Special Report

Spandrel Beam Behaviorand Design

Charles H. RathsSenior PrincipalRaths, Raths & Johnson, Inc.Structural EngineersWillowbrook, Illinois

Presents common precast spandrel beam distress

causes, discusses types of loads applied to spandrel

beams and overall torsion equilibrium requirements,

provides design relationships for spandrel beams,

offers design criteria for spandrel beam connections,

sets forth basic good design practices for spandrel

beams, and gives design examples.

62

CONTENTS

Introduction.............................................64

Pastand Current Problems ... ............................. 64Types of Problems Actual Problems

Typesof Applied Loads ................................... 70Gravity Loads—General

Beam Loading Spandrel LedgesHorizontal Loads Volume Change ForcesBeam End Connections Frame Moment Forces

General Design Requirements ............................. 79Internal Torsion and ShearBeam End Torsion Web FlexureLedge Attachment Corbel End BehaviorLedge Load Transfer Beam Flexure

Considerations for Connnection Design ..................... 92Connection Systems Frame ConnectionsConnection Materials Reinforcement ConsiderationsConnection Interfacing Column Influence

Good Design Practice ......Cross-Sectional DimensionsReinforcementTolerances and ClearancesCorrosion ProtectionLoads

.............................114ConnectionsBearing ConsiderationsUltimate Load FactorsSupporting ColumnsInspections

ClosingComments .......................................120

Acknowledgments........................................120

References..............................................121

Notation................................................122

Appendix—Design Examples ..............................124

PCI JCURNALJMarch-April 1984 63

Spandrel beams, reinforced or pre-stressed, are important and func-

tional elements of precast concretestructures. Given the current designknowledge presented by the PCI DesignHandbook , and the PCI ConnectionsManual,' and basic fundamentals ofstructural engineering mechanics, itwould seem the topic of spandrel beamdesign does not merit further review.Yet, considering the number of precastframed structures experiencing varioustypes of problems and distress withspandrel beams, something is amiss re-garding the designer's understanding ofspandrel beam behavior and design re-quirements.

The purpose of this paper is to reviewsome of the common problems typicallyassociated with spandrel beams, and tosuggest design requirements for them.Towards this end, discussions hereinare devoted to actual problems experi-enced by spandrel beams, load sup-porting functions, general design re-quirements, connections, and good de-sign practice. While spandrel beams areused to satisfy a variety of structuralfunctions, this presentation will em-phasize simple span load supportingmembers.

PAST AND CURRENTPROBLEMS

Difficulties related to spandrel beamsoccur for members supporting floorloads, those which are part of a momentframe, or members that are neithergravity supporting nor part of a momentresisting frame. Typically, simple spanspandrel beams as utilized in parkinggarages appear to be the most problemprone although similar troubles developin office or other "building" type struc-tures.

The difficulties and problems dis-cussed usually do not result in the col-lapse of spandrel beam members.Nevertheless, these problems can create

substantial repair costs, constructiondelays, temporary loss of facility use,and various legal entanglements.

Types of ProblemsThe types of problems experienced by

spandrel beams can be categorized asfollows:

• Overall torsional equilibrium ofthe spandrel beam as a whole.

• Internal torsion resulting frombeams not being loaded directlythrough their shear center.

• Member end connection.• Capability of the spandrel beam's

ledge and web to support verticalloads.

• Volume change restraint forces in-duced into spandrel beams.

Actual ProblemsThe fallowing discussion of actual

case histories relates to projects wherephotographs can be used to illustrate theproblems associated with the abovelisted items. This is not meant to implythat aspects not covered by the easehistories are less significant than thoseconsidered.

The conditions associated with lack ofoverall beam torsion equilibrium areshown in Fig. 1. The non-alignment ofapplied loads and beam end reactionscan be seen in Fig. Ia. Fig. lb shows thebeam rotation crushing of the toppingconcrete caused by the lack of beam andtorsional equilibrium connections. InFig. 1, the torsional rotation problem iscompounded by the presence of neo-prene type bearing pads at the beam andtee bearings where the pad deformationcauses further torsional roll. Generally,the problem of overall spandrel beamtorsional equilibrium represents themajority of the difficulties experiencedby spandrel beams.

Internal spandrel beam torsion dis-tress, frequently within distance "d" ofthe spandrel beam's ends, is often ob-served.* Fig. 2a illustrates a spandrel

64

Fig. 1 a. Lack of overall torsion equilibrium:underside view showing non-alignment ofapplied loads and end reaction.

Fig. lb. Lack of overall torsion equilibrium:top view showing beam rotation andcrushing of topping (arrows).

beam loaded eccentric to its shearcenter and shows the beam's torsionalequilibrium connections (note the teelegs on either side of the column resultin a concentrated load within distance"d"). Internal torsion cracks in thespandrel beam web can be observed inFig. 2b. These torsion cracks result froma combination of internal beam torsionand the flexural behavior influence ofthe beam end torsion equilibrium con-nections. Torsion distress (cracking) atbeam ends is a common problem af-fecting spandrel beams when designs donot consider the influence of loadswithin distance "d" or torsion equilib-rium connection forces.

'Note: "d" denotes the distarive from the extremecompression fiber of the member to the centroid offlexural tension reinforcement.

The lack of overall spandrel beam tor-sion equilibrium is often reflected atcolumn support connections resulting inhigh nonuniform bearing stressescaused by spandrel beam torsion roll.Fig. 3a shows the applied tee loads notaligning with the support column reac-tion. Lack of required overall beam tor-sion equilibrium connections duringerection often results in excessivelyhigh (usually localized) bearing distressas reflected by Fig. 3h. A variation of thesame problems caused by spandrelbeam torsion roll (lack of beam end tor-sion equilibrium connections) is pre-sented by Fig. 4a which produced col-umn corbel failures. Fig. 4h indicatesthe magnitudes of torsion roll that candevelop bearing distress when thenecessary torsion equilibrium connec-tions are not provided.

PCI JOURNAL/March-April 1984 65

Fig. 2a. Underside view of beam end torsion cracking within distance "d"caused by equilibrium connections and internal torsion (arrow indicates locationof reaction).

Fig. 2b. Top view of end cracks (arrows).

66

Fig. 4a (left). Upward view of columncorbel failure caused by lack of any overalltorsion equilibrium connections.

Fig. 4b (above). Example of torsional rollmagnitude at a non-distressed corbel.

N

/ çc

•C .3TOP

Fig. 3a. Underside view of bea •ing distressresulting from torsional roll duo to lack oferection connections (left arrow points tobeam reaction and right arrow indicatesapplied loads). Fig. 3b. Close-up of typical bearing distress.

PCI JOURNAL/March-April 1984 67

Fig. 5. Beam ledge end corbel failure(applied loads and reaction in alignment).

An example of distress resulting frominadequate considerations of structuralbehavior, even though overall torsionequilibrium is assured by applied loadsand beam reactions aligning, is given byFig. 5. The spandrel beam haunch, atthe beam end, acts like a corbel, andwhen not reinforced to resist the entirebeam reaction, as in Fig. 5, distress orfailure develops.

Fig. 6a. Overall view of torsion equilibriumtension insert connection (top arrowindicates bearing pad location and lowerarrow points to failed tension insert).

Fig. 6b. Close-up view of failure (left arrow points to insert and right arrow indicates shearcone crack failure plane).

68

Figs. 6a and 6b show yet another vari-ation of spandrel distress resulting froma failure of the overall torsion equilib-rium tension insert connection. Thenon-alignment of the beam end reactionand the applied tee loads causing tor-sion were resisted by a horizontal coupledeveloped by a steel bolted insert ten-sion connection near the top ofthe ledgeand bearing of the beam web against thecolumn top.

The dap behavior of spandrel beamhaunches (or ledges), particularly atbeam ends, sometimes is neglected re-sulting in haunch failures as shown inFig. 7. This particular member (Fig. 7)failed because the necessary reinforce-ment was not present at the beam end,and because the concrete acting as plainconcrete did not have the necessarycapacity to resist applied shear and flex-ure forces, Another category of span-drel dap and internal torsion problems isshown by Fig. 8, where insufficient dapreinforcement, A IA , was used (refer toFig. 40 and the Notation for the fullmeaning ofA,h).

Spandrel beams employing relativelythin webs have, depending on the webthickness and the type of web rein-forcement (shear and torsion), sufferedseparation of the entire ledge from thebeam as illustrated by Fig. 9. This typeof distress results from inadequate con-siderations of how tee reaction loads tothe ledge are transmitted into the beamweb. The ledge transfer mechanism re-sembles a dap (an upside down dap)subject to both flexure and directtension.

The actual case histories reviewed, andmany others not commented upon, indi-cate that some designers do not under-stand the entire behavior of spandrelbeams. The problems related to span-drel behavior occur in all types ofstructures, are not confined to any onegeographic area, and inevitably resultwhen one or more of the basic en-gineering fundamentals are missed orignored.

[1

Fig. 7. Ledge failure near beam end.

Fig. 8. End support dap distress caused byinsufficient dap and torsion reinforcement(upper arrow indicates epoxied dap cracksand lower arrow points to modified endsupport).

PCI JOURNAUMarcn-April 1984 69

Fig. 9. Complete separation failure of ledge from beam web.

TYPES OF APPLIED LOADSSpandrel beams are subjected to a va-

riety of loads. These loads result fromapplied gravity forces, horizontal impactforces (e.g., parking garage spandrels),end connections, ledges transmittingloads to the spandrel beam, volumechange forces, and frame moments.These loading cases can act separatelyor in combination. The discussionsherein relate to precast spandrel beamsacting as simple span load supportingmembers.

Gravity Loads — General BeamLoading

The gravity loads of a precast spandrelbeam are typically concentrated and re-sult principally from its tee legs asshown in Fig. 10. Fig. I(1a presents theoverall equilibrium requirements forconcentrated loads applied to a simplespan spandrel beam. Figs. lob and 10cshow the resulting beam shear and

internal torsion, respectively, caused bygravity loads eccentric to the beam'sshear center.

Fig. 10 shows the elements which arefundamental to the load behavior re-sponse of spandrel beams. Relative toFig. 10a, ife e equals or exceeds e, (endreactions align with applied loads whene, = e2 ), then no connections are re-quired to develop the resisting torqueT,, necessary for overall gravity torsionequilibrium. The influence of loadswithin distance "d" for spandrel beamsof significant height is shown in Figs.10b and 10c. ACI 318-77 3 Sections11.1.3.1 and 11.1.3.2 indicate that thedesign for shear need only considershears at "d" or "d/2" while Section11.6.4 indicates that torsion, for non-prestressed members, need only he con-sidered at distance "d" or beyond. TheACI 318-77 Code, relative to spandrelbeam design, is incorrect (though notthe Commentary) since using the Codeprocedures can result in precast span-

70

P6 TBP (NOT SHOWN)

J

er PqRB

P6

P2

SHEAR j IP1

CENTERALL LOADS EQUAL AND

TA UNIFORMALLY SPACED

RA

(a) Loads

1 UNIFORM LOAD = LP

` 2 d,

RA 3

d .. 4

\

RB

5

6

(b) Applied Shear

UNIFORM LOAD = SPe-l-

Tp=RAe 1 3

2

TB =Rse,

6

(c) Applied Torsion

Fig. 10. General gravity loads showing applied shear and torsion diagrams.

PCI JOURNAL/March-April 1984 71

SPANDRELBEAM

CURB(OPTIONAL)

TOPPING

TYPICALTEE STEM

TEEEND REACTION FLANGE

AT COLUMN

(a)

H (10K WORKING LOAD)

H,>H2hH

HtSHEAR

CENTER

H2

HORIZONTAL BEAM SPANNINGCOLUMN TO COLUMN

(b)

Fig. 11. Horizontal loads acting on spandrel beam.

72

drel members being designed for onlytwo-thirds of the applied shear and tor-sion load in the end regions, and theconcentrated influence of torsionequilibrium connections at the beamend being neglected.

Horizontal LoadsSpandrel beams, as used in parking

garages, can he required to restrain au-tomobiles which result in horizontalimpact loads as demonstrated in Fig. 11.Horizontal loads to spandrel beams canbe applied at any location along thebeam's span where "a" of Fig. ha canvary from zero to L. Both load support-ing spandrels and non-load supportingspandrels can be subjected to thesehorizontal loads.

Fig. 11b illustrates the "cantilever'method of resisting horizontal loadswhich requires the floor diaphragm(force H,) and the bearn's haunch actingas a horizontal beam (force HQ ) to be theload resisting elements. Alternately,horizontal loads can be resisted by thespandrel beam acting as a simple spanbetween its end supports providing thattorsional equilibrium is maintained bythe required number of connections, orby the beam having adequate torsionalstrength to transmit the torsion loadingto the end torsion equilibrium connec-tions.

Beam End ConnectionsSpandrel beam end connections

which induce forces into the beam can,for the sake of simplicity, be dividedinto three types. The first type is thatassociated with the beam's overall tor-sional equilibrium, the second typedeals with "corbel" support behavior,and the third pertains to dapped endsupport,

The H forces applied by overall beamtorsion equilibrium end connections areshown in Fig. 12. The magnitude of thehorizontal force couple H providingequilibrium results from all the loads

acting upon the beam, not just those lo-cated "d/2" or "d" beyond the end sup-port reaction. Typically, the top H forceof the couple is developed by flexuralbehavior of the beam web. The combi-nation of the torsion equilibrium webflexural stresses, shear stresses, andinternal torsion stresses results in the45-deg cracking repeatedly observed inspandrel beams as illustrated in Fig. 12.Also, the 45-deg cracking is affected byledge concentrated P loads located nearthe beam's end inducing additional webstresses.

