Overload Behavior of anExperimental Precast Prestressed

Concrete Segmental Bridge

Mohamed Abdel-HalimAssistant Professor of Civil

EngineeringYarmouk UniversityIrbid, Jordan

Richard M. McClureAssociate Professor of Civil

EngineeringThe Pennsylvania State

UniversityUniversity Park, Pennsylvania

Harry H. WestProfessor of Civil EngineeringThe Pennsylvania State

UniversityUniversity Park, Pennsylvania

n recent years, interest in segmentalbridges has grown and their behavior

under applied loads has received muchattention. The Pennsylvania Depart-ment of Transportation, with the supportof the Federal Highway Administration,responded to this growing interest bysponsoring the construction of an ex-perimental segmental bridge as a part ofthe 1 mile (1.6 km) oval shaped test trackwhich is operated by the PennsylvaniaTransportation Institute at ThePennsylvania State University.

One of the objectives of this researchwas to study the overload behavior in

order to establish actual safety factors.This required loading the bridge to fail-ure in addition to conducting theoreticalstudies. An analytic procedure based onthe finite element method was de-veloped to predict the complete load-deformation response of the prestressedsegmental bridge. The girder was alsoanalyzed using the standard theoreticalanalysis for prestressed concrete struc-tures, which is a simpler method. Thetheoretical results obtained by those twomethods were then compared with theexperimental results from the failuretests.

102

TEST BRIDGE

The general plan, elevation, and crosssection of the experimental bridge areshown in Fig. 1. The bridge consisted oftwo identical simply supported girderswith segments and joints numbered asshown. Each independent girder con-sisted of seventeen segments whichwere tied together with longitudinal baror strand post-tensioning tendons plusdiagonal bar post-tensioning tendon.The ducts containing the tendons weregrouted after post-tensioning. Steelshear dowels were used to achievealignment during construction and totransfer torsional moment after the gird-ers were built. Epoxy was used as themain jointing material between thesegments.

End diaphragms were introduced inthe end segments, which were ample insize to take the substantial reactionforces from the neoprene bearing padsand torsional anchorages and to provideroom for the post-tensioning end an-chorage plates. In addition, an openingwas made to allow easy access by re-searchers to the inside of the box sec-tion. An open longitudinal joint be-tween the girders was selected to allowan independent comparison of the twogirders. The overload tests were per-formed on Girder B,

The segments for the experimentalbridge were cast individually at a fabri-cation plant by the short line method inone steel form with provisions for ad-justments. They were then hauled about100 miles (161 km) to the test trackfacility where they were erected onsteel scaffolding-type falsework.

The curved box girder was designedfor longitudinal moment using straightbeam theory for the dead load, AASHTOHS20-44 live loading, and prestress.The design was made using allowablestresses and checked for ultimatestrength. For transverse moment, thesegments were designed elastically as abox frame with side cantilever flanges.

SynopsisAn experimental prestressed con-

crete segmental bridge was con-structed and tested at the Pennsyl-vania Transportation Institute of ThePennsylvania State University.

The bridge was designed by thePennsylvania Department of Trans-portation as two independent single-span curved girders with a length of121 ft (36.9 m). Each girder was com-posed of seventeen segments. Thebridge was initially field tested at ser-vice load levels and subsequentlytested for overloads when one girderwas tested to failure.

The incremental loading to failure isdiscussed and these results are com-pared with those obtained from a fi-nite element analysis (SAP IV), whichmodels the cracking patterns andmaterial nonlinearities. In addition, theresults of classical simplified analysesare compared with selected experi-mental and finite element results.

Conclusions are given that relate tothe application of the research.

At the bottom of the webs the frame wasassumed to he simply supported. Eachgirder was analyzed for torsion as a hori-zontally curved beam with eccentricloads. The cross section of the segmentswas approximated as a box section withthe flanges neglected.

The design strength of the concrete at28 days was 5750 psi (39.6 Nlmm 2). In-termediate grade ASTM A615 reinforc-ing bars with a specified minimum yieldstress of 40,000 psi (275 NImr 2) wereused for all mild steel reinforcement.Post-tensioning steel bars with aspecified ultimate stress of 160,000 psi(1100 NImm 2), or steel strand with aspecified ultimate stress of 270,000 psi(1860 N/mm z), were used for all post-

PCI JOUR NAL'November-December 1987 103

HCt Brg South Abutmenl Q Brg North Abutment

Girdefr A

IIA \2A\4A 5A 6A 7A 8A 9A 110A lilA 112-A I3A 14A 15A 16A

Gird r B ~^

^IB 2B 3B 4B 5 6B 7B BB 9B IOB IIB 1213 13B 146 I5B IGB 17Br 7'

Radius = 553,62 LSegment

121'D" C/C BearingsPLAN

Segment

SegmentNumber

— Joint Number

iiDiqgonal Posi-Tensioning Tendons

1 ELEVATION

iB'9-3/4"-- J i8°-3/4"R q di q ]Open Joint HH

Slope=0.1040 t/ft JCurb and —=•—Parapet

(Precast)

Curb andParapet

(Cost-in-ploce)jv ^SegmeniI gO^ VLOnailudinal P qst-

Torsionol Shear Dowels Tensioning TendonsTYPICAL CROSS SECTION

Note : t'=0.3O4Bm1"- 2t.4mrn

Fig. 1. General plan, elevation and typical section of an experimental segmental bridge.

tensioning tendons.In order to take into consideration the

effect of time on the strength of con-crete, concrete cylinders were testedbefore the bridge was loaded to failure.Some of these cylinders were tested forcompressive strength, static modulus ofelasticity, and Poisson's ratio, and otherswere tested for splitting tensile strength.

Table 1 gives the properties for the con-crete in Girder B at the time of testing.Specimens of the 0.50 in. (13 mm) diam-eter strands and of the 1.25 in. (32 mm)stress steel bars were tested by the man-ufacturer and the Pennsylvania De-partment of Transportation. The resultsare also given in Table 1.

