;~::,: ~1.:0' , , ~':':L~<1A- . ' . }~·~O~ :lJ-f

. . -CIVIL ·ENGINEERING STUDIES . . .;

,t;py'1- STRUCTURAL RESEARCH SERIES NO. 228

-~.'

~'Metz Reference Room Civil Engineering De:partment

B19:5'f.~" .~. B~i:~~:g ... _ Uni ve·!lSi 'ty OI .LLLl.n01.6

Urbana,. Illinois 61801 ~

AN' EXPERIMENTAL STUDY eF A: REI·NFORCED

\.£QNCRETETWOk WAY mOOR ~LAB '

WITH SHALLOW'~AMS

\ I

by

__ M:.5VANDERBILT

",M. AJSOZEN'

.. C. P.)SIESS "

A Report to

-- ~ THE REINFORCED CONCRETE RE~~~Gf COUNCIL

OFFICE OF THE CHIEFOJfNGINEERS, U.S. ARMY

GENERAL SERVICES ADMI~USTRATION, PUBLIC:, .~UlLDINGS SERVICE

HEADQUARTERS, U.S. AIR FORCE, DIRECTORATE OF"O¥u._,,~GINEERING -'--

and

U.S. NAVY, ENGINEERING DIVISION, BUREAU OF YARDS AND DOCKS

UNIVERSITY OF ILLINOIS

URBANA, ILLINOIS

OCTOBER 1961

AN EXPERIMENTAL STUDY OF A REINFORCED

CONCREll'E TWO-WAY FLOOR SLAB WITH SHALLOW BEAMS

by

M. Do VANDERBILT Mo A .. SOZEN Co Po SIESS

A Report on a Research Project Conducted by the

CIVIL ENGINEERING DEPARTMENT UNIVERSITY OF ILLINOIS

in cooperation~th the

REINFORCED CONCImrE RESEARCH COUNCIL

OFFICE OF THE CHIEF OF ENGINEERS, Uo S .. ARMY Contract DA-49-129-eng-393

GE:\ERAL SERVICES ADMINISTRATION, PUBLIC BUILDmGS SERVICE

HEADQUARTERS J U" S" AIR FORCE Contract AF 33(600)-31319

and

U. S. NAVY, ENGINEERING DIVISION, BUREAU OF YARDS AND DOCKS

UNIVERSITY OF ILLINOIS

URBANA} ILLINOIS

October 1961

iii

TABLE OF CONTENTS

1. INTRODUCTION .. 0 0 0 0 0 0 0

101 Object and Scope o~ the Investigation . 102 Object and Scope of Report 0 • 0 0 • 0 • 0 0

1.3 Development of Design Procedures for Two-Way Slabs 1.4 Acknowledgments 0 0 0 0 0 • 0 9 0

2. DESCRIPTION OF TEST STRUCTURE

2.1 Design of Test Structure .. 0 0 •

2.2 Description of Test Structure

3 · MATERIAI.S AND CONSTRUCTION

3·1 302 303 304 3·5 3.6

Reinforcing Steel 0 0 0 0 • 0

Concrete 0 0 • 0

Forrrrwor k Q • 0 .. .. 0 0 .. 0

Placement of Reinforcement Ca.sting and Curing . • .. . Final Condition of Structure

4.. TEST SErUP AND PROCEDURE .

4.1 Introductory Remarks 4.2 Loading System 403 Instrumentation 0 0 0

4 .. 4 Test Procedure and Chronology .. ..

5 .. BEHAVIOR OF THE TEST STRUCTURE " ..

5·1 5·2 5·3 5.4 5·5 506

Introductory Remarks Test 404 (1.0 LL + 100 DL) . Test 416 (200 LL + 100 DL) . Test 442 (Test to Failure) 0 •

Distribution of Strains Across Beams Curvature . 0 " • 0 0 .. 0 0

60 MOMENT-STRAIN REIATIONSHIPS

6.1 Introductory Remarks 6.2 Construction of Moment-Strain Curves 603 Use of Moment-Strain Curves ....

7 0 MOMENTS ACROSS FULL WIDTH OF STRUCTURE 0

Introductory Remarks 0 0 • 0 0 Q

MOments Based on Reaction Mea~~ements Moments Based on Strain Measurements Comparison of Measured Strain MDments with Static MOment

~

1

1 2 3 7

9

9 13

16

16 17 18 19 20 22

23

23 23 1"'\\, C'1"

28

30

30 31 33 35 42 44

46

46 46 47

50

50 50 52 53

iv

TAJ3LE OF CONTENTS (Cent 1 d)

80 MOMENT REDISTRIBurroN 0 0 0

801 Introductory Remarks 0

802 Beam~Sl.a-b Redistribution 0

8.3 Positive-Negative Redistribution 0

8~4 Lateral Redistribution 0 0 0 0 0 0

90 EFFECT OF LOADING PAT:rERNS ON MOMENTS AT VARIOUS SECTIONS 0 • 68

9.l Introductory Remarks 0 0 0 0 U 0 0

9.2 Effects of Checkerboard Loadings 903 Single Panel Tests.

lO 0 STRENGTH ANALYSIS 0 0 0 0

10 ,]. Introdu~tory Remarks 0 0 0 0 0

10.2 Panel Strength 0 0 0

10.3 Structu.ral Strength 0 0 0 0 c

10.4 Safety u

ll" SUMMARY u 0 •

J.~.l Te:s~s

12 .• 2 A!lalyses . r.

BIBL IOC:P.;J'EY

TABLES .

FIGi..1RES

68 68 71

72

72 73 74 75

77

77 78

80

82

v

LIST OF TABlES

Table No. Title

3.1 Concrete Properties

4.1 Tests on Test Structure No. 4

7.1 Moments Across Full Width of structure

8.1 Moments and MOment Coefficients for Interior Span

8.2 MOments and Moment Coefficients for End Span

9.1 Slab MOment Coefficients

9.2 Beam MOment Coefficients

Page

82

83

84

85

86

87

88

Yi

LIST OF FIGURES

Figure No" Title ~

2.1 Arrangement of Bottom Reinforcement in Test structure 89

202 Arrangement of Top Reinforcement in Test structure 90

2·3 Arrangement of Reinforcement in Beams in Test structure 91

2.4 Arrangement of Reinforcement in Columns of Test structure 92

301 Typ:"cal stress~Strain Relationship for Sla.b Steel 93

302 Typical Stress~Strain Relationship for Beam Steel 94

303 Representative Stress-Strain Curve, 4 by 8-in. Cylinder 95

3·4 Location of Concrete Batches in Test Structure No. 4 96

4.1 Location apr! Designation of Top Strain Gages 97

402 Lo~ation and Designation of Bottom Strain Gages 98

403 Location and Deaignation of Beam Strain Gages 99

404 Location ~Ld Designation of Deflection Dials 100

405 Over-All View of Test Structure and Loading Frame 101

406 View of West Side of Test Structure 102

407 View of East Side of Test Structure Showing Switch Bar~ 103

501 LClad.~Deflection C1.L::ves.9 Test 404} {loO LL + 100 DL) 104

502 ste~l stresses,)' Test 404" 98 pSf Applied Load. 105

503 S-t.2el St:resses,Q Test 404,9 98 psf Applied Load l06

504 Load~strain Curves} Test 404J (100 LL + 100 DL) 107

505 Crack PatternJ Test 4045 (100 LL + 100 DL) 108

506 Load-Deflection Curves) Test 416, (200 LL + 100 DL) 109

5·7 steel stresses J Test 416) 170 paf Applied Load ilO

508 steel Stresses, Test 416J 170 paf Applied Load ill

vii

LIST OF FIGURES (Cont Vd)

Figure Noo Title

509 Load-strain Curves, Test 416, (200 LL + 100 DL)

5010 Load-Strain Curves, Test 416, (200 LL + leO DL)

50ll Crack Pattern, Test 416, (200 LL + 100 DL)

5.14

5·15

5016

5017

5·19

5·21

5·23

5.24

5·25

5·26

Load-Deflection Curves, Test 442, (Test to Failure)

Load-Deflection Curves) Test 442, (Test to Failure)

Load-Deflection Curves) Test 442, (Test to Failure)

Load-Deflection Curves, Test 442, (Test to Failure)

Load-Deflection Curves, Test 442, (Test to Failure)

Schematic Diagram of Deflections at Maximum Load, Test 442

Steel Stresses, Positive Section, Interior Span, Test 442

steel stresses , Negative Section,- Interior Span, Test 442

Steel stresses, Interior Negative Sectionj End Span, Test 442

Steel stresses} Positive Section, End Span, Test 442

Steel Stresses, Exterior Negative Section, End Span, Test 442

Load-Strain Curves, Test 442

Load-Strain Curves, Test 442

Load-Strain CtL~es) Test 442

Load-strain Curves, Test 442

Load-strain Curves, Test 442

Load-Strain Curves, Test 442

Load-strain Curves, Test 442

Load~Strain Curves, Test 442

.~

112

113

114

115

116

ll7

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

Figure Nou

5,,31

5032

5033

5034

5035

5036

5·37

5 ·38

5039

5040

5041.

601

701

702

7·3

'7 0 l~_

705

801

802

803

8)+

"'-riii

LIST OF FIGURES (Cont ~d)

Title ~

Cracks in Spandrel Beams, Test 442 ~35

Composite View of Top of Test structure A~ter Completion of Testing 136

Cra::.k Pattern on Top of' Test structure j Test 442 137

Failux'e of Beam-·Column Connections J Test 442 138

Distribution of Compressive Strai.ns Across Top of Beams

strain Distribution in Interior Bea.m, ·Test 442

St.rain Distribution in Edge Beam,; Test 442

Curvat;~e Along Posi ti ve Sec.tion,:l Interior Span

G1JrYa·ture Along Negative Section) Lllterior Span

Cu.:.:~"\ra ture Across T-Beam Section, Test 416

Typie;al Moment-Strain Curve

R2:s,ction Moments Versus Applied Load

SLrain ~~m2nts Versus Applied Load

Loa.is ani Reactions on the Interior Panel

STYs.in Moments versus Applied Load., Interior Span

S+rain M::>m~nt5 versus Applied Load_5 End Span

Measur ed Moment versus Applied Load.9 Posi ti ve Section, lUTe"" ~ox S:pan

Moment Coefficients versus Applied Load} Positive Se-:'1:10n Interi.or S~"».

Meas"l..lred Mome~ts versu.s Appi.ied LoadJ Negati ve Sec.-tion., Interior Span

Moment Coef'ficients versus AJ?:P1ied Loa.d, Negative Section., Intierior Span

139

140

141

142

144

145

146

147

148

149

l50

151

152

i53

l54

ix

LIST OF FIGtJBE3 (Conttd)

Figure No. Ti tIe 'Page

8.5 Measured MOments versus Applied Load, Interior Negative Section, End Span 155

8.6 Moment Coefficients versus Applied Load, Interior Negati ve Section, End Span 156-

8. 7 Measured Moments versus Applied Load, Posi ti ve Section, End Span 157

8.8 Moment Coefficients versus Applied Load, Positive Section, End Span .158

8.9 Measured Moments versus Applied Load, Exterior Negative Section, End Span 159

8.10 Moment Coefficients versus Applied Load, Exterior Negati ve Section, End Span l60

80ll Moment Coefficients versus Applied Load, Interior Span 161

B.12 Moment Coefficients versus Applied Load, End Span 162

8.13 Slab Moments Across Positive Section, Interior Span 163

8.14 Slab Moments Across Negative Section, Interior Span 164

9.1 Loe.d.:.ng Patterns Producing Maximum Moments in Slabs v: th Non-Deflecting Supports 195

9.2 Stra.ir..s at a Discontinuous Edge) Test 405 (Panels ACEGJ Loaded) 166

9.3 Stra: !"'.s Along Center of an Edge Row of Panels, Test l.;} 5, (Pa:lels ACEGJ Loaded) 167'

9.4 s~a..::-.s JUong Center of an Edge Row of ' Panels, Test L)~} (Pa."1els BDFH Loaded) 168

9.5 Stra:::s hlong Center of an Edge Row of Panels, Test 4.)9, (Pa.."1el C Loaded) 169

906 S~a~ns Along Interior Negative Section of an Edge Ro1.' of Panels, Test 409, (Panel C Loaded) 170

1" INTRODUCTION

1.1 Object and Scope of the Investigation

Two types of floor slab construction are recognized by the Building

* Code of the Ameripan Concrete Institute (1) " Detailed. design specificati,ons

are given in Chapter 10 of this code for flat slabs with square or rectangular

panels" A second type of floor slab is defined less explicitly by this code

as fttwo_way systems with supports on four sides fi in section nine of Chapter 7

on flexural computationso

The entirely different methods of design presented in these two

cha:pters would lead to the belief that the two types of systems are unrelated,

whereas in fact the flat slab construction may be considered as a special case

of the two-~y system for which the ratio of the stiffness of the beams

supporting a :panel to the stiffness of the panel is zero" The dissimilarity

between the two design methods becomes more pronounced when the total design

moments for the systems are compared. A square panel in a two-way system is

designed to carry a total moment of 0.150 WL where W is the total load on the

panel and L is the span center-to-center of supports. This is 123 percent of

the static moment of 0.125 WL. On the other hand the flat slab may be designed

for as little as 72 percent of the static moment or only 58 percent of the

design moment for the two-way system.

This disparity between the two design methods has arisen primarily

as a result of the differences in their development. Flat slabs were built

before they were analyzed" Hence design procedures adopted by building codes

could do little more than reflect procedures proven acceptable by a long

history of satisfactory performance of flat slab structures" Design methods

* Numbers in parentheses refer to entries in the bibliography.

-2-

for two-way systems have been developed on the basis of analytical procedures

which took into account effects such as live load to dead load ratios and

loadings to produce maximum moments 0 The resulting higher design values for

two-way construction have penalized its use in favor of the empirically

determined flat slab design methods 0 This has led to the anomaly that.!)

because of thickness limi tations j the inherently stronger two--way system is

economically justified only for light design loads on the order of 100 psf

and under u A short history of the development of the current ACI two-way

design provisions is given in Section 1020

In order to 'develop a unified design method for floor slabs, an

e.xt,ensive theoretical and experimental investigation was begun at the University

of Illinois in 19560 The experimental phase of the investigation has included

the cons+:.lct·ion} testing and analysis of five multiple-panel, reini'orced

concrete fl.oor slabs 0 Each of the test structures contained nine 5-ft square

panels at"ranged three~ by-three 0 The structures tested are listed below c

10 20 30 l.L

)0

A A A A A

flat plate flat slab haYing drop panels and column capitals two-way slab having deep~ relatively inflexible beams two-way slab having shallowJ relatively fIeri ble beams fla~ slab reinforced with welded wire fabricc

The resul t.s of tests on the first three structures have been published

in previo~s reports (2,3 J 4,5) 0 Results of tests on the fourth structure are

reported herein Testing on the fifth structure has been completed and the

data are currenLly being analyzed 0

102 Object and Scope of Report

Test Structures 15 2,9 :3 and 5 were all designed according to the

ACI Building Code 0 In the design of Test structure No 0 4, the limiting

criteria assumed in the design were that the total design moment was to be

-3-

0.125 WL or 100 percent of the static moment and that the strength of the

structure was to be intermediate between that of the flat slab and the two­

way slab with deep beams. A detailed discussion of the design is given in

Chapter 2.

The primary objectives of the test program carried out on Test

structure No.4 were to determine Whether the serviceability, as determined

by stresses, deflections and cracking, and the safety, as given by the strength,

of a structure designed on the above bases were ade~uate.

The present report includes a discussion of the design procedure and

the resulting structure in Chapter 2. Materials, construction, test setup and

procedure are described in Chapters 3 and 40 The performance of the structure

is described in Chapter 5 for the 100 LL + 1.0 DL, 2.0 LL + 1.0 DL levels and

for the test to failure. The moment-strain relationships necessary for use

in the analysis of the test structure are discussed in Chapter 6 and the

moments across the full width of the structure determined using these relation­

ships Rre presented in Chapter 7. The redistribution of moments with increase

in load is cO:lSidered in Chapter 8" The effects of various loading patterns

on moments is sho~ in Chapter 90 A stre~~h analysis of the structure is

presented :'r. Chapter 10 and the report is summarized in Chapter 11.

1.3 Developr::ent of Design Procedures for TwO-Way Slabs

(a) De:fir1i tioD

Tvo-way construction is defined in Section 709(a) of the ACI Building

Code as " .... construction, reinforced in two directions, 0 ••• [that] shall be

supported by walls or beams on all sides" 0 Two design methods, which satisfy

all requirements of the section, are included 0 A brief history of the

-4-

development of these two methods and a comparison of some of the design moments

given by the two methods is included belowo A detailed study of these and

other methods is given in Reference 60

(0) Method 2

In point of time,9 Method 2 Vd>S the first method. originatedo Method 2

is a modification of the 1940 Joint Committee Report (7) Which in turn was a

modification of studies published by westergaard in 1926 ( 8) 0

westergaard published design moment coefficients for six different

types of panelss representing six different cases of continuity in a structureo

These coefficients ~re developed by Westergaard in the followin,g mannero

The maximum moments at critical sections of uniformly loaded square

panels having different conditions of continuity with adjacent square panels

were obtained from existing studies based on the theory of elasticityo Solu­

tions not a;vailable were determined from a superposition techni que 0 The

effects or partial loadings were considered in obtaining the maximum values 0

Wasterga&rd then devised approximate equations for rectangular panels by

fi tting 8, curve between the v-c.lues obtained for square panels and the coeffi­

cients "then in vogue for one-way slabs"

'me ma.xilIP.llTI values of moments thus obtained were reduced by 28 per­

cent as in tb.~ cas'2- of flat slab design 0 Then, considering the redistribution

of stresB~S th5;: cOl-ud take place with increasing load,;) the results of tests

on two-way slabs} and. the improbability that some loading patterns would ever

occUX'J he further reduc.ed the moments and prepared a set of design coefficients 0

Since all the analyses were based on the assumptions that the supporting beams

~re both non~deflecting and ~thout torsional stiffness, the final suggested

design coefficients provided for no moment at discontinuous edgeso The moment

-5-

carried by the supporting beams included all the moment not carried by the

slab. However, the 28 percent reduction in slab moment was not made until

after the beam moment was computed~

In 1940 the Joint Committee on Standard Specifications for Concrete

and Reinforced Concrete (7) published recommendations for the design of two-

way slabs that were primarily a modification of Westergaardts worko ~

major modifications ~re made by the Joint Committeeo The first of these . .

was the important stipulation that the slab and its supporting beams were to

be monolithic. This resulted in the proposal of moment coefficients at the

discontinuous edgeso The second modification was a limitation of the ratio

of sideso Whereas westergaard had suggested coefficients for ratios of

short to long span ranging from 0 to 1, the Joint Committee limited this

ratio to from 0.5 to 1.00

The design recommendations of the Joint Committee were adopted by

the ACI in 1947 for inclusion in the Building Code as Method 2J with only

slight modificationso The major change was the elimination of the proviso

that beams and slab were to be monolithic; despite the fact that moment was

still assigned to the discontinuous edgeo

(c) Method 1

Method 1 was developed by Jo Di Stasio and Mo Po Van Buren (9) for

the New York City Building Code and first appeared in the ACI Building Code

in 19360 The method, as it appears in the 1956 Code, is essentially the same

as when it was first adopted; with some changes for simplicity.

The method, as first developed; was basically an elastic frame

analysis consisting of three stepsc The locations of the lines of contra-

flexure were determined using an elastic frame analysiso Once the lines of

-6-

contraflexure were determinedJ the proportion of the lo~ carried in each of

the two orthogonal directions 'WaS determined 0 The moments and shears were

'then computed. using a rigid frame analysis assuming the structure to be so

loaded as to obtain maximum mom.entso For many cases ,the locations of the lines

of ecnt:::a..flexure and the moment and shear coefficients could be determined

directly from provisions given in the Codeo

Tbe moments at critical slab sections vere given by the formula~

-whsre I/f -..;as a one~way construction coefficientp X' A was the-proportion of the

lead cB:;ried in the A direction, w was the unit, load" A the clear span con-

side::>:,::;d. and 2A 'WaS a correction :factor or a factor to account for the non~

'imif..::r.'I1 d.i str:.oution cf loado All the moment not carried by the slab was to

be carri7d by ~he beams lying parallel to the span considered 0

Ir. the general method of' analysis the distribution factor r wa.s

a.ss':jmo::. i -:. va..ry in inverse proportion to the cube of the span between lines of

Yr:= locations of the lines of contrafl'SXtlX'e were determined

ITem a "lgld f~ 9.:1-:: '3-T'l9..~ysi5 'When only the span under consideration was loaded.

The a.dj1;::~r:l,::n· !9.:tor € 'Was assumed to l,e a function of the ratio of the short

to long siio:' of t~~ panelc

In ~he present edition of the ACI Code the factors e and r have been

combined ln~,: a coefficient C which depends on the ratio of sideso The term

(l/f) ap~ars ~s the factor. B and the wA2 as, WLo

(d) Comparison of Methods

As may be expected" the design moment coefficients prescribed by

Methods 1 and 2 assign different proportions of the total moment to the various

-7-

sections.. 'For a square interior panel supported. on' ide,al columns arid 'beams

haVirlg no: width, the moment coefficie.nts gi ven by the ~wo methods are as

'follows:

Section

Method 1 Method 2

POSe Slab

0 .. 0182 000206

Pos. Beam Neg. Slab

0 .. 0303 0 .. 0275

Neg. Beam

0 .. 0606 000606

Total

001508 0.1504

10 statics

120.6 120·3

This is the one case for which the two methods ~e in Glosest agreement. For

an interior rectangular panel having a ratio .of long to short span of 2 the

following coefficients are given~

Method 1 Method 2 Long s~an* Short Span* Long Span Short Span

Posi ti ve Slab 0.00 1 001043 000052 001037 Positive Beam 000586 000138 0 .. 0572 0.0417 Negative Slab 000067 o o 1616 000069 001383 Negative Beam 000852 0.0202 0.0833 000606 Total 001545 002999 0.1526 003443 % Statics 12306 23909 122.1 275·4

The values given above serve as ample evidence to show that the

present deSign methods call for unreasonably high values of design moment

coefficients. Not only is too great a total moment required but also the

distribution of the total moment among the various sections may be in error.

For instance Method 1 assigns an inadequate proportion of the total moment

to the beams in the direction of the short span for panels having a low ratio

of short to long span 0

104 Acknowledgements

The studies included in this report were made as part of an investi-

gat ion conducted in the structural Research Laboratory of the Civil Engineering

Department at the University of Illinois in cooperation 'With the following

organizations:

* All coefficients given as coefficients of WL where W = total load on panel and L = short spano

Reinforced, Concrete Research Council Directorate of' Civil Engineeringj Headquarters, UoSo Air Force General Serv5.ces Administration" Public Buildings Service Office of the Chief of Engineers,9 Uo So Army

The program of in'lestiga:tion has been guided by an Advisory Committee

on which the follo~ng persons have served~

La Ho CorningJ Chairman of the Advisory Committee; Portland Cement Association

GoB 0 BeggJ Jr" 51 Public Buildings Servi ce.9 General Services Administration

Frank Brown; Wire Reinforcement Institute, InCa ~J 0 Di StasiO, Sro J Consulting Engineer, Di Stasio and Van Buren

(Deceased) Ao So Neimanj) Headquarters} U 0 So Air Force N 0 Mo Newma.rkv~ Universi ty of' Illinois DoH ~ Plettaj Virginia Polytechnic Institute J" R 0 Powers, Headquarters J U" S a Air Force Paul Rogers; Consulting Engineer, Paul Rogers and Associates Eo J" Ruble.s, Association of American Railroads W 0 Eo Schaem.9 Office of the Chief of Engineers, U a So Army M u Po Va.."'1 Burenj . Consulting Engineer J Di Stasio and Van Buren C a A~ Willson, American Iron and Steel Institute

The over~all direction of the project has been made by Dr 0 CoP 0 Siessy

PrOf2BSC:: of Civil Engineering, and the immediate supervision by Dr 0 Mo A 0 SozenJ

Associat·e Professor of Ci til Engine,ering 0

In,~uable assistance in the instrumentation of the test structures

and. in -the. deve12pment &'1d operation of the data recording equipment was given

by Prof'essor V v.J 0 McDonald and his staff 0

The following resea~ch personnel have assisted in the const~~ction

and testing of the test strUcture and in the presentation of data~ We Lo Gamble,

Do Re ReyeS-Guerra, and Eo Jo Strougalo

-9-

20 DESCRIPTION OF TEST STRUCTURE

2.1 Design of Test Structure

( a) Introductory Remarks

Test Structure Noo 4 ~s designed to carry a uniformly distributed

load of 75 psf dead load and. 70 psf live load. 0 The 75 psf dead. load repre­

sented the 6-ino panel thickness of the assumed :prototype structure and the

70 psf li ve load. was taken as ty:pi cal for residential or offi ce type buildings 0

The design of Test Structure No 0 4 differed considerably from that

of the other four slabs in the test serieso Each of the other test structures

was designed on the basis of the controlling criteria as set forth in the ACI

Building Code. Test Structure No 0 4 vms designed on the basis of two funda.;;

mental criteria. The first of these 'WaS that the total design moment was taken

as the static moment of 00125 WL. The second was that the behavior and

strength of the structure were to be intermediate between the flat slab and

the two-way structure with stiff beams.