A different force pattern results whenthe spandrel end reaction acts upon theledge. Overall torsion equilibrium ofthespandrel beam is achieved by the reac-tion force R aligning with the applied

PCI JOURNAUMarch-April 1984 ^3

ledge concentrated loads P (neglectingthe beam weight), or being beyond theload P. The projecting beam ledge actslike an "upside down" corbel, as shownin Fig. 13, and the projecting ledge mustbe treated as a corbel if the applied endforces are to be properly considered.

The ends of spandrel beams aresometimes dapped. When daps exist,and the applied concentrated ledgeloads P do not align with the reaction R,the forces and stresses resulting fromthe combined action of the dap and theequilibrium forces (Fig. 12) requirecomplete understanding by the de-signer. Fig. 14 illustrates the combinedaction of all forces when a spandrel endsupport dap is present and the crackingwhich can develop.

End connection forces applied tosimple span spandrel beams also can re-sult from forces necessary to achievecolumn equilibrium and concrete vol-ume change deformations. However,these factors are more appropriately dis-cussed elsewhere in this paper.

Spandrel Ledges

The ledge, or haunch, of a spandrelbeam is the usual mechanism for trans-fer of the applied concentrated loads tothe beam web where the web in turntransmits these concentrated loads tothe spandrel support reaction. TheIedge transfers load to the beam web viaflexure, direct shear, punching shear,and web direct tension.

Two flexure behavior paths exist fortransfer of ledge loads to the spandrelweb. As shown in Fig. 15, one path is atthe vertical interface of the ledge andbeam web while the other is at a hori-zontal plane through the spandrel webin line with the top surface of the ledge.The forces P and N not only induce flex-ure but also create a state of direct ten-sion. Both force paths must he ac-counted for.

The dominant shear transfer mode ofledge loads to the beam web is by

punching shear which also could beconsidered as "upside down" dap shear.The location of a concentrated loadalong the beam's ledge influences theledge's ability to transmit load gener-ated forces. Fig. 16 illustrates thepunching shear transfer of ledge loads tothe web for loads applied near the span-drel's end and away from the end.

Volume Change ForcesVolume change forces resulting from

restraint of concrete deformationscaused by shrinkage, creep, and tem-perature can occur at the beam's sup-porting ledge, all connections, and thebeam end bearing support. The volumechange forces can be axial or rotationalas reflected in Fig. 17.

74

R H30 TO 45 CRACK

P

RFig. 14. Combined action of dap and torsion equilibrium forces.

COMBINED WEB FLEXURE PAND DIRECT TENSION

LEDGE FLEXURE ANDDIRECT TENSION

Fig. 15. Ledge to beam flexural and tension paths.

PCI JOURNAL/March -April 1984

75

Axial volume change forces producingtension in members generally exist, andtheir magnitude depends on the rigidityof restraint to the volume changemovements. For example, welded con-nections or hard high friction connec-tions can develop large N. forceswhereas members joining one anotherthrough bearing pads (soft connections)can result in only minimal N. forces.The N. forces acting on spandrel beamscan control connection designs, and de-pending on their magnitude can mate-rially reduce the beam's shear and tor-sion strength if the N. force acts parallelto the beam's length. Another factor in-fluencing axial volume change forces ina spandrel is the location of the beamwithin the building frame horizontallyand vertically in addition to the location

of the frame's stiffness center position(position where horizontal volumechange movements are zero).

Sun induced temperature differencesbetween the top and bottom of a span-drel beam, where the top surface tem-perature is greater than the bottom, cancreate a positive end moment if thebeam's end connections are actuallyrigid. The positive end moment is de-veloped by a combination of horizontaland vertical force couples as shown inFig. 17b. However, the forces of thecouple typically can be neglected forspandrels since in reality they are smallbecause: minute deformations of theconnections themselves relieve the ro-tational restraint; restraint to expansionreduces the horizontal couple force; re-straint of shrinkage and creep contrac-

TOPCONNECTIONS

N CONNECTIONS TO NSUPPORTED MEMBERS

APPLIED LOADSTO LEDGE

BEAM REACTIONBEARING

N (a} Axial Forces

RIGIDCONNECTIONS T2

T1

TEMPERATUREI EXPANSIONT2>T1

HT

NTRESOLVES INTO HORIZONTAL

RESISTING AND VERTICAL FORCE COUPLES

ROTATIONAL (SEE NON-SHADED ARROWS)MOVEMENT

NT RESULTS FROMNT

EXPANSION RESTRAINT HTVT V1

(b) Rotational Forces

Fig. 17. Types of applied volume change forces.

PCI JOURNALJMarch-April 1984 77

.^_ H M,1

M(_OHM

(a) (b)

Fig. 18. Moment frame connections.

tion produces rotations opposite to thetemperature end rotations; and, for nar-row width beam tops, the internal top tobottom temperature variations are smallresulting in very minor beam axial androtational deformations.

Normally, temperature camber influ-ence is of greatest concern to membershaving a wide top flange width com-pared to its bottom flange such as dou-ble or single tee type beam cross sec-tions when rigid end connections exist.Typically (in northern climates), sun in-duced temperatures result in the flangeaverage temperature being 30 deg F (17deg C) greater than the web tempera-ture.

Frame Moment ForcesSpandrel beams can serve as members

of a rigid frame although this is not acommon application. When spandrelsare part of a moment frame, connectionsat the beam's end are used to develophorizontal couple forces as shown inFig. 18. The horizontal couple forcescan be of varying magnitude and direc-tion depending upon the mode of theframe's sway, deformations, and type oflateral load applied. The moment framehorizontal couple forces are additive orsubtractive to the other forces at thespandrel's end(s) when determiningoverall design forces. If the momentframe spandrel beam also supportsgravity loads, the gravity loads produceadditional moments which must becombined with other frame moments.Gravity dead loads may or may not causeend moments, depending upon whenframe connections are made.

78

WES

T HU

i

'ep eHSHEAR

CENTER PU

* eN

Ni u

TORQUE = Puep- HueH- NueNNOTE:

LOADS PU. HUAND NUDO NOT ALWAYS ACT SIMULTANEOUSLYDESIGN FOR CONTROLLING CASE

Fig. 19. Torque forces.

GENERAL DESIGNREQUIREMENTS

Spandrel beam design requires con-sideration of how all the various appliedloadings are transmitted from their pointof application to the beam and then sub-sequently to the structural element(s)supporting the spandrel itself. Basic de-sign requirements, exclusive of the con-nections to columns or other supportingstructural elements, are:

• Internal torsion and shear• Beam end torsion• Ledge attachment to the web• Ledge load transfer• Web flexure resulting from torsion

equilibrium• Ledge acting as a corbel at beam

end reaction• Beam flexure

Internal Torsion and ShearSpandrel beam torsion results when

applied horizontal and vertical loads donot pass through the beam's shear cen-ter. The resulting torsion to the beam, atany cross section, is the sum of thetorques (shear force times distance fromthe shear center) acting at that crosssection. Moreover, it is possible that theloads acting on the spandrel can varyfrom the time of erection to when alltime-dependent volume change loadsact. Each loading case requires evalua-tion to determine which controls the de-sign.

Fig. 19 shows the loads applied to aspandrel beam eccentric to the shearcenter. The determination of the shearcenter is provided by Fig. 20 4 for a ho-mogeneous uncracked section. Once theapplied torsion and shear are known, the

PCI JOURNAL./March-April 1984 79

internal torsion and shear reinforcementcan he determined following ACT 3183requirements for reinforced members oremploying other relationships 9' for pre-stressed members. If only vertical loadsare applied to the spandrel, the shearcenter can quite conservatively be as-sumed to align with the beam's webvertical centerline.

Beam End TorsionBeam end torsion is defined as the

torsion at the beam's end, within thedistance "d" or "d/2," resulting from thetorsion equilibrium end connections.Typically, beam end torsion created bytop and bottom connections is charac-terized by a single crack, inclined atabout 45 deg, having a nominal width of0.015 in. (0,38 mm) or greater. The 45-deg crack results from flexure in thespandrel's web induced by the beam topHa connection force (see Fig. 21a) re-quired to maintain overall torsion equi-librium. The magnitude of the H. forcesis that required to resist all loads eccen-tric to the shear center, and not justthose loads at and beyond "d" orfrom the beam's vertical end support.The end of the beam length required totransfer the H. equilibrium forces to in-ternal torsion behavior can be consid-ered to be within the distance "d" fromthe beam's end.

Beam end reinforcement to resist theweb flexure caused by the H. forces canbe supplied by horizontal and verticalbars. The orthogonal bars consist of steelareas A,, A., and A, (according to ACI318-77) located on the ]edge side of thebeam's web (see Fig. 21b). The endreinforcement effective in providing thenecessary 45-deg Au steel of Fig. 21d isgiven by Fig. 21c. The web A,, rein-forcing steel required for ultimatestrength is:

A. = H€',(1)04J,

where all dimensions are in inches, the

force is in lbs or kips, the stress is in psior ksi, and = 0.85.

Note that equal to 0.85 results fromusing 0 = 0.90 for flexure and j„ = 0.94such that the denominator for Eq. (1) is:

Oiti d^f, = 0.9 (0.94) df, = 0.85 d^f^,

The spacing of the A,, reinforcement,horizontally and vertically, should notbe greater than 12 in. (305 mm).

If the amounts of the vertical stirrupsand horizontal bars distributed aboutthe spandrel's perimeter differ, thequantity ofA, L, available depends on thelesser amount of A, rD and A" (see Fig.21b):

A. = 2 (1 Al )(2)

V2

or

A 2C A) (3)

^2

whichever results in the smaller valueforA^.. The I A., or!. A,,., represents thetotal amount of reinforcing steel withinthe effective dimensions defined by Fig.21c. Anchorage of the A. and A 1 rein-forcing bars is important. Both ends ofthe, steel must be anchored by hooksor closed stirrups. The A,, bars requirehooking at the end of the beam or a "U"shape for proper anchorage.

The vertical and horizontal rein-forcement comprising the A steel at thebeam's end is in addition to any otherreinforcement necessary to resist shearsince the A, and shear reinforcementshare a common crack plane.

Another type of special beam end tor-sion is discussed in a following sectiontitled "Corbel End Behavior." This spe-cial case, as for the above, requires thebeam's end to be designed to resist thetotal torsion acting at the beam's sup-port.

Ledge AttachmentAttachment of the spandrel beam

80

'.EG 1 - RECTANGLE w 1 by

'DINT B - SHEAR CENTER

DOTE: IF W, AND W 2 SMALL. ex .ey -O.

AND SHEAR CENTER B IS AT A.CONSERVATIVE TO SELECT SHEARCENTER AT POINT A.

CALCULATION OF ex

h 2 I 2 h2 h2w/12

eX 2 (

I__J+J2)

2 +h2w/i2J

h2 h2w2'

ex= 2 [Wlh,3+h2w2]

CALCULATION OF ey

h 1 I^ h1 h1wj /12ey 7T +12) ! 2 [hiw13/12+w2h2/12

h 1h1w 1aey

a 2 h l w l' + w2hz

Fig. 20. Calculation of spandrel beam shear center.

EG 2-RECTANGLE W 2 h2

'DINT A - INTERSECTION OF VERTICAL &HORIZONTAL LEG CENTERLINES

( Y-Y & x-x )

PCI JOURNAL/March-April 1984 $1

U 45 CRACK H - 45C

H

N, Hu

(a) End Web Cracking

H U CENTROID cAwv^2 +At)

A Hu

Awt -L 2W ed ww

e

Hu

(b) End Torsion Nomenclature (d) End Aw

TYPICAL A 1 REINF.

f ^IHORIZONTAL REINF. EFFECTIVE

OVER THIS DIMENSION

TYPICAL Av + At REINF.

VERTICAL REINF. EFFECTIVEOVER THIS DIMENSION

(c) Orthogonal End Reinforcement

Fig. 21. Beam end torsion equilibrium reinforcement.

t #/

82

ledge to the web can be either by thestrength of plain concrete or by rein-forcing steel depending upon the beamdimensions, concrete strength, andmagnitude of the ledge load. The posi-tion of the load Vu also can have an in-fluence on the ledge to web capacity.Accordingly, considering the fabricationtolerances of the framing members, in-terfacing erection tolerances, and de-formation characteristics of the ledgesupported member, the position of V.(see Fig. 22) should be located at ^

The ledge to web horizontal attach-ment is considered similar to the be-havior of two rigid bodies where sep-aration would occur along the entirelength of the beam's web on the attach-ment plane of Fig. 22a. Two separateconditions can exist as shown by Fig.22a, and concern an end load (near thebeam's end) or an inner load (away fromthe beam's end). The concentrated loadsacting are shown in Fig. 22, but theledge attachment also must consideruniform loads. Uniform loads wouldproduce V.'s equal to the uniform loadtimes the ledge length being examined.

The ultimate attachment strength of anon-reinforced ledge depends on thetensile strength of the concrete. Thepoint of maximum ultimate tension is A(see Fig. 22b). The maximum stress f,results from a combination of direct ten-sion and flexure, and is:

f = V,, + 6 V„ (b,o/2 + 3/4 1 p) (4)b u m barn

where s and de have maximum values inaccordance with Fig. 22. All dimen-sional units are in inches and the force isin lbs or kips. Nate that:

m = s for inner concentrated loads

m = d,. + sl2 for end concentratedloads

m = length selected for analysis ofuniform load and V. = ni timesunit uniform load

f, = 3. vrT psi tension maximum at

ultimate where k = 1 for nor-mal weight concrete and 0.85 farsand lightweight concrete

The ft maximum value at ultimate of3a f},' for ff is derived from the tradi-tional concrete cone punching shear di-rect tension limit of 4 , f { using a phifactor of 0.75 and k to account for theconcrete unit weight. Moreover, consid-ering the nominal reinforcements whichusually exist in both the beam web andledge, the value of 3X , f is a lowerhound value when ACT 318-77 or ACI322-72 8 allows f, = q55 f f (0 = 0.65) forunreinforced concrete flexure at ulti-mate. If fg exceeds 3A , ,, attachmentreinforcement is required.

