An investigation of a reinforced concrete rigid frame for ...

IILLINOI SUNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN

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University of Illinois atUrbana-Champaign Library

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AN INVESTIGATIONOF A REINFORCED CONCRETE

RIGID FRAME FOR FARMAND LIGHT INDUSTRIAL STRUCTURES

E. D. Rodda

M. L. Paul

·: ·

A REPORT OF AN INVESTIGATION

conducted byTHE DEPARTMENT OF AGRICULTURAL ENGINEERINGUNIVERSITY OF ILLINOIS

in cooperation withTHE FARM BUREAUOF PORTLAND CEMENT ASSOCIATION

Edited by W. David Penniman and R. Alan Kingery

Illustrated by David C. Hunter

AN INVESTIGATIONOF A REINFORCED CONCRETE

RIGID FRAME FOR FARMAND LIGHT INDUSTRIAL STRUCTURES

by

E. D. Rodda

FORMERLY RESEARCH ASSOCIATE IN AGRICULTURAL ENGINEERING

M. L. Paul

FORMERLY GRADUATE ASSISTANT IN AGRICULTURAL ENGINEERING

ENGINEERING EXPERIMENT STATION BULLETIN NO. 467

© 1963 BY THE BOARD OF TRUSTEES OF THE

UNIVERSITY OF ILLINOIS

(80150) EoLOS

ABSTRACTThe object of this investigation was to obtain information essential to the

development of designs for precast reinforced concrete rigid frames suitable foragricultural and light industrial structures. Tests of four knee frames and onecomplete frame are described and analyzed in this report.

The results of the investigation indicate that behavior of the members underloading can be satisfactorily predicted.

ACKNOWLEDGMENTSThe tests reported herein were performed in the Farm Structures Field Re-

search Laboratory of the Department of Agricultural Engineering, University ofIllinois, in cooperation with the Farm Bureau, Portland Cement Association,Chicago, Illinois.

The program of investigation was guided by the following advisory com-

mittee: M. L. Burgener, W. V. Wagner, Jr., and C. A. Kincaid, representing thePortland Cement Association; and E. L. Hansen and J. O. Curtis, representingthe University of Illinois.

Appreciation is expressed to C. K. Spillman and J. R. Johnstone, respectively

graduate assistant and laboratory mechanic in Agricultural Engineering, for their

contributions to the development and fabrication of test equipment.The authors also wish to acknowledge the helpful suggestions of Dr. M. A.

Sozen, Associate Professor of Civil Engineering.In addition, acknowledgments are due the members of the critical review

board: W. E. Kunze, Manager of the Structural Bureau, Portland Cement Asso-ciation; G. L. Nelson, Professor of Agricultural Engineering, Oklahoma State

University; and J. O. Smith, Professor of Theoretical and Applied Mechanics,University of Illinois.

This bulletin is based on masters' theses by E. D. Rodda and M. L. Paul,written under the direction of Professor E. L. Hansen.

CONTENTS

I. INTRODUCTION 9

A. Object and Scope 9

B. Notations 10

II. KNEE FRAMES 11

A. Description and Fabrication of Test Specimens 11

B. Test Equipment and Procedure 14

C. Discussion of Test Results 17

III. COMPLETE FRAME 20

A. Description of Rigid Frame 20

B. Fabrication of Test Frame 21

C. Test Equipment and Procedure 23

D. Discussion of Test Results 26

E. Conclusions and Recommendations 31

F. Construction Modifications 31

IV. REFERENCES CITED 32

V. APPENDICES 33

A. Construction of Interaction Diagrams for Yield

and Ultimate Flexural Capacities 33

B. Calculations for Theoretical Load-Deflection Curve of Figure 19 34

FIGURES

1. 36-ft-span test frame details 92. 36-ft-span rigid frame: shear and moment diagrams 123. Knee frame test specimens 134. Detail of test specimen numbers C-2 and T-2 and strain gage

positions for compression tests 135. Average stress-strain relationships 146. Compression test arrangement 157. Tension test arrangement 158. Load-deflection curves 159. Crack pattern at failure for compression knee frame C-1 17

10. Crack pattern at failure for tension knee frame T-1 1711. Crack pattern at failure for compression knee frame C-2 1712. Crack pattern at failure for tension knee frame T-2 1713. Knee frames: interaction diagrams for ultimate flexural capacity

of given cross-section (loading curve superimposed) 1814. 36-ft-span test frame: shear and moment diagrams

for uniform vertical load 2015. Reinforcement joint details of 36-ft-span frame 2216. Reinforcing cages for 36-ft-span frame 2317. Test arrangement for 36-ft-span frame 2418. Drawing of test set-up 2419. Load-deflection curves for 36-ft-span frame 2620. Vertical vs. horizontal reaction for 36-ft-span frame 2721. Load-moment curves for 36-ft-span frame 2722. Strain-load curves for 36-ft-span frame 27

23. 36-ft-span frame: interaction diagram for yield and ultimate flexuralcapacity of knee cross section (loading curve superimposed) 27

24. 36-ft-span frame: interaction diagram for yield and ultimate flexuralcapacity of peak cross section (loading curve superimposed) 28

25. Crack pattern for left knee of 36-ft-span frame 2826. Crack pattern for left scarf joint of 36-ft-span frame 2827. Crack pattern for left half of 36-ft-span frame 2928. Crack pattern for right half of 36-ft-span frame 2929. Knee joints of 36-ft-span frame after testing 3030. Scarf joints of 36-ft-span frame after testing 3031. Simplified stress-strain curve for reinforcing steel 3332. Assumed conditions of stress and strain for ultimate capacity 3333. Assumed conditions of stress and strain for yield capacity 3434. Interaction diagrams for yield and ultimate flexural capacities 34

TABLES

1. Test Data for Compression Knee Frame C-2 162. Loading Values for Compression Knee Frame C-2 163. Test Data for Tension Knee Frame T-2 164. Loading Values for Tension Knee Frame T-2 165. Ultimate Loads and Moments Resisted by Knee Frames 186. Test Results for 36-Ft-Span Frame 257. Measured Strains on Tension Reinforcement of 36-Ft-Span Frame 268. Measured Strains on Compression Concrete of 36-Ft-Span Frame 26

I. INTRODUCTION

A. OBJECT AND SCOPE

The investigation described in this bulletin wasundertaken to develop a series of basic designs ofprecast reinforced concrete rigid frames suitable foragricultural or utility structures. Interest in thistype of structural component in reinforced concretehas been generated as a result of the rapid accept-ance of steel and lumber clear-span structures in

the agricultural field. Reinforced concrete has beenused for framing agricultural structures to someextent in other countries, but its use in the UnitedStates has been very limited.

This report is based on the results of tests onone complete full-sized frame, Figure 1 andfour knee frame specimens, Figures 3 and 4.The information presented is confined to one basic

Roof member

B-B

Left leg member

Figure 1. 36-ft-span test frame details

\

BULLETIN 467. INVESTIGATION OF A CONCRETE RIGID FRAME

design for a 36-foot-span gable frame. A constantcross section of 6 inches by 10 inches was main-tained in all test members. Two designs for the re-inforcing detail at the knee joint were investigated.

In this investigation, the primary concern wasexperimental verification of ultimate strength con-cepts as applied to the highly reinforced designcross section. Particular attention was focused onthe behavior and modes of failure of the framemembers involved.

B. NOTATIONS

The most common symbols used in this study arelisted below for reference. Wherever used, theboldface superscripts A, B, C, etc., refer to an indi-cated location on the test frame. Subscripts y and urefer, respectively, to yield and ultimate.

A, = total area of moment reinforcement in tensionA,' = total area of moment reinforcement in com-

pressionb = width of memberC, = total compressive force in concreteC, = total compressive force in compression steela, = deflection in horizontal directionAv = deflection in vertical directiond = distance from the compression face of mem-

ber to the centroid of the tensile steeld' = distance from the compression face of the

member to the centroid of the compressionsteel

e = eccentricity with respect to mid-depth ofsection

Ec = strain in the concrete

eS = strain in the steelc, = crushing strain of the concretey, = yield point strain of the steel

Ec = modulus of elasticity of concreteE, = modulus of elasticity of reinforcing steelfe = compressive stress in concretec' = compressive strength of concrete, as deter-

mined from standard 6-inch by 12-inch con-trol cylinders

f, = stress in the steelf, = yield point stress of the steelh = overall depth of memberj = ratio of lever arm of internal resisting mo-

ment at yielding to effective depth in a sec-tion where no axial load is present

kc = ratio of area of concrete stress block to areaof enclosing rectangle

k, = fraction of depth of compressive zone whichdescribes the position of the compressiveforce C, in the concrete

k, = ratio of maximum compressive stress in con-crete member to cylinder strength

k, = ratio of depth of compressive zone to effectivedepth, d

M = bending momentn = E,/E, = elastic modular ratio taken as

Es1000 f'

N = axial force or loadp = percentage of tensile reinforcement for nega-

tive momentP = total applied load for knee framesD = curvature (radians/inch)R,, = reaction in horizontal directionRv = reaction in vertical directionT = total tensile force in tension steelV = shearVc = safe shear value of concretew = uniform loading (kips/ft)W = total load for rigid frame

II. KNEE FRAMES

A. DESCRIPTION AND FABRICATIONOF TEST SPECIMENS

1. Design of Knee FramesThe basic rigid frame chosen was a 36-ft-span

gable frame with 12-ft sidewalls and a 4:12 roofslope, Figure 1. The frame was analyzed for designloads consisting of dead load, snow load, and windload. A line diagram of the basic frame outlineplus shear and moment diagrams for the two worstload combinations are shown in Figures 2a and 2b.Since the knee joint was found to be the criticalpoint in the frame, the original cross section wasdesigned to satisfy conditions there. Knee frametest specimens were chosen representing that por-tion of the rigid frame included between the pointof contraflexure in the sidewall leg and the point ofcontraflexure in the roof.

