Behavior of PrecastReinforced Concrete

Ledger Beams

Ned M. ClelandChief Structural EngineerShockey Brothers, Inc.Winchester, Virginia

Thomas T. BaberAssistant Professor

Department of Civil EngineeringUniversity of Virginia

Charlottesville, Virginia

he design of ledger beams, com-monly used as spandrels in precast

concrete structures, may not always beadequate under currently acceptedcriteria based on the ACI BuildingCode' and the PCI Design Handbook'due to insufficient accounting for minoraxis bending effects, and potentially,secondary effects.

This paper presents the results of astudy investigating load-deformationbehavior of slender ledger beams. Theconclusions and design recommen-dations drawn may assist engineers inpreventing unserviceable behavior ofsuch members.

To determine the load-deformationbehavior of ledger beams, a program ofexperimental analysis was conducted.Six model beams were tested by pro-

gressive elastic range Ioading at sevendifferent spans in three configurations.The configurations considered werebraced major axis bending underpseudo-uniform loading, uniform tor-sion only, and unbraeed bending andtorsion under uniform eccentric loadingintended to simulate the loads on span-drel ledger beams met in practice.

Measurements were made of the ver-tical and horizontal midspan deflectionsand the midspan rotation under the ap-propriate loading conditions. The dif-ferences between the unhraced bendingbehavior obtained experimentally, andthose estimated by superposition of theother two loading conditions wereexamined for any identifiable secondarybehavior, or other response of potentialdesign interest.

96

BACKGROUND

A spandrel beam is an exterior beamthat carries, slabs, joists, or beams onone side only. This element has beenused since the early years of cast-in-place concrete construction. CurrentACI Code provisions pertaining tospandrel beams include flexure andcombined shear and torsion. The provi-sions reflect the historical importanceand development of monolithic con-struction.

The additional provisions for protec-tion against distress due to lateral insta-bility or deflection are meager and re-flect little substantive research.Monolithic construction rarely includesslender beams without integral com-pression flange support. Hence, lateraldeflections, and stability considerationshave received little attention, since theopportunity for problems have beenfew. The development of precast con-crete structural systems has changedthis situation.

Characteristics of PrecastConcrete Spandrel Beams

Precast concrete spandrel beams areused in a variety of building types andconfigurations. They may be mild steelreinforced or prestressed. Nonpre-stressed beams are potentially moresensitive to deformation effects due tocracking. They are frequently used in-stead of prestressed beams when de-tailed architectural relief or stringentfinish specifications are required. By far,the most common application is thesimple span ledger beam used to sup-port prestressed deck components inparking garages. This configuration isillustrated in Fig. 1.

It is important in parking structures toprovide a perimeter railing which canwithstand impact loading. The totalrailing height for pedestrian safety is re-quired by the BOCA Code to be 42 in.(1.07 m) above the deck leveI.-' Since a

Synopsis

Excessive lateral displacements ofreinforced precast concrete ledgerbeams have been observed duringconstruction of several structures, andhave required expensive remedial ac-tion. To ascertain the cause of deflec-tions, and to gain information uponhow the problem could be avoided, aseries of quarter scale reinforced pre-cast beams encompassing the fullrange of depth to span ratios usuallyencountered in practice were loadedwithin the service load range.

The tests indicated that a slight ro-tation of the principal axes, caused bythe ledge and the eccentric reinforce-ment is a primary cause of lateral dis-placements. Some secondary dis-placements may also have occurred,but appear to be of minor importance.Recommendations for design aregiven, which should reduce the mag-nitude of lateral displacements towithin acceptable limits.

spandrel beam often performs this addi-tional function, deep profiles are com-mon. Depths can range from 4 to 8 ft(1.22 to 2.44 m).

With such depths, it is tempting forthe engineer to increase spans to thelimits of flexural capacity and deflectionto eliminate costly columns. As the spanincreases, the spandrel beam thicknessis kept as thin as possible to controlshipping weight and construction costs.These conditions may cause the beambehavior to reach deflection or stabilitylimits before the predicted flexuralstrength is attained. Spandrels are prom-inent architectural features. Excessivedisplacements or cracking may alsocompromise serviceability.

As a result, these members are moresusceptible to unbraced beam behaviorthan usually supposed. In their final

PCI JOURNAL^March -April 1986 97

SPANDREL BEAM WELDED TORSION

RESISTANT CONNECTIONS

EMBEDDED PLATE FORTEE BEAM TO FLANGE

CONNECTION

DOUBLE TEE

COLUMN

Fig. 1. Typical spandrel beam configuration.

configuration they are often braced byconnection to the flange diaphragm. Toreach this condition, however, the un-braced beams must often accept fulldead load on structures where the actualfuture live load is only a minor addition.For topped systems with coil rods orreinforcing ties to the topping or for un-topped double tee decks, connectionsare not effective before full dead Ioad isapplied.

Experience With DistressA significant number of spandrel

beams in precast structures have experi-enced distress. Many of these problemshave been documented by Raths .4 How-ever, none of the problems reviewed byRaths was related to large displacementsor stability, but he indicated that otheraspects of distress may be significant.Evidence of deflection related distresshas been examined at two separateparking structures in the Washington,D.C., area. In each case, the individual

design requirements for flexure andcombined shear and torsion were met.Distress was the result of unpredictedlateral deformation under load.

