Tailor Made Concrete Structures – Walraven & Stoelhorst (eds)© 2008 Taylor & Francis Group, London, ISBN 978-0-415-47535-8

Development of a rational design methodology for precast L-shapedspandrel beams

G. Lucier, C. Walter, S. Rizkalla & P. ZiaNorth Carolina State University, Raleigh, NC, USA

G. KleinWiss, Janney, Elstner Associates, Inc., Northbrook, IL, USA

D. LoganStresscon Corporation, Colorado Springs, CO, USA

ABSTRACT: Precast concrete spandrel beams are commonly used in parking structures to transfer verticalloads from deck members to columns. These beams typically have slender, unsymmetrical cross-sections andare often subjected to heavy, eccentric loading. These factors produce a complex internal structural mechanismincluding significant out of plane behavior. Traditionally, slender spandrel beams have been reinforced using thetorsion and shear provisions of ACI-318. These provisions assure torsional strength by requiring heavy closedreinforcement and well-distributed longitudinal steel to provide torsional resistance after face shell spalling.The need for such complex and expensive reinforcement in slender spandrel beams is questionable. From asearly as 1961, extensive field observations and limited full-scale testing have documented a lack of face shellspalling and spiral cracking in slender spandrel beams. Rather, out of plane bending appears to dominate slenderspandrel behavior. More recently, extensive full-scale testing has confirmed that the classically assumed modeof torsional distress is not realized in precast slender spandrels. This paper provides background informationand argument for simplifying the reinforcement detailing requirements for slender spandrel beams. The paperpresents an overview and selected results to date of research currently in progress to develop alternative, moreefficient reinforcing schemes and a rational design approach.

1 INTRODUCTION

1.1 Background

Precast spandrel beams are commonly used in parkingstructures, serving the purpose of transferring verticalloads from deck members to columns. In many cases,a continuous ledge runs along one edge at the bottomof the beam, resulting in what is known as an L-shapedspandrel. In other cases, discrete haunches are used inplace of the continuous ledge, creating what is knownas a corbelled spandrel. The ledge or corbels providea bearing surface for the deck members, and thus, thetypical precast spandrel beam is subjected to a seriesof discrete eccentric loads.

Eccentrically loading the slender cross-sectionresults in a complex structural behavior which, cou-pled with typically heavy loadings, often results inspandrel designs requiring conservative reinforcementdetails. Frequently, steel is heavily congested in critical

zones such as the end regions where prestressingstrands and reinforcing bars must weave throughthe numerous closely-spaced closed stirrups that arerequired by the ACI Code (318-05).

The eccentric location of the applied loads withrespect to the unsymmetrical L-shaped spandrel cross-section causes vertical displacement in addition tosignificant lateral displacement and rotation.The max-imum torsional and shear effects occur in the endregions. In resisting vertical loads, precast spandrelbeams are simply supported at the columns. The endsof these beams are also connected to the columns toprevent out of plane rotation about the longitudinalaxis. In addition, deck sections are often connected tothe spandrel web at discrete locations, providing lateralrestraint along the span.

Figure 1 depicts a typical L-shaped slender span-drel. Point loads from double tee deck sections areshown along the ledge, column reactions are shown at

141

Figure 1. Loads and reactions typically imposed on aprecast slender spandrel.

each end, and lateral restrain forces are shown alongthe face of the web.

The current design procedure used by the industryfor torsion is based on test data taken from rein-forced concrete beams having compact cross-sections.When applied to the slender cross-sections of typicalL-shaped spandrel beams, the resulting closed rein-forcement is usually tightly congested and difficult toinstall.While the current design practice results in safe,reliable, and acceptable behavior, limited experimen-tal data have prompted many within the industry toquestion the need for such heavy, closed reinforcementin the end regions of slender spandrels. It has beensuggested that closed stirrups could perhaps be elim-inated from the design of slender spandrels in favorof a more economical and production-friendly openreinforcement approach.

1.2 Current practice

The current practice recommended by the AmericanConcrete Institute (ACI 2005) for proportioning rein-forcement to resist shear and torsion within a concretemember is based on a space truss analogy. Longitu-dinal steel and closed stirrups are provided to resisttorsional stresses which are assumed to develop andspiral down the length of a member. Well distributedlongitudinal steel and closed ties serve to maintain theintegrity of the concrete core enclosed within the stir-rups, allowing inclined compression struts to developand to resist the applied forces.

The ACI approach assumes that later stage memberresponse will be characterized by spalling of the con-crete face shell outside the stirrups, and recommendsdetailing such as 135-degree stirrup hooks to main-tain the integrity of the concrete core after spalling(Mitchell 1976). These detailing requirements oftenrequire tightly congested, interwoven reinforcement,especially in the end regions.