Complete details and design criteria

MI

Table 1. Material properties.

Properties of concrete

Age (year) 4.5Compressive strength (psi) 7,350Tensile strength (psi) 646Modulus of elasticity (psi) 5,232,000Poisson's ratio 0.189

Properties of prestressing bars and strands

Bars Strands

Diameter (in.) 1.25 0.50Yield strength (ksi) 156.5 256.0Ultimate strength (ksi) 169.6 283.7Modulus of elasticity (ksi) 30,555. 28,000.Percent of elongation 5.5 6.4

Note: 1 in. = 25.4 mm; I ksi = 6.895 N/mm.=

for the test bridge can he found in thefinal report on Research Project 72-9,Penn DOT Publication No. 118.'

FINITE ELEMENT ANALYSIS

Modeling of MaterialsConcrete in the bridge has complex

stress distributions resulting from anumber of sources. Success in analyzingsuch a structure requires knowledge ofthe deformational behavior and strengthproperties of concrete under multiaxialstates of stress. Different models basedupon different theories have been pro-posed for the stress-strain law of con-crete under short-term loads. These arebased on plasticity, nonlinear elasticity,model of microstructures, measure ofdamage, endochronic theory of plastic-ity, and mathematical functions. A com-plete explanation of all these models canbe found in Ref. 2.

After examining these various models,it was concluded that, until more ex-tensive and appropriate investigationsbecome available, a type of model thatallows a direct inclusion of the experi-mental data should be preferred.Therefore, Kostovos and Newman's

model ,'- was chosen for the analysis ofthe bridge.

Octahedral Stresses and Strains

It was assumed in this work that com-pressive stresses and strains were pos-itive and that v,, ar , and Q, representthe maximum, intermediate, andminimum principal stresses, respec-tively. The orthogonal coordinate sys-tem o, aZ , and a-3 , which defines thestress space, was transformed into acylindrical coordinate system in whichzcoincides with the space diagonal (Q, =Uq = o) of the original system, and r and9 are the radius and rotational variables,respectively, on the plane perpendicu-lar to the z axis (octahedral plane), asshown in Fig. 2.

The two coordinate systems are re-lated by the following equations:

z=(a1 +Q2 +v3)/f = YWifo (1)

r=(11 3)x•l 0-1 — O'2)2 + (Q8 — ( •,) 2. +(o- —Q^)s

= 3 To (2)

Q, + Qz — 2 63(3)cos O =

r ,^ 6

PCI JOURNAUNovember-December 1987 105

C3

rid)

l3Z

Fig. 2. Schematic representation of the ultimate strength surface.

In these equations, rro and T„ areknown as the normal and the shear oc-tahedral stresses, respectively.

Similarly, the normal (Eo ) and shear(ye ) octahedral strains are defined asfollows:

eo = (E, + E E + e3 )/3 (4)

yo = 7.F (E Z — E,) l + (Ep — E3)2 + ( E3 — E,)2(5)

Here, €,, Ez, E;, are the strains in thedirections of the principal stresses. Ifelastic behavior is assumed, the stress asand strain Eq associated with volumechange are related by the bulk modulusK, and the distortional quantities arerelated by the shear modulus G as:

K = E 63(1 –2v) 3Ea

E __ r„G = 2(1+v) 2y

(7)

For nonlinear materials, l(ostovos andNewman used similar relationships, butin this case, the moduli K and G arefunctions of stress and strain, and can beexpressed as secant moduli in the form:

KR( a 0) = "ra (8)3 E,, (cro )

2 yo(T0) (9)

Concrete in Compression

In their work, Kostovos and Newmanhave shown that concrete compressionbehavior and fracture characteristicsmay be explained by the formation andpropagation of microcracks within theconcrete. Under applied loading, fourstages of behavior can be distinguishedin the stress-strain response for uniaxial,biaxial and triaxial stress cases. Con-sider, as an example, the stress-straincurve for uniaxial compression which isshown in Fig. 3.

As a first stage, consider the region upto 30-60 percent of the ultimate strength(shown as 45 percent in Fig. 3). In thisinitial stage (Stage 1 in Fig. 3), micro-cracks in addition to those preexisting inthe material are initiated at isolatedpoints where the tensile strain concen-trations are the highest. However, thesecracks are completely stable. Localizedcracks are initiated but they do notpropagate.

A second stage (Stage II, in Fig. 3),takes the region up to 70-90 percent ofthe ultimate strength. As the appliedload is increased, the crack system mul-

106

U.S (Ultimate Stress)IQa -^----

0W -

8oFS.(FaS}ress}z

--- - - OUFT

Io}

aFw cn60

o J^a - OSFPCJ, a 40

N j I =1 >I20 ^,i ml m^ @I

(n o^ of al

COMPRESSIVE STRAINFig. 3. Uniaxial stress- strain curve for concrete.

tiplies and propagates, but in a slow sta-ble manner. If Ioading is stopped andthe stress level is maintained at a certainvalue, crack propagation ceases. The in-creasing internal damage, revealed bydeviation of the linear elastic behavior,causes irrecoverable deformation uponunloading. The start of such deformationbehavior has been termed "onset of sta-ble fracture propagation" (OSFP).

A third stage (Stage III in Fig. 3)applies up to the ultimate strength.Interface microcracks are linked to eachother by mortar cracks, and void forma-tion (dilation) begins to have its effecton deformation. The start of this stagehas been termed "onset of unstablefracture propagation" (OUFP). Thelevel is easily defined since it coincideswith the level at which the overall vol-ume of the material becomes aminimum.

A fourth stage defines the region be-yond the ultimate strength. In this re-gion (Stage IV in Fig. 3), the energy re-leased by the propagation of a crack isgreater than the energy needed forpropagation. Thus, the cracks becomeunstable and self-propagating untilcomplete disruption and failure occurs.

Similarly, the multiaxial behaviormodel of Kostovos and Newman has

considered four stages which will beexplained in the following sections.

