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PCI BRIDGE DESIGN MANUAL CHAPTER 15

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NOTATION

15.1 INTRODUCTION

15.1.1 Seismic Activity

15.1.2 Seismic Design Criteria

15.1.2.1 Background

15.1.2.2 Performance Objectives

15.1.2.3 Current Design Specifications

15.1.2.3.1 Standard Specifications

15.1.2.3.2 Caltrans Specifications

15.1.2.3.3 LRFD Specifications

15.1.2.4 Effect of Local Geology and Soil Conditions

15.2 SEISMIC RESISTANT PRECAST CONCRETE BRIDGES

15.2.1 Spliced Precast Concrete Beam Bridges

15.2.2 Current Practice

15.2.3 Seismic Response Characteristics of Precast Concrete Bridge Systems

15.2.4 Integral Precast Concrete Beam System

15.2.4.1 Precast Concrete Pier Segment

15.2.4.2 Cast-in-Place Concrete Bent Cap

15.2.4.3 Drop-In Precast Concrete Segment

15.2.5 Seismic Details

15.2.5.1 Superstructure-to-Bent Cap Connection

15.2.5.2 Ductility of Precast Concrete Piles 15.2.5.3 Pile-to-Cap Connections

15.2.6 Isolation Methods

15.3 SEISMIC ANALYSIS AND DESIGN

15.3.1 Analysis Methods

15.3.1.1 Conventional Force Method

15.3.1.2 Displacement Ductility Method

15.3.2 Computer Modeling

15.3.3 Seismic Design Issues

15.3.3.1 Causes of Failures

15.3.3.2 Preliminary Design Recommendations

15.4 SEISMIC DESIGN EXAMPLEBULB-TEE, TWO SPANS,DESIGNED IN ACCORDANCE WITH STANDARDSPECIFICATIONS DIVISION I-A

15.4.1 Introduction

15.4.1.1 Bridge Geometry

15.4.1.2 Level of Precision

TABLE OF CONTENTSSEISMIC DESIGN


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15.4.2 Material Properties

15.4.3 Seismic Analysis in Transverse Direction

15.4.3.1 Section Properties

15.4.3.1.1 Beam Properties

15.4.3.1.2 Composite Section Properties

15.4.3.1.3 Column Properties

15.4.3.2 Tributary Dead Load

15.4.3.3 Equivalent Transverse Stiffness

15.4.3.4 Period of Structure in the Transverse Direction

15.4.3.5 Elastic Seismic Response Coefficient

15.4.3.6 Column Forces in the Transverse Direction

15.4.4 Seismic Analysis in Longitudinal Direction

15.4.4.1 Equivalent Longitudinal Stiffness

15.4.4.2 Period of Structure in the Longitudinal Direction

15.4.4.3 Elastic Seismic Response Coefficient

15.4.4.4 Column Forces in the Longitudinal Direction

15.4.5 Combination of Orthogonal Forces

15.4.6 Abutment Design Forces

15.4.7 Minimum Abutment Seat Width

15.5 SEISMIC DESIGN EXAMPLEINTEGRAL BENT CAP

15.5.1 Introduction

15.5.1.1 Bent Cap Geometry

15.5.1.2 Reinforcement15.5.1.3 Material Properties

15.5.1.4 Forces

15.5.1.5 Precision

15.5.2 Design Procedure

15.5.3 Principal Stresses in the Bent Cap

15.5.4 Joint Reinforcement Design

15.5.5 Shear-Friction Analysis

15.6 CALTRANS RESEARCH

15.6.1 Test Model Set-Up

15.6.2 Test Results

15.6.2.1 Columns

15.6.2.2 Superstructure

15.7 REFERENCES

TABLE OF CONTENTSSEISMIC DESIGN


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NOTATIONSEISMIC DESIGN

A = total section areaA = seismic acceleration coefficientAc = area of pile core measured to the outside of the transverse spiral rein-