The general shape of the test specimens is shownin Figure 3, which illustrates the compression speci-men. The tension specimens were identical inconstruction except for the inclined portion (repre-senting the roof) being 8 inches shorter and thetwo 2-inch-diameter pipes inserted for applyingload in place of the compression loading faces (seeFigure 7). The external dimensions of the testspecimens were fixed by the following considera-tions.

Three reasons dictated the choice of a 6-inch by10-inch cross section: (1) the indication of sectionsize requirements from preliminary calculationsconsidering the frame as both a column and a beam,(2) the necessity of holding the section size smallto reduce the dead load and to facilitate transporta-tion and erection, and (3) the desirability of mini-mum interference of the structural frame with theinterior utilization of the building.

It was necessary to have the moment, shear, andaxial load combinations exactly duplicate the con-ditions at the critical section as determined byelastic analysis. The length of the inclined memberrepresenting the roof was determined by statics tocomply with this condition. The length of the verti-

cal leg was held as the distance to the point ofcontraflexure.

Because the axial load was small in comparisonto the bending moment, initial selection of the crosssection was made considering bending only.Nominal design values of f,' = 3000 p.s.i. andf= 40,000 p.s.i. were used, and a value of

q P = 0.18 corresponding to American Concrete

Institute (A.C.I.) balanced design was selected.Using an over-all safety factor of two, sectiondimensions were chosen by

M, = bd 2fq'q(l - 0.59q)

taking b and d in the ratio of 1 to 2.Knowing that tensile steel on the inside of the

frame would be required for reversed moments dueto wind loads, it was necessary to consider it ascompressive reinforcement to resist the effect ofdead load and snow load. The effective depth wastherefore decreased to d = 8.5 inches, using a coverof 1.5 inches to the center of the steel. The require-ment for tension steel for reversed moment was thencomputed for the trial section by

Mu = A,'fjd

taking j = 0.86 as satisfactory for the initial trial.Interaction diagrams were then constructed to

determine if the section met all design requirementsindicated by elastic analysis.

The safe value for shear was taken as

V, = 2Vft'bjd

taking j = 0.86 as satisfactory since the section washeavily reinforced in compression. Maximum stirrupspacing was chosen as the over-all depth of thesection.

For the original set of knee frames, two addi-tional reversed stirrups were placed in each kneejoint to provide restraint and confinement (Figure3). Because these proved inadequate, welded strutswere used in the joints of the second set of framesas illustrated in Figure 4.

12 BULLETIN 467. INVESTIGATION OF A CONCRETE RIGID FRAME

.30 k/ft1 1 1 i -

(a) Dead load and snow load

3.28k

18.2 ft-k

----- 36'5.40k

3.28 k

Constant El

Figure 2. 36-ft-span rigid frame: shear and moment diagrams

- ----

II. KNEE FRAMES

Additional design details for the welded rein-forcement at the knee joint have been indicated inFigure 4. It became apparent, from curved beamtheory and from a simplified force analysis at theknee, that the magnitude of the forces in the radialdirection was of the same order as those in thelongitudinal steel. The two bars on the center ofthe bend were therefore selected in the same size asthe longitudinal bars. This was also convenientsince scrap lengths are normally available from anyfabrication process. The ends of the stub lengthswere butt welded to the two longitudinal bars onthe inner side and between the three bars on theouter face. The bars on either side of the bend wereplaced perpendicular to the longitudinal steel at thepoint of tangency of the inside curve, and the samesize was used for convenience. These bars servedto position the steel accurately and provided addi-tional confinement for the concrete in the knee.

2. Materialsa. CONCRETE

Specifications for the concrete were written withregard to normal operating procedure at a precast-ing plant where frames of this type would be manu-factured. Ready-mix concrete was used for all test

specimens considered in this report. A 1:2.5:3.0mix was chosen, and a 1-inch slump specified. TypeIII-A Portland cement was used. The aggregatesused were Wabash River sand and gravel. Bothhave been used in previous investigations and havepassed the usual specification tests. Normal designstrength of the concrete called for f,' = 3000 p.s.i.;actual compressive strength was determined fromstandard 6-inch by 12-inch cylinders.

b. REINFORCING STEELAll longitudinal and radial reinforcement used

was from a single lot of No. 7 deformed bars. Onesample was cut from each of five bars and tested intension. Average yield point stress was determinedas 45,000 p.s.i.

The stirrup steel used was from two lots ofNo. 2 bars that were laboratory tested; the yieldpoint stress was found to be equal to 50,000 p.s.i.for both lots.

Average stress-strain relationships for the rein-forcement are shown in Figures 5a and 5b.

3. Fabrication and CuringThe knee frame test specimens were cast hori-

zontally in wood forms constructed of nominal2-inch lumber.

Steel reinforcing cages for the frames were com-

Figure 3. Knee frame test specimensFigure 4. Detail of test specimen numbers C-2 and T-2

and strain gage positions for compression tests


pletely assembled before positioning in the forms.All bends in the reinforcing bars were made cold.For the two specimens with the revised reinforce-ment design at the knee, the radial reinforcingstruts were welded in position, using an arc welderand E7018 electrodes. The reinforcing cages weresupported in position in the forms by means of"chairs" bent from /4 -inch mild steel bars. Priorto casting, electric strain gages were installed onthe tension steel of each specimen so that strainmeasurements could be taken during testing.

A standard slump test was run for each of thetwo batches of concrete used, one batch being usedfor each pair of frames. For determination of com-pressive strength, two 6-inch by 12-inch controlcylinders were cast from the first batch; four con-trol cylinders were cast from the second batch. Ahigh-frequency internal vibrator was used to placethe concrete in both the forms and the cylindermolds.

After the concrete began to harden, the topsurfaces of the knee frames were troweled smooth.Several hours after casting, the cylinders werecapped with neat cement paste. The knee framesand the cylinders were removed from their formsthe day following casting. Both were cured underplastic film for three days in the laboratory. Fol-lowing this, the film was removed, and the testspecimens and cylinders were stored in the labor-atory until tested.

B. TEST EQUIPMENT AND PROCEDURE

1. Measuring Equipmenta. ELECTRIC STRAIN GAGES

SR-4 electric strain gages were used to measurestrains in the concrete and the reinforcing steel.Strains were read to the nearest 10 micro-inchesper inch with a Baldwin Portable Strain Indicator.Temperature-compensating gages were mounted onunstressed lengths of No. 7 reinforcing bars. Allelectric strain gages were mounted with Ducocement.

Strains in the tensile reinforcing bars were meas-ured with type A-7 gages which have a nominalgage length of 1 inch and a minimum trim widthof 3/16 inch. They were chosen for their narrowwidth, short length, and flexibility. Two gages wereused in each specimen and were located on thetension steel, one on each side of the joint. Theywere positioned on gage lines 21/2 inches from thecritical sections at the joint, as illustrated in Figure

4 for the compression frame. The gages wereallowed to air dry for 24 hours or more after mount-ing. They were then waterproofed with Epoxoid,wrapped with electrical tape, and given a final coatof Epoxoid. Lead wires from the gages were broughtup through the side of the frame.