Elastic Concrete (Stage I) — Undercombined states of stress, the stress-strain relationship is generally non-linear. However, when stress is below45 percent of the ultimate stress, thematerial characteristics are unaffectedby the fracture processes explained pre-viously, the deformation is recoverable,and the stress-strain relationship is al-most linear. Therefore, it is assumedhere that concrete is isotropic, homoge-neous, linearly elastic, and that itsstress-strain relations are describedcompletely by two elastic constants,Poisson's ratio (v) and Young's modulus(F).

Inelastic Concrete (Stage II) — Thisstage represents states of stress between45 percent of the ultimate stress, whichhas been termed the "onset of stablefracture propagation" (OSFP), and 85percent of the ultimate stress, which hasbeen termed the "onset of unstablefracture propagation" (OUFP). In thiszone of behavior, Kostovos and Newmanconsider deformations to be composedof the following components:

1. A component dictated by the ma-terials characteristics and unaf-fected by the fracture process.'

PCI JOURNAL/November-December 1987 107

C-

U)U)U

W ttJU)

w

Et 2ET

TENSILE STRAIN

Fig. 4. Assumed stress-strain curve for concrete in tension.

2. A component expressing the effectof internal stresses caused by thefracture processes.

Relationships between o-o and eo , andbetween To and ye have been expressedusing the experimental results. Theserelationships were formulated as fol-lows:

Eo = A ( •o) (10)

Y. = f2(zo) (11)

Then, the secant expressions of thehulk and shear moduli, given by Eqs. (8)and (9), can be calculated. After that, thesecant values of the modulus of elastic-ityE and Poisson's ratio v were obtainedfrom the well-known formulas of linearelasticity:

E=3K+G(12)

3K – 2G (13)

2 (3K + G)

Inelastic Concrete (Stage III) — Thisstage represents states of stress betweenthe OUFP and the ultimate strengthlevels. In this zone, void formation be-gins to have an effect. Therefore, thedeformations that occur in this stage areconsidered to be composed of threecomponents: the two components ex-

plained in the previous section plus athird component which expresses theeffect of void formation. ' The addition ofthe void formation effect to the first twocomponents gives the total defor-mations. Then, the secant values of themodulus of elasticity E and Poisson'sratio v were obtained following the samesteps explained in Stage II.

Inelastic Concrete (Stage IV) — Thisstage represents states of stress beyondthe ultimate strength level. In this zone,the volume of voids increases dramat-ically, which causes rapid dilation of theoverall volume. At this point, it is evi-dent that the specimen, or the concreteelement as a whole, can no longer beconsidered as a continuum. However,an attempt has been made to use thework of Kostovos and Newman' con-cerning the behavior of concrete beyondthe ultimate strength level. Here, theeffect of the voids beyond the ultimatestrength has been added to the defor-mations at the ultimate level to obtainthe total deformations, that is:

E o = Eo + SEa (14)

Yo = yo + syo (15)

Here SE„ and 3y0 are the hydrostaticand deviatoric components of the voidsdeformations beyond ultimate, respec-

108

tively. And, eo and yo are the hydrostatic hardening of the material was definedand deviatoric components at ultimate, according to the experimental stress-respectively, strain curve.

Concrete in Tension

For concrete in tension, it can he as-sumed without significant loss of accu-racy that linear behavior is obtained upto cracking. Therefore, the stress-strainrelationship has been described by twoelastic constants, Poisson's ratio (p) andYoung's modulus (E). The tensilestrength for the concrete in triaxial ten-sion, or in the tension-tension-compres-sion quadrant, was taken to be equal toits uniaxial tensile strength.

The concrete stress is zero at thecracks, but it is not zero if averaged overthe distance between cracks. Thus, ifthe concept of working with averagestress is considered, an unloading por-tion of the stress-strain curve can be as-sumed. No data are available concerningthe unloading portion of the curve.Therefore, the stress-strain curve forconcrete in tension was taken as shownin Fig. 4. The modulus of elasticity forany tensile strain is taken as the secantmodulus for that point on the curve.

Modeling of the Cracked Elements

The stiffness of the cracked elementswas softened isotropically. This soften-ing was taken into consideration by re-ducing the modulus of elasticity (E) ac-cording to the assumed stress-straincurve for concrete in tension shown inFig. 4. Some shear stiffness was retainedin the cracked elements. Hand et al."show that although retention of someshear stiffness is necessary, the propor-tion of shear stiffness retained, /3, is notcritical, i.e., various values of j3 resultedin similarly good correlation with testresults,

Modeling of the Prestressing Steel

An elastic strain hardening model wasused in defining the material behaviorof the prestressing steel. The strain

Modeling of the Mild SteelReinforcement

The cross section of the bridge isheavily reinforced with mild steel rein-forcement. In order to account for itsexistence, the mild steel reinforcementwas uniformly distributed throughoutthe concrete elements, and new effec-tive values for the modulus of elasticitywere established for individual regionsof the cross section, with each regionencompassing a portion of the cross sec-tion where the reinforcing pattern wasfairly uniform,

General Technique Used for theNonlinear Analysis

Nonlinearity is caused solely by thenonlinear form of the constitutive rela-tions and failure laws of concrete andsteel. Strains are assumed to be smalland, thus, the strain-displacement rela-tions are linear. Therefore, the probleminvolves material nonlinearity only, anda nonlinear solution must satisfy theconstitutive laws and the conditions ofequilibrium and compatibility withinan acceptable margin of error.

The procedure used for the analysiswas as follows:

(a) Discretize the structure into ele-ments by introducing the finite elementgrid, number the nodes, and number theelements. The centroidal characteristicsof each element are considered in all cal-culations to represent the average prop-erties of that element. Apply an initialload, and carry out an elastic analysisusing a linear finite element program(SAP IV in this study) to obtain thenodal displacements and elementstresses. Calculate the correspondingprincipal stresses. Use a scaling factor toraise the load level to cause first crack-ing in an element or region of elements.Then, linearly scale the nodal displace-

PCI JOURNACJNovember-December 1987 109

ments and element stresses to yieldtheir respective values at the crackingload of the structure.