Reinforcement for attachment of thespandrel ledge to the beam's web isshown in Fig. 22c, along with the pa-rameters for determining the amount ofreinforcing steel required. Typically,the depth of the ultimate stress block isless than 1 in. (25.4 mm) for usual designconditions. Assuming the stress blockcentroid is at 0.5 in. (12.7 mm) (a/2) perFig. 22c, and summing moments aboutthis centroid, the reinforcement for at-taching the ledge to the web is:

__ V„ (b,,. + 3/a 1p – '/s)(5)

A e 0 Jv (b.. — dA — 1/2)

where 0 = 0.85, all dimensional unitsare in inches, the force is in lbs or kips,the stress is in psi or ksi, and the ledge toweb reinforcement is uniformly dis-tributed over the length m as previouslydefined.

The Ag reinforcement of Eq. (5) can inpart or whole be supplied by web stir-rups in the beam. The ledge attachmentreinforcement usually is not additive toshear and torsion reinforcing becausethe A, web steel reinforces a differentcrack plane. The amount of beam webreinforcing will be controlled by thegreater of the requirements for comn-hined shear and torsion or ledge attach-ment. The spacing of A, bars should notexceed 18 in. (457 mm).

PCI JOURNAL.IMarch-April 1984 83

EN° Nu

sNu de { 1h

de

h

(a) Punching Shear Transfer

—Ash THIS LEGONLY

3/4 L p 3^4 p

V U vu

AsDAP N JV

^` ^' uPLANE•SHEAR

VERTICAL HAIRPINSAT

^ SHEAR PLANE BEAM END

Ah = Ash/2

(b) Dap Shear (c) Ledge Transfer Reinforcing

Fig. 22_ Beam ledge attachment for non-reinforced and reinforced sections.

84

Ledge Load TransferThe spandrel beam's ledge transfers

uniform and concentrated loads to theweb by shear and flexure. The engi-neering procedures presented fortransfer.of the ledge loads are based onthe PCI Design Handbook,' with somevariations, and are restated to keep thispresentation all inclusive for spandrelbeam design.

The ledge load transfer must satisfyconcrete punching shear if special shearreinforcement is not to be used. Fig. 23aportrays concentrated loads applied tothe ledge and the ultimate punchingshear pattern. The ultimate V. capacityfor inner ledge loadings and end load-ings when de equals or exceeds 2h is:

Fors>b, +2h

V. = 30hx,1l (2lp + b, + h) (6)

Fors -_b, +2h

V. = 0 shA (7)

where 0 = 0.85, all dimension units arein inches, ff is in psi, and h is as previ-ously defined.

The ultimate V. capacity for end ledgeloading, where de is less than 2h, is:

Fors>b, +2h

V. = 4hx7 [21k + (b, + h)12 + de ] (8)

For s _- b, + 2h

V„ = 0hx VT, (dd + sf2) (9)

where the notation is the same as forEqs. (6) and (7).

As for closely spaced concentratedloads, the ultimate capacity for uniformloads applied to the ledge is the same asgiven by Eq. (7), which for an s of 1 ft(0.305 m) provides:

V„=th12hAvf,' (10)

Eqs. (7) through (10) use an ultimateshear stress of 1,/7 on the vertical shearplane shown in Fig. 23b. Unpublished

tests by the author have indicated thatthe ultimate dap unreinforced concreteshear stress capacity, when using thevertical shear plane as the measure, is1.2X[J for normal weight and sandlightweight concretes having an f =5000 psi (34 MPa) and the load appliedon the ledge at 3/alp . A value of 3, isused on all shear planes in Eq. (6) whileEq. (8) uses a value of 2,fJ on the pro-jecting ledge shear area hI,,.

Applied V. forces in excess of the un-reinforced V. capacities determined byEqs. (6) through (10) require dap rein-forcement, .A (see Fig. 23c). The neces-sary A,, to resist the applied V. is:

A. (11)v

where 0 = 0.85, the V. force is in lbs orkips, and the stress f, is in psi or ksi.

The ultimate shearing stress on theledge vertical shear plane when A,,steel is used (see Fig. 23b) should notexceed 10 k,f7 . The vertical shearplane area for concentrated loads spacedfurther apart than b, + 2h is h (b r +h).Fig. 23 can be used as a guide in deter-mining the vertical shear plane area forother loadings.

The A Rh reinforcement determinedfrom Eq. (11) should be totally with bt+h for inner and end loads, d, + (b, + h)/4for end loads when d, is less than (b t +h)/2, and within s for closely spacedconcentrated loads or uniform loadsunless a greater spacing can be justifiedby the longitudinal reinforcement in thespandrel ledge laterally distributing theconcentrated load.

Longitudinal reinforcement,A h , in thebeam's ledge should he, at a minimum,equal to A,Al2 to insure all A,,, reinforce-ment over its distribution width is en-gaged. The longitudinal reinforcementdistributes concentrated ledge loadsalong the ledge by both dowel shear andflexure when the reinforcement is lo-cated near the ledge top as shown inFig. 23c.

PCI JOURNALIMarch-April 1984 B5

Nu

N de42h

eeh

(a) Punching Shear Transfer

Ash THIS LEGONLY

I3^41p 3I4Lp

V Vu

DAP ASN N

SHEAR _

PLANE VERTICAL HAIRPINS AT

SHEAR PLANE REAM END

Ah = Ash/2

(b) Dap Shear (c) Ledge Transfer Reinforcing

Fig. 23. Ledge load transfer.

86

The Ah at the end of the beam shouldconfine the end of ledge, and typicallyhave a hairpin configuration which lapsto the continuous ledge A. The steel re-quired by Eq. (11) is not additive to thestirrups required to resist web shear andtorsion since it basically reinforces adifferent crack plane. However, whenA,^, is required, more stirrups may benecessary at the concentrated V„ loca-tions so the total steel area provides thecalculated A 3h distributed over thelengths previously discussed. If A sh isnot provided by additional stirrups, thencarefully anchored separate reinforce-ment on the ledge side of the webshould be used.

Ledge flexural reinforcement is re-quired to resist the applied V„ and N.loads. The A, steel (see Fig. 23c) can beselected from:

A,= -/,-CV_Q4d )+N„( )1 (12)

where ¢ = 0.85, forces are in lbs or kips,dimensions are in inches, and the f„stress is in psi or ksi.

The A, reinforcing steel using the bentconfiguration of Fig. 23c does not pro-vide bearing confinement steel. If rein-forced bearing confinement steel is nec-essary, special reinforcement in accor-dance with the PCI Design Handbook'is required.

The A, reinforcing of Eq. (12) shouldbe centered on the load and distributedwithin the ledge over the same distanceas the A, i, reinforcing bars for inner andend loads, hut not exceeding b t + h. Barspacing should not exceed h nor 18 in,(457 mm). It is suggested that #3 bars atthe maximum spacing he provided as aminimum for ledge flexural reinforce-ment.

Web Flexure

Two instances of web flexure can de-velop if the spandrel beam's overall tor-sion equilibrium is generated by thebeam web acting against the top of the

members it supports and bottom con-nections at the spandrel's end verticalreaction. This condition is illustrated inFig, 24 where there is no top end con-nection to provide the necessary overalltorsion equilibrium. A similar loadingcondition can occur when horizontalloads are applied to the beam web (seeFig. 11b), except that the forces have adirection opposite of those resultingfrom vertical load torsion equilibrium.

Fig. 24a presents a typical cross sec-tion away from the beam ends showingthe w developed by the toppingacting against the web. The distributionof the unit torsion load w, V against theweb is given by Fig. 24h for a spandrelbeam having equal tee stem reactionsand uniform stem spacing where w,^ is:

iUty T (13)(L/2) h„

and

H = w,„ (L/2) (14)

Note that T in Eq. (13) represents thetotal overturning torque for half thebeam, and the other variables are de-fined in Fig. 24b.

The w^„ force acting against the webcan be transferred by web flexure (seeFig. 24c) to the lower web portion of thebeam and then by the lower web portionto the beam's ends. The height of thelower web portion h u. is shown in Figs.24b, 24d, and 24e. The lower web por-tion h. transfers w, to beam ends byhorizontal flexure as demonstrated inFig. 24d. In turn, this horizontal ulti-mate flexural behavior of the lower webportion can be resisted by reinforce-ment, which is in addition to that re-quired for vertical flexure (see Fig. 24e).

Depending upon force magnitudes,web reinforcement (see Fig. 24c) maybe necessary to resist the .web flexureunless:

f^ = w2J(2 `) ' 3 A v7' (15)w

PCI JOURNAL/March-April 1984 87

Web Flexure

EFFECTIVEHORIZONTAL BEAM

TENSION REINF.

WEB FLEXURE AS

dL Ti THIS LEG ONLY

Wtu

et

hµ, <_ 2bw+h`et/2

SPANDREL Wtu LOCATED 1' BELOW TOPOF TOPPING OR CURB

Bt TOPPINGNO TOP

TEE CONNECTIONST

(a) Construction Arrangement

// Hu

i \ LEDGEet

h wl >J ;--i------ Hu—WtuL/2

k hh (b) Torsion Equilibrium Forces

Hu

(e) Ledge Horizontal Beam

Fig. 24. Torsion equilibrium web flexure.

88

where w, is in lbs per linear foot at ul-timate, e, is in inches, b is in inches,and A and f are as previously defined.

If fo exceeds 3X til f,', the web rein-forcementA, per foot of length is:

AS = w (es) (16)qb d fY

where all dimensional units are ininches, w,, at ultimate is in lbs per linearfoot, 0 is 0.85, and fd is in psi.

The A, determined by Eq. (16) is ad-ditive to the ledge attachment rein-forcement, calculated by Eq. (5) and/orthe A,, steel resulting from Eq. (11) dueto common crack planes, but is not ad-ditive to the web shear reinforcementwhich reinforces a different crack plane.Usual web torsion steel would not berequired if the spandrel beam's torsionalequilibrium is provided by the behaviordepicted in Fig. 24. The spacing of theweb A, should nut exceed 18 in. (457mm) nor 3h.

In actual practice, torsional equilib-rium can be provided by a modified be-havior to that shown in Fig. 24. Thismodified behavior follows when thespandrel beam has adequate torsionreinforcement, proper bottom H,, overalltorsion equilibrium connections (seeFig. 24b), and the top connection is atthe topping level (see Fig. 24a), but onlya limited portion of the topping at thebeam end is involved in developing H,,.

Using the topping to provide one ofthe horizontal force components foroverall beam torsion equilibrium re-quires special attention to the connec-tion of the column to the topping. Thisconsideration is discussed more fully ina following part of the paper.

Corbel End BehaviorWhen the end support reaction of a

spandrel beam aligns with the appliedledge loads, the ledge acts like an up-side down corbel as previously dis-cussed for Fig. 13. The upside downledge corbel can be designed to support

the end reaction by following the proce-dures of the PCI Design Handbook' forcorbels with some modifications.

Fig. 25 shows the usual variables andparameters affecting corbel end behav-ior. In Fig. 25, the end corbel rein-forcement is given by Fig. 25a for inter-nal reinforcing bars and by Fig. 25bwhich represents a combination of asteel bearing plate providingA, and theinternal reinforcement. An elevation ofthe end corbel reinforcement is illus-trated in Fig, 25c. The corbel A„ steel atthe beam bottom is determined from:

A =3 V„l, (17)„

4,4.fYdl

or

_ V" (18)

A 91 Of^, 2x2b , d,

whichever is the greater, but a minimumof at least:

As, = 0 .08b,d1(19)f

Y

where in the above equations A„ 1 is insquare inches, A is as previously de-fined, q5 is 0.85, f„ is in ksi, V., is in kips,and all dimensions are in inches.

The additional ledge reinforcementA nh , using identical notation, is:

V2A cn ^ (20)

of,4x2b,d,

or a minimum of at least:

0 .04 b1d, (21)ADn = I'd

Reinforcement A„ in the beam web atthe corbel end (see Fig. 25a) is requiredto deliver the corbel moment. Thisreinforcing steel can be approximatelyselected using:

A.f = dt (A.,) (22)

PCI JOURNAL/March-April 1984 89

^b w

d2

A S2 THIS _ LLEG ONLY AT END ONLY

A1— 3/4 I p 3^a l P

OTHER REINF.Ip SAME AS (g) P

Avh 1

d^ d1=h

As) (WELDED 4 A51CROSS-BARS) I (STEEL PLATE)

R R(a) (b)

11.5

çztiry __

Avh P

h

2h PACIN

@ h/2 MAX. -

^uVu= bids ^800p51

(c)

Fig. 25. Corbel end reinforcement.

90

where all variables are in the sameunits.

Proper distribution of the reinforce-ment (Fig. 25) is important. For exam-ple, A, 1 and A,2 should be placed within1.5h. The required A^,,, should likewisebe located within 1.5h but also shouldbe distributed from the beam end to adistance of 2h beyond the beam reactionsupport, and should not be spacedgreater than h12. Attention must he paidto all steel anchorages to insure that thebars will develop their strength at criti-cal sections. The steel plate in Fig. 25b,if used to provide A 1 , needs the correctnumber of'headed studs for anchorage todevelop the plate strength.