Strains in the concrete were measured on thecompression face with type A-3 gages, which havea nominal gage length of 13/16 inch. Originallythe results given by the A-3 gages were checkedagainst a type A-9 gage, which has a 6-inch gagelength and gives average strain readings corre-sponding to those given by mechanical strain gages.Thus, for the original compression specimen onetype A-9 gage was placed on each side of the jointone inch from the minimum sections at the joint,with the longitudinal axis of the gage on the center-line of the compression face. Three type A-3 gageswere then placed parallel to each of the long A-9gages to secure measurements over the same gagelengths. Test results indicated that average strain

80 Ultimate stress - 79.2 ksi

60 -_ -

40 f, 45 ksi40 --

(0) No. 7 bars8' gage length

20Modulus of elasticity

30 x 106 psi

0

60

fy= 49.3 ksi

40(b) No. 2 bars

2" gage length

20

0 I 2 3 4 5

Unit stress, per cent

Figure 5. Average stress-strain relationships

I I I I I I

II. KNEE FRAMES

Figure 6. Compression test arrangement

readings had( little meaning in determining ultimatestrain conditions where failure occurs over a shortdistance. The shorter A-3 gages were therefore usedin all succedling tests. Two A-3 gages weremiounted parallel to one another directly oppositeeach A-7 gage on the steel.

1). LOAD I)YNAMOxITERSApplied loads were measured by means of elec-

tric strain gage ring-type dynamometers, cali-brated for use with a Baldwin Strain Indicator.Both dynamometers were laboratory constructed.(Calibration of these instruments yielded constantsof 41.8 lb. per dial division and 34.4 lb. per dialdivision, respectively, for the compression and thetension dynaimometer.

c. I )FI:CTOMETE'A deflectomcter iemploying a 2-inch Ames dial

indicator reading to 0.001 inch was used to measureend deflections. It was placed between the ends of

the frame along the line of action of the appliedload and supported by clamps and brackets securedto the test floor. End points were established by

cementing angles on the top surface of the concrete.

2. Loading Apparatus

Test arrangements for the compression and ten-sion tests are shown in Figures 6 and 7. In both

cases the frames were supported in a horizontal

position by plates and rollers. A 10-ton hydraulicjack provided the load for the tests. The jack wasattached to a reaction bracket anchored to loadrails embedded in the test floor.

In the compression tests, load was transmittedfrom the jack ram to the frame through a 1-inchchrome steel alloy ball in order to maintain a uni-

directional force. The ball was placed between a1/s-inch depression at the end of the jack ram anlda depression of the sameaiC size in the center of a

Qe

a

0=

a.a.

End deflechion, inches

Figure 7. Tension test arrangement Figure B. Load-deflection curves


Table 1

Test Data for Compression Knee Frame C-2

Applied End Steel Strain Concrete StrainLoad Deflection (microin./in.) (microin./in.)(kips) (in.) GA. #1* GA. #1 GA. #2*1.00 0.040 60 110 1002.09 0.097 160 200 1803.09 0.145 260 300 2804.10 0.204 370 420 3804.93 0.262 470 510 4805.85 0.318 560 620 5706.81** 0.376 660 730 6707.73 0.435 760 850 6908.74 0.493 860 970 8909.74 0.561 960 1110 102010.70 0.623 1060 1240 114011.70 0.688 1170 1390 128012.71 0.757 1280 1540 142013.63 0.822 1380 1700 156014.71 0.914 1510 1940 177015.22 0.977 1590 2120 195015.30 0.996 1610 2410 227015.47 1.17215.76 1.23315.93 1.28215.63 1.33215.72 1.38215.80 1.48215.63 1.58215.63 1.68215.59 1.78215.42 1.882

* Located on leg side of knee joint.** Initial cracking.

1-inch thick bearing plate mounted on the loadingface with dental plaster. The dynamometer locatedat the other end of the frame was loaded in thesame manner.

In the tension tests, load was transmitted fromthe jack ram to the frame through a harness at-tached to a 2-inch-diameter pipe cast in the con-crete. The other end of the frame took the reactionthrough two lug straps pulling on a ring-typedynamometer. The dynamometer was attached toa reaction bracket by a 1-inch-diameter bolt in-

Table 2

Loading Values for Compression Knee Frame C-2

P(kips)1.002.093.094.104.935.856.817.738.749.74

10.7011.7012.7113.6314,7115.2215.3015.4715.7615.9315.6315.7215.8015.6315.6315.5915.42

N(kips)0.861.792.643.504.215.005.826.607.468.329.1410.0010.8511.6412.5712.9913.0713.2113.4613.6013.3513.4213.4913.3513.3513.3213.17

e(in.)

0.0210.0500.0750.1060.1360.1650.1950.2260.2560.2920.3240.3580.3940.4270.4750.5080.5180.6090.6410.6670.6930.7190.7710.8230.8750.9270.979

M(in.-kips)

38.479.9

118.4156.9189.0224.5261.5297.0335,8374.6411.9450.9489.9525.8568.3588.1591.5599.1610.9617.7606.7610.3614.3608.5609.2608.2602.4

Computed quantities at critical section, leg side of knee joint:N = P sin 58040'

e = A cos 58040'V = P cos 58040'

M = V(73.5) + Ne

Table 3

Test Data for Tension Knee Frame T-2

AppliedLoad(kips)0.501.892.292.793.293.784.28**4.785.285.786.286.787.287.778.278.779.27

EndDeflection

(in.)0.0190.0890.1080.1300.1560.1850.2190.2560.2910.3280.3670.4110.4530.4920.5380.5800.633

Steel Strain(microin./in.)

GA. #1"20

160190250300360430520600680770870950

1040112012101340

Concrete Strain(microiin./in.)

GA. 1* GA. #2*30 40

140 170140 180160 210200 250240 290270 340320 390350 430390 480430 520480 580530 640590 710660 780730 880840 1010

* Located on leg side of knee joint.* Initial cracking.

serted through holes in the center of the dynamom-eter plates.

3. Testing Procedure

Care was taken to insure proper alignment ofthe test specimens in the testing rig. A small initialpressure was applied to the frames, and final adjust-ments were made before beginning the tests. Loadwas applied in approximately uniform increments,taking smaller load increments as yielding wasapproached. After failure occurred, loading pro-ceeded by increments of deflection.

Following each application of load, deflectionand strain readings were taken. Cracks were ob-served through a low-power illuminated magnify-ing glass and marked with ink. Crack progress wasindicated by number. There was usually a slightdrop in load while readings and observations weremade. However, it was so small as to be insignifi-cant.

Table 4

Loading Values

N(kips)0.441.662.012.452.893.333.774.204.645.085.525.966.406.837.277.718.15

for Tension Knee Frame T-2

e(in.)

0.0090.0420.0510.0620.0740.0880.1040.1220.1390.1560.1750.1960.2160.2350.2570.2770.302

V(kips)0.240.901.091.331.571.812.042.282.522.763.003.233.473.713.954.184.42

M(in.-kips)

17.566.280.197.5

115.0132.4149.8167.1184.5201.9219.2236.5253.7270.9288.2305.4322.6

Computed quantities at critical section, leg side of knee joint:N = P sin 61030'

e = A cos 61°30'V = P cos 61030'

M = V(73.5) - Ne

II. KNEE FRAMES

Figure 9. Crack pattern at failure for compression knee frame C-1

C. DISCUSSION OF TEST RESULTS

1. Behavior

Load-deflection curves for the knee frames arepresented in Figures 8a and 8b. Both curves ofFigure 8a have a recognizable elastic range. FrameC-1 behaved nearly elastically up to first flexuralcracking at approximately 10 kips load. As flexuralcracking continued to develop, deflection increasedand the load-deflection curve became irregular,varying with crack development. Frame C-2 be-haved in a nearly elastic manner up to approxi-mately 14.7 kips load, at which point the tensionsteel yielded. A rather sharp decrease in slope ofthe load-deflection curve is apparent at this point.Neither tension frame developed yield strength.Frame T-1 failed prematurely at the development

Figure 11. Crack pattern at failure for compression knee frame C-2

of initial cracking, which started in flexure butspread rapidly due to a secondary tension causedby outward deflection of the compression steel.Some increase in load was developed, but failurehad already occurred. Frame T-2 also failed pre-maturely. Measured steel strains for this membernever reached the yield point, and failure occurredby fracture of the inner tensile bars which had beencold formed on a sharp bend. The load-deflectioncurve of Figure 8b clearly indicates no yield rangefor this frame. Measured and computed values forframes C-2 and T-2 are presented in Tables 1through 4.

2. Crack Patterns

Crack patterns at failure for the compressionand tension knee frames are shown in Figures 9through 12. Order of crack development is indicatedby number, the first visible crack being designatedwith the number "1."

Crack patterns for the compression specimensindicated flexural failure up to ultimate, althoughthe surface of the concrete of frame C-1 began tobulge, indicating the desirability of additional con-finement at the knee joint. This was provided in

Figure 10. Crack pattern at failure for tension knee frame T-1 Figure 12. Crack pattern at failure for tension knee frame T-2


M in in.-kips

Figure 13. Knee frames: interaction diagrams for ultimate flexural capacity of given cross-section (loading curve superimposed)

Table 5

Ultimate Loads and Moments Resisted by Knee Frames

Mark P max. V N M(kips) (kips) (kips) (in.-kips)

f = 45,000 p.s.i. /' = 4520 p.s.i.C-l 15.49 8.05 13.23 599.4T-1 4.84 2.31 4.25 168.8

f, = 45,000 p.s.i. .' = 3360 p.s.i.C-2 15.93 8.28 13.60 617.7T-2 9.27 4.42 8.15 322.6

frames C-2 and T-2 through the use of six weldedstruts made from No. 7 bars.

