsystem to its desired location. If the subsystem’s connections match with already existing connections of other subsystems KRASTA offers to create a new contact and orientate the new subsystem by contacts.

Another method is generating the structure as a whole and then subdividing it into subsystems. This can be done by using the function “separate marked nodes as subsystems”. For this purpose al l the nodes (including the future connection nodes) that are to be included into the new subsystem have to be selected. When executing the separation the necessary contacts and contact are automatically generated and the connection nodes duplicated. If existing connections and contacts are involved they will be split accordingly. In some cases empty connections may be generated which should be deleted manually.

As it is the case for other objects it is recommended to define meaningful names for the overview and final documentation.

Helpful display setting to view subsystem organization

To get a view of the structure separated into their subsystems, there is an option “subsystem factor” in the dialog “display settings”. If the factor is smaller 1, then the individual subsystems are shrinked towards their geometrical center. By this, the connection nodes are not displayed on top of each other, but separated.

5.15.2 Means for the orientation of the structure

The spatial orientation of a subsystem is defined in regard to the superior (parental) subsystem. This information is stored internally by a distance vector and a rotation transformation matrix. This specification is usually not entered by the user explicitly. For the user, three ways to specify the subsystem orientation are available:

Orientation by “Vector and Angles“

A subsystem is oriented in the parent subsystem by the input of a distance vector and three Euler angles. To avoid warnings, contacts and connections (if present) may no interfere with this geometry.

Orientation by “Contact”

Subsystems are positioned relatively to other subsystems by one or more contacts. The vector and the rotation matrix is then calculated in order to be able to transform coordinates from one coordinate system to another. If the contact consists of nodes in a straight line, one auxiliary vector is needed. If the contact consists of one node only, two auxiliary vectors are needed. For each connection the auxiliary vectors are defined in the individual subsystem coordinate system. KRASTA rotates the child subsystem to match the auxiliary vectors of the connections.


Orientation by “Contact and Angles”

A subsystem is oriented against the parent subsystem by a contact and three Euler angles. The vector is defined by the contacts while the angles have to be entered for the subsystem. If the contact allows rotation about one axis only, the other angles have to meet the orientation defined by the contact. If a kinematic is used, the subsystem orientation will be set to “Connection and Angles” automatically.

Each individual configuration of orientations and contacts can be stored in the KRASTA object “Orientation” an may be reused in evaluation and documentation thereafter. More details are available in the chapter “Orientation (p.115)”.


5.15.3 Example for a subsystem structure

A subsystem tree for a tower crane may look as follows:

The total system and the subsystems of the 1st and the 2

nd level are

shown on the next pages.

Simple model of a tower crane (total system)

First level subsystems

tow er crane

bracingpinnacle

sw ivel joint

counter w eight jib

jib

tow er

tow er base

tower crane tower base tower tower part 1 tower part 2 tower part 3 tower part 4 tower part 5 swivel joint sj bottom sj top pinnacle jib jib base jib part 1 jib part 2 jib part 3 jib part 4 jib end counter weight jib bracing brc counter weight brc jib


Second level subsystems

jib part 2

tower part 5

tower part 4

tower part 3

tower part 2

tower part 1

sj bottom

sj top

brc counter weight brc jib

jib base

jib part 1

jib part 3jib part 4

jib end


5.15.4 Examples for Contacts

In the following, three types of contacts are shown, which differ in the number of required auxiliary vectors. If the orientation is determined by such auxiliary vectors, simple kinematical movements (twisting of the crane, luffing of the jib) can be done by modifying the auxiliary vector of the connection.

Contact without auxiliary vectors:

jib base - jib part 1:

Contact with one auxiliary vector:

Pinnacle-jib base:

→ Luffing of the jib

Contact with two auxiliary vectors:

SJ top - SJ bottom:

Simple kinematical movements (twisting of the crane, luffing of the jib) can be done by modifying the auxiliary vector in the description of the connection.


5.15.5 Connection

A connection consists of a group of nodes and is used to connect two subsystems physically.

Dialog: Connection

The nodes of the connection are selected graphically. Therefore the cursor is to be set into the list box below Graphical Selection. Then the nodes can be selected in the desired order. If required, up to two auxiliary vectors may be defined. By pressing Delete Node the selected node can be removed from the connection. Insert Node makes room for a new node, which can be input afterwards.

Display of Connections

Connections are represented on screen by their name in geometric center, lines to the nodes as well as the ordinal number of the node in the connection.


5.15.6 Contact

A contact connects two connections to a physical contact.

Dialog: Contact

The two connections need to have the same number of nodes and auxiliary vectors (if any). The order of the nodes and their position in the connections must coincide. The first two conditions are checked by the program; as long as the number of nodes and/or auxiliary vectors is different, the OK button remains inactive. The second condition has to be checked by the user himself.

5.15.7 Error messages (Contact) during connection of subsystems

On completion of the dialogs Subsystem and Contact or upon users request the program tries to recalculate the positions of the different subsystems. While trying to do so the program may produce the following error messages:

"Number of nodes/vectors in connections not equal"

Meaning: Two connections connected by a contact do not have the same number of nodes or vectors.

"Subsystem globally inaccessible!"

Meaning: The specific subsystem is neither oriented by vector and angles, nor does it have connections, so its position cannot be calculated.

"Beam Vector Component does not fit locally! Probably subsystem oriented and

connected"

Meaning: A subsystem is oriented by vector and angles or by connection. Additionally further connections (or nodes in a connection) exist, that do not fit to their corresponding counterparts.

"Subsystem Vector/Matrix not calculable!"

Meaning: The specific subsystem is meant to be oriented by contacts, but the current number of nodes and/or auxiliary vectors is insufficient.

If a subsystem is to be oriented by a single contact, the used connections must alternatively consist of at least:

Three nodes, that do not lie on a line

Two nodes and one auxiliary vector not parallel to the connection between the two nodes

One node and two non parallel auxiliary vectors


5.16 Orientation

Structures can be divided into subsystems. The geometrical arrangement of these subsystems (p.103) in relation to each other is subject of the KRASTA object “orientation” which will be described in the following.

Orientations are used to store, modify and re-establish the state of spatial orientation of a structure which consists of subsystems. The orientation is a regular KRASTA object with a name and a comment.

Orientations can be accessed through:

The tree structure on the left hand side of the screen

The menu “Subsystem | Orientation“

Three different types of orientation are available, depending on their purpose:

„Basic Orientation“ A snapshot of the structure to easily reproduce a certain orientation.

„Relative Orientation“ A certain orientation based on a basic orientaion with additional orientational changes.

„Orientation Modification“ A named sequence of orientational changes.

5.16.1 Basic Orientation

A basic orientation includes all subsystem orientational information (subsystem (p.103) / joints (p.42) / contacts (p.113)) in order to describe the geometrical position of a subsystem and its referred connections. It is able to fully describe and reproduce an orientation state.

The basic orientation does not contain any information about the modelling history of an orientation state. It is just a snapshot of the orientation state at a certain time.

In contrast to the multiple execution of kinematics (such as a “Relative Orientation”) the situation will always be reproduced numerically exact.

The reproduction of orientations states of all subsystems can only be successful, if subsequent changes to system are not contrary to the orientation object. Deleted subsystems cannot be reproduced. Subsystems that have been redefined from “orientation by contact” to “orientation by vector and angle” or vice versa will be transferred back into their old state. Newly created subsystems will retain their current position relative to the parent subsystem within the subsystem hierarchy.


Dialog: Basic Orientation

Read actual Orientation Data

The information stored within an orientation will be replace by those of the current state. New information will be added and obsolete information deleted.

Refresh

The orientation item chosen in the window (marked blue) will be newly read from the current state.

Delete

The orientation item chosen in the window (marked blue) will be deleted from the basic orientation.

Execute

Wherever possible, all orientation items are applied to the corresponding structural parts. The model is changed to reflect the basic orientation.

1st

Col.: Concurrence

The equal sign shows that the represented orientation information coincides with the current model conditions. An exclamation mark warns of problems within the orientation information.

2nd

Col.: Type of the orientation item

There are different types of orientation information:

Subsystem: The subsystem [in Col. 3] is oriented relatively to the subsystem [in Col. 4].

Contact: The contact [in Col. 3] connects connection [in Col. 5] and connection [in Col. 6].

Contacts can include information of geometrical positions of subsystems relative to each other. If the subsystem is oriented by vector and angle then both information have to concur. If the subsystem is oriented by contact then one contact has to be sufficient to define the position of the subsystem coordination system.

5.16.2 Relative Orientation

The relative orientation is capable (as the basic orientation) to fully rearrange a subsystems (p.103) orientation state.

A relative orientation refers to a start orientation of the type “basic orientation (p.115)” or “relative orientation”. Based on that start orientation several steps changing the orientation state are defined in the “relative orientation”. Such steps could be:

A „kinematical adjustment“, i.e. the call of a kinematic (p.119) that includes or excludes the information about the target value. If there is no target value defined in the orientation, the target value of the kinematic will be used.

Change of a contact (p.113), i.e. connecting a new set of connections.

A saved „orientation modification”

The relative orientation allows execution of kinematics automatically without the need to consider further parts of the subsystem structure. A relative orientation is more flexible to deal with changed basic data (e.g. longer subsystems) than a basic orientation.


Dialog: Relative Orientation

Start Orientation Defines a start orientation.

Modification Sequence A sequence of different types of orientation changes.

Kinematic Executes a polar kinematic with a defined objective value.

Contact Creates or changes defined contacts.

Orientation Modification Executes an already defined sequence of orientation changes.

[Edit] The [Edit] buttons open a short menu including the most important aspects for the editing of the relevant object.

[Add] The add buttons attaches the chosen modification item information to the end of the sequence.

[Up], [Down] [Delete]

The selected (highlighted) entry of the sequence can be moved or deleted.

[Execute] Saves and executes the modification sequence. The basic orientation will be reproduced first and then the modification sequence will be executed step by step.

5.16.3 Orientation Modification

A „change of orientation“ is basically a relative orientation without a basic orientation and therefore can not reproduce a subsystem orientation state in total.

It can be used as part of change sequence within a relative orientation.

Dialog: Orientation Modification

As dialog „Relative Orientation“ without start orientation.

5.16.4 Methods of orientation


Create New Edit Copy Delete

Orientations can be newly created, edited, copied or deleted just like other KRASTA objects (p.20).

Execute Orientations can be executed. The execution of orientations can be initiated from the applicable menus or from the editing dialog or by drag’n’drop.

Execution of a basic orientation means that a certain system orientation is reproduced.

Execution of a relative orientation means that a certain system orientation is reproduced from a start orientation and subsequent executions of orientation changes.

Execution of an orientation modification means that starting from the current state a sequence of orientational changes is executed. Usually this will not lead to a certain system orientation.

5.16.5 Notifications during the execution of orientations

For the execution of kinematic ‚KIN’ subsystem ‚SUB’ will be changed to orientation by ‘contact and angle’

So far, the position of the subsystem ‚SUB’ was defined solely by the contact (subsystem orientation by contact). This needs to be changed changed.

The subsystem ‚SUB’ uses the contact only to determine its coordinate origin. The position of the angle will be calculated and determined by the kinematic (now the subsystem definition is ‘orientation by contact and angle’)

„unknown Orientation subtype XX“ The type of the orientation ‚XX’ is not known in this KRASTA version. The orientation can not be executed.

"unknown orientation type 'yy' in Execute_BasicOrientation()"

The type the subsystems are arranged relatively to each other is not known in this KRASTA version. This information can not be considered.


5.17 Kinematics

Kinematics are capable of performing planar kinematic movements consisting of any number of substructures which must not have more than one degree of freedom.

Therefore, a predefined substructure, the so-called leading kinematic part, is being moved in small increments. Auxiliary substructures, which have to be made of two substructures, are adjusted afterwards. This will be repeated until a certain objective is achieved (node coordinates, angle, coordinate difference). The increments may be lessened closer to the objective in order to attain a certain accuracy.

This process will be stopped if substructures are “clamped” (shut position) or a given number of iterations is exceeded.

Modelling with kinematics

In KRASTA the substructures of kinematics have to be individual subsystems.

For every kinematic the leading kinematic part has to be connected to a fixed point (relatively to the individual kinematic), the so-called ground plane.

The orientation of the subsystems relative to the superior (parental) subsystem may be automatically changed from “Distance and Angle” to “Contact and Angles”.

The different substructures have to be assigned to the same level within the subsystem hierarchy beneath the parent subsystem.

Subsystems which are “child” of a substructure will be kinematically moved with those as being rigidly connected.

Kinematic plane

The definition of the plane within which the kinematic movent is done can be a principal plane (X-Y, Y-Z, and Z-X plane) of any subsystem coordinate system. This subsystem containing the coordinate system must not be a part of the kinematic substructure. The normal vector of this plane is then automatically the axis of rotation of the individual substructures. The contacts in between the subsystems, which connect the substructures, have to be capable to rotate around this axis. E.g. the nodes of a connection consisting of several nodes have to be located on the same axis parallel to the axis of rotation.

The objective (coordinates, angle, etc.) is defined in the same coordinate systems as the kinematic plane.

Kinematic movability vs. static flexibility

The rotational movability of substructures only exists for kinematics. The joints necessary for the static calculations are not influenced by kinematics in any case and have to be defined as beam attributes. Likewise, two parts which are jointed together can be regarded as rigidly connected bodies.

Modelling of actuators

Contacts of subsystems to other subsystems which are not part of a kinematic are regarded as a contact to the ground plane (unchanging basic rotation points) for the concerned subsystem. The sole exemption is made if the connection nodes of the other subsystem have “free coordinates”. This allows e.g. to model actuators, such as cylinders, spindles, or control shafts which have alternating lengths throughout the movement process. Since this kind of “free” contacts can partly be used to orientate subsystems the contacts have to be explicitly defined to be free in specific kinematics.

The leading kinematic part has to be a subsystem with a (direct or indirect) connection to the ground plane.

Interaction of multiple kinematics

Any number of kinematic objects can be generated, allowing for different combinations of subsystem movements. I.e. a section which has been of variable length in one kinematic can be moved as a rigid body in another one.


Structural parts that are not kinematically dependent but still have to be moved in a certain relation towards each other can be modelled using several kinematic displacements that have to be executed one after the other. Such a sequence can be defined through a “relative orientation”.

Any position or orientation that has to be available for calculation purposes has to be generated by hand only once and then can be saved and later recalled as an orientation object. This has to be done only if changes at the structure have been generated. More about orientation, situation and calculation suite can be found in the according chapter.

The subsystems, contacts and connections can be displayed similar to the display dialog through an “explosion” view. Here subsystems will be reduced in size relative to their geometrical center and hence the contact nodes and connections will diverge.

5.17.1 Dialog: Kinematic

General information

A kinematic has a name and – optionally – a comment like every other KRASTA object

5.17.1.1 Target Settings

Plane and Reference System

The frame of reference and the plane in which the kinematic is located in has to be defined in the second section. The chosen subsystem must not be a child system of the subsystems which will be moved later on. The frame of reference itself can admittedly be displaced during another kinematic, e.g. the revolving platform of a tower crane will be the frame of reference for the displacement of the boom subsystem.

Target

The target that describes the goal of the displacement can be defined in the third section. It is possible that the target coordinate difference can yield two results. This situation depends on the quadrant in which the structure in its initial position was located. In order to achieve a certain solution the structure possibly has to be rotated into the proper quadrant with another kinematic by changing the angles. The following options are available for the target definition:

Angle to Axis

Two nodes have to be chosen of which at least one has to be located on the subsystem which will be displaced. The subsystem will be displaced until the vector from the first to the second node has reached an angle relatively to the chosen axis which is equivalent to the defined in a mathematical positive sense.

Node Coordinate

A node located within one of the substructures has to be chosen. The subsystem will be displaced until the node has reached the defined coordinate within the chosen frame of reference.


Coordinate Difference

Two nodes have to be chosen of which at least one has to be located on the subsystem which will be displaced. The subsystem will be displaced until the distance between the two nodes has reached the defined value.

Projected Coordinate Difference

Two nodes have to be chosen of which at least one has to be located on the subsystem which will be displaced. The subsystem will be displaced until the distance from the second to the first node has reached the defined value in the chosen coordinate direction. The positive and negative value of the number will be observed.

Angle of three Points

Three nodes ( have to be chosen of which at least one has to be located on the subsystem

which will be displaced. The subsystem will be displaced until the angular between the legs and has reached the defined value in the chosen value. The positive and negative value of the number will be observed.

Switch: Best possible

This switch allows the kinematic to be executed even if the target cannot be reached with the predefined accuracy (to be defined under options). E.g. the smallest possible value is sought and the substructure adjusted to this value if the distance is given as zero and the switch “best possible” is ticked. This can be used to adjust two independently modelled structures which are supposed to be joined within a bi-polar system by repeated executions of two kinematics, so that the connections will finally be as close as possible and can then be connected to each other via a connection.

5.17.1.2 Substructures of a kinematic

The substructures of the displacement are defined on the right hand side of the dialog box.

Leading kinematic part

The option for the leading kinematic part can be found right on top of the section. The selection of the leading kinematic part can occur by selecting the substructure in the drop down menu or by pressing the button graphical selection and the subsequent selection of the substructure in the view.

Other kinematic parts

Other kinematic parts can be added through the drop down menu and by pressing the button add. They can be deleted by choosing a substructure and pressing remove.

Kinematically free connections

Those contacts that have free nodes and are to be defined as free themselves within this kinematic have to be chosen (moved to the right hand window) in the section kinematically free connections.

The program will try to execute the displacement after pressing the button execute. If this is successful the system will be displayed in its new position. The system will remain in its current position if any errors should occur.

The button Clear Kinematic Trace can be used to delete any display of the displacement process from the view.

Pressing the button Options allows for the definition of parameters for the kinematic algorithms. The predefined values should usually suffice.


5.17.1.3 Options (Kinematic)

Options are the starting step with which the leading kinematic part will be moved with (standard: 0.1 ), the target precision which has to be reached (standard: 1e-5 m), the maximum number of iterations after which the kinematic will be stopped (standard: 10 000), and the number of steps that will be displayed for the optical control (standard: 0 = none).

Dialog: Parameters of Kinematic


5.17.2 Error messages (Kinematic)

During input, while saving or during executing of a kinematic, warning and/or error messages can occur. Below, possible KRASTA error messages concerning kinematics are listed.

5.17.2.1 Error messages (Kinematic), during the input

Please select subsystem first! “Add” was pressed without having chosen a substructure first.

Subsystem already in list! A subsystem which is already chosen was to be added to the list.

5.17.2.2 Error messages (Kinematic), while saving the object

No reference subsystem selected! The rotary plane and the frame of reference for the target have to be defined.

No leading kinematic part selected! At least one structure that has to be displaced has to be chosen.

Number of other kinematic parts has to be even!