Current DesignThe current practice in design related

to spandrel beams was summarized byRaths.' These requirements include fle-xure, shear and torsion, and end con-nection behavior. Flexural analysis anddesign is well established for reinforcedconcrete beams. Raths mentioned thepossible influence of the rotation of theprincipal axes on these unsymmetricalbeams, but he did not evaluate what thisinfluence means to potential beam be-havior.

Provisions for the design of nonpre-stressed concrete beams under com-bined shear and torsion are found inChapter 11 of the ACI Code.' These re-quirements are based upon superposi-tion of torsion steel area to that requiredby shear. The ACI Code relationships

98

are the product of empirical modifica-tions made to simple theoretical mod-els.5 Additional theoretical models havealso been proposed."-10 For loadbearingspandrel beams with ledges, additionalrequirements for local conditions atstem reactions and end connectionsmust be met.

The ACI Code includes additionalprovisions which recognize potentialproblems with instability. Section 10.4.1states that the unbraced length to comn-pression flange width ratio (Lib)should not exceed 50. Section 10.4.2further states that the effects of lateraleccentricity should be taken into ac-count in determining the spacing of lat-eral supports. The guidelines do notsuggest how this should be done.

Concrete Beam StabilitySince the distress observed in precast

spandrel beams which led to the workreported herein involved unanticipatedlateral displacements and rotations,which are potentially caused by pro-gressive secondary displacements asso-ciated with impending instability, theconsideration of concrete beam stabilitywas considered to be an important partof the experimental and analytical pro-gram.

The first published study in English"of lateral stability of reinforced concretebeams was by W. T, Marshall in 1948.12In Marshall's work, Lib and d1b (depthto compression web/width) stability pa-rameters were considered for concentricloading conditions. Subsequent studieswere conducted by Vasarhely and Tur-kolp,i3 Hansell and Winter,''' Sant andBletzacher,'s and Massey.'b

In each case, research concentratedon the effects of lateral stability on theultimate strength of concentricallyloaded beams. Results were related toLib and d1b ratios. All of these studiesattempted to relate the complex be-havior of reinforced concrete to thehomogeneous elastic solution of rectan-

gular beams from the theory of thin-walled beams 17.18

None of these studies are directly ap-plicable to the present situation. How-ever, although no quantitative approachhas been developed which is applicableto ledger beams, qualitative observa-tions can be made. Since the loading istransverse and eccentric, and thebeams are unsymmetric, the stabilityproblem is one of progressive secondarydisplacements, rather than buckling.That is, the beam may experience signif-icant secondary displacements prior toreaching a stability dictated limit state,beyond which the continued load de-formation behavior will be unstable. Ifsecondary displacements of this type arean important part of the system re-sponse, the unbraced beam should dis-play significantly larger rotations, andpossibly vertical translations than couldbe predicted by major axis bending andtorsion alone.

EXPERIMENTAL PROGRAMThe behavior of precast spandrel

beams under eccentric loading is com-plex. Reinforced concrete is nonhocno-geneous, and only approximately elasticin the lower stress range. The flexuralstiffness depends upon the appliedloading and varies along each beam withthe degree of cracking. Torsional be-havior has been established by largelyempirical methods. The nature of sta-bility related behavior for nonsymmet-ric, eccentrically loaded beams has notbeen established quantitatively. Thesefactors suggest that the most direct ap-proach to the problem of large deforma-tions is experimental analysis.

The experimental approach pursuedwas intended to allow the direct mod-eling of the complex conditions pre-sented by the materials, the nonsym-metric configuration, and the eccentricloading. The primary bending and tor-sional deformations were measured in-

PCI JOURNALJMarch-April 1986 99

dependently under loading designed toeliminate the other responses.

Assuming approximately linear be-havior of the material within the rangeof loadings, the braced bending and tor-sional behavior should be the same asvertical bending and torsion of the un-braced beam, unless secondary defor-mation is important. The degree of va-lidity of superposition and the identifi-cation of additional displacements ef-fects can be determined by direct com-parisons of these responses.

In the studies reported, this approachwas used to identify whether geometricand loading conditions which couldcause significant secondary displace-ments were present. 'n addition, the re-sults were compared to theoretical mod-els of flexural and torsional deformation,and used to formulate additional analy-tical models related to unpredicted be-havior.

The experimental analysis programwas based upon load tests of six modelbeams. The beams were designed toproduce structural similitude for bend-ing and torsion in the range up to ap-proximately 60 percent of ultimate con-crete compressive stress. This allowedmultiple tests of the beams at differentspans without significant degradation ofthe concrete due to cyclic inelasticloading. The dimensional scale factorwas 1 to 4. The sections varied from tor-sionally stiff and shallow to deep andslender. They covered a wide range ofstability related dimensional param-eters. The range ofdlb ratios varied from3 to 16 in the test beams. Each beam wastested at seven span lengths. The L/bratio varied from 15 to 100. A combinedparameter,Ld/b 2 , varied from 45 to 1600.This represents a full range of sectionsused in practical applications.

Prototype Beams and ScaleModel Design

To design the model beams, it wasimportant to determine the practical di-

mensions of the prototype beams. Span-drel beams with 8 in. (0.203 m) ste ins arevery common. Thinner sections aresometimes requested and thicker sec-tions are occasionally required. A rangefrom 6 to 16 in. (0.152 to 0.406 m) waschosen. Spandrel beam depths var y de-pending upon the depth of the elementssupported by those beams, the depth ofthe ledge and the railing treatmentabove the deck level.