Experience indicates that the unit endcorbel shear stress at ultimate shouldnot generally exceed 800 psi (5.5 MPa).Also, the spandrel web beyond 1.5hfrom the beam's end should be designedto resist the total torsion developed bythe end reaction acting eccentric to theshear center.

When corbel end behavior is used toprovide overall torsion equilibrium,careful evaluation must be given tononuniform bearing stresses at the ledgeface, the bearing pad, and the support-ing column member. If bearing pads areused where corbel end behavior pro-vides overall torsion equilibrium, tor-sional roll of the beam may result fromthe pad's deformation depending on thetype of bearing pad employed.

Beam Flexure

General spandrel beam flexure in-volves two distinct loading conditions -one at service level and the other at ul-timate state. Depending upon thebeam's cross-sectional dimensions, andwhether or not the spandrel employsreinforcing bars or prestressing strands,the methods of analysis can be basicallythe same or fundamentally different.

If connections between the spandrelbeam and the structural units supportedby the spandrel do not prevent torsional

rotations, then it may be necessary toconsider the influence of principle axesof inertia relative to service loads. Span-drel beams usually do not have sym-metry about either axis. And, if thedepth of the beam is shallow, then whendetermining elastic stresses at servicelevel, for either reinforcing bars or pre-stressed reinforcement, the orientationof the principle axes possibly can becritical. Fig. 26 presents the concept ofprinciple axes of inertia found in mosttextbooks on strength of materials.

The influence of principle axes of in-ertia can typically be neglected for deepspandrel beams. However, for smalldepth spandrels, and particularly thoseemploying prestressing, principle mo-ments of inertia may require considera-tion. The orientation of the principleaxes is:

B – ya tan ' f 2I, 1 (23)

where the angle B, in degrees, is posi-tive counterclockwise for the dimen-sional orientation (the ledge to the rightside) given in Fig. 26. The principlemoments of inertia are:

z[mar = S y+ r 2 'l ) + J2

, , (2

(24)

and

Ima„ = Ir 2 [ffl

-F

y + 122

(25)

Flexural analysis of spandrel beams atultimate should fellow the requirementsof ACT 318-77, Chapter 10. The analyticprocedures can be based upon approxi-mate methods or the specific require-ments pertaining to strain compatabilitywhere it is desired to account for all thereinforcements relative to their dis-tributions in both the tension and com-

PCI JOURNAL'March-April 1984 91

C .G.

X

Xp

XpAND YpDEFINE1

ORIENTATION OF PRINCIPLE)AXES

Fig. 26. Orientation of prrindpll

,p

+8

-X

_ IMAX.Sbp Ybp

of inertia.

Yl Y p

Y

Yp y^+e

pression zones. When making an ulti-mate flexural analysis, considerationmust be given to those longitudinalreinforcements which are required toprovide for torsion and torsionalequilibrium, and therefore cannot con-tribute to the flexural strength.

CONSIDERATIONS FORCONNECTION DESIGN

Spandrel beam connection design issimilar to the design for other precastprestressed concrete connections. All ofthe PCI requirements'.' apply to con-nections associated with spandrelbeams. The critical aspects of spandrel

connection design are understandingthe concepts, accounting for all connec-tion forces, and evaluating the beam'sloading history from the time it is firsterected through application of in-useservice (or ultimate) loads.

This discussion on spandrel connec-tions is intended to supplement the PCIconnection design requirements by re-viewing the concepts and parametersinvolved. Discussions on connectionsherein relate to connection systems,connection materials, connection inter-facing, frame moment connections, in-ternal connection reinforcement, andconnection loads resulting from equilib-rium requirements of the column sup-porting the spandrel beam.

92

Connection Systems

Spandrel connection systems can beseparated into three groups. Thesegroups are the basic beam-to-columnconnections, connections between thespandrel and the members supported bythe beam, and those connections re-quired at the time of erection.

Some of the more common spandrelbeam-to-column arrangements areshown in Fig. 27. The conditions ofFigs. 27a and 27b result in non-align-ment of applied ledge loads and the col-umn reaction thereby requiring con-nections to achieve overall torsionequilibrium. The equilibrium connec-tions use inserts and bearing pads to de-velop the horizontal force couples. Theconditions reflected in Figs. 27a and 27bare for parking garages where the curb isalso part of the overall connection sys-tem and influences the volume changeforces induced into the connections,column lateral equilibrium reactions,and requirements for erection connec-tions.

Figs. 27c and 27d depict spandrel endconnections where the applied ledgeloads and column reactions align. Thedap of Fig. 27d uses a modification tothe beam end to insure load and reactionalignment. This modification requirescareful consideration of the tee legspacing [5 ft (1.52 m) spacings typically]and layout of the tees, and its use is gen-erally limited to a maximum column di-mension of 18 in. (457 mm) for the col-umn face shown in the Fig. 27d eleva-tion.

Spandrel beam-to-column arrange-ments for a building, shown in Fig. 28,require overall torsion equilibrium con-nections. The top connections used atthe floor and roof levels employ weldsrequiring special details to limit themagnitude of the volume change forcesto the connections. When using topwelded torsion equilibrium connec-tions, the magnitude of the volumechange force can be limited to the

plate's yield stress force by controllingthe cross section of the attaching plateand placing welds only at the plates'ends to allow for deformation strain be-yond yield. The attachment plate width,plus holes in the plate if required tolimit its tension yield capacity, andthickness should only be that necessaryto resist the torsion couple shear force. Ifthe building spandrel-to-beam detail issimilar to Fig. 27c, torsion equilibriumconnections are not required.

In Fig. 28b, the column is shown asprojecting to the top of the spandrelbeam rather than having the beams bearupon the column top. The projection ofthe column to the top of the beam is re-quired to achieve the spandrel torsionequilibrium in addition to providing thecolumn top with the necessary horizon-tal reaction for its lateral equilibrium.

Structural design requirements forin-place conditions, or for temporaryerection stability and equilibrium, candictate the need for connections be-tween the spandrel beam and the mem-hers the spandrel supports. An exampleof this type of spandrel connection isshown in Fig. 29. Regarding the attach-ment plate connections of Fig. 28, theplate cross section (Fig. 29) should belimited to control the magnitude of thevolume change or other structural de-formation tensile forces which can beattracted to the connection. Generally, ai/a in. thick plate, 2 in. wide and 4 in.long (6.3 x 51 x 102 mm), can be used forA36 steel which limits the attachmentplate's yield force to 18 kips (80 kN).

This type of controlled yield design isachieved with welds only at the plateends to insure adequate deformationbeyond initial yield. An alternatemethod of achieving the same resultwould be to use an angle welded only atits toes. The attachment plate of Fig. 29,when in tension due to volume changes(N. forces), induces torsion into thespandrel that is additive to the torsioncreated by the gravity loads.

Erection connections can be part of

PCI JOURNAL/March-April 1984 93

BEARING

liCONNECTION

TOP OF CURBII

L

OR TQ ING CURB (SHOWN)

x

II TENSIONCONNECTION

1• BEARINGPAD

Elevation Section

(a)

IjF . 0L ^_ TENSION{ CONNECTION

x

I I

I ^

I--

I^1 BEARING CONN.- ^n

BEARING PADOR WELDED(OMIT IF WELDED) V

PLATE CONNECTION

Elevation Section

(b)

Fig. 27. Parking garage beam-column connections.

94

__ _ ICONCRETE STEEL SECTION

CORBEL ENCASED INV CONCRETE

Elevation Section

(C)

8" MAX.

Elevation Section

(d)

Fag. 27 (cont.). Parking garage beam-column connections.

PCI JOURNAL/March-April 1984 95

WELDPLAN OFLOCATIONS

TOPPING

BEARING P AD ^AIJpLE WELDEDTO BEAM

Elevation Section

(a) Floor Level

WELDLOCATIONS PLAN OF FE

TEES (NOTSHOWN)

Elevation Section

(b) Roof Level

Fig, 28. Building spandrels_

96

WELDS AT ENDS

HAIRPIN REBARCURB

EACH STEM TOPPINGINTO CURB

TEE FLANGE

Fig. 29. Tee to spandrel connection.

the final permanent connection system,or they can be connections which aretemporary and serve only during theerection process. The erection connec-tion, if temporary, can remain in-placeand be hidden within later construction(such as topping, curbs, and above ceil-ings), left exposed to view, or removed.Erection connections that are not re-moved also can serve as secondary con-nections tying the spandrel to the col-umn.

Erection connections are needed tosatisfy overall torsion equilibrium, forproviding necessary structural ties he-tween beams and columns and beams totees (slab type members), and to de-velop the stability of the erection brac-ing. The stability requirements of theframing system during erection can in-duce forces into connections which aregreater at the time of erection than theultimate in-place Ioads to the completedframe. The design of erection connec-tions for spandrels and other membersgenerally requires a more comprehen-sive understanding of structural designand the criteria for the design than doesjust the design hr final in-place condi-tions.

PC! JOURNAL, March-April 1984

Connection Materials

A variety of readily available materialscan be used to satisfy the forces and thebehavior characteristics of spandrelbeam connections. Among some of thecommon materials used in spandrel orother connection assemblies are bearingpads, concrete inserts, steel plates,welds, coil or threaded rods, reinforcingbars or stud type anchors, and concrete.

Bearing pads are used to transmit thespandrel reaction to the supporting col-umn or to transfer loads to the spandrelledge from the members supported bythe beam. Pads likewise are employedin torsion equilibrium connections (seeFig. 27). The main functions of hearingpads are to provide uniform bearing bythe pad's ability to accommodate non-parallel bearing interfacing surfaces andto minimize the development of volumechange forces because of the pad's sheardeformation characteristics. Most bear-ing pads (rubber, neoprene, cotton duck,and fabric reinforced rubber types) can-not be relied upon to develop torsionalequilibrium couple forces if the coupleforce depends on the shear behavior orstrength of the pad.

97

I

Concrete inserts can be used to satisfymany different connection functions.Inserts commonly are employed to pro-vide the torsion equilibrium tensionfarce couple as illustrated in Fig. 27, orto tie spandrel beams and columns to ahorizontal diaphragm using threadedrods into concrete topping, curbs, orwhere concrete is the connecting me-dium, When selecting inserts for use inspandrels, the designer must considerwhether the insert's capacity is con-trolled by the mechanical properties ofthe insert steel or the insert's concreteshear cone (full or partial).

Metal plates have a multitude of usesin spandrel beams. The plates can serveas a means to transfer or develop bear-ings, tension, compression, or shearforces. These plates can be made of A36steel, higher strength steels, or stainlesssteels (generally AISI 304). Plates bydefinition can mean flat plates, bentplates, or angles.

The use of plates requires considera-tion of environmental factors relative topossible corrosion. Corrosion evalua-tions can result in the plate(s) not havingany protective coating, having properlyselected paints (primers and secondcoats) and surface preparations, ? beinggalvanized (per ASTM A153) with thenecessary galvanized thickness, orbeing stainless steel. Plates used inparking garages, plates exposed tomoisture, or plates exposed to salt waterair (coastal regions), should be galva-nized at a minimum. Plates used in othermore aggressive conditions should be ofstainless steel or be a suitable metal ca-pable of resisting the specific chemicalattack.

Welds are important in making span-drel beam connections. They are used tofabricate connection hardware, to com-plete connections between concreteembedded plates, and to attach rein-forcing bars to plates. If welds are toserve their intended purpose, the typeof the weld electrode, pre-heating re-quirements, environmental tempera-

tures at the time of welding, type ofweld, weld heat distortion, weld shrink-age (cooling), and inspection (qualitycontrol) all must be considered.

Coil and threaded rods are selected tomake many connection types. Thecoarse threaded coil rods find wide usein connecting spandrels to concretecurbs and topping, in addition to con-necting columns supporting spandrelsto horizontal diaphragms. Coil andthreaded rods are used with concrete in-serts requiring the insert capacity to hematched with the capacity of the rod.Coil rods, generally ½and 3 in, (12.7 and19 mm) in diameter, are most frequentlyselected for connections in cast-in-placeconcrete because oftheir coarse threads.

Reinforcing bars are the main part of alarge number of spandrel connectionssuch as ledges, webs, bearing, daps, andplate anchorages. Alternately, deformedbar anchors or headed concrete anchorscan serve the same spandrel connectionpurposes. When using reinforcing barsfor connections, attention must be paidto the influence of the bend radius (norebar is bent at a right angle), weld re-quirements (bar chemical composition,low hydrogen electrodes, and pre-heat-ing), the bar configuration, and place-ment tolerances.

Concrete is often selected for con-necting spandrels to other structuralmembers. Typically, cast-in-place con-crete curbs and topping serve not onlyas the connection load transfermechanism but also constitute themeans to prevent axial volume changeforces from being induced into the con-nections between spandrels and col-umns. The use of concrete as a connec-tion device requires it to have theproper cross section, reinforcement,rebar cover, constructability, strength,durability, and mix quality.

Connection Interfacing

Similar to all precast concrete con-nections, spandrel beams require inter-

98

facing of the connection(s) with otherparts of the beam and other structuralmembers. Connection interfacing dealswith tolerances, clearances, dimen-sional variations, skews, and positionconflicts between connections and re-inforcements within the beam.

Recommended tolerances for con-nections are given in the PCI DesignHandbook. € But, when considering tol-erances, evaluations must be made re-garding the cumulative effect of all thetolerances involved. The critical tensioninsert, providing part of the spandreloverall torsion equilibrium of Figs. 27aand 27h, serves as an interfacing exam-ple.