(b) Modify the material properties ofthe cracked elements to account for ten-sion stiffening of the concrete. The loadis then increased by increments ofvarying magnitude, with each cycle ofloading reflecting the changing prop-erties of the materials.

The following computational stepswere involved in a typical cycle ofloading:

1. Increase the previous load by an in-crement of loading (P t = P {_, +Perform an elastic analysis for thestructure under load P t, using the up-dated stiffness matrix at the end of theprevious load. That is, if [K ] f_, is theupdated stiffness matrix at the end ofloadP 1_,. Then:

{Pk = [K]1 -1 fo}<

where {P} ; and { A}, are the load vectorand displacement vector for generalsystem at cycle i, respectively. Calculatenodal displacements {0}, and elementstresses.

2. Calculate the corresponding prin-cipal stresses.

3. Check concrete cracking and in-elasticity and check steel inelasticity.

4. Examine the stress level for eachinelastic concrete element Then definethe stage of behavior for each inelasticelement.

5. Modify the material properties ofthese inelastic elements,

6. Modify the material properties ofthe old and new cracked elements to ac-count for tension stiffening of the con-crete and modify the steel propertiesusing its experimental stress-strain dia-gram.

7. Update the structure stiffness at theend of the load P t, using the new mate-rial properties in preparation for the nextload level.

This computational cycle was re-peated until the ultimate load wasreached and the complete behavior of

the structure was determined in terms ofdisplacements, stresses, and crack pat-terns for each desired load.

In checking for cracking, it is impor-tant to note that when the calculatedtensile stress, v,, in any element ishigher than the ultimate tensile strengthof the concrete, ft , the stresses in all theelements must be scaled down to re-move the stress increment (v, – fe ), andthe Ioad and nodal displacements mustalso be scaled down to yield their re-spective values.

It is important to mention that thestresses (forces) released from thecracked elements in cycle i, for example,will be redistributed to the neighboringelements in the next cycle, cycle (i + 1).

Use of SAP IVSAP IV is a finite element structural

analysis program for the static and dy-namic response of linear structural sys-tems. The program is written in FOR-TRAN. The user's manuals describes thelogical construction of the program, theanalysis capabilities, the finite elementlibrary and the input data.

Two of the elements were used for thebridge problem. The three-dimensionaltruss element was used to represent thelumped prestressing tendons, and thethree-dimensional solid (eight-nodebrick) element to represent the con-crete.

Discretization of the Structure

Nodes and subdivision lines andplanes were located at positions wherethere were abrupt changes in geometry,changes in material properties, changesin prestressing tendons, and points ofloadings. Figs. 5 and 6 show the longi-tudinal and cross-sectional discretiza-tion of the structure, respectively

The precise arrangement for the pre-stressing steel was not modeled becauseit would have required too many nodepoints. Instead, tendons were lumpedtogether and the cross-sectional areas of

110

C)LO Joint 1 2 3 4 5 6 8

noSegment O 2O Q ® lJ © lf1 f

3 (19) — (20)m 39)

3(2!) {22 ) {23} Qm

199)

(IBI) (182} {183)1

(219)

{241}

1202) {203)I (220)

Division I 2 ^ Q ^ ® ® ^ © ®7 8^ O9 f0 II 1^2 13 {4 15 16 9 IB

Section II 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 !71819 20 22(1), (2), (3),.... E lement Numbering

• Points of Loadings

Fig. 5. Longitudinal discretization pattern.

1

West East

30" 30" 8 16" 24" 24" 24" I6" 8 30" 30"

7 ••

6.25" 7 6710.25"

6.75' _7.37"5.386.00"3.50•,3.50° Note: I ° = 25.4 mm.

2" 30 6 24 24 24" 6" 10" 2"

Fig. 6. Typical discretization for interior section.

certain truss members were given dif-ferent values along the beam, depend-ing on the areas of steel lumped in eachdivision. The effective values of themodulus of elasticity for these trussmembers were used where appropriate.

Symmetry was used in the analysis ofthe bridge with one-half of the totalstructure represented by finite ele-ments.

Prestressing Analysis

The material properties of concreteand steel depend on the stress or strainstate of the material. The state of stressin a prestressed concrete element isproduced by the prestressing forces andtoads applied to the structure. There-fore, at any state of loading, stressescaused by prestressing forces should becalculated and added to those caused bythe applied loads in order to define thematerial properties of the element.

The force that a tendon will exertupon the structure is a function of sev-eral variables. The most important ofthese are the jacking forces, P, appliedat the anchors, losses of prestressingforce, and position and geometry of thetendon. In this study, the effects of allthese variables were taken into account.The time-dependent losses were calcu-lated in detail according to standard

procedures 1 ° and the equivalent loadmethod 1 ° 1 ' was used to compute theforces applied by the tendons on thestructure.

The effective prestress force afterlosses are accounted for is called Pe.These effective prestressing forces wererepresented as nodal forces on the finiteelement model. The effects of thechange in the vertical alignment of theprestressing tendons and the horizontalcurvature in the beam axis were consid-ered in this representation.

The initial stresses in the bars andtendons, caused by the effective pre-stressing forces Pe, were calculated bydividing the force Pe + A P, in any bar,by the cross-sectional area of that bar.Here, is the force caused by elasticshortening, and it was added to correctfor the elastic shortening effect whichtakes place when the effective pre-stressing forces are applied as nodalforces on the finite element nodel.

Cases of LoadingThe cases of loading needed in the

analysis procedure are defined as fol-lows:

— Experimentally, the deflectionsand surface strains due to live load (LL)only were measured. Thus, to comparethese experimental results, theoretical

112

LL LL— The beam

DL

Pe ------------ -----------e

Cracked region

(a) Load case 1, cracked beam

The beam

DL

P: -----------------------------------P.