It was determined that the range ofprototype depths from 4 to 8 ft (1.22 to2.44 m) would provide adequate repre-sentation of practical sections and varia-tion for the study of the load-deforma-tion characteristics, including stabilityrelated behavior. Ledger beams mayhave shallower depths than considered,but these beams would not have theflexural stiffness necessary to ade-quately span the maximum test distance.Beams of shallow depth often have widestems, and are unlikely to have stabilityrelated problems.

The prototype ledges were all set at 6in. (0.152 m) wide and 12 in. (0.305 m)deep, representing a common size. Theprototype spans varied from 20 to 50 ft(6.1 to 15.2 m) to reflect the range ofpractical prototype systems.

Dimensional AnalysisModel materials were chosen to pro-

vide the same strength and moduli asthe prototype materials to simplify load,stress, and strain similitude, The dimen-sional length scale was chosen as 1 to 4to minimize size effects and to accom-modate available space and equipment.The model sections were labels A, B, C,D, E, and F. Dimensions and details ofthe sections are given in Fig. 2 andTable 1.

Reinforcement DesignThe evaluation of loading for rein-

forcement design of the model beamswas determined from prototype loads,

^t3W —1 2 (38mm)

GAGE 6BARS TIES

(76 GAGE "dmm)AT SPACING

n SPACES "AT 3

"S°(76) h

BARS,GAGE °a"

3"(76BARS, mm)GAGE "b

BARS"c'_ _

LEDGE TIES, 10 GAGEAT SPACING S"

Fig. 2. Model spandrel beam section.

Table 1. Model ledger beam dimensions.

Section dimensions Bars

Mark b,, h h/bo a b c d n s

A 1' in. 18 in. 12 10 1-10 2-#4 8 3 2½,m.(38 mm) (0.46 m) 1-8 (57 mm)

B lye in. 24 in. 16 10 10 2-#4 8 5 2% in.(38 mm) (0.61 m) (67 mm)

C 2 in. 12 in. 6 12 1-12 2-#4 8 1 2l in.(S1 mm) (0.30 m) 1-1() 1-#3 (63 mm)

D 2 in. 18 in, 9 10 10 3-#4 6 3 2% in.(51 mm) (0,46 m) (67 min)

E 2 in. 24 in. 12 1-8 8 3-#4 6 5 2''16 in.(51 mm) (0.61 m) 10 (71 mm)

F 4 in. 12 in. 3 10 1-10 4-#5 4 1 1'/a in.(51 mm) (0.30 m) 1-6 (48 mm)

Notes: 1. Column "a" bars are listed top to bottom.2. Column "h" bars are listed left to right.3. Bar sizes are in sage, unless indicated otherwise.

PCI JOURNAL/March-April 1986 101

the scale factor analysis, and ACI Codelimits for each section. Torsional load-ing was computed as the product of theuniform flexural load and the distancefrom the center of the ledge to the centerof the stem. No attempt was made tomodify this moment to account for theshift in shear center due to the presenceofthe ledge, as suggested by Raths ° Theload was taken as vertical and uniform,parallel to the vertical axis of the unde-formed beam.

A detailed analysis of loading and re-inforcement design was conducted indetermining the final reinforcement ofeach section. The primary bending re-inforcement was selected first to pro-vide bending resistance to scaled equiv-alent loads carried by the prototypebeam used in parking structures for themaximum test span. The resulting ulti-mate uniform load capacity for shorterspans was computed from this govern-ing design.

The analysis and design for combinedshear and torsion reinforcement wasmade in accordance with ACI 318-77.The use of the limit of shear and torsionto the distanced from the supports wasnot applied since the load was appliednear the bottom of the section. A de-tailed study was conducted to determinea uniform closed stirrup layout forloading at the maximum allowable stresslimits. The limiting loads were deter-mined in this analysis.

A comparison of the capacity limitedby torsion and that limited by flexureindicated that the torsion limit governedin all but the Iongest spans of the mostshallow and compact beams (C and F).As a result, the interior sections of thebeams were reinforced somewhat moreheavily than necessary under the condi-tions of uniform load at the longer spans.This approach allowed greater use ofeach model beam. Deformations mea-sured from these models may underes-timate those of prototype beams de-signed for ordinary conditions.

Longitudinal reinforcement for tor-

Sion was distributed around the stirrupperimeter in accordance with ACI Coderequirements for maximum spacing,scaled by the length factor to 3 in.(0.076 ni). Section 10.6.7 of the ACICode, requiring maximum spacing to bethe web width in the tension zone forcrack control, was not followed. How-ever, no detrimental cracking effectswere observed during testing.

Ledge reinforcement was designedaccording to the procedure recom-mended in the PCI Design Handbook .2

Maximum spacing of ledge ties followsthese recommendations in not exceed-ing the 3 in. (0,076 m) ledge depth. Thedesign was conservative to protect theledge against large local stresses devel-oped by the loading system at shortspans. Stirrup spacing for the modelbeams is noted in Table 1. Reinforcingmaterial was ASTM A615 deformed barsand ASTM A496 deformed wire.

MicroconcreteThe microconcrete was designed to

reproduce the same strength and modulivalues as the prototype concrete asclosely as possible. The mix design wasdeveloped by scaling the sizes of aggre-gates, and eliminating the fines belowthe 100 sieve. Removing these fines im-proved the workability and water de-mand of the mix.

To ensure comparable results, testcylinders were made for both prototypeand model mixes. Tests of full sized 6 x12 in. (0.152 x 0.305 m) cylinders ofprototype concrete were compared to 2x 6 in. (0.051 x 0.152 in) cylinders ofmodel concrete to allow for size ef-fects. The compressive strengths werecomparable, ranging from 3500 to 5200psi (24 to 36 MPa) for the six modelbeams tested.