The element which must be adjust-able to accommodate the tolerances in-volved is the size of the insert hole inthe beam (see Fig. 30). The tolerancesshown in Fig. 30 that must be reviewedare:

• The as-fabricated location of thecolumn insert as defined by di-mensions a, and b,. The plannedposition ofa, and b, can vary a pos-sible maximum of% to' in. (9.5 to12,7 mm), plus or minus.

• The a, and b, location dimensionsof the hole in the as-made beammay vary a maximum of % to ' in.(9.5 to 12.7 mm), plus or minus.

• Skew of the insert in both the x andy directions that cause the insertcenterline to vary by as much as aya in. (6.3 mm) at the beam face.Similarly, x and y skew of the holein the beam can occur.

• The length of the spandrel beam c,can vary up to '/s in. (12.7 mm) ormore causing the centerline of thebeam hole to change relative to thecolumn insert by the same amount.

• The location of the column can bedifferent than planned because ofthe footing's location or the posi-tion of anchor bolts within thefooting. The column erection posi-tion dimension c, thus can vary byyi to 1 in. (12.7 to 25.4 mm).

• The tolerance variations in dimen-sions a, b, and c can be in oppositedirections and, combined with in-sert and beam hole centerlineskew, thus result in a connectionthat cannot physically be madeeven though all tolerances are sat-isfied.

The foregoing pertains to any span-drel connection and connections in gen-eral (such as precast, steel, cast-in-placeconcrete, and masonry). Normally, tol-erance variations of each dimension in-volved do not occur all at the same time,and some variations offset others. Theprevious tolerance example regardingspandrel equilibrium tension insertsdoes, however, demonstrate the needfor an experienced engineer to reviewthe design when selecting connectionsand their related clearances.

Interfacing tolerances are usually ac-counted for by selecting appropriateclearances. The insert tolerance circle ofFig. 30 provides an illustration of clear-ances. The hole diameter D,, can he se-lected once the insert rod diameter D , isknown, insert location tolerances areestablished, and the clearance dimen-sion D, between the rod and the holeside is determined. A D a of 21/2 in. (63.5mm) results for a tin. (25.4 mm) D 5 , a %in. (9.5 mm) insert tolerance, and clear-ance D, of % in. (9.5 mm). Allowing thebeam hole to also have a location toler-ance variation of % in. (9.5 mm) resultsin D. becoming 3'/4 in. (82.6 mm).

Connection plates embedded intospandrel beams or other precast struc-tural members encounter a variety ofinterfacing conditions. Bearing plateskew, positioning tolerances, and plateanchor interference represent the ma-jority of interfacing concerns.

Skewed bearing plates, as shown inFig. 31, must be considered when de-signing spandrel connections. The skewcan result in highly nonuniform bearingpad stresses, alter significantly the loca-tion of applied loads to ledges or theconnection supporting the spandrel, and

PCI JOURNALJMarch-April 1984 99

as aC Y

X X

Cs Y

i ei ^ I

Cc

(a) Elevation

Y SKEW I I +1/4

SHOWN VARIATION

rb D 45*

Da

/1 PO p P

INSERT

(c) Tolerance Circle

(b) Section

Fig. 30. Tolerance interfacing.

100

^^ 70 ^16 if(a) Beam End Bearing Skew

LOAD POSITION

(b) Ledge Bearing Skew

Fig. 31. Plate skew.

increase N. forces on account of theplate skew cutting the bearing padcausing steel to concrete or steel edgeloading with its increased friction coef-ficient. Concerning the bearing plateskew, a skew of 1/s to %a in. (3.2 to 4.8mm) should be considered between anytwo corners of the plate.

Plate positioning and the related tol-erances are influenced by plate anchorinterference. The type, dimensionalsize, and the location of anchors shouldhe evaluated at the time of design todetermine if conflicts exist between anyof the anchors and other materials orreinforcements within the beam. At aminimum, plate anchors require a clear-ance of 3 in. (19 mm) from any otheritems in the adjacent concrete area un-less rigid placement tolerances [± Vs in.(3.2 mm)] are absolutely assured.

When plates are positioned in beams,and no anchor interference develops, aplate position tolerance in plan or ele-vation of ± 1/z in. (12.7 mm) in any direc-tion can be expected to occur. Positiontolerances for plates apply to plates onboth sides of the connection. It is notunusual to observe one plate being outof position by +½ in. (12.7 mm) and theother by – '/z in. (12.7 mm), creating acombined misalignment of 1 in. (25.4mm). Positioning tolerances, like allother practical real world tolerances, arecumulative.

An example of cumulative tolerancescompromising the effectiveness of aspandrel connection is shown in Fig.32a where it is incorrectly assumed thatboth beam and column plates will heflat, level, and aligned. Details similar toFig. 32h should he used since they arenot tolerance sensitive. Proper planningand consideration of tolerance can elim-inate most tolerance interfacing prob-lems.

Connection interfacing difficultiescan develop independent of tolerancevariations. Fig. 33 presents the bearingpad interfacing between the spandrelledge and a long span prestressed dou-

PCI JOURNAtlMarch-Aprik 1984 101

LOOSE WELD PLATE

fL A Ip B

VERTICALMISALIGNMENT

OF S%POSSIBLE -

(a) Accumulative Tolerances

(b) Detail Providing Interfacing

Fig. 32. Tolerance interfacing.

102

TEE ENO I.

ROTATION

BEARING PADCAMBER - STRESS

ROTATION

BEARING PAD

Fig. 33. Camber interfacing.

hie tee's end camber rotation. The cam-ber rotation results in nonuniform padbearing, and depending upon the mag-nitude of the nonuniform stress candamage the bearing pad. Plates cast inthe tee end can be skewed thereby fur-ther increasing the nonuniform hearingstress or exaggerating the camber effect.Camber interfacing requires the designanticipating nonuniform bearing andselecting the proper type of bearing pad.

A variation of the plate interfacing tol-erances is shown in Fig. 34 whereshared bearing develops. Shared bear-ing consists of the bearing pad contact-ing both the concrete and steel in thehearing area. The use of shared bearingcan he satisfactory only when interfac-ing is perfect. Commonly, shared bear-ing creates distortions and distress inhearing pads, thereby reducing theireffectiveness or causing damage. Con-ditions which can result in sharedbearing should always he avoided. Fig.34a relates to shared bearing difficultieswhile Fig. 34h shows the method toprevent it. The common bearing of Fig.34b employs a plate in the beam's endlarger than the one in the column corbel.

Interference of plate anchors with

other materials within the beam is onlyone type of connection component in-terfacing. Spandrel beam connectionsemploy a range of materials as previ-ously discussed. All of these materials,such as inserts and reinforcements, mustfit together. Interfacing fit-up problemsin most instances are the direct result ofinadequate design planning and thepreparation of improper schematic typedetails.

Proper connection internal fit-up in-terfacing requires the designer to pre-pare details showing all materials whichexist at the connection location. Further,the details must illustrate the items oc-curring in the plane of the detail in ad-dition to other items perpendicular tothe detail plane. Connection fit-up in-terfacing requires three-dimensionalevaluations of all materials of the con-nection. ACI 315-74, 8 Chapter 6, re-garding design guidelines provides anexcellent summary of interfacing.

Frame ConnectionsFrame connections between spandrel

beams and columns can be achieved bypost-tensioning, reinforcement and

PCI JOURNALJMarch-April 1984 103

BEAM END -

STEEL {^

BEARING PAD

COLUMNSTEEL I. -

(a) Shared Bearing

r ^L

(b) Common Bearing

Fig. 34. Shared support.

cast-in-place concrete, or welding. Theusual method is by welding, and henceonly welding will be discussed.

A basic criterion of precast frame con-nections is to use only those needed andno more. This criterion is based uponthe greater costs associated with frameconnections and the volume changeforces attracted to the connections be-cause of increased column and beamfixity stiffness. Two types of full framebeam-to-column moment connectionsam given in Fig. 35. Both types can pro-vide the same moment capacity.

The flat plate type (see Fig. 35a) hasseveral disadvantages as discussedbelow, Welding destroys whatever cor-rosion protective coating has beenapplied, thus requiring field touch-upwhich does not have the same protectiveability as the original coating. Also, theflat plate connection results in hardbearing creating the possible need ofsome internal bearing reinforcement toprovide for bearing stress concen-trations, The top connection pocketshown in Fig. 35a requires a filler, andbased on actual experience the fillerneeds periodic maintenance.

The vertical plate connection (Fig.35b) employs a 4 x 6 in. or 4 x 8 in. (102 x152 min or 102 x 203 mm) grout columnto provide for shear transfer and alsogive corrosion protection to the weldplates. The grout shear keys minimizereaction shear to the vertical connectionplates which can result from frame ac-tion or elastic and creep deformations ofthe thin [ 1/4 to % in. (6.3 to 9.5 mm)]bearing pad. A drawback to the verticalplate connection is the dimensionalvariation in the 4-in. (102 mm) gapcaused by member and erection toler-ances. Back-up bars used with full pen-etration welds allow for a dimensionalvariation of V in. (6.3 mm). Differentsized plates are required to accommo-date the tolerance variations [ viz., 3½, 4,and 4½-in. (89, 102, and 114 mm) platewidths] .

The details of the embedded plates

constituting the frame connections (Fig.35) are illustrated in Fig. 36. The angleplate (Fig. 36a) requires not only rein-forcing bars to resist the H force, but alsoadditional bars to counter the momentcreated by the eccentricity of the Hforces, The vertical or horizontal plate(Fig. 36b) welded to the embedmentshould employ a structural steel tee or aflat plate with stiffeners. The tee stein orstiffeners are necessary to transfer theloose plate force directly to the rein-forcing bars of the embedment.Moreover, the distribution of the looseplate force may not he even to the em-bedded reinforcing bars consideringtolerance variations such as dimensionaloffsets in the placement of the connec-tion hardware in the beam and column.

The use of welded frame connectionsemphasizes the need to consider the se-quence of the beam-to-column weldedconnections and at what stage of theconstruction these connections will bemade. Typically, if the beam is sub-jected to gravity loads, the frame lateralstability connections should not bemade until all or most of the dead load isin place. The sequence of making thebeam-to-column frame welded connec-tions should be that which minimizesthe frame's volume change forces re-sulting from weld shrinkage.

Structures which use spandrels orother beams in a moment frame to resistlateral loads and to provide the neces-sary lateral stability require theirwelded frame connections to be prop-erly inspected. The weld inspection andrelated testing must be applied to theparts embedded in the beams and col-umns in addition to the field welds, Ifrigorous welding inspection and testingare not employed, welded frame con-nections should not be used. Likewise,proper specifications are required todetermine the welding requirementsand procedures as controlled by thereinforcing bar chemical compositionand weld electrodes employed.

Frame analysis to determine forces in

PCI JOURNA11March-April 1984 105

EPDXY FILL OR _ EPOxY GROUT - _~`-

BLOCKOUT

It

(a) Flat Plate Connection

SHEAR KEYS

THIN BEARING PAD

SECTION

(b) Vertical Plate Connection

Fig. 35. Welded frame connections.

106

-DC)

^VCZ

CC)

caOD

H

F=H1

LOOSE _____ H 2 OR o.aH

H2 BARS

HACK-UP (Q ^^ H,,, OR O.6H

TOLERANCE VARIATIONS N STRUCTURALPOSSIBLE STEEL TEE

(a) Angie Plate (b) Vertical or Horizontal Plate

q I Fig. 36. Frame weld plate details.

the beams and columns, and to calculatethe frame deformations, must considerthe effect of the various member sizes.This is necessary if the proper stiffnessof the column is to be correctlyevaluated. Figs. 37a and 37h reflect thecomputer analysis models for the Fig. 35frame connections. The more conve-nient analysis model of Fig. 37c cannotbe used since it is incorrect and willproduce erroneous results. For example,if the floor-to-floor dimension of the col-umn is 10 ft (3.05 m), the column lengthfor Fig. 37c would he 10 ft (3.05 m)whereas the clear column height of Figs.37a and 37b could be only 6.5 ft (2 m). Adifference in the column height of 3.5 ft(1.1 m) has a significant influence on themagnitude of the volume change forcesinduced into the frame connections, andupon the beam and column forces.

Reinforcement ConsiderationsSpandrel beam ledge and end support

connections use internal reinforcementin connections. The reinforcementacross critical crack planes and forbearings must have proper anchorageand be correctly oriented if it is to per-form its function. Additionally, the con-nection steel requires more accurateplacement than the usual beam flexuraland shear reinforcement. And, if thespandrel is used in an exterior environ-ment, concrete cover and reinforcementcorrosion demand increased attention.

Ledge reinforcement, as shown in Fig.38, can serve solely as flexural steel or ascombined flexural and confined bearingsteel, The reinforcement of Fig. 38ashould be considered only in providingfor ledge flexure, and the bearing designfor V. and N. should employ plain con-crete analysis methods since the criticalbearing failure crack plane can by-passthe reinforcing steel because of its endbend radius. If the ledge reinforcementis also to accommodate bearing (ulti-mate bearing stresses exceed that al-lowed by plain concrete bearing),

proper anchorage must he insured asshown in Fig. 38b. Anchorage for bear-ing can be achieved either by weldedcross-bars or alternate methods usingreinforcing bars bent and placed in amanner that will provide the positiveanchorage. Often, supplemental bearingreinforcement is supplied using platesand deformed bar anchors, as given inFig. 39, to develop the required con-fined bearing capacity.