forcement

Ag = gross area of pileAh = area of hoop reinforcementAi = area of a segment in a bent cap sectionAjv = vertical reinforcement to be placed over a distance of hb/2 from the

column face

Aps = area of prestressing steelARS = acceleration response spectrumAs = area of reinforcing steel passing through shear plane including

prestressing steel

Asc = total area of longitudinal reinforcement in column section

Avi = interior vertical joint stirrup areabb = bent cap width parallel to the longitudinal axis of the bridgebje = effective width of bent capCb = compression forceCc = column compression forceCs(long) = elastic seismic response coefficient in the longitudinal directionCs(tr) = elastic seismic response coefficient in the transverse directionD = column diameterD = core diameter of spirally confined columnDi = force in diagonal compression strut within the superstructure/

substructure joint where i = 1 through 3Ecc = modulus of elasticity of deck and column concreteEcs = modulus of elasticity of concrete in the beam and bent capEs = modulus of elasticity of nonprestressed reinforcementF = bent cap prestressing force after all lossesFi = force in each quadrantfc = specified compressive strength of concretefoyc = over-strength stress of column reinforcement including strain hardeningfh = average horizontal stress (due to prestress) in the horizontal directionfv = average joint axial stress in the vertical directionfy = specified yield strength of non-prestressed reinforcementfyh = yield strength of hoop or spiral reinforcementfyv = yield strength of joint vertical reinforcementg = gravitational acceleration (32.2 ft/sec/sec)H = average column height in framehb = cap beam section depthhc = column length from top of footing to center of gravity of the superstructureIC = importance classification


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Ic = moment of inertia of columnIs = moment of inertia of superstructure cross-section about vertical axis

through centroid

K = equivalent transverse stiffness

Kc = column shear stiffnessL = span lengthL = length of longitudinal frame between expansion jointsla = assumed length of column anchorage reinforcement in jointM = total contributory mass of superstructure and columnMobot = column over-strength moment capacity at column bottomMoi,bentcap = moment at middepth of bent capML = longitudinal momentMT = transverse momentMotop = column over-strength moment capacity at column topN = minimum abutment support lengthn = modular ratioP = axial forcePDL,BOT = axial force due to dead load at bottom of columnPDL,TOP = axial force due to dead load at top of columnPe = axial compression load on the pilept = principal tensile stressq = uniformly distributed loadR = response modification factor

Rcol = column seismic shear forceRSA = response spectrum analysisS = angle of skew (degrees) measured from a line normal to the spanS = site coefficientSPC = seismic performance categorysreqd = required spacing of hoop reinforcementT = external torsionTc = partial tension force in columnTc = partial tension force in columnT(long) = period of structure in the longitudinal directionT(tr) = period of structure in the transverse directionVc = column shear forceVoi,column = horizontal shear force at top of columnVjh = horizontal joint shear forcevjh = nominal horizontal shear stress in the jointVL = longitudinal shear forceVT = transverse shear forceVT(Abutment) = abutment transverse shear force



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VV = vertical shear forceW = total contributory weight of superstructure and columnxi, yi = distances defining location of quadrant force, Fi

Yb = distance to centroid of superstructure cross-section from extreme

bottom fiberZ = force reduction factor = longitudinal or transverse superstructure displacement at intermedi-

ate support(s)

1 = longitudinal or transverse superstructure displacement at intermedi-ate support(s)

2 = longitudinal or transverse superstructure displacement at intermedi-ate support(s)

= coefficient of friction over the interfaces = ratio of volume of spiral reinforcement to total volume of concrete

core (out-to-out of spiral)

s,min = minimum required value ofs = shear friction stress



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The threat of seismic hazard is often thought to be limited to California and a fewother western states. However, the discovery of new fault zones and an increasedunderstanding of their activity have prompted many other states to include someform of seismic design requirements in their bridge design specifications. Althoughmost states have not had significant levels of earthquake activity during recent history,the occurrence of a few notable earthquakes indicates that there may be a significant

earthquake hazard in many states. For example, the most notable earthquake affect-ing South Carolina was the one that shook the Charleston-Summervale area in 1886causing loss of life and considerable damage. Small earthquakes still occur in theregion and seismologists indicate the potential for another damaging earthquake.

