AN EXPERIMENTAL STUDY OF CONTINUOUS COMPOSITE BEAMS: University of the Ryukyus Repository

(1)

Title

AN EXPERIMENTAL STUDY OF CONTINUOUS

_{COMPOSITE BEAMS}

Author(s)

Hamada, Sumio; Longworth, Jack

Citation

琉球大学理工学部紀要. 工学篇 = Bulletin of Science &

Engineering Division, University of the Ryukyus.

Engineering(12): 79-90

Issue Date

1976-09-28

URL

http://hdl.handle.net/20.500.12000/26714

(2)

AN

EXPERIMENT

AL STUDY OF CONTINUOUS

COMPOSITE BEAMS

by

Sumio HAMADA*

and J

a

c

k

LONGWORTH

料 ABSTRACT

Present design specifications for composite beams are based to a large extent on elast且ctheory. Elastic design is not entiely routine in the case of continuous beams， because the beam stiffness is different in positive and negatiue moment regions. An ultimate design approach elimnates this complication.

The present investigation was planned with particuiar reference to the effect of longitudinal slab reinforcement on ultimate strength， failure modes and general behavior. Three two-span beams were tested under concentrated loads app!ied at the midsqan.

From the test results main conclusions are; (1) The test beams exceed-ed the theoretical ultimate load based on simple plastic theory. (2) Prin -cipal failure modes in continous composite beams are crushing of concrete in positive moment regions and local flamge buckling in negative moment regions. The primary failure is aHected by the amount of longitudinal slab reinforcement

INTRODUCTION

Present designspecifications for composite beams are based to a largeextent on elastic theory.2.5 Elastic design is not entirely routine in the case of continuous beams

，

because the beam stiffn色ssis different in positive and negative moment regions. An

ultimate design approach eliminates this complication. Design based on ultimate strength may tend to produce a reduction in steelsection size and in total depth.

Research on ultimat告 strengthof composite bεams has been conducted since1960

by several investigators. Culver et alB tested a two-span continuous composite beam with a small amount of longitudinal slab reinfgrcement and conclud.ed that only the steel section was effective in the negative moment region. Barnard3 tested four continuous three-span beams. Two beams failed by crushing of concrete and the other two failed due to lat巴ralbuckling of the st色elsection in the negative moment region. The r巴sults

indicated that the ultimate load capacity of continuous composite beams can be determined

Recieved April 30， 1976

* Science and Engineering Division， University of the Ryukyus. 料 Dept.ofcivilEngineering， Universtity of alberta， Canada.

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80 Hamada， Longworth : An Experimental Study of Continuous Composite Beams.

by the conventional plastic hinge method if the positive moment hinge is the last to form. Daniel and Fisher10tested four continuous two-span beams which had been previously fatigue tested. The results indicated that the longitudinal slab reinforcement in the nega-tive moment regions attained its yield stress and consequently plastic analysis adequately predicted ultimate loads. Similar results were reported by Park.14 Recently a large number of tests have been conducted in studies of behavior in negative bending at the University of Cambridge7• 12and the University of Alberta.9. 13.15

The present investigation was planned with particular reference to the effect of longitudinal slab reinforcement on ultimate strength

，

failure modes and general behavior. Three two-span beams were tested under concentrated loads applied at the midspan.

A N AL YSIS OF COMPOSITE BEAMS

ElasticAnalysis-Elastic analysis for composite beams is based on the following assumptions: (i) Stress-strain relationships for steel and concrete are linear.

(ii) Concrete does not have tensile strength.

(iii) Slip between the concrete slab and steel beam is neglected. (iv) Longitudinal reinforcement in the slabiseffectiveinbending.

These assumptions produce different stiffness in positive and negative moment regions of continuous beams

，

and the principal ofsuperpositionis not valid. Stress and deformation calculations are therefore performed by an iterative procedure. For the particular case of a two-span beam with concentrated loads at each midspan， formulas for determining reactions and deflection at the center of each span are given in Re

f

.

4.

Ultimαte Strength--Assumptions made in the evaluation of ultimate strength of composite sections under positive and negative bending are as follows:

(i) The longitudinal slab reinforcement is effective in negative moment.

(ii) The steel section and the longitudinalslabreinforcement attaintheir negative yield stresses.

(iii) In positive moment region， the total compressive force in the concrete is determined on the basis of a rectangular stress block with a stress ordinate equal to 0.85 f'c. (iり Tensilestress of concrete is neglected.