The location of the ledge connectionreinforcement and all other spandrelconnection reinforcing bars is importantto the connection in developing its de-sign strength. Therefore, specified di-mensions for positioning the reinforce-ment are essential. Along with provid-ing the steel's location, specific po-sitioning tolerances must be deter-mined. A realistic tolerance for control-ling critical rebar positions should be±' in. (6.3 mm) as shown in Fig. 38.

The concrete cover dimension c forprecast spandrel beams producedunder plant controlled conditions andexposed to weather should not be lessthan 1i in. (31.8 mm) 3 for #5 bars andsmaller. However, if the spandrel is ex-posed to a severe corrosive environment(chloride salts) the minimum covershould he 2% in. (57.1 mm) forconnectionrebars if a ' in. (6.3 mm) tolerance isspecified. Also, severe exposure mayrequire the spandrel's concrete to have amaximum water-cement ratio of 0.4 byweight 9 to provide the necessary corro-sion protection for steel.

The design planning of re info rcernentfor connections and other reinforcingbars in spandrel beams requires equal orgreater skill than the reinforcementbased on structural design. The span-drel's reinforcement design, selection ofbar sizes, bend radius, concrete coverrequirements, and interfacing of all thebeam's steel can control or dictate thespandrel beam's cross-sectional dimen-sions as can the width of the compres-sion flange relative to the beam's span(width = span/50).

108

COLUMN

3 //JOINT NO. 3

\® /

r

MEMBER NO.

^ I^} ^5 1 1 b

BEAM 20Ib

2 2

a

(a) Fig. 35a Model

COLUMN

QQ 7 Ib7 6

201bb [^j 1 Yb1

5®2 C BEAM 5 Ib O Ib

®4 3® Ib 30lbQ 4

a

(b) Fig. 35b Model

a= DISTANCE 0, COLUMN 3TO BEAM REACTION

b- DISTANCE BETWEEN 1CONNECTIONS

C-DISTANCE t BEAMTO BEAM BOTTOM Q

(c) Centerline Model

Fig. 37. Computer analysis models.

PCI JOURNAL/March-April 1964 109

vu

N

C}I/4•

POSITIONINGBEARING CRACKP

RS y (PLAIN BEARING)BARCRITICAL CRACK

PLANES

C C f '/4 °

(a) Ledge Flexure Only

VU

3 CROSS-BAR

WELDE

►u -- c±t14'

POSITIONING BEARING CRACK Alternate LedgeBARS (REINF. BEARING)

Rebar DetailsCRITICAL CRACK

PLANES

C

(b) Ledge Flexure & Bearing

Fig. 38. Ledge reinforcement.

110

vu

Ne

C C

Fig. 39. Supplemental ledge bearing reinforcement.

Fig. 40 shows a typical arrangement ofreinforcement. It becomes immediatelyapparent that concrete cover and bend-ing radius limit the locations of othersteels. The 2-in. (51 mm) grid for locat-ing the prestressing strands is not com-pletely available. Study of reinforcingbar bends can be important because thebar bends influence where other rein-forcing bars can be positioned. Anotherreinforcing bar consideration relates tosome bars being necessary to secure orprovide for dimensional positioning ofkey steel, such as the ledge A s bars.

An additional factor to be evaluatedregarding the influence of the rein-forcement dictating, in part, the po-sitioning of the prestressing strands (seeFig. 40) is the non-alignment of thestrand's centroid with respect to thespandrel's principle Y, axis (see Fig.26). This non-alignment can result inhorizontal sweep of the beam.

Fig. 40 shows reinforcement ar-rangements without any provisions for

tolerance. Tolerances for locating thevarious bars within the cage and withinthe beam must be considered, as mustthe bars' having an outside diameter ofVs in. (3.2 mm) greater than their normalsize on account of the ribs. Fabricationtolerances for individual bent bars mustalso he evaluated. The fabrication toler-ance for stirrups and ledge A. bars is Vsin. (12.7 mm) on specified dimensionsplus another Vs in. (12.7 mm) for out ofsquare configuration.

The preceding discussion on spandrelreinforcements, and the many criteriathe bars must satisfy, emphasizes thefact that the designer must select thethree-dimensional reinforcements andmake sure his design can actually bebuilt. A cause of many spandrel beamproblems and distresses is that beamreinforcements are selected without anyconcern for interfacing between them,and critical reinforcements end up sig-nificantly out of position.

The reinforcement considerations

PCI JOURNAUMarch-April 1984 111

10"

A t TORSION BARS --" - AV, A t OR Ash BARS

1

11J2COVER TYP gSHOWN _ LEDGE A5 BAR

POSITION BARS & / 3/4k BEARINGAt BARS CHAMFER

CS

d f • • `" Ah '12'

N

CAGE AND/OR P/S STRANDSBEAM A 5 BARS

2 STRAND GRID

Fig. 40. Reinforcement interfacing.

presented herein relate to ledge andweb reinforcement alone. The rein-forcement concepts discussed applyequally to spandrel beam ends with re-gard to daps, ledge corbel behavior, orbeam end torsion. Typical connectionreinforcement details can only he typi-cal when they interface with all rein-forcement conditions,

Column InfluencesConnections which attach the span-

drel beam to the column for the basicpurpose of supplying the beam's overalltorsion equilibrium can be subjected toadditional column equilibrium loads.

The influence of column equilibriumloads on the spandrel torsion stabilityconnections is even more pronounced ifno direct connection is made betweenthe column and the horizontal dia-phragm (floor or roof level). In this in-stance, additional horizontal forces areinduced into the beam end torsionequilibrium connections which can rep-resent a marked increase in the requiredconnection design load. Spandrel con-nection designs which do not considerthe additional column equilibriumforces have resulted in connection fail-ures and expensive connection repairs.

Depending upon the framing ar-

112

rangement of the spandrels to the col-umn, the analyses to determine beamend connection forces can be very com-plex. Fig. 41a illustrates the framing andpertinent dimensions for a two-storyparking garage where the spandrelbeam torsional equilibrium is providedby end connections. In addition to theend connections, the column is attacheddirectly to the horizontal diaphragms asis the beam for its lateral support. Thediaphragm horizontal connections areachieved with inserts, coil rods, andconcrete topping. The horizontal dia-phragm is in turn laterally supported byshear walls or moment frames.

The analysis to determine the con-nection forces resulting from both beamtorsion equilibrium and column equilib-rium is best made using computer meth-ods. The analytical model and require-ments of the model to duplicate the ac-tual frame behavior are presented inFig. 41b. The spandrel beam verticalspan properties (see Fig. 41c) can bedetermined from the web width of 8 in.(203 mm) acting over the lesser hori-zontal length of eight times the webwidth or the total height of the spandrelbeam.

The model (Fig. 41b) deals only withthe additional column equilibriumforces to which the beam-to-columnconnections are subjected. Anotherloading condition which must he re-viewed is that resulting from volumechange deformations acting parallel tothe tee span. The beam-to-column con-nections can be considered as not re-ceiving any additional loadings fromvolume change movements providing adirect column-to-diaphragm connectionexists. However, when no column-to-diaphragm connection is used, the ad-ditional connection forces must be ac-counted for. Instead of the rigid hori-zontal supports of Fig. 41b, horizontalframing members, per Fig. 42, should beused to simulate the volume changedeformations so the total forces to theconnections can be determined.

GOOD DESIGN PRACTICE

The design of spandrel beams en-compasses not only an understanding ofengineering fundamentals but alsoproperly requires an appreciation ofpracticality and experience. The fol-lowing outline on general designguidelines for spandrels is based inlarge part upon observations of pastperformance, both good and bad. Amongthe many aspects involved in spandrelbeam design, those set forth representsome of the more pertinent factors.

Cross-Sectional Dimensions• The spandrel web width generally

should not be less than 10 in. (254mm), and never less than 8 in. (203mm).

• The horizontal ledge projectionshould not be less than 6 in. (152mm).

• The vertical height of the ledgeshould not be less than 10 in. (254mm), and for beams supportinglarge concentrated reactions a14-in, (356 mm) height or greater isrealistic.

• The final beam cross-sectional di-mensions may be dictated by theneeds of practical non-congestedreinforcement arrangements to in-sure the spandrel can be realis-tically built within its selected di-mensions.

• Blockout and connection fit-up re-quirements in spandrels, particu-larly moment frame beams, maycontrol the cross-sectional dimen-sions if all internal components areto he properly integrated withinthe beam's final dimensions.

Reinforcement• Bars have a radius at bends, and are

not bent at a sharp 90-deg angle.• Fabricated reinforcing bar config-

orations have tolerances and usu-ally will be out of square.

PCI JOURNAL/March-April 1984 113

11181

CURB

TOPPINGF

^- 4^4 B* 5

° 24 DOUBLE TEE °p COLUMNC7 HORIZ. TIE

BEAM R't OHORIZ. TIE

F

`pO 18'x 18 COL. ° 8w

AT 24'- 0' oCOLUMN

t, CURB TIED TO BEAMAND COLUMN BY

GRADE SLAB THREADED RODS

- --- Rt - TEE STEM REACTIONiy Rb = SEAM END REACTION

(a) Framing Arrangement

Fig. 41. Connection loads induced by column equilibrium.

114

COLUMN

18 10 BEAM Ft CONNECTION

U I

FLOOR DIAPHRAGM 17 9 FLOOR DIAPHRAGM—BEAM HORIZONTAL SUPPORT oT H COLUMN HORIZONTAL SUPPORT

16 Q aY S P G0.25

15 T

1d L 6 BEAM F1 CONNECTIONp- E —( SPANDREL END REACTION0 N1

FLOOR DIAPHRAGM 1 13 5 1FLOOR DIAPHRAGM

BEAM HORIZONTAL SUPPORT ECOLUMN HORIZONTAL SUPPORTN D N

N 12 K 4 C+i - BEAM Ft CONNECTIONM11 a ^n BEAM VERTICAL

n! SUPPORT CONNECTION0.50

1/2 COLUMN PERSPANDREL BEAM END

B

-TOP/FOOTING LEVEL

2IMAGINARY COLUMN LENGTHTO SIMULATE PARTIAL

A FIXITY RESULTING FROMFOOTING (20 TO 50% FIXED

1 TO 18 - JOINT NO. 1 COL. BASE)A TO R - MEMBER NO.

(b) Computer Analysis Model

Fig. 41 (cont.). Model for analyzing connection loads induced by column equilibrium.

PCI JOURNAL/March-April 1984 115

SUPPORT JOINTS

Jt. No. Type

I pin - y roller2 pin - no rollers5 pin - y roller9 pin - y roller

13 pin - y roller17 pin - y roller

MEMBER PROPERTIES

Member End Jts. I - in4A 1,2 8748/28 2,3 8748/2C 3,4 8148/2D 4,5 874812E 5,6 8748/2F 6,7 8748/2G 7,8 8748/2H 8,9 8748/21 9,10 874812J 3,11 9()00*K 4,12 0.1**L 6,14 0.1**M 11,12 2731N 12,13 27310 13,14 2731P 7,15 9000*a 8,16 0.1**R 10,18 0.I**S 15,16 2731T 16,17 2731U 17,18 2731

JOINT LOADS(Service Loads)

Jt. No. Loads

II BP=56KandCouple* = 28 Ft.-K

IS EP=56KandCouple* = 28 Ft.-K

* Couple acts counter-clockwise

A - in2 Joint Releases324/2 none32412 none324/2 none324/2 none324/2 none324/2 none324/2 none324/2 none324/2 none0.1** none9000* pin @ each end9000* pin @ each end512 pin @ I512 none512 none0.1** none9000* pin @ each end9000* pin each end512 pin (al 16512 none512 none

* Arbitrarily selected small to simulate an x-roller or to simulate no flexuralstiffness

** Arbitrarily selected large to simulate axially rigid connection or to simulateflexural rigidity

(c) Analysis Data

Fig. 41 (cont.). Data used in computer model for analyzing connectionloads induced by column equilibrium.

116

T16S15

14

lZ

NOTE:

1. MEMBERS V,W,X & Y HAVE ARBITRARILYLARGE AREAS.

2. VOLUME CHANGE INFLUENCE RESULTS FROMASSIGNING A DECREASE IN LENGTH TOMEMBERS V,W,X & Y WHICH CAUSE ADISPLACEMENT AT JOINTS 5,9,13 & 17EQUAL TO THE DESIGN VALUE.

3. REMAINDER THE SAME AS FIG. 41b

Fig. 42. Computer mode! for analyzing connection loads induced bycolumn equilibrium and volume change deformations.

20

2.25'

PCI JOURNAL/March-April 1984 117

• Actual bar diameters, consideringribs, are about ' in. (3.2 mm)greater than their nominal size.

• Spandrel internal reinforcementfor connections typically should be#3, #4, ur#5 bars.

• Details should be prepared duringdesign to check that the three-dimensional interfacing require-ments for reinforcing bars aresatisified.

• The arrangements and positions ofthe steel must he such that ordinaryworkmen can fabricate and con-struct them.

• Clearances of 3/4 in. (19 mm) be-tween spandrel reinforcements indifferent planes should be plannedto accommodate reinforcing bartolerances and interfacing.

• Special welding requirements andprocedures should be determinedwhenever welded reinforcing barsare used at critical connections.

• Reinforcing bars should not bewelded near cold bends, andshould never be tack-welded.

Tolerances and Clearances• A 1-in. (25.4 mm) minimum clear-

ance between spandrel beams andall other framing members shouldbe selected. Long span spandrels,spandrels of large depth [48 in,(1.22 m) and greater], and span-drels supporting members span-ning 60 ft (18.3 m) or more mayrequire clearances between theother structural components of upto 1 1/2 in, (38 mm) to provide fortolerance fit-up interfacing.