Other notable sources of earthquakes include the New Madrid Seismic Zone, theCentral Virginia Seismic Zone; the Giles County, Virginia, Seismic Zone; and theEastern Tennessee (or Southern Appalachian) Seismic Zone. Low seismic waveattenuation in the Eastern United States has the potential to cause significant shak-ing over broad areas, sometimes covering several states. The 1811-1812 New Madridearthquakes, for example, caused seismic shaking of Intensity VI on the ModifiedMercalli Intensity scale as far away as South Carolina. Figure 15.1.1-1, from the

Standard Specifications, shows contours of current estimates of peak ground accelera-tions, expressed in terms of the gravitational acceleration coefficient, g. The accelera-tions shown have a 10% probability of being exceeded in a 50-year period.

The first United States highway bridge design standard was published in 1931 by American Association of State Highway Officials (AASHO), predecessor to theAmerican Association of State Highway and Transportation Officials (AASHTO).Neither the first edition nor subsequent editions of the standard published priorto 1941 addressed seismic design. The editions published in the 1940s mentionedseismic loading only to the extent that bridge structures must be proportioned for

earthquake stresses.

The California State Department of Transportation (Caltrans) has been at the fore-front in the development of specific seismic criteria for bridges. The first generalrequirements for seismic design of bridges were formulated in 1940. Specific forcelevel recommendations for earthquake design were established in 1943.

The collapse of several California freeway structures during the 1971 San Fernandoearthquake was a major turning point in the development of seismic design criteriafor bridges in the United States. Prior to 1971, AASHTO and Caltrans specifications

SEISMIC DESIGN

15.1INTRODUCTION

15.1.1Seismic Activity

15.1.2Seismic Design Criteria

15.1.2.1Background


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Caltrans bridge engineering practice generally embraced deterministic groundmotion hazards as established based on Caltrans 1996 California Seismic HazardMap. A technical report published with the 1996 Map can be reviewed for furtherinformation on the considered seismic sources. Caltrans uses the mean event forstandard practice and refers to it as the Maximum Credible Earthquake (MCE).

Caltrans Seismic Design Criteria (SDC) V1.3, 2004, documents the current stateof the practice. These criteria are intended to achieve a No Collapse condition forstandard ordinary bridges using one level of Seismic Safety Evaluation.

Design spectra for three magnitudes of earthquake established in ATC 32 is used forthe one level Seismic Safety Evaluation unless site-specific spectrum is recommendedaccording to SDC V1.3. Design spectrum adjustment for long period structures andproximity to a fault is prescribed in SDC V1.3. The SDC uses a strictly displacementapproach that compares displacement demands obtained from an elastic analysis todisplacements capacities obtained from inelastic static analysis commonly referredto as Push Over Analysis. The Engineer is referred to SDC V1.3 for a thoroughdescription of the displacement approach adopted and practiced in California.

The AASHTO LRFD Specifications incorporates many of the seismic provisions ofthe 1992 Standard Specifications, but has updated them in light of new research devel-opments. The principal areas where provisions were updated are:

1. The introduction of separate soil profile site coefficients and seismic responsecoefficients (response spectra) for soft soil conditions.

2. Definition of three levels of importance, namely critical, essential and other asopposed to the two defined in previous AASHTO provisions. The importancelevel is used to specify the degree of damage permitted by the use of appropriateResponse Modification Factors (R factors) in the seismic design procedure.