The selection of these two criteria is in keeping wQth the over-all

object of the floor slab investigation of determining a unified system of

floor slab design. The selection of the static moment is the only logical

choice. If it is desired to raise or lower this coefficient the same result

may be achieved morE directly by changing the maximum allowable working stress.

The second cri terion is in keeping wi th the philosophy of allOwing a deSigner

more freedom to design 0 As the code is now written the designer of a two-

way structure is forced to build stiff, deep beams because the code apportions

about 2/3 of the design moment to the bea.ms., If the designer desires shallow

beams he is forced to use compressive reinforcement.

-10-

(b) Safety and. Serviceability

The design of any structure is a blend of satisfying safety and.

serticeabili ty requirements 0 If design is made using working-stress methods

then serviceability is presumably insured if the maximum working·, stress and

tt.d.ckness limitations axe not exceeded 0 The factor of safety is then

apparently the ratio of the yield to the working stress 0 However.~ it is

becoming i.ncreasingly more recognized that the true strength of a structure

I-;an only be assessed by a limit method of analysis and that the true factor of'

safety of a .• str·ootm.''',e .m.a.v{-:3Q~y,.:.:be;·.4~j;.er:mi-nad from-. the_ ratio of the ultimate

.:~~paci ty~' to.> the~·:worY..i.ng.;;c·ap.~c1~y.;·~

Whi.le the strength and safety of a structure may be accurately

computed only by a consideration Of its ultimate capacity there still remain

the requirements cf serviceability 0 M9.ny different distributions of rein­

for~ement would still allow the attainment of the same strength 0 However J

some of these distributions would result in a structure that exhibited

unacceptable cracking and deflection at service load 0 Hence the reinforcement

must be dJ.,stributed to insure a serviceable as well as a safe structure 0 Since

at working loads a reinforced concrete structure may be assumed to be reasonably

1.ITeL, re:present,ed by an elast:i.c stru,ct-tl.re} a distribution based on elastic

analyses should be ad~quate 0 In the design of Test Structure No 0 4 the strength

of the structure was determined by a yield line analysis and the distribution

of the tensile reinforcement was based on elastic analyseso

(c) Strength Requirement

The distribution of moment between slab and beams is a function of

their relative strengths at the ultimate load level and of their relative

-11-

stiffnesses at the service load levels~ The optimum strength condition occurs

when the strength of a panel in a multi-panel structure is equal to the

strength of the structure as a whole 0 For a structure consisting of uniformly

reinforced square I>anels, the yield capacity of an interior panel is given as

W = yp

24 M ys L

and. that of the structure by

W = ys

8(~ b + M ) Y ys

L

where L = span

M = total moment in slab at yield ys

Myb = total moment in beam at yield

W = total load on panel at yielding yp

W = total load on structure at yielding ys

In order to have the two capacities equal it is necessary that

If the yield capacity of the beams is greater than twice the moment carried

by the slab then a panel failure 'Will occur 0 If the yield moment of the slab

is greater than one-half that of the beams then a structural mode of failure

is insured. The test structure was designed so that the panel strength was

greater than the beam strength thereby insuring a structural failure ..

(d) Distribution

The distribution of moment at 'Working loads is a function of the

relative stiffness of slab to beams. Once the relative stiffness is deter-

mined, the distribution of moment may be made on the basis of existing elastic

solutions. However, the determination of the relative stiffness is no simple

-12~

matter 0 In a monolithic structure it is difficult to define where the beam

stops and the slab begins 0 Inclusion of various amounts of the slab width

within the T-beam flange has a large effect on the ratios of relative stiff-

ness cO!Il.J!uted~ Also the cracking that accompanies increase in loading changes

the relative stiffnesso

For Test Structure Noo 4 the ratio of beam to slab stiffness was

taken as unity 0 For this condition Appleton (10) has determined that half'

the total moment should be apportioned to the beams and half to the slabo

This -was the distribution used in each of the nine panels of the test structure.

Since the edge beams had the same depth and stem width as the interior beams

the stiffness ratio may have varied somewhat from unity in the edge and corner

panels but this was not considered in the designo

After the total moment to be carried by each slab and beam section

was determined) it was necessary to divide the moment among the negative and

positive sectionso This division again w-as based on elastic analyses.,

simplify the design the structure was considered as containing two typical

spans 0 The first of these was the interior span, which included both spans

in the interior panel and _-the span in an edge panel parallel to the edge, and

the second was the exterior span which included both spans in a corner panel

and the span in an edge panel perpendicular to the edge 0 The negative to

posi ti ve ratio determined for the interior span was 2 to 10 For the exterior

span the ratio of interior negative to positive was 104 to 1 and for the ratio

of exterior negative to posi ti ve it was 0" 9 to 1 0

The spacing of the slab reinforcement across the 'Width of the panel

was taken as uniform., For the condition of equal slab to beam stiffness the

curvature is uniform across the width of the structure and hence a uniform

spacing i~ necessary 0

-13-

The .. above discussion indicates that the amount and distribution of

the design moment were different than that "Would be called for by conventional

design methods 0 In other aspects of design such as minirp.um cover, cut-off

points for rein:forcement, minimum steel percentages, etco, the stipulations .

of the ACI Building Code were follo"Wedo

2.2 Description of Test Structure

The test structure contained nine square panels arranged :3 by 3 °

Each panel measured 60 in ° from center to center of columns. The over-all

dimensions of the structure 15 ft - 4 ino square by 13 7/8 ino high 0 The

thickness of the slab was 1 1/2 ina All rein:forcement used in the slab con­

sisted of 1/8-in. square plain steel bars 0 The bottom slab bars were 55 1/2 in ..

long and were placed with the ends staggered by 4 1/2 ino The top slab bars

were 25 1/2 in 0 long and were placed with their ends staggered by 4 in. The

slab reinf'orcement was tied together in mats before placing in the slab 0 The

centerline of each top mat over an interior beam was placed 2 1/4 ino away

:from the centerline of the beam and toward the centerline of the structure.

The bars over the edge beams were 11 in. long with a 2 in. extension extending

down into the beam. The amount and location of the slab reinforcement is sho'WIl

in Figures 2.1 and 202.

The beams were all 3 in 0 wide and had a total depth of 3 in 0 The

reinforcement used consisted of the 1/8-ino square bars and Noo 2 plain round

bars. The bottom bars were 60 ino long 0 The top bars over the interior

columns were 30 in. long and the top bars at the edge cmd corner columns were

16 1/2 in 0 long with a 2 in 0 extension down into the columns 0 All reinforce­

'ment lengths and cut- off points "Were the same as in Test Structure No 0 3 0 The

-]4·~

spandrel beams were not designed to carry any wall load. 0 Stirrups were pro­

vided in all beams in an ef'fort to prevent shear and torsional failure 0 The

stirrups in the interior beams were U-shaped and were spaced at l-ina intervals~

Six stirrups 'W'ere placed at each end of each interior beamo The stirrups used

in the spandrel beams were U-sha:ped and in addition the six stirrups adjacent

to the columns were closed with inverted stirrups 0 The:s'ix closed ,stirrups,

were placed at 1 ino intervals and an additional ten open stirrups were placed

at· l 1/2 ina int.ervals a The amount and locat,ions of the beam reinforcement

and stirrups are shown in Fig 0 2 Q:3 0

The col1..m1IlS were overdesigned to prevent premature column failure 0

The col1.uTIIls were all reinf'orced with No 0 :3 deformed bars tied m.th ties bent

from the 1/8-i!L sqU3re stocko Number 2 plain rou-l1d bars were welded around

the top of each col'ID..."1 to provide additional anchoragea Each column was sup­

po!"ted C!j, a 3/ L l.n. thi ck st·eel plate wt.:.i ch rested on a steel ball a All

colUlDllS meas'.1Ied ::'3 '7/8 inQ from the top of the slab to the center of the

ball" The :r:te;::::':." C01U1"['JlB were 6 :Lna squar,s~, the corner columns were 4 in·o

squars j a:-.i tt.:: r~e columns were ·4 ino by 6 ina The length of the columns

was chose!) J... ~ ~.,:l: t ~e sti ffness of one col.umn in the test structure would be

cOI1J])ara:cJ ~- • '" .... :" !:~ !.!'frl~sS of' two columns in the prototype structure, one

above th~ :::0: e.:~ O:1e below, each colum.1J. having its far end fixedo The

amount ani :"'"':'7 ~('=ent cf the rein:forcement in the columns is shawn in

Figo 2).L o

It Eho'~j be no~ed that in the design. of the test structure j little

reference was rrYI-1.~ to the prototype structure 0 If a prototy:pe structure had

been designed it would have been a nine panel structure arranged 3 by :3 with

a center~to-center of column span of 20 ft and a slab thickness of 6 ino This

-15-

'Would have represented one intermediate floor in a multi-story bUilding having

a story height of' 8 f't center-to-center of slab. The only considerations of

the prototype structure made in the design of the test structure were in the

proportioning of' the column lengths for the desired stiffness and in the pro­

portioning of the dead load. Hence the test structure is a true structure in

its own right and. is not a scaled down model of a prototYJ;>e.

~16~

30 MATERIALS AND CONSTRUCTION

301 Reinforcing Steel

(a) Slab Reinforcement

The reini'orcing steel used for the sla.b reinforcement, the stirrups,

and for part of the beam reinforcement consisted of intermediate grade} 1/8-in"

square ba:rs 0 Tensile test specimens cut from these bars were tested in a

hydraulic testing machine equipped ~th an automatic load-deformation recordero

Trie stress-strain curves obtained exhibited the sharply defined yield point

and flat yield plateau commonly assumed in yield line analysis 0 The average

yield point was 47J 600 psio A representative stress-strain curve is given in

Fig 0 3010

In order to prepare the square bar reinforcement f'or use it was

necessary to remove a heavy coat of mill scale 0 This 'Was accoUlJ?lished by

washing the steel in a hot bath of 50 percent hydrochloric acid solution}

brushing it with a stiff wir'e brushp rinSing, and then placing the steel in a

fog room 0 'W.Dll·2 in t.he fog room the reinforcement was turn over every two days

to insure uniform T"l.lsting 0 After removal from. the moisture roomJ the steel

was washed.;, dried., and brushed to remove all loose rust 0 The :final appearance

of the steel sho~ed small pits which improved the bond qualities of the rein­

forcement"

(b) Beam Reir~or~ement

~ne reinfor~ement used in the beams consisted of l/8-ino square

barsJ as des::ribed above,? and 1/4-ino diameter plain round bars 0 stress­

strain curves obtained using the automatic recording device showed a short,

c.urved transitional phase from the initial elastic region to the :fl'at; plateau

-17-

of" the stress-strain curve 0 The average yield point of this steel was 50, 000

psi. A representative stress-strain curve is shown in Figo 3020

'When received, the bars were coated with a film of grease 0 This

was removed "With solvent and the bars were then treated with hydrochloric

a.cid and placed in the fog roomo After this treatment, the surface of the

bars :,was pitted.

(c) ,Column Reinforcement

The column reinforcement consisted of Noo 3 deformed bars having

a yield point of 55, 000 psi 0 The bars were clean and required no treatment

before use. The column ties were bent from 1/8-in. square bars.

302 Concrete

The small sizes of the sections used in the test structure and the

clearance requirements necessitated the use of a mix containing only small

aggregatee The mix design was further controlled by the criteria that the

28-day concrete strength was to be at least 3,000 psi, that the mix was to

be easily workable, and that excessive bleeding was to be avoided. Since the

mix used in this test structure was similar to those used in previous test

structures, no trial batching was necessaryo

The concrete was mixed in 600-lb batches in a 6-cu. ft, non­

tilting drum, rotary mixer. The aggregate used was 80 percent coarse Wabash

River sand by weight and 20 percent fine lake sand, with a maximum aggregate

size of 1/8 in. The fineness modulus of the blended aggregate was 2.80

Alpha brand Type I cement was used. Sixty-six 2 by 4-ino cylinders were

cast from the ten batches of concrete placed in the test structure. In

addition, modulus of rupture beams and 4 by 8-ino cylinders were :cast fr0m

every second batch 0 The modulus of rupture beams contained no reinforcement

and were ~8 by 1 3/4 by 1 1/2 in.

=18a>

The :first load. test was perf"ormed 50 days after the structure was

casto At this time 39 of the 2 by 4=ino and lO of the 4 by 8~ino cylinders

were tested 0 The average strength of the small cylinders was 3550 psi with

values ranging from 2540 psi to 4270 psi 0 The average strength of the 4 by

8-ino cylinders was 4090 psi with values ranging from 3920 psi to 4200 psio

The average value of the initial modulus of deformation was 303 x 106 :psio

A typical str>ess-strain C1.lrITe for the concrete is given in Figo 3,,30 A

summary of the water·~cement ratios and st~ength pro:perties is given in

Yne reQaining test specimens were tested at the completion of

Test h.42 j 92 days af"t·er casting 0 The a,yerage strength of' the 26 2 by 4-in 0

cylinders wa~ 3900 psi 'wi th values ranging from 3080 psi to 4710 :psi 0 The

average streTIgth :::f the ten 4- by 8~in 0 cylinders was 4360 :psi -with a range

of values fr:JO 3720 psi to 5060 psi ~ Test,s of 11 modulus of rupture beams,

loaded 3."t "the t~r1 points) gaye an ayerage c<Jalue for the modulus of rupture

of" 940 ps i Vl ~ ~ all valu,::s lying between limits of 860 and 1020 psi 0

w,..· :>f :~"= !ormwork 'WaS cut from .3/4~i.no plywood sheetso The

bot·t~m E!;-:-"· s ~:; .... ~ o. sla~ s':;ctions we:r= sup]?orted by 2 by 6~ino stringers

and on The. 2 by 6-ino stringers were in turn su:pported by

4 by 6- in b-ea.;:'..: V=-...:..:h y,=sted on the reac:tion piers and the tie~beams of

the r'23.:~ io!". f:r .0..::1(:

Steel C!~~elE were used in the const!~ction of the outside edge

of -the form in orde:" to gi1Te a rigid. and uniform outside edge and. to establish

a stableJ plans refer2nce surface for the placement of the remaining formworko

-19-

The remaining edge beam forms were bolted to the edge channels. The bottoms

of' the edge beam forms were cut from 2 by 6-in .. stock. The interior beam

forms had bottoms cut from 2 by 6-in" stock and sides of 3/4-in .. plywood.

The column forms were assembled from 3/4-ino plywood and 2-in.

stock. The column forms fitted on a 3/4-in. thick steel plate that contained

a recess to fit on the polished steel ball on the tripod reaction dynamometer.

Each plate had 2-in 0 pieces of" No. 3 bar welded to it so that the pieces

extended upright wi thi.D .. the column form.. These provided for the transfer of

horizontal thrusts from the column to the dynamometer 0 A one-inch diameter

hole was cut in one side of the bottom of each form to check that the columns

were completely filled with concrete during castingo

The formwork was carefUlly aligned and leveled to give the best

possible dimensional control. Bracing was supplied against the reaction

frame and supporting piers to give the necessary rigidity.

After the forms were completed they were coated with "Slippi t ff form

oil.

304 Placement of Reinforcement

The column reinforcement was assembled in cages to aid in its place­

ment. A No. 2 round.. bar was welded around the top of each column cage to

provide add..itional bond strengtho

The positive beam reinforcement and stirrups were tied together

before placement in the slab. The posi ti ve beam reinforcement and column

cages were placed at the same time as it was necessary to mesh them together.

Most of the posi ti ve beam reinforcement 'WaS cut off at the face of the

column cage to facilitate placement 0 Af'ter the column and posi ti ve beam

=20-

steel had been tied in place} the negative beam steel was woven into the

stirru.ps and column cage and tied in place 0 The 1!4-in 0 bars 'Welded around

the tops of the column cages were cut where necessary to allow the beam

steel to pass th1::'ough ~

The slab reinforcement was assembled. into mats -with the aid of

jigs before placement in the structure 0 About three~fourths of the bar

intersections of the positive mats and all of the intersections of the

negative mats were tied 0 The nine bottom mats and the 24 top mats were

held in place by spacers cut :from 1!4~ino square steel bars 0 These bars

contained 1/S-ino square slots cut at the correct height to insure proper

posi tioning 0 The spacers that held the top steel in place were also clipped

to th2; bottom steel 0 The mats 'Were supported and tied to the forms at

numerous points to insure that the steel would not be displaced during the

placing o:f the concrete 0

Cork blockouts were tied to the beam and slab steel at each point

at which a strain gage was to be placedv These blockouts were attaChed to the

p08iti~5 beam and all the slab reinforcement before the steel was placed in

the slat· and to the negative beam steel af"te.r it had. been tied in place 0 All

ba:rs we:r8 smoothed. wi.th an ele·~tric grinder -before the cork blocks were

att,acned 0 In the case of the posi ti ve beam steelJ the cork blocks also

served as space~so

3 e 5 Casting and Curing

Th~ slab -was cast on 24 May 19600 Ten 600-lb batches of concrete

'were requiredo Mixing 'WaS staxted at. 8~30 aomo and the last batch was

placed by ll~40 aome

-21-

The concrete was mixed for three minutes, removed :from the mixer J

and test cylinders and b~ams \rere cast. The concrete was placed one bucketful

at a time) :pushed into place by hand, and vibrat~d with electric vibratorso

Prio~ to the placemen~ of the concrete three temporary pipe screed rail~ had

been placed across the slab dividing . it into four parallel strips <> The

location of the screed rails and of each of the ten batches of concrete is

shown in Figc 3.40

The concrete in the columns and beams 'Was carefully consolidated

by placing the vibrator on the inside of the form as the concrete was placed

and then on the outside when the form appeared full 0 The concrete in the

slab was consolidated using a vibrating screed made by attaching an electric

vibrator to a four-inch cbannelo After the adjacent strip had been placed

and vibrated, the concrete was given a second screeding using a wooden finish­

ing screed. A:fter two adjacent strips had received their finish screeding,

the temporary screed rail was removed and the remaining trough -was filled

with concrete and troweled smootho The final finishing consisted of troweling

with a steel trowelo

Eight hours after the casting had been completed, the structure

was covered with burla:p and wetted dO"¥.nlo Twenty-four hours after casting,

the test speci~ens "Were removed from their f'orms and placed on the slab

under the bur lap. The burlap was kept wet for seven days. The burlap was

then removed and the forms struck 0 The entire surface of the structure

was then painted with ''Traffic White tI paint to reduce moisture loss. The

test specimens were painted at the same time and stored under the structure.

-22-

3.6 Final Condition of Structure

After the formwork was removed the structure was examined for voids

but none were found 0 Prior to the beginning of testing the thickness of the

slab 'WaS measured at 8l points located at the cri tical sections 0 The average

thickness 'Was 1048 ino which -was 99 percent of the design thickness of

1.50 in~ The ma.x:i.nrum deviation was 1/8 ina and the average deviation was

1/64 ino

The slab was examined for shrinkage cracks before the loading

eCluipment 'Was placed but no cracks were found 0 The corner columns had.

lifted off the tripod reaction dynamometers because of shrinkage and it ~s

necessary to shim the dynamometers up about 1/32 ino until contact was

restored 0

~23-

40 TEST SETUP AND PROCEDURE

4.1 Introductory Remarks

The test structure was constructed on the same reaction frame used

for the three earlier test structures 0 The loading frame, hydXaulic system"

instrumentation, and test procedure used ~ere nearly identical to that used

for Test structure No.3 (4)0 Therefore, it is necessary here to describe

only the general features of the test setup and procedure 0 Detailed descrip­

tions of component parts are contained in :previous reports 0

A description of the essential features of the loading system is

contained in Section 4020 The instrumentation is described in Section 4.3

and a discussion of the test procedure and chronology of testing is pre­

sented In Section 4040

4.2 Loading System

The test structure was constructed in place on the reaction frameo

This frame consisted of concrete :piers 18 ino square and 5 ft high which

were tied together at the top wlth steel beams cast in the concrete to resist

overturning forceso

Load was applied tc each panel by a single hydraulic jack 0 The

load was distributed equally to each of the 16 steel loading plates on the

panel by a series of five H-frarnes constructed of steel bars. The steel plates

were 8 by 8 by 3/4 in. and rested on 3/8-ino thick sponge rubber padso The

sponge rubber pads helped to insure a uniform distribution of load and reduced

lateral forces 0 A small H-frame ·was placed on top of each of the four sets of

four loading plates. A large H-f'rame was placed so that it rested on the

centers of the smaller H-frames and so that its center lay directly over the

center of the slab 0 The large H-frame also served as a beam. dynamometer for

the measurement of applied load a A smaller ring dynamometer was placed on

the center of the large H=frameo All connections between steel plates and

large and small R~frames consisted of one-inch diameter steel balls fitting

into 3/8-ino deep recesses 0

Each of the hydraulic jacks was suspended from one o~ the three

steel bents which crossed the slab in a north-south directiono The verticals

of the frame were IO-ino 'WF sections,9 which were bolted to the floor, and

the cross beams ~re 18~ino channels 0 The lower flanges of the channels

served as supports for the two carts suspended above the slab for use in

searching for crackso

The hydraulic system consisted of the nine 20-ton capacity jacks,

an electric hydraulic pump, a control manifold, and the- necessary hoses and

f'i ttings 0 The control manifOld contained valves so that each jack could be

cut off :from the system thus allOwing the structure to be loaded in various

patt,erns 0 An over-all view of the structure shOwing the loading equipment

and. reaction frame is given in Figo 4050

403 Instrumentation

Instrumentation was required for the measurement and recording of

strains>, deflections) aPl?lied loads3 and reactions 0

(8,) Strains

strains were measured at 310 locations on the reinforcing steel

and at· 54 locations on the concrete. There were 82 gages on the positive

slab reinforcement) 116 gages on the negative slab reinforcement.~ 37 on the

posi ti ve beam steel a...l1d 75 on the negatiye beam steel 0 All gages on the

steel were Type Al2 SR-4 electrical resis~l1ce strain gages having a nominal

·";;25-

gage length of' one-inch and a trim width of 1/8 ina The gages on the concrete

were Type A3 SR-4 gages. The location and designation of' all gages is given

in Figs. 401 through 403 <> All gages were mounted using Eastman 910 a.cThesi ve ..

Since the structure was symmetrical about both centerlines and both

diagonals only one-eighth of' the structure required instrumentation. However,

three panels were fully instrumented, two others ~e almost f'ully instrumented,

and the remaining panels contained gages at critical sections as checks ct

In the fully instrumented panels strain gages were placed on the

positive slab reinforcement along the c~nterlines and at the quarter points

of the panels, and on the negative slab reinforcement centered over the faces

of the beams supporting the panel 0 Gages were placed on the posi ti ve beam

reinforcement at t~e centers of the beams and on the negative beam reinforcement

centered over the faces of the columns supporting the beam.. The slab gages at

the panel quarter points were omitted in the panels that received only partial

instrumentation. The panels that were instrumented only as checks contained

two gages at t!1e center of the panel and one at the center of each side. In

addition the partly :nstrumented beams contained one gage at the positive

section fL~ O~e at each of the negative sectionso

(b) Deflect~o~s

T'!le Y~:-~ica.l deflections of the structure were measured at the

centers of eac!"~ c! t...~e 24 beams and 9 panels with O.OOl-in. dial gageso The

locations a~ des:b~tions of the deflection dials are shown in Fig. 4.4.

Tors~o~bl rotations were measured on the west edge beam during the

test to :failure. Pairs of 0 .00l-in.. dial gages were :placed at the centers

of an edge and a corner panel spandrel beam and at the centerlines of an edge

and a corner column.