The crack patterns for the tension specimens areshown in Figures 10 and 12. The pattern for frameT-1 was directly opposed to that of sudden failure(as characteristic of shear), and flattened out al-most parallel to the compression face as it pro-gressed. Examination of the failure revealed that thecompression steel had moved outward, producing atensile force in the concrete in this area and thusaccounting for the change in direction of the crackpattern. The crack pattern for frame T-2 was con-centrated at the joint due to the type of failure.

3. Modes of FailureNeither of the knee frames with the original

joint design failed in a clearly defined manner.Frame C-1 approached flexural failure throughyielding of the tension steel, but ultimate failurewas by secondary crushing of the concrete in bear-ing under the tension steel at the knee. Frame T-1

failed prematurely by outward deflection of thecompression steel, which in turn caused crackingin the concrete on the plane of principal stress.

The revised joint design incorporated in thesecond set of frames proved more satisfactory.Frame C-2 failed in a well defined and desirablemanner. Initial yielding of the steel, followed bycrushing of the concrete, produced a flexural failurecharacteristic of an under-reinforced section. Re-moval of some concrete after testing indicated thatthe radial reinforcing arrangement at the knee hadnot been affected under the test load. Tensionframe T-2 failed by fracture of the tension steel atthe bend in the joint. This frame showed no yieldrange, failing in a brittle manner. Fracture wasattributed to the severe cold bending of the innersteel bars during fabrication. This bending pro-duced strains well beyond the yield range of thesteel. When the frame was then tested, an addi-tional tensile strain was imposed upon the bentsection of the bars and a tension force was exertedby the radial reinforcing spokes. The combinationof forces produced a state of stress at the bendsufficient to cause fracture. Although this type offailure was undesirable, it nevertheless proved moresatisfactory than the failure of frame T-1 becausethe longitudinal steel was held from any lateralmovement. Since only flexural cracking developed,the compression concrete could thus act to full

II. KNEE FRAMES

advantage, allowing nearly twice the total load-carrying capacity of frame T-1.

4. Comparison of Test Resultswith Interaction DiagramsInteraction curves predicting ultimate flexural

capacities of the cross sections for both compressionand tension loading are shown in Figures 13athrough 13d. The assumptions and procedures fol-lowed in obtaining these curves are outlined inAppendix A. The interaction curves are based onactual strength of the materials used, that is, theaverage ultimate compressive strength of the con-

crete as determined from the cylinder tests and theaverage tensile yield point stress of the steel asgiven by the stress-strain relationship of Figure 5a.

Loading curves for the knee-frame tests areplotted on the appropriate interaction diagrams.The terminal point on the loading curves indicatesthe maximum axial load and moment resisted byeach frame at the critical section. It can be seenfrom the diagrams that this ultimate point waspredicted quite closely for frames C-1 and C-2.Loading values for the tension knee frames T-1 andT-2 did not reach the interaction curves due to thetype of failure experienced.

III. COMPLETE FRAME

A. DESCRIPTION OF RIGID FRAME

1. Introductory RemarksUpon completion of the knee-frame tests, the

behavior of a complete reinforced concrete rigidframe tested to failure under uniform loading wasstudied.

To simplify the test arrangement, the fixed-endrigid frame of Figure 2a was reduced to a two-hinged arch with sidewall height equal to one-halfthat of the original. This approximated the condi-tion of the actual frame at ultimate, since at ulti-mate load the point of contraflexure in the leg is atmid-height. The two-hinged arch was analyzed inthe same manner as the fixed-end frame. Shearand moment diagrams for a uniform loading of wkips per foot on the hinged frame are shown inFigure 14. A comparison of the diagrams of Figure2a and 14 reveals that slightly different values ofV and M would be produced at normal workingloads.

2. Design of FrameDesign was based on ultimate strength concepts

and results of the knee-frame tests. The frame wasdesigned to be cast in three component parts -two leg portions similar to the knee frame testspecimens and a roof section to be included betweenthe leg members. This design feature was includedfor ease in handling and transportation. Details ofthe test frame are shown in Figure 1.

A constant 6-inch by 10-inch cross section wasmaintained throughout this frame. A tapered sec-tion was found to give little savings in materialsbesides being somewhat more difficult and expensiveto fabricate. Moreover, tests reported in BulletinNo. 307 of the University of Illinois EngineeringExperiment Station indicated that a haunch at theknee would not significantly increase the over-allload capacity of the frame. A deeper section at theknee in this statically indeterminate structure wouldhave increased the stiffness in that portion of theframe and thus attracted more moment. The netresult would have been a shift in the location ofthe critical section. A constant section was there-fore selected for maximum ease and economy offabrication, plus added flexibility in the modifica-tion of forms for different spans.

Constant El

/8.0W I 36' .I 18.0 W

0¶Figure 14. 36-ft-span test frame: shear and moment diagrams for uniform vertical load

III. COMPLETE FRAME

The amount and arrangement of moment steelin the leg sections of the frame was identical to thatof the knee frames- three No. 7 bars on the outertension side and two No. 7 bars on the inner side.For the remaining roof portion of the frame, themoment steel was reduced to two No. 7 bars foreach side of the cross section. Under usual loadingconditions this center portion of the frame is sub-jected to positive moment and the inner reinforce-ment thus becomes the tension steel. The distancebetween the moment steel was decreased to 61/2inches throughout this frame as compared to 7inches for the knee frames. This additional 1/ inchon each side of the reinforcing cage allowed easierplacement of concrete in the forms and momentcapacity was still adequate, based on a safetyfactor of two. The knee and peak joints were fabri-cated in the same manner as the knee joints forframes C-2 and T-2; that is, the radial weldedspoke design was used.

A scarf joint was designed for fastening thethree sections together into a completely assembledframe. This joint was located at a point of theoreti-cal zero moment as indicated by the elastic analysisof Figure 2a. The primary concern, designing foraxial force to be resisted in this region, was accom-plished by bolting. Two %-inch high-strengthbolts inserted through each joint and torqued to310 ft-lb. were found to provide sufficient normalforce so that adequate friction could be developedbetween contact surfaces of the scarf joints. Dueto shifting of the point of contraflexure for otherloadings, some moment capacity had to be providedat the joint. For moment consideration, the criticalsections of the scarf were at the ends of the joinedmembers. Calculations showed that the 3/-inchhigh-strength bolts spaced 8 inches center-to-centerprovided adequate capacity. To help preserve theintegrity of the joint at the ends of the joinedmembers, two pieces of No. 7 bar were welded inbetween the inner and outer reinforcement on anangle parallel to the joint faces. Small confiningstirrups were bent completely around the converg-ing reinforcing bars and tack welded.

The mechanics of designing the scarf joint re-quired only the application of statics. An estimateof the maximum moment capacity which might berequired at the critical sections of the scarf jointwas obtained by assuming a parabolic momentcurve between the positive ultimate at the peaksection and the negative ultimate at the knee sec-

tion. This condition corresponded to a collapsemechanism of a plastic hinge at each knee and aplastic hinge at the peak. The minimum momentcapacity of the critical section at the beginningof the scarf joint as shown in Figure 1 was thencomputed, considering the inclined bars as tensionsteel. A comparison of the computed minimum ulti-mate and the maximum moment which might berequired gave a factor of safety in excess of three.

A scarf joint slope of 15 degrees was selectedas an efficient angle for transmission of axial loadbased on preliminary work at the Portland CementAssociation Structural Research Laboratory, anda conservative estimate of 0.5 was made for thecoefficient of friction between the concrete surfaces.The axial load to be transmitted in the joint wasdetermined from elastic analysis. A comparisonof the normal force required to transmit axial loadand the bolt forces required to provide a momentcouple equal to the minimum ultimate at the criticalsection showed that the moment requirement wasthe controlling factor. Two 4 -inch-diameter A-325bolts were selected to provide the normal forcewhen torqued to proof load, as prescribed by theResearch Council on Riveted and Bolted StructuralJoints of the Engineering Foundation. The spacingof the bolts within -the limits of the joint was deter-mined to provide a moment couple equal to theminimum ultimate moment at the critical section.

