Tii-Ai91 712 COMPUTER-AIOED STRUCTURAL ENGINEERING (CASE) PROJECT R 1/1CASE PROJECT STUDY V(U) AUMY ENGINEER WATERMAYS

EXPERIMENT STATION VICKSBRG MS NFOR D RAISANEN

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This program is furnished by the Government and is accepted and used bythe recipient with the express understanding that the United StatesGovernment makes no warranties, expressed or implied, concerning theaccuracy, completeness, reliability, usability, or suitability for any par-ticular purpose of the information and data contained in this program orfurnished in connection therewith, and the United States shall be under noliability whatsoever to any person by reason of any use made thereof. Theprogram belongs to the Government. Therefore, the recipient further

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I REPORT NUMBER 12. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER

Technical Report ITL-87-2 A 6 / ; -..-4. TITLE (aned Subtitle) S. TYPE OF REPORT S PERIOD CO.ERED

A CASE PROJECT STUDY OF FINITE ELEMENT ANALYSIS Final reportOF CONCRETE FLAT SLABS Final____report______6. PERFORMING ORG. REPORT NUMBER

7. AUTHOR() 8. CONTRACT OR GRANT NuMBER,'

David Raisanen and the CASE Task Group onFinite Element Analysis

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT PROJECT, TASKAREA & WORK UNIT NUMBERS

%I. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

DEPARTMENT OF THE ARMY January 1987US Army Corps of Engineers 13, NUMBER OF PAGESWashington, DC 20314-1000 _5614. MONITORING AGENCY NAME & AODRESSi'll dlfferent from Controlling Offico) IS. SECURITY CLASS. (01 this report

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-N printed on the inside of the back cover.. KEY WORDS (Continue on reveree side if necooasv aid identify by block number)

Computer-aided designConcrete slabsFlooring, ConcreteFinite element method\CTSTRUDL (Computer program)I\ 0rT ACT (C motwe am v eres t I t noswmeaV md ident fy by block number)

\ This is a study aimed at providing guidance for the use of finiteelement analysis programs. As part of the Computer-Aided Structural Engineer-ing (CASE) Committee study, it focuses on techniques for concrete flat slabs.

With a purpose of developing criteria for finite element analysis of flat slab

floors, this report has two objectives. To compare methods for the most ac-

ceptable yield and to apply these guidelines to the active design problem'./(Continued)

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20. ABSTRACT (Continued)

requires that this report include element selection, initial assumptions, com-parisons of verification study, results, discussion of results, conclusions,and recommendations using the finite element methods. A powerhouse erectionbay floor slab was selected for the problem solutions, with the GTSTRUDL pro-

gram's "IPBQQ" element the only one suited to this problem.(r III

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af 1 -j "Q

PREFACE

This report is aimed at providing guidance for the use of the finite

element method of analysis for the design/analysis of concrete floor slabs.

The work was sponsored under funds provided to the US Army Engineer Waterways

Experiment Station (WES) by the Civil Works Directorate, Office, Chief of En-

gineers (OCE), US Army, as part of the Computer-Aided Structural Engineering

(CASE) Project.

Input for the report was obtained from the CASE Task Group on the Finite

Element Analysis. Members and others who directly contributed to the report

were:

David Raisanen, North Pacific Division (Chairman)

Rich Flauaus, St. Louis District

Dick Huff, Kansas City District

Paul LaHoud, Huntsville Division

Jerry Foster, Federal Energy & Regulatory Commission

Ed Alling, USDA - Soil Conservation Service

Paul Weirsma, Seattle District

Lucian Guthrie, OCE

N. Radhakrishnan, WES

Robert Hall, WES

H. Wayne Jones, WES

Kenneth Wills, Georgia Institute of Technology

The report was compiled and written by Mr. David Raisanen. Dr. Radha-

krishnan, Chief, Information Technology Laboratory (ITL), WES, and CASE Proj-

ect Manager, along with Dr. Robert Hall, Research Civil Engineer, ITL, WES,

and H. Wayne Jones, Civil Engineer, ITL, WES, monitored the work. This report

was edited by Ms. Gilda Shurden, Information Products Division, ITL, WES, with

Ms. Frances Williams coordinating text and figure layout. Mr. Lucian Guthrie,

Structures Branch, Civil Works Directorate, was the OCE point of contact.

COL Allen F. Grum, USA, was the previous Director of WES. Col Dwayne G.

Lee, CE, is the present Commander and Director. Dr. Robert W. Whalin is

Technical Director.

1111111 1111 i I ~ e -0 1 In N 1

CONTENTS

Page

PREFACE ............................................................... 1

CONVERSION FACTORS, NON-SI TO SI (METRIC) UNITS OF MEASUREMENT ............. 3PART I: INTRODUCTION .................................................. 4

Background ......................................................... 14Purpose ............................................................ 14Objectives ......................................................... 7Scope .............................................................. 7

PART II: ELEMENT SELECTION .............................................. 8

Criteria ........................................................... 8Problem Idealization ................................................ 8

PART III: MODELING TECHNIQUES ........................................... 11

E3SAP Model...................................................... 1GTSTRUDL Model ..................................................... 11Validity of Mesh ................................................... 13

PART IV: FINITE ELEMENT ANALYSIS RESULTS ................................ 16

PART V: INTERPRETATION OF RESULTS ..................................... 43

Comparison Indications ............................................. 143Slab Analysis......................................................143Slab Analysis with Elastic Spring Supports .......................... 144

PART VI: CONCLUSIONS AND RECOMMENDATIONS ............................... 45

Conclusions........................................................145Recommendations....................................................145

APPENDIX A: GTSTRUDL INPUT FILES ........................................ Al

APPENDIX B: THEORETICAL RESULTS FOR THE SIMPLY SUPPORTED PLATE ........... B1

2

CONVERSION FACTORS, NON-SI TO SI (METRIC) UNITS OF MEASUREMENT

Non-SI units of measurement used in this report can be converted to SI (met-

ric) units as follows:

Multiply By To Obtain

feet 0.3048 metres

inches 2.54 centimetres

kip-feet 1355.818 newton-metres

kips (force) per square foot 47.88026 kilopascals

kip-inches 112.9848 newton-metres

pounds (force) per square foot 47.88026 pascals

pounds (force) per square inch 6.894757 kilopascals

3

A CASE PROJECT STUDY OF FINITE ELEMENT

ANALYSIS OF CONCRETE FLAT SLABS

PART I: INTRODUCTION

Background

1. This study has been prepared as part of the Computer-Aided Struc-

tural Engineering (CASE) Project study of finite element analysis techniques

for concrete flat slabs. It is part of a Corps-wide program to provide guid-

ance for the use of finite element analysis programs.

2. Information contained in this report is based on results from a

study developed in 1983 by the CASE Finite Element Methods (FEM) Task Group.

Flat slabs with large openings present a common design problem for the Corps,

and standard analysis procedures do not adequately cover the effects of these

openings. This study also investigated the effects of including the

contribution of shear to the transverse deflections of the slab by including

an eiement which could adequately capture this behavior. The problem selected

for study is a concrete floor slab in a powerhouse erection bay and the above

problem areas are included in the investigation along with corresponding

illustrations. Plan and elevation views are shown in Figures la and lb. The

slab has overall dimensions of 123 by 76 ft* and is 2 ft 9 in. thick. It is

made of 3,000 psi concrete and is reinforced with 40 grade Rebars in both

faces. There are two large hatchway openings which measure 27 by 20 ft. The

floor is supported by walls on three sides and by three rows of interior

columns on approximately 20-ft spacings. The main design load is a 1,-psf

uniformly distributed load.