• Separate evaluations of fabricationand erection tolerances should bemade for each design rather thanrelying solely on "usual" industrytolerances.

• The influence of structural defor-mations during erection should beconsidered when selecting toler-ance and clearance requirements.

• Tolerances generally accumulateand this effect should be consid-ered.

• Designs should be based upon thetolerances and clearances selectedwhich produce the greatest forces.

Corrosion Protection• Concrete cover to reinforcing bars,

considering placement tolerances,should be selected considering allinfluencing factors.

• Coatings to metal plates should hespecified in detail and not he refer-enced as simply rust inhibitivepaint or galvanized.

• Welding to hardware in beams thathave corrosion protective coatingsshould be done prior to the coatingapplication.

• Parking garages using metal platesexposed to the elements should re-quire all plates to be galvanized ata minimum.

Loads• Loads to spandrel beams and their

connections during erection maybe greater than the permanent de-sign loads.

• The design should consider thecombined effect of the differentpossible loading cases.

• The influence of volume changeloads axially and rotationally, andother deformation caused loads,should be accounted for in the de-sign. All connections should be de-signed for a minimum N. tensionforce equal to 0.15%x.

• Loads to spandrels generated bythe beam's torsional equilibriumrequirements and by the support-ing column's lateral equilibriumforces should be determined.

Connections• Connections or other means must

be used to provide for spandrel

118

beam overall torsion equilibrium atthe time of erection and for the in-place permanent conditions.

• Where possible, avoid using ten-sion insert connections to providefor spandrel beam torsion equilib-rium because of tolerances.

• Consider all load combinationsfrom construction to final in-placeforces when designing and detail-ing spandrel connections.

• Evaluate the influence of toler-ances on all the various spandrelconnections.

• Do not count on hearing pad shearbehavior as a means of providingoverall beam torsion equilibrium.

• Select connection details which arenot tolerance sensitive.

• Insure that connection hardwarecan he practically integrated intothe spandrel without interferenceor conflict with other materialswithin the beam.

• Connections using loose fieldwelded plates or threaded barsshould require the anchoringhardware embedded in the beamand/or the adjoining member tohave a load capacity one-thirdgreater than the loose connectingplate.

• Complete free-body diagramsshould be developed for each con-nection design to insure that allforces are accounted for and thatstatics are satisfied.

Bearing Considerations• Employ plain concrete bearing in

combination with bearing padswhenever possible.

• At service load levels, nominal PIAbearing stresses for ledges andbeam ends should be in the 800 to1000-psi (5.5 to 6.9 MPa) range.

• Avoid using plates for bearing sur-faces whenever practically possible.

• When using plain concrete bear-ing, always provide some mini-

mum internal reinforcement to re-sist N. forces.

• Consider using preformed padscomposed of synthetic fibers and arubber body, % to 'A in. (9.5 to 12.7mm) thick, for most bearing condi-tions.

• Avoid using neoprene pads forgeneral bearing conditions exceptwhen control of volume changedeformations (not at expansionjoints) is a critical design parame-ter, and then use only non-com-mercial structural neoprene gradessatisfying AASHTO specifications.

Ultimate Load Factors• Loads resulting from volume

change deformations shouldemploy the same ACI Code 1.7load factor as required for liveloads.

• All spandrel beam connectionsshould use a load factor of at least 2(2 = 4/3 the usual combined ulti-mate dead and live load factor of1.5).

• Connections which rely upon con-crete shear cones for capacityshould use a load factor of 3 unlessa lower load factor of 2.5 can beprudently justified.

Supporting Columns• Loads to the column resulting from

spandrel beam torsion equilibriumconnections and the beam reactionshould be analyzed to insure thatthe column is correctly designed.

• Column design requires that theinfluence of the column's and thespandrel's actual size be consid-ered by the analysis rather than justusing simple beam-to-column cen-terline dimensions for the analysis.

• Spandrel beams at the uppermostlevel, or elsewhere, should nothear directly upon column tops butinstead be supported upon column

PCI JOURNAL/March-April 1984 119

haunches or corbels, thereby pro-viding for the top of the column tobe approximately level with the topof the beam.

Inspections• Connection reinforcements should

be inspected for placement posi-tion and arrangement by the de-signer or his representative duringspandrel beam fabrication.

• Welded moment frame connectionhardware embedded in spandrels(and columns) requires weld in-spection and testing of the rebarand plate welds.

• Field welds employed to completemoment frame connections requireweld inspection and testing.

CLOSING COMMENTSThe behavior, design considerations,

design relationships, and generalguidelines on spandrel beams as pre-sented are based upon the author's de-sign, construction, failure investigation,and repair experience.

Spandrel beam design, if it is to besuccessful, requires consideration of thefollowing items:

• No magic details or solutions exist.Each project's design requires theengineer to evaluate all the cir-cumstances, determine the designcriteria, and develop the appropri-ate solutions.

• Spandrel beam design cannot be

considered as only a simple com-ponent design. Rather, there mustbe "one" in-charge designer to in-sure that the spandrel beam's de-sign satisfies the overall criteria,that building frame interfacingstructural requirements are met,that deformation and restraint con-ditions have been evaluated, se-lected tolerances and clearancesare satisfactory, and the connec-tions have been correctly inte-grated.

• The hindsight key to good spandrelbeam design is that the in-chargedesigner he meticulous regardingrequirements and details.

The concepts discussed and the re-quirements reviewed for spandrel beamdesign apply equally to all aspects ofprecast prestressed concrete design, andto engineering design in general.

ACKNOWLEDGMENTSThe graphic figures were prepared by

Steven E. Adams of Raths, Raths &Johnson, Inc.

The author wishes to express his ap-preciation to the many individuals whoreviewed his manuscript and whosupplied many constructive comments.In particular, he wishes to thank AlexAswad, Kamal R. Chaudhari, Ned M.Cleland, Arthur R. Meenen, A. FattahShaikh, Edward R. Sturm and H. CarlWalker.

Note: Discussion of this paper in invited. Please submityour discussion to PCI Headquarters by November 1, 1984.

120

REFERENCES1. PCI Design Handbook—Precast Pre-

stressed Concrete, Prestressed ConcreteInstitute, Chicago, Illinois, 1978, 369 pp.

2. PCI Manual on Design of Connections forPrecast Prestressed Concrete, PrestressedConcrete Institute, Chicago, Illinois,1973, 99 pp.

3. AC! Committee 318, "Building Code Re-quirements for Reinforced Concrete (ACI318-77)," American Concrete Institute,Detroit, Michigan, 1977, 103 pp.

4. Roark, R. J., and Young, W. C., Formulasfor Stress and Strain, Chapter 7, "Beam;Flexure of Straight Bars," McGraw-Hill,Inc., New York, N.Y., 1975 (Fifth Edition),624 pp.

5. 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. 32-100.6. AC! Committee 332, "Building Code Re-

quirements for Structural Plain Concrete(ACI 332-72)," American Concrete Insti-tute, Detroit, Michigan, 1971, 7 pp.

7. Keane, J. D., Systems and Specifications,Steel Structures Painting Manual, SteelStructures Painting Council, Pittsburgh,Pennsylvania, V. 2 (Third Edition), 1982,382 pp.

8. AC! Committee 315, "Manual of StandardPractice for Detailing Reinforced Con-crete Structures (ACI 315-74)," Chapter 6,"Structural Design Details for Buildings,"American Concrete Institute, Detroit,Michigan, 1974, pp. 54-59.

9. AC! Committee 201, "Guide to DurableConcrete (ACT 201.2R-77)," AmericanConcrete Institute, Detroit, Michigan,1977, pp. 20-23.

Note: An Appendix giving design examplesis included following the Notation Section.

PCI JOURNAUMarch-April 1984 121

NOTATION= distance from end of beam to

horizontally applied load orheight of ultimate strength rec-tangular stress block

AA = longitudinal reinforcement inbeam ledge near ledge top, sclin.

A, = longitudinal torsion reinforce-ment about beam perimeter, sqin.

A,, = reinforcement to resist flexureand/or direct tension, sq in.

A,,, = hanger shear reinforcementacross inclined dap crack, sq in.

Ad1 = corbel type reinforcement, beamledge bottom, at beam end sup-port, sq in.

A, = beam web reinforcement, non-ledge side, at beam end support,srq in.

A, = beam torsion reinforcement,closed stirrups, ledge side ofweb, sq in.

A, = web shear stirrup reinforcement,sq in.

AvA = corbel type reinforcement, beamledge, at beam end support, sqin.

A. = beam end 45 deg torsional equi-librium reinforcement ledgeside of web, sq in.

A = beam end longitudinal compo-nent of A,, torsional equilibriumreinforcement ledge side ofweb, sq in.

A1,,, = beam end vertical component ofA,, torsional equilibrium rein-forcement ledge side of web, sqin.

bt = bearing width of concentratedledge load, in.

b,,, = width of.beam web, in.bl = effective width of ledge corbel

at beam end support, in.C = clear concrete cover to reinforce-

ment, in.d – distance from extreme compres-

sion fiber to centroid of flexuraltension reinforcement, in.

d, = distance from end of beam toend concentrated load closest tobeam end, in.

d,' = distance from centroid of tensionreinforcement to extreme ten-sion fiber, in.

d1, = distance from non-ledge side ofbeam web to centroid of 45 degA,, web reinforcement posi-tioned closest to ledge side ofbeam, in.

d, = distance from centroid of A +, totop of ledge for corbel end sup-port, in.

d 2 = distance from beam web face,ledge side, to centroid of corbelend A,2 vertical web reinforce-ment. in.

e d = distance from beam end at top ofledge along an inclined 45 degline on the web to a 90 deg inter-secting line passing through theH, equilibrium connection cen-troid (Fig. 21b), in.

er = distance from 1 in. (25.4 mm)below the top of the concretetopping to the top surface of thebeam ledge, in.

e m = perpendicular distance from theH. equilibrium connection cen-troid to the inclined 45 deg linealong which e Q is measured (Fig.21b), in.

e l = distance from beam ledge load,uniform or concentrated, to thebeam shear center, in.

es = distance from beam end reactionto the beam shear center, in.

= compressive strength of beamconcrete, psi

fl = beam concrete combinedflexural and tension stress, psi

f = beam web flexure tension stress,psi

= yield strength of reinforcementor steel, psi or ksi

h = vertical height of beam ledge, in.

122

h h = vertical distance from 1 in. (25.4mm) below concrete topping toforce centroid of beam H. bot-tom equilibrium connection atbeam end (Fig. 24h), in.

h,o = vertical height of beam lowerportion acting as a horizontalbeam (Figs. 24b and 24d), in.

H = horizontal applied load or hori-zontal torsion equilibrium con-nection force, working or ulti-mate, lbs or kips

H. = ultimate beam end horizontalequilibrium connection force,lbs or kips

= maximum principle moment ofinertia, in.4

= minimum principle moment ofinertia, in.4

I r = moment of inertia about x axis,in.4

I product of inertia, in.4

I„ = moment of inertia about y axis,in.4

N. = ultimate volume change hori-zontal load applied to beam, lbsor kips

P = concentrated load applied tobeam ledge, lbs or kips

P„ = ultimate concentrated load ap-plied to beam ledge, lbs or kips

R, R,,, Ra = beam end support reaction,lbs or kips

s = spacing between concentratedloads, in.

S bp = principle section modulus atbeam bottom, in.3

T, TA, TB = beam end equilibriumtorque, in.-lbs or ft-kips

V„ = ultimate shear load applied tobeam ledge, lbs or kips

= ultimate lateral loads per unitlength applied to beam for beamtorsional equilibrium (Fig. 24),lbs per ft

Ybp = distance from beam cross-sec-tional centroid to extreme bot-tom fiber along inclined vertical

1„ = ratio of ultimate internal mo-ment resisting arm to d, in.

1 p = horizontal projection of beamledge from web, in.

L = span ofheam, in.

m = variable defining length of beamledge attachment to web de-pending upon type and locationof ledge load

N = volume change horizontal loadapplied to beam, lbs or kips

axis, in.= coefficient based upon unit

weight of concrete, 1.0 for nor-mal weight and 0.85 for sand-light-weight

= ultimate strength reduction fac-tor, 0.65 for plain concrete ten-sion, 0.85 for shear, and 0.90 forreinforced flexure

= summation symbol= angle of inclination of principle

inertia axes

PCI JOURNAilMarch-April 1984 123

APPENDIX-DESIGN EXAMPLES

The following three numerical exam- for an end support corbel plus a sampleples address the design of a typical calculation for determining the princi-spandrel beam for a parking garage in- pie moments of inertia for a buildingcluding the reinforcement requirements spandrel beam.

EXAMPLE 1 — PARKING GARAGE SPANDREL BEAM

Spandrel Beam Data Beam reinforcementf„ =60ksi

Normal weight concrete The spandrel beam details are shown inf,' = 5000 psi the sketch.

CP I'_ Q••^o"' Io"x 32 "77`30", (cwT)

/O~3 "TOPPING

is 14`

S= 4'"WT o. 84 k I^'

p P P f P P

CLEAR /8's--

Spandrel beam details

124

Hu

ffu

N T p WES 'z

Design LoadsLive Load = Weight of Cars + '/2 Snow

Weight=50+'/2(30)= 65psf

Note that there is no live load reduction.

Concentrated load per tee stem(D + L) = 25.3 kips (working)

Find Shear CenterRefer to Fig. 20.

W1 = 10 in., W. = 14 in.

hl = 65 in., li e = 11 in.

_ 11 11 (14)_ 3

es

210(65)+ 11 (14)g

= 0.060 in.

e x = + 0.060 = 5.06 in.