B. FABRICATION OF TEST FRAME

1. FormsForms of nominal 2-inch lumber were con-

structed to permit horizontal casting of the framesections. Dimensions were closely checked through-out construction. The side forms were secured to1/-inch-plywood bases, and the separate assemblieswere held in position by fastening to anchor clipsin the laboratory test floor. Holes were drilledthrough the forms on the interior face of the scarfjoints at the bolt locations. Pieces of /s-inch-diameter tubing were later placed through the holesand supported on the exterior face by the 3-inch by3-inch by 12 -inch steel washers, which were tackedin position on the inside face of the forms. Thesetubes were to provide holes through the concretefor later insertion of the bolts. Prior to casting, theforms were oiled to prevent loss of moisture fromthe concrete and to facilitate form stripping.


b. Peak joint

c. Scarf joint

d. Base joint

Figure 15. Reinforcement joint details of 36-ft-span frame

2. Reinforcing Cages

The reinforcing steel used in the fabrication ofthis frame was from the same lot as that used forthe knee frames. Bending and welding operationsnecessary for the fabrication of the reinforcingcages followed the same procedure as that for kneeframes C-2 and T-2.

Stirrups were wired in position and spaced asshown in Figure 1. They were placed with thehooks in the compression side of the member asindicated by the moment diagrams in Figure 2a.The small confining stirrups in the scarf joint sec-tions were tack welded in position.

Radial reinforcing spokes were welded in at thetwo knee joints and at the peak. The diagonalreinforcing pieces were also welded in between theinner and outer reinforcement of the scarf jointarea. In each leg of the frame the base ends of thereinforcing bars were cut off at an angle of 30 de-grees to the axis of the bar and welded to a 1-inch-thick base plate cut to the dimensions of the crosssection. This base plate acted both as an end sec-tion of the form and as a load plate to transmit thereactions during testing.

Details of the previously discussed joints areshown in Figure 15. Over-all views of the assembledreinforcing cages positioned on top of their respec-tive forms are shown in Figure 16.

The completely assembled reinforcing cageswere supported in the forms by means of the"chairs" previously described. Prior to casting,electric strain gages were installed on the tensionsteel.

3. Casting and Curing

The concrete used in this frame was from asingle batch of ready-mix material. Specificationsfor the mix were the same as that for the kneeframes. The concrete was placed immediately uponreceipt. A standard slump test showed that theconcrete had a 1-inch slump. Six standard 6-inchby 12-inch control cylinders were made for deter-mination of compressive strength. The concrete was

placed in the forms and cylinder molds with aninternal vibrator. Special care was taken in placingthe concrete around the scarf joint reinforcement.

Approximately two hours after casting, the topsurface of the frame sections were steel troweled,and the test cylinders were capped with neat cement

paste. Forms and cylinder molds were removedthe (lay after casting. The frame sections and thetest cylinders were cured under plastic film in

111. COMPLETE FRAME

a. Lenter roor memoer

b. Left leg

c. Right leg

Figure 16. Reinforcing cages for 36-ft-span frame

the laboratory for four (lays. The film was thenremoved and the frame sections and cylinders werestored in the laboratory until tested. During thistime, the three sections of the frame were boltedtogether with four high-strength bolts tightened toa torque of 310 ft-lb, and the ends of the scarfjoints were packed with a stiff sand-cement grout.A small amount of aluminum powder was added tothe grout to prevent shrinkage.

C. TEST EQUIPMENT AND PROCEDURE

1. Measuring Equipmenta. ErLTC'RIC STRAIN GAGES

Twelve SR-4 strain gages were used to measurestrains at three critical locations in the frame. Thegages were of the same type as those used for theknee frames of this report. All of the gages were

installed in the same manner as described for theknee frames.

A pair of A-7 gages was mounted on the tensionsteel at each knee joint and at the peak joint. Gagelocation was on a line 21/% inches from each of thecritical sections at the joints. The mounted gagescan be seen in the joint details of Figures 15a and15b. A single A-3 gage was mounted on the com-pression face of the concrete in a position directlyacross the section from each A-7 gage at the knees.At the peak, the A-3 gages were not placed directlyopposite the A-7 gages on the 21.-inch gage line.Here the compression face of the concrete was onthe top side of the loaded roof, and load shoes onthe jacks did not permit relative gage placement.The peak A-3 gages were therefore located 10inches from the top edge of the peak in positionsbetween the loading sloes.

Wires from the gages were connected to aswitching board at the recording table. All leadwires were equal lengths of plastic coated No. 20solid copper wire.

Strains were read to the nearest 5 micro-inches

per inch with a Type "NB" Baldwin StrainIndicator. Temperature-compensating gages weremounted on unstressed lengths of No. 7 reinforc-ing bar.

1). LOAD I)YNAMOMENII1TEs

Two 30-kip strain gage load cells were used tomeasure the vertical reactions. Each load cell waslocated between the bottom of one of the frame legsand a reaction bracket. The horizontal reactionwas measured by means of a 10-kip strain gagetension link, which was inserted in the center of atension rod connecting the base of the frame legs.All three of the measuring devices were laboratory-made. They were self-compensating for tempera-ture and measured only pure compression andtension.

Leads from the load dynamometers were car-ried to the recording table where switching wasaccomplished by three Jones plugs. Load measure-ments were determined using a Type "K" BaldwinStrain Indicator. Calibration of the dynamometers

prior to use gave constants of 136.3 lb. per divisionand 134.6 lb. per division for the two 30 kip loadcells, and 64.5 lb. per division for the tension link.

c. DIAL INDICATORS

Nine Ames dial indicators, all reading to 0.001inch, were used for measuring deflections. Onesuch indicator having a 4-inch plunger travel was


Figure 17. Test arrangement for 36-ft-span frame

used for measuring the deflection at the roof peak.The remaining eight dial indicators were used toobtain other pertinent measurements. One 2-inchindicator was located at each knee to measuresidesway deflection. One 1-inch indicator was lo-cated on the inside base of each leg in order tomaintain constant distance between frame legs. A1-inch indicator was also used at the bottom of eachleg to indicate any deflection in the reaction brack-ets. By means of another two indicators, onelocated at the top of each frame leg, it was thoughtthat some indication of leg shortening might begiven, but due to large rotations at the knee thislatter measurement was meaningless. All dial indi-cators were supported by either ring-stands andclamps or by adjustable holding brackets attached

to the laboratory floor. Plungers of the indicatorslocated at the peak and at the knees bore againstshort pieces of 1-inch by 1-inch by li-inch anglescemented in centerline positions to the top surfaceof the concrete. The indicators which measureddeflection in the reaction brackets bore againstheavier pieces of steel angle positioned near theleg bases.

2. Loading Equipment

The test setup is shown in Figures 17 and 18.The frame was tested in a horizontal position, andwas supported at intervals on 1i, 2-inch pipe rollers.

a. UNIFORM LOAI EQUIPMENT

An approximately uniform roof load was pro-vided by eighteen hydraulic jacks connected in

parallel with a hydraulic pump. The jacks weresupported by separate brackets anchored to thelaboratory test floor. The jacks were spaced twofeet on center and were held off the floor at such aheight that the action line of the load was through

the center line of the frame's 6-inch dimension andin a plane parallel to that of the frame. Load wastransmitted from the jack rams through 4-inch steelload shoes on the frame roof member at 1-footintervals.

Each vertical leg reaction was transferred toa load cell through a 1-inch-diameter chrome steelalloy ball placed between 1/8-inch depressions inthe face of the leg base plate and the top of theload cell. The load cell for the left leg of the frame

Figure 18. Drawing of test set-up

III. COMPLETE FRAME

bore against a steel reaction bracket. The bracketwas bolted to a 1- by 8-inch steel plate fastened toloading rails embedded in the test floor. The loadcell measuring the right vertical reaction was in-serted in the same manner as that on the leftexcept that it rode on a rack of rollers bearingagainst a reaction bracket.

To prevent any possible lateral movement ofthe frame, the left leg was hinged to a horizontalreaction bracket. A 1/-inch machine bolt studwith a flat steel clevis welded to the head end wasthreaded into the outside edge of the base plate.This clevis held a %/-inch roller bearing which rodein a slot in a piece of 3-inch by 3-inch by %-inchangle. The slot was machined on a radius so thatthe leg base was free to rotate. The slotted anglewas bolted to the reaction bracket, which wasmounted on a steel plate fastened to the load rails.

b. HORIZONTAL REACTION EQUIPMENT

Horizontal reactions were taken by a %-inch-diameter tension rod connecting the leg base plates.The strain gage tension link and a turnbuckle wereinserted into the rod. The turnbuckle was used tomaintain a constant distance between the framelegs.

3. Testing Procedure

Before testing began, a small initial pressurewas applied to the jacks and final adjustments weremade in the test setup.

Load was applied in approximately uniformincrements as measured by the left load cell upthrough initial yielding, after which time loadingproceeded using approximately /-inch incrementsof peak deflection. The test required approximatelyeight hours from the beginning of loading.

Under the normal loading procedure, the ap-proximate load increment was applied, the turn-buckle was tightened to pull the frame legs back tooriginal spacing as shown by the Ames dial indi-cators, and then all load, deflection, and strainreadings were taken.