Since the primary thrust of the studywas determination of service load de-formations, it was felt that duplicatingthe modulus of elasticity E, Poisson'sratio v, and the tensile strength f,. was

102

LATERAL BRACE (TYPICAL)

j: a ^: 1 AI+q A e_ ^ u

a;;14 BRACING BEAM

LOAD DEVICE

C -44dBRACING BEAM ^^i^

ROD TO WHIFFLETREE

Fig. 3. Isometric view of vertical test configuration.

important. The measurements ofE and vfollowed the procedure prescribed byASTM C469 using full sized cylindersfor both prototype and microconcretemixes.

The model mix modulus of elasticitywas approximately 7 percent lower thanthe prototype concrete's, even thoughthe model compression breaks were 400psi (2.8 MPa) higher.

The model concrete Poisson's ratiovalues were about 10 percent lower thanthe prototype. Within the range of accu-racy of the limited number of tests, thiswas determined to be acceptable.

Tensile strength tests were conductedaccording to ASTM C496. Even thoughmodel mixes customarily have highertensile strengths, the results of thesetests were close due to the higher thanaverage tensile strength of the prototypemix.

TEST EQUIPMENTAND SETUP

The test frame was designed to allowmodifications to provide for each of thethree primary test configurations and tohandle the dimensional variations ofeach of the six specimens and sevenspans. In the first configuration, thebeams had to he supported vertically ateach end and braced to provide end tor-sional restraint without restrainingbending rotations. They had to be free todeflect vertically, horizontally, and ro-tationally except at the bearings.

The second configuration was similarto the first, except that horizontal dis-placements and rotations were re-strained along the beams. A cutawayisometric view of the test frame at mid-span with a beam configured vertically,with braces in place is shown in Fig. 3.

PCI JOURNAL/March-April 1986 103

WIRE ROPE

<— LOAD DEVICE

SUPPORT BEAM

TORSION LOAD BAR

ROD TO WHIFFLETREE rL ~ ^t3

Fig. 4. Isometric view of horizontal test configuration.

The load was applied to discrete pointsalong the ledge. The uniformly distrib-uted torsion load was applied by pullingdown on the face of the ledge and up onthe top side of the stem.

A whiffletree system, operated by asingle hydraulic ram was used to ap-proximate the uniform loading by dis-tributing the ram load to the ledge loaddevices. The load points were at 9 in.(0.239 m) centers for the 16 point and 8point trees, and at 12 in. (0.305 m) cen-ters for a four point tree. This was donebecause the beams under study are ac-tually loaded by stemmed components,giving a series of closely spaced pointloads.

The adjustable braces attached to thesupport beams, one of which is shown in

Fig. 3, were located 7.5 in. (0.191 m)apart, coinciding with the span incre-ments, and allowing them to be used forboth vertical configurations. Tominimize the restraint to vertical de-flection, ball and socket casters werewelded to the braces at the contactpoints. Vertical support for shorter spanswas provided by a separate pair ofstands.

Each beam was fabricated with ½ in.(12.7 mm) round channels to receive thenoses of the loading devices to preventthe beam from moving out from underthe load. This detail was necessary forsafety, and consistent placement of theloads. A disadvantage of this condition isthe introduction of a horizontal con-straint force when significant horizontal

104

Fig. 5. Horizontal test setup.

displacements or rotations occur. Thecentral load to the whiffletree was pro-vided by a 20 kip (88.9 kN) capacity hy-draulic ram, mounted to the laboratoryfloor.

For the third configuration, the beamwas turned to a horizontal position andsupported uniformly against translationat the centerline. The torsion load wasapplied through the whiffletree, bypulling down on the face of the ]edgeand up on the top of the stem. A cutawayisometric view of the horizontal testframe is shown in Fig. 4. Pairs of pulleyswere attached to the underside of aceiling mounted beam to carry thedownward force of the whiffletreethrough the cables to lift up on the beamweb. Fig. 4 also shows a typical torsionloading mechanism of the horizontalbeam test, schematically. The horizontaltest setup is shown in Fig. 5.

InstrumentationInstrumentation of the tests consisted

of three parts. A universal flat load cellwas mounted between the ram and thecenter whiffle tree rod to measure theforces in the loading system. Deflec-tions were measured with dial gauges,each having a maximum throw of 1' in.(38.1 mm), and a reading accuracy of0.001 in. (0.025 mm), and located at thebean midspan as indicated in Fig. 6.

To check deflections and control thelevel of stress, four general purposesingle direction type strain gauges weremounted at midspan. Each strain gaugewas attached at a "corner" of the rein-inrcing cage as shown schematically inFig. 6. The strain gauges were measuredusing a quarter bridge configuration.

Test ProcedureFor each test series, the beams were

initially set up in the vertical position atthe longest span. The first test run wasthe 12 ft 6 in. (3.81 in) span unbracedtest. This test provided the most severecombined loading to establish the pat-

PCI JOURNALJMarch-April 1986 105

2 3

1 1

2 1 4

3 •

2 4

4 3

0 DIAL GAUGES

4 n STRAIN GAUGES

(a) VERTICAL TESTS (b) HORIZONTAL TESTS

Fig. 6. Dial and strain gauge locations at midspan.

tern of cracking for each beam. All sub-sequent tests were conditioned by thisbehavior. The unbraced vertical test wasrepeated. After repeating the unbracedvertical test twice, the horizontal brac-ing was moved into position to preventhorizontal displacement or rotation, andtwo loading sequences were non in thebraced configuration.