The number of other kinematic parts always has to be even because of the explanations in the chapter General.

No target node selected! The node necessary to define the target was not selected.

No second target node selected! For a function where two nodes are necessary (angle, coordinate difference) only one has been selected.

5.17.2.3 Error messages (Kinematic), during the execution of a polar kinematic

Reference subsystem is part of kinematic part!

The frame of reference is identical with the child subsystem of one of the kinematic subsystems.

Leading kinematic part has no contact to ground!

The leading kinematic part is not directly connected to the ground plane (the fixed part, relatively to the given kinematic).

Connection nodes are not in direction of rotation axis!

In a contact with multiple nodes between two subsystems of different substructures not all of the nodes are located on the common axis of rotation. This can only be due to numerical inaccuracies. If necessary the nodes of one subsystem (preferably of the fixed subsystem) can be forced into a straight line by manually entering the exact coordinates and the connection nodes of the second subsystem can then be relocated graphically.

Connection nodes are not in direction of rotation axis!

Several contacts may exist between two substructures which are not located on the common axis of rotation. Again, this can only be due to light numerical inaccuracies.

No target node on kinematic part! None of the nodes used to define the target are located on the moving part of the structure, therefore the target can never be reached.

Disconnected kinematic parts! The substructures are not connected with the leading kinematic part, with each other or are “free” at one end and not on the ground plane or another kinematic part.

Too many iterations, abort! The program aborts the calculation due to exceeding the maximum number of iterations. Either the number of allowed iterations is too small, or the target precision too high, or an unknown error inhibits a proper solution. In order to help finding the reason the last situation is displayed graphically.

Unreachable target! The program cannot execute any further displacements (clamping). In order to help finding the reason the last situation is displayed graphically.


5.17.3 Example: (Kinematic)

For example we will look at a double jointed crane, which will be moved kinematically.

First the existing system will be subdivided into the subsystems boom, actuator bar, tension bar, coupler bar, counter weight, and base using the function “split off marked nodes as new subsystem”. The node at the end of the hydraulic actuator will be defined as “free”.

Now it is possible to describe a kinematic object (see Dialog: Kinematic (p.120)).

The subsystem base will be defined as the reference subsystem with its X-Y plane as the plane of displacement.

The chosen leading kinematic part will be the actuator. Boom, tension bar, coupler bar, and counter weight (the order is of no matter here) will be the other kinematic parts.

The program will offer a contact (cylinder DL) containing free nodes. This contact is supposed to be free within the kinematic, hence it will be chosen.

actuator (leading kinematic part)

Boom Tension bar

Secondary member 1

Counter weight

Coupler bar

Secondary member 2

Base


The user can now choose a target. In this example it will be the X coordinate of the node at the tip of the boom, which will be moved to the position x=-26500mm. After pushing the button “execute” the boom will be moved into its new position.

Another possibility to describe the target could be the length of the actuator.

The figure above shows such an example. The actuator will be moved into a position where its length will be 3500mm.

Pay attention to the selection of the two nodes. One of both (in this case [Drucklenker] DL 8) has to be part of a kinematic substructure, otherwise no change in length can be achieved. The “free” node on the other side will only be displaced later during the reassessment of all coordinates.


5.17.4 Further possibilities to model kinematic displacements

Alternating connections

In order to display different orientations a subsystem can be connected to different connections so that it can be oriented in a different way relative to its connection mate. Thus, substructures can be displaced linearly (e.g. a travelling trolley of a bridge crane) or rotated (e.g. a rotation assembly sluing wreath).

In contrast to the kinematics of multiple substructures described above, only the different angles of the substructures relative to each other will be changed via the orientation vectors of the contacts.

Usually it is sufficient to alternate one of the contacts used in a connection to generate a new orientation of the whole structure. I.e. one side of the connection or one contact usually remains unchanged, whereas alternative, though similar, contacts will be used on the other side.

The respective alternative contacts can be generated through a copy of an exemplar contact, where only the individual orientation vectors have to be changed.

Afterwards, the connection of this contact will be transferred to the new contact (edit connection) and the new orientation can be saved. Free nodes, attached to the displaced structure, will be displaced automatically.

The rotating assembly of a rotating substructure can alternatively be represented by a polygon. Different angles of rotation can then be generated through within the separation by relatively shifting the sequence of assigned contacts.

Modified angles within the subsystem

The coordinates and angles in a subsystem oriented through vector and angle or contact and angle will be saved within the orientation. Thus, they can be used to display kinematic displacements too by directly editing the orientation of a subsystem and subsequently saving this object as a new orientation.


5.18 Situation

Situations are used to reproduce and calculate certain states of a system repeatedly (e.g. construction or operating states of a structure) with their specific system definitions, orientations, bearing conditions and load cases. A situation includes an orientation (p.115), a list of associated load cases and a list of members to be inactivated.

The situation includes the formerly known “position” and additionally incorporates administrative tools that had to be executed manually within older KRASTA versions. The descriptor “position” will therefore be omitted in future to account for the technical nature of a situation and to avoid any confusion with the tasks of the object type orientation.

For further description of a calculation result, a reference to a situation object will appear instead of a position number. Now, the name of the situation will appear on the surface instead of a number. Internally a position number will be used for the PAS calculations sequence which coincides with the internal sorting number of the situation.

Situation can be accessed via:

The tree structure on the left-hand side of the screen

The menu „Calculation | Situation“

If no user defined situations are present for KRASTA system the program will simplify input and output accordingly. An internal situation “$uncertain” (p.128) will instead be automatically entered and used.

5.18.1 Methods of situations

Create New Edit, Copy, Delete

Situations can be newly created, edited, copied or deleted just like other KRASTA objects (p.20).

Execute Orientations can be executed.

The execution of orientations can be initiated from the applicable menus or from the editing dialog or by drag’n’drop.

The execution of a situation leads to execution of an associated orientation (p.115).

If calculation results are represented graphically KRASTA can reproduce the relevant situation. The results shown match with the current situation.

Calculate Provide or (re)calculate result data for the specific Situation.

See “Calculate specific Results” for Details.


5.18.2 Dialog “Situation”

Orientation Refers to an orientation.

Active Load Cases Specifies which load cases will be calculated for the situation.

A list of load cases can be selected. The content of that list is shown as additional information.

Inactive Beams Specifies which beams will not be considered during calculation for this situation.

NOTE: Loads and masses of inactive beams are not considered.

A list of beams can be selected. The content of that list is show as additional information.

Calculate Compensation Load Cases

If ticked, compensation load cases for constraint conditions are calculated.

[Edit] The [Edit] buttons open a short menu with the most important topics for editing of the relevant object.

[Execute] Saves and executes a situation. I.e. the chosen orientation will be reproduced.

5.18.3 The situation “$uncertain”

For systems without user defined situations (p.127), calculations and evaluations show no releation to a certain situation. No information about orientations is available in the model, all load cases and all members are active. The situation “$uncertain” cannot be edited and only calculation suites can access this situation. Thus, calculations can be done without having to define orientations, situations and calculation suites first.

KRASTA implies the “uncertain” state, as long as no explicitly defined situation can be found in the system, not even in the solver result file. In this case, KRASTA does not ask for situations in dialogs and shows no certain situation in outputs. Nevertheless, internally the situation “$uncertain” is used in all cases.

Referring to the situation “$uncertain” means:

When creating solver input sets: No (certain) situation is set before, the static system is used in its current state.


When evaluating result sets: There is no (certain) situation associated with the individual result. KRASTA cannot determine that situation, which leads to the result. The result is shown in the current, maybe different, situation.

5.18.4 Create situations for orientations

Apart from creating situations "manually", there is assistance in creating situation for existing orientations. Situations can be created automatically for specified orientations. The newly created situations share the base name of the orientation and the orientation is referred to in the situation.

For single orientations this can be done by right-clicking on an orientation in the object tree and selecting "Create Situation". If multiple situations shall be created the menu item "[Situation] Create for Orientations..." in the main menu "calculation" can be used.

KRASTA 9.6 Manual Calculation 131

6 Calculation The following chapter describes components of KRASTA involved solving the statically problem, such as calculation suite, core solver, result and log files.

Error and warning messages that can occur during a PAS solver run are listed as well.


6.1 Calculation Suite

A calculation suite is used for the repeatable calculation of a list of situations (p.127). Apart from a list of situations it contains information about the chosen solver, the method of calculation and further solver settings.

Two standard calculation suites are available for PAS, 1st and 2

nd order theory with the situation

“$uncertain” (p.128).

Standard calculation suite can be edited. Copies can be made and edited in order to copy the default settings.

Calculation suite can be accessed via:

The tree structure on the left-hand side of the screen

The menu „Calculation | Calculation suite“

6.1.1 Available solvers and computation theories

KRASTA supports several the following solver:

6.1.1.1 PAS III

Calculation of a spatial framework according to 1st and 2

nd order theory, considers mass load cases,

knows (semi-)rigid and/or conical cross sections. It is shipped with the KRASTA package.

6.1.1.2 PAS IV

The same capabilities as PAS III with accelerated calculation core.

6.1.1.3 MOD (modal analysis)

The modal analysis of spatial frameworks, calculates natural frequencies and natural modes, it considers bearing rigidity and mass cases. It is shipped with the KRASTA package.

6.1.1.4 STAB88 / NODYA [OPTION]

Calculation of a spatial framework according to 1st and 2

nd order theory, capable of nonlinear calculations

for both geometry and material. STAB88 / NODYA is a third party solver and is not shipped with the KRASTA package.

6.1.2 Methods of calculation suites

Create New Edit Copy Delete

Calculation suites can be newly created, edited, copied or deletedjst like other KRASTA objects.

Execute Calculation suites can be executed.

The execution of calculation suites can be initiated from the applicable menus or from the editing dialog or through the menu “Calculation | Execute >”.

The execution of a calculation suite means the reproduction and calculation of predefined situations.

134 Calculation KRASTA 9.6 Manual

6.1.3 The default calculation suites „PAS linear“ and „PAS ThII”

The calculation suites "PAS linear" and „PAS ThII“ are available by default. The program starts the solver PAS IV when executing these calculations suites in order to calculate all basic or ThII load cases. All members are considered active and all compensation load cases are calculated if necessary. The results are assigned to the situation “$uncertain” (p.128) instead of any defined situation.

The calculation suites "PAS Linear" and „PAS ThII“ can be edited and deleted.

6.1.4 Dialog: Calculation Suite

Calculate immediately ticked: Solver input files are created and sent to the solver.

unticked: Solver input files are created but are not sent to the solver. The solver may be started for these input files manually.

Clear results before All results are deleted before. This does also include results for situations which are not to be calculated with this calculation suite.

Clear calc log before The log file with messages from previous calculations is deleted before.

Available The list in the left window shows which situations are available to solve.

Calculate The list in the right window shows which situations are to be solved.

Solver Specifies which solver and which theory will be used.

[Solver settings] Opens a dialog with detailed solver settings when available (see below).

No setting details are required for PAS III and PAS IV.


6.1.4.1 Dialog: Solver Options Modal Analysis“

Mass load case The mass case for which natural modes and frequencies are to be determined.

Number of natural modes The number of the natural modes and frequencies to be determined.

6.1.4.2 Dialog: Solver Options NODYA“

Register: General

For descriptions of the individual entries refer to the NODYA documentation.


Register: Nonlinear Calculation

For descriptions of the individual entries refer to the NODYA documentation.

6.1.5 Calculate specific Results

The KRASTA object tree provides a quick way to calculate or update results (internal forces, displacements and support reactions) for specific Situation (p.127)s or Load Event (p.85)s.

The following context menu items (right mouse button) are available for situations and situation lists:

Calculate with PAS linear

Calculate with PAS THII

Available for load Events is the context menu item:

Calculate with PAS.

The default settings for calculations with PAS are used. In case of Situations, results to all individually active load cases are (re)calculated. In case of Load Events, only the particular associated result set is (re)calculated and the actual load case type determines the method of calculation theory.


6.2 Calculation according 2nd Order Theory

6.2.1 2nd Order Theory, Basics

The following theory is implemented for 2nd

order calculation of PAS:

For the single beam the differential equation system (DES) is solved according to the technical bending theory. The equilibrium is formulated in a deformed condition in order to consider term is considered for bending:

The stiffness matrices for beams with constant cross section is determined analytically, the stiffness matrices for beams with conical cross section is determined numerically with a tolerance of approx. 1 0/00. The torsion is considered according to St. Venant theory. Single beam matrices are assembled geometrically linear (Williot plan of displacement). The solution of the equation system is iterated over the normal forces.

A prerequisite of 2nd

order calculation is, that in spatial frames the differential equations for bending of both cross section axes are decoupled, both for strain and for torsion. In [1] prerequisite conditions to this decoupling are discussed and shown.

In which conditions these can prerequisite can be seen as fulfilled is shown in [1].

For 2nd

Order theory calculations the equilibrium is formulated for the deformed framework. Inner forces refer to axes of the deformed beams. Loads and predeformations are considered in undistorted working direction but with a relocated working point. Geometrical effects due to inner beam deflection or shortening are neglected in general. If this seems to be not appropriate this can be corrected by creating additional nodes along the beam. Load components in beam direction may have an influence on the beam stiffness. This influence is only taken into account correctly if the loads are applied at begin or end of the beams.

Beam loads and beam predeformations are already considered to calculate inner forces in the 1st load

step. Loads applied at the start node of beam (L=0) are considered for the beam itself, further loads (L>0) are considered at the start of the next beam.

It is possible to determine the ideal bifurcation load (ideal buckling load). This is done by iterative increaments of the loads up to the factor when the stiffness matrices’ determinant denominator becomes zero (or negative).

Literature: 2nd

Order Theory

[1] Möller, K.-H. , Mörchen, H., Völkel, G.

Zur Berechnung ebener und räumlicher Stabwerke – Theoretische Grundlagen zu PAS – (mit weiteren Literaturangaben)

Veröffentlichungen des Institutes für Statik und Stahlbau der TH Darmstadt, Heft 9, 1970.

6.2.2 Th. II, Modelling techniques

The count of the equilibrium iteration steps needed depends on the nature of the system. Criterion to check is the determinant dominators rate of change. Often, one equilibrium iteration step is sufficient, especially if the load steps are not too wide.

Relevant steps in normal forces should only be present at beam ends, i.e. at nodes. If needed, one should create intermediate nodes to be able to distribute beams loads and masses concentrated to these nodes.

Using wider beam lengths or relevant non-constant normal forces, affected beams should be split up to appropriate shorter beams parts.

See also:

Load Case 2nd Order (p.80)

Brief Information for Review (p.225)


6.3 Situation-independent calculation

Using the menu item “Situation independent calculation” KRASTA allows to create solver input (resp. result) sets indcated by “position numbers”.

The “Situation independent calculation” is equivalent to the solver interface of version 9.2 and older. That way to specify a “position” is obsolete and should not be used anymore. Please use the more modern and flexible calculation suite introduced with version 9.3 instead.

Obsolete Idiom “Position”

In KRASTA 9.2 and older, the idiom “position” was used. The user was able to identify result data, loosely specified at the time of solver execution. The user had to track position numbers and according structural system himself. No means were available to automatically recreate the static situation referred to by the position number.

Since KRASTA 9.3 the concept of “Situations” allows switch between different static situations in a systematic and comfortable manner.

For favor of the more general “situations” the usage of “position numbers” has become obsolete.


6.4 Content of the result file

The result file contains inner forces of beams at particular sections points (p.44) and support forces (p.45) of nodes, resulting from certain load cases (p.75) in certain situations (p.127).

If the result file already contains inner forces for a given load and a certain situation these results are overwritten.

Only the results of basic load cases (p.75) and (if any) TH II load cases (p.80) are stored into the result file. Load combinations are always superposed according to their actual definition. Stresses are newly determined referring the actual cross sections (p.51).


6.5 Process Solver Input Files

A solver input file is a self consistent calculation order for a specific solver (p.133).

Input files are created by calculation suites (p.133). Usually the according solver is started to process the solver input file. The results are stored in the Result File (p.141) for later analysis (p.216).

However, calculation suites may just create solver input files without starting the solver. Such suspended input files may be sent to the solver with the menu item “Calculate solver input file”.


6.6 Calculation Log

The calculation log stores messages, which occur during the execution of a solver input file (p.143), e.g. start and end time, available disk space, storing places etc. as well as all output of the solver (p.133).

The solver may fail to solve a problem due to numerical problems or an insufficiently constraint model. Even if the solver finishes the solution errors and warnings may have occurred (refer to e.g. PAS error messages (p.147)).

A 2nd order theory (p.137) calculation may be used to determine the maximum stable load factor (Euler buckling). In this case an error 455 indicates unstable load factors.

The calculation log can be reviewed after the solver finishes through menu item “Show Log-File”.


6.7 PAS error messages

This chapter describes the most frequent PAS error messages/warnings, their causes and methods to identify the sources of error.

Assistance and suggestion are given to eliminate the errors. Usually different options to eliminate the source of error are available for the desired static system.

6.7.1 Error/Warning Nr. 229

Error message

Fehler oder Warnung (229) aufgetreten!

Cause

No support conditions were defined, the structure is not supported.


Error message


Warnung Nr.

451 : DAS TRAGWERK ODER TEILE DAVON SIND KINEMATISCH UEBERBESTIMMT.

451 : The structure or parts of are kinematically underdetermined

Cause

There is a closed structure of (partially) rigid beams (example #1)

There is a open structure of (partially) rigid beams but rigidly supported (example #2)

Finding the culprit

Mark all beams with rigid and/or partly rigid cross sections (menu item “Selection | Beam property | Cross Section”) and display all support conditions. Places, in which several (partly) rigid beams are present, must be examined for closed and/or rigidly supported beam chains.


Example: Error/Warning Nr. 451, #1

A massive structural element in your structure is modeled using rigid beams. This could be a casting with several beams of the structure attached.

Since the casting is quite rigid and not in the scope of your calculation anyway, you have decided to model the outline shape of the casting with rigid beams. The individual rigid beams are connected rigidly to each other.

The closed ring causes an error Nr. 451 during the calculation.

Fault repair

Open the ring by deleting one segment of the beam chain. The rigid beams and their rigid connection remain a rigid and distortionless structure.


Example: Error/Warning Nr. 451, #2

Next to supports you model a shear panel with the help of rigid beams. Therefore, you introduce a bracing with a coupling node at the intersection of the bracings. All four rigid beams use this node as an end node.

Rigid beams and rigid support together, achieve a rigid structure (Fig. “rigid Support”, dashed line) and cause an error Nr. 451.

Fault repair:

Here, several possibilities are available to remove the fault. You have to decide which one is compatible with the needs of your static system.

Release a support in direction of the connection line between the support nodes (Fig. “Release Support”).

Apply a joint condition to three of the four beams to enable a cross angle change (Fig. “with Joint”).