Purpose

3. The purpose of the study reported herein is to develop finite

element analysis criteria for flat slab floors in situations in which ordinary

design methods will not suffice. These criteria will address modeling meth-

ods, deflections, and stresses.

* A table of factors for converting non-SI units of measurement to SI (met-

r to) inits is presented on page 3.

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Objectives

4. This study has two objectives. The first objective is to compare

FEM models with closed-form or other analytical methods to ensure that

modeling techniques, mesh criteria, and element types will yield acceptable

results for design. These results will then be used to develop guidelines for

future analyses. The second objective is to analyze the above slab and to

show how these guidelines are usd in an actual analysis.

Scope

5. The scope of this study is to analyze deflections and stresses

caused by the slab's dead load and a uniform live loading of 1,000 psf due to

generator and turbine parts. Neither temperature and curing stresses nor

interaction of the slab with the remainder of the structure will be

analyzed. The following will be presented:

a. Element selection.

b. Initial assumptions.

c. Comparisons of verification study with closed-form analysis.

d. Results from FEM analysis of the slab problem.

e. Discussion of FEM results of the slab problem.

f. Conclusions and recommendations on analysis of flat slabs usingFEM.

7A

5.

PART II: ELEMENT SELECTION

Criteria

6. Based on the requirements for a slab analysis, the fcllowing factors

were considered in element selection:

a. It must be able to accommodate concentrated and uniform loading.

b. Output shall be displacements and stresses at nodal points.

c. Shearing deflection contributions shall be taken into accountsince the span/depth ratio of the slab is less than 10.

d. In-plane stresses will not be considered.

On the basis of the above criteria, the GTSTRUDL program has an element suited

to the problem. The "IPBQQ" element will allow for shear deflection and

bending deflection.

Problem Idealization

Verification study problems

7. Two finite element programs and two different elements were chosen

for the verification study. The membrane element from E3SAP was used to model

plate-bending action without the shear deformation capability. The GTSTRUDL

TPBQQ element was used to study the same problems, but including the effects

of shear deformation. This verification study consisted of two problems. The

>irst being a 20 by 20-ft slab (Figure 2a), simply supported along all edges

"nd subjected to a uniform loading. This problem was analyzed by the use of

four meshes: the first has 1 element, the second, 4, the third, 16, and the

fourth, 64, each succeeding mesh being the result of dividing each element in

the previous mesh into 4 equal elements (Figures 2b, 2c, 2d, and 2e). Only

one fourth of the plate was modeled, allowing for symmetry. The second prob-

lem used the same meshes and loading, but was representative of an interior

Panel of a continuous slab supported at each corner by a column. The boundary

conditions were modified to reflect this support condition.

Powerhouse slab study

8. The slab was modeled for both the E3SAP and the GTSTRUDL analyses,

.Fith 16 elements per panel, as suggested by the verification study. The only

!ifoference in the these analyses was that the IPBQQ element of GTSTHUDL al-

.ows for shear deflections. Mesh refinement around reentrant corners was not

'.n -he general model since an actual design would isolate these areas

8S.

with a smaller model for separate analyses. The slab was assumed fixed at all

edges which were framing into walls. Supporting columns were modeled as "pin"

supports. Figure 3 illustrates the three lines where results from the analy-

sis were interpreted. Y

20 FT

a. Complete slab problem--only the shaded portion tobe modeled by finite

elements

DI X-

b. Quarter model mesh-- c. Quarter model mesh--1 element 4 elements

---- =- - - . -

d. Quarter model mesh-- e. Quarter model mesh--

16 elements 64 elements

Figure 2. Meshes for slab verification study

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PART III: MODELING TECHNIQUES

E3SAP Model

9. The verification study showed that acceptable results would beobtained with a mesh of 16 elements in each slab panel. This pattern was used

in forming the meshes for the powerhouse slab. The slab was analyzed using

the mesh shown in Figures 4a-4Ic. The TYPE 6 membrane element was used. This

element requires four nodes per element. Element thickness is an input

item. The boundary of the slab at wall intersections was modeled as a fixed-

edge condition with all deflections and rotations set to zero. The nodes at

interior columns and walls were allowed to rotate with the deflection still

set to zero. Loading was set at 1,000 psf live load due to stacking of

generator and turbine parts plus the slab dead load. Loading on the ha.ch

covers was transferred as concentrated loads at the nodal points on the

periphery of the hatch opening. Material properties were set at values

corresponding to a concrete with fl , ultimate concrete strength, equal to

3,000 psi at 28 days.

GTSTRUDL Model

10. The slab was analyzed using the mesh shown in Figures 5a and 5b.

It uses the IPBQQ element which requires eight nodes per element, four corner

nodes plus four intermediate nodes along the sides. Element thickness is an

input item. The verification study showed that this mesh would produce

acceptable results. The problem was analyzed with two different sets of

boundary conditions. For the first analysis, the boundary of the slab at the

wall intersection was modeled as fixed with both rotations and deflections set

to zero. Columns were handled the same as for the E3SAp model described

above. The second analysis modeled the walls and columns as springs with

axial and moment stiffness coefficients. These coefficients were calculated

from frame analysis runs made for a 1-ft strip of wall, representative of the

wall configuration at the node in question. This run was made to provide a

more accurate representation of the slab boundaries than could be provided by

using the simplified pinned or fixed assumptions of the first analysis. The

GTSTRUDL input files for both runs are shown in Appendix A.

11

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Figure 4a. Finite element mesh for running E3SAP model

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12

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11. The mesh selected gave elements with a maximum aspect ratio of

1.83:1, well under a ratio of 4:1 which is suggested as a maximum based on

' past experience. This ratio allows for accurate results in both deformation

]and stress calculations. High stresses exist at reentrant corners in the

i] actual slab, however this particular mesh is not refined in these areas. This] mesh gives an approximation of moments sufficient for design, although the

designers should bear in mind that a refined grid in areas of high stress

gradient may be necessary for some problems.

131

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PART IV: FINITE ELEMENT ANALYSIS RESULTS

12. Results from the GTSTRUDL and E3SAP verification problem for a

simply supported slab with a uniform load are shown in Figures 6a and 6b. The

results for the fully fixed edge slab are shown in Figure 7. These results

indicate that four elements are adequate for modeling one quarter of a square

plate for either set of boundary conditions. The theoretical results for the

simply supported plate are shown in Appendix B. Timoshenko's plate theory

equation is shown with added coefficients to account for shear deformations.

As seen from these results, the shear deformations are important and the

GTSTRUDL element matches the theoretical results. A theoretical solution for

the continuous slab was not available.

13. The powerhouse slab analysis with fixed edges was analyzed using

the programs, E3SAP and GTSTRUDL. Selected results and graphed comparisons

for deflection and moments are shown in Figures 8 through 14b.

14. Selected results form the GTSTRUDL analysis using elastic springs

to model the wall and column supports are compared with the GTSTRUDL fixed-

support analysis in Figures 14c through 17. Figures 18 through 20 show the

contour plots of the moments, Mxx , Myy , and Mxy , respectively, for the

GTSTRUDL analysis of the slab with fixed supports. Figures 21 through 23 show

the contour plots of the moments, Mx,9 Myy , and Mxy , respectively, for

the GTSTRUDL analysis of the slab with elastic spring supports. All runs were

checked to ensure equilibrium of the model. All reactions were totaled and

compared with the original loading conditions. The values for the spring

constants were calculated by using a 1-ft strip model of the structure for

each wall configuration with a moment applied at the slab support level. The

Corps' CFRAME computer program was used for making the analysis of these 1-ft

strips.