After each load increment, cracks were observedthrough low power, illuminated magnifying glassesand marked with ink. There was usually somedrop in load between loading steps, but this wasvery small. Even at higher pressures it was notfelt that it was significant enough to record. Photo-graphs of the test frame were taken at importantstages during the test and after failure. The controlcylinders were tested the same day the frame was

Table 6

Test Results for 36-Foot-Span Frame

R AV(kips)0.501.492.503.524.405.376.207.067.978.859.849.46

10.2810.6710.9911.6511.4111.7411.6812.8812.7412.9112.66

RE

(kips)0.581.642.703.584.475.336.227.057.938.879.859.85

10.4211.0511.4712.2012.4412.8112.6313.9013.6613.7713.74

W(kips)

1.083.135.207.108.87

10.7012.4214.1115.9017.7219.6919.3120.7021.7222.4623.8523.8524.55

26.7826.4026.6826.40

W/2(kips)0.541.562.603.554.435.356.217.057.958.869.849.65

10.3510.8611.2311.9211.9212.27

13.3913.2013.3413.20

BaH(in.)

0.0090.0490.0990.1490.1990.2520.3120.3700.4290.4930.5580.5720.6100.6490.6930.8271.0021.192***

DH

(in.)0.0080.0450.0830.1200.1610.2180.2740.3320.3920.4600.5300.5270.5690.6070.6470.7020.7300.837**

* Computed quantities:

MB = (68.5)R + (A B

) R

MD = (68.5)RH + (A} R ,R

M C

= (108) - 144 - AC) RA2 3

NC 3 RA3.16 H

** Reloading increment used afterreleasing load previous day of test.

*** Sidesway deflections not measuredbeyond this point but their contribu-

tion to MB and MD was taken as thatcomputed for load increment 18.

A

(in.)0.0290.1430.2750.4050.5370.8030.8681.0401.2161.4071.6101.6421.7631.8772.0002.3652.8253.328

4.5695.3055.9536.7427.500

MB*

(in.-kips)22.171.2

121.8168.4205.4248.8287.4330.5374.6413.9461.0434.4461.8491.2513.5560.6555.7572.0

550.8541.1536.7533.6

MD *

(in.-kips)22.171.2

121,7168.3205.3248.6287.1330.2374.2413.6460.8434.2461.5490.9513.3559.5553.4568.7

547.6537.8533.4530.3

MC*(in.-kips)

12.219.525.931.450.660.674.577.885.0

104.3116.5151.1171.7168.6163.9149.0165.7179.6

353.9358.6387.7384.5


Table 7

Measured Strains on Tension Reinforcement of 36-Foot-Span Frame*

LoadIncrement

123456789

1011121314151617181920212223

Left Leg

Ga. #1 Ga. #2

35 30135 120240 220345 325445 420575 540705 660845 790

1,005 9201,160 1,0851,330 1,2301,395 1,2951,485 1,3801,565 1,4651,665 1,5901,825 1,970

12,535 2,55013,115 3,095

Peak

Ga. #3 Ga. #40 10

10 2535 4050 6070 8095 100

120 130150 160180 180215 210250 235330 290360 315370 330395 360500 445600 580720 710

985 9451,170 1,1101,300 1,2151,290 1,220

* All strain values in microinches per inch.

Right LegGa. #5 Ga. #6

35 40120 145215 250315 355415 460525 580650 710785 800930 980

1,085 1,1201,245 1,2501,320 1,3151,410 1,4001,495 1,4901,605 1,6102,570 2,560

10,185 11,67011,940 12,390

Table 8

Measured Strains on Compression Concrete of 36-Foot-Span Frame*

LoadIncrement

1234567891011121314151617181920212223

Left LegGa. #1 Ga. #2

20 4080 180

165 340255 485340 610430 755515 900590 1050680 1200760 1370855 1565805 1570860 1680920 1790970 1885965 2045795 2080590 2140

515 3060710 3155730 3510710 3420

Peak Right LegGa. #3 Ga. #4 Ga. #5 Ga. #6

* All strain values in microinches per inch.

Tension gage locations

tested. Average compressive strength of the con-crete was 5,220 p.s.i.

D. DISCUSSION OF TEST RESULTS

1. Presentation of Test Data

Test results for the frame are given in Tables

6, 7, and 8. Measured reactions include the effects

of the hydraulic jacks only, since the frame was

tested in a horizontal position. Theoretical and

actual load-deflection curves are shown in Figure19. Figure 20 gives the relation between verticaland horizontal reactions, Figure 21 gives the rela-tion between total load and moments, and Figure22 gives strain-load relations. In Figures 23 and24, actual loading curves for the knee cross sectionand for the peak cross section are plotted on theirrespective interaction diagrams so that the actualfailure loads can be compared to values predictedby the theoretical failure curve.

Figures 25 through 30 show crack patterns for

the test frame at the indicated stages of loading.

2. Behavior Under Load

The test frame behaved according to elasticanalysis up to initial yielding at the knees; that is,the deflections, strains, and moments were nearlyproportional to the load. With yielding of the ten-sion steel at the knee joints, cracks grew wider, and

Compression gage locations

larger rotations occurred, resulting in increased side-sway and peak deflection. As a result of this yield-ing, the horizontal reaction increased very littlewith additional vertical load, and the roof memberof the frame developed increased moment as asimple beam.

3. Crack PatternsCrack patterns for the test frame are shown in

Figures 25 through 30. The order of crack develop-ment is indicated by a number corresponding to the

30.0

22.5

15.0

75

0o

Peak deflection, inches

Figure 19. Load-deflection curves for 36-ft-span frame

dr d

III. COMPLETE FRAME

U0

*(1

§cI

Z

Horizontal reaction, kips

Figure 20. Vertical vs. horizontal reaction for 36-ft-span frame

load increment. First cracking occurred in theregions of highest moments at the knees at loadincrement No. 6, or a total uniform load of 10.7kips. It should be noted that this corresponds veryclosely to the design load of 10.8 kips. Figure 25shows the crack pattern for the left knee of theframe at this loading stage. Although the crackpattern spread as the load increased, hardly anycracking occurred in the region of the scarf joint.Figure 26 shows the left scarf joint photographedjust after load increment No. 11 was applied andbefore the knee joints had yielded. It is of interest

W, total vertical load. kips

Figure 22. Strain-load curves for 36-ft-span frame

90

S60

30

.

o 30

O

M, bending moment, inch-kips

Figure 21. Load-moment curves for 36-ft-span frame

0 /50 300 450 600 750


Figure 23. 36-ft-span frame: interaction diagram for yieldand ultimate fexural capacity of knee cross section

(loading curve superimposed)


/20

90

-6C

60

30

0


Figure 24. 36-ft-span frame: interaction diagram for yieldand ultimate flexural capacity of peak cross section

(loading curve superimposed)

to note how the crack pattern shifted from the toplto the bottom of the roof member at opposite sidesof the scarf, verifying the position of the point ofcontraflexure.

Initial cracking at the scarf joint occurred at1.3 times design load when a hairline crack devel-oped at the critical section on the leg side of theright joint. No cracking occurred at the left jointuntil load increment No. 13, approximately twicedesign load. The initial crack at the right scarfjoint progressed a short distance at the same time.No further cracking occurred at the critical sectionsin the joint during the remainder of loading to 2.5times design load. The joints remained intact andexhibited no signs of distress at any time.

Final crack patterns for the frame, includingclose-ups of the knees and scarfs are shown inFigures 27 through 30.

Figure 25. Crack pattern for left knee of 36-ft-span frame

Figure 26. Crack pattern for left scarf joint of 36-ft-span frame

4. Load-Deflection Curves

Load versus peak-deflection curves are shown inFigure 19. Both theoretical and actual curves areplotted.

For the theoretical curve, loads were based onthe computed yield capacities of the cross sectionat the knee and at the peak as given by the inter-action diagrams. Theoretical deflections corre-sponding to yielding at the knees and then yieldingat the peak were determined from curvature dia-grams for the loaded frame. The two deflectionquantities were obtained using the moment-areamethod in conjunction with the curvature diagrams.Ordinates to the curvature diagrams were assumedto vary in direct proportion with the ordinates ofthe moment diagrams. Two different relationshipsbetween moments and rotations were involved, re-flecting the effect of the two cross sections used.

Calculations for the theoretical load-deflectioncurve are given in Appendix B.

The actual load-deflection curve may be con-sidered in three regions. The first region is a some-what linear range up to first yielding at the knees.A second range involves yielding of the steel andcrushing of the compression concrete at the kneeswith some increased load capacity as the roof sec-tion develops moment. A third region occurs wherethe curve flattens out due to yielding near the peaksection.