It is important to mention that within the torsionprovisions of ACI-318-05, there is a stipulation allow-ing for alternative approaches to the torsion design ofsolid sections having an aspect ratio (height divided

by web thickness) of three or greater. ACI-318 states“it shall be permitted to use another procedure, theadequacy of which has been shown by analysis andsubstantial agreement with results of comprehensivetests.”

For many years, the precast prestressed concreteindustry has recommended an alternative procedurefor torsion design developed by Zia and Hsu (1978).The procedure is outlined in the latest edition of thePCI Industry Handbook (PCI 2004), and, similar tothe ACI approach, makes assumptions of face shellspalling and spiral cracking. Currently, this procedureis commonly used to proportion shear and torsionreinforcement in slender spandrel beams.

1.3 Challenges to current practice

The approaches to torsion design advocated by ACIand PCI are widely accepted, and are routinely appliedto the design of both compact and slender mem-bers. While the appropriateness of these approachesis well documented for compact sections, many havechallenged the validity of applying the same designmethodology to slender precast members (Logan2007). Decades of field observations (Raths 1984),limited experimental testing (Klein 1986), and obser-vation of slender section behavior (Logan 2007) havesupported the argument that design approaches rely-ing on assumptions of spiral cracking and face shellspalling are inappropriate for application to slen-der members. If torsional distress is not generatedby eccentric loading of slender precast members,then classical torsion design procedures and detailingrequirements cannot be justified.

1.4 Skewed failure plane

It is well established that the failure mechanism for aslender reinforced concrete section subjected to com-bined flexure, shear, and torsion will be in the form ofskew bending (Zia 1968, Hsu 1984). This skew maybe idealized by four edges, each inclined at 45-degreeswith respect to the next, forming a distorted surface.This skewed failure mechanism does not exhibit thecharacteristic spiral cracking and face shell spallingassumed as the basis of the current ACI and PCIapproaches.

In compact, rectangular sections, this failure planeis crossed effectively on all four faces by closed ties.For slender sections, however, the value of the shorterlegs of the ties is questionable because the projectionof the failure plane crossing the narrow face of themember is often less than the longitudinal spacing ofsuch ties.

Considering the slender spandrel as an example,the tie legs crossing the top or bottom edge of the webprobably have minimal effect on the overall torsional

142

resistance of the member. Rather, it is the vertical legsof such closed ties which are providing the bulk oftorsional resistance, since these legs cross the failureplane along the much longer inner and outer faces ofthe web.

For a slender spandrel beam with an assumed fail-ure angle of 45 degrees, the short legs of any closedties would effectively contribute to torsional resistanceof the member only if tie spacing were maintained atone-half of the web thickness. Tie spacing greater thanthe web thickness creates a situation in which the topedge of the failure surface will likely pass betweenadjacent ties.

Thus, for a typical web thickness (200 mm) of aslender spandrel, the contribution of the short legs ofstirrups spaced at more 100 mm is questionable. Suchtight stirrup spacing is uncommon for long, slendermembers, and thus, the geometry of the skewed failuresurface itself seems to indicate that the short legs ofclosed ties do not significantly contribute to torsionalresistance in slender spandrels.

1.5 Field observations

Field observations of precast slender spandrel behav-ior have been discussed among precast producers andengineers for over six decades. However, the in-servicebehaviors of precast slender spandrel beams werenot well documented until Raths reported on span-drel beam behavior and design in 1984. A substantialportion of his report describes field observations ofstructural failures and structural distress. This docu-ment, perhaps the most thorough account of precastspandrel behavior to date, contains no evidence of aprecast slender spandrel developing internal torsionaldistress. Instead, extensive out of plane bending andweb face cracking were observed to resist what Rathsrefers to as “beam end torsion,” the end couple actingto restrain the beam from rolling inward due to theeccentrically applied loads.

1.6 Previous testing and research

Informal load tests on precast L-shaped spandrelbeams have been documented since the early 1960s.Informal testing of this nature was commonly car-ried out by precast producers to investigate designissues which had not been formally researched at thetime. A test conducted in 1961 was unable to generateeither torsional rotation or torsional distress in a pre-cast L-shaped spandrel subjected to eccentric verticalloading. From this early stage, the necessity of provid-ing complex torsion reinforcement in L-shaped precastmembers was called into question (Logan 2007).