( c) Load Measurement

The load. applied to the structure was measured by two sets of load

dynamometers 0 One set consisted of the 5-ino WF beams that formed part of

the larger H-frames used in. the load distribution system 0 The second set

~s a set of ring dynamometers3 each of which consisted of a ring of T-l

steel sup:ported on steel balls and mounted between two steel plates 0 One

ring dynamometex was placed directly above the center of each beam dynamometer 0

Strain gages were mounted on each dynamometer and were wired to

form a four arm bridge 0 The beam dynamometers had a sensi ti vi ty of 90 Ibs

per dial division on the strain indicator" The ring dynamometers had a

sensi ti vi ty of' 25 Ibs per dial. division 0 The strain indicator was read to

-within 1/2 dial. division so that the load 'WaS read to 0,,5 psf 0

( d) RI5action Measurement

The column reactions were measured at each of the 16 columns with

a tr"ipod. dynamometer 0 These dynamome-tex's were instrumented with strain

gages and were calibrated to give the vertical reaction and the horizontal

react·ions in tw:> orthogonal directions" The reaction dynamometers were

bolted to st.eel plates "Which were fastened to the tops of' the concrete piers 0

Each t:ripod was recessed at the to!, to contain a 3/4-.ino polished steel ballo

Each ball in turn fitted into a recess in the steel bottom plate of the

column. supported by the dynamomete~o The vertical sensitivity of the dyna­

mometer was 60 lb per dial division and the horizontal sensitivity was 40 lb

per dial division on the strain indi.cator 0 A view of the underside of the

structure showing the tripod dynamometers and deflection dials is shown in

Figo 4060

( e) Reading and Recording

All strain gages were wired to a large s~tchboard which contained

one switch point for each strain gage, load dynamometer) reaction dynamometer

leg} and.. check gage. A switch point was also provided for each dummy gage

needed to match the different types of strain gages. The check gages were

strain gages mounted on a steel plate. They were read before and after

each load increment to provide information on the magnitude and direction of

electric drift during testingo A view of the switch bank is sho'WD. in Fig. 4.70

The switch bank was connected to a strain indicator which was

balanced semiautomatically by an external servomechanism mechanically coupled

to the indicator. The strain reading which appeared on the strain indicator

was fed into an analog-to-decimal converter unit 0 Each strain reading 'Was

then punched into an IBM card and typed out by an automatic typewriter. The

strain data} including computation of reactions, were reduced using IBM

equipment.

The load dynamometers were read and recorded manually be~ore and

a:fter each load increment 0 Including the 18 load dynamometers J there were

465 strain readings taken for each load. increment. About 30 minutes were

required to apply a load increment, read and record all data.. About 100,000

strain readings were taken in 44 tests ..

Other data taken during each load increment included the de:flection

dial readings, oil pressure} and time at the beginning and end of each load

increment, and general information on the behavior and cracking of the

structure.

4 a 4 Test Procedure and Cbronolog;[

Ca) Test Procedure

-28-

Each load test performed on the test structure consisted of

meas1..lring and recording the zero load readings for each of the strain gages

a..11.d deflection dials J applying load in the desired pattern, and again

reading and recording all strain and deflection readings 0 The load was

applied in i.ncrements and the strain and deflection readings were taken for

each inc1:'e!I1ent 0 .A...ft~r the desirEd maximum load. 'WaS attainedy the structure

was unloa.ded and z~o readings recorded 0 The structure was then reloaded

in one increment to the maximum load. level previously attained and readings

wer'2 r'2ccrded Q The load. was then removed and zero readings taken 0

If 'the a:r:~lied load or loading pattern vas expected to cause moments

b.ig]:-.i.eJ: tb3.n ttoS? previously attained} the structure 'WaS examined for cracks

wi th th? aid. ':': e s~ven-po'We:!:' lens 0 Any cracks found were marked 'With pencil

and tb? ~·eS1: n'=.~er and load inc.rement, were recorded by the crack"

(b) Cb:ror .. o2.c~·

Fe· ... ,: .. -j·· fo'z lead tests wer,=: pe:!'formed on the test structure during

t,he pericd :'T .:)'::: - J1~:: 1960 to 19 September 1960 c Test 400 consisted of the

meaSlJTeneut5 • :~'."?r-. before and aft,er the load distribution system was placed

:'e~ t U04 was the f.':i.rst test in which the total load on

the 8ty-UC''t'.L''"~ reJ.,:!1ec. ":!iE' design level o~ l45 psf 0 Tests 405 through 415

consisted o!' ~:':-...-=:e pa:le1 and ~checke.rboard~j tests at the design load levelo

Tests 416 ~~d ~:~ ~e~e the first tests during which the total load on the

structure :reached the 2.0 LL + 1. 0 0 DL level of 215 psf 0 Tests 418 through

441 were single panel and pattern loading tests at the 200 LL + 100 DL levelo

· .. 29-

Test 442 was the first test to failure. The total applied load attained was

approximately 425 psf for a total load of 466 psf 0 Test 443 was the second.

test to failure. During this test the middle and. south strip were loaded to

failure. A complete chronology is given in Table 401.

-30-

5 0 BEHAVIOR OF THE TEST STRUCTURE

501. Introductory Remarks

The behavior of a reiriforced concrete structure, as it is subjected

to load) is described by the formation of cracks and the resulting crack

pa,tternss the deflections of the structureJ and measured steel strains and

the cor~esponding stresses 0 Related elements that co~tribute to a study of

the beha"'"n.or are the com:puted curvatures fo::;' various sectionS and the sequence

of yi s:di.ng of the reinf'oreement as the ultimate :Load carrying capacity of the

struct::n:'e is approached 0

A discussion of the behavior of the test st~~cture is necessary in

o:;::cd. -:::::' -:0 show how "Well the governing criteria f'or maximum allowable deflections

fu~d s~~~s~e=) as given by the ACI Building CodeJ were fulfilled by the test

S~:r':lct'j:re at se:vi.~e loadsJ and to indic8~te the mode of failure as the

st-r'.:c-:· ... - = wa~ loaded to its ul t,ima.te capacity 0

Th~ beh9.vior of the structure in Tests 404)1 416 and 442 is discussed

in thE f~llc·Vi ng sectiens 0 Test 404 "Was the test to design loadJ Test 416 was

th~ tes-: :c 2 0 1: ~ 1.0 DL and Test 442 ~was th.e test to failure 0

:0 .:;.':'::plify fu\"ther discussion) each of the beam sections considered

is gi V'=r! a mr..e:- i ,:a.l d.esignation as sho-wn in the sketch below 0 Sections one

-t·hrO"J.gh "! 1"'': 8,. .. ~ 5 e :-ti:·~ in a spandrel beam and sections six thr°ough ten refer

to an lnterlor beal:L Slab sections axe designated as sections -wi thin an edge)

coZ'ner~ ~r interioT panel" Negative sections were taken at the faces of columns

or be~ a~~ P0sltive sections at the center of the spanso

Spandrel Beam Sections

-- Int,erior Beam Sections

5.2 Test 404 (1.0 LL + 1.0 DL)

(a) Loading

Test 404 was the first test in which the structure was loaded to the

design load level. The maximum load that had been. applied in previous tests

was 60 psf. Load was applied in three increments of approximately 60, 20,

and 20 psf for totals of 58, 81 and 98 psi'. The sum of the dead load and the

highest level of applied load was 139 psf which was four percent less than the

total design· load of 145 psf. Deflection measurements and strain readings

were taken at each load level.

(b) Deflections

Typical load-deflection plots are given in Fig. 5.1 for several

points on the structure. The load-deflection relationships for the thirty­

three points on the structure, at which deflections were measured, were all

nearly linear.

The largest deflection measured for the applied load of 98 psf was

00043 in. at the centers of panels A and Co The deflection caused by the

dead load was 0.015 ino J giving a total short-time deflection for 139 psi'

of 0.058 in. This corresponds to one thousandth of the span center-to-center

of the columns, a deflection to span ratio that would be acceptable under the

most rigorous requirements. Eighty-five percent of the maximum deflection

caused. by the applied load was recovered within 24 hours after its removal.

(c) Steel stresses

Steel stresses are shown plotted along one-half the width of the

structure for the five typical sections of the structure in Figs. 5.2 and 5.3.

For clarity, the stresses measured in the beam steel are shown continuous

or32..,

'Wi tb, those of the slab reiTl..:forcement 0 The stresses sho'WIl were obtained from

the strains measured for the applied load of 98 psf by taking the modulus of

elastici t,y as 30" 0007 000 psi c

The maximum stress measured ~uring the test was 8600 psi at the

posi ti V"'c section of the beam between panels B and C 0 For the total load of

139 psf..'! this would be 10,700 psi 0 The maximum stress measured in the slab

reinforcement was 5300 psi at the interior negative section of panel F (Gage

F41.) 0 The total. stress at this gage for 139 psf was 6000 psi 0

TbP relationship between applied load and measured steel strain is

gi yen in Fig? 504 for a number of gages c Ttie nearly linear relationship for

some gages,9 such as E23 and CN3.9 1.s t:y"pJ.cal for u...'1.cracked sections" The

sharp -t·:r.eak in the load~8train cu;:::"Yes for gag'e2 GNl j CFl., etc OJ indicates that

the sec~ion8 sor~esponding to theSe gages cracked betw~en loads of 58 and

8~ rsf" The brok~~n lines connect; the measured residual strain to the maximum

p:Ji:.J.t on -t·h~ CUI'iTe" The discussion of the cracking that occurred" gi ven in

~<rl.e following section; is based up~n obseJ':'.rat,ions of the load~,strain curves 0

(d) Sequen:~.E of Cracking

At the beginning of Test 4045' the structure was uncrackedo At a

load c-£ 52 psf:. cne=r~,lf of the beam secticns '7 and. all of the s~ctions 8

cra::ke·:i 0 itt 8, load. of 81 psf the :rest of the sections 7 cracked,? all of

the sections 6 and 9 cracked as well as some of the sections 2y 3p and 100

At 98 ps~'the ~emaiTl~r~ section 10 and a few more sections 2 and 3 cracked 0

At -this 1.0 ad. the: fir~:st cracking of" the slab occ-urred at negati ve sections

clo8e t,Q the beams in seye!"al~ panels 0 Cracking at all sections was determined

from the change in shape of load.~ strain ~uryes v The structure was examined

-33-

with the aid of a seven-power magnifying glass but no cracks could be foundQ

The cracking that was detected with the help of the strain gages in Test 404

is shown in Figo 5050

5.3 Test 416 (200 LL + 100 DL)

( a) Loading

Test 416 was the first test to a load level of 200 LL + 100 DLo

Tests 405 through 415 consisted of various loading patterns at a load level

of 100 LL + 1.0 DL. Load was applied on all panels in increments of approxi­

mately l04, 35 and 35 psf" The three levels of applied load that were attained

were 102, 138 and 170 psf 0 The maximum total load reached was 211 psf 'Which

~ two percent less than the 200 LL + 100 DL total of 215 psfo Deflection

readings and strain measurements were taken at each load level.

(b) Deflections

Typical load-deflection plots are shown in Fig. 5.6 for several

points on the structure 0 The curves shown do not include the residual

deflections that existed at the beginning of Test 416. The load-deflection

curves for all points on the struc.ture showed a sli~t decrease in slope

wi th increase in load 0 The maximum deflection in a load test considered

allowable by the ACI Building Code (1) is L2/l2.9 OOOt where L is the span,

t is the thickness of the slab and all dimensions are in the same units.

This requirement would limit the allowable deflection of the test structure

to 00200 in 0 The maximum deflection measured during the test was 00078 in 0

at the center of panels A and Jo Inclusion of the dead load deflection

raises the maximum deflection to 00094 ino which was less than one-half of

that allowed based on the loading test criterion 0 While the load remained

on the structure for only about one hour,., rather than the 24 hours called

for by Section 203J it is apparent that the structure more than adequately

fulfilled thi s requirement 0

The proposed load. test criteria for the edition of the ACI Building

Code to follow ACI 3l8~56 at"e that the t,otal test; load is to be taken as

lu7 LL + 103 DL and that the maximum permissible deflection is L2/20,oOOt

if the re('o~T'~ry ~riterion is to be waived" The results of Test 416 can be

:proje~lE·d. -t:o com:pare "'tdth theBe criteria" Accordingly, In7 LL + 103 DL =

21605 psfu Since in later tests increase in load up to 21605 psf resulted

in an essentially linear load-deflection relationshipj the maximum deflection

mea3~~ed in Tes~ 416 for 211 psf can be extrapolated linearly to yield

00096 in, 0: say 001 in" f'or 2l605 pS~o This is still smaller than the

allO'wa.b~~ 2 of 0,12 lno based O:l L /20J OOOto

(c) S~-=-el S-:T€sses and. Stra.ins

PIG'":5 of s"t,eel stresses aJ:'e shown in Figs, 507 and 508 for the

fiy= Tvpi:a..:. 5ec.tlons of the test st.!"uctureo The stresses sho'WD. a.re those

measu-:'".;:1. f:;:- :':1~ 3.pp1ied l~ad. of' 170 psi' an~i do not include residual and

Tn.::: maidm1lID stress measured during the test 'W""8.S

~J.~ resii'.l5.l stTains accT'"lled "GO the begilli"ling of Test 416 were

one- £1 ftc :-: ~:Jt =-"t-rains measured at the applied load level of 170 psi 0

TrJ.is ~a-:::..: "''''SI.E ::'8.sed. an t.hE residual deflections as discussed in Section 7030

Inclusi~D ~: the dead load stress and the residual stress results in a total

maximum stress af 17,700 psi caused 'by the full load of 211 psf (200 IJ.., +

·~35-

Typical load-strain curves are given in Figo 509 for several gages

on the slab reinforcement and in Figo 5,10 for strain gages located at each

of the ten beam sections 0 The linearity of some of the load-strain curves,

for exam:ple C33 and F53, is typical of uncracked sections 0 The large strains

for Gages B35 and E55 indicate that the slab steel at these :points 'Was working

wi th the beams ..

Cracking

Very little additional cracking occurred at a load level of 102 psf

in Test 4l6o At a load of 138 psf some of the remaining beam sections 2, 3,

and 4 cracked as well as some of the negati ve slab sections 0 By the time

the maximum applied load of 170 psf had been reached all of the beam sections

1 had cracked, additional cracking of negative slab sections had occurred,

and the first cracking of positive slab sectionsJ in the corner :panels and

in the span of the edge panel perpendicular to the spandrel beam, was detected.

At the end of Test 416 all of the beam sections were cracked 0 Figure 5 <> II

is a plan view of the structure showing all of the sections that were cracked

at the end of Test 4160

5.4 Test 442 (Test to Failure)

(a) Test Procedure

Test 417 was the second test with all panels loaded to an applied

load level of l74 psf (200 LL + 1,,0 DL) 0 Tests 418 through 440 consisted

of single panel and checkerboard loadings at the same level of applied

1000.0 Test 441 was originally planned as the test to failure but it was

necessary to discontinue testing after an applied load level of 174 psf

had been reached because of malfunctiOning of the strain reading equipment 0

In Test 4·42 load. was applied in eleven increments in a period of 17 hours 0

The levels of applied load. that were reached are shown in the following

table 0

Load Number Beginning Load; psf Final Load, psf

, 39 )9 ..L.

2 108 108 3 182 182 4 250 249 5 290 290 6 321 320 7 346 345 8 375 364 9 405 374

10 422 Not taken 11 425 373

The load measured at the beginning of a reading period ~ measured

wit.h the ring dynamometers wr.s.ile that measured at the end of the period was

based on both the ring and the tripod reaction dynamometerso At most load

levels the load measured at the beginning of the reading period was within

one or two percent of that measured at the end of the period., At higher

load levels t.he diffe.rence was larger;> as shown aboveJ primarily because of

relati Yely highe:r' loss of oil from the hydraulic loading system at higher

loads~ and because the tendency of the structure to creep from under the

load was more pronoun·:;ed at the higher load levels 0

Defle~-:·ion measuremen.ts a..11.d strain readings were recorded for each

load increment ex::ept for load. ten u BecalLse of the lffi"ge loss in load for

load nine) after load t.en was applied only the deflections and load dynamo-

meter readings were taken 0 Four :pairs of deflection dials were mounted along

the west side of the slab to measure rotations at the tops of columns one"'and

:fi ve and at the centers of the s:pandre1 beams in panels A and Do

-57-

(b) Deflections

Load-deflection curves for severa.l :points on the structure are

given in Figs. 50 l2 to 5.160 The ini tiaJ_ portion of each plot consists of -' <:

the load-deflection curves measured for Tests 404 and 4160 The de~lection

co-ordinate for zero load for the c~~e representing Test 442 is the

residual deflection existing at the beginning of Test 4420 The envelope

of the load-deflection curves is sho'WIl as a broken li.ne on the figures.

This envelope represents the load~deflection curve that would have been

measured if the structure had been tested to fail~e in Test 4040 The

effect of the rapid decrease in load that was measured for loads 8, 9, and

11 is reflected by the Usaw-tooth" shape of the load-deflection curves at

these load levels. The negative slope of the load.-defblection curve between

the initial and final load readings for these load incz·ements indicates

that the less in ceasured load may be attributed to the tendency o~ the

structure ~ continue deflecting under decreasing load as well as to loss

of oil pr~55~~ ~n the loading system 0

A s~~e~~~:c view of the structure, shOwing the maximum deflections

measured is given in Fig. 50170 Tne deflections shown are

thos~ :::eacze: ':L~ ~:.[ the test and do not include residual deflections 0 The

maxim~ ~c:~e:::~~ =easured was 1030 ino at the center of panel A. The

north str:r c: r~.e:~) composed of panels Ay B, and C, showed the greatest

defornatlO::Z :!·z ~;.'c: t.!J.e testJ and was c8nsidered as, the seat of failure of

the str~c~~e. ~~e =axiwxm deflection for a beam section was 0.79 in. for

the beam bet.~e:: panels A and Eo The deflections for the center of the

strip ABC vere about t~ce the deflections for corresponding points on the

strip GRJ.

(c) Steel Stresses and Strains

The stresses measured along the five sections of the test structure

for applied load levels of 249 psfy 320 psf and 425 psf are given in Figso

5018 through 5 u 220 The stresses labeled Hmaximum tI in Figs c 5021 and 5022 were

measured for either load 9 or II 0 The maximum stress at some points was

measured at load 9 since the torsional failure of the beams occurring at

these loads reduced the stress at these points between the application of

loads 9 and II 0

The stresses shown are those that were measured for applied load

only and do not include the effects of dead load and residual stresseso The

max:i.mum stress measured for an applied load. of 249 psf was 30,600 psi at a

beam section 1 (Gage AW3) 0 The next highest; stress at a beam section was

25J OOO ~si 'which was also measured for a section lG The highest stress

measux'ed in the slab reinforcement was 27,500 psi at the interior negative

section of panel F (Gage F54) " The residllal strain at the beginning of

Tes"t, 442 was four times the residual in Test 4160 Inclusion of the assumed

residual stress and the dead load stress gives a total maximum stress of

34,9 400 psi at Gage AW3 for a total load. of 290 psf (301 LL + 1 DL) 0

At an applied load. of 320 psf one slab gage (H61) and one beam

gage (AW3) re.gist.ered strains somewhat higher than the yield strains of'

the reinforcement 0 By the time the ultimate load had been reached most

of the rein:forcement. had yielded 0 The sections of the edge and corner

slab framing into a spandrel beam were never highly stressed since the

spandrel beams could not furnish the requisite torsional stiffnesso Addition

of residual and dead load stresses raises the maximum stress at most sections

to the yield level except as noted aboveo

-:39-

Load-strain curves are given in Figs 0 5023 through 5031 for a

number of points on the structureo In general)' the sha:pe of the curves

is typi cal except at higher load levels 0 The curve for Gage B25 shows

that the concrete cracked between loads of 182 and 249 psf and that from

there on the behavior was linear until redistribution from the interior

negative to the positive section began at a load of 375 psfa The small

strains measured for gages B63, c63~ and c64 indicate that the edge beams

had little torsional stiffnesso

The strains measured at a number of pointsJ for example B51,

B35J B33, H51, CF5 and others) showed a marked change in slope and even

a reversal of direction.'! for loads of 375 psf and higher ~ This may be

att,ributed, in most instances,~ to the torsional cracking and the resulting

loss of torsional stiffness that was taking place at these high load levels.

The ~mum strain measured was 000093 for Gage E63 at load eleven.

(d) Cracking

At the begirming of Test 442 all of the bea."11 sections and most

of the negative slab sections framing into interior beams were cracked 0

The positive slab sections showed additional cracking d-uring Test 442 at

an applie.d load level of 182 psf 0 Between load levels of 182 and 249 psf

all the positive slab sections crack~d except for one small portion of ~D

edge panel adjacent to an edge beam 0 Tr.d.s portior-. cracked by the time a

level of 290 psf was reached 0 The negative sections of the edge and corner

panels framing into the spandrel beams showed cracking only in the portions

adjacent to the beRm~o The portions lying at the centers of the edge

negative sections of these panels did not begin to crack until a load of

-40-

320 psf was reached 0 Some addi tiona.l cracking occur.red at these sections

as th~= loading was increased above 320 psf} but some sections remained

1L~cracked at failureo

The first visual observation of cracks was made at a load. level

of' 249 psi' 0 Cracks could be found. only with the aid of a magnifying glass

and -then "With difficulty 0 At a load level of 290 psf the maximum crack

width was on the or:ier of 00002 in" At a level of 345 psi" the largest crack

widths "Were on the order of 00010 ino and occurred around the tops of the

edge and corner columns c The largest, cracks on the bottom of' the structure

wer l7; a.bout 00005 inc in 'Widtho At failure some of the cracks around the

t.opB,of the e.xt.-::~iar columns had opened up to as much as 0005 ina in width.

In add.i tlon to cracking caused by the flexure of the beams,

to~sional ~racklng was caused by the moments acting on the beam in a direc­

tion pe.rpcn:li cllar t·o -r·hE: longitudinal axis of the beam 0 Thi s effect was

more pronou:l:ei fcy the ,=dge beams than for the interior beams 0 Some

slight. tors:.o:-..3.l =:-acking occu:rred in the edge beams in Test 416 and in the

tests i!:~~r'.rc:!"..:.:-.c ~e:W2er. Tests 416 and 4420 However, no extensive torsional

c:r>acklnt; c:':'~e:: ~::'l a load. of 290 psi tJad. been applied in Test 4420 At

thi E load :: '''':-'''£ :- : '..L: :.or 5:' cnal cracks appeared in the edge beams., As the

loading .as l~:"";;ase::' frcm 290 psf to failure J additional torsional cracking

aPP=B.:red a: :.~~ ~:li5 of all o:f the edge beams and in some of the interior

beamE, Fer ~'::'C' ed,e-= bea:o.s these cracks started at the top of the structure,

propagated CL~~~ ~~e 2uLside faces of the beamsJ and in some instances finally

extended completely around the beam" Final failure of the structure was a

combination of general yielding and torsional failure at the j unctions of

the edge beams with the edge and corner columns 0 An expanded view of the

crack p8:tterns for an edge beam i.s shown in Figu 50320

The final condition of the slab, after Tests 442 and 443 had been

completed~ is shown in Figs 0 5,,33 through 50350 Figure 5033 is a mosaic

sho~"ing the top of the structure after all loading eq,uipment had been removed.

Figure 5034 shows the crack patt~rn on t}J.e top of the structure at the end

ofTe st· 442, The "membrane IV cracks J shown in Fig 0 5 o34J are those cracks that

extended completelythro1~ the structure at the end of Test 4420 Figure 5035

ShO"i<TS the pattern of flexural and torsional cracking that occurred at an edge

and a corner column as well as the crushing of the beams and columnso

(e) Sequence of Yielding

Stresses in the reinforcement first reached the yield level at an

applied lGad level of 320 psf in Test 442nThe two points at which yielding

occurred at this load were a beam section 1. (Gage AW3) and the interior

negati ve seC~lon of an edge panel (Gage H61) 0 At a load of 345 psf one gage

aD. the positive slab reinforcement (E22) registered a strain above the yield

level; add..:. tional beam sections l yielded} and. the negat.ive slab reinforce­

ment in seve:-a:. pa.'1els yielded 0 Yielding of the negative slab reinforcement

usually begO:l a ~ t!1€ portion of the p8.J."lel incl'uded wi t:b...in the T-beam flange

and then pro~essed inward toward the ~enter of the panel but in some instances

the reverse "'''8..5 trlle_

Extensive yielding of the negative slab reinforcement occurred at a

load of UOS psf, Some positive slab reinforcement yielded as well as a number

of beam Eec~ior.s 3) 6,<; and.. 80 As the load was increased. from 405 to 422 psfj

extensi ve yielding t.ook place at all parts of' the structure 0 Yield lines

developed in the negative and positive sections extending completely across

the structure 0 These yield lines passed through the slab and beam sections

in a nearly straight line indicating a structural failure mode 0 The most pro-

nounced yie.ld lines were in the north strip of panels 0

5ry5 Distribution of Strains Across Beams

fa) \ , Introductory Remarks

Two orthogonal rows of gages to measure concrete strains were placed

on the upper surface of the structure at the c~~ter of the interior spans as

shown in Figo 4010 Eight gages in each row were placed over or adjacent to the

interior beam and five were located at the edgeo The gages ~re placed directly

oye:." the posi ti ve slab and beam reinforcement where possible 0 The spacing

between gages was about two inches 0 Gages to measure concrete strain were

also placed on the lower surface .of the structure 0 These gages were placed

as nearly as possible 'underneath gages that were on the negative reinforcemento

Tne conc:r'ete gages were placed on the slab in an attempt to determine

the eff,?cti.ve 1.ndtt.. of the T-beam f'la..11ge 0 The distribution of strains across

the tops or the beams gave an indication of how much of the slab was working

wi th the beam c The distribution of strains ac;ross the depth of the structure

gave the location of the neutral surface which could be used to give an approx-

imat,e value for th,= ~dtb. of T~beam f'1a.llge0 The distribution of strains across

the depth of tne beam also gave the curvature at the sections and showed the

transi tion in c'U.--..vature from beam to slab 0

(b) Distribution Across Top S1..l.1'."i'ace of Beams

The distributions of compressive strains across the tops of an interior

and an edge beam are shown in Figo 5036 for several load. levels in Test 4420 At

low load. levels the compressive strains on both slab and beam were of about

the same order of magnitude 0 As the load was increased,., the strains measured

directly on the beam increased more rapidly than those measured on the slab)

indicating that a relatively smaller portion of the slab was included within

the T-beam flange at the higher load levelso

(c) Strains Across Depth of Beam

The gages to measure concrete strain were placed as nearly as possible

over the tensile reinforcement in the beam and slab 0 By assuming a linear dis­

tribution of strains across the depth of the beam the location of the neutral

axis may be determined from the measured compressive and tensile strainso

Strain distributions across the depth of the beam are shown in Figs 0

5 ·37 and 5038 for an interior beam and a.T1 edge beamo For the interior beam the

depth to the neutral surface from the compression face was 0.9 ino at load 2

and decreased to 006 in 0 at load. 90 The depth to the neutral surface in the

slab at a po int 1 0 5 in 0 from the edge of the beam was 0 085 in 0 at load. 2 and

decreased to 004 ino at load 9.