(v) Sufficientshear connectors are provided in order to resist the shear force between the concrete slab and steelbeam.

TEST PROGRAM

Test S pecimens-The size of beam specimens was determined to a large extent by limitations imposed by laboratory facilities. W12 x31 and W12 x27 steel sections were selected， prin -cipally because these sizes had been used in previous tests at the U niversity of Alberta in studies of negative bending behavior. Furthermore the flange width thickness ratios for W12x31， W12x27 and WlQx21 sections are approximately equal to the maximum value

(4)

Bull. Science & Eng. Div.， Univ. of the Ryukyus CEngineering) 81 of 54)/1";;allowed by CSA Standard S16・19695for compression flanges and plastic design

fora yieldstress of 44 ksi.

A 4" slab thicknessand a 4'-0" slab width were selected

，

since these dimensions had been used in pr巴vioustests at the University ofAlberta. The amount of longitudinal reinforcement

，

which is a major variable

，

was selected to produce different failure condi -tions. The longitudinal bars were placed at mid-depth in the negative moment regions. Transverse reinforcement was introduced to control longitudinal cracking. Ferrierll_e_n

-countered longitudinal cracks in beam specimens with transverse steel in the amount of 0.2 p色rcentof the concrete ar巴a

，

which corresponds to temperature reinforcement req・

uirements. Johnson et a112 have reported longitudinal splitting under negative moment of composite beams containing transverse reinforcement in the amount of 0.24 percent of concrete slab area. The present beams were reinforced transversely with 詳3bars at4

V

z

"

spacing throughout the length of the beam. This reinforcement is equal to 0.67 percent of the concrete slab area or approximately three times temperature requirements. 3/4"ゆx3"headed stud shear connectors w巴reprovided in accordance with provisions of

CSA Standard S16・1969，which are based on ultimate connector strength. Complete

details of the testspecimens are shown in Fig. 1 and Table 1.

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(5)

82 Hamada， Longworth: An Experimental Study of Continuous Composite Beams.

Instrumentation-Deflections were measured by means of a precise level focussed on graduated scales suspended from the bottom

f

1

ange of the specimen at the midspans and at locations 30 inches from the interior supports. Rotations were measured by means of mechanical rotation meters at th邑 beamends and by means of sets of two dial gages at locations 30 inches on each side of the interior support. Curvatures at the interior support and the load points were obtained from strains measured by means of electric resistance gages. Points of inflection were determined from strains measured by two pairs of two electric resistance strain gages. Since inflection points were expected ap -proximately 30 inches from the interior support

，

gages were positioned on the face of the compression flange at 24 and 36 inches from the support. Assuming that strains in the lower flange vary linearly

，

the inflection point can be determined from measurements ob -tained from these two gages. Once inflection points are located

，

reactions and bending moments may be evaluated from an analysis of a statica

l

1

y determinate structure.

Test Procedure-Test specimens were supported at the mid-length on a hinge reaction unit anchored to a concrete pedestal and at each end by a roller unit fitted with a rocker plate assembly seated on a concrete pedestal

，

as shown in Fig. 2. Two types of lateral support were provided as shown in Fig.3. At each support

，

steel channels resisted lateral rotation of the specimen. Near midspan

，

the slab was supported laterally by rollers on vertical guides.

FIG.2 TEST SET-UP

Load was 8.pplied in increments of 10 or 20 kips untilinitial yielding occurred in the steel section. Then load increments were gradually reduced to provide sufficient values to plot an accurate load-de

f

¥

ection relationship. After maximum loading the test was continued in order to obtain the

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￨

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x 40

(6)

Bull. Science & Eeg.Div.， Univ. of the Ryukyus (Engineering) 83 falling portion of the load-deflection curve. Beams were tested well beyond ultimate load conditions to the point where concrete crushing occurred in the positive moment regions and/or significant flange buckling occurred in the interior support.

Material Properties-Results of tests on coupons

，

two from each flange and three from the web， are shown in Table 2A. Results of tension tests performed on samples of持3，都4 and梓5bars used as longitudinal and transverse slab reinforcement are shown in Table 2B. Eight concrete cylinders were cast for each beam and cured under the same conditions as the beam specimens. Five cylinders were tested in compression and three were subjected to a splitting test at the time of th巴 loadtest of the corresponding

beam. Test results are shown inTable 2C.