Please also consider chapter “Notes on using rigid cross sections”



Error message


Warnung Nr.

453 : DAS TRAGWERK ODER TEILE DAVON SIND BEWEGLICH.

453 : The structure or parts of are free to move.

Cause

Joint and/or support conditions allow a part of the structure to move/rotate without resistance. The movable part can be an underconstraint node, a rotating beam as well as a larger kinematic part of the structure.

Modelling faults, which cause warning 453, fall into two categories: “real movability” and “rotating objects”.

Fault finding

Looking for the fault, the knowledge of the linkage between nodes and beams as well as between nodes and inertial system (fixed base, earth) is necessary

The linkage between beam and nodes is determined by joint conditions of the beam (beam property), the linkage between nodes and fixed base by support conditions (node property). In each case, six degrees of freedom are available, three translational and three rotational (Fig. “Degrees of Freedom”).

fixed base

support cond.

node

beam

joint cond.

Fig. „Degrees of Freedom“


6.7.3.1 Real Movability

Generally real movability can be sought out easily by examining the bending line. Uncommonly large deflections indicate the movability.

If there is no load in the direction of the movability, it may necessary, to introduce additional loads in this direction (e.g. additional load cases with horizontal acceleration).

Approach:

Display a selected bending line and show the whole system (fully zoomed out).

If no extra ordinary deformation is shown then either the load case is unappropriate or there is no real movability.

If the display looks like fig. “huge deformation”, select the beams with the huge deformation (in mode “beam selection” click the bending line with left mouse button and select all offered beams).

Choose the display setting “minimal” and show the whole system (fully zoomed out). The selected beams indicate the area of movability (fig. “area of movability”).

6.7.3.2 Rotating Objects

In order to find this error, the KRASTA model must be scanned for usual error patterns. Here all joint and support conditions should be displayed.


In large systems it can be helpful to cut the model into smaller parts. Eventually delete a part of the model, supporting the remaining part if necessary and evaluate again. If the error still occurs then the error is part of the remaining structure otherwise of the deleted part. Keep attention of not producing further errors by dividing the model.

Node can rotate

Type of Fault: At a bearing support in the model both a support condition (ball bearings) and a joint condition (ball joint) is defined as shown in fig. „rot. node #1“. The node is neither rotational linked with the fixed base system nor with the beam, thus it can rotate freely.

Proposal: Modelling bearing condition, one should always use support condition wherever possible. Connect the beam rigidly to the support node and apply the desired support conditions to the node.

If this is not applicable, because the desired support condition cannot be defined in the node coordinate system, fix the node in all degrees of freedom and apply the joint conditions to the beam.

Type of Fault: All beams are connected to a node with joints (Fig. “rot. node #2”). The node is rotational connected with none of the beams, thus it can rotate freely.

Proposal: Connect one of the beams rigidly with the node.

Beam (chain) can rotate

Type of Fault: A beam or a beam chain is not fixed against rotation about the center line (Fig. “rot. beam #1”, Fig. “rot. beam #2”, Fig. “rot. beam #3”).

Proposal: Define support conditions, joint conditions of the beam (chain) or adjoinded beams in a way to fix the rotation.


Error message


Warnung Nr.

455 : DIE BELASTUNG LIEGT ÜBER DER NIEDRIGSTEN VERZWEIGUNGSLAST

455 : THE LOAD LIES OVER THE LOWEST BIFURCATION LOAD

Cause

Calculation according 1st

order theory:


In 1st order calculations error 455 usually occurs in combination with warning 453. Eliminating warning 453 eliminates error 455.

Calculation according 2nd

order theory:

In 2nd

order calculations this error message occurs if a beam or a structural part exceeds the ideal buckling load (bifurcation load).

Note: Unfortunately there is no way to spot out the affected beam(s). Buckling, in the sense of applied theory, is a system fault not caused by single beams. The bending line of the 2

nd order results just below

the buckling load may be evaluated to get an idea of the failing members or substructure.


6.8 Modal Analysis

KRASTA supports the calculation of natural frequencies and according Eigen vectors (modes) of elastic systems. Rigid, partially rigid or conical cross sections have to be replaced with elastic or constant cross sections.

A modal analysis requires the selection of a mass case (usually the "Permanent Mass") and a maximum number of natural frequencies to calculate. The results of the analysis can be output in textual form for further computations.

Eigenvectors can be displayed and animated in a user defined scale by the menu item “View | Eigen Vector”.

KRASTA 9.6 Manual Analysis and Documentation 157

7 Analysis and Documentation The following chapter describes the possibilities to analyse, evaluate and document KRASTA systems.


7.1 Proofs

Proofs and results (p.211) are handled by KRASTA in similar manner (see Proof- / Result-Control-Sets (p.215)). In both cases, the evaluation pattern, the type of evaluation, extremation and textual output are specified.

In contrast to result controls sets proof controls sets compare a result value to a permissible value according to a standard leading to a utilization.

Classifications

To determine permissible values according to a standard it is usually necessary to provide additional information, e.g. for materials (p.67). Usually this information is a so called “classification”.

E.g. a classification can be something like this: “The material named ‘StE 355’ is in terms of DIN 15018 to be classified as ‘St 52’”


7.1.1 Proof of fatigue based on damage accumulation

Modern proofs of fatigue are based on damage accumulation to evaluate the operating characteristics in detail. Therefore, the operation is summarized in form of particular load sequences and design spectra.

Load sequences result in unique stress time histories at every point in the structure. KRASTA performs a rainflow analysis to determine the stress ranges and associated number of occurrence.

The fatigue damage analysis is done according the linear damage accumulation hypothesis by Palmgren-Miner as described below. The analysis results in a “total sum of damage” which is often reformulated to damage equivalence factors or effective stress history parameters.

The partial damages are evaluated in respect to S-N curves and safety factors according to individual standards.

The current KRASTA version offers the following proofs of fatigue based on damage accumulation:

DIN 13001-3-1:2005-03 (p.169) resp. prEN 13003-1-1:2009 (p.175)

EN 1993-1-9:2005 (EC 3) (p.185)

The specification of a design spectrum replaces the specification of a S class (or similar) as well as the load evaluation pattern.

162 Analysis and Documentation KRASTA 9.6 Manual

7.1.1.1 Linear damage accumulation according to Palmgren-Miner

The following description is kept standards independent, no additional factors according to standards are considered..

Diagram: Linear damage accumulation acc. Palmgren-Miner

As an example, one S-N (Wöhler) curve from [EC 3] is shown, whereas:

Inverse slope of S-N curve above fatigue limit according to notch case.

Inverse slope of S-N curve below fatigue limit and above cut-off limit acc. [StK].Chap.1.1.4.2.

stress range , number of stress cycles

, actual number with stress range

, characteristic stress range

√

⁄

, fatigue limit stress range

√

⁄

, cut-off limit stress range

{

(

)

(

)

Number of stress cycles to failure for periodic stress range with (constant) amplitude .

The “partial damage” for a given stress range is the ratio of actual number of stress cycles to the number of stress cycles to failure .

∑

∑

Linear accumulation of partial damages gives the total damage.

(Damage summation according Palmgren-Miner rule)

The proof is fulfilled if (e.g.: lt. [EC 3].Appendix A)

Some standards allow values different from 1.0 for the total damage.


The linear damage accumulation hypothesis according to Palmgren-Miner assumes that partial damages are independent from each other. Thus, they are independent from the earlier stress history. The non-linearities of the S-N curve are already included in each partial damage.

Therefore, linear damage accumulation allows to

evaluate and document normal and shear stress damage separately

associate a partial damage to a particular working cycle

7.1.1.2 Result values of a damage accumulation

Additionally to the result items commonly used in KRASTA proof of fatigues (notch case, maximum stress range, tolerable stress range and utilization) there are items specific to damage accumulation such as stress collective values and sum of damage.

For the point of proof of stresses showing the highest utilization the textual output additionally lists the partial damages (see example below).

Example: Textual Output in case of Damage Accumulation beam sect i on pnt W ds c m si g s si g max si g l pS mi n si g l ps ds Sd ds Rd ut i si g D si g O

Pi vot Fr ame . . . U 109 47. 2 3 8. 0 3. 0 . 047 - 1. 87 14 - 7. 65 4 5. 78 16. 45 . 351 . 043 b . . . Root Abspg. 4 2. 3E+03 1 8. 0 3. 0 . 091 12. 94 29 1. 65 6 11. 29 13. 19 . 856 . 627 b Abspg. 5 . 0 2 8. 0 3. 0 . 043 13. 82 15 2. 43 3 11. 4 16. 88 . 675 . 308 b . . . HT 14 . 0 7 8. 0 3. 0 . 094 - . 79 1 - 6. 57 29 5. 78 13. 05 . 443 . 087 b HT 15 . 0 - 1 8. 0 3. 0 . 059 2. 71 4 - 11. 44 15 14. 15 15. 18 . 932 . 81 b HT 16 421. 75 7 8. 0 3. 0 . 043 - . 39 1 - 5. 08 15 4. 69 16. 92 . 277 . 021 b . . . HT 15 . 0 - 1 8. 0 3. 0 . 059 2. 71 4 - 11. 44 15 14. 15 15. 18 . 932 . 81 a Spec t r al Component s Damage: Number / Wei gt hi ng x Load Sequence - > D_si g 7500. 0 x unl oad 55t B<>D - > . 01 40000. 0 x unl oad 45t A<>F - > . 273 100000. 0 x unl oad 25t A<>F - > . 336 100000. 0 x unl oad 15t C<>F - > . 191 . . .

Example of a textual output of a proof acc. DIN 13001-3-1:

For each point an individual stress history parameter is determined and listed.

It is possible to show the stress utilization as well as the damage

For the point of proof of stresses with the maximum utilization the partial damages are

shown for each component (working cycle) of the design spectrum ( ∑ ).

Literature: Damage Accumulation

[EC 3] EN 1993-1-9:2005

Ausgabe: 2005-07

Eurocode 3: Bemessung und Konstruktion von Stahlbauten - Teil 1-9: Ermüdung

[StK] Stahlbaukalender, 2006 8. Jahrgang, Herausgegeben von Prof. Dr.-Ing. Ulrike Kuhlmann

Abschnitt 2: Grundlagen und Erläuterungen der neuen Ermüdungsnachweise nach Eurocode 3 Dr.-Ing. Alain Nussbauer, Dr.-Ing. Hans-Peter Günther


7.1.2 Proof of Fatigue acc. DIN 15018

A proof of fatigue according to DIN 15018 requires the classification of the used materials and the classification of the points for proof of stresses into notch conditions.

The loading group may be determined for every individual proof.

Points for proof of stresses, that have not been given a notch case, may be supplied with a default notch condition. If no default is selected, only points with classified notch conditions are considered for the proof.

The proof may be applied to normal stresses only, shear stresses only or combined stresses. These three possibilities can also be used together.

For each subtype of proof an individual output format has to be selected.

In the case of normal and shear stresses the search for extreme values is carried out along the util ization of the permissible stresses, for combined stresses along the resulting comparison value of the two utilizations, that is to be compared to 1.1 (DIN 15018, Part 1, 7.4.5).

If more than one subtype of proof is carried out simultaneously, it is possible to output the worst case only. The worst case is the one with highest utilization.

The proof of combined stresses can either be done "simplified" by combining the two maxima of normal and shear stress without consideration of their coincidence or as proposed by the standard.

It can be selected whether the permissible shall be calculated according to the formula for struc-tural elements or welded joints (DIN 15018, Part 1, Table 19).

Proof: DIN 15018

Def.: | | | | ;

| | | | ;

Table 18 (DIN 15018)

Equations for permissible upper stresses depend on , according to Table 17 and

(tensile strength) according to the classification of the material.

(alternating domain)

(tension)

(pressure)

(swelling domain)

(tension)

(

)

(pressure)

(

)

Furthermore is considered: (yield point acc. classification of the material).



Permissible stress for structural elements and welding.

Structural Elements

(acc. W0)

√

Welding

(acc. K0)

√

proof of normal stresses:

proof of shear stresses:

combined proof: (

)

(

)

For non simplified combined proofs, the sum shown above is maximized. For simplified combined proofs the maximum normal stress and maximum shear stress utilization are evaluated first. They are combined later.

Materials: DIN 15018

St 37

St 52-3

Notch Cases: DIN 15018

W0

W1

W2

K0

K1

K2

K3

K4

Loading Groups: DIN 15018

B1

B2

B3

B4

B5

B6


7.1.3 Proof of Fatigue acc. DIN 22261

A proof of Fatigue according to DIN 22261 requires the classification of the points for proof of stresses into notch cases.

Points for proof of stresses, that have not been given a notch case, may be supplied with a default notch case for the proof. If no default is selected only classified points are considered for the proof.

The proof may be applied to normal stresses or shear stresses. These two proofs can also be used together.

Extreme values are searched for the utilization of the admissible stress differences (Cond. 66 and Cond. 67). The fatigue factor can be specified.

If both subtypes of proof are carried out simultaneously, it is possible, to output the worst case only. The worst case is the one with highest utilization.

Notch case: DIN 22261

Notch cases for DIN 22261 are:


Notch case G0 G1 G2 G3 G4 G5

adm [kN/cm²] 25,0 22,4 20,0 18,0 16,0 14,0

Notch case G1 G2 G3 G4 G5 G6

adm [kN/cm²] 18,0 16,0 14,0 12,5 (11,2)* ) 10,0

*) Notch case G5 is not specified in Table 17 explicitly and is added here analogous to K5.


Notch case K1 K2 K3 K4 K5,K5 K6,K6

adm , [kN/cm²] 18,0 16,0 14,0 12,5 11,2 10,0

Notch case K7,K7 K8,K8 K9,K9 K10,K10 K11,K11 K12,K12

adm , [kN/cm²] 9,0 8,0 7,1 6,3 5,6 5,0

Proof: DIN 22261

Consideration of fatigue factor :

Conditions of the proof of fatigue:

The stresses are signed.

Def.: ,



1.) Parts beyond zones of welded joints:

normal stress :

1.1) ,

Cond.66:

√

( Row 1 )

1.2) ,

Cond.66:

√ ( Row 2 )

1.3) Cond.66: √ ( Row 3 )

shear stress :

1.4) Cond.67: ( Row 4 )

2.) (Welds) and Parts within zones of welded joints:

normal stress :

2.1) Cond.66: ( Row 7 )

2.2) Cond.66: ( Row 8 )

shear stress :

2.3) Cond.67: ( Row 9 )

The -condition in universal form is:

The utilization is calculated by:

At small stress differences at a high pressure stress level, it is possible to calculate negative utilization values. These values satisfy the proof.


7.1.4 Proof of Fatigue according to DIN CEN/TS 13001-3-1:2005-03

In the following the concept of the proof is explained first. After that, the implementation in KRASTA and used calculation formula are shown. Finally according program dialogs, output formats and value tables are described.

DIN CEN/TS 13001-3-1:2005, Method of Proof

Based on the operating method, notch case and accessibility, permissible stress ranges are determined and compared against characteristic stress ranges. The workflow in detail is as follows:

Operating method:

In general, the operating method is specified by a range of load working cycles of which each is weighted with a relative frequency, i.e. by a certain load spectrum.

S-Classes:

The S-class is derived from a load spectrum considering further parameters like the class of load spectrum factors Q0 to Q5 (see [13001-3-1:2005], Tab 4) and the S-class S0 to S9 (see [13001-3-1:2005], Tab. 11 and Tab. 12) respectively. Alternatively, a guidance for empiric selection of S-classes is given in [13001-3-1:2005], Annex B.

Notch cases:

Structural details are covered by classification of notch cases (see [13001-3-1:2005], Annex A and E).

With the classification of a certain notch case, a characteristic stress range or and the inverse

slope of the /N-curve is determined. Notch cases consider connection geometry, weld characteristics and (partly) material and structural part thickness.

Characteristic stress range and slope can be determined by fatigue testing (see [13001-3-1:2005], Chap. 6.2.4) also. Thus, a slope between (material in welded connections) and (flat material or shear in longitudinal welds) can be taken into account by the proof.

Notch cases are specified individually for normal and for shear stresses.

Resistance factor :

To consider fail-safe or non fail-save components, accessibility and hazards for persons a fatigue strength specific resistance factor is used according to [13001-3-1:2005], table 10:

Inspection and access Fail-safe components Non fail-save components

without hazards for persons

with hazards for persons

Periodic inspection and maintenance Accessible joint detail

Periodic inspection and maintenance Poor accessibility

Stress history parameter :

Each load cycle causes individual nominal stress cycles in every location and therfore individual stress spectra. Based on the shape of the stress spectra and the slope values specified by the notch case

individual stress history parameters are calculated according to [13001-3-1:2005], Chap. 4.3.4.

For each stress component (normal or shear stress) a unique stress history parameter is associated.


Permissible stress ranges:

The permissible (limit) stress range is calculated for each stress component separately as follows:

√

The dependency between S-classes and is defined as follows:

Class S02*) S01

*) S0 S1 S2 S3 S4 S5 S6 S7 S8 S9

0.002 0.004 0.008 0.016 0.032 0.063 0.125 0.25 0.5 1.0 2.0 4.0

*) The table is expanded by the S-Classes “S02“ and “S01“ according [13001-3-1:2009].

The formulation may be transformed using stress spectrum factors and according to

[DIN 13001-3-1] Chap. 4.3.4. Because of

it is:

√

mit √

The stress spectrum shape is covered by the ratio parameter . All other parameters are independent

from the stress spectrum.

Analyzing the stress spectrum shape is done for a proof based on damage accumulation (p.173). A proof following the simplified procedure (p.172) is using as a substitute, as mentioned in DIN-Chap. 6.5.3.4. This allows a save approximation of permissible stress range independent from the actual stress spectrum.

Design stress ranges:

In general, the design stress range is the difference between maximum and minimum stress component present in the stress spectrum.

For thermally stress relieved or non-welded structural members the compression portion of the stress range may be reduced to 60%.

Utilizations:

For different stress components the proof shall be executed separately. To each stress component an utilization is calculated by comparison of permissible to design stress range.

Additionally a combined utilization may be determined. See “Types of proof” below.


DIN CEN/TS 13001-3-1:2005, Implementation in KRASTA

Classification of notch cases:

A proof of fatigue according to DIN 13001 requires the classification of the “Points for Proof of Stresses (p.51)” in regard to:

characteristic stress ranges and

inverse slope of /N-curve and .

For or values out of a given list are available (see Chapter Notch Cases 13001-3 (p.183)).

The slopes or can be chosen in a range of 3.0 to 5.0.

The combined specification of characteristic stress range and inverse slope is called “notch case” in the following. For a point for proof of stresses individual notch cases for normal and for shear stresses are assigned (see Dialog: Classification of Points for proof of Stresses according to DIN 13001-3 (p.181)).