The variation of the depth to the neutral axis is not very sensitive

to changes in the effective flange width for the amount of reinforcement used

in the beams of the test structure. Conversely,., the computed flange width is

very sensitive to changes in the neutral axis depth. Consequently, the deter­

mination of the effective flange width from indirect or even direct measurements

of the neutral axis depth is not reliable. Nevertheless,., such a calculation

assuming that the neutral axis depth is 006 in. J would indicate an effective

flange width of about 10 to A 1.2 ino for the interior beam" and this magnitude

is apprOximately the same as that indicated by the distribution of concrete

strains. Changes in the. slab concrete strain in the vicinity of the beam

-44-·

indicate a reduction in liT-beam action U as the higher loads are approachedo

This is compatible with observation of the conditions around the bearne At

higher loads) the separation of' the beam from the slab as a result of

negative moment cracks was more severeo

The depth to the neutral surface in the edge beam was 008 inc at

load 2 and decreased to 004 ino at load 100 The depth to the neutral sur-

face in the slab adjacent to the beam was 007 .in 0 at. load 3 and decreased to

The curvature of a reinforced concrete section may be computed

from the -:--elaticnship

where ~ is ~he ctL~ture, E~ is the steel strain measured in the tensile !;;)

reinforc:er:=r.~, ane. kd is the depth from the compression face to the neutral

surface, :c:=P,J-t:' :d. from the st:raight,~line formula 0

?1.b1Zes 5 -39 and 5040 show values of computed curvature plotted

along a posi-:~E a~a a negative section in the interior spano The values

plott~d.. fer a. lo':l..:i level of 58 psf in Test 40lL show the distribution of

curvat-...rre :!""; ~'r.-= 'l:::::rac:ked structure 0 Before the sections cracked} the

dis·t.T'ibutiC!1 cf '':'J.r,;a'ture was fairly uniform for both positfve and negative

sections. Tee ~-1ues for the fully cracked sections are shown for a load of

290 psf in T~st 442. The distribution for both positive and negative sections

~ne transition from beam to slab in the test structure was less

abrupt than is indicated in Figso 5039 and 5040 by the computed values of

curvature, which were based on an assumed width o:f T-beam flange. This is

illustrated by Figo 5.41 which compares computed curvatures and curvatures

determined from measured steel and concrete strains for a beam section 10

and at two adjacent slab gages on either side 0 The computed and measured

curvatures compare favorably :for the beam gages and for the slab gages that

were relatively undisturbed by the influence o:f the beam deformation. The

curvatures computed :for Gages E25 and F2l do not compare as well with the

measured curvatures J primarily because the value o:f kd used in their computa­

tion was based on the assumed T-beam acting as an isolated member, whereas in

the real structure the neutral sur:face was continuous from the slab to the

beam 0

~46-

60 MOMENT-STRAIN RELATIONSHIPS

60l Introductory Remarks

In order to determine ~he bending moment acting on a reinforced

concrete section from measured. steel strains it is necessary to know the

relationshi:p between measured strain and momento If the "straight-line

formula!S were correct this moment strain relationsp~p would be a straight

line and analysis would -be relati vely sim:ple 0 Ho'Wever, primarily as a result

or tensile forces in the concrete~ the moment strain relationship for rein­

forced concrete sections in nonlinearo

Tests made by Mila. (ll) on small reinforced concrete beams have

shown that the moment.=strain cu.r-:-re may be represented reasonably well by a

C"lJ.1..''''re consisting of two :straight lines.~ one extending from the origin to the

cracking moment} and a second extending from the cracking moment to the yield

moment 0 Ttie assumptions made and the procedures used in constructing the

moment~strain curves liSled in the analysis of the test structure are discussed

in Section 6020 The use of the moment=sT.zoain c:J.!:"ve is explained in Section 6 0:3 0

602 Gonst.ructicn of Mome!lt~Strain Curves

In:>rder to ~on8t:ruct a moment-strain curve it is necessary to know

the co~orQina:t·-=s of the points representing cracking and yield moments 0 The

yield moment may b~ ie-r,ermined fai.I'ly ac.curately -u.sing the straight line

fornrLlla pro~,rided th~ cc:n~::,ete strain at yiel·::l is less than about 00001. For

the test structur",s the yield strain of the slab reinforcement 'WaS taken as

0000159 and that'of the beam steel as 0000167 (fy/E2/ Es = 30,OOO,?OOO psi) 0

Determination of th~ cra~king moment is complicated by the necessity

of choosing a value for the modulus of rupture of the concrete and both cracking

and yield moments are inf'luenced by the assumed. width of the T-beam flange 0

The cracking moments were based on the transformed section using a modular

ratio of ten" The values used for the modulus of rupture and the width of

the T-beam flange were determined as follows~

Modulus of Rupture 0 The average value of the modulus of rupture of

plain concrete beams, cast from the same concrete as used in the structure,

was 940 psi 0 As a result of the shrinkage of the concrete, the reinforcement

was placed in compression and concrete in tension" This had the effect of

reducing the apparent modulus of rupture 0 The reduced values of the modulus

of rupture used were 550 psi for the slab sections and 500 psi for the beam

sections 0 The cracking strain for the concrete was taken as 0000020

Width of T-Beam Flange <> In a monolithic structure there can be no

defini te separation of beam and slab 0 For the test structure strain gages

were placed on the concrete above the centers of four beams and on the slab

on either side of these beams" From plots of compressive concrete strains

versus the location of these gages (Figo 5036) and from the distribution of

the strains in the negative slab steel bordering the negative moment sections

of these same beams, it was determined that a flange width of three times the

slab thickness c'Ould be assumed 0

603 Use of Moment-Strain Curves

Moments are determined from the moment-strain curve by entering

the moment-strain curve with a strain and reading off the corresponding momento

In USing the curves constructed for the analysis of the test structure two

operational problems aroseo These were the determination of the dead load

strains and the use of the moment-strain curve for strains that were less

than those previously measured at a sectiono

·-48-

Dead Load Strains 0 The steel strain measured during a test is

only the strain resulting from the a:pplied load.. The st+:"ain caused by the

dead load is a constant for a given section and must be determined before

the moment-strain curve can be usedo The dead load strains for the test

struci:;ure were determined from load-strain plots for Test 401. Strains

were plotted versus loads 'of 30 and 60 psf and the resulting straight lines

were extended backwards through the erigin to a load of minus 41 psf, which

represents the dead weight of the test structure. The resulting values of

dead load strain were then laid off from the origin of the curve and the

dead load moment was determined 0 Figure 6.1 shows a typical moment-strain

curve with the dead load strain and moment :plotted on the curve. .Moments

resulting from applied load were then determined by summing measured and

dead load strains and measuring strains from the origin.

Rebound Moment-Strain Curves 0 As long as the sum of the dead load

and live load strains vas higher than any strain previously reached the moment­

st,:rain relationship was that expressed by the initial two straight lines.

However, since loading to failure was not continuous) the strains measured in

some tests were smaller than those measured in :previous tests at the same

section. Whenever tf1..is occu."'tTed it was necessary to construct an additional

portion on the mement·-strain curve. This portion is called the nrebound rt

moment-strain curve

In Fig. 6.1 the rebound moment-strain CtL~e consists of the dashed

line connecting points A and B G Point A represents the highest point reached

on the curve for any tes"":. performed prior to the tests in which the lesser

strains were measured 0 Point B represents the residual strain accrued in

-~4St:"

that test. Strains measured during subsequent tests 'Were laid off from

point BoThe intersection of a line perpendicular to the strain axis "With

the rebound curve gave the rebound moment.

~5o.~

7 0 MOMENTS ACROSS FULL WIDTH OF STRUCTURE

7 e 1 Introd.uctory Re.maxks

The total moment across the full \-.Yfdth of the structure may be

determined from the measured reactions and from the measured strains. The

yalues ,")f moments obtaine:i from :t"'eactions axe of interest only in that they

gi ve an indication of the behavior of t.he structure c A comparison of the

total measured. strain moment 'With the total static moment gives an indica­

ti.on of the acc·uracy of the computed moment=strain curves 0 The procedure

used in determining moments from reactions and a discussion of the results

obtained is given in Section 7020 The method used in determining strain

moments and res'.llts obtained arc considered in 7030 A discussion of the

static moment and a comparison of the static with the total moment based

on st~ain meas-~ement is given in 1040

702 Moment~3 Based on React,ion Mea,s-arements

The two orth~gonal. horizontal reactions and the vertical reaction

were deterrrdned ~C~ ~a~h of the cclunL~s by means of the tripod dynamometers

des8Z"ibed i.n Secti':)rl iLo3(d) 0 Tti.e load was determined to "Within 30 Ibs and

the ho~i%ont3,l reacti.on -t:: "Wi thin 20 .lbs 0 For an a.pplied load of 174 psf,

correspcmdlng tc a tc tal, load. of 200 LL + 100 DL,~ 30 los was about 006

pe~Ce:t1t of an int2:t-'i8:r col-r.1J1ll vertical !"eaction and about 3 0 7 percent of

the vertical r:;;act.icn fars.. ::-;crner column 0 At the sa."'D.e load a 20-10 variation

in a horizontal rea(;:tion amo1..LTlted to about two percent of the horizontal

reactions :for au edge c.olumn 0 Since the ho~i zontal. reactions for the interior

columns were smallJ a 20~lb V&t'iation was about 20 percent of the measured

horizontal reactionQ HoweVer) these reactions had relatively little effect

on the ~eaction momentso

-.51-

In order to determine the reaction moments the structure was con­

sidered as a two dimensional frameo Each of the reaction components was

plotted versus the total of the four corresponding vertical reactions around

a corner panel 0 This was done in order to detect any irregularities in

readings obtained 0 Values that deviated :from a smooth curve 'Were adjusted

to fit 0 Only a few adjustments were necessary and these were small in

magni tude 0 Corresponding reaetions were averaged to give a completely

symmetrical structureo Differences between adjusted reactions and the

average reactions on the symmetrical structure were generally smallo Since

the structure resulting from these adjustments ~s symmetrical about either

diagonal ~~d both center lines only one-fourth of it 'Was considered in

anaLysis 0

A plot of computed reaction moments versus applied load is given

in Fig 0 7.10 Tabulated values of reaction and strain moments are given in

Table 701u The negative sections l} 3J and 4 were taken at the faces of

the corresponding beamso The positive sections 2 and 5 were taken at the

center of the spano It should be noted that the curves for the moments

computed for loads of 170 psi' and below are not. necessarily continuous with

those lying above 182 psfo The moments for loads of 102 psf to 170 psf

were measured in Test 416 while those for a load of 182 psf and above were

determined fer Test h420 A total of 26 tests were performed in the 26 days

separating these two tests 0 The upward shift in ]?osi ti ve moment, and the

corresponding decrease in negative moment, shown as occurring between the

loads of 170 psf and 182 ps~was caused by differences in the measured

horizontal reactionso The vertical reactions for the t~o loads were pro­

portionately the same, while the horizontal reactions changed considerablyo

~52-

This change may be ascribedJ at least in partJ to the changes in relative

stiffness th~t were caused by the c~acking that occurred in the intervening

tests 0 The apparent drop-off in posi ti ve moments above loads of 345 PSI,

especially for the interior span) must be regarded as in error. For these

high 10M levels the indi viclual horizontal reactions for the edge columns,

and similarly for the corner columns, were no longer all of the same order

of magni t,ude due to -:'he t.orsional failure that was taking place in some of

the columns and spandrel beamso HenceJ the replacement of the 3-dimensional

structure by the syrnmetricalJ two-dimensional; structure. was in error at these

load levels 0 A sec.ond source of error that ent~red in at high loads was

the fact that the assumed center~line representation of the structure was

changing d'..1e t·o the large def"lections which occurred at high loads 0

7 03 Momen-:s ~€d on ST·rain Measurements

T~E SGraln Doment for a section is determined by entering the

appropria--:e r:J.O::1-2:lt-strain C1J.rve -w"i.th a strain and reading off the moment.

For a be~ 5e2t~o~ t~e m~ment is given directly in kip-in. The '

tot.al. mone!1t a:.!" )SS 9. S lab section is the area under the curve of moment

intensi"':y c'" '...::: •• :::-~:::-.e!1't. J;lot~,.ed along the length of the section 0 For the

analysis c: 4";ie t r=s~ '::~='..lc:"ture the valUe of the moment measured at each

gage ·ws.s c.O:-.~:':!E;':':! ':~ b~ cO:!lstant across a tribut,a...ry widtho This width

was tak-=n as ":.:l~· ~ [. ~a.::~e from t.he gage in question half'way to the adjacent

TIle diff'erence between the moment obtained in

this manne:- a!l;:! t~~a': ~bta.iI!ed by meas"Uring the 'area under a smooth plot of

momen~ along tbe Eec~ion was small 0

The strai~ wbich is used in entering the moment-strain curve is

the sum of the strain measured during a t,est.9 cO!Tected for electrical drift,

and the residual strains remaining from previous tests 0 The residual strains

cannot be determined accurately 0 Summing U}) the residual remaining at the

end of each test gave values that were too high, primarily because of time­

dependent recovery 0 The method finally used was based on the proportion of

residual deflections accrued up to the beginning of Test 416 to the deflections

measured at 170 psf in Test 4160 Based on this proportion the residual strain

was taken as 002 times the strain measured at 170 psf in Test 4160 Based on

the same reasoning, the residual strains used in Test 442 were taken as four

times the values used in Test 4160 Residual strains were assumed for all

sections except for the exterior negative slab sectionso

In Figo 702 the values of strain moments obtained are plotted versus

applied load for the same sections as shown in Figo 7010 The total moment

meas~ed fo~ any section was the sum of the moments measured for an edge beam}

an in~e~ior b~am, the full ~dth of one edge or corner panelJ and one-half the

width of' the adjacent interior or edge panelo The posi ti:ve moment sections

lay at the center Qf the spanso The negative moment was the sum of the slab

momentE ~~sured at the faces of their supporting beams and the beam moments

measured at t!le faces of their supporting columns 0 The values of moments

shown be:':,v a. lo~ ~f 170 psf are not necessarily continuous with those lying

at and above 2~9 psf.

7.4 C:):::pari.son sf Measured Strain Moments wit.h Static Moment

TIle total moment in one span of' a continuous structure is the sum

of t.he posi ~i ve r:1oment and the average of the negative end moment,s 0 A com­

parison of the total measured strain moment with the static moment furnishes

an indication of how well the assumed moment~strain curves represented the

actual moment~strain relationships and hO'~T "r!iTell. the assumed values for

residual st!'ains matched the real values (> The total moment determined from

reactions ~~ll always equal the static moment in the assumed two-dimensional

The static momentjl in th1a interior panel of the test structureJ

was determined by assuming that there was no shear between the slab and the

ex.-tensions of the coll.linns into the slab and that. one-fourth of the load

carried by the panel was transferred by shear to each of the surrounding beams.

Based on these assumptions the loads and shears that, acted on the interior

panel we!'e as shown in Figo 703 () The total static moment in the panel was

then deterIT~ned by summing moments of the loads &~d shears about the center

line of the panel.Q The static moment ~T8,S computed. to be 001062 WL where W

equ.als the tot3.1 la.giL applied. to th'~ panel and L = 60 inches 0 In a similar

rnan.ner the total st,atic mcment ·lI'18.5 computed as 00 1093WL for the edge and

corner panels" Wn.ene.ver moments. were sum.m.ed. across one-half the structul."'e

for a ccmpa:"lscn wi tJ:. the static moment;.;, 'W 'was taken as one~sixth the total

load on the s t.:r-U(2 t:u.re 0

The valuss of ·the total strain moment meas1..J.red across one-half the

strue::tUT.'e at different:. load l.evels as 'Well as the corresponding total beam

and t:tal. slab mClli2n"i: are giv-en in Figo 704 fc:r the interior span and in

The straight line in both figures labeled M o

desigr.!Rt.ss +j:e -:.t.ec:r~ti. :::;al total sts,tic moment ~ Fo:::" the interior span the

total meas"'Jrsd. sTrain moment '¥yas 104 percent of the static moment, M J at o

138 psf.~ f,~ll t·e 92 perc:ent of' M at 290 psi' and then increased to 100 percent o

at 374 psi' 0 'me t.otal beam moment was consistently below the total slab

moment until the negati ye slab sections yielded at a load of 364 psi' 0 The

~55-

ratio of beam to slab moment lay between 0 77 and 092 for loads of 138 to

364. psf. At 374 psf the ratio reached 1003 Q In the exterior span the

total moment ranged between 99 percent of the static moment at 138psf and

93 percent at 345 psf 0 For the end span the total beam moment was generally

higher than the total slab moment 0 'Fne ratio of beam to slab moment was

0098 at 170 and 249 psf and increased to 1024 at 374 psf.

In general, the total moment measured in either the interior or

the end span was a few percent less than the total static moment. This

deficiency may be primarily attributed to errors in the values taken for

residual strainso In Test 442 a large amount of electrical drift occurred

with some check gages registering drift by the end of the test of as high

as 200 micro-inches per inch (equivalent to 6000 psi steel stress) 0 The

corrections made to account for this drift may also have resulted in some

error 0 However, the total moment· measured was enough to show the moment

distribution at any load and trends in redistribution that occurred ~th

changes in load.

8" MOMENT REDISTRIBTJrION

801 Introductory Remarks

The pl~se of this chapter is to discuss the redistribution of

moments trJEt, oc.curred in the test, structure as it -was loaded from service

loadst,o failure 0 The redistribution which took place can be sho'WIl by the

changes in both moments and moment coefficients ~th increasing loado Values

of moments and moment coeff'icients are presented in tabular form in Tables

801 and 802 and as plots of moments and moment coefficients versus applied

load or as moments across the 'Width of a slab section in Figs 0 801 through

80140

lL order to consider the effects of moment redistribution it is

neceS5s .. :r y ~·o ::li Vide the structure into sections 0 These divisions may be

clea~ly ~ellneatedj as bet~een negative and positive sections; or they may

be less clea;ly definedJ as for example the division of beam and slab in a

Tt~ bases upon wtrich the division of beam and slab was made have

been d.i3':.'1::,~:-d ir: Chapter 60 T"ne separat,ion of positive and negative

sect-ion::: :.:: s:l.f eviden"to The structure may be fu.-r.ther divided into

sepa.:r:at:- Ia.:.~:S ::r into sections extending across one-half' the widtb. of

:: the struct·ure is considered as consisting of separate

pan.elE an ~"'bi 'Cra.ry di ~.rision of' the beams between panels must be made 0 To

avoid thlS t::-le se':tions considered in this report were taken as extending

across one-~f 0: the st~~ctureo Hence) five separate sections are involved

in the di5cu~sion. These are the negative and positive sections in the

interio~ span ~~d the interior negative} positive and exterior negative

-51tb

sections in the end span 0 Each of these sections contains one edge and one

interior beam) the full width of the slab in one panel, and one-half the

slab width in the adjacent panelo

Three types of redistri oution are considered 0 These are ~

(a) Redistribution between beam and slab within a section) designed as i~eam-slab i! redistribution in this report 0

(b) Redistribution between negative and positive sections) designated as uposi ti ve-negati ve i1 red.istri bution 0

(c) Lateral redistribution along a slab sectione

Beam-slab redistribution is discussed in Section 802J positive-negative

redistribution in Section 803~ and lateral redistribution in Section 8c4~

802 Beam-Slab Redistribution

As the loading on a reinforced concrete structure is increased within

a short time, the relative stiffness of the ~~ious sections changes as a

result of cracking of the concrete and at higher load levels because of the

yielding of the reinforcement 0 As the relative stiffness of the sections

changes., the distribution of the total moment among the various sections also

varies 0 The distribution of moment between slab and beam within a section

may ch~~ge as well as the propo~tion of the total moment carried by the section.

In this section the redistri.bution of' moment -within each of the five sections

listed in 801 is discussed 0

(a) Positive Section, Interior Span

in Fig.

A plot of measured momentJ in kip-ino, versus applied load is given

o ., Oo..Lo rue moment coefficientsy C, deter~~ned from these moments are

shown in Fig. 8020 MOments and coefficients are given for the total moment

carried by the section and for each of the four constituent partso Tabulated

-58,.,

values of moments and moment coefficients for the interior span are given in

Table 8010 It should be noted that the plots of moments and moment coefficients

'versus applied load are not continuous between the load levels of 170 psf and

249 psfo

The total moment carried by the interior positive section decreased

from C = 00040 for an applied load. of 170 psf t,o 00034 at 374 :psf 0 While the

tctal S'~ decreased~ the distribution within the section showed that the

interior positive beam section carried proportionately more, moment with

inc!:easing load 0 For the interior beam) C increased from 00010 at 170,:psf

to 00013 at 374 psf for an increase of 30 percento The edge beam, however,

show,::;d no simil8.l,"" increase 0

1:he positive slab moment increased -with load to 290 psf and then

de':::::'8asedJ while the moment coefficient began decreasing, at 249 psf o. This

pa"t-tern of i.ncrease and subsequent decrease may be attributed ,to ;the sequence

of cracking of the concrete and to the shape of the moment-strain curveo At

a ~oad l2vel of 170 psfJ the positive slab sections had not yet cracked

whereas all cf the beam sections and most of the interior negative slab sec­

·~i.ons had c.rackedo Hence j for this load level, the relative stiffness of the

positive slab section was bigh and conse~~ently it attracted proportionately

mo:re moment·, Bet:ween load levels of 182 psi and 249 psf in Test 442 almost

all of th-2 posi t,i ve slab sections cracked 0 After the slab cracked the

section acted. almcst as a hinge and no further increase in resisting moment

~as possible since the moment~strain curve for this positive slab section had

a negative slope f'or the portion between cracking and yieldo For this reason

the total moment coefficient dropped fTom 00024 at 249 psf to 00016 at 374 psf

while the total moment carried by the section remained nearly constant after

-59"

cracking} varying between the limits of 13074 and 13026 kip-in 0 There was

no significant change in the relative amount of moment carried by the one­

half interior panel with respect to the edge panelo After both sections

vere fully cracked the one-half interior panel generally carried one-half

as much moment as was carried by the full edge panel 0

The ratio of the total beam moment to total slab moment varied

from 1001 at 138 psf to a low of 0064 at 249 psf and then increased steadily

to 1023 at, 374 psf 0 With some of the slab steel acting as beam reinf'orce­

ment in the T~beam flanges,:! this ratio approached 1,,34 at complete yielding

of the sectiono

(b) Negative Section, Interior Span

Plots of moments and moment coefficients versus applied load are

given in Figso 803 and 804, respectively. The total moment coefficient for

the section ranged between the limits of 00072, for 138 psf and 374 psf} and

00060 at 249 psfo

The only significant redistribution that occurred within the section

took place between load levels of 364 and 374 psfo Yielding of the negative

slab steel began at a load of 345 psfo Yielding of the negative slab steel

began at a load of 345 psf 0 By the time a load of 374 psf was attained the

entire slab section had yieldedo After the slab had entirely yielded it

could no longer pick up moment and any further moment carried by the section

had to be taken by the beams 0 That this occurred is shoYm by the increase

in the slope of the moment and moment coefficient curves that appears between

loads of 364 and 374 psfo

As for the positive section, the one-half interior slab section

generally carried about one-half as much moment as the full edge slab section.