Formal research into the behavior of slender span-drel beams was published in 1986. Research fundedby the Precast/Prestressed Concrete Institute included

full scale testing of L-shaped precast spandrel beamsloaded eccentrically through the ledge. This researchconfirmed that neither spiral cracking nor face shellspalling occurred in any of the tested beams.Again, theneed for complex reinforcement detailing was calledinto question for slender L-shaped members (Klein1986).

More recently, a group of precast producers part-nered with North Carolina State University to conductpreliminary research and failure testing on full-scaleprecast slender spandrel beams. Four beams weredesigned neglecting conventional torsion procedures.As such, closed stirrups were replaced by open webreinforcement proportioned to resist out of plane bend-ing. For the purpose of the experiments, additionalreinforcement was added to protect against potentialfailure modes outside of the end regions, allowing forobservation of end region behavior at ultimate. Theresults from this study demonstrate the skew bend-ing failure mode, and confirm the absence of classicaltorsional distress (Lucier et al. 2007).

The promising results of this preliminary researchcombined with a strong industry desire for simplifiedslender spandrel detailing requirements prompted thePrecast/Prestressed Concrete Institute to embark onan extensive research project at North Carolina StateUniversity aimed to rationalize and simplify slenderspandrel beam design.The ongoing research has exten-sive experimental and analytical components whichare summarized below along with preliminary resultsand conclusions.

2 CURRENT RESEARCH

The objective of the ongoing research program isto develop a rational design methodology for pre-cast slender spandrel beams loaded eccentrically alongtheir bottom edge. It is intended that any underly-ing assumptions of the proposed methodology closelyreflect the observed response and failure modesof slender spandrel members. In addition, the pro-posed design methodology should allow for simplifieddetailing of reinforcement when compared to currentpractice. The methodology itself must be straightfor-ward enough to be used in everyday practice.

2.1 Experimental work

The research program includes extensive experimen-tal work. Results from the experimental testing willfacilitate characterization of slender spandrel behav-ior, and will allow for an investigation into parametersthat influence this behavior. In all, 13 full-scale precastspandrel beams, each nearly 14 meters long, will betested to failure in the laboratory. In addition, resultsfrom the preliminary research mentioned above will

143

be combined with the current work, creating a collec-tion of 17 experimental tests. To date, 10 of these testshave been completed. The cross-sections under con-sideration have an aspect ratio (height divided by webthickness) of approximately 7.5. A web thickness of200 mm has been chosen for the experimental tests, asthis represents a lower bound of thicknesses actuallyused in production.

The experimental test matrix includes L-shapedspandrels along with spandrels having discretehaunches (or corbels) instead of a continuous ledge.In addition, prestressed and conventionally reinforcedmembers are studied. While the majority of beams donot have any closed stirrups (instead having open webreinforcement), control beams reinforced with cur-rently accepted design procedures are also included.A variety of open-web reinforcement schemes are eval-uated experimentally. In addition, tests using both slidebearings and typical bearing pads at ledge and col-umn reactions are included. Out of plane behavior isa crucial element in spandrel response, and friction atbearing locations serves to restrain this behavior.Thus,slide bearings were included in most tests to evaluatemember response under the worst case conditions.

2.2 Specimen design

All specimens were designed to resist typical dead,live, and snow loadings for parking structures. Thedesign assumed that each 14 m spandrel supported halfof an 18 m span continuous deck.

It is important to note that many of the beamsincluded in the test matrix were constructed with spe-cial reinforcement details to prevent failures outsideof the end regions. This extra detailing was providedto allow for study of the end regions at ultimate. Forexample, steel angles were embedded at ledge bearinglocations to delay punching failure in the ledge. Carewas taken to ensure that these additional measuresdid not influence end region behavior. For example,additional mild steel was provided at midspan to delayflexural failure, but this steel did not extend into theend regions. Spandrels without special detailing wereincluded in the test matrix to eliminate concerns aboutunintentionally altered end-region response.

For specimens with open-web reinforcement, steelwas provided to satisfy only the requirements of in-plane flexure, vertical shear, ledge or corbel hangersteel requirements, and out of plane web bending. Alltorsion design provisions found in ACI-318 and thePCI Industry Handbook were ignored. Web bendingforces were determined from the eccentricity of theapplied loads and the spacing of the web tie-back con-nections. A 45-degree failure plane originating fromthe lower connection was assumed for design.

Figure 2 compares closed and open reinforcement.The open reinforcement configuration shown was

Figure 2. Comparison of Closed and Open Reinforcement(Spandrels shown outer face down, as typically formed).

Figure 3. Profile view of experimental test setup.

chosen for some of the tested specimens. The primaryadvantage in using open reinforcement over conven-tional closed reinforcement is a substantial savingsin labor and material during production. Configura-tions of open reinforcement other than that shown arepossible.