Consideration of material and part thickness by the user:

When selecting the notch cases in the scope of [13001-3-1:2005] tables A.1 and A.2 the user himself has to consider part thickness or the yield stress of the material.

Welding thicknesses have to be considered by the user.

Proof Control Sets:

For each proof the following is specified (see Dialog: Proof of fatigue according to DIN 13001-3 (p.174)):

Either a design spectrum or a s-Class according to DIN Tab. 11 and DIN Tab. 12 or Appendix B (see Loading Groups: DIN 13001-3 (p.183))

A fatigue specific resistance factor according to DIN-Tab. 10

If the compression portion of the stress range shall be reduced to 60%

Optionally default notch cases for unclassified points for proof of Stresses.

Thus, the proofs have to be formulated separately for different S-Classes, specific resistance factors, compression stress evaluation and (if any) default notch cases. But proofs can be combined into lists to be evaluated together.

If no default notch case is specified only classified points for proof of Stresses are proven. If no classification is given the point is not taken into account. The notch case to be taken into account is determined for normal and for shear stresses independently.

Types of proof:

The proof can be done separately

for normal stresses,

for shear stresses

combined

It is also possible to do all three types simultaneously. For each of these proofs a specialized output format is available.

If more than one type of proof is done simultaneously it is possible to output the worst case only. The worst case is the proof with highest utilization.


Proof: DIN CEN/TS 13001-3-1:2005 (simplified procedure)

Stress History Parameter:

In the simplified procedure, the stress history parameter is given by the specified S-class

according to [13001-3-1:2005] Tab. 13.

Evaluation pattern:

The evaluation pattern is a list of load events consisting of load case and situation. The S-class (see above) is used as an indication on load ranges and frequencies within the evaluation pattern; it implies a certain load spectrum.

Extremation:

KRASTA determines stress differences or design stress ranges for every possible combination of two load cases out of the evaluation pattern. For each stress difference the according utilizations are computed. The cases which result in highest utilizations are documented.

KRASTA assumes for the simplified method.

Def.: or whereas compression portions are reduced to 60%, optionally.

:

√

√

:

√

√

with:

, bzw. according to individual classification of the points for proof of Stresses.

according to Proof Control Set.

according to [13001-3-1:2005] Tab.13 for an S-class according to proof control set.

save approx.*)

Type of Proof Utilization

Proof of normal stresses:

Proof of shear stresses:

Combined proof: √(

)

(

)

with and

save approximated*).

*) KRASTA is using KRASTA , given by DIN Chap. 6.5.3.4 Simplified method for slope (see: DIN 13001-3, Method of Proof, Permissible stress ranges (p.169)).


Proof: DIN CEN/TS 13001-3-1:2005 (damage accumulation procedure)

Design Spectrum:

The design spectrum completely specifies the mode of operation with load sequences and their frequencies.

Time History Parameter:

The time history parameter is determined by a damage analysis according to the hypothesis of

linear damage accumulation (Palmgren-Miner rule) of stress histories specified by design spectra.

DIN CEN/TS 13001-3-1 uses a simplified S-N curve with a constant slope parameter with consideration of fatigue limit and cut off stress ranges.

The result of the analysis, given in form of collective coefficient and relative total number , is listed in

combined form as the time history parameter .

Def.: bzw. whereas compression portions are reduced to 60%, optionally.

∑(

)

∑(

)

with:

Analog to the simplified procedure. The design stress range is the difference between maximum and minimum across all load events present in the design spectrum.

relative total number of cycles, ∑

√

√

with:

, bzw. according to individual classification of the points for proof of stresses.


according to design spectrum, determined for each point for proof of stresses individually.


stress related value damage related value


( )


)

Combined proof:

√(

)

(

)

with


Dialog: Proof of Fatigue according to DIN 13001-3

If specifying a design spectrum (damage accumulation procedure)

If specifying a S-Class (simplified procedure)

In the “Proof of” area of the dialog, design spectrum or S-Class (“Loading Group”), specific resistance factor and the kind of consideration of compression portion are specified.

Default notch cases enable proof for points for proof of stresses without individual classifications according to DIN 13001.

The stress components for the proof can be selectable independently from each other. If desired, the textual output can be limited to the worst case.

For each stress component a specialized Output Format (p.182) is available.

Literature: DIN CEN/TS 13001-3-1:2005-03

[DIN 13001-3-1] DIN CEN/TS 13001-3-1:

Ausgabe: März 2005

Krane, Konstruktion allgemein, Teil 3-1: Grenzzustände und Sicherheitsnachweis von Stahltragwerken Deutsche Fassung CEN/TS 13001-3-1:2004

Cranes – General Design – Part 3-1: Limit states and proof of competence of steel structure German Version CEN/TS 13001-3-1:2004

[13001-3-1:2009] prEN 13001-3-1:2009

Ausgabe: 2009-10

Krane, Konstruktion allgemein, Teil 3-1: Grenzzustände und Sicherheitsnachweis von Stahltragwerken

Cranes – General Design – Part 3-1: Limit states and proof of competence of steel structure


7.1.5 Proof of Fatigue according to prEN 13001-3-1:2009


prEN 13001-3-1:2009, Method of Proof


Operating method:


S-Classes:

The stress history parameter is derived from the total damage considering further parameter.

Alternatively, the damage equivalence factor may be specified by selecting a certain S-Class S0 to S9 (s. [13001-3-1:2009] Chap. 6.3.4).

Notch cases:

Structural details are covered by classification of notch cases (see [13001-3-1:2009], Anhang D und H).


slope of /N-curve is determined. Notch cases consider connection geometry, weld characteristics and (partly) material and structural part thickness.

Characteristic stress range and slope can be determined by fatigue testing (see [13001-3-1:2009] chapter 6.2.3) also. Thus, a slope between (material in welded connections) and (flat material or shear in longitudinal welds) can be taken into account by the proof.


Resistance factor :

To consider fail-safe or non fail-save components, accessibility and hazards for persons a fatigue strength specific resistance factor is used according [13001-3-1:2009] tab. 9:

Inspection and access Fail-safe components Non fail-save components

without hazards for persons

with hazards for persons

Periodic inspection and maintenance Accessible joint detail

Periodic inspection and maintenance Poor accessibility

Stress history parameter :

Each load cycle causes individual nominal stress cycles in every location and therefore individual stress spectra. Based on the shape of the stress spectra and the slope value specified by the notch case

individual stress history parameters are calculated according [13001-3-1:2009] chapter 6.3.3.

For each stress component (normal or shear stress) a unique stress history parameter is associated.


Permissible stress ranges:

The permissible (limit) stress range is calculated for each stress component separately as follows:

√

The dependency between S-classes and is defined as follows:

Class S02 S01 S0 S1 S2 S3 S4 S5 S6 S7 S8 S9

0.002 0.004 0.008 0.016 0.032 0.063 0.125 0.25 0.5 1.0 2.0 4.0

The formulation may be transformed using stress spectrum factors and according to

[13001-3-1:2009] Chap. 6.5.3.3. Because of

it is:

√

mit √

The stress spectrum shape is covered by the ratio parameter . All other parameters are independent

from the stress spectrum.

Analyzing the stress spectrum shape is done for a proof based on damage accumulation. A proof following the simplified procedure is using as a substitute, as mentioned in [13001-3-1:2009] Chap. 6.5.3.4. This allows a save approximation of permissible stress range independent from the actual stress spectrum.


In general, the design stress range is the difference between maximum and minimum stress component present in the stress spectrum.

For thermally stress relieved or non-welded structural members the compression portion of the stress range may be reduced to 60%.

Utilizations:

For different stress components the proof shall be executed separately. For each stress component the utilization is calculated by comparing permissible to design stress range.



prEN 13001-3-1:2009, Implementation in KRASTA


A proof of fatigue according to prEN 13001-3-1:2009 requires the classification of the “Points for Proof of Stresses (p.51)” in regard to:



For or values out of a given list are available (see chapter Notch Cases 13001-3 (p.183)).

The slopes or can be chosen in a range of 3.0 to 5.0.

The combined specification of characteristic stress range and inverse slope is called “notch case” in the following. For a point for proof of stresses individual notch cases for normal and for shear stresses are assigned (see Dialog: Classification of Points of Proof of Stresses according to DIN 13001-3 (p.181)).


When selecting the notch cases in the scope of [13001-3-1:2009] Tables D.1 and D.2 the user himself has to consider part thickness or the yield stress of the material.


Proof Control Sets:

For each proof the following is specified (see Dialog: Proof of fatigue according to DIN 13001-3 (p.174)):

Either a design spectrum or a S-Class according to [13001-3-1:2009] Tab. 10 (see Loading Groups: DIN 13001-3 (p.183))

A fatigue specific resistance factor according to [13001-3-1:2009] Tab. 9

If the compression portion of the stress range shall be reduced to 60%

Optionally default notch cases for unclassified points of proof of stresses

Thus, the proofs have to be formulated separately for different S-Classes, specific resistance factors, compression stress evaluation and (if any) default notch cases. But proofs can be combined into lists to be evaluated together.

If no default notch case is specified only classified points of proof of stresses are proven. If no classification is given the point is not taken into account. The notch case to be taken into account is determined for normal and for shear stresses independently.

Types of proof:


for normal stresses

for shear stresses

combined




Proof: prEN 13001-3-1:2009 (simplified procedure)

Stress History Parameter:

In the simplified procedure the stress history parameter is given by the specified S-class according

to [13001-3-1:2009] Tab. 10.

Evaluation pattern:


Extremation:


KRASTA assumes for the simplified method.

Def.: or whereas compression portions are reduced to 60%, optionally.

:

√

√

:

√

√

with:

, bzw. according to individual classification of the points of proof of stresses.

according to proof control set.

according to [13001-3-1:2009] Tab. 10 for an S-class according to proof control set.

save approx.*)




Combined proof: √(

)

(

)

with and

save approximated*).

*) KRASTA is using KRASTA , given by [13001-3-1:2009] Chap. 6.5.3.4 Simplified method for

slope (see: DIN 13001-3, Method of Proof, Permissible stress ranges (p.175)).


Proof: prEN 13001-3-1:2009 (damage accumulation procedure)

Design Spectrum:


Time History Parameter:

The time history parameter is determined by a damage analysis according to the hypothesis of

linear damage accumulation (Palmgren-Miner rule of stress histories specified by design spectra.

DIN CEN/TS 13001-3-1 is using a simplified S-N curve with a constant slope parameter with consideration of fatigue limit and cut off stress ranges.

The result of the analysis, the collective coefficient and relative total number , is shown in combined

form as the time history parameter .

Def.: bzw. whereas compression portions are reduced to 60%, optionally.

∑(

)

∑(

)

with:


relative total number of cycles, ∑

√

√

with:

, bzw. according to individual classification of the points of proof of stresses.


according to design spectrum, determined for each point for proof of stresses individually.




( )


)

Combined proof:

(

)

(

)

( )


Dialog: Proof of Fatigue according to EN 13001-3-1



In the “Proof of” area of the dialog, design spectrum or S-Class (“Loading Group”), specific resistance factor and the kind of consideration of compression portion are specified.

Default notch cases enable proof for points of proof of stresses without individual classifications according to DIN 13001.


For each stress component a specialized Output Format (p.182) is available.

Literature: prEN 13001-3-1:2009

[13001-3-1:2009] prEN 13001-3-1:2009

Ausgabe: 2009-10

Krane, Konstruktion allgemein, Teil 3-1: Grenzzustände und Sicherheitsnachweis von Stahltragwerken

Cranes – General Design – Part 3-1: Limit states and proof of competence of steel structure


7.1.6 Common information to proof of fatigue according to EN 13001-3

This chapter describes common dialogs, output formats and load groups available in KRASTA for proofs of fatigue according to EN 13001-3.

Details of the individual proof and their implementation in KRASTA are given in the chapter “Proof of Fatigue according to prEN 13001-3-1:2009 (p.175)” and “Proof of Fatigue according to DIN CEN/TS 13001-3-1:2005-03 (p.169)”.

Dialog: Classification of Points for proof of stresses according to DIN 13001-3

Classification of points for proof of stresses according to DIN 13001-3 is done by specifying characteristic

stress ranges and and associated inverse slope of /N-curve and , see „Implementation in KRASTA (p.177)“.

Specification of a specific resistance factor as well as a reduced compression portion is done by proof

control sets, see below.


Output Formats: DIN13001-3

The layout of an Output Format (p.221) can be defined freely. To build up or edit output formats the following items are available:

General data (e.g. beam, section point, sectional point, load case or stresses)

Proof data (e.g. origin of extremes or if proof(-portion) is satisfied)

Specific items of the individual proof (e.g. parameter of the proof, intermediated results or utilizations)

Specific items, available in the output format:

Symbols Tab.-Head Value

, ds c

dt_c characteristic stress ranges

, m(s)

m(t) inverse slope of the /N-curve

, ,

sig max

sig min

tau max

tau min

stress components, causing stress ranges.

gamma Mf fatigue specific resistance factor

60% information, if reduced compressive portion is to be considered.

, ds Sd

dt Sd design stress range (may be reduced).

, ds Rd

dt Rd permissible stress range.

part of proof fulfilled if:

uti sig normal stress utilization

uti tau shear stress utilization

uti res resulting utilization

comp res resulting comparison value

*) In the scope of DIN 13001-3, KRASTA does not distinguish resulting utilization and comparison value.

Prepared Output Formats

Type of Proof Format

Proof of normal stresses: DIN 13001-3 sig one line, wide page, contains normal stress proof values.

Proof of shear stresses: DIN 13001-3 tau one line, wide page, contains shear stress proof values.

Combined Proof: DIN 13001-3 res three lines, wide page, contains both groups from

above and the res. comparison value „comp res“.


Notch Cases: DIN 13001-3

Standard sequence with a ratio of 1.125. See also section “DIN 13001-3, Method of Proof (p.177)”.

355 N/mm²

315 N/mm²

280 N/mm²

.

.

.

8.0 N/mm²

7.1 N/mm²

6.3 N/mm²

Loading Groups: DIN 13001-3 (S-Classes)

See also section “DIN 13001-3, Method of Proof (p.175)”.

S0

S1

S2

S3

S4

S5

S6

S7

S8

S9


7.1.7 Proof of Fatigue according to EN 1993-1-9:2005 (EC 3)


EN 1993-1-9:2005, Method of Proof


Operating method:


Damage Accumulation:

The damage parts of each working cycle defined in the load spectrum are calculated based on the Palmgren-Miner rule (p.162). These individual damages parts are, weighted by their relative frequencies, accumulated to a total sum of damage

S-Class:

Damage equivalence factors and are derived from the total damage considering further parameter. Alternatively, the damage equivalence factor may be specified by selecting a certain S-Class S0 to S9 (see [EC 1] Tab.2.12).

Notch cases:

Structural details are covered by classification of notch cases (see [EC 3] Tab.8]).


slope of /N-curve is determined. Notch cases consider connection geometry, weld characteristics and (partly) material and structural part thickness.


Resistance factor :

To consider the safety concept and consequences of failure a partial safety factor for fatigue strength is used according to [EC 3] tab. 3.1:

Safety Concept Consequence of failure

low high

Damage tolerance concept

Safe life concept


In general, the design stress range is the difference between the maximum and the minimum stress present in the stress spectrum.

For thermally stress relieved or non-welded structural members the compressin portion of the stress range may be reduced to 60%.


Damage equivalence factor :

Each load sequences cause individual nominal stress range collectives for each location. Based on the shape of this stress range collectives and the S-N curve specified by the notch case the damage equivalence factor is determined according to [EC 1] Eqn.2.16.

An individual damage equivalence factor is determined for each stress component (normal or shear stress).

If a S-class is specified for the structural part is given by [EC 1].Tab.2.12:

S-Class S02*)

S01*) S0 S1 S2 S3 S4 S5 S6 S7 S8 S9

0.126 0.159 0.198 0.250 0.315 0.397 0.500 0.630 0.794 1.000 1.260 1.587 m=3

0.289 0.331 0.379 0.436 0.500 0.575 0.660 0.758 0.871 1.000 1.149 1.320 m=5

*) The S-Classes ”S02” and “S01” are not natively known by this standard. Use them is not compliant with the standard.

They are additionally available following EN 13001 ( √

√

)

Equivalent constant amplitude stress range or

The equivalent stress range related to cycles is determined based on damage equivalence factor or and design stress range or :

and

Utilization:

For the stress components the proof shall be executed separately. For each stress component an utilization is calculated by comparison of equivalent stress range to characteristic stress range.



EN 1993-1-9:2005, Implementation in KRASTA


A proof of fatigue according to to EN 1993-1-9:2005 requires the classification of the “Points for Proof of Stresses (p.51)” in regard to:



For and values out of a given list are available (see chapter Notch Cases EN 1993-1-9 (EC 3)).

The slopes an can be chosen in a range of 3.0 to 5.0.

The combined specification of characteristic stress range and inverse slope is called “notch case” in the following. For a point of proof of stresses individual notch cases for normal and shear stresses are assigned (see Dialog: Classification of Points of Proof of Stresses according to EN 1993-1-9 (EC 3) (p.181)).


When selecting notch cases in the scope of [EC 3] Tab.8 the user himself has to consider part thickness or the yield stress of the material.

Welding thicknesses (p.51) have to be considered by the user.

Proof Control Sets:

For each proof the following is specified (see Dialog: Proof of fatigue according to EN 1993-1-9 (EC 3)):

Either a design spectrum or a S-class according to [EC 1] Tab.2.12 (see S-Classes: EN 1993-1-9 (EC 3))

A fatigue specific resistance factor according to [EC 3] Tab.3.1

If the compressive portion of the stress range shall be reduced to 60%

Optionally a default notch cases for unclassified points of proof of stresses

Thus, the proofs have to be formulated separately for different design spectra or S-classes, specific resistance factors, compression stress evaluation and (if any) default notch cases. But proofs can be combined into lists to be evaluated together.

If no default notch case is specified, only classified points of proof of stresses are proven. If no classification is given, the point is not taken into account. The notch case to be taken into account is determined for normal and for shear stresses independently.

Types pf proof:


for normal stresses

for shear stresses

combined




Proof: EN 1993-1-9:2005 (simplified procedure)

Damage Equivalence Factors:

In the simplified procedure, the damage equivalence factors or are given by the specified S-Class according to [EC 1] Tab.2.12.

Evaluation Pattern:


Extremation:


Def.: bzw. whereas compressive portions are reduced to 60%, optionally.

mit:

The design stress range is the difference between maximum and minimum across all load events present in the evaluation pattern.