Th.=. ratio of' total beam moment to total slab moment varied between limits

of 0080 and 0087 for all load lev',=ls except for 374 :psf where the ratio was

0,,980

(c.) Interior Negative SectionJ End S~

Pl0JtS of moments and moment coefficients versus applied load are

given in Figs 0 8 Q 5 and 806, respectively n Tabulated values of moments and

moment coef:fi cients :for each of t,hc tbree sections in the end span appear

in Table 8020

The behavior of the interior negative section of the end span 'was

very simi.lar to that of the negative section of the interior s:pan 0 The

t·::rr:,al momeL:t coefficient lay between the limits of 0,,076 and 000700 Beam­

sl3.b Y."edist:roibution began at a load of 345 psf with the first yielding of

th.:? slab :reinfor(;em~nto Figure 805 shows tbR.t R.l1 of the slab steel had.

yi3lded "by -t·he time a load of 364 :psi" was reached and that the slope of the

moment~l.oad. curve increased beginning at a load of 345 psf 0 The change in

slope i is more prol1.o·,:.mc2d for the inteT.'io!' heam tha.n. for the edge beam}

sin(~e first. yielding of the sl.ab OC:Cur-r8d. clos~ t,o the interior beam 0

'I'tie p:C'cportion of thE: moment. c~aT.'r"i'2;d by the slab remained nearly

constant w"'l-t·.il. Th·:; slab yielded.>, af't'3Y.' wl'dc:I"1. the slab moment coefficient had

to d,=:(;:resP2wl -Sr. incr"~ase in .load 0 The moment caJ:"ried by t,he one-half edge

panEl ':,i&S almost -7,xs,ctly onc.~half o:f that c.ar~.ried by the corne!'" panel for

all. l.c~ads <> Th=- t:;tal beam. moment ~Ta8 83 to 88 percent o:f the total slab

moment until yielding of' the slab steel occurred. After the slab yielded

th~ beam moment increased to 102 percent of the slab moment at. 374 :psf 0

(d) P,9si ti ve SecticlilJ End Sp~

Values of moments and moment coefficients plotted against applied

load are given in Figs 0 807 and 808 Tor the positive section of the end span"

The total moment coefficient for the positive section varied between

limi ts of 00047 and 00050 sho'Wing that the proportional share of the total

moment carried by the section changed by only a small amount 0 The behavior

of this section was in many ways analogous to that of the interior span

positive sectiano The interior beam momen~ coefficient increased from 00014

at 170 psf to 00020 at 364 psf, at which load the beam reinforcement yielded.

The edge beam coefficient remained at· a constant 0 0008 and increased. to 0.009

when the interior beam yieldedo

The moment~strain curve for the end span positive slab section had

a positive slope for the portion between cracking and yieldingu Therefore,

the posi ti ve slat moment could increase with increasing load 0 HOireyer.9 the

SlOPE was gradual and a relatively large increase in strain caused only a

small incyease in moment n For this reason, the slab moment increased at a

lower rate ~~en the beam moment and the moment coefficients for the slab

decreased vi-t:~ ::'ncr.c;;asing load 0 The total moment coefficient for the slab

sectieD fEll :TX 0 < 027 aT· 139 psi' to 00021 at 345 psi' and remained at this

T:-~e ~c ~.,a::' ::::2:lcnT carried by the posi 1:·i ve section of the corner

pane~ var :e:' ::::: 101 percent to 105 pe:rc;ent of t·he moment· carried by the

corn:plet.E eriE·: S~ti.t ;>:;;:tlV -= section 0 The ratio of total beam moment to

t,otal sl5.t: :::':::'.if': .• , ~ :1~!"eas,=d. from 0079 a.t 170 :rsf to 1035 at 364 psi' 0

(e) Ext-Sy::::: :;~ ;-r .. • -:. vo:: Sectionj End Spa.~

~:J.,? eJ.:e::~_ c: ::he beam~slab redistribution which occurred in the

exterior.' neg~:.::'ve se':tion is shown in Figs 0 8c9 ·and 80100 In general} the

behavior of the beams was very consistent, while that of the slab sections

'Was somewhat erratic at higher load levels due to torsional cracking in the

spandrel beams 0

The total moment coefficient for the section ranged from 0.037

to 000420 For the edge beam C decreased from 00010 at 139 psi' to 00008

at 374 psf -while for the interior beam C fell from 00018 at 138 psf to 0.016

at 249 psfJ where it remained until it increased to 00017 at yieldo The

moment, coefficient showed a very slight, decrease for the edge beam while

for the interior beam it increased slightly with increase in loado

~he values of the moment coe~fici~~ts for the two slab sections

showed a general tendency to increase with an increase in load. 0 This

tendency was more pronounced for the edge panel section than for the corner

panel 0 Tne value of C, ~th one exception, was either 0.008 or 0.009 for

the ~orner panel, while for the one~half edge panel it increased from 00004

at 139 psi' to 00008 at 374 psi' 0 Figure 809 shows a marked drop in the moment

carried by the corner panel at a load of 345 psf, and a less noticeable

drop in the moment carried by the edge panel at a load. of 364 psf 0

The moment that can be carr"ied by the slab section framing into a

span~~el beam l.s a Dlnction o~ the properties of the cross section of the

slab.? as expressed. by the moment strain curvesJ and of the torsional stiff­

ness of the spandrel beam 0 The slab moment acting on the edge beam nrust be

resi.sted by torsional moments acting on the beam at the junction of the beam

wi th i ts s~o_pporting columns 0 As the load wa::, increased on the test structure,

torsional cra~ks began appearing at a load. of 320 psf" A large number of

cracks appea1"ed with subsequent increases in load and t.he resulting loss in

torsional stiffneSS w~s reflected by the drop in moment carried by the sections.

Further increase in the moment carrying capacity of' this slab sect,ion 'WaS

~urnished by the remaining concrete and the closed stirrupso

The total moment carried by the complete edge slab section was 111

percent o~ that carried by the corner panel section at a load of 139 psfo

Except for loads of 345 and 364 psf ttris percentage increased steadily 'With

increasing load until it reached 170 percent at a load of 374 psf'o The

ratio of total beam moment to total slab moment fluctuated between 1052 and

10880

803 Positive-Negative Redistribution

The total moment in one span of a continuous structure is the sum

of the positive moment and the average value of the negative end moments 0

With changes in loading} the relative stiffness of the sections may change

and consequently the proportion of the total moment carried by anyone section

may be al·tered 0 In this section the cha...71ges in the distrrbution of the total

momen-t,J with ine:rease in load, are discussed -ror the interio:r. and end spans,

(a) I:nte:r'i.or S;p8.J."1.

In Fig 0 801ly the total moment· coefficients for the interior span

positive and negative sections; as well as the sum of' the two} are plotted

As "WaS pointed out in Chapter 7.? the total of the measured strain

moments d..oes nc'" eqoJ.B.l the stati.c moment ViM n in all cases 0 For the interior. o

span) the total meas~ed moment was 104 percent of the static moment at a load

of 139 psfJ dropp~d ~o 92 percent at 290 psf and then increased to 100 percent

at 374 ps!, Fa: "this reason a P8l:"t of the apparent change in the total moment

carried by anyonE section must be ascribed to errors in the measured moment

and not to redistributiono HoweverJ while a small percentage of the total

moment was not measured with the assumed moment strain curves, enough of the

moment has been measured so that the trends in moment redistribution may be

clearly discernedo

For the interior section the two negative end moments are equalo

Hence) only a discussion of the redistribution between the positive and one

negative section is necessaryo 'The total moment coefficient for the positive

section was 00039 at 139 psf, 00040 for 170 and 249 psf, and it then decreased

steadily with increasing load. until it r'eached a value of 00034 at 374 psf c

The general trend of the moment coefficient for the negative section was to

decrease When the positive coefficient was increasing and then to increase

when the positive section began to carry proportionately less momento The

total moment coefficient for the negative section was 00072 at 139 psf, 00066

at 170 psf, 00060 at 2119 psfJ and then increased steadily until it again

rea~hed 00072 at a load. of 374 psi" 0 Sfue ratio of negative to positive moment

declined. f:"COtl 1,87 at: 139 psi" to 1052 at 249 psf and then increased to 2014

at 374 psfc When both sections were fully yielded this ratio vas 2.20.

(b) End Span

The to~;;2 ::anent in the end span :i.s the sum of the po.si ti ve moment

and th2 averB€e c~ 'th~ int.erior and exterior end moments 0 The total measured

moment vari~i be.: +"o.T"'~e~ 99 :percent of the static moment at 139 psf to 93 percent

at 345 ps:, ;.. r:.::~ c: come nt, coefficient for each o:f the three sections and

for the 1.:.--':a.:. :.:.e~::·!:':icnt for the end span is given in Figo 80120

C:J:::r~: ~J \."t.at happened in the interior span little negative­

positivE red:st;~~~·~o~ c2c"urred in the end spano The total coefficient for

thE: pC3i -ri ve 51!"':: :"C:-. lay betveen the limits of 00047 and 00050. For the

interior nega-+:: ".":: se~t io!} the range of values 'Was from 0.070 to 0.076 and 'for

the exterior n=ga~iv~ section from 00037 to 000420 At a load of 345 psf, the

exterior negative section showed a maI'ked decrease in moment carried. If any

redistribution between sections had taken place it would have appeared in the

form of an increase in moment carried by the other two sections 0 There was

only a slight increase in the positive moment coefficient and there was a

decrease i,n the value of C for the interior negative section 0 This drop can

be attributed primarily to experimental scatter 0

804 Lateral Redistribution

In the previous discussionJ the moment carried by any particular

slaD section has been considered as a ur~t with no mention being made of how

the intensity of moment. varied along the width of the slab section 0 As

disc~.lssed in Chapter 6) th'3 tot,al moment carried by a slab section is equal

to the area under the curve of moment in kip-ino per inch plotted along the

widtt. :Jf the slat, Changes in the shape of this curve indicate the extent of

la;t'2~9..1 yedistrib'.ltion oc.curring along the width of the slab 0 The lateral

redistYibution Vhich occurred in the slab with increasing load is discussed

below for ea.::t~ cf "thE- five sections under consideration 0

I~ shc,·J..l:i be ncted. that both the redistribution discussed in

Sectio!} ,5.2 a.'1:1 ::or: ::r::.s section are forms of lateral redist.ribution. In

bea.m= slat !" ~d..l :: tr ~ ~'';':: cr: the section was consi.dered as consisting of foUl'"

parts:, 'tve 1:>e3.::'. 5~ :-:i ::;ns and. two slab secti.onsJ and the lateral redistribution

'bet:"..,.ree.r: "'::-~e 5 -: :: :::;< :-_~:1t parts -was dis~ussed 0 In this sec"tion the lateral

redistri bu.-: ':'::':. . ;~D." : ~ :'z~ed -wi thin the two component slab parts is discussed 0

Pcsi ~ 1",·::- S~::-"":. ::J:-.. !r.t.erior Spa:Q

:3 :s a plat of the intensity of the slab moment (including

bott. dead ~"ld. l..\,'·2 :"cad. ::laments) in kip-ino per in~} plotted along the width

of the sEction" 7:-~E: cra:kj.ng moment for this section was 00215 kip-in 0 per

ino and the yield m~ment was 00209 kip-inc per ino For applied load levels

of 98 and 170 psf) the positive slab sections behayed essentially as Helastic"

-66-

sections since the slab was uncrackedo For these load levels the moment

intensity tended to decrease from a maximum value at the center of the

structure to a minimum at the edge 0 By the time a load of 249 psf was

reached almost all of the section had cracked and the moment distribution

was nearly uniform 0 Gage F25 indicated cracking strain by the time a load

of 290 psi' had. been applied and from then on the moment distribution was

uniform.

(b) Negative Section, Interior Span

A plot of moment intensity along the width of the interior span

negative section is given in Figo 8014 (the plotted values include dead

and live 1.oad moments) 0 For this section the cracking moment was 00225

and the yield moment 00462 kip~ino per ino Both the interior panel slab

and the edge panel sections showed the same pattern of having the moment

at the center of the panel lower than that at the edges 0 This is to be

expected since the Rislab reinforcement H in the vicinity of the T-beam

flange3 was influenced by the large deformations of the beams. Little

lateral redistribut·ion took place until a load of 364 psf was reached 0

This charact.-=ristic iitrough gj pattern was maintained until yielding began

at 364 psi' 0 At a load. of 374 psi' the entire section yieldedQ

(c) Interior Negative Section, End Span

The pattern of moment distribution along the interior negative

section of the end span was similar to that of the interior span negative

sect,ion 0 For loads of 98 and 170 psf the plots of moment distribution along

the two sections were nearly identical in shape 0 At higher loads the dif­

ference between the moment values for the center gages and those included

within the T-beam :flange was less pronounced for the end span section. The

section reached f~l yield at a load of 364 psf~

-61-

(d) Positive Section, End Span

Before cracking the distribution of the moment across the positive

section of the end span was similar to that of the interior span positive

sectiono After cracking the distribution of the moment was nearly uniform

across the section and remained nearly uniform for all further increases in

load. 0 None of the reinforcement of the section had yielded by the time a

load of 374 psf had been reachedo

Exterior Negative Section, End Span

The behavior of the exterior negative section was complicated by

the changes in torsional stiffness of the spandrel beam that occurred with

increasing load 0 For load levels of 249 psf and below the distribution

across the section was similar to that of the other two negative sections in

that the 1IDit moment at the center of the edge and corner panels 'Was much

lower than that measured for the gages included within the T-beam flangeo

At higher load levels, especially for those above 320 psf, the behavior was

more erratic due to torsional cracking in the edge beamso At these load

levels the values of moment determined from the strains measured by each of

the gages along the sections increased or decreased erratically with increase

in load 0 Of those gages located between the edges of the T-beam flange.,

only thOSe in the edge panel showed that the concrete had. cracked by the

time a load of 345 psf was reached 0 For the corner panel.~ the two gages

closest to the edge beamJ that were not included within the T-beam flange}

showed that the concrete had not yet cracked at a load of 374 psf 0 Only

the gages wittan the interior beam flange registered yield strains at 374 psfo

-68-

90 EFFECT OF LOADING pA.TrERNs ON MOMENTS PI! VARIOUS SECTIONS

901 Introductory Remarks

One of the objectives of this study was to determine the effects

of different patterns of loading on the moments at various sections of the

structure 0 To this end tests were made at the 100 LL + 100 DL and 2 00 LL +

100 DL levels consisting of single panel (SF) and "checkerboard ft (CB) load­

ings 0 Th2 results discussed in the follo'Wing sections are those that were

obtained fTom strains measured at the 200 LL + 100 DL level as the strains

measured at- the one live load. level were too small to give reliable results

when used ~th the moment-strain curveso

Th-= SF and CB loadings at the 200 LL + 100 DL level were obtained

by load.ing all nine panels with 34 psf to bring the total load up to the

100 DL lev~l 8.!ld then increasing the load on the desired panel or panels

to the 2 0 U + 1,0 DL level 0 The ilcheckerboard rt patterns that were applied

were ~hos~ ~hat ~ve the maximum moments at various sections in an ideal two-

way s"tz-uc:'",;: o;? cc~is"!.ing of a continuous plate supported on non-deflecting

beaIIlE . 7:.. :. :"E> p3.: -: :;rns that were applied are shown in Fig" 9 0 1 0 The sections

at 'Nfl' c~ "':>~sr~ r,a::~ns ideally ca"'..lsed the maximum moment are also indicated.

T~.,; ~::fe::t5 of the CB loadings are discussed in Section 9020 A

diS~-U5.si:)Q a: ":~.7 SF loadi.ngs is given in Section 9030

902 Effe~~3 =~ C~~ckerbGsrd Loadings.

~b~~~t~ ~~d moment coefficients were determined from the measured

strains fo:::- th? various sections at which the CB loadings produced theoretically

the maxim'-1ID mooer::t.s < The results obt.ained are presented in Tables 9 Gl and 9.2

in the form of coefficients of WLo The coefficients computed for Test 416,

-69~

in 'Which all panels 'Were loaded to the same load levelJ are included and'

are designated as the ituniform load n (UL) coefficients 0 The moment coef­

ficients re:ported in SRS 211 (4) for Test struc.ture No 0 3 are also included 0

In general there were no large di~ferences between the UL and the

CB moment coefficients measured for the ten typical slab sections 0 The

four posi.tive and two of the negative sections showed an increase in moment

for the CB loading in comparison with the UL loading 0 The two negati ve

sections which showed an increase were the interior negative section in a

corner panel and the negative section in an edge panel perpendicular to

the edgeo The largest increase was measured at the positive section of the

span in an edge panel parallel to the edge 0 At this section the CB coeffi­

cient (00026) was 30 percent larger than the UL coefficient (00020)0 At

the other five sections which showed an increase the CB coefficient was

from 3 percent to 15 percent larger than the UL coefficiento The moment at

the interior negative section of an edge panel was the same for both CB and

'lJL loading 0 A decrease in moment was meas'u.red for the CB loading at the

exteri.or negative sections in the edge and corner panels and at· the negative

section of the interior panelo

Tbi.s decrease in moment for the CB loadings may be attributed to

two :factors c The first, of these is that a beam between a loaded and an

unloaded panel is relatively stiffer and can carry proportionately more of

the load t·han the same beam when both panels are fully loaded 0 A second

factor influencing the moments computed is that the true behavior of the

structure did not correspond to that of the idealized two-way slab 0 In the

actual structure the beams were flexible and coul,d defornlo Hence) the moment

in the loaded panels could ~vleak n into the adjacent unloaded panels 0

-70~

This uleakage if may be sho'WIl by the strains recorded for the loading

patterns () Figures 902 through 906 aJ,"e plots of strains along v8X'ious sections

of the test structure for different loading patterns 0 These figures are all

for strains measured at the 100 LL + 100 DL level since at the 200 LL + leO DL

level some load was applied to all panels as explained above 0 These plots

of strains along the sections -give a clear indication that the tmloaded panels

were assisting the loaded panels in ca:r;rying the load a

The values of moment coefficients given in Table 9()2 for the ten beam

sections show relatively small Changes in moment for the CB loadings in com­

parison to the UL moments () All of the beam sections but one showed an increase

in moment when the CB loading was applied a At one section), the posi ti ve

section in an edge beam in an edge panel, the same coefficient was measured

for both the UL and the CB loadings 0 The la.r'gest increase 'Was measured for

a beam section 70 At this section the CB coefficient (0 (026) was 30 percent

greate~ than the UL coefficient (00020) 0 The second largest increase was 26

percent, at a section 30 At the other sections which showed an increase} the

CB coe.fficients were from 3 percent to 13 percent larger than the UL coefficientso

Included in Tables 901 and 902 are moment coefficients for Test

st:ructure No Q 3 c The coefficients designated as ~1uniform load n coefficients

were 8btained :from a test in which all panels were loaded t? _ the same load

level 0 The coefficients designated as nmaximumu were obta.ined from CB loadings

or from the superposition of s:i.ngl.e panel testso A comparison of these coef'­

fici.e:'J.t,s 'With those reported for Test structUI"e No 0 4 shows that .generally the

moments at like sections in the two structures tended to change in the same

direction 'when the CB or ~Smax:imumii loading patterns were appliedo The

-:'~'''' coefficients given also indicate the differences in the apportionment of the

total moment to the various sections of the two test structures 0

903 Single Panel Tests

The shape of the plots of strains along the various sections for

the CB and SF loadings, as sho'WIl in Figs 0 902-9.6) and the observed structural

failure mode of the test structure are indications that the test structure

behaved more as a flat :plate than as a two-wa.y structure. The loading tests

that were performed on the test structure consisted of tests with single

panels loaded, all panels loaded} and some panels loaded in the CB patterns

previously describedo

The maximum positive moment in a flat slab is produced when every

other row of panels is loaded 0 The maximum negative moment is produced when

two adjacent strips and then every other strip on either side are loaded 0

Practically" it is sufficient to load only two adjacent strips 0 An attempt

has been made to compute the effects of strip loadings on the test structure

by means of superimposing single panel tests. These computations were com­

plicated by the presence of the one-half dead load on all panels when the SP

'teS'tBwas performed at the 200 IJ. + 100 DL level and by the necessity of using

"the rebound moment-strain curves~ It has not been possible to obtain results

'Wi.th a satisfactory degree of accuracyo However} the studies made to date

indicate that strip loadings would have produced maximum moments at the

positive slac sections about one-fourth larger than the CB loadings and would

have had a lesser effect on the negative slab moments and. the beam momentso

-72-

100 STRENGTH ANALYSIS

1001 Introductory Remarks

The strength of the test structure was assessed by the uyield-

line fI method of analysis developed by K" W 0 Johansen (l2). The resisting

moment of each section was determined using the expression

where M :::;

u

A = s

f = y

d :::;

p =

pf M :::; A f d (1 - 004 ~)

u s y cu

ultimate moment

area of tensile reinforcement

yield stress of tensile reinforcement

effective depth to reinforcement

rei.nforcement ratio

f = 007 fS eli C

f ~ = cylinder strength c

This expression gives the ultimate moment capacity of an under-

reinforced section 0 For a greatly -ander-reinforced section the difference

between the moment at yield and the ultimate moment is small" For the test

structure the yield and ultimate moments were nearly identicalo

For a two-"way structureJ there are two possible patterns of

failure 0 The structure may undergo a localized panel failure or the entire

structure may fail as a whole 0 As was pointed out in Chapter 2J the :point

at which the structure is theoretically balanced between a "structural

failure i1 and a lI:panel failure H occurs ideally when two-thirds of the total

moment is carried by the beams and one-third by the slab" Hence} the

apportionment of one-half the moment to the beams insured a structural

-13-

:failure 0 That this occurred 'WaS clearly shown by the behavior of the structure.

The yield capacities of the individual panels and of the structure are dis­

cussed belowo The yield capacities are expressed in psf based on a 5 ft spano

1002 Panel Strength

(a) Interior Panel

In analyzing the strength of the interior panel, the panel was taken

as having a span extending from face to face of its supporting beams c The

average depth to the posi ti ve reinforcement was used 0 The analysis of the

panel was made by assuming that yield lines :formed symmetrically in such a

way as to divide the panel into four equal and clearly delineated segments,

and considering the equilibrium of one segment.

The yield capacity of the panel computed on this basis was 15 kips

or 600 psfo If the possible formation of corner levers had been considered

a slightly smaller capacity 'Would have been computed 0 However, since the

600 psf capacity given above was more than 50 percent greater than the

structural capacity, the effect of corner levers was not investigated.

(b) Corner Panel

The yield capacity of the corner panel was determined in a similar

manner as for the interior pauelo Tne assumed yield line pattern was sym­

metrical about the diagonal extending through the corner and interior columns 0

The yield capacity ·~s computed to be 596 psfo

( c) Edge Panel

~~e yield line pattern for the edge panel was found by a trial

and erro:r" procedure to divide the panel into four segments with the four

positive yield lines all intersecting at a point lying 27~ino from the inside

face of the spandrel beamo The yield capacity of the edge panel computed for

this pattern was 583 psfo

10G3 structural Strength

(a) Interior Row of Panels

If the structure fails as a whole, then the yield lines wQll extend

completely across the structure at the negative and positive sectionse A

modified psttern is possible in which the positive yield line does not cross

the spandrel beams but branches and runs into the outside corners of' the

edge panele 0 HoweverJ this pattern did not appear in Test Structure No 0 4

and was not considered in analysis 0 In making all computations for structural

failure modes the width of the T-beam flanges was taken as three times the

slab thicknesso

Based on the above considerations the yield capacity of the

interior row of panels of the structure was 405 psf 0 The maximum. dead plus

live load carried by the structure was 466 psf vhich was' 115 percent of' the

computed maximumo

(b) Exterior Row

The failill"e pattern :Ear the edge row of panels was similar to

that for the int.erior row except that the posi ti ve yield line was located

27 in 0 from the inside face of" the spandrel beam instead of at the center

of the row 0 Tr.a.e computed yield load -was 388 psf) the measured ultimate load

being 120 percent of thi s value G

TniE "Was the lowest yield. capacity computed and inclicates why the

major failure occurred in the north row of panelso The yield. line method

aSBUIDeS that th~ supporting beams have the requisite torsional stiffness to

ins:xre the formation of the yield lines 0 In the edge and. corner panels no

yield. lines formed at the discontinuous edges since the edge beams failed

in torsion at the junctions of the beams with their supporting columnso

Hence, the failure capacity computed taking this torsional failure into

account would be a few percent less than the 388 psf given aboveo

10 .. 4 Safety

The discrepancy between computed maximum load and the maximum

load actually carried by the test structure is in keeping wi th t~e behavior

that has been observed for other testso Johansen stated in his original

paper that the yield load computed by his method could be expected to be

80 percent to 90 percent of the actual maximum 0

Various reasons have been put forward as an explanation for this

difference between observed and computed ~um valueso Possible explana­

tions include the strain hardening of the reinforcem~nt, membrane action,

and do~e actio~ o~ t~e formation of ve~y flat arches w~thin the panels.