The gradually decreasing slope in the firstrange of the curve is due to cracking of the tensionconcrete. Yielding at the knees begins at a load ofapproximately 22 kips. From this point the curvebends over, and large peak-deflections occur as aresult of increased rotation at the knee joints. Theinitial crushing of the concrete at the knees oc-curred during the seventeenth and eighteenth load

III. COMPLETE FRAME

increments (a load of approximately 24 kips). Ad-ditional load was withstood up to a total frame loadof slightly over 26.5 kips. This approximately2.5-kip load increase resulted from the simple beamaction of the roof section as plastic hinges formedat the knees. The curve becomes horizontal at themaximum load as the frame continued to deflectunder constant load. Total deflection measured atthe peak was 71/.-inches, although this measurementwas limited by the full extension of some of thejack rams.

The theoretical curve agrees quite well with theactual curve. Load capacity indicated by the actualcurve, as compared to the theoretical, is less (due tothe large peak deflection. Thus, if a free-body

diagram of the left half of the frame is taken, the a. r<oor portson

lever arm of Rn hias decreased, and to maintainequilibrium, Rd must decrease accordingly, whichmeans that the total load decrease is doublethe decrease in Rv.

b. Leg portion

Figure 28. Crack pattern for right half of 36-ft-span frame

5 Strnin-Lnnr Curvec

OleeL s raiL 1ll versus Ltlt 1roJ oa curves are

shown in Figure 22. Gages at the knee section indi-cated a sharp increase in strain rate at a valueslightly greater than 1500 micro-inches per inch,the average yield strain of the reinforcing steel.This increased strain rate in the steel is reflected inthe load-deflection curve. The peak gages indicateda rapid increase in strain rate before yield strainwas reached. It is believed that peak yielding didnot occur at the point of measurement but ratherat a point slightly away from the gage.

Concrete strain versus load relations are notshown. The concrete gages were placed primarilyfor checking symmetry of loading, but they also

b. Leg portion served to indicate the maximum compressive strainsFigure 27. Crock pattern for left half of 36-ft-span frame relative to their postion. The critical side of the

a. Roof portiont., l, t i,, : , .„„,, ,, ^.l f^ l d.,e i„, , ,


knee joint is on the leg portion of the frame; there-fore A-3 gages No. 1 and No. 6 gave the determin-ing values. Maximum compressive strain asmeasured by gage No. 1 occurred during load incre-ments 15 and 16, and that for gage No. 6 occurredduring load increment 18. The first signs of crush-ing noted by visual inspection were at load incre-ments 17 and 18 for the left and right knee joints,respectively. This corresponds to a total roof loadof approximately 24 kips. Maximum strain read-ings were not obtained at the peak, and the concretenever crushed in this area.

6. Other Relationships

The plot of vertical versus horizontal reaction

is presented to show that a nearly linear relationexists between the two up to yield load, or ameasured vertical reaction of approximately 11kips. It should be noted that the measured valuesof vertical and horizontal reaction are in the ratioof 3:2, which agrees with the theoretical elasticanalysis of Figure 14.

Relationships between total loads and momentsare given in Figure 21. Again for the knee sectionapproximate linearity is exhibited up to yield,deviations being due only to eccentricity created bysidesway. This tends to increase moment on the

c. LerT Knee

a. Lerr scarr

d. Kign? Knee

Figure 29. Knee joints of 36-ft-span frame after testing

D. RKiga scurr

Figure 30. Scarf joints of 36-ft-span frame after testing

a. Left knee

b. Right knee

III. COMPLETE FRAME

section as indicated in Table 6 and by the fact thatthe actual points would fall slightly to the right ofa theoretical curve given by M = 22.8W in whichsidesway is ignored. The plot of total load versuspeak moment has a steeper initial slope than theother curve, since the peak moment is equal to 6Wif deflections are ignored. With yielding in theknees the horizontal reaction remains nearly con-stant, but the vertical reaction continues to increase.As a result, the moment increases more rapidly perload increment, producing a curve of flatter slopewhich eventually becomes horizontal.

7. Mode of Failure

Failure occurred in flexure, with yielding of thetension steel occurring first, followed by crushingof the compression concrete. Over all, the framegave a very desirable ductile type failure, remain-ing safe from sudden collapse even when the peakdeflection reached 71/2-inches. The radial reinforce-ment was effective in maintaining the position ofthe moment steel, permitting the formation ofplastic hinges at the knees and preventing thetrouble experienced in the early knee-frame testswhere stirrups were used.

8. Comparison of Test Resultswith Interaction Diagrams

Figures 23 and 24 show the loading curves forthe knee and peak cross sections superimposed ontheir respective interaction diagrams. Yield andultimate capacity as indicated by the interactioncurves were based on the average strength of thematerials used in the frame.

Although theoretical ultimate capacity was notreached, failure was nevertheless predicted withreasonable accuracy, as indicated by the terminalpoint of the loading curve. Based on design mo-ments given by the M diagrams of Figure 14, theactual moments provide a factor of safety of 2.25for the knee and 4.07 at the peak. A safety factorof 2.48 on total design load was obtained.

E. CONCLUSIONS AND RECOMMENDATIONS

Based on the tests reported, it can be concludedthat the ultimate capacity of a gable frame sub-jected to uniform load is predictable with satis-factory accuracy.

The design for the radial reinforcement at theknees and peak of this type frame proved to bequite satisfactory in providing a rigid joint capableof withstanding the large radial forces. It is rec-ommended that the longitudinal steel for the insideof the knee be hot-bent. By this procedure the steelwould not be over-stressed as it was in the cold-bending method followed in this study. The appar-ent cause of the fracture failure experienced in thetest of T-2 would then be eliminated.

The scarf joint proved very satisfactory, but toobtain best results it is recommended that a thinlayer of mortar be placed between the surfaces ofthe scarf and allowed to harden before final tor-quing. This will assure more uniform pressure overthe contact area and thereby lessen the danger ofcracking the scarf joint while tightening the bolts.

For easier casting operations it is suggested thata somewhat higher slump be used than the 1-inchvalue specified in these tests.

F. CONSTRUCTION MODIFICATIONS

Based on experience gained during the commer-cial fabrication and erection of two experimentalprecast rigid frame buildings since completion ofthe tests, the basic section has been enlarged from6 inches by 10 inches to 8 inches by 12 inches toreduce the bar size and to permit larger clearancesfor placement of concrete. Architectural modifica-tions such as precast lips on the frame to supportpurlins and wall panels were also made but did notincrease the strength of the basic section. At thecritical sections of the frame, the additional con-crete area is always on the tension side of themember for controlling moments due to dead loadplus snow load and thus does not increase the effec-tive concrete area.

IV. REFERENCES CITED

1. Tung Au and D. L. Baird, "Bearing Capacity ofConcrete Blocks," Journal of the American Con-crete Institute, Vol. 31, No. 9 (March, 1960), p.869-879.

2. R. D. de Cossio and C. P. Siess, Development ofDesign Criteria for Reinforced Concrete BoxCulverts, Part I: Strength and Behavior of Re-inforced Concrete Beams and Frames (CivilEngineering Studies, Structural Research SeriesNo. 163). Urbana, Ill.: University of IllinoisCivil Engineering Department, September, 1958.

3. W. H. Munse, D. T. Wright, and N. M. New-mark, Laboratory Tests - High Tensile BoltedStructural Joints (Civil Engineering Studies,Structural Research Series No. 46). Urbana, Ill.:University of Illinois Civil Engineering Depart-ment, September, 1952.

4. M. L. Paul, "An Investigation of a ReinforcedConcrete Rigid Frame for Farm Structures,"

unpublished M.S. thesis, University of Illinois,Urbana, Ill., 1961.

5. F. E. Richart, T. J. Dolan, and T. A. Olson, AnInvestigation of Rigid Frame Bridges, Part I:Tests of Reinforced Concrete Knee Frames andBakelite Models (Engineering Experiment Sta-tion, Bulletin No. 307). Urbana, Ill.: Universityof Illinois College of Engineering, 1938.

6. E. D. Rodda, "Strength of Reinforced ConcreteSubjected to Combined Bending, Axial Load, andShear," unpublished M.S. thesis, University ofIllinois, Urbana, Ill., 1960.

7. "The Welding of Concrete Reinforcing Bars,"Booklet 527-A, Bethlehem, Pa.: Bethlehem SteelCompany, 1959.

8. Wind and Snow Loads on Farm Structures (Agri-cultural Research Service Bulletin 42-5), U.S.Department of Agriculture, October, 1956.

V. APPENDICES

A. CONSTRUCTION OF INTERACTION DIAGRAMSFOR YIELD AND ULTIMATE FLEXURALCAPACITIES

A procedure for computing the flexural capacityof under-reinforced beam members subjected tocombined bending and axial load is presented in thissection. The term "beam" is used to emphasize thatthe members involved are subjected primarily tomoment as compared to columns in which axialload is predominant. Since the members are sub-jected chiefly to beam action, most of the assump-tions regarding the behavior of beams can beapplied.