, According to [EC 1] Tab.2.12 for an S-Class according to proof control set.


stress related value for the purpose of comparison recalculated

as damage related value


⁄


⁄

Combined proof:

( )

Currently, KRASTA uses . All load safety factors have to be already considered at the load definition.

http://dict.leo.org/ende?lp=ende&p=5tY9AA&search=for

http://dict.leo.org/ende?lp=ende&p=5tY9AA&search=the

http://dict.leo.org/ende?lp=ende&p=5tY9AA&search=purpose

http://dict.leo.org/ende?lp=ende&p=5tY9AA&search=of

http://dict.leo.org/ende?lp=ende&p=5tY9AA&search=comparison


Proof: EN 1993-1-9:2005 (damage accumulation procedure)

Design Spectrum:


Damage Equivalence Factors:

The damage equivalence factors or are determined by a damage analysis according to the hypothesis of linear damage accumulation (Palmgren-Miner rule) of stress histories specified by design spectra.

The result of the analysis, the coefficient or and relative total number or , is shown in combined

form as the damage equivalence factor .

Def.: bzw. whereas compressive portions are reduced to 60%, optionally.

∑(

)

∑(

)

√

√

with:


∑ Total number of stress cycles (

Reference number of stress ranges

with: , According to the design spectrum, determined for each point for proof of stresses individually.




⁄


⁄

Combined proof:

( )

Currently, KRASTA uses . All load safety factors have to be already considered at the load definition.


Dialog: Proof of Fatigue according to EN 1993-1-9 (EC 3)



In the “Proof of” area of the dialog, either a Design Spectrum (p.89) or a S-Class (p.192) (“Loading Group”), specific resistance factor and the kind of consideration of compression portions are

specified.

It is not possible to enter a safety coefficient for loads or stresses. Where needed, safety factors can

be considered at definition of the loads. KRASTA is using the loads specified by the evaluation pattern or the design spectrum without any further factors.

Default notch cases enable proofs for points for proof of stresses without individual classifications according to EN 1993-1-9 (EC 3) (p.192).


For each stress component a specialized output format is available.

Dialog: Classification of Points for Proof of Stresses according to EN 1993-1-9 (EC 3)

Classification (p.192) of points for proof of stresses according to EN 1993-1-9 (EC 3) is done by specifying characteristic stress ranges or

and associated inverse slope of the

/N-curve or , see „Implementation in KRASTA (p.187)“.

Specification of a specific resistance factor as well as a reduced

compression portion is done by proof control sets, see below.


Output Formats: EN 1993-1-9 (EC 3)



Proof data (e.g. origin of extremes or if proof(-portion) is satisfied)

Specific items of the individual proof (e.g. parameter of the proof, intermediated results or utilizations)



, ds c

dt c characteristic stress ranges

, m sig

m tau inverse slope of the /N-curve

, ,

sig max

sig min

tau max

tau min


gamma Mf fatigue specific resistance factor

60% information if reduced compressive portion is to be considered.

, ds Sd

dt Sd design stress range (may be reduced).

, ds E2

dt E2 equivalent stress range


, A sig

D sig normal stress utilization bzw.

, A tau

D tau shear stress utilization bzw.

Ausn ges resulting utilization

Verg ges resulting comparison value*)

*) In the scope of EN 1993-1-9 (EC 3), KRASTA does not distinguish between resulting utilization and comparison

value.



Proof of normal stresses: EN 1993-1-9 sig one line, wide page, contains normal stress proof values.

Proof of shear stresses: EN 1993-1-9 tau one line, wide page, contains shear stress proof values.

Combined Proof: EN 1993-1-9 res three lines, wide page, contains both groups from



Notch Cases: EN 1993-1-9 (EC 3)

Standard sequence with a ratio of 1.125.

355 N/mm²

315 N/mm²

280 N/mm²

.

.

.

8.0 N/mm²

7.1 N/mm²

6.3 N/mm²

Loading Groups: EN 1993-1-9 (EC 3) (S-Classes)

S-Class

Damage Equivalence Factor

, (m=3) , (m=5)

S02*)

0.126 0.289

S01*) 0.159 0.331

S0 0.198 0.379

S1 0.250 0.436

S2 0.315 0.500

S3 0.397 0.575

S4 0.500 0.660

S5 0.630 0.758

S6 0.794 0.871

S7 1.000 1.000

S8 1.260 1.149

S9 1.587 1.320

*) The S-Classes “S02” and “S01” are not known by the standard. Use is not compliant with this standard.

They are additionally available following EN 13001 ( √

√

)

Literature: EN 1993-1-9:2005

[EC 1] prEN 1991-3:2002

Ausgabe: 2002-09

Eurocode 1: Einwirkung auf Tragwerke - Teil 3: Einwirkungen infolge von Kranen und Maschinen

[EC 3] EN 1993-1-9:2005

Ausgabe: 2005-07

Eurocode 3: Bemessung und Konstruktion von Stahlbauten - Teil 1-9: Ermüdung

[StK] Stahlbaukalender, 2006 8. Jahrgang, Herausgegeben von Prof. Dr.-Ing. Ulrike Kuhlmann

Abschnitt 2: Grundlagen und Erläuterungen der neuen Ermüdungsnachweise nach Eurocode 3 Dr.-Ing. Alain Nussbauer, Dr.-Ing. Hans-Peter Günther


7.1.8 Proof of Fatigue acc. FEM 1.001

The proceeding is analog to DIN 15018.

Classification of materials,

Classification of points for proof of stresses in notch cases (or specifying a default notch case),

Specification of a loading group (called “structural element group” in FEM).

Proof: FEM 1.001

Def.: | | | | ;

| | | | ;

Equations for permissibl upper stresses, depend on ,

according to Table T.A. 3.6.1 and (tensile strength) according to classification of the material.


(tension)

(pressure)

(swelling domain)

(tension)

(

)

(pressure)



Structural Elements

(acc. W0)

√

Welding

(acc. K0)

√



combined proof: √(

)

(

)



Materials: FEM 1.001

St 37

St 44

St 52-3

Notch Cases: FEM 1.001

W0

W1

W2

K0

K1

K2

K3

K4

Loading Groups: FEM 1.001

E1

E2

E3

E4

E5

E6

E7

E8


7.1.9 Proof of Fatigue acc. ISO 5049-1

The proceeding is analogous to DIN 15018.

Classification of materials,

Classification of points for proof of stresses in notch cases (or specifying a default notch case),

Specification of a loading group (called “cycle classes” in ISO).

Since in ISO 5049-1 the values for the permissible fatigue strength are given only in graphic form, the arithmetic values had to be determined by measuring several points.

Proof: ISO 5049-1

Def.: | | | | ;

| | | | ;

Equations for permissible upper stresses, depend on , have been taken over from FEM


(tension)

(pressure)

(swelling domain)

(tension)

(

)

(pressure)



Structural Elements

(acc. W0)

√

Welding

(acc. K0)

√

The values for are measured from tables 19, 20 und 21 of the standard!



combined proof: √(

)

(

)



Materials: ISO 5049

Fe 360

Fe 430

Fe 510

Notch Cases: ISO 5049

W0

W1

W2

K0

K1

K2

K3

K4

Loading Groups: ISO 5049

A

B

C


7.1.10 Proof of Fatigue according to DASt-Ri 011

Proof: DASt-Ri 011

Def.: | | | | ;

| | | | ;

Table 12 (DASt-Ri 011)

Rows 4-7: Equations for tolerable upper stresses, depend on ,

acc. Table 12 acc. classification of the material.

(tension)


(swelling domain) notch cases W0 and K0 other notch cases

⁄

(pressure)


Rows 8-9: Tolerable stress for structural elements and welding.

Structural Elements

(acc. W0)

√

Welding

acc. Col. “other notch cases” with acc. DIN15018: Material St52-3, notch case K0 for B0 und B7 added analogous.

√



combined proof: (

)

(

)

For non-simplified combined proof the sum above is maximized. For simplified combined proof the maximum normal stress and the maximum shear stress utilization are determined separately and combined later.


Materials: DASt-Ri 011

StE 460

StE 690

Notch Cases: DASt-Ri 011

W0

W1

W2

K0

K1

K2

K3

K3/4

K4

Loading Groups: DASt-Ri 011

B0

B1

B2

B3

B4

B5

B6

B7


7.1.11 Proof of Fatigue acc. AS 4100:1998


AS 4100, Method of Proof

Based on the operation method, notch cases and accessibility, permissible stress ranges are determined and compared against characteristic stress ranges. The workflow in detail is as follows:

Operation method:

In general, the operation method to analyze is specified by a list of load working cycles, each of them weighted with own relative frequency, i.e. by specifying of a certain load spectrum.

Stress range weighting:

For hollow sections, other cross sections and connections the stress ranges are multiplied by a factor between 1.0 and 2.0 (ref. AS 4100, Tab. 11.3.1).


For each load oscillation event a partial damage is determined and accumulated according to its

individual number of stress cycles (ref. AS 4100, Chap. 11.8.2). Hints on how to determine a single,

effective number of load cycles are given in chapter 11.3.2.

Notch cases:

Detail categories are covered by classification of notch cases (ref. AS 4100, Tab. 11.5.1).

With the classification of a certain notch case the reference stress range

or

is determined. The

notch case accounts for stress concentration, material and material thickness. Notch cases are specified individually for normal and for shear stresses.

S-N Curve:

The inverse slope of the S-N Curve is a function of the number of stress cycles.

normal stress: {

shear stress:

Uncorrected fatigue strength:

The uncorrected fatigue strength is determined by reference stress range and number of stress

cycles:

normal stress:

{

√

√

shear stress: √


Thickness effect

A material thicknesses correction factor is taken into account to determine the corrected fatique

strength as follows:

with {

(

)

Comparison fatigue strength determined by capacity factor:

The proof is made by comparing of design stress range against a corrected fatigue strength scaled

by the capacity factor .

The comparison fatigue strength is .

The maximum capacity factor is 1.0. According to accessibility, type of stress determination, regularity of stress cycles and redundancy of the load path even smaller. Especially for non-redundant load paths a capacity factor has to be chosen.

Utilizations:

For different stress components the proof shall be executed separately. For each stress component the utilization is calculated by comparing the design stress range with the comparison fatigue range.

(proof of constant stress ranges)

A combined proof is defined according to AS 4100-Suppl-1999 Section C11.3.1.b as:

(

)

(

)

with defined in chap. 11.1.6

AS 4100, Implementation in KRASTA

Stress range weighting:

No stress range weighting according to table 11.3.1 is done by KRASTA. If required, the weighting factor can be considered by the user by an attenuated capacity factor (see below). This is not applicable for combined proofs.


The proof is done acc. AS 4100, chap. 11.8.1 for a certain number of load cycles . By this, the

maximum stress range is considered as constant stress range in the sense of the standard.

Individual number of load cycles , assigned to different stress ranges (damage accumulation) is not implemented in KRASTA for proofs according to AS 4100.


A proof of fatigue acc. to AS 4100 requires the classification of the “Points for Proof of Stresses (p.51)” in regard to:

Reference fatigue strength

For reference fatigue strength

values out of a given list are available (see Chapter

Notch Cases AS 4100 (p.205)). Intermediate values are covered safely by specifying the next smaller value available.

The reference fatigue strength for shear stresses is fixed in KRASTA to

.



When selecting the notch cases in the scope of AS table 11.5.1(2) the user himself has to take into account the according part thickness of the material.


Proof Control Sets:

For each proof the following is specified (see Dialog: Proof of fatigue acc. AS 4100 (p.203)):

A number of load cycles

A capacity factor

Optionally a default notch case

for unclassified points of proof of stresses.

Thus, the proofs have to be formulated separately for different number of load cycles, specific capacity factors and (if any) default notch cases. But proofs can be combined into lists to be evaluated together.

If no default notch case is specified, only classified points of proof of stresses are proven. If no classifica-tion is given, the point is not taken into account. The notch case to be taken into account is determined for normal and for shear stresses independently.

Types of Proof:


for normal stresses,

for shear stresses

combined

It is also possible to do all three types simultaneously. For each of these proofs, an individual, specialized output format is available.

If more than one type of proof is done simultaneously, it is possible to output the worst case only. The worst case is the one with the highest utilization.

Evaluation pattern:

The evaluation pattern is a list of load events consisting of situations and loadcases. At present, there is no information in regard of frequency of load cycles associated. Analyzing load spectra is not implemented in KRASTA.

Extremation:

KRASTA determines stress differences and design stress ranges for every possible combination of two load cases out of the evaluation pattern. For each stress difference the according utilizations are com-puted. The cases which result in highest individual utilizations are documented.


Proof: AS 4100

Def.:

√

√

√

with:

{

(

)

according to individual classification of the points of proof of stresses.

according to proof control set.




Combined proof*): (

)

(

)

*) The definition of the combined proof in AS 4100-Supplement-1999, C11.3.1 use non defined

parameter and . Therefore KRASTA offers a combined proof in an analog sense but not in a form defined by the standard. For that purpose KRASTA includes the following assumptions:

resp.

Note: To interpret under- or over-utilizations, please consider the different power law of single and combined stress utilization.


Dialog: Classification of Points of Proof of Stresses acc. AS 4100

Classification of point for proof of stresses according to AS 4100 is done by specifying a reference fatigue strength for normal stress , see „Implementation in KRASTA (p.200)“.

Specification of a specific capacity factor is done in proof control sets, see below.

Dialog: Proof of Fatigue acc. AS 4100

In the “Proof of” area of the dialog, number of load cycles and the capacity factor are specified.

Default notch cases enable proove of points for proof of stresses without individual classifications according to AS 4100.

The stress componets to proove are selectable independently. If desired, the textual output can be limited to the worst case.

For each type of proof, a specialized Output Format (p.204) is available.


Output Formats: AS 4100



Proof data (e.g. origin of extreme values or if proof(-portion) is satisfied)

Specific items for the individual proof (e.g. parameter of the proof, intermediated results or utilizations)



,

,

max sig

min sig

max tau

min tau


delta s

delta t design stress ranges

fr_n,

fr_s reference fatigue strengths (notch cases)

beta thickness correction factor

fc_n,

fc_s corrected fatigue strength

,

fa_sig,

fa_tau admissible comparison fatigue strength


A sig normal stress utilization

A tau shear stress utilization

Ausn ges resulting utilization

Verg ges resulting comparison value

*) In the scope of AS 4100 KRASTA does not distinguish resulting utilization and comparison value.



Proof of normal stresses: AS 4100 sig one line, wide page, contains normal stress proof values.

Proof of shear stresses: AS 4100 tau one line, wide page, contains shear stress proof values.

Combined Proof: AS 4100 res three lines, wide page, contains both groups from



Notch Cases: AS 4100

See also section “AS 4100, Method of Proof (p.199)”.

180 N/mm²

160 N/mm²

140 N/mm²

.

.

.

45 N/mm²

40 N/mm²

36 N/mm²


7.1.12 Proof of Stresses el.-el. acc. DIN 18800:1990-11

A proof of stresses elastic-elastic according to DIN 18800, element (747) requires the classification of the used materials (p.67) as well as the input of the according material thickness at every point for proof of stresses.

Proof: DIN 18800 el.el.

It can be selected for the proof to consider normal stress utilization only

(Cond. 33):

or the shear stress utilization

(Cond. 34):

or the combined value in detail (Cond. 33 - 35):

(Cond. 35):

and

and

with √

Extreme values are searched for the utilization of the permissible stresses.

If, in the case of a combined proof, the normal or shear stress utilization is lower than 0.5 the higher one of the two is used a combined utilization.

Materials: DIN 18800

Materials may be classified for DIN 18800 as:

St 37

St 52-3

StE 355

GS-52

GS-20 Mn 5

C 35 N

Element Thickness: DIN 18800

Structural element thickness for DIN 18800:

Steel Thickness

[mm]

Yield Point

[N/mm²]

Tensile Strength

[N/mm²]

St 37

St 52-3

For the points for proof of stresses to be considered in the proof the according part thickness must be defined. For standard, parametric and thin-walled cross sections these are known from cross sections geometry. For direct input cross sections the user has to enter a thickness for every point for proof of stresses.

Points for proof of stresses that have no according thickness are considered to fall into the class with the least thickness.


7.1.13 Proof of Stresses, Buckling acc. DIN 4114-1:1952-07 (Omega-Method)


Proof: DIN 4114 Buckling (Omega-Method)

As a function of beam slenderness , material and cross section the coefficient is determined based on the tables. The permissible stress is to be chosen according the applied standards, material and security concept.

The proof to satisfy is:

DIN 4114 Buckling (Omega-Method), Implementation in KRASTA

KRASTA evaluates the mono-axial defined proof separately for both principal axes. KRASTA allows taking into account bending stress components. According to [DIN 4114] bending stress components will be weighted uniformly with .

The normal stress coefficient is determined in respect to the slenderness of the actual axis:

( ) ,

The proofs are:

( )

( )

The associated utilizations are defined as:

,

resp.

Dialog: Proof of Stresses Buckling DIN 4114 (Omega-Method)

The extremation can be chosen to cover the maximum utilization or to cover only the utilization of

one particular axis or .

Only results of that chosen utilization are shown in text or plots. Therefore, the normal use case will be to perform an extremation of .

There is no classification of materials or cross sections in respect to the omega method in KRASTA. The classification is part of the proof control set and has to be done by individually for each proof control set. The available classifications cover tables according to [DIN 4114] (Steel) and additionally tables according to [DIN 4113] (Aluminium).


Output Formats: DIN 4114 Buckling (Omega-Method)


General data (e.g. beam, section point, sectional point, load case or stresses),

Proof data (e.g. origin of extremes or if proof(-portion) is satisfied),

Beam Buckling data (e.g. beam length, buckling length (coeff.) or slenderness) and

Specific items for the individual proof (e.g. parameter of the proof, intermediated results or utilizations)



, om_y,

om_z normal stress coefficients acc. -table

, s_om_y,

s_om_z -stress for proofs of y- resp. z-axis

b(M)y,

b(M)y

Effective coefficient of resulting moment ( )

for proofs of y- resp. z-axis:

( ( ) ) ⁄

( ( ) ) ⁄

, a_y, a_z utilization for proofs of y- resp. z-axis


a_max maximum of both utilizations



Proof of y-axis: Omega-Verf.(y) one line, wide page, contains proof values regarding y-axis.

Proof of z-axis: Omega-Verf.(z) one line, wide page, contains proof values regarding z-axis.

Combined Proof: Omega-Verfahren one line, wide page, contains proof values regarding both axes, effective coeff. and maximum utilization.

Literature: DIN 4114 Buckling (Omega-Method)

[DIN 4114] DIN 4114-1:1952-07

Ausgabe: Juli 1952

DIN 4114: Stahlbau Blatt 1: Stabilitätsfälle (Knicken, Kippung, Beulen); Berechnungsgrundlagen, Vorschriften

[DIN 4113] DIN 4113-1:1980-05

Ausgabe: Mai 1980

DIN 4113: Aluminiumkonstruktionen Teil 1: Aluminiumkonstruktionen unter vorwiegend ruhender Belastung; Berechnung und bauliche Durchbildung


7.2 Results

Proofs (p.159) and results are handled by KRASTA in a similar manner (see Proof- / Result-Control-Sets (p.215)). In both cases, the evaluation pattern, the type of evaluation, extremation and textual output are specified.