For a str..l.C't'l.::-e \,-: t:: very stiff beams, some of the load carrying capacity

may be at-:ri c'.l1:,ed. t,o at"ching or dom.e actiono It is doubtful that TIIlICh, if'

a;ny) of the lea..::! ':ocld have been c.arried in to.is way by the test structure

since t!1E sp.o:.:!:f.:: bea::ls were too -weak tc provide t,he t.h...rue.t required. in

the edge ,:"":'\.' a.: • .:! : ::e c enters of the interior row of panels deflected enough

in respe:--: t:: .i...4'>_:" [· ... ~p::>rt:ing beams tb.at any i1dome il would have been nearly

flat 0

\'e:--:: :.. ... ::'e) if any) of the additional carrying capacity may be

attri but: ~d. :-e [,:.:- ~~:. ::.a.rdening of the reinforcement. The slab reinforce­

ment showe1 a ~:u: :cpped stress-strain relationship until a strain of

about 3 percer.. -: wa..s reached 0 The largest strain measured during the test

to failure vas less than 1 percent.o Some of the rein:forcement may have

been strained into the strain hardening region but even here the increase

in stress with increase in strain is too small to account for much increase

in momento

Some of the increase in capacity may be explained by membrane

action 0 ~ne ordinary theory o£ flexure of plates defines membrane action

as beginning when the deflection is about one-half the thickness of the

plate" For the north row of ~anels the deflections of the centers of the

panels were all greater than 1 ino and in res~ect to the deflections of

the beams this was a deflection larger than one-half the panel thickness.

It is readily apparent that the safety of the structure was more

than adequate 0 The structure carried a maximum total load of 466 psf which

was e qui valent to 100 DL + 5 0 6 LL" Hence the factor of safety against

collapse was 302" This load. was carried for only a brief period of time

and then decreased both because of loss of p~draulic fluid and because of

continued deflection of the strQcture under load 0 However, even after the

structure had been loaded to i ts ultimate capaci ty for over· . one-half hour

it was still carrying 414 psf Vhich was 209 times the total design load.

This should certainly satisfy even the most stringent requirements.

llol Tests

-77-

110 SUMMARY

This report is one of a series describing the results of tests of

quart,er~scale models of reinforced concrete floor slabs <; This report describes

the behavior and results of analyses of a nine~panel~ two-way floor slab

having rela"ti vely flexible beams.

The test structure was designed on the basis that reinforcement

was to be provided l.n each panel to ca:r:ry a total moment of 00125 WL" This

was considered to be the logical intermediate point between the ACI Building

Code requirements for flat slab and two-way slab design 0 The structure was

se proportioned that the ratio of beam to slab stiffness was unit Yo For

this ~a~io existing elastic solutions prescribed an equal distribution of

the total mOr:lent between slab and beamso Both the strength and m.oment dis­

tributicn of the test structure were intermediate between the flat plate

and the ~v:::>-\oTay st.L·Llcture with deep beams 0

Fo:-"t:r-four load tests were performed on the test structure. These

incluiec: ~,I?st~ 'Io."i th all p8.-nels l.oaded a.nG. t,ests \?i th some panels loaded in

pa~~e:::-ns .r: xpe: :.ed. ~o c.rsate maximum mome:o:ts in a, tWO-1vay struGture 0 The

beha'V:i.o!' ::: tte test str-u.cture under lJr.Qform load is described for tests to

the desigT~ :"'::>a..i level) 2 00 LL + 1 .. 0 DL level.:> and to failure 0 Results of

analyse~. are :p:oesented for the latter tiNO tests.

~:J:'. 'the standpoint of serviceability the behavior of' the structure

was excellent, The maximum stress measured in the tensile reinforcement w.as

10,700 psi fo~ the design level of 145 psf and 17,700 psi at the 200 LL +

100 DL level 0 First yi~=lding of the reimorcement was detected at a load

-78-

of 400 IL + 100 DLo The m.aximum deflection measured at the design load was

00058 ino or one thousandth of the center~to-center of column spano The

maximum deflection measured at the 200 LL + 100 DL level was 0.094 in 0 whi ch

was less than one-half the deflection considered allowable on the basis of

load testso At the design load level. no cracking could be found ~th the

aid of a seven power magnifying lens and only a few cracks were found at

the two live load . level 0 It is apparent that the performance of the test

structure 'was more than adequate in all respectso

1102 Analyses

The dist~ibution of moments at service load levels and the redis­

tribution of moments with increase in load to failure were determined -with

t·he aid of: id.eal.ized moment~strain Cl..L..-rves 0 In generaly the measured moments

were comparable to the design moments 0 The measured moments in the slab

sections framing into the spandrel beam were lower than expected because of

lew to:rsior..al. stiffness of the spandrel beams 0

Tb.'? effects or loading patterns on moments at various sections

were i.n"'iJ'estigatedc T'ne moments at the 'beam sections measured for the

checke:r'boa.rd leading patterns were f'rom zero percent to 30 percent larger

than -the mom.:;-n+.s msas1,l.red at the same sections when all panels were loaded

to the same lead. l~vE 10 The moments meas'ared at the slab sections for the

checkerboard lca.ciing patterns 'Were':; from 20 percent less. than to 30 percent

great,er -:-,t-.L8.Il th~ moments measured at the same sections when all panels were

loaded 0 A.n atterrr:pt 'to simulate strip loadings by the superposition of single

panel tests sIlo-wed ~Jhat, stri.:p loadings 'Would have produced somewhat larger

moments at the positive slab sections than were produced by the checkerboard

patterns 0

"!79-

The yield capacity of the structure was computed using the yield

line method of analysis 0 The yield capacity of an edge row of panels,

failing in a structural mode j was computed to be 388 psf" Actual failure

of the structure was a combination of general yielding and torsional

failure at the junction of the spandrel beams with their supporting columnso

The maximum load. carried by the test structure was 466 psf which was 302

times the total design loadQ

BIBLIOGRAPHY

1" Ac"TIerica..n Concrete Insti tuteJ Building Code Requirements for Reinforced C,:.:m~r;?,t,,= CAeI 318-56) 0

20 Go To Mayes.;, Me AD Sozen, and C. Po SiessJ iVTests on a Quarter-Scale Model of a Multiple-Panel Reinforced Concrete Flat Plate Floor;'.ft Civil Enginee!'ing Studies} Structural Research Series No 0 l8l} University of Illinoi:=,) LJ£ba.naJ Illinois.9 September 19590

30 D u S 0 Hatcher.~ Mo A 0 So~en, and CoP 0 Siess j i~ Experimental Study of a QLBX-ter-Scale Reinforced Concrete Flat Slab Floor.9 n Civil Engineering S"tud..iese St·ructi.I!"al Research Series Noo 200,9 University of Illinois, "Ur"barra5 .' :r.llinois.~ June 19600

40 wo Lc Gamble) Me Ao Sozen" and Co Po Siess) nAn Ex]?erimental Study of' a Reinf8~~ed Concrete Two-Way Floor SlabJ

u Civil Engineering Studies, Struc-+:ural Research Series No 0 211.~ University of Illinois,P Urbana, Illinci.::, J:me 1961o

50 D, S, Hg-r:cfr=r.~ Me A 0 So zen.\' and CoP 0 Siess j ~!A study of Tests on a Fla-t: Pla~-= and. s, Fla.t Slab,9 II Civil Engineering Studies, Structural R~Se2rC~ ScTi?s Noc 217; Unive~sity of IllinoisJ UrbanaJ IllinOis, July 19610

'7 " 0

JL~ Ca~iU9.s Go de Lo and. Co Po Siess; H!Comparative Studies of Design Pr'O':Ed.:Z-::S for 'IVo,-Way Reinforced Conct'ete Slabs,? ~? Civil Engineering S~"'..ld.ie=, S":T"'J.C'tUI"ll Res2arch Series No" 215.9 University of Illinois, ·l)r'oana· l~i :1:: i 6. MSoy 19610

Jci!Ji: c-:~ ~~~-:- ::r:. standard Specifications for Concrete and Reinforced C2::lC:7 ":'=. '!\=-::':::r:Jr:l~I1.d:~d. Practice and. Standard Specifications for Concrete o.nj F<:; 1:-": c: :: e:" Con::::re"t,8y ~~ Report to Affiliated - Commi tteesJ June 1940"

::10 E. ~..;-: .. ~:,," ;;;..a.rd" "Formulas for the Design of Rectangular Floor Slabs =-n1 ~ ~.-:- ~.... S-1pF~r1:ln.g Girders} IS ACT Froe,.' V 0 22) 1926} pp 0 26-46.

9 v J < :h S·,.;; = i0 9::j ~L F, Van Bur l2D.y nSlabs Supported on Four Sides, fj

ACI ;":.....-~~l. J~ -Fe'D-, 1936J Froco Vol 0 323 ppo 350-3640

100 ] 0 E 0 _:';::i.~ ~ - ~ 11)esign Considerations for Reinforced Concrete Slabs} It

Ph. D _ 1:"-=.=::.::) Departmen"t, of Civil EngineeringJ Uni versi ty of' Illinois, 1959,

110 F 0 ;; 0 Mil~, ·~.-=lB.tionsb.i:p Between Reinforcement Strain and Bending Moment in. Rein!s'-: :;~d C:)ne:.reteJ ~1 a report of the research project:, ~'Investigation of MLll ti:ple-~P3,n~l Reimorced. Concrete Floor Slabsji n Civil Engineering De~artment5 University of IllinoisJ July 19600

-81-

12 0 K. W 0 J ohansenj "Beregning af krydsarmerede Jaernbetonpladers Brudmoment, ft

Bygningsstatiske Meddelansen (Copenhagen), Vol 0 3, 1931 g . (See also: Eivind Hognestad, t~ield-Line Theory for the Ultimate Flexural Strength of Reinforced Concrete Slabs, rr Proco ACl j Volo 49, 1953, ppo 637; Phil Mo Ferguson, "Reinforced Concrete Fundamentals, tI John Wiley and Sons, New York, 1958, ppo 2510)

TABLE )01

CONCRETE PHOPERTIES

-'._~-~-_~_-~'::"""T"=:.~..;..~._..,--~~-_-~_-=-_-._=-=;-:".",-~.~-,

C omI':r:"8 S Ri.ve stJ,"engt.h Modulus of

Wa.te r 50 days 92 days Rttptu't'e Bah:~b_ .. ,' -,.- - - ' ~I 'hy--li-~-~-- ~--u~b~7tr~~~=~ '2--llY 4"- - 4· by S rement

Nn) \)f fl Nl"' 0 of f? Noo of fr Noo of f~ Noo of f Test.s

c TAsts c Tests c Tests I~ Tests r

psi. psi. psi psi psi, ,---,,-=::-o::-::~~~~ ..... _~-,-- .. _.-_-=::~~~.

1 Ov71 3 3230 2 4420 2 0072 4 3240 2 4000 4 3610 2 4200 3 960

3 0074· 3 4030 2 3620

4· 0074 6 4000 2 4200 4· 3600 2 4230 3 9W I co (\)

5 0074 3 3280 2 3790 I.

6 0,7'+ 6 3670 2 4D80 3 4000 2 4490 2 920

7 0074 3 3450 2 4100 8 0073 6 3350 2 4·180 4 3980 2 5000 3 920

9 0073 3 354D 2 4200 10 0072 2 3470 2 4000 2 4080 2 3860

Averages 3550 4090 3900 4360 940 standard Deviat,ion 4·20 110 475 500 54

TABLE 4~1

TESTS ON TEST STRUCTURE NOo 4

Test NOe Date Panels Loaded Remarks

400 7 July 1960 All Measurements made during assembly of load distributing system

401 13 All 100 psf* 402 14 ACEGJ f!

403 15 BDFH ~~

404 18 All DL + lLL 145 405 19 ACEGJ ii + 41 psi' all other panels 406 21 BDFH " 91

407 22 A ~i ~1

408 22 B ~y fS

409 25 c il " 410 25 D iV it

411 26 E Ii !~

412 26 F if B

413 27 G rr~ Sf

414 27 H gi n

415 27 J ii if

416 28 All DL + 2LL 215 417 29 All 11

418 29 ACEGJ ss + 75 psf all other panels 419 2 August BDFH IY u

'+20 3 A it if

421 4 B Ei ~1

422 4 C tv ~i

423 5 D If S?

424 5 E H u

425 8 F i~ .,

426 8 G H il

·427 9 H fj Ii

428 9 ,. u n I:.l

429 10 ABCFH ~1 H

430 11 BCDRJ n Y!

431 11 BDGFJ i, ii

432 15 ABFGH ?1 ~i

433 15 BEGJ Y'l B

434 16 AEFG Ii !Y

435 17 ACEE: i? Vi

436 17 CDEJ ft f~

437 18 ABDEJ it H

438 18 BCEPG iV n

439 19 AEFF..J II H

'+40 22 COOliE Yf H

441 23 All 215 C 442 24 All Test to. Failure 466 psi'

443 19 Septo DEFGRJ 425 + 215 on ~

* All values of uniform load given in this table include the weight of the test slab (l9 psf) and the load distributing system (22 pSi') 0