2.3 Test setup

Each spandrel specimen measures nearly 14 meterslong. Spandrels were simply supported and attachedat their ends to a steel testing frame. Specimens wereloaded by hydraulic jacks through short double-teedeck sections to mimic field conditions.

Loading was quasi-static up to failure, and includeda 24-hour holding period at the factored design loadfor each test. A variety of instrumentation was used tomonitor loads, deflections, and strains. A profile viewof the test setup is shown in Figure 3 while Figure 4shows an overview photograph.

2.4 Analytical study

In addition to the experimental work, the researchprogram includes significant analytical study.

144

Figure 4. Overview of spandrel, short decks, and load-ing rig.

The analytical program augments the experimentalprogram by allowing for examination of parametersthat may be impossible (or cost prohibitive) to testexperimentally. Data from the experimental programare used to validate, refine, and calibrate the analyt-ical models, providing confidence in the analyticalmethods. The most important task to be accomplishedanalytically is to identify and to define boundary con-ditions that limit the applicability of the proposed openreinforcement concept.

The analytical component of the research has twoelements. The first is to develop and calibrate a three-dimensional nonlinear finite element model (FEM) tostudy various parameters influencing slender precastspandrel behavior. The second is to use the analyti-cal results from the FEM along with the experimentalresults to develop a rational model describing thebehavior of precast slender spandrel beams. This ratio-nal model will form the basis from which to proposea new design method.

The finite element code ANACAP is being used foranalytical modeling. The code is known for advancednonlinear capabilities of the concrete material model.Modeling half of a typical slender spandrel beam (sym-metry at midspan) requires roughly 1500 20-nodebrick elements. Reinforcing bars are modeled indi-vidually as discrete sub-elements within the concreteelements. The stress and stiffness of the reinforcingsub-elements are superimposed on the concrete ele-ment in which the reinforcing bar resides. Appliedloads are increased incrementally to failure. Details ofthe analytical FEM can be found elsewhere (Hassanet al. 2007).

In conducting the parametric study, several key fac-tors are being examined. The first of these is the aspectratio (web height divided by web thickness). The FEMis being used to generate results for a variety of aspectratios within practical limits to examine the influenceof aspect ratio on behavior and failure mode. Thisinformation will be used to define a key boundarycondition, namely the limit of what can be considereda slender spandrel cross-section.

Another key factor being studied analytically is theinfluence of deck connections on spandrel behavior.The typical welded connections between the innerspandrel face and the deck sections tend to developsubstantial forces which influence lateral motion inthe upper portion of the spandrel. The effect of deckconnections on spandrel behavior is being evaluatedanalytically.

The analytical model is also being used to evaluatefriction forces which develop at the bearing reactionsunderneath each deck stem. Due to the large degree oflateral motion, bearing friction at these locations playsa major role in slender spandrel response. Evaluatingthe influence of friction has been done experimentally(by varying bearing pads), but more extensive studycan be conducted analytically.

3 SELECTED RESULTS

To date, all specimens have been configured to studyfailure in the end regions. The end regions for eachof these specimens were designed to resist requiredfactored loads (dead, live, and snow). In every case,including those with completely open web reinforce-ment, the specimen resisted the sustained factoreddesign load for a 24-hour period with no significantsigns of distress. Ultimate loads ranged from approx-imately 1.25 times the factored load level to nearlytwice the factored load level.The analytical models areable to closely predict the experimental failure loads.

As would be expected, end regions reinforced athigher ratios sustained higher loads than did those rein-forced at lighter ratios. End regions reinforced withclosed ties at a high ratio combined with additionallongitudinal steel (the current code approach) wereable to sustain approximately 25% more load thanwere end regions reinforced with entirely open rein-forcement at significantly lower ratios. When an endregion with closed ties is compared to an end regionwith open ties, both reinforced at the same ratio, theincrease in load carrying capacity due to closed ties isapproximately 10%.

Test results indicate that closed ties do enhance endregion capacity. However, it is apparent that end regionload carrying capacities are more than sufficientlyconservative with appropriate open tie designs (at least25% above factored design loads). It is important to putthe differences in load carrying capacity into perspec-tive by noting that fabrication of a typical experimentalopen tie design requires approximately 30% less steeland half the labor when compared to the closed rein-forcement required by the currently accepted codeapproach.

3.1 Cracking pattern and failure mode

In all tests, the cracking pattern was observed as shownin Figure 5. The inner web face exhibits diagonal

145

Figure 5. Typical cracking pattern for precast slenderspandrel.