1. AssumptionsIn developing expressions for the flexural

strength of under-reinforced concrete members, theassumptions listed below have been made. Thevalidity of procedures based on these assumptionshas been established experimentally by manyinvestigators.

a. The strains vary linearly within the crosssection.

b. No tension is carried by the concrete.c. The stress-strain characteristics of the reinforc-ing steel are known, or can be closely approximatedby a simplified curve shown in Figure 31.d. The properties of the concrete stress block areknown, or reasonable assumptions can be made forthe values of the necessary parameters.

fY

&

»'4

e, .)ITfl

Figure 31. Simplified stress-strain curve for reinforcing steel

e. The concrete crushes at a limiting strain. Inaddition, all of the expressions derived in this sec-tion are for members in which the steel stress atfailure is equal to the yield point stress; i.e., themembers are under-reinforced.

In this report the load necessary to cause firstflexural yielding of the reinforcement has been de-fined as the yield load or yield capacity. The loadwhich causes crushing of the concrete after orsimultaneously with flexural yielding of the tensionreinforcement has been referred to as the ultimateload or ultimate capacity.

In a section of a member subjected to axial loadand bending, for any value of axial load there corre-sponds one moment at which flexural yielding orultimate flexural capacity is reached. Interactionexpressions are used to determine the combinationsof axial load and moment sufficient to cause failureof the under-reinforced section.

2. ProcedureLet Figure 32 represent the conditions at ulti-

mate capacity for simultaneous crushing of concreteand flexural yielding of the tension reinforcement.The net axial load N is assumed to act at mid-depth of the member. Figure 32 shows the assumedstrain distribution and the assumed compressivestress distribution, the resisting moment M, themagnitude and location of the compression in theconcrete C0, the force in the compression steel Cs,the tension in the tensile steel T, and the net axialload N. By summation of horizontal forces:

N = C1 C2 - T

Figure 32. Assumed conditions of stress and strainfor ultimate capacity


Figure 33. Assumed conditions of stress and strainfor yield capacity

Taking moments about the center of the section:

M = C, (h/2 - kkd) + C, (h/2 - d')+ T (d - h/2)

Succeeding points are calculated by rotating thestrain line about E,, taking increasing values ofstrain for the tension reinforcement until a minusvalue of N is obtained or the curve intersects thehorizontal axis. This intersection represents theultimate flexural resisting moment when the axialload N is zero.

The procedure followed in obtaining the yieldinteraction curve is similar to that for the ultimatecapacity curve; however, in this case tension steelstrain is assumed constant at Ey, as shown inFigure 33. Succeeding points are calculated byrotating the strain line about Ey, taking decreasingvalues of strain for the outer fibers of compressionconcrete. For this case, the assumption of a fullydeveloped concrete stress block is no longer valid.However, reasonable assumptions can be made froma trapezoidal-shaped stress-strain curve approxi-mating the actual stress-strain curve for the con-crete. This was done, using a stress blockcorresponding to the appropriate portion of thetrapezoid.

Figure 34 shows interaction diagrams for yieldand ultimate flexural capacities based on the pre-vious discussion.

t*,

09

0

M, Bending moment, inch-kips -

Figure 34. Interaction diagrams for yieldand ultimate flexural capacities

· I

(400 - 145) = 255 in.-kips = W(2)8

255 X 8thus: W(2) = 36 X 12 = 4.72 kips

36 X 12

B. CALCULATIONS FOR THEORETICAL LOAD-DEFLECTION CURVE OF FIGURE 19

1. Theoretical Loads

a. Load capacity when yielding occurs at theknees:

Trial #1

From yield curve of Figure 23 try M = 570in.-kips, N=8 kips

But from Figure 14 MB = (72w)12 in.- kips

Substituting and solving:

Mn 570wY = = 0.66 kips/ft72 X 12 72 X 12

BN, = 18(0.66) = 11.08 kips

Since the two values of N do not agree veryclosely another trial will be necessary.

Trial #2

Try M = 580 in.-kips, N = 12 kips

580S72 12 = 0.671 kips/ft

' 72 X 12NY = 18(0.671) = 12.08 kips O.K.

thus: Wy = W(1 = 2(12.08) = 24.16 kips

b. Remaining load capacity until yielding oc-curs at the peak:

From Figure 14, when MB is at yield, M =

M 580(18w,)12 = = 4 = 145 in.-kips

N in roof member at this point3 3 (12w

= 3.16 R = 3.16 (12wy)

thus: N = 316 (12 X 0.671) = 7.65 kips

Using this value of N as an approximateaxial load when yielding occurs at the peak,it is determined from the yield curve ofFigure 24 that M c = 400 in.-kips.

The difference between M c and Mc whenMB is at yield, is the remaining momentcapacity to be developed at the peak. Sincehinges have formed at the knees this re-maining capacity will be developed as asimple beam and may be expressed as:

(M M) (2)2 W(2)8

V. APPENDICES

The total theoretical load capacity is then:

W(total) = W(1) + W(2)

= 24.16 + 4.72 = 28.88 kips

2. Theoretical Deflections

Assumptions and calculations for knee crosssection:

1.75" A's.2sqin nA's 5.75(1.2)=6.90sq in.

* * x kd

8.25" '

nA,=5.75.8)=-iO. 35sqin. ( - -kldsee---- ---

S6", A -=.8sqin.Cross section Transformed section Strain distribution

E,_ 30,000,000 _ 30

Ec 1000 f' 5.22

From transformed section:

6x 22 + 6.90(x - 1.75) = 10.35(8.25 - x)

SolvingSolving:

3.50x = kd = 3.50 in. .'. k =

8.25

From transformed section:6x 26 2 + 6.90(x - 1.75) = 6.90(8.25 - x)2

Solving:

3.03x = kd = 3.03 in. .. k = -- = 0.367

8.25

From assumed strain distribution:

-e 0.0015'" (1-k)d - (1-0.367)8.25

= 0.000288 rad/in

From the interaction diagram of Figure 23,My for section = 400 in.-kips

Assumed M - qp curve for section:

My =

400

M=1.39 0

I M inch-kipsS =radians per inch x 10

*f'yZBB au= 0.424

From assumed strain distribution:

•E 0.0015"= (1-k)d (1-0.424)8.25

= 0.000316 rad/in

From the interaction diagram of Figure 23,My for section = 580 in.-kips

Assumed M - p curve for section:

My =

580

The calculated peak deflections are determinedfrom curvature diagrams for the roof member.Since the frame is symmetrically loaded, the peakdeflects downward with no rotation at the joint.Therefore only the roof member BC need beconsidered in calculating the necessary quantities.

The moment diagram for member BC of thetest frame is repeated here for the uniform load-ing w,= 0.671 kips/ft, the loading that theoreti-cally produces yielding at B.

M=1,84 #

M inch-kips I0 = radians per inch x 10 6

Oy = 316

Assumptions andsection:

calculations for peak cross

Cross section Transformed section Strain distribution

rod.Note: Ordinates to curve -_ X 10'

In.

Areas under curve = rad. X IO1


a. Deflection when yielding occurs at the knees:

Assuming the cross section to change at thepoint of zero moment in the member BC, andmaking use of the previously derived M - p re-lationships, a curvature diagram representingthe two cross sections can be obtained asfollows:

For the negative portion of the M-diagram

Muse ý = 841.84

For the positive portion of the M-diagram

Muse - 1.39

Thus, for the condition of first yielding of theknee B

MY = 580

Mc= 145

B 580p, = -8 = 3161.84

c 145 1= 1. = 104q-1.39

The curvature diagram is shown below and isactually made up of two curves having a com-mon zero ordinate.

12,130 X 2.23 X 12= 325,0001

A = 2,345,000 in. X 10-6

Thus when B is at yield:

c c 3A = A(l) = 2.345 X .1 = 2.22 in.

b. Remaining deflection until yielding occurs atthe peak:

The remaining moment capacity was given as:B

(MY M- ) = 400 - 145 = 255 in.-kips

255.'. pc = = 184

(2) 1.39

Since the M-diagram for BC is now completely

positive, the M - relationship for the knee

cross section is no longer valid. The remaining

deflection can be calculated reasonably well

considering the M - relationship for the peak

as representative throughout the length of the

member.

The curvature diagram for this calculation is

shown below.

C

rod.Note: Ordinates to curve = - X 10

in.

Areas under curve = rad. X 10O

Using the moment-area method:

8580 X 13.05 X 12=1,345,000'7360 X 15.02 X 12=1,325,0001

2,670,000'

Note: Ordinates to curve = in. kips

AB= 27,900 X 11.85 X 12= 3,970,000 in. X 10- 6

c c 3A= A 2) = 3.97 X 3.1 3.77 in.

The total theoretical deflection is then:

A (total) = A()+ A( 2)

= 2.22 + 3.77 = 5.99 in. 1

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