':rABLE 701 MOMENTS ACROSS FULL WID~rH OF SirRTJCTURE

SectioDB

~~~_ ~-~~ .-.r=-..........: ......... =<:....::=->~."'-:=.-:o::::::::.==~~...-~~=_:.~.:_~:.....,..-,-:-___ ---=...,.~r- -=-.=:.:~-~~..--~-. &:OC.~......c

'rest ApJ!l1.~d (a) MOmf-::nt-t3 Comp1rtc.;d tC(lffi React:t.oTIS (ld.:p"ino) Total Moment L08il, pst: 1. 2 3 J+ 5 Inte:cior Span End Span

~-~~_~~~--=-=-=-:~-~~. -:_=::-.r---"-.:l-

416 103 '" 9"l 11.0) ",2009 =19J+ 607 2601 2605 138 ~~1)+ 08 120 '7 =,3007 =2807 6s4 3501 3505 170 ,~15 07 180:5 ~'35 02 =3205 lo~8 4,303 4309

442 182 -1.4'07 2209 ~'33 01 =2900 1700 4600 4608 249 ~21 04· 3006 =45·6 ,~41 00 2201 6301 6~'ol 290 ~26JO 3507 ·~52 03 ~4706 2600 7306 7'-1·.9 !

co 320 ,.,29·5 3802 ~'59 04 -·51} 09 2604 8103 8206 .):-~

i

345 ·,·32.6 3902 ~6700 =61-09 2507 8706 8900 364 =35·5 38o~' =7602 ~7207 2002 9209 9402 3J4 =3709 3107 ~9108 -9001 500 9501 9605

{b) Moments Computed from Strains ·~kipcoin.)

416 138 ~1206 150'-1· =2306 -2203 1109 3402 3305 170 ~1504 1804 -2607 -2504 1502 4006 3904

~ 4'+2 249 ~2200 2708 -4004 -3305 2201 5506 59·0 290 ~2506 3107 =4604 =4005 23·6 6401 6707 320 =2807 3400 -51.1 -4602 2506 7108 7309 345 -2geO 3703 ~5402 ~5000 2700 76.9 78.9 364 ~3301 4001 -59·3 -55·2 27·9 83.2 8603 374 =35·6 41.6 =6201 -60·9 28 .. 5 89.4 9005

Test LoadJ

psf

416 139 170

442 249 290 320 345 364 374

Test Load) psf

416 l39 170

442 249 290 320 345 364 374

TABLE 801

MOMENTS .AND MONENT . COEFFICIENTS FOR INTERIOR SPAN

Positive Section

Beam Moments Slab Moments Section 5 Section 10 1/2 Int. Panel Edge Panel M* c** M C M C M c

2028 0007 3070 0012 2034 0008 3057 .012 2082 0007 4,,00 ,,010 3010 0008 5016 0014

3005 ,,005 5055 0010 4050 0008 9000 ,,016 3015 0005 6070 ,,010 4056 0007 9018 0014 3040 0005 8050 0012 4048 0006 9019 0013 3065 .005 9080 ,,013 4048 0006 9006 .. 012 3 090 0005 lO055 0013 4044 0005 9004 oOll 4005 0005 11020+ 0013 4035 .,005 8091 oOll

Negative Section

Beam Moments Slab Moments Section 4 Section 9 1/2 Int 0 Panel Edge Panel M C M C M C M C

3070 0012 6020 0020 4028 0014 8.<>15 0026 4015 0011 7010 0018 4071 0012 9046 0025

5040 0010 10020 0018 602l oOll 11.07l 0021 6035 0010 llo70 0018 7054 0012 14092 0023 7.10 0010 13080 0019 8066 0012 16067 ,,023 7055 0010 14090 0019 9034 0012 18016 0023 8045 0010 16090 0021 9096 001.2 19093 0024 9080 0012 20040 0024 10018+ 0012 20056+ 0024

* Moment in kip-ino

** C = M/WL where W = total load on 1 1/2 panels and L = 60 in"

+ Signifies section had yie1dedo

-86-

TABLE 802

MOMENTS AND MOMENT COEFFICIENTS FOR END SPAN

Interior Negative Section

Test L:JadJ Beam Moments Slab Moments psi' Section 3 Section 8 1/2 Edge Panel Corner Panel

M* c** M C M C M C

416 139 4050 0014 6040 0021 4040 0014 8032 .027 170 4090 0013 7060 0020 4075 0012 9,,47 0025

442 249 6095: 0012 11040 ,,020 7039 0013 14079 ,,026 290 7055 ,,012 13060 0021 8036 ,,013 16086 0026 320 8)tO ,,012 14090 0021 9014- 0013 18066 .026 345 8060 oOll 16000 0021 9064 0012 19·96 ,,026 364 9045 0012 19,,10 0023 10018+ 0012 20056+ 0025 374- 10055 0012 20083+ ,,025 1001B+ 0012 20056+ .024

Positive Section

Test Load._~ Beam Moments Slab Moments psi" Section 2 Sect,ion 7 1/2 Edge Panel Corner Panel

M C M C M C M C

416 139 2~65 0009 4045 0014 20B4 ,,009 5 .. 56 0018 170 2090 0008 5020 .. 014 3062 0009 7030 0019

11.42 249 4030 0008 B070 0016 4088 0009 9091 0018 290 1)000 0008 11020 0017 5004 0008 10045 0016 320 50 li() 0008 12070 0018 5014 ,,007 10077 ,,015 345 c:: Pc. 0008 15005 0019 5027 0007 11012 ,,014 ,/ 0 --",/

364- 6.65 0008 16040+ 0020 5050 0007 11059 0014 'A7!.:.. ~<35 0009 16040+ 0020 5088 0007 ll097 0014 ./ - .

Exterior Negative Se~tion

Test If.)ady Beam Ivloments Slab Moments psi' S~.c.-::ion 1 Secti.on 6 1/2 Edge Panel Corner Panel

IV) C M C M C M c

416 139 ).05 0010 5070 oOl8 1039 0004 2050 0008 -170 'A 7r::

./ . ;./ 001.0 6)+0 0017 1092 0005 3.42 ~009

442 24-9 5025 0009 B085 0016 3023 0006 4,,72 0008 290 5J30 0009 10025 0016 3096 0006 5056 0008 320 6030 0009 II 0 ~)5 0016 4072 0006 6.15 .00B 345 6055 0008 l2040 .016 5025 0007 4083 0006 364 6095 0008 l3055 0016 5007 0006 7.49 0009 374 7020+ uo08 14036+ 0017 6052 0008 7.67 0009

* ~loment in ki:p~i.no ·a C =: M/Wl -where '\tl :=; total load on 1 1/2 panels and L= 60 jno

+ Signifies section. had yieldedo

TABLE 901 ,:It,

SLAB MOMRNT CO'EITICIENTS

-- ----------~- -- ------ ---------------------..--- --.-..-...

In t '-'r i' 1t Fj l(!,f' (Pe r pc nd i cuI o.r ) Edge (Pa.rallel) ( Ext. )

+ 4-

------ -- -- -----.--.---- ----DESIGN 0< () 113 o Ojr, o.OY:5 0.025 0,021 0,018 00035 MEASURED

Uniform Land o 024 o .03'r 0.037 00028 00015 00020 00035 "Checke:cboar.d" 0.027 0.0.36 00037 00030 00012 00026 00039

Test structutoe # 3 Uniform Load 0001~, 0002~· 00030 00015 00013 00014 o 002~· "Maximum 11 00016 00023 00032 00014 00015 00017 00024

* Coefficients of WL where W = the total applied panel load, and L = 60 ino

Corner (Ext.)

+

00035 00025 0,,021

00037 00026 00013 00038 00030 00011

00030 00016 00009 00033 00017 00008

I· co

-.,:.,J I,

~~ABLE 902

.* BEAM MOME~r COEFFICIENTS

: ___ -..: ... ~---"'-.. ~.~_ ~~ ... ~==..~~..:..=..=_~~~~:..:=.....x_=~~_

Interior Beams Edge Beams ,~~~-~--

Beam Sect:i.oll Noo 10 9 8 7 6 5 4· 3 + + +

--~--~~-~-:::....;; ...

DESIGN 00018 CL035 00035 00025 0002.1 00009 00018 00018 MEA.SURED

Uniform Load. 00016 00028 00030 00020 00025 00011 00016 00019 "Checkerboard" 00018 00029 00034· 00026 00028 00011 00017 0002)+

Te st Structure 113 Uniform Loan 00022 00058 00055 00032 00028 00015 00028 00021 "Maximum" 00027 00059 00058 00035 00025 00019 00029 00021

* Coefficients of WLJ where W =: the 'total applied panel load, and L ::: 60 in.

:=r~.-::;.,~~~~~

2 1 +

00012 000.11

00011 00013 00012 00015

00013 00012 00014 00013 I

OJ OJ

I.

~(>------l'I~-----hf>------~' I 1 ~ bon II 19 bars II 19 bars I I 1/ II I I j II j II j I I .~ · II ~ II· ~ I I I! 1.11 r-~~ _____ ~.~~ _____ y~ _____ ~ 1-~-----h0.rr=-----f-1.--r-:!----- -r\-I I . T I /

I 13bo1'5 II 13 bars II 13 bon I I ~ II j II j I I ~ II M II ~ I I - II - II -I " I ' ! It-r--------~\r-------F~-----r--:...t ~r------H:TJt~-~ --, --~ft-----1 I 1 9 ban II . 1 9 bars . II 19 bars I

I II II I I j II j II j I 0- . Mo-l - II _. II - . r-L~_ - - - --~L---- -J-lr---- - - -J-Note: All bars were liB-in. square and 55 1/2 in. long

I I

FIG. 2.1 ~ OF BOTTOM REINFORCEMENT IN TEST STRtmURE

-90-

.~

IF-16~--~r-16~-;~-16~~ I ~ ~ II II eel I~ ~ II II ~ ~ I 1 27 bars II 27 bars II 27 bars I ± ~... I I I I . __ H-

- 1------- ~1."-----'.~~"1- ---- r-t-t:=------~1~-----~; ----~

I II II I

16 j II II j j I I; ~ II II ~ ~ I I II II I

1+ _'- I I , I _"- ~ r~ ------ f-r""l-r------- ~~ r------~-1+ ------ K,,.t r-------~.) r---- ---t

I 1 27 be" ~II 27 bars I I 27 bars -- f Ij: ~ i: II j e I

I!j ~ II II ~ ~ I I; 16 bon . II, J 6 bars II 16 bars I ,¥---- -- .----I~~~~----~·~------~I Note: All~. ¥ere liB-in. square. The bars over the interior

beama wve 25.5 in. lODg. The bars over the exterior beams were II in. long •

FIG. 2.2 ARRANGEMENT OF '!'OP REINFORCEMENT IN TEST STRlVrUBE

I

r--~~=9~-------- -t-------~-O.. --t 51-0"

-I .. No. 2 I I

16.5111

1 N 2 13" I 1S" 2 No. 2

15" I 1SU 165" I 1// o. r -;- /// \~- -1~-----1 2 No. 2 \ I.. • .11 1.-3/8"

I 1-1/8 Cl bor

1/2" typ:lcal I II-I

~!2.5"

6 stirrups at 1" and 6 stirrups at 1 1/2" (typical for 12.5 tt)

1 No.2 2-1/8° bars 1 No.2

3 No.2 2 No.2

6 stirrups at 1'" and 10 stirrups a.t 1 1/2" (typical for 18.5 ")

No~e: All reinforcement was No. 2 plain round bars or 1/8-in. plain square bars. Web reinforcement consisted of 1/8-in. square open U stirrups. The six stirrups at I-in. spacing in exterior beams were closed.

EXTERIOR BEAM3' INTERIOR BEAMS

FIG. 2., ARRANGEMENT OF REINFORCEMENT IN BEAMS OF TEST STRlX!TURE

.-~ •••• " -,t 11 :- ,J' ,,' :-0 1 C( :--il' jl,l' .,,'~' 1\ "if'1O.. .. v.~ --:.-_ .... -- .... tl <'>/'". l.d.IJIJ Lt. 1 •• c.iU.!l,\ 'A'i..ii.fll

I

~ I

No. 2 bars welded to vertical rei.nforcement tor anchorage

I· tt . 4 No. 3 bars

,,-/f'\.. """'I

~"lIt l,)J ~ ?

. IL~""

U l/8-in. square ties at 4 in. (typ.) Q

I I I I 3/4-.in. base plate with 2-in. vert~ical studs (typical)

Corner Colunm Interior Column

8 No. :; bars

FIG. 2.4 ARRANGEMENT OF REINFORCEMENT IN COI.UMNS OF TEST STRtCTURE

1- I... 6 No.3 bars

[3""'1 .

fi:=-f Ia... __

n Edge Col\mlIl

• 'is ,

. - .

oM ttl .!i4

... Vl to Q)

~

50

40

30

20

10

o o 1.0

~ ~ ---~ ~

.

l/8-in. square bars

AISI B-lll3 steel

2-in. gage length

Ultimate stress 61.0 kai

Modulus of Elasticity

30 x 106 psi

2.0 3·0 4.0 5·0 6.0 Uni t Strain, percent

~

FIG. 3.1 TYPICAL STRESS-STRAm RELATIONSHIP FOR SLAB STEEL

'0

1.0

I

8.0

• \0 \.N

I

'M 10 ~

~

CO Ia G)

b til

50

40

30

20

10

o o

I'

1.0

~ -----~ ~

1/4-in. round bars

AISI C-I018 steel

2-in. gage length

Ul timate stress 67.1 kai

MOdulus of Elasticity

30 x 106

psi

-----_.- -

2.0 3.0 4.0 5.0 6.0 Unit strain, Percent

FIG. 3.2 TYPICAL STRESS-STRAIN RELATIONSHIP FOR BEAM STEEL

1.0 8.0

, \0 .J:'" I

5~OOO

~K)()()

.r-! ~ . ~)ooo ...

Ul Ul Q)

.f:1 til

~~OO

1000

o

/ I /

v ~ r'\.

// \ I\..

IJ I '" "-f """' ~ ~ '~ 6 E1 = ,., x 10 psi '" /

-

/ V

5 "

strain

FIG. 3.3 REPRESENTATIVE STRESS~STRAIN CURVE, 4 BY 8- IN. CYLINDER

..

7

I \() VI

I

I

Provisional pipe support for screed.

1---' --1'--- -Ir--- --I

I Batch 1110 II Batch 9 I

I II II I 1--- II II -- I L___ _)L ____ ~ __ _ r-----~r_----~r --- -) I~t~ II ~t~ __ ll Bctch8 1

I II I I Batch 5 II Batch 114 I L -----Jl_ _ __ ~L__ _~ r -----~r- ---~r_- --1 ~----~~~~--~~~~ ~_I

- I

I II II I I II I Batch 1 II Batch 2 i i Batch 3 i

L-----)-L ---~ ------J-

FIG. :;.4 LOOATION OF CONCRETE BATCHES IN TES1' STROC"I'URE NO. 4.

J

-97-

FIG. 4.1 LOCATION AND DESIGNATION OF TOP STRAIN GAGES

-98-

~ N

- Gage on Reinforcement

- Gage on Concrete

FIG. 4..2 LOCATION AND DESIGNATION OF :oo.rI'OM STRAm GAGES

-99-

FIG. 4.3 LOCATION AID DESIGNATION OF BEAM S'l'BAIN GAGES

-100-

FIG. 4.4 LOCATION AND DESIGNATION OF DEFLECTION D~

FIG. 4.5 OVER-ALL VIEW OF TEST STRUC'IURE AND LOADING FRAME

~ o ~

102

~ 0

~ t1)

E-I

&3 E-I

~ 0

r£I ~ H o:l

E-I

~ ~ 0

~ H > \0 . ...:::t . ~

~

~ ~

FIG. 4.7 VIEW OF EAST SIDE OF TEST STRUCTURE SHOWING SWITCH BANK

I-l o \J.I

• ..I ............................................................................................................................................ ..

A I B A l( D 0° ( 0 B 0

fH aD Pt

100

1 50

1 ;q

!

I I.

I rf

I I

r I

II , ,

1/ o Al

"

•

'1

o I

Eo Fl

I , q

)1 "

I . I

IV

1/ '// 1/

1

l o

I

~3

I

l /1

I,' .-, .

I Jf ,

I I I •

I -

1

/ I •

~ ! J. r I

~.1 I "

J~ 11 r I I •

I, I I II .

I I . I "

I

~ I // ' I I

I , r I

/; J I 1 II

I I ,

II /1 I ,

I . J

I, ,

I , r I I

1 1! o o 1 3 1-0.05 in.-J

_ FIG. 5.1 LOAD-DEFLECTION CURVES, TEST 4o~, (100 LL + 1.0 DL) .. . ,

I

-l05-

I I I I

6~r---r---+---+---+---4---~--~

O~~+-~+-~~~+-~4-~4-~~~

B63 BC5,6 C62 c64

Exterior Kegati"le Section, EDd Span

O\--I....--+--.J...-+-+Y--t--~-+-.....I..--+-~-+-~-+--++'

B23 003,4 C22 024 CK:;,4

Positive Section, End Span

8~~--~--~--~--~--~--~--~ . I ,I

6f--l--~---I~--+----t----t-------+-----f

2f--l--+--+-+--+--+---+---+---f---I--f

'ol~~I~1 ~I~~I ~I~I~~,~I_·~~I~~ 123 EF3,14. 122 1'24

P08itive Section, Interior Span

FIG. 5.2 SBEL STRI5SES, TEST 1404, 98 PSF APPLIED LOAD

I

"" • .kI .. CD CD ., ~ M ., U .p til

6

4

2

. 0

F53

-106-

III I III I III I III I

I I I

I I I I

I I

I~ 1\ . I

I

/: :~ V I '

~ / I

I I ~~ I

I I I II I I I I I

I . I -. I I

CFl,2 C52 CIn,2

Interior Begati ve Section, End Span

III I! I I I I

I I I I II I

I

: I

6 r--t---t---+---+---+---+---+----.:...-.j

E23

I I I I

BE56 B32 B3~

Regati ve Section, Interior Span

Blf4,5

FIG. 5.; s-.rEIL S~, 'lEST 404, 98 PSF APPLIED LOAD

I

-107-

100 ~--~--~--~--~--~--~--~

o -~.&.-.&.._---'--~_"&"-_--------------'

B23 B33 B63 C3; C23 E23

100 I i I !

~ m Pot .. ] 50

'8 ..... r-t

~ 0

E33 F23 F53 J6; CK5 CN3 eNl BB4

100

50

I CF; CFl BEl. BE5

FIG. 5.4 LOAD-STRA.IN CURVES, TEST 404, (1.0 LL + 1.0 DL)

--108-

01 01 ®I IGJ - h"trr-==. ==_::=:'"':"'--===_=:r.:;'1" -s=====-=---=====:rT:;"1:=~=-:-:-·=====_=_~~ -

I I I I 11 I I I I I

I I 1 II I I I

@I

I I I 1 1 I

1M I I I I I I

@'I ----~---- + ----~----

I I I I I I I I I I I I

II ~ I I I I I I I I I I I I

I I 1 ~ I I I I I I I

(3)11 I ® - - - - .::J. - - - -= ]~~t: - - - - j::- - - - - _ _ _ _ _ ::-£' ___ ::; ~_~ ~ _ _ _ _ t

I I I I I I I I I I , I -hl II I I I . I I I I I 1

® II I ® ====3f==== ~'l----

- Top Cracks

I ;' / Bottom Cracks

FIG. 5.5 CRACK PArl!EHH, TEST 404, (1.0 LL + 1.0 DL)

A ( D f. (

IH lQ Pf

200

1 //

... 'it 100 .9

/' . I

at

i <

L

I I I

I

I I

I

I f , I

II o Al

0

B (~\

o~

EO C[) F ( -0 I 1 F}

/ /.1

1/

V/ A o

I I

1 I I I

II

1

1/ // // // I I I I I

Bl

, 11 /'

I; // h jj ~i

B o

I

II // //

1/ 1-/

I E

. 0

I

I

w

. /. /1

If Ii I I I

I I I

! ~Fl

I

I I I

I

I !

, I I I

II

I I , I , I

I I

i

F3

FIG. 5.6 LOAD-DEF:r..lOC:TION CtmVES, TEST 416, (2.0 LL + 1.0 DL)

I-- 0.10 in~

I

b \0 .. '

... .. • b Ol

.....

J til

-110..;

5r-~--+--+~--~---+---4----~--~

O~~4-~~~+-~~~-+~~~~+-~

B63 BC5" 6 c62 c64

Exterior Ifegati ve Section, End Span

A

ft' I I

i I I

10

/: I i I ~ I I I

/i 1 ! /: ' I r--- I \ '--

5

I 1 - r---. .11 I I I I I I

" I Ii o ~3,4 C22 c24

Positive Section, EDd Span

10

II 1\ I 5 1 I \ I

r- ::\ l -........... ~ I I '---r----~ __ ~ '-- t / I

I I I Or-~r-~41-+~~~r-~+-t~--+~--+~~

1,'23 EF3,4 F24 P08itive Section, Interior Span

FIG. 5.7 SftEL S'lRESSES, TEST 416, 170 PSF APPLIED LOAD

I

-lll-

. 10r-+---~--~~~---+--~----~--~

O~~~~-r~+-~-+~-+~~~~+-~ F53 CFl,2 C52 C54

Interior Negative Section, End Span

I I I I

CBl.,2

o~~+-~--~+-~~~-+~~--~+-~

E33 BE5,6 B32 B34 Blf4,5

Begati ve Section, Interior Span

FIG. 5.8 S'.rEEL STRESSES, T&S'r 416, 110 PSF APPLIED LOAD

-ll2-

:863 B35 200 I -

~3 B B

~3 I - I - C33 c23

---

- I F53

E53 - I E23 F23

I

J63

o ~ __ ~ __ ~~~ __ ~~~ __ ~ __ ~ B2; B33 B6; c;3

200

\04

& ... ] 100

~ or-t r-I

~ 0

C23 ~3 E53 F2; F53 J63

200

o ~ __ ~ __ ~ __ ~ __ ~ __ ~ __ ~~ __ ~~~ __ ~ __ ~ __ ~ B35 E55 I- O.OOOl~

FIG. 5.9 LOAD-s-.rRAm~, TFS.r 416, (2.0 LL + 1.0 DL)

fH CtI Pt

i .3 'i ~

~

-113-

iBN3 CN4 BEll BE5, CFl

~.."..--.".---=- -I BE; CF3

-

JS2

eN; en

200

100

0 Blf3 CF5 CF6 CF3 CFl

FIG. 5.10 LOAD-STRAIN CURVES, TEST 41.6, (2.0 LL + 1.0 DL)

I

f.--

CK5 CFo CF5

-114-

01 01 ®I 18

--h~~===_==.~===_==~~====~r-=====~~====~r-=====_~ I I I I I I I

ff I I I I

@II _ - - - :--!- - - - ~~~~~~~-~-~-=----'- - :l- - - - -- - - - s:::::!:.- - - - - - - - -::!:: - - --=----.... ..

I I I I

'I I

I~l I I I I I I I I

I I I I I I I r # I I I I I I

@ II .... ~--

==~~~==== ~ ====t===~=~~ I I I I I I

~ II I I I I I I

--tt~~-====~~====~~====~~====~UE=-====~====-==~~--®I

Top Cracks

{ : I I Bottom Cracks

FIG. 5.11 CRACK PATfERlf, TEST 416, (2.0 LL + l~O DL)

I

! 1

I I I I I I I !

I 1

I 1

J ! i

; i I

I i

i I

I

I

:

I I !

o 0 I

~1l5-

--.. -----.....

\. ---r---------r----. III: :::.- ----~

~ ---~ ~

............

" ~.::::::--

~ --- --~-- --~ -~--...........

~ ~

..........

" ~ ........ "

\ ....... ~--~

'\

'" ~ ~, ~ . ~~

"" I'---

o o tt\

'. ~

o @

------. ....... ~

I

r--.. -... ----

o t

r'"

~ . U'\

I

I -1l6= I

~s:i ~--~~~~--~--~--~--~--~------~~I ~

~ - . o

-t

~ e:-.... ~ r-----r----- - - --...;

1-- __ 10......

~

,.--r-----..... ~

............... -~ ~ ~ ......

~ ~

\\ ~ \

~ " ~

o 0 ~ IQ

~ ---...~ t::---~ t::----

) - t::::------- --....; = o

o

,.-- --..........

\

\ \ ~

" -r-- -....

~ \~

1\" k. ~

r-I '" ~

....

-r-1

<

-1l7-

t-..... ............... ~

~ ~ .........

I----~

~ ~ ...

o o tt'\

~ I-----

~ -..... -~.:: -....

~ I----

r--..---- """--...... ----

~

r-----

------

~

-

I'----~

~ ::---1-

"""-.. """-.. r-------

-r----o o r-f

0<"'

...:t r-I . tI'\

"" fIl P4

j

400

300

S200 '8 ~.

! 100

o -

E2 ,... '\oJ

El Po' Eo

orF 3

I--

.14"/ ~-\. ~r"1 n ,;

~J

/ V~V

) /' If J J

V V II I V I I / / /

'I

I J I I I If / I / " II ,J

:

'/ / I

I I II

j

I I I I J

,(J I

I ,

I ! / I I , I

/ I / I I I

I '/ I J J - J

o 1 '2 1 3

FICl~. 5.15 LOAD-DEFIJOOTION ClBVES, TEST 442, (~TO FAILURE)

I ,

.~ h i

.;r I

~ ~ 0.10 in.

I

~ )0

---.. ~~ .~

-

I

\

\ > . ~

~ o 0

Ikt '\ r-I

Jr..

-1l9-

I--..... -----~

-----

~ ~

"" ........ ~ o o IC\

----~ r---. r-.;;-.:

~ ~

~ --~....:;

,-...

~ ~ ~

----r----r---I '-'

... ~

~

- I r- __ --.:.. - r-t ...

lire

~ ~

ti I ~ ~ ~

~ I

~ ~

• Lt'\

• a JSt

;::::::--:::::::::--t::---

o

~

~

.~

Column l,}

Note: All deflections in inches

FIG. 5.11 SCHEMATIC DIAGRAM OF DEFLrorIONS AT MAXIMUM LOAD, TEST 442

425 -dsr

40 ~ t- ~. _L - ---11 --- ___ I_J __ J_. --l-----------+-. -----------1------ -r------ ------r - --- -- - - I 1 I I I,' I

..-t .= 30 ...

to co Q)

b rn r-f 4) GJ ..., rn

.201-1 --

i I I I I ----t' - ----f---I I I I

_~ _____ ~__ _____ _ __ - I I

I I t--~

I ~---J I I I VI I f ---t-----r-- 1.,\1--1 il-~-t--t--- -~---~. --------1,1--: I I I "

"1 - . ---1----- ~ 1- I' -'If, -----'-24(r~Bt---- --- -----

F23 F24 o~1 I, I '1,lil,-I, II 'I I'll

E23 E24 E25 EF:~, 4 F22

FIG. 5.1B STEEL STRESSES, POSITIVE Sn;TION, INTERIOR SPAN, TEST 442, (TEST TO FAILURE)

~ I-' II

.,.. Vl )4

... ua CD

! ,... f)

$ til

~I 7

4251p8f

40.---

~--l---I 1 3201 pat I ~-+- --- --+____ _ ___ J _________ L

E34 E35 BE5,6

FIG. 5.19 STEEL STRESSES, NEGATIVE SECTION, INTERIOR SPAN, TEST 442, (TEST TO FAILURE)

1

-I

~ I:

orf

.= ... • at .,

b Ul

M G» t)

~

50, 71~· ~ 1"\,

425 pst I I

i

40

I I i

I

-- - -I -- -- i I

! l' I , ______________ _ -- ------1- ----T I

I I I ,

! I I 1-

30

20 !"'-".-----j--

I

I I i - i I ----- ----t------l-------t--~

, I 10 o-----------~--____ - ----

o I I . I';

F53 C54 F54 C55 CN1,2 C52 C53

FIG. 5.20 STEEL STRESSES, INTmIOR NmATIVE 8ECT.ION, END SPAN, TEST 442, (TE5T TO FAILURE)

I

I\) \).I I'

"r"t

.= ~

II»

j r-f t)

~

50 r III(

40 I---f----

,0 f f---- ----+-------

10

~ +--------~ I' -, mum I' !I I -

I I I

~2Jp;fJ -- ---lJ ---t I

I i

- -1----- --t------t------t-----1------I i I

o ~ I I I . III' I t22 ~ 5 B~~3 B24 B25 ~ 3 t 4 C C 3 C~4 C~5 b , 4

FIG. 5.21 STEEL STRESSES, POSITIVE SroI'ION, END SPAN, TEST .4.42, (TEST TO FAILURE)

I

"'. T

'f"t

.= .... • I)

CfJ

b 00

M ., Gt

~

50

f--- --+--------

40

--------~-------- +- -----,t----t

}o1 i--I ----t- --- ----!

-+---~--- ----- -+---+--+------I 20

I

~ I

I i

I I I I

--1------- ---- -----~--I I I I

10 -_J~ . OJ I I . III' I I - I

1'33 F34 F35 CF5,6 C31 C32 C33 C34 C35 CN5

FIG. 5.22 STEEL STRESSES, EXTERIOR NEGATIVE Sl~ION, END SPAN, TEST 442, (TEST TO FAILURE)

400

300

\of CD Pt

i .s 200

rg .,.... r-t

~ I

100

o H2

B6

I I B25 A21

I

H21

~

V I

I I

t/? ~-~ ~ ~~ V--L ~ / j

I , / I V-

i / / / V / I / ~ 1 I / / .

I ~~ 1I V V I / / ~ / / / ~

LI I I If I

, / / I I

1 I , V-I V / I / ~ / If

I

~ 0'\ Ii

( I / / / /

I I I , I V / /1 I l / i

I / / I

/ I / I 1 f

V / I / V I I I

- - - -1-- I 0.0005 --l

FIG. 5.23 LOAD-STRAIN CUIwEs 1 TEST 442

f;; B;l f- I IB4 Bq:-~~ '-

--" ... -.- - • ,,- ~-.. - -... -- --~.-- --~-

... t-·--- _ ·.o·~_ ~. --- - -,. __ . __ ..

1/ 400 ~ lJI--- -_. -- r- v---

~ I ~~ ./

300

\04 • Pt

i .3 200

~ ;q

! 100

VV / V ~ .' / / ~ V / v V V / / / / /'

/V I.' IV / IV

( - ,/ V JV / I I /' / / ./ V

)

It' / / / / I

II /' II V 11 I

I I a

B43 B45 B51 B61 B35

FIG. 5.24 LOAD-STRAIN CURVES, TEST 442

I--

-- ~

~ v,'

,I I

I I ~

LV /

VI I ,

I I

I

I

~ -[7

/

V V

I-- 0.0005 -l

,I

I\) ......;J I·

\-t OJ Pt ..

400

300

] 200

~ ~

~ 100

'0

C23

c63 c64 i > 'I I i

C43

• .~

I I

I I

I I I

5 55 ~ 0.0005--1

FIG. 5.25 LOAD-STRAIN CURVES, Tlm' 442

E29 I

E2 ~ I ~ I E25 I

E43

400

I -~ I 300

ft..I Ul Po.

I

I

I r~ y v-- V 1/

]. 200

'2 .,... r-t

~ 100

;

:

o E23

--

I I

E24

~-

." ~

~ ,.....,.

~-

~ / ~

:/ ~ :;:: V I

~ / io-""'"

( . / / -. -----

/ / /'

( / v

// )'

/ I / E25 .E43

FIG. 5.26 LOAD-STRAIN CURVES, TmT 1~42

~ ~ ,

/ / / ./'

~ V 1

-

V I

I , I

~ 0.0005 -l E29

V

~ \0 ,

ft.I GO Pf

1 'B ;q

~

400

300

I 200

I

100

o B33

./

B313-

l;),-_ E34 E313-

/ V

v~ V

"

/ I

I I

I

I /

/ I

J

I

", I

./ L! ./ L:? V " / I

/ I ~ I ~ V

/

/ I V ~ I ./"

I v / / I I V

I / I / ~ V

E33 E34 E35

FIG. 5.27 LOAD-STRAIN ClEVES,TEST 442

Io..~

V/" ~ v

L

/ V

L.-..-

v---~

I-- 0.0005 -l

~ '-" o

I

· - .

CH CD Pc .. 'i .9 ~ ;q ~ -<

400

300

200

100

o H61

I

:

II H61 I J63 , ,

H51 II- --H31 J53

~ ~ ~ ~

~ V- / V

/ ~ ----- / ~

V ~ V/ ~ / ' ~

L L ~ ,.

L~ / I / /' VI

/ I ~

~ / I ( ( ( / ,

/ - I /

/ j -'-,

~ ~ ~ /

'L J63 H;l H51 . J53

FIG. 5.28 LOAD-STRAIN CURVES, TEST 442

~ I""t>

V L ~ " I

/ / L

/'

~ ~ r-

~- -

I-- 0.0005 ~

I

~ ..... I

. - ,

tH CD Pot

400

300

1 200

rg ;q

!: 100

BEl OFI ~5

BE5 CF3 I

V /,

1/ •

/ / ~ II

/ / / /

V / I

V, I

I I

7

/

j

/ V o

(~5 CF3

r~ ~ [::>

.,..7

/ / ./

/ ,,/' / V

V

/ / / 7 / /

/

1 1 V j

Vr

/ / / ! I II

V ~ /1 'I

CFl BE5 BEl

FIG. 5.29 LOAD-STRAIN CmvES, TEST 442

-~~ ~ rt

J ~""

/ V V '/ I I

/ / I

/; " -L

I / / / /

I

~ •

! I /

I / I , ,

/ / I . /

/

/ I

/ I

I- 0.0005.--t

\of • PI

400

300

~

~ 200

'Ii ;q

~ 100

/ V o

CK5

BIB __ C~ " BNI4 CNl PK5

/' .------ /

V ,

/ ~ ~/ / ./

V / / v /

/ / / :/ V v V

./ / / /

v / v v / / / I V I ( I /

V / -,

I I II / / /1 I I

V / I J /

I

CN3 CNl BN4 BN3

FIG. 5.30 LOAD-STRAIN CURVES, TEST 442

."..

V

:/

~ .............. ...,. - ...--...~

r v V

/

I if

.~ 0.0005 -I

I: ~ \uJ ~ I

. - - .

400

300

CH

~

1 200

'8 .,-t .... ~

100

V o _

BE3

BE'+-f-... - .. - . .._. .. - .. -.-- -.

DE3 EF} ~I r:r-... _- t -."

I

I t I- .. -----... -----.•. -

V- Ir--.. - .-........ 1 --:7

7 I V v

/ I II .---::?

/ v

~ ~ v-

./ V -- II

/ / v /1,

/ / II

! /~ / IT

I II

l7 V if ~'

I / I )

/ / / I / I

/ / I / I

V V I V II EF3 EF4 DE3

FIG. 5.31 LOAD-STRAm CURVES, TEST 442

V )/

/ V /

/ I .

. V

/ I

A

lV i/;

I

1 /

/ I

I

I

I I

I

~ 0.0005 ~

II

t: -4=" 1\

, - ,

-C-:--.-.--~-(~-;.,_ ~ _1Il-=..aW ---..... ~~~ W"III.W"'IM-'L.A ............... _

Top Exterior Face

Bottom Back

Column 1

/ -1 Bottom of Slab

I I I I

(tj '- -..j Column 3

I I

Top Exterior Face

Bottom Back .

Bottom of Slab

Main yie~ llne

strain Gage

FIG. 5.32 CRACKS IN SPANDREL BEAJ.5, TEST 442

Column 5

Crushing of concrete

Column 2 II

~ \.11.

1\

FIG. 5.33 COMPOSITE VIEW OF TOP OF TEST STRUC'IURE AFl'ER COMPLETION OF TESTING

01 - "t

®

'I I I I I

I I

11 II I I I

@I

I I I I

II I I I I

-137-

®I ---------

---- -----------+-t --------

18

I I I I II I I I I

II I I I I

®

- l:l~.ot:'-=====:::...:::..:::======~t..il:::::::===:..:::::====:::c:i..:±...Ct:::::==::::::~====-==4.tJ I

@J I \ I@

Cracks

. . . -. . - -. Membre.ne Cracks

FIG. 5.34 CRACK PATTERN ON TOP OF TEST STRtVrUBE, TEST 442

-_. ; ~ .'. .

Corner Column

Edge Column

FIG. 5.35 FAILURE OF BEAM-COLUMN CONNECTIONS, TEST 442

0.0005 I I I I I I "

o .0004 I ±..t A I \I

0.0003

s= oM

n til

0.0002 Ld9 Ld7 Ld6

Ld5 0.00011 1 1 :::;:;0-1 I 1 ==r-"'k::: ~=r- Ld4

0, ~+---~----~----~----+-~--~----+-~

X01 X02 X03 X04 X05 x06 X07

Interior Beam

Ld3

j til

0.0005

0.0004

0.0003

0.0002

0.0001

o x09 XlO Xll Xl2 X13

Edge Beam

Ld9 .l; f-J

Ld -~ 1 I

Ld6

Ld5

Ld4

I.d3

FIG. 5-36 DISTRIBl1rION OF COMPRESSIVE STRAINS ACROSS 'lOP OF BEAM9, TmT 442 (TEST TO FAILURE)

~ ...-..-.. _ ... ~ _7"':"-~ ___

------------Ld5.

I

140 120 100 80 60 40 20

Beam Steel Strain x 105

i~ n I -==:5

60 . 40 Slab Steel strain x 105

20 B A

E~IG. 5.37 STRAIN DISTRIBurION IN INrERIOR BEAM, TEST 442

Concrete Strain x 165 A 10 20 30 40

"Bottom of Slab

· s:a ..-i

r-II(\J M

· ~ ..-i

r-liOJ Ii M

..-i I I r-II~ ~ t

A -5 Concrete strain x 10

B

10 . ~ ,0 40

T · ~

oM

r-Ito ~

1 s:I .....

tr\t:O

-------------Load ?-:Q-------

i -.- iii ~5i 140 120 100 &J 60 40 20

Beam steel strain x 165

B A

+--t-

B IA Load 10

---,-- --I , I J

120 100 80 60 40 Slab Steel strain x 105 20

FIG. 5.38 STRAIN DISTRIBUTION IN EDGE BEAM, TEST 442

Concrete Strain x 105 A 10 20 30

T . !i

"Bottom of Slab

,-fl(\J

+ Ji +t

~ ~ M~ru I t I -....,

-~#

Pr A

Concrete strain x 165

B 10

B

• ~ ~

L R oM

t<'\t:o

~I~ ad Morl

&

100

I 90

80

70

60

50

40

30

20

10

-t------ t---:-+ i-- --t=:e:t :j~:ia:j---- - -I i------+- --1.---- ---- -- -------k---t--:l--1 I ---L---- --f-I~-m- ---l- ---1--- \--+--+---- ----- 1--__ :

r---l--- j--- --- '.- -:1- :-----1------ .. -.-- -ll N--T-----ii1 -----+-,- -.--- --1

-T---t -: -------1 i+ __ ----l~:pl t'Telt~j -.. '---r - - - ---j-----i -----+- t----1---- rrr- ... ---;-i---+---r-- -----l----t------------- ---1--- ----j :-1--- -'-"- '-1--- i" -: -. -- . r- -... --. ----t-::.:.+-~+ ". ~-+:-=.T--~-+-I-- -- ... 158-p)~-Te8i 4041--

°b ~~ IJ51'~~,I~ I ~ F4:5 ~~ I ~I F25 3

FIG. 5.39 ClmVATURE ALONG POSITIVE SECTION, INTERIOR SPAN

i t-:-' iG I

100

90

80

70

60

~r 50 I 8 ~oM .. e-

40

;0

20

10

.... ·T-~·-·! --: I : I "\ I : --;1 ----- ----+- --- -~------L------'+1. III: i __ I I I I

I ---I n·--- t--- . --1- --t-

tl

. 11 ~ ... -~~:t:-·~~ -._/-.- ~-.- ~!.-~~ 1_29_ ~-:.~J~~-.. ~-_r~----

-- ----- --- ------- -----1-1- ---- ------1----------- -t - L 1----+-----~ ! I I i ---- -i - - --- -- ----- ----I ----- I

: I I ! I ! I ,r----~I ---t-L-- ------- I II l I I I : I : .. - -T·~ _ ....... 1-· ···-~-r·r- 1

-L--t-···-~l----- ------t-------- ---------i- +- - ! I - I Iii . i --··~e.-ot~+Beam- l_-~_~_et---III------ ---I ~ ._-_.... -+t : ~ .. .1

1

1

... ·1········ . r·) ~~-·-l--T·' --- --·t r=-r ... r- .. I ·1 I I i - .. -.l?-~-p.".t, T~~ _~~ .... __ 1 I

(-

~ I

E3'; E314 +. B~'5 B~4 ' 3 iM'

FIG. 5.40 CURVATURE ALONG NEXlATIVE SECTION, INTERIOR SPAN

. .. .

200

I'

"

'i I~ 100 ~'r-f ~

~--,......

o E24

r-- Assumed Width of T-Beam Flange ---I T T I

--

-- ----- .----.--. --r-C0f~~~::::-~+-U---+---L-L~ ________ ~~ /V; ~~r-- I :

/v V I, ~II~~~ ,---t--+--~ ,,~ "" . ,,--............ "L '\. r-...... -.....:: ...

... f'-. '" -~ to-. I "I'- ,,- .... ~

'- 1 I COmp1 ted \ -- "" , I. \ ' .-

'V '-. ' I V'--..:::I- I I

-"'~ ~~ '..... I~V ~ "' _--- _ / " -r--~ __ Meaau'ed

__ ... _v ... - r--__ '-'",,~ -!"- -- --- ,,- ...... ..,

....... ,

-' '1 I I I

II~IT~~~~~ ~~ ._ I I I I

:F 4- 'l'N)1 I I 1:'. Yc:2 5 3

FIG. 5.41 CURVATURE ACl.\OSS T-BEAM SPm'ION, TEST 416

110 pst

102 psf

t I-J

f

. .. .

,t;

!

M yield

- -- --------- - - - - _._---------..".

M dl

---J ed1 ~ e residual -L- e

rebound .J

Steel strain

FIG. 6.1 TYPICAL K>MmT-STRAIN CURVE

I I I I I I I I

eyield

~.­

$ I

-146-

t.l"\

... -..............

~ (\ .".. ~

.. ----, I

.. I

K' " , . , & I 'IK\ 1\ M 0

0

\ ~ \ 1\ \ \

t<"\

~\ \ \1 \\ , ;,1 \ \ \ . \ fH

'i\\ \ \ I I \

I •

A\ ~\ 1\\ ~ r-I

(Q

Pt ...

o ~ @ ~

'i .,-f

~\ =; l\I

~. \~ •

r-I

~ I

I \ \ ~ , I , I' I t.l"\--

\'- I i ,

\) ~II ...::t - - ,~~ ~ I r<'\_ =- CD

~I ~,

0 0 r-I

C\l - >- ~ I I . I I i

I I r-1-t=- I I I I I I I I I

I I II I I I I I I 10 o Q

o ~

o

§ B ...:I P-c ~ gs

~ til

I ~ H

i r-I . r:-. e H f%.c

I

80

· .~ 60 I

~ .... ~ ., ~ 40

20

o

1 2 345

I' I I 'I' I Sections

3 ~4

-""",~, , ~~tI"

,,/~ "~.,,

~ " _ _" ~2 ,~ , ~

,.'" ----VV 1 -~

3~~ - ~~ _-------5 f--- ---f-------f--4-...... --t-~----l-- ~I- --- ~--~ _--:::::: --f----I-t--+---+--+-~---J

5:::r~ ----~--.~---~--~---+--~--~----L--I