The loading mechanism was then dis-assembled, the shorter span supportpylons were placed, and the loadingmechanism was reconstructed for thenext shorter span. After the braced con-figuration was loaded twice, the hori-zontal braces were retracted, and theunbraced tests were run at this span.Testing proceeded in this manner forconsecutively short spans until all sevenspans were completed. After completionof the vertical tests, the frame was rear-ranged for the horizontal test series.

Again, the tests proceeded fromlongest span to shortest. Each beam wasthus tested at 12 ft 6 in., 11 ft 3 in., 10 R,8 ft 9 in., 7 ft 6 in., 6 ft 3 in., and 5 ft (3.81,3.43, 3.05, 2.67, 2.29, 1.90, and 1.52 in)spans.

Data Conversion andInterpretation

To obtain comparable values, it wasnecessary to convert the raw data intonet displacements and rotations. Thisrequirement was considered in the de-sign of the frame and instrumentation,so that the gauges would he located toprovide results which were easy tointerpret. Redundancies were used tominimize systematic error and to iden-tify poor results. Vertical displacementswere directly obtained from the verti-cally oriented dial gauges. Strain gaugereadings were also used to estimate ver-tical displacements. This displacementmeasure, while relative, did not containsystematic error found in some of thedial gauge readings of the braced verti-cal tests. To convert strains to displace-ments, a simple Bernoulli-Euler bend-ing model was used. Strains were usedto estimate the curvature at midspan.

Assuming a uniform load, and uniformsection properties, an equivalentEl wascomputed and used in the equation fordisplacement of a uniformly loaded,

106

simply supported beam. This methodmay produce computed deflectionswhich vary from the true value due tothe assumptions, but it does provide areliable means to compare vertical dis-placements of the braced and unbracedtests.

Values for both horizontal displace-ments and rotations were obtained fromthe horizontal dial gauges, The net hori-zontal displacement was computed asthe average of the displacements at thetop and bottom of the beam. The angleof rotation was found from simple trigo-nometry, using the difference of the topand bottom displacements and the dis-tance between the measurement points.For the horizontal tests, the rotationangle was obtained with the same rela-tionship.

ANALYSIS OFTEST RESULTS

Since six beams at seven differentspan lengths were considered in thepresent study, it would be impractical topresent the complete test results here.Instead, two beams which displayedrepresentative behavior are consideredin some detail. Readers wishing furtherdetail should refer to Refs. 4 and 5.

The two beams to be discussed in de-tail are Beams A and C, as described inTable 1. Beam A had the second largesthlb ratio (hlb = 12) of the beams tested.Beam C had the second smallest hlbratio (h/b = 6) of the beams tested. Figs.7(a) and 7(b) show the displacementsand rotations of Beam A at a 6 ft 3 in.(1.90 m) span. Figs. 8(a) and 8(h) illus-trate the displacements and rotations ofBeam A at a 10 ft (3.05 m) span. Figs. 9(a)and 9(b) are the displacements of BeamA at a 12 ft 6 in. (3.81 m) span.

Since two test runs were conducted ateach configuration and span, the valuesplotted are the averages of the valuesobtained during the two runs. There waslittle variation in the strain gauge databetween runs in most cases, while the

Table 2. Horizontal/verticaldisplacement ratios.

Beammark

Itb

Deflectionratio

F 3 1.02C 6 1.28D 9 2.96A 12 2.53E 12 2.64B 16 2.77

dial gauges were somewhat less precise.The torques in vertical tests plotted in

Figs. 7(b), 8(b), and 9(b) are computedsimply as the magnitude of the appliedload times the distance from the hori-zontal load point to the center of theweb. A somewhat better plot would beobtained if the distance to the shearcenter were used, but determination ofthe shear center location for a crackednonsymmetric reinforced concrete beamis difficult.

Figs. 10(a) and 10(b) present the dis-placements and rotations of Beam C at a6 ft 3 in. (1.9 in) span, while Figs. 11(a),

Table 3. Notation for response figures.See Figs. 7 through 12.

l: BD — Vertical displacements ofunbraced configurationestimated by dial gaugemeasurements

B1) — Vertical displacements ofbraced configurationestimated by dial gaugemeasurements

UBS — Vertical displacements ofunbraced configurationestimated from strain gaugereadings

BS —Vertical displacements ofbraced configurationestimated from strain gaugereadings

l Ili — Horizontal displacements ofunbraced configurationestimated from dial gaugemeasurements

PCI JOURNAL/March-April 1986 107

F 12 (534) UBS HIDKIPS BS UBD(K Al)

10.; /..

'iii A,

8 ^X

6 (26.7) f f

BD. y

.^ r

2 '41..

(1.0) (2.0) (mm)

01 .02 03 .04 .05 .06 .07 08 INCHES

(a) Translations

18 (2.03) KN-m

16 (1.81)

14 (1.55)

I. 12- (1.36)Horizontal (2)

10- (1.13)

Z g (.40)O_

6 (.F8)

OH

2

Unbraced Vertical (2)

Horizontal (1)

0 1 2 3 4 5 6 7 8 9 10 I1 12 13 14

ROTATION (Radians, x .001)

(b) Rotations

Fig. 7. Beam A displacements for 6 ft 3 in. (1.91 m) span (see Table 3).