(b) Load case 2, uncracked beam

Fig. 7. Cases of loadings for cracked and uncracked beams.

deflections and surface strains due to(LL) only are needed.

— To define the material propertiesafter any load increment, the totalstresses due to live load (LL), dead load(DL), and prestressing force, P,, in theconcrete and steel elements, areneeded.

Therefore, two load cases, as shown inFig. 7, were used after each load incre-ment. Load case I was used to find thetotal stresses needed to define the mate-rial properties. For concrete, thestresses obtained from the results of loadcase 1 were used directly to define thematerial properties for the concreteelements. However, for the steel, theinitial stresses caused by Pe + AP,.,forces were added to those obtainedfrom the output of load case 1 to obtainthe total stresses in the steel due to Pe +LL + DL. Here, the term A P, is addedto negate the elastic shortening effectwhich occurs to the steel, due to P e, inload case 1.

Deflections and surface strains due tolive load only were obtained by sub-tracting the results of load case 2 fromthe results of load case 1.

PROCEDURES FORANALYZING PRESTRESSED

CONCRETE STRUCTURE

This procedure was used to calculatemoment-curvature relationships at dif-ferent load levels. Theoretical deflec-tions were then calculated by loadingthe conjugate beam with the curvaturediagram. The girder was idealized as astraight line structure which had thesame geometry as the centroid of thecross section and torsion was neglectedin the analysis.

The following assumptions were usedin this analysis procedure:

1. Complete bond was assumed be-tween tendons and concrete. Therefore,changes in strain in the steel and con-crete were assumed to be the same.

2. After first cracking, tension in theconcrete was neglected.

3. Strains at the various section levelswere assumed to be directly propor-tional to the distance from neutral axis.

4. The actual stress-strain diagrams forthe prestressing bars and strands wereused in the analysis.

PCI JOURNAL/November-December 1987 113

5. At ultimate strength, the maximummoments and curvatures were calcu-lated using the rectangular stress distri-bution for the concrete and an ultimatestrain of 0.00.3.

Up to First CrackingThe total moment causing cracking

was found by setting the concrete stressat the bottom face, due to all loads plusthe prestress force, equal to the modulusof rupture of the concrete.

For moments smaller than the crack-ing moment, there was an uncrackedsection and the stresses were in theelastic range. The curvature was calcu-lated front the strain diagram and stressdue to all loads plus prestress force cal-culated using the combined axial forceplus bending moment equation. k°

After First CrackingFor cracked prestressed concrete

beams, calculation of stresses aftercracking is a complex matter. The neu-tral axis location and effective sectionproperties depend not only on thegeometry of the cross section and thematerial properties, as for reinforcedconcrete beams, but also on the axialprestressing force and the loading. Theaxial force applied by the steel to theconcrete is not constant after cracking,but depends on the loading and on thesection properties. Nilson[' has de-veloped a method for calculatingflexural stresses in prestressed beamsafter cracking. This method works forstresses in the elastic and inelasticranges but a complete stress-strain dia-gram for all materials must he known.

Ultimate Flexural StrengthThe ultimate strength of the girder

was determined by the strain compatibil-ity method using stress-strain diagrams ofthe prestressing tendons. A complete ex-planation of the strain compatibilitymethod has been given by Nilson. '5

BRIDGE TESTING

The Loading SystemThe bridge was tested with static

loading using the loading frames shownin Fig. 8. The loading frame includedfour hydraulic jacks. Directly above therock anchors, four openings for the jackswere cut through the concrete bridgedeck. The jacks were hinge connected tothe steel loading beams at their top endsand attached to the anchor assembly forthe rock anchors at their lower ends.The rock anchors were drilled andgrouted approximately 75 ft (23 m) intothe ground, 20 ft (6 m) of which were insound rock. Each rock anchor was capa-ble of resisting a load of 500 kips (2225kN), which was equal to the capacity ofthe loading beams.

Each loading beam consisted of two27 x 114 wide flange beams placed on aroller support at one end and a hingedsupport at the other. The beams deliv-ered the loads through 2 in. (51 mm)thick steel plates to concrete pedestalslocated over the webs to give a lon-gitudinal bending type failure. Theloads were monitored by separate pres-sure gages for each jack and verifiedthrough strain readings on each ram.

InstrumentationThe bridge was instrumented to

monitor deflections, transverse rota-tions, change in alignment, surfacestrains in the concrete and forces indiagonal and anchor tendons.

Deflections and Rotations

Deflections and rotations for all loadincrements were measured using sixdial gages with two placed at each endand two placed at midspan. All dialgages measured the displacements in adirection perpendicular to the bottomsurface of the girder.

After the girder started yielding, thedeflections were measured with an en-gineer's level, which was set tip at a

114

Fig. 8. The loading frame of the bridge.

distance from the girder, and two levelrods, which were permanently mountedat the midspan of the girder.

Strains at Midspan

Strains at the middle of Segment 9Bwere measured at each load incrementusing metal foil electrical resistancestrain gages. This segment, which is atmidspan, was chosen because of thelarge bending moment at that location.The strain gages were placed on theupper surface, the lower surface, andboth sides of the bridge girder as shownin Fig. 9. Only longitudinal gages wereused since bending was of primaryinterest. All strains were used with aModel P-350 Budd Strain Indicatorusing a half-bridge circuit with temper-ature compensation gages.

Testing ProcedureA crack survey was made for the out-

side and inside of the girder before

overload testing began. Most of thesecracks were caused by temperature andshrinkage. They were traced with blackfelt-tipped pens to differentiate themfrom those caused by live load.

The load was applied in increments of100 kips (445 kN), one increment eachday. After each increment of loading, thebridge was completely unloaded andreloaded incrementally in the next dayof testing. The testing of the bridge wascompleted in 9 days. For a typical day oftesting, the following steps were carriedout:

1. The pressure on the hydraulic ramswas released and the steel loadingbeams were lifted up until there was nocontact between the loading beams andbearing points on the concrete pedestals.