~~~~~~~~~-+~~L o 200

Applied Load, pst

}OO 100 400

FIG. 7.2 STRAIN IDMENTS VERSUS APPLIED LOAD

I

~ I

-148-

I 60 in. I

-~ t +--,..r. - ----~----" I I I I I I I ~

. I I d I orI I I I &

I I I I I I I I

~----- ____ f + +

22 in.

I ~I ~ 17~~' I I

I I I i I i I

I

l[ V

v 4 27 in. 1;

2~ in. c.

v = total load on panel

FIG. 7.3 LOADS.AND REACTIONS ON THE INTERIOR PABEL

100

80

. = ort I 60 s:ac .,...

.!4

..;

I 40

20

o o 100 200 300

Applied Load, psf

FIG. 1.4· STRAIN r«>MENTs VERSUS APPLIED LOAD, INTERIOR SPAN

M o

.400

• $ •

100

80

· .~ 60

~ -

..r J 40

20 v

//

L V 1

o 0

/ /

L '!!I""

I 1 100

I

/'

V L Total

L ~

"..,....-

I I

200

Applied Load, pst

~ L

~ Y

~ ? ~

I 300

FIG. 7.5 STRAIN M:>MENTS VERSUS APPLIED LOAD, END SPAN

L..

L L V

-

/ V

.",.--

""--"" ~ ~lab

M o

400

I' J.:.I

~ I

• ~

~ }O

J 20

10

o o

I

.-L..--t...-'"" . Total ~,......

/ - -

-~

II ~J

/ - ~ -,' -V lif10tM Slab

-' -II'"

I . - ~ ~.-

81"" ..-- -~ Y- au. Edge~

Tota:, Beam ~ - - i-J'anel--':::- -..,...... -- ~ -- I~

Beum SeC· ion ~9-="""~~ Slab. 1/2.~ Bel~ Sec;.ion 51. - ...; -t--Pane , .-:-- I- - -. - - - - - - -- - - .,.

-'--01------ ,

100 200

Applied Load, pst

300

FIG. 8.1 MEASURED mMENT VERSTJS APPLIED LOAD, POSITIVE SECTION, INTERIOR SPAN

~ VI

~

400

. - .

0.05

0.04-

0.03

0.02

0.01

C

0

0.03

0.02

0.01

0 0

Tot ~ V ------.. I----- ---........ ~

-Total 81a10

V -- r----~' r-----... r---.. "'--- ~le.b, lEdge F ~e~ -----~ ------/ ~ - r-----...,

--- Slab, 1/2 In ~J. t. p8Jj _I -, ~

"TotaJ Beazll.. - -~ ~~ -Beam lSeetle II

~.5"" -- ---' Beam !Sectl~

..... '"

"" 100 2C k) 300 400

Applied Load, ]~sf

FIG. 8.2 mMENl' COEFFICIENTS VERSUS APPLIED L()AD, POSr.J~IVE SECTION, INTERIOR SPAN

I

I l I

i

I

I

,~ f\) I

. - - '

50

40

d OM

• 30 .~ M

... ~ ~ i 20

10

o

JI

~V I /V

/ V -

Total /

/'

il -=r- ~ ~

~ ) ~VI ..... V ...... J

" ~ ",r

Total Slab ..... ~ ..... , ..... .., ./

V ---r-- V . .,/.... V" i ~ ~~ I ~ ~ ",. I ~~ "I t...-- -~,.

Total Beam - Slab, Ed8e I _____ V" ~ -~ - -____ ... .".. __ ~e] ~.,.,.". I,... .... -- .... ---~ -

_ Be8~ Sect~on 9 .....--_.~-- Slab, 1/2 lint. -....-- --~' - . Panel -- ::--- -It ---- -- --- -

I

~" •

BeeJu Seetfl.on 4J..---·I---

_.- •... _- ------ --

o 100 200 300 400

Applied Load, psf'

FIG. 8.; MEASURED IDMENTS VERSUS APPLIED LOAD, NEGATIVE SPX!TION, INTERIOR SPAN

0.07

0.06

0.05

0.04

0.03

0.02

C 0.01

0

0.03

0.02

0.01

0

o

-

-.....

~

-100

'" Tc ital ~

~

Tota~ Slab

r---.-. ~ "'-..

~. ol.aO, m.ge l¥8Jle.L

- ~ ~ Slab, 1/2 II t. Panel -

Tou ~ Bear

........... / ~ ~ - -...

Bear Sect: on 9

----............ _r ..... ...........

Be81 ~ Sect' on 4

- ~ ---.

200

Applied Load, psf

-/

-------

----------

-

/

./

/

300

FIG. 8.4 IDMENT COEFFICIENTS VERSUS APPLIED LOAD, NEGATIVE SECTION, INTERIOR SPAN

I

400

I 1-' V1

r

• R ..... I

~ ~

~

50

40

30

i 20

10

o o

- . ;

/ /

V /

v

V Total /~

V I

/ ~

.--J V ~ / I

I / I-i.I

// .."", / ~

~ I

," Total Slab ~

V ",.--

~.".-~

/ - -~.-i' -

V ~" ~ ~ /

~ /

I ------- -~

~ ........ ~lab, porneJ: ~ ~---:- ---

.""..,. .----- !panel ~ ~---Total Beam .,-.' V --'I

1---- .... -' BearnE ectioI 8 --- -- .--- ---1---- .,.,.. .--- Slab, 1/2 li'r

la. _ ~- I-- ---In r ...L~ '7 rn- ....... , :.....---=:- tp-

1"-Q>6U .. l~v"''''V'''' ,./ - ~; ; -~ --

100 200 300 400 Applied Load, pSf

FIG. 8.5 MEASURED l-DMENTS VERSUS APPLIED LOAD, INTERIOR NEGATIVE SlOC!TION, END SPAN --

· - .

0.01

0.06

0.05

0.04

0.03

0.02

c 0.01

0

0.03

0.02

0.01

o 1---.

)

Total

""'" ---- ~. -

. ,---- M. ____ .,. ___ .,_._ r--

Tote.: SlAb - - -_ .. ,,,.--._- ~----.----. ......... ..,/ -- I-------.-

~ V --...

--. Slab; Cornel "Pan~ ...

----- v ---....... Slab, 1/2 & ~. P8.I ~.l

....... --........ ... V-- ~

Tot&: ~ Beam.

:/ ......... .................. ~ ---r--Beam. ~ctio ~ 8

---- -r---- ~ - - Beam Sect,i ~n 3 - I---- -I--- -- ..--'

100 ~ )Q 3< )()

Applied Load, 'pst

FIG. 8.6 r«>MENT COEFFICIENTS VERSUS APPLIED LOAD', INTERIOR NmATIVE SlOOTION, END SPAl~

I

400 1

I

~ ,C('

50

40

· R .,.... I

30 ~ .!4

1 20

10

o o

-- --

."

To1 ~ Bel ~ -.... 1'--::--Beamf ~t101 7 .......... "",.

--- --Beam f ~ctiOl 2_ r-- :::::

100

---

/ 'X(

/ ~UU/

V~ Tc tal S.,j ~b

V , Q.,.l ,.. -

~- VPan~ li __ ~

~;:: SlabJ 1/2' ] ~e

~ ~Pane .. ~::

200

Applied Load, psf

/

/ v

v ~ V

"'~ ",

./

",../ ~",

~ ~. j,,-j

....... ~ -",'

1

~ ..,...~

.-.i

~ ~ ..

",

-- -- ..... ,....,......,. I- _-oil 1"--

300

FIG. 8.7 MEASURED MOMENTS VlmBUS APPLIED WAD, POSITIVE SEVrION, END SPAN

4do

I I-' VI -:J I

o~,o6

0 .• 05

0,.04

0.03

0.02

0.01

C 0

0.03

0.02

0.01

o o

---

-

--..

100

Tc)ta,,"

// ---r-----~;

Tertal Slab

/ ..... i'...

...,.17' ~,

Slla.b, Corne ~ - I-Pla.ne ~------ -

Sllab, 1/2 E tlge Pal

---...--...

'\. "

Total Beam

~ V/ ~. ----..' 'D ......... ~AJ'\+·f ""n 7 ,

"" ~~ '-......... -' Beam Sect1 pn 2

1----- .......... , -

200

Applied Load, :psf

r-----.. r---...-. ....,;..

~el

~

........ ..-.-

,.......

300

FIG. 8.8 M1MENT COEFFICIENTS VERSUS AF'PLIED LOAD, POSITIVE S»JTION, END SPAN

-

-400

I t-J V1 )D

Ito

~ 30 .,...

k ~

i Toj r-----/

20

/ .-

/ V

-Total Beam .",.,. --- '.L'OuaJ o.L8.D

V t---

Bel ~ Sec~ ,ion 6 -- -:1 "slab) Corn4 tr Pan~ -- ......

10

..",...,. ::.--==/ Bel -.m Sec ~ion 1 :::::. - .... Slab) 1/2 ] r:dge PI; -o o

Applied Load, pst

~ /

~ ~

.... 1- ~ ~.,..,.-.

10---

-- .-. -- --.-: ::;:::..:: :.,..;;....---1 - .-. --~ ~17

3 :)0

~

~."",,-

-- -~ ~

.- --~ --

1/

,;~ -

V v-3

40

I ...... ~ I

FlO. 8.9 .MEASURED MJMENTS VERSUS APPLIED LOAD, EXTERIOR NmATIVE SECTION, END SPAN . .. ,

~ . .

0.05

0.04

0.03

0.02

0.01

C o

0.03

0.02

0.01

o o 100

To~ ~ - --- -t---

Total Slab

V ----.. ~ - Slab, C---' 'WA~

--"-~ Slab 1/2

Edge Panel

- r- To ~Be --Beam Sect1

--. .... L----- Beam Sect1 l-----"

200

Applied Load, pst

~ ~ Pane~

V

~ pn 6 ~

pn 1

---

./ ~ '"

~ ~

~ ~ -- -

--

300

FIG. 8.10 l«>MENT COEFFICIENTS VERSUS APPLIED LOAD, EXTERIOR NmATIVE SFX:TION, END SPAN

400

I ..., 2i •

0.11

().10

0.09

0.08

fJ.07

10.06 I

0.05 ~ c

0.04

0.03

0.02

0.01

o 0 ;

Applied Load, pst

FIG. 8.11 mMENT COEFFICIENTS VERSUS APPLIED UlAD, INTERIOR SPAN

c

O .. ll

0.10

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

o o

-- ....

""

"-

--

100

~ Total --

Intel: ior

"- l/B,eSl: tive

/ Posi tiv.

----_I

Exterj or -FNege.1 ~1ve

.

200

App1i~L Load, pat

~ ---.

-

-

300

:b'IG. 8.12 ~ COEFFICIEN'l'S VERSUS APPL1'ED LOAD, END SPAN

- /

~

-~

r-----""

I

400

I ~

Ri I

. -- '

f--.

,0.4

• ~ ......... 0.3 -• ~ I

~ ~ J 0.2

r r---.........

0.1 --

o E23

-- .- .

·----1--249 ];1 sf'

_I \ - '""'" -..... .---374 Pfllf ~ ~

I ~

170 pst- ....... ~ I

1 - ..... 1 .............

98 /'-.. ~

-............. ~ 1~8f' ~

/ - I~ I

---... ............... .. _-

~es of' T-Beam F~es I I I I I I i

E24 m5 F21 122 123 F24

FIG. 8.13 SlAB IDMERrs ACROSS POSITIVE S:rorION, INTERIOR SPAN

--...

~ 1',

-.

I

F25

• ...., &' I

0.5 314 pst ~

----~ - ,64 psf'- -........... ~ -r--.-.... ---- ~' -""""" V--' I

---- -- I I

- 3~ ~ pst - ...... -..... ~ ./ ~, ~ ........ ~ - ~

0.4 ,....

~

. ~ ~ 0.3 . ~ I

~ ~ H 0.2

i

245 pst /~ _ ... - ... ~

t- ----- ~ ..... ~ -~~ ~

....

I- ... 17( pst.. • ~ ~-'"" ~--

---- '--

~ ........ .---~, ~ I--"""'" - 9l t----..... -----pst ~';rt ~ -,.....

~", JII' ~-- '. r---..... r-

~ --... ~ .... " V

I""'" ~ ~, ..... ~ ~ -~ ~ ... .....""""'"

~

r-0.1

- - ECl8e. cot->r1eaml Tangee -

I

·B~ 1-

E .... :3 E; ,4 E35 B31 B33 B34 B35 o

FIG. 8.14 SIAB MJMEM'S ACROSS NEGNrIVE SELYION, INTERIOR SPAN

I

I

X *'~ (b

* X X

X -~-

X X X

X~, p~X X'

~'"

X y

I / " I I ,

-165-

XI IX X

X< DX '....< ' .....

* X XC) X

o Unloaded Panel

I X I lDaded Panel

Slab Section at which Maximum lGnent occurs.·

o Beam Section at which M&ximum Moment occurs.

FIG. 9.1 LOADING PATtERNS PROD~ING MAXIMUM IDME!f.rS IN SLABS WITH NON-D~G SUPPORrS

I

I

I.t'\ 10 r-t H

j til

I I 11--j I I I

I I I

I I I

I I I I I~·II -t--f--+--l-J

I

I I I I I ~II~ __ +--L~i T----~-- -- -,- I ----- -----

I 104 pat I J Load 104 t 6 ~--~---r---~~--~~~---~--~--~~~~--~~~--~~~

I

5 f

I ~~~~-~~--4---+~~--~--~~~--~~

I 2 I

I I

1 ~--~--+---~~--~+--+--~~~~~~-+~--~~~~~-L~~

I o I ,I

JS5 J32 J34 FJ5,6 132 134 CF5,6· C32 C34 CB5

FIG. 9.2 STRAms AT A DISCONTDlUOts EDGE, TEf>'T 405 (PANELS ACJiXJJ LOADED)

• _I .

10

9

8

1

~ 6 1M

H

~. 5 ~

16-

;

2

1

0 J'

~ i- - -- --~ r -- -- --I I I I I

I I 1 I I . --- - -.-- -t f1 t ---- ---- I I I

1 I··

I I I I I

I J - ~ - - t ~ +-- --.--.-- ------t I I

\

I i I 1 I(

I I I I I I I . I f-- -- _.- p. - --_. - ---.. _-- .- .- ---.~- ----- I I I I ~ I I I I I

r--' I 1

I I il\l

1(~4 pat I No Im ~ I 104 p. t

I I I I 1

I I I 1

I I J I ~ 1 .

I I I I I ~ I /' ! I -~ I ~ ~ J ..1

:V~ ~

" I

1 I V '1\ i ~ I I I J 1 I /

11- ~I iV I ~ ~ I I I 1 ~ 1 I I ,--r- 1 i

I I I I

I I I I I I

4-. . .L .1. i L i.1 I I I I I 1 I i I 1 I . . I , , I , ;, CN),

F:IG. 9.3 STRAINS ALONG CElfl'ER OF AN EDGE ROW OF PANELS, TEST 405 (PANELS ACmJ LOADED)

I

• I-'

~ •

, _I ,

· -~ ,

ll'\ 10 r-f

H ~ oj .fj til

1.0

9

B

7'

6

5,

~.

31

2

1.

o J

I I I I I I I I I I I I I I I 1 I I I I

I I I I I I I .. I I I I 11,1

I I I I I I I I I I

I I I

I I I I "

I I I

I I I I I

I I

I I

1 No Load ~o4 :pa ~ 1;1 No w ~ I I I I I r I I I I I I I I I I I I I I I I' I I

I ~,

~II I I I V ~ I lL1 L....--- I ! I I I I I

I -' VII 1,1, ~ I 1 I

I / V I J I I ........

'" ,ft. I I I I I .1 + I ~ ... ' ,

FIG. 9.4 STRAINS ALONG CENTER OF EDGE ROW OF PANELS, TEST 406 (PANELS BDFH LOADElD)

I I I I I I

I I I I I I I

I I I

I

T

I

~ I I I I I

1

I I I ' I I

1

I I

4

9

8

7

~

I~ 6 H s:I at 5 ~

4

, 2

1

o

T I 1 I I I

, I I " I I I I I 'I I I T I 1 T I'

I I I I I I

-+ I I I I I -.--

I I

I I I

I No Load , I 1[0 LoM 104 1 sf I

I , I I I I . . I I 1 Ifill II I I I I I I

I I I

I I I I ~ I

I I I ' I ,

I I T I

I I ,

I I, I I I I 1 I I I I

, 1 T T , I v-----I , I /' ~

I I I I ;! , ~ .. ! I

I

I IV ""'1 I I I I I

I I, I ~, I I I I I V I I I

L/ ' ,

'~ I I I " I I I I

I \l I 1 ~ I I 1- ,-~ ./ I , I

J

I I • I. I I I '1'1 I' • T

JS3,4 JJ2 J14 FJ3,4 F12 F14 CF3,4 C12 c14 CN3,4

FIG. 9.5 STRAINS ALONG CEm'ER OF AN EDGE ROW OF PANELS, TEST 409 (PANEL C LOADED)

I' I-' $ I

11

10

I I I I I I~ I I I I I

ri---- -------- ---------- ------- ---t-t- ----"---- f----- I I I I I I I

9

8

7

~ 10 6 M

H s:I aI 5 .f! CJ)

4

:5

2

1

r--t---- -- ~--+---- .---"_._- -- I I I

I I I I

I I I I

I I I I I I . I --.- - t I 1- -.---.- ~----

I I I

11 I N< Load I I No :to. ~ I I 104 ] sf ~I-- ----- -_ .. _- ---- -- ----t-t·· I I

i I j,: I I I I ! t I

I I I I

V I II I I~ I

I I I j .1 I . I I :1 / I

I 1 I I I I I J I I I

I I / I 1 I 1 I I J 1 I

I

I I I IlL Y I

I ~ ~ 1

I 1 I .1 I 1 I I I Vi i -I

r I I V I I I ..l - I ..l Ii'--~ I ,_ .---~ I I .- I

~ I I I I I l Ll . I 1 .1 I I . . o .. I

JSl,2 J52 J54 F54 C54 FJ1,2 F52 CFl,2 C52 CN1~2

I

~ I

FIG. 9.6 S'l'RAms ALONG INTERIOR NFnATIVE EDGE OF AN EDGE ROW OF PANELS, TEST 409 (PANEL C LOADED)