The following result control sets are available:

inner forces,

stresses,

delta stresses (p.213),

beam displacements,

node displacements,

spring forces and

support forces.


7.2.1 Delta Stress Results

The result control set “Delta Stresses” allows to search and document maximum normal stress ranges or shear stress ranges respectively.

Extremation:

KRASTA determines stress differences for every possible combination of two load cases out of the evaluation pattern. The cases with highest delta stresses are documented.

Types of extremation:

“sigma” : delta of normal stresses caused by normal forces and bending

“tau” : delta of shear stresses caused by lateral forces and torsion

Dialog: Extremation of delta stresses

In the “Extremation of” area of the dialog, the type of delta stress to be evaluated is specified.

The extremation can be done for structural elements or welded joints separately.

For each type of proof a specialized Output Format (p.221) is available.


Output Formats: Delta Stresses

The layout of an output format can be defined freely. To build up or edit output formats the following items are available:

General data (e.g. beam, section point, sectional point, load case or stresses),

Extremation data (e.g. origin of extremes or if proof(-portion) is satisfied) and

Specific items for the individual extremation (e.g. extreme and according stress components)


Tab-Head Item

s max, s min

ds max

normal stress components, building the normal stress range

maximum normal stress range

t(smax), t(smin)

dt(dsmax)

acc. shear stress components

acc. shear stress difference

t max, t min

dt max

shear stress components, building the shear stress range

maximum shear stress range

s(tmax), s(tmin)

ds(dtmax)

acc. normal stress components

acc. normal stress difference


Type of Extremation Format

delta normal stresses: Delta Normal-St. one line, wide page, contains normal stress extremation values.

delta shear stresses: Delta Shear-St. one line, wide page, contains shear stress extremation values.

Delta Stresses three lines, wide page, contains both groups from above.


7.3 Proof- / Result-Control-Sets

Proofs and results are treated in a similar way by KRASTA. In both cases the load cases to be evaluated, the type of evaluation, extremation and output have to be described.

In contrast to a result a proof considers permissible values depending on certain standards to calculate utilizations.

Dialog: For Proofs and Results

The information to be specified by the user is grouped into four groups “Options for search of extreme values”, “Evaluation”, “Eval. Pattern” and “Output”

7.3.1 Options for search of extreme values

Whether you want to search extreme values indicated by the check box.

Extreme values of which type, e.g. in case of inner forces:

normal force x,

shear force y or z

torsional moment x,

bending moment y or z,

resulting shear force, √

resulting bending moment, √

resulting section force √

resulting section moment. √


The Type of Extremum, generally:

maximum

minimum

maximum magnitude

minimum magnitude

The extend of the Output of extreme values: extreme value of all beams (1 value), extreme value per beam (1 value per beam), extreme value per section, extreme value per point for proof of stresses (if applicable), all values.

7.3.2 Evaluation

It is possible to do the evaluation for all section points, at the start, at the end or at start and end of beams and for following Beams referred to in a list of beams.

With the option Filter, the extend of result output can be limited. It is possible to output only values which are greater (or smaller) than a selectable value. Several conditions can be combined via "and" or "or".

The filtering is done before any extremation. Therefore, the extreme values of the already pre-filtered data set are shown.

Dialog: Filter

7.3.3 Output

At the output area of the dialog the way to show the results is specified.

7.3.3.1 Textual Output

Output formats define which result items are listed, how they are arranged in a result table and what a format is to be used.

For the textual output of results and proofs default output formats are available. Additionally, output formats can be modified, added or imported.

The amount of the textual output can be specified in more detail by the “Details”-Button. Section “Details of Output (p.220)” gives a description of the available options.

Textual Output Format

An output format for the results is to be select here.


7.3.3.2 Creation of load event objects according relevant load events

Sometimes it is required to further analyse a load event that has been relevant for a certain point (e.g. a certain Permutation of a Logic Load Case (LLC)). For this purpose the context menu (right mouse button) offer individual for each relevant load event:

To create an according load event object using the related situation and according created Combination (CLC) or 2

nd Order (THII) Load Case.

To create an according Combination (CLC) or 2nd

Order (THII) Load Case (without relation to a certain situation).

7.3.3.3 Border Lines

A Border Line is used to display extreme values graphically by border lines with a certain numbering style and an adjustable view factor.

7.3.3.4 Color Gradation

A Color Graduation is used to display extreme values as colored gravity axis using an adjustable color palette. Color palettes are defined in specific physical dimensions, palettes using “unit” can be adapted to the range of result values by using the button Adaption. Use Remove to remove them.

7.3.4 Evaluation Pattern

The Evaluation Pattern is used to select the load cases in corresponding situations for which results are to be evaluated.

Using List of Situations

Especially in systems with some structural degrees of freedom many different orientations and/or situations have to be considered. To simplify the handling of these sets of situations so-called “Lists of Situations” exist.

“Lists of Situations” can be used for a clear definition of evaluation patterns, as they are found in the KRASTA result and proof control dialogs.


Example: Evaluation Pattern

The number of situation/load case couples to be analyzed (the evaluation pattern) may be extensive.

The list of situations „0° bis 90° e+a“ contains the required situations [1] defined in a correct order [2],

Using a list of situations the same evaluation pattern can be formulated in a substantially simpler fashion.

The list of situations is a replacement for its expanded content. To analyze a given evaluation pattern all used lists of situations will be expanded internally to a simple linear list of situation / load case couples.

“Wvaluate each line separately” means that each line of the expanded simple list is evaluated independently. This, there will no evaluation across different situations if lists of situations are used.

The list of situations can also be used in calculation suits:

[[22]]

[[11]]


Example: Adopt existing evaluation pattern (automatically)

Longer lists of individual situation / load case couples may be required for an evaluation pattern. The same evaluation pattern may be needed for different result and/or proof controls. For this purpose, it is possible to adopt evaluation patterns from other result or proof control sets.

The evaluation pattern does not have to be defined locally (“as defined here”), but can be copied from any other result control.

The local evaluation pattern copy is updated automatically every time the result control set is evaluated (used) or edited. The template evaluation pattern (e.g. the evaluation pattern of the result control “SigmaV”) is copied to the local evaluation pattern again.

Even if the template result control set is deleted the evaluation pattern remains accessible locally. The evaluation pattern is redefined “as defined here”.


7.3.5 Details of Output

The amount of the textual descriptions can be specified in detail separately for the pure textual list of results (“text output”) and the text description of plots (“plot output”).

Dialog: Details

The following options are available:

Description of Options: A detailed description of the proof. If not wanted, only the name of the proof is listed.

Description of Evaluation Pattern: Each load event to evaluate is listed. If not wanted, only the statistical summary is listed.

Expand Lists of Objects: The content of the lists of beams or nodes to proof are listed. If not selected, only the name of the list is listed.

Description of Tables as well as Bounds: The parts of the table (of the format) and (if any) specified limits to regard small values as zero are described in detail. If not selected, nothing in this regard is listed. In particular, this can be reasonable, if several results are listed in series and this type of information is redundant.

Description of Load Events (p.85): The composition of the decisive load events mentioned in the result table. If not selected no description is given.

In the Description of Load Events, can be listed including Compensation Load Cases (p.92) and with individual Timestamps of associated Calculation Results. If no individual Timestamps are wanted, only a summary of the timestamps is listed at the end of the text block.

Warnings: If any.

Description of Filter (p.216)


7.4 Output Format

Output formats define which result data are to be output at which line and column in which length and precision.

Standard formats are supplied for every type of proof/result. Individual formats can be defined by the user.

Dialog: Output Format

The list of items “Text and Results” summarizes the layout of the output format. Additionally, a preview is available (see below). The items can be arranged in the table layout at fixed columns (as shown here) or relative to each other with given spacing. It is easier to (re-)arrange new topics in relative mode. It is possible to toggle between the absolute and the relative mode at any time.

A specific item is created or edited in the edit pane “Topic Layout”. The “Topic” selection box lists all available items in regard of the actual output format. In a format for inner forces, utilization items will not be available. The extend of item layout specification depends on the item type. Common to all types of items is the positioning part.

All Columns: Column positions can be set absolute or relative manner. If set absolutely (as in the example dialog above), the number is used as column position, if set relatively, the position is determined by the prior position and width plus the number as gap in between. The default number is 0, i.e. without gap.

All Widths: The widths of individual items can be set explicitly, by a width number > 0 (as in the example dialog above) or as automatic; by a width number = 0. An item width set to automatic, is replaced by the actual default width at the time of usage.

The current Text Output Layout is displayed in an extra window:

Preview: Text Output Layout


7.5 Palettes

A color gradation palette defines according colors for ranges of values. The border values of the color sections may have dimensions (stress, force, moment, length, angle and fraction) or may be dimensionless.

The dialog to edit a Palette offers the following items:

Dialog: Palettes

The dimension of the Value needs to be specified.

The Number of Colors and the border values can be determined by user. For values with dimensions these values are the border values. For dimensionless palettes have to be scaled to fit the displayed values.

The border values must have an increasing order from bottom to top.

For values outside the defined color range black is used as a fallback. This may be avoided by very large upper and very low lower limits.

Interpolation may be used for your convenience. After pressing the buttons Values or Colors a column of buttons appears next to the values, adjusted to the values or the colors. As soon as two buttons are pressed the colors or values in between are interpolated.

Adaption of a Palette

When adapting a dimensionless palette for values with a dimension, the dimensionless values (e.g. 0 and 1) are related to the corresponding absolute values in the adequate unit (e.g. 0 N/mm² and 180 N/mm²). The reference values may be generic (e.g. minimum or maximum of values to display). Each dimensionless palette has a default adaption (preset to 0=minimum; 1=maximum) so it can be used without changes. It is certainly possible to adapt the palette for proofs or results individually.


7.6 System Documentation

All textual and graphical output is stored in files. The system tracks which files were created and allows printing in user defined orders with consecutive page numbering.

7.6.1 Textual Documentation

The textual documentation is controlled by output controls that contain information on which attributes of which objects are to be output.

Additionally it can be selected whether the output should be object oriented (e.g. all data of one beam together) or attribute oriented (e.g. each type of beam attribute in table form).

7.6.2 Graphical Output

The structure can be output with different properties or results displayed (e.g. cross sections on beams, loads, inner forces). All plots may be created with hidden lines. Plots of thin walled or parametric cross sections can also be produced.

KRASTA 9.6 Manual Brief Information for Review 225

Further information are available by:

Kühne BSB GmbH Mina-Rees-Straße 5A DE 64295 Darmstadt

Phone Fax

Hotline

+49 (0) 6151 397690-0 +49 (0) 6151 397690-200 +49 (0) 6151 397690-222

Web Email

www.krasta.de [email protected]

8 Brief Information for Review In this short information you find the essential information and definitions about the program system KRASTA.

KRASTA has been developed at the Fachbereich Fördertechnik und Lasthebemaschinen der TH Darmstadt (Institute of Lifting Appliances at the Technical University of Darmstadt ) in cooperation with the industry. The work has been supported by the Fachgemeinschaft Fördertechnik im VDMA (Verband Deutscher Maschinen und Anlagenbau) and FKM (Forschungskuratorium Maschinenbau)

The program KRASTA/PAS III is maintained and purchased by Kühne BSB GmbH since 1991 and will be further developed in cooperation with universities and industry. The program system has been ported on Windows and other operating systems since 1995.

KRASTA is used in material handling, mechanical and structural steel engineering.

KRASTA and KRACAD are registered trademarks.

KRASTA is a program system for beam statical and modal analysis of spatial structures in the fields of general steel construction, material handling and plant manufacturing. Structures or parts of structures can be moved in different positions for calculation. Results can be evaluated across positions.

The structural model is created graphical interactive by means of beam elements and nodes.

8.1 General

The calculation continues up to the proof of stresses (e.g. acc. DIN 18800 or Omega-Method acc. DIN 4114) and fatigue incl. damage accumulation (e.g. acc. DIN 15018, DIN 22261, DIN 13001, AS 4001, ISO 5049-1, EN 1993-1-9 (EC3) and other).

The nominal stresses are determined on the base of technical bending theory of the beam and the St. Venant torsion theory.

For a calculation according to theory 2nd

order partial safety coefficients and predeformations can be considered.

Input and output of data can be done in German and English.

The program PAS III used as solver has the following theoretical foundation.

For the single beam the differential equation system (DES) is solved according to the technical beam bending theory. As the inhomogeneous DES is solved the loads and predisplacements can be placed inside the beams without definition of intermediate nodes.

The calculation may be according to theory 1st or 2

nd order. The equilibrium is calculated in the deformed

state. Theory 2nd order iterates over the normal force of the beam. The buckling load (eigen value) can be determined iteratively.

PAS III contains a theory of small displacements which means that the plan of displacement is built linear.

Each of the 6 cross section values (area, shear areas, bending- and torsional inertia moments) can be set rigid or elastic. Elasticity equations for rigid are replaced by equilibrium conditions. Structures that show great differences in elasticity or regions that cannot be modelled by beams, can be modelled in this way so that the global flow of forces can be determined correctly without numerical difficulties in solving the equations.

The optional solver program STAB88 is a finite element program with geometrical nonlinear calculation of beam -, bar - and rope structures. Loads are increased step by step according to a time function. After each step of load the equilibrium between inner and outer forces is improved by a iteration of equilibrium.

http://www.krasta.de/

mailto:[email protected]

226 Brief Information for Review KRASTA 9.6 Manual

8.2 Coordinate Systems KRASTA provides 4 coordinate systems:

Inertial System

Subsystem Coordinate System

Beam Coordinate System

Principal Axes Coordinate System

The Inertial System (IN-CS) is a space fixed cartesian coordinate system.

Each subsystem has its own Subsystem Coordinate System (SS-CS), in which the according objects are described. In the KRASTA-basic version the SS-CS is equivalent to the IN-CS.

For each beam a Beam Coordinate System (BM-CS) (x0, y0, z0) is defined, whose relative position to the SS-CS is described by start of beam, end of beam and an auxiliary vector (Aux.). The longitudinal axis shows into the x0- direction. The cross sections are described in the BM-CS.

The direction of the longitudinal axis runs from the start node to the end node. It defines the x0- axis.

The other two axes are defined by input of an auxiliary vector like this:

The positive local x0- and y0-axis form a semi plane. By input of an auxiliary vector (H) in this semi plane, the position of the local beam coordinate system is defined in the subsystem or in the inertial system respectively.

The definition of the local beam coordinate system can be described as follows:

The local x0-axis is known by input of the start- and end node.

An aux.-vector (H), described in global coordinates, is input to the set the other local axes.

The cross product of x0 and aux. results in the local z0- axis.

From the cross product z0 with x0 follows the local y0- axis.


Example: Input of Aux.-Vectors (H):

The Principal Axes Coordinate System (PA-CS) is rotated by a principal axis angle against the BM-

CS. At double- or single symmetrical cross sections the PA-CS corresponds to the BM-CS. Inner forces and beam deformations are described in principal axes.


8.3 Properties of Beams

In KRASTA, beams are defined statically by the location of the end nodes, the cross section geometry and orientation, a material, an opt. additionally mass and specifications of end hinges and springs resp.

8.3.1 Beam Spring

The connection between beam and node is rigid by default. To represent elasticity between beam and node, springs can be defined.

Beam springs are described in the local beam coordinate system.

8.3.2 Joints

Beam joints provide translational and rotational degrees of freedom between beam end and node. Beam joints are beam properties, they are described in the beam coordinate system of the beam.

If the beam coordinate system does not correspond with the desired directions of the joint axes a short (rigid) beam with the desired local axes has to be created.

8.3.3 Material

KRASTA allows the definition of different materials like steel or aluminium by the input of specific material properties.

8.3.4 Force Conditions

For elements that can only transmit forces that are higher or lower than a certain value, force conditions can be defined. They behave like an ideal elastic-plastic material. Typical applications for such elements are ropes, which only transmit tension, wheels and legs, which only transmit pressure or hydraulic buffers, which only transmit a limit force.

Each load combination is calculated first without consideration of the force conditions. At each force condition a unit beam predeformation is applied at the affected degree of freedom. After the elastostatic calculation the force conditions are met by superposition of the unit predeformations multiplied by factors. The factors are calculated by iterative solution of an equation system.

These force conditions work only in connection with linear theory and cannot be used with nonlinear theory or 2

nd order theory.

8.3.5 Beam Buckling Data

Beam Buckling Data define beam buckling properties of each individual beam. They are used in proof of beam buckling (e.g. acc. DIN 4114 (Omega-Method)).

Slenderness

For each principal axis separately, the actual beam slenderness is evaluated based on the directly or

indirectly defined beam buckling length and cross section properties and resp. :

√ ⁄ resp.

√ ⁄

In case of conical beams the minor of both inertia radii associated to the end cross sections is taken ( ). This is results in a save upper approximation of the slenderness of a conical

beam.

8.4 Properties of Nodes

8.4.1 Support Conditions

Support nodes can be defined as rigid, jointed or elastic. Each individual degree of freedom can be defined as rigid, jointed or can be given a spring rate.


8.5 Cross Section

Cross sections differ in standardized cross sections, thin-walled input cross sections, parametrical cross sections and directly input cross sections.

For the usual standardized cross sections libraries are delivered.

Thin-Walled Cross Sections can be described individually. The input of the parts takes place in the beam coordinate system. The cell distribution is determined independently. The number of the cells is not limited.

Point areas can be used to substitute parts, which are small compared to the total dimensions (rolled radius, welds, etc.) For the inertia moments only the Steiner-parts of the point area are considered.

For each plate part the unit stresses at start and end point (stresses as a result of inner forces = 1.0) are calculated. Negative point numbers mean part start, positive signs mean part end.

Shear stresses are positive in arrow direction.

With the Direct Input Cross Sections the six cross section values have to be input.

Individual (or even all) cross section values may be set rigid by input of a negative number in the specific field. The weight of the cross section is calculated from the magnitude of the cross sectional area Ax.

Examples for the use of rigid cross sections are offsets as used for the modelling of eccentric connections or points of application of load.

Ropes are usually defined with the cross sectional area Ax only. All other cross section values are set rigid.

For Parametrical Cross Sections the shear areas are calculated by means of a shear factor from the cross section.

The center of shear forces is calculated relative to the input system.

Statical Moment

∫

∫

The Center of Gravity is calculated relative to the input system.

Torsional Moment of Inertia

∮

(2nd

Bredt Formula)

For thin-walled open cross sections (H, C and L-Sections) the Bredt Formula extends to:

∑

For determination of IT a corrective factor is used at thin-walled sections. The exact value is shown at the description of the specific cross sections.