T ABLE 1 TEST SPECI乱1ENS

1

SLABDlMENSION ILONGITUDINAL

1 _

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.

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1 -

REIN. REIN. IREINFORCEMENTI ..， n"J'~~J~ IREI~r::.~R.C~'1.ENT

SECTlON !wIJ)TH[THJC~NESS ーー FORCEMENT IAREA

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T ABL E 2 PROPERTIES OF STEEL AND CONCRETE A STEEL SECTIONS

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(7)

84 Hamada， Longworth: An Experimental Study of Continuous Composite Beams.

DESCRIPTION OF F AILURE

Beam CBI-No visib1e cracks cou1d be found in the concrete slab at the time of test. At a load of 30 kips， cracks appeared on the top surface of the slab in the negative moment region. These cracks extend邑d to the bottom surface of the slab at a 10ad of 50 kips.

Cracks appeared on the bottom surface in the positive moment r巴gions a t a 10ad of 50

kips. Spalling of the white wash on the stee1 section began at a 10ad of 80 kips in the negative moment region and at a 10ad of 100 kips in the positive moment regions. Crack司

ing progressively spread throughout the slab and crushing began at the top surface at a load of 131 kips. At a load of 135 kips it was still possible to stabi1ize conditions in the beam， though crushing extended over 15 inches. The load waヨthenraised to 137 kip3 but deflectionscont~nued to increase and after 15 minutes the slab was crush色dacross its

entire width. Local flange buck1es then formed and the 10ad dropped off.

Beam CB2-This beam， the first t告stedin this program， was loaded initially without th邑

lateral bracing system. However， at a load of 70 kips th色 beamrotated transversely to

such an extent that the test was terminated. After the bracing syst巴m was introduced，

the beam was loaded to failure without further difficulty. The first cracks were observed at a load of 20 kips in the negative mom巴ntregion and at a load of 50 kips in the positive

moment regions. Local flange buck1ing initiated in the nagative moment region at a load of 120 kips and extended gradually with increasing load. Local buckles were completely formed at a load of 130 kips. At this load crushing of concrete started at the load loca -tions. Deflections were stabilized at a load of 133 kip3. However， it was not possible to stabilize deflections at 136 kips and the load decreased to 130 kips. During unloading

，

web buckling occurred between the 10ad point and th巴 interior support at a load of 126

kips. Finally a section of the concrete slab at a load point spalled off at a load of 116 kips.

Beam CB3--A visible crack existed on th巴 topsla b surface near the interior support prior

to loading. Tension cracks b色ganto aT'pear in the nagative mom色ntregion at a load of

10 kips， and in the positive moment regions at 50 kips. Loca1 flange buckling initiat巴d

at a load of 85 kips and slowly developed as the load increased. At a load of 92 kips crushing of concrete occurred at a load point and at a load of 94 kips the concret巴 was

completely crushed. The flange buckles were complete1y formed at the interior support as the deflection increased.

PRESENTAION OF DATA

Load-deflection

，

load-rotation and load-moment relationships are shown in Figs. 4

，

5 and 6， respectively. Moment-curvature relationships at the interior support and at thc 10ad points are shown in Fig. 7. Slip distributions betwεen the concrete slab and steel beam are shown in Fig. 8 for Beam CB1. Strains measured in the transverse reinforcing

(8)

85

bars at the longitudinal centerline are shown in Fig. 9 for Beam CB2. Fig. 10 shows the ratio of slab edge strain to slab centerline strain at the load points for various load values. An example of cracking patterns is shown in Fig. 11.

Bllu. Science& Eeg. Div.， Univ. ofthe Ryukyus (Engineering)

~ 3000 ト-Z 2000 w 2 0 ::;: 1000 C o 0.2 0.4 06 0，8 10 1.2 1.4 16 CURVATURE (rodions perinch x 103)

FIG.7 MOMENT-CURVATURE

RELA TIONSHIPS FOR BEA恥1CB1.

0

4

U

巳

一

LOAD-DEFLECTION RELATIONSHIPS.