2. Initial readings were taken at zeroload for strains, deflections, horizontaloffsets, and elevations of the deflectionpoints on top of the girder.

3. The four rams were activated by anelectric pump, and the pressure read-

PCI JOURNAL^November-December 1987 115

120.0° 120.0" ^l

64.d" 64.0°

ITS.D^ ^15.0^

LongitudinalStrain Gage

o

O

io YiN-

JJ

Fig. 9. Locations of strain gages at middle of Segment 9.

ings were adjusted until the load level ofthe previous day was obtained.

4. Readings of strain gages, dial gages,horizontal offsets, and level rod read-ings were taken for the applied loadlevel.

5. Cracks were cracked, traced withred felt-tipped pens, identified with theload at which they formed, and re-corded. Hand magnifying lenses wereused in tracing the ends of the cracks.

6. On the next day of testing, Steps 1to 5 were repeated, except that the loadin Step 3 was increased by 100 kips (445kN).

Steps 1 to 4 were carried out beforesunrise in order to minimize the effect oftemperature on the readings, then thecrack survey was made during the daywith the live load still on the girder.

The bridge was loaded to failure onthe last day of testing. Ultimate load wasdefined by crushing of the concrete. afterthe prestressing reinforcement hadyielded and gone into the strain hard-ening range. After careful examination,there was no evidence of any shear orbond failures.

COMPARISONS OF TESTRESULTS WITH

THEORETICAL VALUESThe main purpose of this testing was

to study the elastic and inelastic be-havior of Girder B. Here, the experi-mentaI results are reported and com-pared with the theoretical values. Thetests focused mainly on the determina-tion of experimental deflection andstrains from which the stresses weredetermined. Theoretical results wereobtained by the finite element methodand by the standard theoretical flexuralanalysis of prestressed concrete struc-tures. Numerous comparisons weremade between observed and calculatedquantities, but only a few will be re-ported here. More comparisons areavailable in a report by McClure, West,and Abdel-Halim.'2

Deflections at MidspanTo obtain the total experimental de-

flection at any load, the permanent set

116

was added to the measured deflection.This was necessary so that all experi-mental deflections were measured fromthe same origin. Finite element deflec-tions were obtained by subtracting thedeflections due to load case 2 from loadcase 1 (see Fig. 7). The standard theo-retical analysis procedure for prestressedconcrete structures was used to calcu-late curvature at different load levels.Theoretical deflections were calculated.by loading the conjugate beam with thecurvature diagram.

The experimental and theoreticalmidspan deflections are shown in Fig.10. The figure shows good agreementbetween finite element and observeddeflections with the finite elementmodel showing less stiffness than thereal structure. That is, under a givenload, the simulated structure deformsmore than the actual structure.

Fig. 10 also shows the results of thestandard analysis for prestressed con-crete beams which shows good agree-ment with experimental values up to

first yielding. The remaining part of thecurve was defined by two points, Thefirst point was the first yielding of thebars and the second point was the ulti-mate condition assuming that concretefails by crushing when the compressionstrain reaches a value of 0.003. In thispart of the curve, the theoretical deflec-tions are much larger than the experi-mental ones.

Table 2 shows the observed, finiteelement and the standard calculatedvalues for loads and deflections at firstcracking, first yielding of bars, and atbridge failure, The first yielding load forall solutions was taken to be equal to thetheoretical yielding load, and the corre-sponding deflections were comparedaccordingly. The percentage differencesbetween the observed and theoreticalvalues are also shown in Table 2.

Longitudinal Stresses/Strains atMidspan

Finite element stresses were obtained

Ullimate Load

y • ^C7•First Yielding '" ^'of Bars i

-0-0 Experimental

-.------Finite -Finite Element/ Frst Crack

—r-- Standard Theory

Note: I in. = 25.4 mm,I kip = 4.440 kN.

Fig. 10. Load -deflection diagrams of Girder B.

1000-

900-

800'

700-

In 600.Y

a- 500C

400

300

200

S•

a 40 80 12.0 l60 20-0 24.0MIOSPAN DEFLECTION (inches)

PCI JOURNAL/November-December 1987 117

Table 2. Observed, finite element, and calculated values of loads and deflections.

StageLoad anddeflection

Observedvalues

Finiteelementvalues

Percentdifference

Standardcalculated

valuesPercent

difference

First Load (kips) 376.0 420.0 +11.70 439.0 +16.76cracking Deflection (in.) 1.49 2.01 +34.90 2.79 +87.25

First Load (kips) 700.0 700.0 0.00 700.0 0.00yielding Deflection (in.) 6.00 7.68 +28.00 5.29 -11.83

Failure Load (kips) 955.0 920.0 -3.66 901.() -5.65Deflection (in.) 21.27 22.10 +3.90 43.49 +104.47

Note: 1 in. = 25.4 mm; 1 kip = 4.4471 kN.

Table 3. Observed, finite element and calculated strains at top surfaces.

FiniteApplied Observed element Calculatedload (P) strains strains Percent strains Percent(kips) (. in,/in.) (s in./in.) difference (µ in./in.) difference

439 -254 -302 +18.90 -350 +37.80600 -359 -509 +41.78 -521 +45.13700 -449 -616 +37.19 -630 +40.31

Note: 1 kip = 4.448 kN.

by subtracting the stresses of load case 2from the stresses of load case 1 (seeFig.7), Then the longitudinal strainswere calculated using the generalizedHooke's law for a three-dimensionalstate of stress. Here again, the perma-nent set strains should be added to themeasured strains in order to obtain theabsolute surface strains which should hecompared with the finite elementstrains. However, permanent set strainswere not measured, and this was one ofthe main reasons for the deviation instrain results between the finite ele-ment analysis and test results.