Moments of Inertia

The moments of inertia for the individual cross sections are calculated with the help of the Steiner Theorem, radii are considered with their moment of inertia and the Steiner part. More complicated cross sections are decomposed in partial cross sections, for which the individual moments of inertia are calculated and combined.

∫

∫

∫

For asymmetric cross sections (L-Sections) the principal axis angle and the moments of inertia round the principal axes are calculated.


Moments of Resistance

The torsional moment of resistance for St. Venant torsion is calculated according to the Bredt Formula.

(1st Bredt Formula)

For thin-walled sections

∑

The bending moment of resistance is calculated out of the moment of inertia and the distance of the section center line to the outer fibre.

Stresses

Stresses as a result of normal forces are calculated out of the force acting in longitudinal direction of the beam and the cross sectional area.

Bending stresses are calculated from the bending moment and the bending moment of resistance.

Torsional shear stresses are calculated from the torsional moment and the torsional moment of resistance.

Shearing force shear stresses are calculated out of the shear force, the statical moment, the moment of inertia and the thickness according to the "Dowel" Formula.

At open cross sections the shear stresses resulting from torsion and shear forces are positive in positive beam coordinate direction, at closed cross sections (tube and rectangle tube) in mathematical positive direction of rotation.

Plastic Moment of Resistance

The plastic moment of resistance is determined from the double statical moment round the area bisectric.


8.6 Mass Cases

Mass cases are useful for modelling fixed, variable or moveable masses placed on the structure.

Mass distributions, as occurring in practice, are composed of permanent available masses, masses variable in magnitude (e. g. counter weight, pay load) and moveable masses (e. g. trolley positions).

The net mass distribution of the construction is calculated from product of cross sectional area and density. Usually the real mass is greater. Connections, transverse diaphragms, electrical equipment and further parts are added, which are not included in the statical model. To describe the mass distribution more exactly, beam mass factors can be applied to represent evenly distributed additional masses. For local mass concentrations node- and beam masses (concentrated or distributed) can be defined.

In KRASTA three kinds of mass cases are distinguished:

Mass case "Permanent Mass"

Basic mass cases

Combination mass cases

Permanent Mass comprises masses which are directly stored with the objects beam and node and therefore are carried with these objects if they are copied or imported with subsystems [OPTION].

Basic Mass Cases containing mass factors and individual masses can be defined for variable or moveable masses or to describe parts of a model that are to be accelerated

Mass factors can be applied to the permanent mass where you can select whether it should be applied on the distributed mass (resulting from sectional area and density) only or also on the beam- and node masses.

This mass information is assigned to beam- and node lists. On calculation of the mass the permanent mass (beam mass factors, beam masses, node masses) of the given objects in the lists is then multiplied by the respective mass factors. Additional individual masses are added.

Basic mass cases can be supplied with factors and combined to Combination Mass Cases.

Different mass distributions can easily be described by this means. Basic- or combination mass cases are used in description of inertia load cases and for the modal analysis. With a consequently mass orientated input all inertia loads can be generated with ease.


8.7 Load Cases

In load cases the loads on the structure resulting from outer forces or predeformations acting on beams and/or nodes is described.

In KRASTA different types of load cases can be defined:

Basic load cases

Combination load cases

Logic load cases

Load cases for 2nd order theory (PAS III)

Load cases for geometrical nonlinear calculation with STAB88

Nonlinear logic load cases

A Basic Load Case can consist of directly input loads and/or generated loads. The loads described below can be used with the solver PAS III. For STAB88, which supports node loads only, all beam loads are automatically converted into equivalent node loads

On beams it is possible to define any concentrated, uniformly or trapezoidal distributed beam loads or beam predeformations.

Loads with constant directions can be described in the inertial system, loads that are to be moved with a subsystem or beam, can be described in the subsystem- or beam coordinate system. If there are any principal axis angles, loads will automatically be transformed to the principal axes at creation of solver input file.

The following described loads can be used in connection with PAS III:

Distributed Loads can be projected for spatial beams if desired, where the force or the moment per unit of length is input in the inertial- or subsystem coordinate system. The program carries out a load projection. The load is adjusted so that the resultant is constant.

Node Loads can be input in the according subsystem- or in the inertial system. One node load can consist of up to 6 components.

With Temperature Loads a steady and a different heating at beam upper side or beam underside is intended. Out of the coefficient of thermal expansion, which is saved in material data and the temperature details, substitute predeformations are determined.

The complete structure or parts of it can be accelerated translational or rotational and rotated (centrifugal forces). For a translational acceleration the direction of acceleration and its magnitude has to be described. For a rotational movement the axis of rotation, the rotational acceleration and/or the angular velocity are to be input. The acceleration loads are generated from acceleration description and the mass distribution described by a mass case. As a special case of translational acceleration the acceleration due to gravity is implemented, where the direction of action of the weight has to be given only.

Different Wind Profiles can be defined. Only the wind direction, the height range with according pressure and the direction of the height range gradation is input. Effects as resistance coefficient, cross sectional height, wind shadowing, aerodynamic effective length etc.) can be considered by input of one factor per beam

At Rope Loads the rope force and a series of nodes, which the rope shall touch, have to be input. To model a pulley the rope force can be given a different factor between each two nodes. This calculation is suitable for 1

st order theory only, as the course of the rope is modelled by constant-

directed forces.

Basic load cases can be provided and combined with partial safety coefficients (factors). These Combination Load Cases can be combined with other combination- and basic load cases again. The number of combination levels is not limited.

This kind of load case corresponds to the current standardization (CEN, ISO) as well as DIN 15018, part 3, which intends the working with partial safety coefficients according to the method of limit states.


In many cases, especially such where many acceleration loads are involved (as often used in material handling), it is not always possible to tell in advance, which combination of loads leads to the biggest stresses in one certain point. That is why logic load cases can be defined.

The following parameters describe a logic load case:

Of the load cases in the logical combination acts "Exactly One", "One or None", "All" or "All Possible Combinations".

Each load case can be given a factor

Each load case can possibly be defined to act in positive or negative direction.

The level of logic load cases is not restricted.

Structures can be calculated according to theory 2nd

order. The equilibrium is formulated in a deformed condition, so that in the differential equation for bending,

the term is considered.

The torsion is considered according to St. Venant theory. Single beam matrices are assembled geometrically linear (Williot plan of displacement). The solution of the equation system is made by iteration of normal forces.

Buckling loads can be determined by iterative increase of the loads. The condition is, that the denominator determination becomes zero.

The program STAB88/NODYA [OPTION] allows the Geometrical Nonlinear Calculation of beam structures.

Using this type of load case, individual loads can be gradually applied according to a time function. After each load step the equilibrium between inner and outer forces is improved by an equilibrium iteration. Basic- and combination load cases can be multiplied by factors, provided with according time functions and combined to a geometrical nonlinear load case.

Geometrically nonlinear load cases can be comprised to a Nonlinear Logic Load Case. Then they are connected with „or“.


8.8 Results

Solver input files can be created for different kinds of calculation. Calculations according to theory 1st or 2nd order or nonlinear calculations respectively are possible. The input can be made for the calculation programs PAS III and STAB88 [OPTION]. Different positions of the systems can be considered.

Proofs and Results are treated in a similar way by KRASTA. In both cases the load cases to evaluate, the type of evaluation, extremation and output have to be described.

In contrast to a result a proof considers permissible strain values, depending on certain standards to calculate utilizations.

The following categories of results of calculations can be output

inner forces

stresses

delta stresses (stress ranges)

beam displacements

node displacements

spring forces

support forces.

8.9 Sign definition of inner forces and stresses

Inner forces and beam deformations are output in the local principal axis system.

Section banks are set according to the convention that at the end of beam positive inner forces show into positive coordinate direction (positive section bank).

At the start of beam positive inner forces show into negative coordinate direction (negative section bank).

Stresses as a result of normal force, bending, torsion and shearing force can be output individually each or in combination.

In addition the combined stress can be output according to the theory of v. Mises (GEH), the shear stress hypothesis (SH) or the Normal stress hypothesis (NH).

KRASTA 9.6 Manual Index 235

9 Index

$

$uncertain, Situation ..................................... 128

2

2nd

Order Theory ............................................. 80

A

Acceleration .................................................... 77 Acceleration Loads ......................................... 77 Adaption of a Palette ..................................... 222 Alternating connections ................................. 126 altitude range .................................................. 78 Angle of three Points ..................................... 121 Angle to Axis ................................................. 120 Archive / Dearchive ......................................... 25 Area Moments of Intertia ................................. 52 AS 4100 ........................................................ 199 AS 4100, Implementation in KRASTA .......... 200 AS 4100, Method of Proof ............................. 199 Assistant: Equality ........................................... 98 Assistant: Friction Element ........................... 100 Assistant: Hydraulics ....................................... 99 Assistant: Rope Polygon ............................... 100 Assistant: Slotted Hole .................................. 101 AutoBack.zip ................................................... 26 auxiliary beams ............................................... 52 Auxiliary Vector ................................. 39, 43, 111

B

Balance / Total ................................................ 18 Basic Load Case (BLC)

Acceleration .................................................. 77 Beam Load ................................................... 76 Beam Predeformation .................................. 76 Node Load .................................................... 76 Rope Load .................................................... 78 Temperature Load ........................................ 79 Wind Load .................................................... 78

Basic Mass Case (BMC) ................................. 71 $Permanent Mass ........................................ 73 Beam Mass ................................................... 73 Mass Factor .................................................. 73 Node Mass ................................................... 74

Basic system without constraint condition ...... 96 Beam

Coordinate System ................................. 39, 43 Copy ....................................................... 48, 49 Displacement ................................................ 44 Joints ............................................................ 42 Load .............................................................. 76 Mass ....................................................... 43, 71 Mass Factor .................................................. 43 Mirror ............................................................ 49

Move ............................................................. 48 on top of each other ...................................... 49 Predeformation ............................................. 76 Reverse ........................................................ 48 Split ......................................................... 47, 49 Spring ........................................................... 42

Beam (chain) can rotate ................................ 152 Beam Buckling Data ........................................ 44 beam length..................................................... 44 Beam list .......................................................... 69 Beam Loads and Beam Predeformation ......... 76 Beam Mass ..................................................... 73 Beam Mass Factors ........................................ 43 Beam Masses.................................................. 43 Beam or Node Lists

Drag'n'Drop ................................................... 17 Beam or Node Lists creation ........................... 69 Beam or Node Lists editing ............................. 69 Beam Springs .................................................. 42 Bending Moment of Resistance ...................... 56 Bending Stresses ............................................ 57 BLC 75 Border Lines .................................................. 217 Bredt Formula............................................ 55, 56 Brief Information ............................................ 225 Buckling ................................................... 44, 209

C

Calculation formulas ........................................ 55 Calculation Suite ........................................... 133

Default ........................................................ 134 Methods ...................................................... 133

Center of Gravity ............................................. 55 center of rotation ............................................. 19 Center of Shear Forces ................................... 55 Circular Tube ................................................... 65 Classification ............................................. 51, 67

Material ......................................................... 67 Classifications ............................................... 159 Clean Up

Cross Sections.............................................. 66 Lists .............................................................. 70 Materials ....................................................... 67

Color Gradation ..................................... 217, 222 Colors .............................................................. 31 Combination Mass Case (CMC) ..................... 74 Comment ......................................................... 20 Comparison between force condition and

general constraint condition .............. 93, 94 Compensation loads ....................................... 91 Composition list ............................................... 70 Connection .................................... 105, 107, 112

Alternation ................................................... 126 Display ........................................................ 112

Consideration of constraint conditions ............ 92 Constraint Conditions

Assistant Equality ...................................................... 98 Friction Element ....................................... 100

236 Index KRASTA 9.6 Manual

Hydraulics .................................................. 99 Rope Polygon ........................................... 100 Slotted Hole .............................................. 101

Buffer .......................................................... 101 compatibility ................................................ 102 Consideration ................................................ 92 Error bounds for .......................................... 102 Example

Friction Element ......................................... 94 Overload Clutch ......................................... 93 Tension element, Rope .............................. 93

General ......................................................... 91 Contact .......................................... 105, 107, 113

Auxiliary Vector ........................................... 111 Error Messages .......................................... 113 Examples .................................................... 111

Contact and Angles ............................... 108, 119 Contact with one auxiliary vector: ................. 111 Contact with two auxiliary vectors: ................ 111 Contact without auxiliary vectors: .................. 111 context menu ................................................. 217 Coordinate Difference ................................... 121 Coordinate System

Beam............................................................. 39 Inertial ........................................................... 39 Subsystem .................................................... 39

Copy ................................................................ 48 Copy an Object ................................................ 21 Copy Subsystems ......................................... 103 Create an Object ............................................. 20 Creation of load event objects according

relevant load events .............................. 217 Cross Section

Conical ........................................................ 155 Direct Input ................................................... 52 Parametric .................................................... 55 Rigid .............................................................. 52 Standard ....................................................... 66 Thin-Walled ................................................... 54

Cross sectional area .................................. 52, 55 Cross Sections ................................................ 43

Clean Up ....................................................... 66 Drag'n'Drop ................................................... 17 Import ............................................................ 66 Plot ................................................................ 66

C-Section ......................................................... 60 Current Selection

Changing by beam or node prop. ................. 28 Changing graphical interactive ..................... 27

current subsystem ......................................... 105 Cut Subsystems ............................................ 103 Cycle Classes ................................................ 195

D

Damage Accumulation .................................. 185 Damage equivalence factor .......................... 185 DASt-Ri 011 .................................................. 197 dead weight ..................................................... 43 Default Wind Pressure .................................... 78

Delete an Object .............................................. 21 Delete Subsystems ........................................ 103 Delta Stresses ............................................... 213 Design Spectrum ............................................. 89 Details ............................................................ 216 Diagram: Linear damage accumulation acc.

Palmgren-Miner ..................................... 162 Dialog: Acceleration Load ............................... 77 Dialog: Basic Load Case ................................. 75 Dialog: Basic Mass Case................................. 72 Dialog: Basic Orientation ............................... 116 Dialog: Beam Buckling Data ............................ 44 Dialog: Beam Mass ......................................... 73 Dialog: Captions .............................................. 31 Dialog: Classification of Points for proof of

stresses according to DIN 13001-3 ....... 181 Dialog: Classification of Points for Proof of

Stresses according to EN 1993-1-9 (EC 3) ............................................................... 190

Dialog: Classification of Points of Proof of Stresses acc. AS 4100 .......................... 203

Dialog: Colors .................................................. 31 Dialog: Combination Load Case ...................... 80 Dialog: Combination Mass Case ..................... 74 Dialog: Connection ........................................ 112 Dialog: Constraint Conditions .......................... 92 Dialog: Contact .............................................. 113 Dialog: Cross Section - Direct Input ................ 52 Dialog: Design Spectrum ................................. 89 Dialog: Details ............................................... 220 Dialog: Displacement Conditions .................... 45 Dialog: Extremation of delta stresses ............ 213 Dialog: Filter .................................................. 216 Dialog: For Proofs and Results ..................... 215 Dialog: Force Conditions ................................. 93 Dialog: General Constraint Condition ........ 93, 94 Dialog: Kinematic ........................................... 120 Dialog: Languages ........................................... 35 Dialog: List ....................................................... 69 Dialog: Load Event .......................................... 85 Dialog: Load Sequence ................................... 87 Dialog: Logic Load Case ................................. 81 Dialog: Mass Factor ......................................... 73 Dialog: Material ................................................ 67 Dialog: Name Assignment ............................... 41 Dialog: Node Mass .......................................... 74 Dialog: Orbit-Settings ...................................... 19 Dialog: Orientation Modification .................... 117 Dialog: Output Format ................................... 221 Dialog: Page Layout ........................................ 34 Dialog: Palettes ............................................. 222 Dialog: Parameters of Kinematic ................... 122 Dialog: Printing ................................................ 33 Dialog: Proof of Fatigue acc. AS 4100 .......... 203 Dialog: Proof of Fatigue according to DIN

13001-3 .................................................. 174 Dialog: Proof of Fatigue according to EN 13001-

3-1 .......................................................... 180 Dialog: Proof of Fatigue according to EN 1993-

1-9 (EC 3) .............................................. 190


Dialog: Proof of Stresses Buckling DIN 4114 (Omega-Method) ................................... 209

Dialog: Purge System ..................................... 25 Dialog: Put KRASTA System into archives ..... 26 Dialog: Relative Orientation .......................... 117 Dialog: Reverse Beam .................................... 48 Dialog: Rope Load .......................................... 78 Dialog: Rounding............................................. 49 Dialog: Situation Dependent Load or Mass Case

................................................................ 83 Dialog: Solver Options Modal Analysis" ........ 135 Dialog: Solver Options NODYA" ................... 135 Dialog: Split Beams ......................................... 47 Dialog: Structural Input of thin-walled Cross

Sections ................................................... 54 Dialog: Subsystem Import ............................. 104 Dialog: Temperature ....................................... 79 Dialog: Text and Graphic Sizes ...................... 32 Dialog: Units .................................................... 35 Dialog: Wind .................................................... 78 Dialog: Windprofile .......................................... 78 Dimetrie ........................................................... 29 DIN 13001 ............................................. 169, 175 DIN 13001-3

Permissible stress ranges .................. 169, 175 Types of proof..................................... 171, 177

DIN 15018 Proof of Fatigue .......................................... 165

DIN 18800 Materials ..................................................... 207 Proof of Stresses el.-el. .............................. 207 Thickness ................................................... 207

DIN 22261 Proof of Fatigue .......................................... 167

DIN 4114 ....................................................... 209 DIN 4114 Buckling (Omega-Method),

Implementation in KRASTA .................. 209 DIN CEN/TS 13001-3-1:2005, Implementation in

KRASTA ................................................ 171 DIN CEN/TS 13001-3-1:2005, Method of Proof

.............................................................. 169 Direct Input Cross Section .............................. 52 Displacement Conditions .......................... 45, 91 Display Everything .......................................... 29 Display of Connections ................................. 112 Display of physical units .................................. 23 Display Settings .................................. 29, 32, 92

Drag'n'Drop ................................................... 17 Display Subset ................................................ 29 Distance and Angle ....................................... 119 Drag'n'Drop

Beam or Node Lists ...................................... 17 Cross Sections ............................................. 17 Display Setting.............................................. 17 Load Case .................................................... 17 Mass Case .................................................... 17 Material ......................................................... 17 Orientation .................................................. 117 Projection Setting ......................................... 17 Situation ................................................ 85, 127

E

EC 3 .............................................................. 185 Edit an Object .................................................. 20 Eigen Vectors ................................................ 155 Element Thickness: DIN 18800..................... 207 EN 13001 ...................................................... 175 EN 1993 (EC 3) ............................................. 185 EN 1993-1-3 (EC 3)

Types of proof ............................................. 187 EN 1993-1-9:2005, Implementation in KRASTA