FIG.4

。

く

o d

FIG.8 SLIP DlSTRIBUTION FOR BEAM CBl. 。古川 e 一山 9 u m p ← = 2 0

一

lh ① 4 H FJ 1..ーーーー山ームーーー一一一ー-' 1000 1500 20CO STRAIN 110-'1 ①

LOAD-END ROT ATION RELATIONSHIPS. FIG.5 。︿ 0 4 3500 3000 LOAD-TRANSVERSE STRAIN RELATIONSHIPS FOR BEAM CB2. 1500 50C FIG.9 LOAD-MOMENT RELATIONSHIPS. FIG.6

(9)

Hamada， Longworth : An Experimental Study of ContinuoU5 Composite Beams. "0

・

'M '"0 86 。 . ，， b O 0 0 0 2 .

‘

g ﹄的凶 Z -d u 出 h Z 凶 ) 。﹄ Z -4 、信﹄叫刷。。 ω 也 0 0 = ︽儒 SOUTH fNO 4

"

-0 2 0 0

CRACK PATTERNS FOR

BEA恥1CBl. FIG. 11

RATIO OF SLAB EDGE STRAIN TO SLAB CENTERLINE STRAIN. FIG. 10

DISCUSSION OF TEST RESULTS

Transverse rotation may occur asa result of initial warping in the slab orsteel section. This transverse rotation was eHectively resisted by the lateral bracingsystem.

The ody :nitialcrack observed was in Beam CB3. This crack may have been due to

shrinkage， or， since it was locat巳dover theinterior support， it may have occurred during positioning in the test apparatus. In a11tests first transverse cracks appeared in the negative moment region. Later transverse cracks appeared on thebottom surface in the positive moment regions. Diagonal cracks developed at the approach of failure.

gitudinalsplitting was effectively prevented by means of the transverse reinforcement.

Although a few longitudinal cracks developed near th巴 loadiocations before faiJure

，

they did not appear to affectthe ultimate moment capacity of the beams.

Failure of Beam CBl was a concrete crushing failure. Local buckling followedas a result of reduced stiffnessinthe positive mornent regions. The amount of longitudinal reinforcement inBeam CBl was 1.6 in2 _o_r₁₇_p_e_r_{cent o}_f_t_h_e_area_o_f_t_h_e_s_t_e_e_l_s_e_c_t_i_o_n_，

which was the smallest percentag巴 inthe threebeams. Failure of Beam CB2 occurred

asa result of local buckling followed by concrete crushing. The amount of longitudinal reinforcernentwas 3.1 in2

，

i. e.

，

38.9 percent of the area ofthe steel sectionwhich was

thelargestp色rcentagein the threebeams. Failure of BeユrnCB3 resulted from concrete

crushing followed by local buckling. Although local buckling initiated prior to crushing of concrete， itdid not produce a sudden fallure. The areaof longitudina¥ reinforcement inBeam CB3 was 32.3 percent of thearea ofsteelsection.

Load-deflectionand load-rotation relationships shown in Figs.4 and 5 have similar

characteristics. They consist of three ranges， i. e.， elastic， p¥asticand unloading ranges. The deflections at maximurn load were 2.6， 1.8 and 2.1 inchesforBea:nCB1， CB2 and

CB3， respectively. These va¥ues indicate an increase indeflection with decrease inthe

ratio of theareaof¥ongitudinalreinforcement to the area of thesteel section. End ro -

(10)

Lon-Bull.Science& Eng. Div.， Univ. of the Ryukyus (Engineering) pr1 tations at ultimate load were approximately 5 times the rotations at initial yielding. The unloading portions of the load-rotation curves are different to those obtained for isolated simple beams under negative bending due to the fact that continuous beams have greater duct

i

1 i

ty than isolated simple beams. Differences between test and theoretical deflection va¥ues in the elastic range are likely due to shear deformation. Since th色 testspecimen

was short and since the web only is effective in resisting shear， shear deformation is more than 25 percent of bending deformation.

Reactions were determined from the location of points of inflection. The moment diagram is linear for concentrated loads.

I

f

the concrete slab does not have tensile cracks

，

the strain can be assumed to vary linearly along the span and the location of a point of inflection may be determined by linear interpolation between strains measured on each side of the point of inflection.