I1

19

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& GTSTRUDL (P1002 ELEMENT

zS E3SAP ELEMENT

0 50 100 150 200 250 300

NUMBER OF DEGREES OF FREEDOM IN MODEL

______NUMBER OF DEGREES OF FREEDOM IN MODEL ____PROGRAM 5 9 14 46 66 211 290 863

GTSTRUDL 18.215 17,708 17,341 17.263

E3 SAP 18.815 18,301 17.888 17.780

1 ELEMENT 4 ELEMENTS 16 ELEMENTS 64 ELEMENTS

Figure 6a. Comparative graph and tabular recordings of moments atcenter of slab, Mx or M , from verification study using

programs GTSTRUDL and ESPfor simply supported slab

17

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0 50 100 150 200 250 300

NUMBER OF DEGREES OF FREEDOM IN MODEL

PROGRAMNUMBER OF DEGREES OF FREEDOM IN MODEL

5 9 14 46 66 I 211 290 863

GTSTRUDL 0.0253 0.0262 0.0262 0.0262

E3 SAP 0.0155 - '0.0228 0.0252 - 0.0258 -

1 ELEMENT 4 ELEMENTS 16 ELEMENTS 64 ELEIMENTS1

Figure 6b. A comparative graph and tabular recording of deflec-tion at center of slab, from verification study using programs

GTSTRUDL and E 3SAP for simply supported slab

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18.63 19.65 2792 = RESULT IN KIP-IN. PER IN.

73 .5795 of 6

Figure Hla. Tabulation of E3SAP moment, M , results along line 2

in powerhouse slab (results at element centers)

23

- I i

_____201 AVERAGE 219 AVERAGE51.32 51.32 51.32 -18.66 -18.86 -40.64

65 202 74 220 -E20.85 0.84 20.85 -26.85 -26.91 -26.88

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66 204 L0 75 222 L9-19.23 4 -19.26 -19.24 -20.4440 -20.51 -20.48

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67 206 76 224-17 55, -1766 -17.61 39.09 39.40 39.25

-9.52 207 _9.70 225 *-9.5 2 .28 25.90 99.60 100.24 94.23

-42.10 -42.28 88.23 88.8668 52 77 61

38.38 38.25 - 27.98 28.22 28.10

116.94 209 17.71 117.14 -33.38 227 -33.48116.56 117.33 -7.44 -7.54

-20.46

69 210 78 228 235.84 35.71 -10.574 -10.62 -10.60

-46.77 _211 -46.95 -1320 229 -13.22-31.71 - 3.00-16.46 -16.64 -12.78 -12.81

70 54 79 3-2718 40 2-27.28 -27.23 -3.96 -3.98 -3.97

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73 57

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Figure lb. Tabulation of GTSTRUDL moment, y p results along line 2,(results at nodes)

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360.292 361-36.10 68-35.0888 89 204 205

-50.02 317-50.08 -27.64 709-27.62 LEGEND-51.29 "-51.34 -70.08 -70.06 292 = NODE NUMBER

4497 43.86 129 3 .0104 = ELEMENT NUMBER42293 79 -36.07 = RESULT IN KIP-IN. PER IN.

104 105 220 221

36.22 367-36.30 1 104.29 "759 75.9481,95 -82.03 186.85

8.57 40392 34 07962.59120 121 231t 108.82 4778.50 793-40.85

199.08 1.35

437 8134p 68.28 0 -20.9541131 241

Figure 12a. Tabulation of GTSTRUDL moment, Mx resultsalong line 3 (results at nodes) X

26

17.33 18.12 -13.81 -25.280 0 08 9 141 251

-15.58 -14.70 -15.93 33.91

24 25 151 259

-12.94 -12.72 32.93 4.41 6.32* 0 0 S40 41 159 272 273

37.26 30.49 9.64 9.01 -33.07 -27.31* 0 0 0 0 056 57 172 173 288 289

28.61 23.10 -27.49 -26.96 -17.92 -16.610 0 0 0 072 73 188 189 304 305

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-- -LEGEND

-39.56 -33.34 103 1.1 188=- ELEMENT NUMBER

0 -27.49 RESULT IN KIP-IN. PER IN.

104 105 220 221

6.12 8.68 36.170 0

120 12123

39.95 -15.22

S S ..131 241

Figure 12b. Tabulation of' E3SAP moment, Mx , resultsalong line 3 (results at element center)

27

(MRS

00

-U-0

%A

Ln EIn

In 0L.

Cn L

OD 0

cc 4. 14

C4

Z

0N x2

CI 0

00

(N

N 04.)

Nu 4

LU (U

CN

60 6n

N DIM

b~~~~~ d ~ NU)A" V .L 3Y V

T

28N

LOAD CASE 1

Figure 13. Deflected shape plot of powerhouse

slab from E3SAP, fixed support condition

29

1 0

Z12 5.4696 HORIZONTAL IN UNITS PER INCH a

1264698 VERTICAL 1IN UNITS PER INCHX ROTATION Z -30.0 'V 0.0 X -70.0

Figure 114a. Deflected shape of powerhouse slab fromGTSTRUDL, fixed support condition

Z 125 460 HORIZONTAL IN UNITS PER INCH"26 1S4696 VERTICAL IN UNITS PER INCH

X ROTATION Z 30.0 YV 0.0 X -70.0

Figure 14$b. Deflected shape of powerhouse slab fromGTSTRUDL, elastic support condition

30

I.- 0

e~0

-4

N

Qf)L

0.cc

0m 0

z 0 V

z0. 0

L

00V.

u Cc

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cc C-1-.

Z. OL XNI 'N0I±D31 A30

31

NODE MKXX"FIXED" ANALYSIS "SPRING" ANALYSISNUMBER KIP-IN. PER IN. KIP-IN. PER IN.

1 0.00 0.003 21.63 6.53

5 39.00 11.05

7 42.38 14.37

9 44.24 17.42

11 47.28 19.21

13 49.10 20.16

15 47.14 20.40

17 45.65 20.84

19 50.47 20.69

21 52.69 18.17

23 49.99 16.46

25 45.79 14.71

27 37.17 11.24

29 25.68 7.51

31 9.94 3.24

33 0.00 0.00

Figure 15a. Tabular record of moment, Mx I along line 1

of powerhouse slab from GTSTRUDL comparing fixed-edgeanalysis versus elastic spring supports

32

ijV

N) 0C

'-. 0

/ x tDc0

CC.)

E3 0C

0 C4'U

Li. 0 -WI

N --

0 CL

33E

201 21963.46 55 76 -25.34 -27.44

65 49 74 5817.32 17.25 -34.53 -34.40

-2878 203 -28-79 -41 94 221 -42.40-21.13 -21.14 -40.33 -40.80

66 50 75 59-31.36 -31.42 -26.67 -26.79

-40.95 205 -41.16 -11.02 223-11.86

-38.17 -38.39 -35.80 -36.65

67 51 76 60-32.07 -32.18 55.91 55.97

-2488 207 -26.64 151.17 225 143.24-45.63 -47.39 32.68 24.75

68 52 77 619.26 9.98 -4.33 -3.72

69.81 209 58.32 -37.76 227 -38.97137.69 126.19 -25.60 -26.81

69 53 78 6235.75 36.42 -28.13 -28.13

-60.12 211 -61.73 -29.88 229 -29.99-22.20 -23.86 -30.12 -30.22

70 54 79 63-33.71 -33.73 -20.16 -20.12

67 213 231-98-4267 -43.18 -9.95 -9.89-42.83 -43.33 -13.91 -13.86

71 55 80 64

-30.75 -30.78 17.26 16.80

-16.28 215 -17.94 48.17 233 4817-49.08 -50.74

72 56 LEGEND39.47 40.14 233 = NODE NUMBER

133.54 1217 122.30 80 = ELEMENT NUMBER16.80 = MOMENT IN KIP-IN. PER IN.