As more is learned about the effect of soil-structure interaction (SSI), new guidelines andprocedures continue to be developed to enhance the accuracy of predictions of the bridgeresponse to seismic loading. However, practical limitations prevent detailed incorporationof SSI effects in every project. Where a situation warrants the development of a site-spe-cific spectra, extra effort in site investigation, laboratory testing and modeling may berequired. On very long bridges, the subsurface conditions may vary to the extent that asingle-response spectra is not an accurate representation of the soil conditions. In thesecases, multiple-support excitations may be specified. Multiple-support excitation requiresthe use of time history analysis, i.e., RSA cannot be used.

15.1.2.3.3LRFD Specifications

15.1.2.4Effect of Local Geology

and Soil Conditions

SEISMIC DESIGN15.1.2.3.2 Caltrans Specifications/15.1.2.4 Effect of Local Geology and Soil Conditions

15.1.2.3.2Caltrans Specifications


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On large, important structures where the presence of large piles or drilled shaftscan significantly influence the soil response, free-field response spectra may not beaccurate. In these exceptional situations, state-of-the-art knowledge in the area of SSIshould be utilized to improve prediction accuracy.

In addition to SSI analyses, site stability issues should be addressed. These issuesinclude soil liquefaction, soft-clay sites and slope hazards. Soil liquefaction includesthe analysis for lateral spread, loss of support, dynamic settlement, as well as possiblemeans of mitigation (site improvements). Large site amplification effects are usuallyconsidered for soft-clay sites. Earthquakes have been recognized as major causes ofslope hazards.

Spliced precast concrete beam techniques have received interest in recent years as evi-denced by the amount of research in this area and the number of spliced-beam bridg-es built. The impressive performance and the increased use of these techniques signifyan emerging application, which is expected to expand in coming years. Spliced beamsprovide an effective alternative to steel and cast-in-place concrete bridges in the 150-to 300-ft span range, a range previously unattainable by precast concrete beams. Asa result of continuity, spliced-beam bridges also provide increased redundancy andimproved ductility and seismic behavior. The precast, prestressed concrete industry,in cooperation with Caltrans, has sponsored the development of a competitive pre-cast concrete beam system that can be used in areas of high seismicity.

Seismic design practices and requirements vary from region to region, depending

on the level of anticipated seismic activity. For example, integral superstructure-to-substructure connections may not be necessary to resist earthquake forces in areas oflow to moderate seismicity. However, precast concrete bridge systems developed forsome level of seismic resistance may offer certain desirable qualities which can resultin better and more economical designs, even when earthquakes are not among themajor design considerations.

The most common form of concrete bridge consists of a cast-in-place (CIP) concretedeck on precast, prestressed concrete beams. The beams are set on elastomeric bear-ing pads, which rest on the multi-column bents consisting of circular or rectangularcolumns with a rectangular bent cap or abutments. The columns, in turn, are sup-ported on either isolated or combined footings.

In California, cast-in-place prestressed concrete box girders monolithically connectedto the substructure are used to create longitudinal frames with multiple spans. Thebox girders are, in some cases, supported on single columns. Multi-column bentsare usually provided on wider bridges. Unlike the precast concrete beam system ofa drop-cap pier, the CIP box girder system with a monolithic connection to thesubstructure resists longitudinal forces in double curvature bending of the columnas shown in Figure 15.2.2-1. This is a decided advantage in areas where large longi-tudinal forces are possible such as from a seismic event. However, CIP constructionrequires extensive falsework and formwork, which can result in lengthy periods forconstruction with possible traffic disruptions in roadways below the bridge.

15.2SEISMIC RESISTANTPRECAST CONCRETE

BRIDGES

15.2.1Spliced Precast Concrete

Beam Bridges

15.2.2

Current Practice

SEISMIC DESIGN15.1.2.4 Effect of Local Geology and Soil Conditions/15.2.2 Current Practice


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The lack of monolithic action between the superstructure and bent cap in precast, prestressedconcrete beam systems causes the column tops to act as a pinned connection. Consequently,

while the transverse stability of multi-column bents is ensured by frame action in that direc-tion, stability in the longitudinal direction requires the column bases to be fixed to thefoundation supports. This requirement places substantial force demands on the foundationsof multi-column bents, particularly in areas of moderate to high seismicity. Developing amoment connection between the superstructure and substructure makes it possible to intro-duce a pinned connection at the column bases. This results in less expensive foundations.