108

F 12 • (53 4) UBSKIP N) i 6 C BS HDPS BD UD

F ^6

'`4 / /,

2

.-'- {5.os).10 20 .30

(a) Translations

(10.2) (mm)

40 INCHES

s

1$ (2.03) K`-H

16 (]..8i)

14- (1.58)

° 12 Horizontal (2)

10- Horizontal (1)

Z $ (.90)

rn6 (,68)

OF-

4-

2

Unbraccd Vertical (1)

0 1 2 3 4 5 6 7 8 9 10 It 12 13 14

ROTATION {Radians, x .001)

(b) Rotations

Fig. 8. Beam A displacements for 10 ft (3.05 m) span (see Table 3).

PCI JOURNALJMarch-April 1986 109

F 12 (53.4) BSKIPS BD UBD S UBS

(KN)10 f

IS //,ç' l HD

6 (26.7) / (

4 r , !

2

(508)1

0.1 0.2 0.3

(1Q.2)(mrn)

0.4 INCHESs

(a) Translations

18 (2.03)KN-m

16 (^.8)Unbraced Vertical (1)

14- (1.58)

12 (1.36)

10 (1.13)

8 (.9n) 4z0W 6 (.68)

Horizontal (1)Q 4 (.45)

Horizontal (2)

2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

ROTATION (Radians, x .001)

(b) Rotations

Fig. 9. Beam A displacements for 12 ft 6 in. (3.81 rn) span (see Table 3).

Unbraced Vertical (2)

ME

UBS

F 6 -(26.7)BS BD D HD

KIPS!•' UBD

(KN) 5/^'14 (17.6)

31iv2 (e.9) /,•'

Z '

0 (10) (2.0) (mm)

0 .01 .02 .03 .04 .05 .06 .07 .OS INCHES

(a) Translations

KN-m12 (1.36)

Unbraced Vertical (2) 3 Unbraced Vertical (1)G 10 (1.13)

8 (.90)

6 Cl^forizontal.66)( (2)

Horizontal (1)

p 4- (.45)

2

0 1 2 3 4 5 6 7 8 9 10

ROTATION (Radians, x .001)

(b) Rotations

Fig. 10. Beam C displacements for 6 ft 3 in. (1.91 m) span (see Table 3).

PCI JOURNALJMarch-April 1986

^i

.1) (mm)14 .16 INCHES

S

FKIPS6(KN)

5

4

3

2

1

0

•HD

02 04 .06 .08 .10 .12

BS

(a) Translations

KN-m

12- (1.36)Unbraced Vertical (1)

10 (1.13)

a Unbraced Vertical (2)8 (0.90)

6 (0.68)zO

a 4 (0.45) Horizontal (1)OI--

z (.22) Horizontal (2)

0 1 2 3 4 5 6 7 8 9 10

ROTATION (Radians, x .001)

(b) Rotations

Fig. 11. Beam C displacements for 8 ft 9 in. (2.67 m) span (see Table 3).

112

UBD $S HD

F 6 (26.7) B SUBS

KIPS /i

(K N) 5 ^' - "•"j^

4 (178}

/ .%

2 (e.9)

1 ,.

0 (1.27) (2.54) (381) (5.08Xmm)

.05 .10 .15 ,20 INCHES

8(a) Translations

KN-m12 (1.36) Unbraced Vertical (2)

Unbraced Vertical (1)]p (1,13)

C

8U90)

6 (68) Horizontal (2)

zO

A (.41) Horizontal (1)O

2-

0 1I

2 3 4 5 6 7 8 9 10

ROTATION (Radians, x .001)

(b) Rotations

Fig. 12. Beam C displacements for 11 ft 3 in. (3.43 m) span (see Table 3),

PCI JOURNAL/March-April 1986 113

11(b), 12(a) and 12(b) present the samedata at an 8 ft 9 in. (2.67 m) span and an11 ft 3 in. (3.43 m) span, respectively. Inthe displacement figures, the symbolsare given in Table 3.

The plots chosen are reasonably rep-resentative of the test results,

Discussion of Test ResultsThe strategy used in the experimental

studies was to compare measurementsof the general behavior of the beams tothose for tests controlled to behave inthe manner assumed by design criteria.Comparison of vertical displacementsdid not reveal any consistent tendencyfor increasing rate of vertical displace-ment with load, even at the highestloads.

The rotational data, typified by Figs.7(b) to 12(h), were also examined for in-dications of secondary behavior. In gen-eral, the rotational responses in thehorizontal (pure torsion) tests werenearly linear, with a slight curvature in-dicating some torsional softening withincreasing torque. The responses ob-tained in the unbraced vertical tests aremore varied. In these tests, the nominaltorque to midpoint rotations appear tobe a hardening curve, a tendency whichis generally more pronounced for thelonger spans.

It appears likely that several factorscontributed to this observed trend. First,as the beams rotate, the ledge loads tendto move toward the shear center, a con-sequence of the load application posi-tion near the bottom of the section. Sec-ondly, accompanying the beam rotationswas a significant horizontal translation,which will be discussed in further detailshortly.

These horizontal translations had tworelated effects upon the rotations. Asmall rotation of the line of action of theloads from the whiffletree occurs, tend-ing to be additive with the ledge rota-tion in moving the line of load applica-tion toward the shear center. The mid-

span load components tend to move to-ward the shearcenter ofthe undeformedbeams. Thus, even if the loads from thewhiffletree remained vertical, thetorque about the beam support points isreduced by the lateral deflection.