I

f

the concrete slab has tensile cracks

，

the location of a point of inflection is related to the section modulus with respect to the lower flange in positive and negative moment regions and measured strains in positive aコd negative moment regions. However， the effect of cracking is not significant since the distances between strain gages are small and since the ratio of section modulus with respect to lower flange in a positive moment region to that in negative moment region is close to unity. Strains at 24 and 36 inches from the interior support did not exceed yield st1"ai:1values

in any of the tests. The points of inflection in each span were almost equidistant from the interior support and therefore the two exterior reactions and the moments at the load positions were almost equal in the elastic rang巴 However

，

in the plastic and unloading portions they differed slightly， and this is probably due to imperfections in the beams af -fectingsymmetry. Fig. 6 shつwsslight moment redistribution in Beams CBl and CB2 for loads greater than 90 kips and significant redistribution in Beam CB3 for loads greater

than 50 kip5.

Although moment.curvature relationships for Beam CBl indicate that stiffness in the positive moment regions was greater than in the negative moment region for elastic conditions

，

inelastic stiffness was approximately the same in both regions. Therefore the ratio of inelastic to elastic stiffness in the negative moment region is greater than that in the positive moment regions. This may be related to the descending portion of the stress

-strain relationship for concrete. This effect was apparent in a11 beams tested.

Maximum slip occurred at locations near the load

，

as shown in Fig. 8. This be -havior is similar to that observed in simple span beams. 11. 17 Since shear forces are in opposite directions on opposite sides of the load， slip deformations reverse at the load locations.

Fig. 9 indicates that strains in the transverse reinforcement exceed yield strain in the positive moment regions but not in the negative moment regions， which implies that the transverse reinforcement may be reduced in the negative moment regions. 1n the positive moment regions transverse strains increase with bending moment.

(11)

88 Hamada， Longworth: An Experimental Study ofContinuousComposite Beams.

ofstrain attheedge ofslabto thatatthe c巴nter，'Y(f>was approximately 70 percent as

shown inFig. 10， though itvariedwidely. The theoreticalstraindistribution over slab

width is an exponentialfunction.16_Assuming_t_h_e_f_u_n_c_t_i_o_n_a_s_a_p_a_r_a_b_o_l_a_，_t_h_e_c_f_f_e_c_t_i_v_e_s_l_a_b

width， b e， may be expressed as

e=

ぺ[

1

寸

For the beams tested， b= 6. 5 inches， bc=48 inches and γ{= 0.7. Therefore the effective

slab width

，

be

，

is39.7 inches. The ratio ofeffectivewidth to actual width (be-b) /

(bc -b) equalsto0.8l. In studiesatImperialCollege，6 valuesofthe effective wicth to

actualwidth ranged from 0.35 to0.7 fora width tospan ratioof 0.5 and ranged from

0.55 to l.0 fora width to span ratioof0.25. Based on a theoretical analysis proposed

by Adekola，l a ratio ofeffectivetoactual width equal to0.71 results forthepresent

test beams.

Three crack patterns developed in the slab

，

i.e.

，

transversecracking

，

longitudinal cracking and herringbone cracking.Transverse cracks developed inthenegative moment region at relativelysmallloads due totensile stress. Longitudinal cracks inthe vicinity

of load pointswere produced along the centerline of the beam atlarg巴 loads

，

when the

tnsile strain in thetransversereinforcement suddenly increased due to yielding. Her-ringbone cracks were inclined atapproximately 450 _t_o_t_h_e_{beam c}_e_n_t_e_r_l_i_n_e_{near t}_h_e_ends

of the beams. This angledecreased as theload point was approached.

CONCLUSION

(1) Principalfailuremodes incont;nuous composite beams arecrushing ofconcretein

positive moment regionsand local flange buckling in negative moment regions. The

pumary failureisaffected by theamount oflongitudinalslabreinforcement.

(2) The testbeams exceeded the theoretical ultimate load based on simple plastic theory.

(3) Tests show slightmoment redistributionafter yielding.

(4) Shear connectors in thenegative moment region must be adequat巴 to carrythe

horizontalshear forcesinthelongitudinalslabreinforcement.

(5) Transverse slab reinforcement amounting to0.67 percent of theslab area was suf

-ficient to prevent cracks from significantlyreducing theultimate str巴ngthof the test

beams.

ACKNOWLEDGEMENTS

This investigation is partof a continuing project"B巴havior ofComposite Fiexural

Members" inprogress in the Department of Civil Engineering， the University0ぱfAl肋be訂rt凶a

(12)

Bull. Science & Eeg. Div.. Univ. of the Ryukyus (Engineering) REFERENCES

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b Flange width bc Concrete slab width be Effective siab width

f ~ 28-day cylinder strength of concrete Fy Yield strength of steel

Ml， M2 Bending moments P Load