A comparison of measured and finiteelement strains did show fair agreementup to first yielding where permanent setstrains were small but did show a devia-tion of results above first yielding wherepermanent set strains were relativelylarge. Strains increased almost linearly

up to the first cracking load of 376 kips(1670 kN). At a load of 476 kips (2120kN), the strain gages located near thebottom became inoperative due tocracks developing. 12.13

A sample for the experimental and fi-nite element strains obtained is shownby Fig. 11 at a load on the bridge equal to476 kips (2120 kN), which is a loadbelow first yielding. The figure shows areasonable agreement between ob-served and finite element strains. Thetrend observed for deflections is sus-tained here; that is, the experimental re-sults are smaller than the finite elementresults.

Based on the standard theoreticalanalysis, compression strains at the topsurface of the girder were calculated atloads of 439, 600, and 700 kips (1950,2670, and 3110 kN). These strains werecompared with the average compression

118

Observed Strains (/1. in/in)Finite Element Strains (p.m/in)

-3 W77—^--__ -377 -346 -312 -299279) (-322) (-343) (-270) ^--- (-253:

-150 -129(-177) (-124)

^ ObservedElement

129 1! 166

(99) (114)

Fig. 11, Longitudinal surface strains at middle of Segment 9 for load of 476 kips (2120 kN).

strains obtained experimentally and bythe finite element method. The resultsare shown in Table 3. This table indi-cates that the finite element methodgives better agreement with the ob-served results than does the standardtheoretical analysis. The same indica-tion was obtained by the load-deflectionresponse (see Fig. 10). The percentagedifferences between the observed andtheoretical values are also shown inTable 3.

Cracking and Failure of the Bridge

In the first and second days of testing,up to load P = 276 kips (1228 kN), therewas no visible cracking on the bottomsurface of.the bridge. In the third clay oftesting, at load P – 376 kips (1672 kN),the first visible cracking was observed atthe bottom surface between the pointsof loading. As the load was increased,cracks increased in number, and thosebetween the points of loading widenedand extended toward the compressionzone. In the transverse direction, it wasnoticed that cracks began at the innerside of the girder and progressed gradu-ally toward the outer side.

Nothing unusual was noticed until theeighth day of testing, at load P = 876kips (3876 kN), when two Io>icl sounds

were heard at different times and thepressure gage readings dropped downslightly. It sounded like a strand or bartendon had broken each time. At thisload, the cracks at Joints 8 and 9 openedwidely and extended upward toward thetop slab.

In the last day of testing, at load P =945 kips (4203 kN), two events occurred:first, a noise was heard and the deflec-tion increased suddenly by 0.25 in. (6.35mm); second, two loud sounds, simlartothose which occurred at P = 876 kips(3896 kN), were heard, Again, de-flection increased suddenly by another0.25 in. (6.35 min). Pressure readingstarted to fall off, but reached a constantvalue. As the load was slightly increasedto the failure load of P = 953 kips (4250kN), the crack at one of the middle joints(Joint 8) opened widely and the con-crete in the compression zone crushedand spalled on the surface. The mode offailure of the bridge is shown in Fig. 12.Upon inspection of Joint 8, it was foundthat all the strands were broken and thesolid bars were holding the bridge inplace.

The finite element load at first crack-ing was estimated at P = 420 kips (1868kN) which is 11.70 percent larger thanthe observed value, The cracking load

PCI JOURNAUNovember-December 1987 119

"I,.

(a) Plan (bottom surface) (b) Elevation

Fig. 12. Mode of failure of the bridge.

calculated from conventional theory wasP = 439 kips (1953 kN) which is 16.76percent larger than the observed value.Also, the finite element load at failurewas estimated atP = 920 kips (4092 kN)which is 3.66 percent smaller than theobserved value. The failure load calcu-lated from conventional theory usingstrain compatibility was P = 901 kips(4000 kN) which is 5.65 percent smallerthan the observed value. These valuesare given in Table 2.

With the failure load of 955 kips (4250kN) on the girder, the ultimate live loadmoment in the midspan section be-tween points of loading was 26,024kip-ft (35, 288 kN •m) for the 121 ft (36.9m) simply supported span. If Girder Btakes two lanes of AASHTO HS20-44design load plus 20.3 percent for impact,the design live load moment would be:

2 (1901.3)(1.203)= 4575 kip-ft (6204 kNnn)

The load factor for the live load would

then be 26,02414,575 = 5.69, assuming aload factor for dead load equal to 1,00.

For a dead load of 4.514 kips/ft (65.86kN/m), the maximum dead load momentat midspan would be:

1/8 (4.514)(121)2= 8261 kip-ft (11,201 kN•n)

The load factor for live load wouldthen he 134,285 - 1.3(8261)1/4575 = 5.15if the load factor for dead load was con-sidered to be 1.3 as recommended byAASHTO. Both of these live load factorsexceed the 2.17 value recommended bythe current AASHTO specifications forload factor design. The reason for theexcessive load factor for live load is thatextra steel was required in the girder tosatisfy allowable stresses under unfac-tored loads.

Crack PatternsSketches were drawn for the crack

patterns for the inside and outside of

120

® ^o

it 8 w Jt 9

Girder B, at load P = 776 kips (3453 kN),and at failure. Fig. 13 shows the outsidecrack pattern for the bottom of Girder Bat failure for the three segments nearestmidspan. At failure most of the crackingoccurred on these three segments. Dot-ted lines on this figure represent thecracks that occurred after load P = 776kips (3450 kN) up to failure. The thickerline indicates the joint that opened wideand caused the failure.