............................................................... 187 EN 1993-1-9:2005, Method of Proof ............. 185 Error messages (Kinematic), during the

execution of a polar kinematic ............... 123 Error messages (Kinematic), during the input

............................................................... 123 Error messages (Kinematic), while saving the

object ..................................................... 123 Evaluation Pattern ......................................... 217 Example: Acceleration by drives ..................... 82 Example: Adopt existing evaluation pattern

(automatically) ....................................... 219 Example: Constraint Conditions ...................... 92 Example: Contacts ........................................ 111 Example: Copy an Object ............................... 21 Example: Edit an Object .................................. 20 Example: Error/Warning Nr. 451, #1 ............. 148 Example: Error/Warning Nr. 451, #2 ............. 149 Example: Evaluation Pattern ......................... 218 Example: Expanded Combination Load Case 80 Example: Input of Aux.-Vectors (H): ............. 227 Example: Load Sequence "cycle 15t A<>D" ... 88 Example: Load Sequence "PS 15t D->A" ....... 88 Example: Logic Load Case ............................. 82 Example: Permanent Mass ............................. 71 Example: Rotational Acceleration Load .......... 77 Example: Situation Dependent Load or Mass

Case ........................................................ 83 Example: Subsystem Structure ..................... 109 Example: Sum of Masses ............................... 74 Example: Suspension between tower and boom

............................................................... 106 Example: Textual Output in case of Damage

Accumulation ......................................... 163 Example: Use of rigid cross sections .............. 53 Execute

Calculation Suite ......................................... 133 Load Event.................................................... 85 Orientation .................................................. 117

Expand Subset ................................................ 29 Extreme Values ............................................. 215

F

FEM 1.001 ..................................................... 193 Filter list ........................................................... 70 First level subsystems ................................... 109 Folder .............................................................. 17 Force Conditions ....................................... 42, 91 Format ........................................................... 221


Friction Element ...................................... 94, 100

G

General Constraint Conditions ........................ 91 General information ....................................... 120 Geometrical Specifications .............................. 48 Graphical Output ............................................. 25 Graphical Selection ......................................... 23 Gravity ............................................................. 77 Gravity Load .................................................... 77

H

Height ranges .................................................. 78 Helpful display setting to view subsystem

organization ........................................... 107 Hide Subset ..................................................... 29 Hotkeys............................................................ 20 Hotline ............................................................. 10 H-Section ......................................................... 59 Hydraulics with constant hydraulics volume.... 97

I

Import an Object ........................................ 21, 66 In- and Output Language ................................ 13 In- and Output Units: ....................................... 13 Inertial Coordinate System .............................. 39 Information ...................................................... 20 Information Window ................................... 15, 18 Inner Forces .................................................... 44 Input of numerical values ................................ 23 Input of points and vectors .............................. 23 Insert new objects into lists ............................. 49 Interaction of multiple kinematics .................. 119 ISO 5049-1 .................................................... 195 Items of the Status Line................................... 18

J

Joints ............................................................... 42

K

Kinematic movability vs. static flexibility ........ 119 Kinematic plane ............................................. 119 Kinematically free connections ...................... 121 KRASTA Main Window ................................... 15 KRASTA Main Window/ .................................... 9 KRASTA Objects ............................................. 20 KRASTA Start Window ...................................... 8

L

Language .................................................. 13, 35 Layout ............................................................ 221 Leading kinematic part .................................. 121 Left Mouse Button ........................................... 27 Lifetime ............................................................ 89 Linear Beam Predeformation .......................... 79

Linear damage accumulation according to Palmgren-Miner ..................................... 162

List 69 Clean Up ....................................................... 70 composition list ............................................. 70 filter list .......................................................... 70 proof list ........................................................ 69 result list ........................................................ 69 simple beam list ............................................ 69 simple node list ............................................. 69 simple object list ............................................ 69

Lists of Objects ................................................ 21 Lists of Situations .......................................... 217 Literature: 2nd Order Theory ......................... 137 Literature: Damage Accumulation ................. 163 Literature: DIN 4114 Buckling (Omega-Method)

............................................................... 210 Literature: DIN CEN/TS 13001-3-1:2005-03 . 174 Literature: EN 1993-1-9:2005 ........................ 192 Literature: prEN 13001-3-1:2009 ................... 180 Load

Rope.............................................................. 78 Temperature ................................................. 79

Load Case Basic ............................................................. 75 Combination .................................................. 80 Drag'n'Drop ................................................... 17 Logic.............................................................. 81 Nonlinear ....................................................... 81 Nonlinear Logic ............................................. 82 Situation Dependent ..................................... 80

load event ................................................ 85, 220 governing / relevant .................................... 217

Load Event Object ................................... 85, 217 Methods ........................................................ 85

Load Sequence ............................................... 87 Loading Groups: DASt-Ri 011 ....................... 198 Loading Groups: DIN 13001-3 (S-Classes)... 183 Loading Groups: DIN 15018 .......................... 166 Loading Groups: EN 1993-1-9 (EC 3) (S-

Classes) ................................................. 192 Loading Groups: FEM 1.001 ......................... 194 Loading Groups: ISO 5049 ............................ 196 Logic Load Case ............................................ 217 Logic Load Case (LLC).................................... 81 L-Section ......................................................... 61

M

Main Menu ....................................................... 15 Main Window ................................................... 15 Manager .................................................... 13, 35 Mase Case

Sum of ........................................................... 74 Mass

Permanent .................................................... 71 Sum of ........................................................... 74

Mass Case ............................................... 71, 155 Basic ............................................................. 71 Combination .................................................. 74


Drag'n'Drop ................................................... 17 Permanent .................................................... 73 Situation Dependent ..................................... 74

Mass Factor .............................................. 71, 73 Mass of Beam ................................................. 43 Mass of Node .................................................. 45 Masses, Sum of .............................................. 74 Material ..................................................... 43, 67

Classification ................................................ 67 Clean Up ....................................................... 67 Drag'n'Drop ................................................... 17

Materials: DASt-Ri 011 ................................. 198 Materials: DIN 15018 .................................... 166 Materials: DIN 18800 .................................... 207 Materials: FEM 1.001 .................................... 194 Materials: ISO 5049 ...................................... 196 Melt a Subsystem.......................................... 106 Menu item

Calculation Calculate solver input file ......................... 143 Show Log-File .......................................... 145 Situation indipendet calculation ............... 139

File ................................................................ 25 Help .............................................................. 10 Info ................................................................ 10 List ................................................................ 69 Option ........................................................... 35 Property ........................................................ 41 Selection ................................................. 17, 27 Sum of Masses ............................................. 74 View ................................................ 29, 31, 155

Merging ........................................................... 49 Methods of Load Events ................................. 85 Minimal ............................................................ 29 Minimal Text Only ........................................... 22 Mirroring .......................................................... 49 MOD .............................................................. 133 MOD (modal analysis) .................................. 133 Modal Analysis .............................................. 133 Modelling of actuators ................................... 119 Modelling with kinematics ............................. 119 Modified angles within the subsystem .......... 126 Moments of Inertia .................................. 56, 229 Moments of Inertia about the Principal Axes: . 56 Moments of Resistance ................................ 230 Mouse

Left Button ............................................ 27, 105 Right Button .................................................. 18

Move ............................................................... 48 Multiple Object Selection ................................ 22

N

Name ............................................................... 20 Natural Frequencies ...................................... 155 net length ........................................................ 44 New Object ...................................................... 20 Node

Copy ....................................................... 48, 49 Free ............................................................ 126

Joint .............................................................. 45 Load .............................................................. 76 Mass ....................................................... 45, 71 Merging ......................................................... 49 Mirror ............................................................ 49 Move ............................................................. 48 on top of each other ...................................... 49 Spring ........................................................... 45

Node can rotate ............................................. 152 Node Coordinate ........................................... 120 Node list .......................................................... 69 Node Loads ..................................................... 76 Node Mass ...................................................... 74 Node Masses .................................................. 45 NODYA .......................................................... 133 NODYA / STAB88 [OPTION] .......................... 91 Nonlinear Load Case ...................................... 81 Nonlinear Logic Load Case ............................. 82 Normal Stress Ranges .................................. 213 Normal Stresses as a result of Normal Force . 56 Notch case: DIN 22261 ................................. 167 Notch cases................................................... 185 Notch Cases: AS 4100 .................................. 205 Notch Cases: DASt-Ri 011 ............................ 198 Notch Cases: DIN 13001-3 ........................... 183 Notch Cases: DIN 15018 ...................... 165, 166 Notch Cases: EN 1993-1-9 (EC 3) ................ 192 Notch Cases: FEM 1.001 .............................. 194 Notch Cases: ISO 5049 ................................ 196 Notes on using rigid cross sections ................ 52

O

Object .............................................................. 20 Comment ...................................................... 20 Copy ............................................................. 21 Delete ........................................................... 21 Edit ................................................................ 20 Import ............................................................ 21 Information .................................................... 20 Multiple Selection ......................................... 22 Name ............................................................ 20 New ............................................................... 20 Single Selection ............................................ 21

Object list ......................................................... 69 Object Lists ...................................................... 21 Object Tree ................................................ 15, 17 OK and Cancel ................................................ 22 Omega-Method ............................................. 209 Operating method ......................................... 185 optimised coupling .................................... 96, 98 Options (Kinematic) ....................................... 122 Orbit - Activations ............................................ 19 Orbit - Center of Rotation ................................ 19 Orbit-Settings .................................................. 19 Orientation ..................................................... 107

by Contact ................................................... 107 by Contact and Angles ............................... 108 by Vector and Angles ......................... 105, 107 Drag'n'Drop ................................................. 117


Execute ....................................................... 117 Modification ................................................. 116 Modification Sequence ............................... 117 Modified Subsystem Angles ....................... 126

Orientation Modification................................. 116 Other kinematic parts .................................... 121 Output

Border Lines ............................................... 217 Color Gradation .................................. 217, 222 Layout ......................................................... 221 Palettes ....................................................... 222 Plots .............................................................. 25 Text ....................................................... 25, 221

Output Format ............................................... 221 Output Formats: AS 4100.............................. 204 Output Formats: Delta Stresses .................... 214 Output Formats: DIN 4114 Buckling (Omega-

Method) ................................................. 210 Output Formats: DIN13001-3 ........................ 182 Output Formats: EN 1993-1-9 (EC 3) ........... 191 Overload Clutch ............................................... 93

P

Page Layout .............................................. 22, 34 Page Partitioning ............................................. 34 Palettes.......................................................... 222 Parabolic Beam Predeformation ..................... 79 Parametric Cross Section................................ 55 Partial Rigid Cross Sections .................... 52, 155 Partial Summation ........................................... 18 PAS

Error/Warning Nr. 299 ................................. 147 Error/Warning Nr. 451 ................................. 147 Error/Warning Nr. 453 ................................. 150 Error/Warning Nr. 455 ................................. 152 Partial rigid cross section ................................ 3 Theoretical foundation .................................... 3

PAS III ........................................................... 133 PAS IV ........................................................... 133 PAS linear ..................................................... 134 Paste Subsystems ......................................... 103 Permanent Mass ............................... 71, 73, 155 Permutation ................................................... 217 Picture ............................................................. 22 Plane and Reference System ....................... 120 Plastic Moment of Resistance ................. 57, 230 Plots ................................................................. 25

Details ........................................................... 22 Minimal Text ................................................. 22 Print ............................................................... 22 Save .............................................................. 22

Point for Proof of Stresses ...................... 51, 165 Position, oboslete idiom ................................ 139 Predeformation

Linear ............................................................ 79 Parabolic ....................................................... 79

prEN 13001-3-1:2009, Implementation in KRASTA ................................................ 177

prEN 13001-3-1:2009, Method of Proof ........ 175

Pressure .......................................................... 78 Preview: Text Output Layout ......................... 221 Principal Axes .................................................. 40 Principal Axis Angle: ........................................ 56 Printer Settings ................................................ 32 Projected Coordinate Difference ................... 121 Projection Settings ........................................... 29

Drag'n'Drop ................................................... 17 Proof list ........................................................... 69 Proof of Fatigue

acc DIN 15018 ............................................ 165 acc. AS 4100 ............................................... 199 acc. DASt-Ri 011 ........................................ 197 acc. DIN 22261 ........................................... 167 acc. FEM 1.001 ........................................... 193 acc. ISO 5049-1 .......................................... 195 according to DIN 13001 ...................... 169, 175

Proof of Fatigue according to EN 1993 (EC 3) ............................................................... 185

Proof of Stresses Buckling acc DIN 4114 (Omega-Method) ... 209 el.-el. acc. DIN 18800 ................................. 207

Proof: AS 4100 .............................................. 202 Proof: DASt-Ri 011 ........................................ 197 Proof: DIN 15018 ........................................... 165 Proof: DIN 18800 el.el. .................................. 207 Proof: DIN 22261 ........................................... 167 Proof: DIN 4114 Buckling (Omega-Method) . 209 Proof: DIN CEN/TS 13001-3-1:2005 (damage

accumulation procedure) ....................... 173 Proof: DIN CEN/TS 13001-3-1:2005 (simplified

procedure) ............................................. 172 Proof: EN 1993-1-9:2005 (damage

accumulation procedure) ....................... 189 Proof: EN 1993-1-9:2005 (simplified procedure)

............................................................... 188 Proof: FEM 1.001 .......................................... 193 Proof: ISO 5049-1 .......................................... 195 Proof: prEN 13001-3-1:2009 (damage

accumulation procedure) ....................... 179 Proof: prEN 13001-3-1:2009 (simplified

procedure) ............................................. 178 Pulley Factor ............................................ 78, 100

R

Real Movability .............................................. 151 Rectangle Section ........................................... 63 Rectangular Tube ............................................ 62 Reeving ......................................................... 100 Register: General .......................................... 135 Register: Nonlinear Calculation ..................... 136 Resistance factor ........................................... 185 Result list ......................................................... 69 Result values of a damage accumulation...... 163 Results ........................................................... 211 Review ........................................................... 225 Right Mouse Button ......................................... 18 Rigid................................................................. 52 rope 52


Rope Loads ..................................................... 78 Rotating Objects............................................ 151 Rotational Acceleration Load .......................... 77 Round Section................................................. 64

S

safety factor for fatigue strength ................... 185 Scaling ............................................................ 49 S-Class .......................................................... 185 Scope .............................................................. 51 Screen after copying a subsystem ................ 105 Screen Settings ............................................... 32 Second level subsystems ............................. 110 Section

C 60 Circular Tube ................................................ 65 H 59 L 61 Rectangle ..................................................... 63 Rectangular Tube ......................................... 62 Round ........................................................... 64

Section Points ................................................. 44 Select Picture Details ...................................... 22 Selection ......................................................... 51

Graphical ...................................................... 23 Multiple Objects ............................................ 22 Single Object ................................................ 21

Sensitivity / Direction ....................................... 19 Sensor and actuator, case 1 ........................... 97 Sensor and actuator, case 2 ........................... 97 Sensor degrees of freedom ............................ 96 Shear Areas .............................................. 52, 55 Shear Force induced Shear Stresses ............. 57 Shear Stress Ranges .................................... 213 Simple beam list .............................................. 69 Simple model of a tower crane (total system)109 Simple node list ............................................... 69 Simple object list ............................................. 69 Single Object Selection ................................... 21 Situation ................................................ 127, 217

$uncertain ................................................... 128 create for orientations ................................. 129 Drag'n'Drop ........................................... 85, 127 Execute ....................................................... 127 Methods ...................................................... 127

SLC 80 Slenderness .................................... 44, 209, 228 Slotted Hole ................................................... 101 SMC ................................................................ 74 solver input file .............................................. 143 Spring .............................................................. 42 St. Venant torsion...................................... 59, 80 STAB88 ......................................................... 133 STAB88 / NODYA [OPTION] ............ 81, 91, 133 Standard Cross Section .................................. 66 Statical Moment ...................................... 55, 229 Status Line ................................................ 15, 18 Stress Differences ......................................... 213 Stress Range

Design Value .............................................. 185 Stresses ........................................................ 230 Stretching ........................................................ 49 Structural Thickness ........................................ 51 Substructure

Copy ............................................................. 48 Mirror ............................................................ 49 Move ............................................................. 48 Project ........................................................... 49 Scale ............................................................. 49 Stretch .......................................................... 49

Substructures of a kinematic ......................... 121 Subsystem ..................................................... 103

Cut, Copy, Paste ........................................ 103 Delete ......................................................... 103 Error Messages .......................................... 113 Hierarchy .................................................... 103 Import .......................................................... 103 Melting ........................................................ 106 Orientation .................................. 105, 107, 126 Splitting ....................................................... 106

Subsystem Coordinate System ....................... 39 Support ...................................................... 10, 45 Support Conditions (Joints/Springs) ............... 45 Switch: Best possible .................................... 121

T

Table 10 (DIN 22261) .................................... 168 Table 12 (DASt-Ri 011) ................................. 197 Table 17 (DIN 22261) .................................... 167 Table 18 (DIN 15018) .................................... 165 Table 19 (DIN 15018) .................................... 166 Table 20 (DIN 22261) .................................... 167 Target ............................................................ 120 Target Settings .............................................. 120 Temperature Loads ......................................... 79 Tension element, rope .................................... 93 Text 25

Print .............................................................. 22 Save .............................................................. 22

Text Output Layout ........................................ 221 Textual Documentation ................................. 223 Textual Output ......................................... 25, 216 Textual Output Format .................................. 216 TH2 \b .............................................................. 80 Thin-Walled Cross Section .............................. 54 Titlebar ............................................................ 15 Toolbar ............................................................ 15 Torsional Moment of Inertia .................... 55, 229 Torsional Moment of Resistance..................... 56 Torsional Shear Stresses ................................ 57 Total / Balance ................................................ 18 tower crane .................................................... 109 Translational Acceleration Load ...................... 77 Trimming picture ............................................. 22 Tube

Circular ......................................................... 65 Rectangular .................................................. 62

Types of Parametric Cross Sections ............... 58


U

uncertain, Situation ........................................ 128 undo/redo ........................................................ 25

redo/undo ...................................................... 25 Units .................................................... 13, 18, 35 User 13, 35 User Defined Folder in Object Tree ................ 17 Using force condition ....................................... 93 Using general constraint condition ............ 93, 94 Using List of Situations .................................. 217

V

Vector and Angles ................................. 105, 107

W

Welding seams ................................................ 51 Williot plan of displacement ............................. 80 Wind direction .................................................. 78 Wind Loads ..................................................... 78 Wind Profile ..................................................... 78 Wind resistance ............................................... 78 Window: Information ........................................ 18 Window: Object Tree ....................................... 17 Window: Working Area .................................... 16 Wizard: Beam as Subsystem ........................ 106 Working Area ................................. 15, 16, 18, 23

Krasta Manual English

Documents

Transcript of Krasta Manual English