108.82 97.57

73 5716.86 17.95

-67.51 219 -69.61 L

Figure 16a. Tabular record of moment, Myy

along line 2 of powerhouse slab from GTSTRUDLwith elastic supports (results at nodes)

34

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PART V: INTERPRETATION OF RESULTS

Comparison Indications

15. This study indicated that the selected GTSTRUDL element will

produce results approaching the theoretical values for the simply supported

slab. Convergence to these values occurs on an asymptotic curve and practioal

results can be obtained by using a relatively coarse mesh. The comparison

between the E3SAP membrane element and the GTSTRUDL IPBQQ element indicates

that as the span/thickness ratio decreases, the contribution of shear to the

deformation becomes more important. The practical guide in past years has

been to neglect shear deformation if the span/thickness ratio is 10 or

larger. In this study, for a span/thickness ratio equal to 10, the shear

deformation resulted in only a 2 percent difference in deflection.

Slab Analysis

16. The powerhouse slab has a maximum span/thickness ratio of 7.3 and a

minimum ratio of 5.1. Comparisons of the E3SAP and GTSTRUDL models (refer to

Figures 9 and 10) show that the deflections increased by as much as 56 percent

when shear deformations were included with the IPBQQ element. Moments

increased by a maximum of 30 percent in some areas, although the moment curves

are usually quite close (Figures 11c and 12c). Compared to the results of the

verification study, it can be seen that decreasing the span/thickness ratio

smaller than 10 caused large changes in the shear deformation.

17. Upon closer 3tudy of the finite element solution for the slab, par-

ticularly the GTSTRUDL analysis, it became apparent that the mesh used for

this inalysis gave good overall results. However, in areas where the moment

is rapidly changing, the stress analysis falls short of the desired

solution. Figure 11b. Myy along line 2, and Figure 12a, Mxx moments along

line 3, show the disparity in computed moments at a common node in areas where

the moment is rapidly changing. The reader must realize that a finer mesh is

desirable in areas such as around the pinned supports used to model the

supporting columns, and in areas where the geometry changes abruptly, such as

the corners of the openings in the slab.

L~TM

Slab Analysis with Elastic Spring Supports

18. The deflection comparison along line 2, Figure 14c, dramatically

:ilustrates the large change in deflections in the slab analysis when the

fixed supports are replaced by elastic spring supports. It is evident that

the "pin" assumption for the column in the previous analysis was not

-nrticularly valid. The moment comparison along line 1, Figures 15a and 15b,

sho"s the large change that took place for the negative moments along the end

waJ.. The maximum moment decreased by 61 percent due to rotation of the endwall. Interestingly, the moment along line 2 changed very little from the

2,r-avious analysis, as indicated in Figures 16a and 16b. Also, inspection of

Mxx along line 3, Figure 17, shows that it has not changed from the fixed

support condition except at the connection to the end wall where, again,

elastic rotation of the wall caused a reduction in negative moments.

19. The major difference between the two analyses is the deflections at

the columns and rotation of the end wall in the elastic support analysis.

-44

•r , 1,f

PART VI: CONCLUSIONS AND RECOMMENDATIONS

Conclusions

20. The finite element program GTSTRUDL can be used to advantage in the

analysis of concrete slabs with configurations that rule out conventional

analysis methods. The IPBQQ element in the GTSTRUDL library is particularly

useful if the slab has a span/thickness ratio of less than 10. This study

bears out the assumption that the contribution of shear to deflections become

a major contributor to the deflection of this type of slab when the ratio is

less than 10.

Recommendations

21. The engineer should make some verification studies for his particu-

lar problem so the proper mesh size can be selected to give usable results.

The IPBQQ element allows stress and moment contour plotting as shown in

Figures 18 through 23. This graphical interpretation of the output makes the

job of the engineer more pleasant. The analyses pointed out the necessity for

finer meshes in high stress areas. Should the engineer be interested in

moments and shears near discontinuities, such as corners of openings or con-

centrated loadings, a finer mesh size at these points must be used.

22. The elastic spring supports analysis suggested that engineers look

closely at fixity assumptions when modeling concrete slabs. Wall rotations

and column shortening will give dramatically different deflection values, and

negative moments will lessen considerably in some instances, as the example

for this study shows.

23. When the slab has a span/thickness rati.o of 10 or less, the design4Jengineer should evaluate the need for using an element that models the shear

contribution to deflections.

'45

APPENDIX A: GTSTRUDL INPUT FILES

1. A verification study of the GTSTRUDL model involied analyses of the

problem with two different boundary conditions. Input files for slabs with

fixed supports and slabs with elastic spring supports are shown in this

appendix.

Slabs with Fixed Supports

2. The GTSTRUDL input file for slabs with fixed supports is printed on

this and the following pages.

STRUDL 'SLAB' 'BONNEVILLE ERECTION BAY SLAB'UITS FEET KIPSTYPE PLATE 1EHDINGGENER 33 JOINT ID I I X S. S. Y LIST G. 2.375 5.715 3.625 11.5 13.215 -15. 17.5 20. 22.S Z5. 27.5 30. 32.S 3S. 37.5 40. 43.S 47. 49.5 52. -54.25 56.5 S8.2S166. 62.S 6S. 67. 69. 71. 73. 74.5 76. SLIP

MODIFY 4 ID SO X S. Y 0.GENER 33 JOINT ID 251 I X 25.5 6. YV LIST 0. Z.371 5.75 8.62S 11.5 -13.25 15 17.5 20 22.S52S 27.5 30 32.S 3S537.5 40 43.5 47 49.52 -54.25 56.5S 58.2S So 62.5 6S 67 69 71 73 74.S 76. SUPMODIFY 3 ID SO X 5.5' ye.GENEP 17 JOINT ID 34 1 X 2.5 0. V LIST 0. 5.75 11.5 15 20 2S 30 35 -40 47S2 56.5 60 6S96973 76 SUP