Figure 6. Slender spandrel end-region at failure.

cracking in the end regions which gradually flattenand arch towards the center of the beam. The outerweb face exhibits vertical cracking extending upwardsfrom the bottom of the beam. This outer face crack-ing is due to in plane and out of plane flexure. Nospiral cracking is observed. As load is applied, thebottom of the spandrel moves down and away fromthe decks at midspan, while the top moves down andinward towards the decks. Resistance to this tendencyto overturn is provided by the lateral column reactions,creating a warped deflected shape and significant outof plane bending demands along the diagonal cracksin the end regions.

The failure mode observed in most tests was that ofskew-bending in the end regions along a primary crackangle of approximately 45-degrees. This failure modeis shown in Figure 6. Recall that the specimens testedto date have been specially configured to study endregion behavior at ultimate. Thus, in upcoming tests ofbeams configured with the same end region reinforce-ment, but typical detailing elsewhere, it is anticipatedthat other failure modes will control long before end-region skew bending develops. The analytical modelis able to accurately predict a skew bending failure.

3.2 Sample test data

Out of plane behavior dominates slender spandrelresponse. Measured lateral deflections often exceedvertical deflections at ultimate. Figure 7 presentsexperimental and analytical lateral deflections for a14 m prestressed L-shaped spandrel beam. This figure

Figure 7. Experimental and analytical lateral deflectiondata.

highlights the opposing lateral motion at the top andbottom of the beam at midspan. Analytical predictionsare shown for a range of assumed bearing pad frictioncoefficients.

4 CONCLUSIONS

The potential benefits of simplified detailing for pre-cast slender spandrel beams are significant. Open rein-forcement provides greatly enhanced constructabilityover traditional closed stirrups, and thus, the potentialfor increasing precast plant productivity is substantial.The research described here aims to make the con-cept of simplifying precast slender spandrel designa reality by developing a safe, simple, and rationaldesign guideline for use by the precast prestressedconcrete industry. The guideline will be based on theconcept of providing open web reinforcement to resistthe out of plane bending forces that develop as a resultof interaction between flexure, shear, and torsion ina slender member. The challenge in creating such adesign guideline is in evaluating the large numberof relevant factors, both experimentally and analyti-cally, and defining appropriate limitations for the newapproach. The authors believe that, once completed,the significant research effort presented here will allowthe industry to fully embrace the concept of usingopen reinforcement for slender precast spandrel beamconstruction.

ACKNOWLEDGEMENTS

The authors would like extend a special thanks to thePrecast/Prestressed Concrete Institute for sponsoringthe research. In addition, the authors are extremelygrateful for the support and assistance providedby individual PCI Producer and Supplier Membersincluding: Metromont, Stresscon, High Concrete, Tin-dall, Finfrock, Gate, and JVI.

146

REFERENCES

ACI Committee 318. 2005. Building Requirements for Struc-tural Concrete (ACI 318-05). Farmington Hills, MI:American Concrete Institute.

Hassan, T. et al. 2007. Modeling of L-Shaped, Precast, Pre-stressed Concrete Spandrels. PCI Journal 52(2): 78–92.

Hsu, T. 1984. Torsion of Reinforced Concrete. NewYork: VanNostrand Reinhold.

Klein, G. 1986. Design of Spandrel Beams. Specially FundedR & D Program Research Project No. 5 (PCISFRAD #5),Chicago, IL: Prestressed Concrete Institute.

Logan, D. 2007. L-Spandrels: Can Torsional Distress BeInduced by Eccentric Vertical Loading? PCI Journal52(2): 46–61.

Lucier, G. et al. 2007. Precast Concrete L-Shaped SpandrelsRevisited: Full-Scale Tests. PCI Journal 52(2): 62–76.

Mitchell, D. and Collins, M. 1976. Detailing for Torsion. ACIJournal 73(9) 506–511.

PCI Industry Handbook Committee. 2004. PCI Design Hand-book: Precast and Prestressed Concrete. 6th ed., pp. 4–57to 4–65. Chicago, IL: Precast/Prestressed Concrete Insti-tute (PCI).

Raths, C.H. 1984. Spandrel Beam Behavior and Design. PCIJournal 29(2): 62–131.

Zia, P. 1968.TorsionTheories for Concrete Members.Torsionof Structural Concrete, ACI Special Publication SP-18.103–132.

Zia, P. and Hsu, T. 2004. Design for Torsion and Shear in Pre-stressed Concrete Flexural Members. PCI Journal 49(3):34–42. May–June. (This paper was previously presentedat the American Society of Civil Engineers Convention,October 16–20, 1978, Chicago, IL, reprint #3424.)

147