It should be noted that all cracks be-tween the points of loading were flexuralcracks, and as one goes farther from thepoints of loading, the cracks bend morein a diagonal direction, These areknown as flexure-shear cracks. It can benoted also that at the maximum loadlevel, there was a tendency in segmentalstructures to concentrate strains or cur-vatures and yielding of tendons at one ormore joint locations. This is because themild reinforcing bars are not continuousacross the joint. For Girder B, at load P= 945 kips (4200 kN), Joints 8 and 9were wide open, and strain concen-trations were approximately equal atthese joints. At the failure load of P =955 kips (4250 kN), however, Joint 9started to close, all strain concentrationsappeared at Joint 8, and a flexural typefailure occurred at this joint

CONCLUSIONSThe material reported in this paper

does not cover all of the topics that werecovered in the research study. Morecomprehensive findings have been re-ported by McClure, West, and Abdel-Halim. 12,1 The following conclusionscan be made as a result of this study:

1. The results of the three-dimen-sional finite element analysis, deflec-tions and stresses (strains), which usedthe Kostovos and Newman materialmodel for concrete, compared rea-sonably well with experimental valuesin the elastic and the post-crackingranges.

2. The experimental deflections andstrains (stresses) at midspan from lon-gitudinal bending were always less thanthe corresponding finite element values.This indicates that the actual structure isstiffer than that predicted by theory.

3. Cracking, first yielding, and ulti-mate loads were found to be in goodagreement with their respective finiteelement values.

4. The general analysis approachbased upon the finite element methodgives a great amount of information ondeflections, strains, stresses, and forcesin the prestressing steel, which can beused in judging the behavior of bridgesif the structure is properly modeled.

5. Theoretical deflection and strains(stresses) obtained by the standardanalysis procedure for prestressed con-crete structures were found to agreeclosely with observed values up to firstyielding, but after first yielding agree-ment was not good.

6. The standard prestressed analysiscan be used to calculate loads, deflec-tions, and strains (stresses), tip to thefirst yielding of the steel, but after firstyielding, calculations are not reliable.The ultimate load still can be conserva-tively predicted by these standardmethods with a good degree of accu-rac y.

7. A bending type failure occurredbetween the points of loading. Therewas no sign of a shear type distress nearthe ends. The bridge had an adequatebut conservative factor of safety againstfailure.

8. The standard prestress analysis wasused in the design of the experimentalsegmental bridge for longitudinalbending, shear, and torsion. For futuredesigns of this type, the standard pre-stress analysis can he safely used. How-ever, an analysis based on the finiteelement method would also give safe re-sults which are less conservative. Someeconomy in design might be achievedby using the finite element method ofanalysis in the design.

122

ACKNOWLEDGMENT

This study covers a portion of a major6-year investigation on an experimentalsegmental bridge which was conductedat the Pennsylvania Transportation In-stitute located at The PennsylvaniaState University. The study was spon-sored and funded by the PennsylvaniaDepartment of Transportation and theFederal Highway Administration. Thecontents of this paper reflect the viewsof the authors who are responsible forthe facts and the accuracy of the data.The contents do not necessarily reflectthe official views or policies of the spon-sors.

REFERENCES

1. Koretzky, H. P., and Tschernelf, A. T.,Final Report for Research Project No.72-9 on the Design of an ExperimentalPost-tensioned Segmental Concrete BoxGirder Bridge, Pennsylvania Depart-ment of Transportation, Publication No.118, September 1974.

2. Chen, W. F., Plasticity in ReinforcedConcrete, McGraw-Hill Book Company,New York, N.Y., 1982.

3. Kostovos, M. D., and Newman, J. B.,"Generalized Stress-Strain Relations forConcrete," Jou rnal of the EngineeringMechanics Division, American Society ofCivil Engineers, V. 104, No. EM4, Au-gust 1978, pp. 845-856.

4. Kostovos, M. D., and Newman, J. B., "AMathematical Description of the Defor-mational Behavior of Concrete UnderComplex Loading," Magazine of Con-crete Research (London), V. 31, No. 107,June 1979, pp. 77-90.

5. Kostovos, M. D., "A Mathematical De-scription of the Strength Properties of Con-crete Under Generalized Stress," Maga-zine of Concrete Research (London), V.31, No. 108, September 1979, pp. 151-158.

6. Kostovos, M. D., and Newman, J. B.,"Behavior of Concrete Under MultiaxialStress," ACI Journal, V. 74, No. 9, Sep-tember 1977, pp. 443-446.

7. Liu, T. C. Y., Nilson, A. H., and Slate,F. 0., "Biaxial Stress-Strain Relations forConcrete," journal of the Structural Di-vision, American Society of Civil En-gineers, V. 98, No. ST5, ProceedingsPaper 8905, May 1972, pp. 1-25-1934.

8. Hand, F. R., Pecknold, D. A., andSchnobrich, W. C., "A Layered FiniteElement Nonlinear Analysis of Rein-forced Concrete Plates and Shells,"Structural Research Series No. 389, CivilEngineering Studies, University of Il-linois, Urbana--Champaign, August1972.

9. Bathe, K. J., Wilson, E. L., and Paterson,F. E., "SAPIV—A Structural AnalysisProgram for Static and Dynamic Analysisof Linear Structural Systems," EERCReport No. 73-1I, College of Engineer-ing, University of California, Berkeley,June 1973, Revised April 1974.

10. Nilson, A. H., Design of PrestressedConcrete, John Wiley & Sons, New York,1978.

11. Lin, T. Y., and Burns N. H., Design ofPrestressed Concrete Structures, ThirdEdition, John Wiley & Sons, New York,N.Y., 1981.

12. McClure, R. M., West, H. Ff., andAbdel-Halim, M., Overload Testing ofan Experimental Segmental Bridge,Interim Report, Project 75-3, ThePennsylvania Transportation Institute,University Park, Pennsylvania, July1982.

13. Abdel-Halim, M. A. H., Nonlinear Anal-ysis of a Segmental Concrete Bridge byFinite Element Method, PhD Thesis,The Pennsylvania State University,March 1982.

14, American Association of State Highwayand Transportation Officials, StandardSpecifications for Highwa y, Bridges,Washington, D.C., 1983.

NOTE: Discussion of this article is invited. Please submityour comments to PCI Headquarters by August 1, 1988.

PCI JOURNAL/November-December 1987 123