MODIFY 3 ID 50 X5. Yg.-GENER 17 JOINT ID 234 1 X 22.75 0. Y LIST 0. 5.75 11.5 I5 20 2S 30 -3S 40 47 5Z 56.5 60 SS 69 73 76 SUIPMODIFY 3 ID SO X S.5 Yw 0.GEllER 22 JOINTS ID 446 1 X 47.5 0. 'V LISI 0. 2.27S 5.75 8.625, 11.5 46. -43.S547 49.S552. 54.255S6.55S8.2 60 62.56SS67 6971 73 74.S976 SUPMODIFY I ID 34 A 5.5 YV 0.GENEN 12 JOINTS ID 434 1 X 44.75S 0 V LIST 8 5.75 11.5 40 47 S2 56.5 60 -65, 69 73 76. SUPMODIFY I ID 34 X 5.5 YV 0.GEMEN 19 JOINTS ID S13 I X 59.5 0. YV LIST 0. 2.87S 5.75 8.625 11.5 40. -43.S 47 49.S 52 54.25 56.5 58.25 60 62-S 65 73 74.5 76 SUPGENER 11 JOINTS ID 502 1 X 55.75 0. YV LIST 0. 5.75 11.5 40 47 52 56.5 60 6573 76 SuPMODIFY I ID 36 X 5.5 'V 0.4ENER 33 JOINTS ID 543 I X 64. 0 Y LIST 0. 2.275 5.75 3.625 12.5 03.25 IS -17.S 20 22.5 25 27.5 30 32.5 35 37.5 40 43.5 47 49.S S2 54.25 56.5 53.25 -60 62.5 65 67 69 71 73 74.5 76 SUPMODIFY 4 ID SO X 5.25 YV 0.GENER I? JOINTS 10 576 1 X 66.62S 0 YV LIST S. 5.75 11.5 IS 20 25 30 35 46 -475S2 S6G5 606S569 7376 SUPMODIFY 3 ID S0 X 5.25 Yv 0.GENEN 92 JOINTS ID 731 1 X 90.5 0. YV LIST 0. 2.87S 5.75 3.62S, 11.5 40. 43.547 49.6 S2. 54.25 56.5 53.29 60. 62.5 6S67 6971 73 74.5 76 SUPMODIFY I ID 34 X 5.5 'V 0.

r ERU 12 JOINTS ID 776 1 x 87.75 0. Y LISY 0. 5.75 11.5 4S047 52 56.5 60 -1 973 76 SuPMODIFY,I ID 34 X A .V S.GEMEN 19 JOINTS 10ID I X 101.5 0. V LIST 0 2.875 5.75 8.62S 11.9 40 43.S-47 56.5538.2560 62.S565 6769 71 73 74.S 76 SUPGENER 11 JOIN I0 844 1 X 94.75 0. V LIST 65S.75 11.5 40 47 56.5 60 65 69 73-76 SUPMODIFY 1 Io 30 x 5.5 V 0.GEME11 33 JOINTS ID 835 I X 107. 0. 'V LIST 0. 2.375 5.75 3.62S 1I.S 13.2S IS -17.520 22.S 2S27.S530 32.53S537.S 40 43.5 47 49.S95254.2556f.551.2560S -

Al

.T -k!DL :nput 'ile for slats with fixed supports--continued

6.S 6E C? 69 71 73 74.S 76 SUP,.' 3 Ir SO X 5.333 Y 8., !- JOINtTS ID 918 1 X 109.666 0. V LIST 0. 5.75 11.5 15 20 25 30 35 40 -.C e&t 60 65 69 73 76 SUP.

r SO, : :5 X S-.333 Y 0.

_,'r -F 35 TO 49 S2 TO 82 85 TO 99 102 TO 132 135 TO 149 152 TO 182 -, ; 202 TO 208 210 TO 2,6 218 TO 224 226 TO 232 235 TO 249 252 TO 282 -

2; T( 2 v 382 TO 332 335 TO 349 352 TO 382 385 TO 399 462 TO 408 410 TO 416 -426 TO 432 435 TO 444 447 TO 466 469 TO 478 481 TO 500 503 TO 511 -

514 TO 530 533 TO 541 544 To 550 S52 TO 558 560 TO 566 568 TO 574 577 TO 579 -SF: TO 59l 594 TO 600 602 TO 624 627 TO 629 631 TO 641 644 TO 650 652 TO 674 -67- -0 67; 681 TO 691 694 TO 790 702 TO 724 727 TO 729 731 TO 741 744 TO 750 -

'7 10 TS3 760 TO 766 768 TO 774 777 TO 786 789 TO 808 811 TO 820 823 TO 842 -. S. "0 2 856 TO 872 875 TO 883 886 TO 892 894 TO 900 962 TO 908 910 TO 916 -

S;j 3 S:6 TO 966 969 TO 983 986 TO 1016 1019 TO 1033 1036 TO 1042 1044 -)L 141.2 TO 1058 1060 TO 1O66 418 TO 424

20) 217 22 5 Ig 417 425 559 567 759 767 893 901 909 1043 1051 -'051 10O9 MOMENT Y MOMENT X51 5C 601 630 651 680 701 730 751 MOMENT X

! L-EI-NT ID '. I FROM 1 2 TO 51 2 TO 53 2 TO 3 2 TO 34 1 TO S2 2 TO -

)D- D I- FROM 50 TO 50 TO 50 TO 50 TO S TO 50 TO 50 TO 50rtER 2 -LErEiT ID 129 1 FROM 401 2 TO 446 2 TO 448 2 TO 403 2 TO 434 1 TO -

447 2 TO 435 1 TO 402 2-O3DIY I ID 10 FROM 45 TO 34 TO 34 TO 45 TO 34 TO 34 TO 34 TO 45

GENER 2 ElEMENTS ID 131 1 FROM 417 2 TO 451 2 TO 453 2 TO 419 2 TO 437 1 TO -452 2 TO 433 1 TO 418 2MODIFY I ID 10 FROM 34 TO 34 TO 34 TO 34 TO 34 TO 34 TO 34 TO 34GEIoER 2 ELEMENT ID 149 1 FROM 480 2 TO 513 2 TO 515 2 TO 482 2 TO 502 1 TO -S14 2 TO S03 1 TO 481 2MODIFy I ID 8 FROM 33 TO 30 TO 30 TO 33 TO 30 TO 30 TO 30 TO 33GENER 5 ELEM ID 151 1 FROM 485 2 TO 518 2 TO 520 9 -0 487 2 TO 505 1 TO 519 -2 TO 506 I TO 486 2MODIFY I !D 8 FROM 33 TO 41 TO 41 TO 33 TO 30 TO 41 TO 30 TO 33ELE9 156 INCID 499 529 531 501 511 530 512 500SLEM 164 IN CID 529 573 575 531 541 574 542 530GENER 16 ELEn ID 165 1 FROM 5432 TO 593 2 TO 595 2 TO 545 2 TO 576 1 TO 594 -2 TO 577 1 TO 544 2MODIFY 3 ID 16 FROM 50 TO 5i TO 50 TO So TO 5 TO 50 TO 50 TO 50 TO 50GErbER 2 ELEM 10 229 1 FROM 743 2 TO 788 2 TO 798 2 TO 745 2 TO 776 1 TO 789-2 TO 777 1 TO 744 2MODIFY IID 10 FROM 45 TO 34 TO 34 TO 45 TO 34 TO 34 TO 34 TO 45

'Q 8 ELER ID 231 1 FROM 759 2 TO 793 2 TO 795 2 TO 761 2 TO 779 1 TO -. C"80 I TO 760 2

MODIFY I ID 10 FROM 34 TO 34 TO 34 TO 34 TO 34 TO 34 TO 34 TO 34GEHER 2 ELEM ID 249 I FROM 822 TO 855 2 TO 857 2 TO 824 2 TO 844 1 TO -856 2 TO 845 1 T0 823 2MODIFY I ID 8 FROM 33 TO 30 TO 30 To 33 TO 30 TO 30 TO 30 TO 33GEHER 2 ELEM ID 251 8 FROM 827 33 TO 860 41 TO 862 41 TO 829 33 TO 847 3-TO 861 41 TO 848 30 TO 828 33GEIER 5 ELEM ID 252 1 FROM 833 2 TO 363 2 TO 865 2 TO 83S 2 TO 849 1 TO -864 2 TO 850 I TO 834 2MODIFY 1 ID 8 FROM 30 TO 44 TO 44 TO 30 TO 30 TO 44 TO 30 TO 30GEMER 16 ELEM ID 265 1 FROM 8852 TO 935 2 TO 937 2 TO 887 2 TO 918 1 TO -936 2 To 919 1 To 886 2MODIFY 2 ID 16 FROM 50 TO SO TO SO TO 5S TO SO TO SS TO SO TO 5ELEEM PROP