In general, however, as the spanstested increased, the rotations measuredin unbraced vertical tests increased rel-ative to the rotations in the horizontaltests. The onset of significant deviationbetween the two cases occurred at Libratios between 37 and 70, and at Lh /b2ratios between 315 and 960.

These trends are evident in Figs. 8(b)and 11(b) for Beams A and C, respec-tively. The vertical unbraced test rota-tions showed some tendency but pro-vided no conclusive evidence of thesoftening usually associated with stabil-ity related secondary displacements.Thus, any recommendations must con-sider the limitations of the results.

Perhaps the most significant findingof the experimental studies was themeasurement of substantial horizontalbeam displacements. In general, thehorizontal displacements tended to in-crease with span length, although therotation of the whiffletree, and the beamsection may have reduced the horizontaldeflections at the longest spans.

This trend is particularly noticeable inthe hardening HD load-deformationcurves of Figs. 11(a) and 12(a), andsuggests that horizontal deflections inpractice may be somewhat larger thanindicated by the present tests. Signifi-cantly, the tests indicated that the hori-zontal deflections may exceed the verti-cal deflections by a factor of two ormore.

Examining the test results in Figs. 7(a)to 12(a) suggests that the observed hori-zontal displacements do not display sta-bility related behavior, since there is noobserved softening trend of horizontaldisplacement versus load. Rather, thehorizontal deflections are a direct con-sequence of the asymmetry of the ledgerbeam configurations. Because of this

114

asymmetry, the principal axes are ro-tated slightly about the vertical.

Consequently, the vertical loadingcontributes a component in the minoraxis as well as in the major axis direc-tion. Since the minor axis bending stiff-nesses tend to be significantly smallerthan the major axis stiffnesses, substan-tial lateral deflections can result. Thelargest difference in deflections was ob-served in Beam B at a 60 in. (1.52 m)span (not shown).

This is quite understandable, since,referring to Table 1, it is seen that BeamB was 24 in. (0.61 in) deep and had astern width of only 1 1/2 in. (38.1 mm).Following this reasoning, one wouldexpect the magnitudes of horizontal dis-placements relative to the vertical dis-placements to increase as a function ofthe dlb ratio, independent of any secondorder effects.

To verify this, the average ratios ofhorizontal to vertical beam displace-ments were computed for all six testbeams, after discarding obvious outlierscaused by the test system restraint.These values are shown, together withthe dlt ratios in Table 2. Except forBeam D, which had larger than ex-pected horizontal deflections, Table 2shows a general trend of increasing de-flection ratios with increasing d/b ratio.

In considering the overall effects ofhorizontal displacements on service-ability, a comparison of measured hori-zontal displacements with the overallspan length is important. Criteria tolimit this ratio have not been proposedfor concrete beams.

Significant cracking of exposed fin-ished surfaces or increased torsion dueto increased eccentricity may resultfrom ratios of span to horizontal dis-placement as high as 500 or 600. Valuesof this magnitude were observed in thetests. In some of the longer spans, hori-zontal displacements as large as 1/400 ofthe span were observed, in spite of therestraint apparently introduced by thewhiffletree.

If such displacements should occur ina 50 ft (15.2 m) prototype structure, thenhorizontal deflections on the order of 11to 2 in. (38 to 50 mm) would not be un-expected. If the beams supported on theledge do not introduce restraining forcessimilar to those contributed by thewhiffletree in the tests reported herein,even larger lateral displacements mightbe possible.

CONCLUSIONS

The load-deformation characteristicsof precast concrete spandrel beams havebeen studied in an effort to identify ef-fects not customarily considered in de-sign, but which may affect their service-ability or safety. The results of thisstudy, confined to the elastic range ofbehavior, suggest:

1. Some additional rotation may occurin unbraced vertical bending, over thatwhich would be predicted by a pure tor-sional test result. There was not a clearindication, however, that these in-creased rotations are a consequence ofstability related secondary deflections.

2. Substantial horizontal displace-ments, due to the rotation of the princi-pal axes in asymmetrical beams, willconsistently occur in unbraced spandrelledger beams. These horizontal dis-placements may be twice as large as thevertical dispacements, and may causeserious serviceability, and potentiallysafety, problems, such as cracking offinished surfaces, or increased load ec-centricity. Prevention of this behaviorby limiting Lib ratios, lengths, or by acareful consideration of erection proce-dures and lateral bracing during erec-tion is indicated when the ACI Codelimits oFLlb are approached.

3. Additional research is needed intothe prediction of precast and prestressedconcrete spandrel beam load-deforma-tion behavior, in both the elastic andultimate behavior range. With the load-ing points of precast units near the bot-

PCI JOURNAL/March-April 1986 115

tom of such ledger beams, particularlyduring the construction stage, additionalresearch is needed to ascertain the con-straint or lack thereof against lateral de-flection introduced by the presence ofthe precast units on the ledge. A studyjust completed by the PCI SFRADACommittee No. 5 project includes datain this area. Additional research into themagnification of torsional rotation in theultimate behavior range is needed.

4. Cracking that was observed wasflexural. Vertical cracks appeared atmidspan and developed at regular inter-vals to about the quarter points. No tor-sional cracking was evident at the limitof service loading. Cracks were wider onthe face than on the ledge side. The re-inforcement design and detailing actedto control and distribute cracks, but notto prevent them.

ACKNOWLEDGMENTSThe support of Shockey Brothers, Inc.

and the Academic Computing Center atthe University of Virginia are gratefullyacknowledged.