65 [ 65 (10) 3 1e "

2 L65(i0)a+14(11),)= 25.26 in.

e„ = 2 + 25.26 = 32.26 in

Location of beam center of gravity:

z = 5.84 in., y = 32.97 in.

SHEAR_ GENTEK

dX

Id

Determination ofshear center

Beam End DesignRefer to Fig. 27b for beam-to-column

details.

Design data:1. Refer to Fig. 21.2. Consider shear center aligns with

web centerline.3. ZP = 3 (25.3) = 75.9 kips (working)

Find ultimate load factor:

PD+L = 25.3 kipsPD = 15.4 kipsPy = 9.9 kips

Spandrel beam end design

PCI JOURNAIJMarch-April 1984

125

LF = 1.4D+ 1.7LD+ L

_ L4(15.4)+ 1.7 (9.9)25.3

= 1.52Find J1H a forces to beam web, use LF = 1.52.

H 1.52 (75.8) 9.5' 62

= 17.7 kips

to top tension insert at ultimate.Find e d and e:

ed = 2 (50+5)=38.891n.

2 ed = 2(38.89)= 77.8 in.

0-f5+5-e^ l 2 5 = 31.8 in.

Determine A ^, reinforcement:UseEq.(1).d,,-10- 1.5= 8.5 in,

A - 17.7(31.8)U' 0.85 (8.5) 60

= 1.30 sq in. (minimum)Find minimum A,, and A,1:Use Eqs. (2) and (3).

rAeon = A k,, = 2 A = 2 (1.30)

= 0.92 sq in.

Distribute 0.92 sq in. horizontally over

2 (2 ea) = 55 in.

Select#4 stirrups for A.o and A.

Ao from: End to 1.65 R = 0.32 sq injf1.65 to 6.65 ft = 0.17sgmill

Am„ + A, = 0.92 + 0.17/2= 1.00sgin. (1.65to6.65 ft)

#4 stirrup spacing:

0.201.08/55

= 10.2 in.

A,,, bar size per 12 in. spacing:

12( 55 )= 0.20sgin.

Use #4 bars at 12 in. center to center.

Determine tension insert ultimateloads:I. Steel ultimate = (4/3) (LF) (Working

Load)2. Concrete punching shear beam web

and insert shear cone requires a loadfactor equal to three.

3. H Steel:

(4/3) (26.8) = 35.7 kips

4. H, Concrete:

3(. 2fi.8 _ 52.9 kips1.52

Summary

1. Use #4 closed stirrups at 10 in. cen-ter-to-center over a length of 5 ft frombeam end.

2. Use #4 bars for A! at 12 in. center-to-center about beam perimeter. Usehairpin bars according to Fig. 25 atbeam end.

3. Note that other design cases maycontrol reinforcement.

Ledge Attachment Design

Determine ultimate stem load:Note that the above steel area includesthe c, reduction due to torsion. V. = (4/3) (1.52) (25.3) = 51.3 kips

Am „ + Ad = 0.92 + 0.3212 Check end shear V„ for f1 at ultimate:= 1.08 sq in. (end to 1.65 ft) Use Fig. 22 and Eq. (4). % i = 4.5 in.

126

d emo, = 2h =2(14) =28 in.

de = 19.75 in. controls de selection

s,^Rr = bt + 4 h = 4.75 + 4 (28)= 116.75 in.

s = 60 in. controls

m = d, + s/2 = 19.75 + 6012= 49.75 in.

51,300 6(51,300)(10/2 + 4.5)f` 10 (49.75) + (10)2 49.75

691 psi

fi greater than

3X j7 = 3 (1) 5000 = 212 psi

Therefore, ledge reinforcement is re-quired.

Select ledge attachment reinforcementat end V.Use Eq. (5):

_ 51.3(10+4.5-0.5)A^ ^ 0.85(60)(10- 1.5- 0.5)

= 1.76 sq in. over length m = 49.75 in.

#4 bar spacing:

49.75

1.7610.20 = 5.65 in.

Use #4 stirrups at 6 in. center-to-centerover a length 4 ft 6 in. from beam end.

Determine inner o„ ledge attachmentreinforcement:

V. = 51.3 kips

By inspection, if f, > 3 X J ,, reinforce-ment is required.Use Eq. (5) and previous example.

A, = 1.76 sq in. over length m = 60 in.

#4 bars with a spacing of:

60 = 6.82 in.1.76/0.20

Use #4 stirrups at 7 in. center-to-centerstarting at 4 ft 6 in. from each end.

Summary1. Consideration should be given to in-

creasing h,o to 12 in. if greater rein-forcement spacing is required.

2. Note that other design cases maycontrol.

Ledge Load Transfer Design

V,, = 51.3 kips per tee stem (see Fig. 23)

Concrete shear capacity inner V„

s - 60 in. greater than

b t + 2 h = 4.75 i- 2 (14) = 32.75 in.

Use Eq. (6)

Vq-3.8)14(1)U X

100

[2(6) +4.75+ 14] = 77.6 kips

Plain concrete shear capacity isgreater than applied V. = 51.3 kips.Therefore, no reinforcement per Eq.(11) is required for inner loads.

Concrete shear capacity end V.:

d, < 2 li, de = 19.75 in., and 21: = 28 in.

Use Eq. (8):

V =0.85(14)

1x" 1000

12(6)+ (4.75 + 14)12+ 19.751= 34.6 kips

Plain concrete shear capacity is lessthan applied V. = 51.3 kips. Therefore,reinforcement per Eq. (11) is requiredfor end V,,.

Select end V,, reinforcement:Check applied shear stress.

Shear Area = h (b, + h)= 14 (4.75 + 14)= 262.5 sq in.

?CI JOURNAUMarch-April 1984 127

c. 51,300= 262.5 = 195 psi Select two #5 bars with end hairpins.

This stress is satisfactory since it is lessthan lox VT = 707 psi.

Use Eq. (11):

_ 51.3

Agh 0.85 (60) = 1.01 sq in.

over length b t + h = 18.75 in.since d e > (b + h)12.

AYh steel area provided by ledge rein-lorcement at 6 in. center-to-center forend V. (see previous calculations) is:

0.20 (18.75/6) = 0.62 sq in.

Provide 1,01 - 0.62 = 0.39 sq in. ofadditional steel reinforcement.

Use two #4 closed stirrups in additionto other reinforcement at each end V.

Determine A h = A,h12 = 1.0112 = 0.50sq in.

Select ledge flexural reinforcement.Use Eq. (12):

d -h - 1.5 = 14- 1.5 = 12.5 in.

A1= 0.851(60)[ 51.3 ( 4 12.5

+ 0.15 (51.3) 14 112.5 J

= 0.53 sq in, per tee stem load.

Use #4 bars at 12 in. center-to-centerwith two additional bars at each tee stemdistributed over b, + h = 18.75 in.since de > (b + h)/2

Design SummarySee Fig. 27b for design details. FollowACI 318-77 (Chapter 11) for shear andtorsion reinforcement.

Reinforcement details:

Location frombeam end A, + 2A, A,

0 ft to 1 ft 7Y, in. #4 bars at 5.6 in. #4 bars at 12 in.*1 ft 73/4 in. to 6 ft 7% in. #4 bars at 10.4 in. #3 bars at 12 in.*

Analysis of calculations:Afl includes v. reduction due to torsion.

Location frombeam end A,+ 2 A t Ar

0ftto4ft1%in. #4 barsat5.6in.

0ftto4ft7in. — #4 barsat12in.*4 ft 1% in. to midspan #4 bars at 6.8 in.

*At each web face.

Additional reinforcement: 2. Furnish #4 bars at 12 in. center-to-center plus two additional bars at

1. Provide two additional #4 stirrups at each tee stem load for ledge flexuralend V. tee stem loads. reinforcement.

128

EXAMPLE 2-PARKING GARAGE SPANDREL BEAMLEDGE CORBEL

Refer to Fig. 27c for spandrel beam de- From Eq. (19):tails. 0.08 (21) 12.5

Any «m,nfmY^^ = 60Design Data1. See Example 1 for loads and dimen-

sions.2. The beam-to-column details are

shown in Fig. 27c. The spandrelbeam is torsionally stable withoutany end connections.

3. Design corbel end using methodbased on corbel behavior.

4. Refer to Fig. 25 for corbel require-ments.

5. Consider ledge corbel loads to resultonly from applied tee stem loads.

Determine Ultimate Applied Loads DistributeA 15 per Fig. 25c and consider

Ultimate shear load: only one leg (lower) of closed stirrupeffective (see Fig. 25d).

V. = (4/3) (1.52) (3) (25.3)= 153.8 kips Spacing for #4 bars:

Ultimate shear stress: 1.5 b, (bar area) _ 21 (0.20) Estimate d, = 1.2.5 in. A 0.44 -

9.6 in.n^

Corbel width = 1.5 h = 1.5 (14) = 21 in.

= 0.35 sq in.

Using Eq. (20), determine A1.5 steel:

_ 153.8A"` 0.85 (60) 4 (1) 21 (12.5)

= 0.44 sq in. (controls)

From Eq. (21):

0.04 (21) 12.5A (minimum) 60

= 0.18 sq in.

01= V. = 153,800 586 psi b, c1 21 (12.5) p

The calculated shear stress is thereforesatisfactory since it is less than therecommended 800 psi maximum.

Find Ledge Corbel ReinforcementUsing Eq. (17), determine A 11 steel:

3 (153.8) 6= = 1.09 sq in,

0.85 (4) 60 (12.5)

This steel area controls. Select four #5bars with welded cross-bars.

Using Eq. (18):

_ (153.81`^" 0.85(60)22(1)21(12.5)

= 0.88 sq in.

Maximum spacing:h/2 = 14/2 = 7 in. center-to-center

Using Eq. (22) determine A ft steel:Estimate d2 = 10 - 1.5 = 8.5 in.

= 12.5A,2 8 5 (1.09) = 1.60 sq in.

Select #4 bars.Total required = (1.60/0.20) = 8 barsOver 1.5 h = 21 in.

Note that no ledge attachment rein-forcement is required due to beam reac-tion for end tee stem V..

Add #4 stirrups so that additional stir-rups plus shear and torsion stirrups pro-vide 1.60 sq in. over the beam's end 21in.

PCI JOURNAUMarch-April 1984 129

Design Summary1. Cross-harwelds (#5 cross-har) for the•

four #5 A 8, bars should he in accor-dance with the PCI Design Hand-book requirements and completelyspecified.

2. Analysis of bearing pad bearing

stresses at a working load of 3 (25.3)= 75.9 kips is required consideringthe bearing is not uniform-

3. The ultimate concrete bearing stresson the extreme edge of the ledge mayrequire the use of additional bearingreinforcement according to Fig. 39.

EXAMPLE 3- DETERMINATION OF PRINCIPLE MOMENTSOF INERTIA FOR A BUILDING SPANDREL BEAM

Assume a spandrel beam for a build-ing with a configuration and dimensionsshown in cross section below. Dividebeam into two parts.

Beam Propertiesx 8.12 in.y = 15.66 in.I 54,024 in.4Sn = 3450 in?I,, = 13,283 in.4A l = 476 sq in.A E = 60 sq in.

Determine Product of inertial,„From strength of materials:

IS„= 1xtytAiIsv = x , y , A, + xa y z Asx, =7-8.12=-1.12 in.y, = 17- 15.66= +1.34 in.xz = 17 – 8.12 = +8.88 in.yZ = 5– 15.66= –10.66 in.Izj = (-1.12) (+ 1.34) 476 + (+8.88) x

( 10.66) 60 = – 6394 in.'

Find Orientation Angle tRefer to Fig. 26 and use Eq. (23):

B = tan' [ 2 (-6394)2 13,283 – 54,024

_ + 8.71 deg (counterclockwise)

Find 'max

Use Eq. (25):

r

AilPARrO

^

^y _ PARtO

X

Building beam data.

'VfX

C.G•Q

X

Determination of principle moments ofInertia.

130

, max — 54,024 + 13,283 +2

( 54,024 — 13,283 )2 + (- 6394)l 2 J

= 55,003 in

Find IminUse Eq. (26):

54,024 + 13,283I^rn = 2

( 54,024 — 13,283 ^^ +(_6394)22

12,304 i.n,4

Find Sb min Associated With 'max

a = , (15.66) 2 + (11.88)2

= 19.66 in,

11.88^3 =sin 1 19.66= 37.18 deg

(3-8=37.18-8.71= 28. 47 deg

Ybn = (a) cos (ji — B)= 19.66 cos (28.47)= 17.28 in.

Determine S b mi at Point AImar

b mth =

_ 55,00317.28

= 3188 in,"

which is less than the value ofS b = 3450in.3 for I , found previously.

Summary1. Ifthe beam is prestressed, the inter-

nal prestress moment is the productof the strand force times the distance

1P

c,L ___7Lp

^Q X `41IbPX

yily

PDetermination of minimum sectionmodulus.

from the beam center of gravity to thestrand center of gravity where thedistance is parallel to line y, — yF.

2. The above procedure for unsymmet-rical members can be used generallyfor all precast prestressed concretemembers.

3. A graphical approach is recom-mended for determining all dimen-sions such as ya p once B, I m. r , andI,,,,, have been calculated.

METRIC (SI) CONVERSIONFACTORS

1 ft = 0.305 ft1 sq ft = 0.0929 m2

t in. =25.4mm1 sq in. = 645.2 mm2I in.3 = 16,388 mm31 in.4 = 42,077 him;L kip = 4.448 kNI lb = 4.448 N1 ksi = 6.895 MPa1 psi = 0.006895 MPa1 psf = 0.04788 kPa

PCI JOURNAllMarch-April 1984 131