A2

GTSTRUDL input file for slabs with' fixed supports--concluded

I To 312 TYPE 'IPIOG' THICK 2.75UNItTS INCHESC014STAMTSE 3120. ALLpoISSO" .17 ALLCTE .000006 ALLUNITs FEETLOADING IELEMENT LOADSI TO 31a SURF FORCE PZ -1.4125JOINT LOADS465 747 547 989 FORCE Z -24.1407 749 549 891 FORCE Z -58.5409 751 551 893 411 753 553 895 413 755 555 897 - -415 7S7 55? 899 FORCE Z -68.841? 559 759 901 FORCE Z -3.929 903 96? 833 FORCE Z -9.5862 906 863 831 FORCE Z -20.495 569 573 499 FORCE Z -7.5571 497 FORCE Z -21.528 529 FORCE Z -14.UNITS INCHESSTIFFNESS ANALYSISLIST DISPLACE ALLLIST CTRFSSES ALLLIST ELEMENT FORCES ALLLIST REACTIONS ALLSAVE DIRECT 'DRSLAB'F INI SH

A3

a~~~ Arm, a~

Slabs with Elastic Spring Supports

,LS~hULDL input file for slabs with elastic spring supports is

and the following pages.

STh'AL -,LA8'- -,eULLE £CCTZOH &AV SLADU04Is ri T CIPSTYPE PLATE IENDINGCEpE& 33 JOINT ID 1 I X 0. 0. V LIST 0. 2.87S S.71 8.62S 11.5 13.21 -1%. 17.1

. 2.5 RS. 27.S 30. 32.S 36. 37.S 40. 43.S 47. 43.5 Sit. -

C4,, S6.6 5.2S 60. 6 . 6S. 67. 69. 71. 73. 74.S 76. SUPRODIFY 4 10 SO X S. v 0.argE1 33 JOINT 10 251 1 X 2S.S 0. V LIST 0. 8.67S S.?S 2.6 2 i. -S

7T, iS 17.5 2* P. S 2 27.S 30 3R.S 3S 37.S 40 43.S 47 49.S S -t.4, "S S.S 53.S &4 62- 6S 67 69 71 73 74.S 76. SPfv0D:ry 3 iD So X S.S V 0.CfmER 17 JOINT ID 34 1 X 2.S 0. V LIST 0. S.?S 11. IS 0 ZS SO 31 -.0 47 52 S5.S 60 SS 69 73 76 SUP

40DIF' 3 ID So X S. Y 0.QEp#s 1' JOTT 1D 234 1 X 2.7S 0. V LIST 0. S.7S 11.S IS a 02S 30 -3Se 47 C.2 56.S 60 6 5 69 73 76 SLPVODIFv + 'D 50 x S.S V 0.AME[R :? ID 446 1 X 47.5 0. V LIST &. .27S 5.7S 9.62S 11.S 40. -q3.S 47 42.5 . . 54.2 S.S S3.2S 60 62.S 65 67 61 ?1 73 74.5 76 SUP?%ODllF 1 ID 34 X S.5 V 0.GENE* 12 JOINTS ID 434 1 X 44.71 0 Y LIST 0 S.?S 1I.S 40 47 S2 S.S 50 -65 69 73 76. SUPMODIFY I ID 34 X 5.5 V 0.

5EMER 19 JOINTS ID S13 I X S3.S 0. V LIST 0. 2-87S S.7S 1.62S II.S 40. -43.5 47 49.5 52 54.25 SG.S 53.2S 60 62.S 6S 73 74.5 76 SUPGENER 11 JOINTS ID 502 I X SS.7S 0. Y LIST 6. S.7S 11.S 40 47 S2 S6.S 60 Go -73 76 SUPMODIFY 1 I1 30 x 5.5 v 0.QEMER 33 JOINTS I S43 I X 64. 0 V LIST 0. 2.275 5.75 8.62S 11.5 I3.2S IS -17.S 20 22.5 25 27.S 30 32.5 35 37.S 40 43.S 47 49.S S2 64.2S S4.S S3.25 -14 62.5 6S 67 69 71 73 74.5 76 SUPMODIFY 4 ID SO X S.25 V 0.GEPER 17 JOMNTS ID S76 I x 66.62S 0 V LIST 0. S.7S I.S IS no as 30 3S 40 -47 S2 56.5 60 65 69g 73 76 SUPMODIFY 3 ID SO X S.2S V 0.GENE* 22 JOINTS ID 783 1 X 90.S 0. V LIST 0. 2,875 S.7S 2.62S 11.S 40. 43.5 -47 49.5 S2. 54.25 58.S 58.2S 64. 62.1 6S 67 69 71 73 74.S 76 SUPMODIFY I ID 34 X S.s V S.GQER 12 JOINTS ID 776 1 X 37.75 0. V LIST 0. S.7S 11.S 40 47 S 24.S 60 -SS 69 73 76 SLIPMODIFv 1 .. 34 X S.s v 0.IPEER 19 JOINTS ID 3SS I X 101.S 0. V LIST 0 2.87S S.7S $.U2S ll.S 40 43.S -

'S.S S3.25 60 62.5 6S 67 69 71 73 74.6 76 SUP"+R It Jo:.' ID .44 1 X 94.7S 0. V LIST 0 5.71 11.5 40 47 5S.S 606 O69 73 -

'VV I ID 34 X S.5 V 0.[R 33 JOINTS ID 12S I X 107. S. V LIST 0. 2-.875 .75 8.68 11.S 13.S IS -

- . 282.6 2 27. 30 32.5 3S 37.S 40 43.S 4? 49.5 S S4.S S6.6 55.25".5 65 67 69 71 73 74.5 76 SUPMODIFY 3 ID SO X S.333 V 0.am*E[ 17 JOINTS ID 913 1 X 109.6 0. V LIST 0. 5.7S 11.5 IS 208 I 30 3S 40 -47 Se S6.5 Go66 69 73 76 SUP.1"IloV 2 ID SO X S.333 V 0.$TmT8 FREE 35 TO 49 S2 TO Be RS TO 910 e TO 132 13 TO 149 IS2 TO 182 -135 TO 1g 2*2 TO M03 210 TO 216 218 TO 824 M TO M3 235 TO 849 M1 TO 233 -8 05 TO 299 302 TO 332 33S TO 349 NO TO 30a331 TO 39 41 TO 409 410 TO 416 -420 TO 432 431 To 444 447 TO 44 469 TO 473 431 TO S0 503 TO all -

14 TO 530 S33 TO S4t S44 TO S0 55 TO S5j 35 TO S0 S63 TO 5F74 577 TO S79 -53i TO 591 594 TO 140 602 TO 614 67 TO 62 031 TO 641 644 TO O0 M TO 674 -677 TO 679 11 TO 691 94 TO 700 70M TO 784 77 TO 789 731 TO 741 744 TO 710 -762 TO 7S 760 TO 766 768 TO 774 777 TO 736 79 TO WS il TO 889 3 TO 242 -14 TO IS3 1S6 TO 178 67S TO 303 364 TO 9 134 TO 00 000 TO ai 1s TO via --19 TO 933 930 TO 9"6 969 TO 903 936 TO 1016 1019 TO 1033 103l TO 1048 1044 -

A4l

v %1,-%

K"3S7KL .4 it~ t'ile for slabs with elastic spring suppor-'s--cont :ntwJ

To jSOe 1OS TO I00 1060 TO 164 413 TO 484UNITS IlNCHESJOINT RELEASES33 K FZ "90il.