DESIGNRECOMMENDATIONS

1. The ACI Code required Lib ratiolimit of 50 is a safe guideline that shouldnot he exceeded for spandrel ledgerbeams without specific erection proce-dures to control horizontal displace-ments. Caution for sensitive appli-cations should he exercised for values ofLib as low as 35.

2. When possible, prestressing ofthese beams should be used to preventthe stiffness reducing flexural crackinginherent to nonprestressed beams.Complexity of setup and formwork con-straints must be considered in deter-mining the feasibility of this approach.

3. For any loadhearing precast span-drel panel of long span and slender pro-file, rotation of principal axes from thedirection of loading should be consid-ered. Use of uncracked section prop-erties for this evaluation should be ade-quate to identify potential hazards.Determination of the rotation of princi-pal axes leads directly to deflection re-lations between horizontal and verticalaxes.

APPENDIX -- NOTATIONh = compression flange width of led-

ger beamh,n = width of ledger beam (see Fig. 2)d = distance from extreme compres-

sion fiber to centroid of flexuraltension reinforcement

E = modulus of elasticity of concretefr = tensile strength of concreteF = applied load

h = vertical height of ledger beam (seeFig. 2)

I = moment of inertia of ledger crosssection

L = unbraced span length of ledgerbeam

t = thickness of ledger beam8 = measured deflectionv = Poisson's ratio of concrete

116

REFERENCES

1. AC! Committee 318, "Building CodeRequirements for Reinforced Concrete(ACI 318-83)," American Concrete In-stitute, Detroit, Michigan, 1983.

2. PCI Design Handbook –Precast Pre-stressed Concrete, Third Edition, Pre-stressed Concrete Institute, Chicago, II-linois, 1985.

3. Building Officials and Code Adminis-trators International, Inc., The BOCABasic Building Code/1981, InterstatePrinters and Publishers, Inc., Danville,Illinois, 1981.

4. Raths, C. H., "Spandrel Beam Behaviorand Design," PCI JOURNAL, V. 29, No,2, March-April 1984, pp. 62-131.

5. Hsu, T. T. C., Torsion of ReinforcedConcrete, Van Nostrand Reinhold, NewYork, 1984.

6. Collins, M. P., and Mitchell, D., "Shearand Torsion Design of Prestressed andNon-Prestressed Concrete Beams," PCIJOURNAL, V. 25, No. 5, September-Oc-tober 1980, pp. 32-100.

7. Mitchell, D., and Collins, M. P., "Diago-nal Compression Field Theory — A Ra-tional Model for Structural Concrete inPure Torsion," ACI Journal, V. 71, Au-gust 1974, pp. 396-408.

S. Rabbat, B. C., "A Variable Angle SpaceTruss Model for Structural ConcreteBeams," PhD Thesis, University of To-ronto, Ontario, Canada, 1978.

9. Rabbat, B. G., and Collins, M. P., "AVariable Angle Space Truss Model forStructural Concrete Members Subjectedto Complex Loading," Douglas McHenryInternational Symposium on Concreteand Concrete Structures, ACI SpecialPublication SP-55, American ConcreteInstitute, Detroit, Michigan, 1978, pp.,547-587.

10. Rabbat, B. G., and Collins, M. P., "TheComputer Aided Design of StructuralConcrete Sections Subjected to Com-bined Loading," Computers and Struc-tures, V. 7, No. 2, April 1977, pp. 229-236.

11, ACI Committee 438, ACI BibliographyNo. 12 – Torsion in Concrete (Anno-tated), American Concrete Institute,Detroit, Michigan, 1978.

12. Marshall, W. T., "The Lateral Stability ofReinforced Concrete Beams," Journal,Institution of Civil Engineers (London),V. 30, No. 6, April 1984, pp. 194-196.

13. Vasarhely, D., and Turkolp, I., "LateralBuckling of Slender Reinforced ConcreteBeams," The Trends in Engineering atthe University of Washington (Seattle),V. 6, No. 3, July 1954, pp. 8-10.

14, Hansell, W., and Winter G., "Lateral Sta-bility of Reinforced Concrete Beams,"ACI Journal, V. 56, August 1959, pp.193-213.

15. Sant, J. K., and Bletzacker, R. W.,"Experimental Study of Lateral Stabilityof Reinforced Concrete Beams," ACIJournal, V. 58, December 1961, pp.713-736.

16 Massey, C., "Lateral Instability of Rein-forced Concrete Beams Under UnifiirmBending Moments," ACI Journal, V. 64,March 1967, pp. 164-172.

17. Timoshenko, S. P., Theory of ElasticStability, McGraw-Hill Book Company,New York, 1961.

18. Vlasov, V. Z., Thin-Walled ElasticBeams, Translated from Russian by Y.Schechtman, National Science Founda-tion, Washington, D,C., 1959.

19. Cleland, N. M., "Identification of Sec-ondary Behavior in Combined Bending,Shear and Torsion of Reinforced Con-crete Ledger Beams," PhD Dissertation,University of Virginia, Charlottesville,August 1984.

20. Cleland, N. M., and Baher, T. T., "Be-havior of Reinforced Concrete LedgerBeams in Combined Bending, Shear andTorsion," Structural Engineering andMechanics Reports, No. SEMR 85-01,Department of Civil Engineering, Uni-versity of Virginia, Charlottesville, Vir-ginia, March 1985.

NOTE: Discussion of this paper is invited. Please submityour comments to PCI Headquarters by November 1, 1986.

PCI JOURNALJ March-April 1986 117