To 4 KFZ 9171. CRY 749430.7 LS F-Z 9871. CRY SS396O.

84 31 KFZ 91a. KMV 4S8a4.to T 16 eO 26 KFZ 11613. KMVY Gl172.

11 19 KFZ 1393S. CRY 732100.18 KFZ 16263. Cm 912400.I CZ 11o32. CMY 16000.8 87 CFZ 10)45L. CRV 553450. I

83 a TO 30 KFZ 9290. CY 621440.1a KFZ 6963. CRY 391000.o 3 150 350 FZ 13335. KPIX 1280100.

100 133 183 20 809 KFZ 13333. KMX 13437040.a33 SS 1017 1034 (FZ 14000. KHX 1935800.M 512 531 542 321 343 IFZ 14666. KKX 202800.

213 3" 383 445 467 479 501 354 373 384 KFZ 14666. 1(4X 14081".333 592 62S 642 675 692 725 742 KFZ 14000. KMX 1344100.400 KFZ 16000. KMX 1636100.433 KFZ 15333. KMX 147al 0.7S KFZ 13000. KMX 12481f0.787 (FZ 120"4. KlMX 1659300.917 934 967 984 KFZ 14440. KIX 1336640.1067 KFZ 7120. KMX 983400.34 51 84 101 334 (FZ 11520. KfMX 3394046.134 151 184 KFZ 11520. KMX 3643800.201 301 KFZ 129;4,. KMX 3326040.234 251 284 KFZ 12672. KMX 400200.31 434 446 468 480 502 513 532 310 3 , 244 81S 374 KFZ 12672. (Mx 3733400.384 KFZ 13824. (MX 4072800.401 (FZ 13248. KMX 3903000.S43 (FZ 12348. (MX 3648500.70 69P3 626 643 676 693 726 KFZ 12096. KMX 3563700.743 KFZ 11232. KMX 3309100.776 CVZ 10368. CMX 3054600.718 KFZ 11520. KMx 3394000.SIS ..FZ 12473. KiMX 3676400.

P 918 3 5963 985 1018 CFZ 1230. KFIX 36 24N.1035 KFZ 6123. KMX 1306000.20 217 225 409 417 425 S69 567 759 76? 393 901 90 1043 10S 1069 -

FZ 3424. KIRX 1617700". RY 16177000.631 5 30 730 7S1 KFZ 8424. (MX 161770"0.01 701 KFZ 11433. KMX 141S100.030 810 KFZ 13534. KMX 14115000.@S1 CFZ 15717. KCX 14151000.LIMITS FEETOVIER If EUqNT I 1 1 FROM 1 2 To 61 TO S 38 TO 3 TO 34 1 TO 52 2 TO -35 1 TO 8 a9ODIFY 7 I 1I FROM SO TO SO TO SO TO 50 TO 10 TO S0 0O TO SOwI i IELEqEJT t 129 1 FROM 401 2 TO 444 1 TO 448 1 TO 403 It TO 4 34 1 TO -447 8 TO 436 1 TO 402 80ODIFY I ID 10 FROM 41 TO 34 TO 34 TO 45 TO 34 TO 34 TO 34 TO 41GOVMER 8 ELEMENTS ID 131 1 FROM 417 2 TO 451 2 TO 4S3 8 TO 419 Z TO 437 1 TO -412 2 TO 438 1 TO 418 2MODIFY I ID 10 FROM 34 TO 34 TO 34 TO 34 TO 34 TO 34 TO 34 TO 34GlEMR 2 ELEINT ID 149 1 FROM 480 I TO 113 8 TO IS 12 TO 43a8 MTO S0 1 TO -S14 2 TO S03 I TO 481 2MODIFY t ID 8 FROM 33 TO 30 TO 30 To 33 TO 3 TO " TO 30 TO 33CEMIER i CLEM ID IS1 I FROM 436 2 TO S12 8TO 102 0 TO 437 I TO SO1S TO 519-e O STOa I To 486 2MODIFY I ID I FROM 33 TO 41 TO 41 TO 33 TO 30 TO 41 TO 30 TO 33[LIr 154 INCIS 499 129 131 SOt t11 S30 13 6"0

o "1

[] ,,,,I

( 7~' I mnut file for slabs with elastic spring supports--concluded

gjfi 144 IOCKS 189 573 S79 531 541 574 543 S30qfp": So CLEM I 16 S I FROM S43 I T0 103 8 T0O5 SSaTO 5451 8TO 1761 TO 604-Jk To S 1 T0 144 8

01 3 ID Is FROM So 10 100 S o o So T O So o TO SoRI I ELEA 10 M33 I FRO 74323 0 733 1 iO79a1 t0 746S TO Io TO ato s-a 1o 777 I TO 744 1Maj1~tv 1 10 10 FROM 4S 10 34 T0 34 TO 4S T0 34 T0 34 TO 34 TO 41*j"p S CLEM ID 131, 1 FROM 710 a 10 733 1 T0 736 8310 761 8 TO 773 1 TO -O4 a T0 730 1 TO M6 2

Os@IFY 1 10 10 FROM 34 10 34 To 34 To 34 10 34 TO 34 TO 34 70 34OCHE a CLEM 10 340 1 ROs a a To 85S I TO SS? I31384 31 3O 44 1 TO -SS503 TO 54S1 TO 383 a4o0IFY 1 10 3 FROM 33 TO 30 TO 30 10 33 TO 30 TO 30 TO 30 TO 33eEI 3 ELEA 19 351 8 FROM Ss7 33 105860 41 toD 368 41 TO ON 33 TO 347 30-TO0361 41 TO 843 30 TO0@a*333CEME S [LEM I 1E2SE ISG FRO 8310353 a T to I6 TO 3 8tu TO091TO -"44 a to0&SO I T0 334 8MODIFV 1 10 1 FROM 30 10 44 T0 44 10 30 TO 30 TO 44 TO 30 T0 30CEMES 16 ELEA I0S I FRO US0 33 TO 103S 2 TO 337 LP TO 387 & TO 3131 10 -336 a TO0919 1 T0 gas e'oAify 2 10 1S FROM SO T0 5O T0 S0O TO 10 TOSO TO SO TO SO TO SO

i!L[ENN PROPI TO 312 TYPE 'IP9QQ' THICK 2.75

P0165094 Z7 ALL-' .0004"~ .- LL.,"ITS FEETLOADING IELEMENT LOADSI TO 312 SURF FORCE P2 -1.412SJOINT LOADS401 747 S47 329 FORCE Z -24.1437 749 S49 391 FORCE 2 -13.1409 711 S11 893 411 713 113 31 413 711 551 397-41S 7S? S57 399 FORCE Z -63.3417 $SO 7S9 901 FORCE 2 -34.43On 903 907 133 FORCE Z -9.5O6R 90 61 231 FORCE 2 -10.49S 549 S73 493 FORCE 2 -7.6371 437 FORCE z -a1.S" als FORCE z -14.hUNITS INCHES

LIST 0ISPLACE ALLLIST 313(30(3 ALLLIST1 ELEMNT FORCES ALLLIST REACTIONS ALLPLOT DIVICIE SCOPE 4014 VIRUS 130

PROJCT *CIAIE 2 -30. v 0. x -70.9 E. HODES

LOT PROJECT W I Ml .1 ROTATE 2-30. Vs9. X -79.ENDFINISH

APPENDIX B: THEORETICAL RESULTS FOR THE SIMPLY SUPPORTED PLATE

1. Calculation of theoretical deflections and moments for a simply sup-

ported slab considering shear deflections are given on this page, for plate

having the following dimensions and loads;

a = 20 ft

h = 2 ft

P 1 1 ksf

2. Using the following coefficients by Salerno and Goldberg,*: for

h/a 0.1, b/a = 1.0

0.04437 = 0.04632

: 0.0481 81 0.0481

for v = 0.3 Timoshenko's** coefficient (TC) = 0.00406.

3. Correcting for different Poisson's Ratio:

0.04632 Pa4

0.04437 (0.00406) = (0.004238)(1)(20 ) 4 (12)(1 - 0.172

0.044h3 ] (3120 - 144)(2)30.002199 ft

- 0.02638 in.

(MY) = S1Pa 2 0.0481(l)(20)2 = 19.24 kip-ft/ft

Since Mx and My are equal at the plate center,

(Mx) = 19.24 kip-ft/ft

(This moment does not take into account differences due

to the actual v = 0.17 and Timoshenko's v = 0.30)

---

* V. L. Salerno and M. A. Goldberg. 1960 (Mar). "Effect of Shear Deforma-tions on the Bending of Rectangular Plates," American Society of MechanicalEngineers.

** S. Timoshenko and S. Woinowsky-Krieger. 1959. Theory of Plates andShells, 2d ed., McGraw-Hill, New York.

BI

WATERWAYS EXPERIMENT STATION REPORTSPUBLISHED UNDER THE COMPUTER-AIDED

STRUCTURAL ENGINEERING (CASE) PROJECT

Title Date

Tecrncai Report K 78-1 List of Computer Programs for Computer-Aided Structural Engineering Feb 1978

rstr.ctor Report 0-79-2 Users Guide Computer Program with Interactive Graphics for Mar 1979Anaiysis of Plane Frame Structures (CFRAME)

T ...- c3. Report K-80-1 Survey of Bridge-Oriented Design Software Jan 1980

Ta Reporl K-80-2 Evaluation of Computer Programs for the Design Analysis of Jan 1980Highway and Railway Bridges

, r o,. * r, K-80-' Users Guide Computer Program for DesignReview of Curvi- Feb 1980linear Conduits Culveris (CURCON)

Report K-80-3 A Three-Dimensional Finite Element Data Edit Program Mar 1980

-s'" ,ct:cr Report K-80-4 A Three-Dimensional Stability Analysis/Design Program (3DSADIReport 1 General Geometry Module Jun 1980

Report 3 General Analysis Module (CGAM) Jun 1982

Report 4 Special-Purpose Modules for Dams (CDAMS) Aug 1983

m"st' c ' Report K-80-6 Basic Users Guide Computer Program for Design and Analysis Dec 1980

of Inverted-T Retaining Walls and Floodwalls (TWDA)

eort K-80-7 Users Reference Manual Computer Program for Design and Dec 1980Analysis of Inverted-T Retaining Walls and Floodwalls (TWDA)

Tec '.,cai Report K-80-4 Documentation of Finite Element Analyses

Report 1 Longview Outlet Works Conduit Dec 1980Report 2 Anchored Wall Monolith, Bay Springs Lock Dec 1980

Ra Report K-80-5 Basic Pile Group Behavior Dec 1980

' r Report K-81-2 Users Guide Computer Program for Design and Analysis of SheetPile Walls by Classical Methods (CSHTWAL)

Report 1 Computational Processes Feb 1981Report 2. Interactive Graphics Options Mar 1981

nstrjcton Report K-81-3 Validation Report Computer Program for Design and Analysis of Feb 1981Inverted-T Retaining Walls and Floodwalls (TWDA)

rnstructon Report K-81-4 User's Guide Computer Program for Design and Analysis of Mar 1981Cast-in-Place Tunnel Linings (NEWTUNM

Report K-.'-6 Users Guide Computer Program for Optimum Nonlinear Dynamtc Mar 1981Design of Reinforced Concrete Slabs UrL er Blast Loading,CBARCSi

-" .'° , " -,.rt K 8'-' Jier s Guide (7imputer Program for Ds'C g or lrvestgation o ,

,Drth qonal > ,,erts (CORTCUL"

- : -.. ".~ . 3 J"'-rs Gulce Computer Program fror T - -D mursoral Arai,,sis A jq '98'f Br. dng Systems CTABS0W

A ' K 8'-2 c'' orel c:al Bass t.)r CTABS80 A Cm >,ter P--' ram lr . 'Tr-ree-Dimers,ona[ Analysis of Burd rg Ssems

,.*r Repr K-82-6 Users Guide Computer Program for Analysis of Beam-Cuumr Jun 1982

Structures with Nonlinear Supports iCBEAMCi

"", t or Report K-82-7 Users Guide Computer Program for Bearing Capacity Analysis Jun 1982

of Shallow Foundations (CBEAR)

(Continued)

I Ii..A

,jLMY~,

WATERWAYS EXPERIMENT STATION REPORTSPUBLISHED UNDER THE COMPUTER-AIDED

STRUCTURAL ENGINEERING (CASE) PROJECT

(Concluded)

Title Date

Instruction Report K-83-1 User's Guide: Computer Progra'm With Interactive Graphics for Jan 1983Analysis of Plane Frame Structures (CFRAME)

Instruction Report K-83-2 User's Guide: Computer Program for Generation of Engineering Jun 1983Geometry (SKETCH)

Instruction Report K-83-5 User's Guide: Computer Program to Calculate Shear. Moment. Jul 1983and Thrust (CSMT) from Stress Results of a Two-DimensionalFinite Element Analysis

Technical Report K-83-1 Basic Pile Group Behavior Sep 1983

Technical Report K-83-3 Reference Manual: Computer Graphics Program for Generation of Sep 1983Engineering Geometry (SKETCH)

Technical Report K-83--4 Case Study of Six Major General-Purpose Finite Element Programs Oct 1983Instruction Report K-84-2 User's Guide: Computer Program for Optimum Dynamic Design Jan 1984

of Nonlinear Metal Plates Under Blast Loading (CSDOOR)

Instructon Report K-84-7 User's Guide: Computer Program for Determining Induced Aug 1984Stresses and Consolidation Settlements (CSETT)

instruction Report K-84-8 Seepage Analysis of Confined Flow Problems by the Method of Sep 1984Fragments (CFRAG)

f-struclion Report K-P4-tI User's Guide for Computer Program CGFAG, Concrete General Sep 1984Flexure Analysis with Graphics

Technical Report K-84-3 Computer-Aided Drafting and Design for Corps Structural Oct 1384Engineers

Techrical Report ATC-86-5 Decision Logic Table Formulation of ACI 318-77, Building Code Jun 1986Requirements for Reinforced Concrete for Automated Con-straint Processing, Volumes I and II

Tecnical Report ITL-87-2 A Case Committee Study of Finite Element Analysis of Concrete Jan 1987Flat Slabs

(7