Integral bent caps are also beneficial in precast, prestressed concrete beam systems with single-column bents. By introducing moment continuity at the connectionbetween the superstructure and the cap, the columns are forced into double-curva-ture bending, which tends to substantially reduce their moment demands. As a result,the sizes and overall cost of the adjoining foundations are also reduced.

In a seismic event, it is essential to have plastic hinging occur in the column rather thanthe superstructure or footing. This is because plastic hinging is accompanied by a certaindegree of damage in the form of inelastic displacements, cracked and spalled concrete andyielded reinforcement. Allowing such damage to occur in the superstructure near the ends

of a span could reduce the load-carrying capacity of the superstructure, thereby increasingthe likelihood of collapse. Damage to a footing or pile system is not easily detected andis extremely difficult to repair. Plastic hinging in the column can be quickly identified byinspection and sometimes repaired. More importantly, a properly confined column willcontinue to carry axial load and therefore structural collapse may be avoided.

The longitudinal moment in a typical beam near the pier consists of the sum of the deadload and a portion of the column seismic (plastic) moment on one side of the pier, and thedifference between dead load and the remaining portion of the column seismic (plastic)moment on the other side. The result is a high, rapidly changing moment on the sidewhere the moments are additive and a smaller, relatively constant positive moment on the

15.2.3Seismic Response

Characteristics of PrecastConcrete Bridge Systems

SEISMIC DESIGN15.2.2 Current Practice/15.2.3 Seismic Response Characteristics of Precast Concrete Bridge Systems

Precast Beam (Non-Integral) System - Single Curvature

Integral Bent System - Double Curvature

Shape

Force

Force

Moment diagram

Shape Moment diagram

Fixed

Fixed

Fixed

Pinned

Figure 15.2.2-1Single- versus Double-

Curvature Column


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opposite side. This distribution is reversible depending on the direction of the earthquakeforce. Therefore, the beams must be designed to carry both a high negative moment near

the pier, and a smaller positive moment for an extended length on each side of the pier (seeFigure 15.2.3-1). The dead load moment considered should properly account for time-dependent and construction staging effects, which are not included in Figure 15.2.3-1.

Recently, a precast concrete girder system was developed, tested and introduced inCalifornia to address the requirements of superstructure and substructure continuity, aes-thetics and minimized traffic impact during construction. Cross-sections for both singleand two-column bents are shown in Figure 15.2.4-1. The superstructure of this bridgesystem consists of three basic components as described in the following sections.

15.2.4Integral Precast Concrete

Beam System

SEISMIC DESIGN15.2.3 Seismic Response Characteristics of Precast Concrete Bridge Systems/

15.2.4 Integral Precast Concrete Beam System

30'

Support atexpansion joint

or abutment

140' 160' 160'

Reactionfrom

adjacentframe

Field splice

Dead loadEarthquakeDead load + earthquake

Figure 15.2.3-1Moment Distribution

along the Superstructure of aLongitudinal Frame Unit

Two-Column Bent

Single-Column Bent

Figure 15.2.4-1

Typical Bridge Cross-Sections withSingle- and Two-Column Bents


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The precast concrete pier segment as shown in Figure 15.2.4.1-1. It is a variablelength section comprised of a prismatic bulb-tee beam continuous over the columns.The length is variable in order to locate the splice at the approximate point of inflec-tion for a given span arrangement. Subject to weight limitations, the web in the cen-tral portion of the pier segment may be thickened to accommodate the large negative

moments and shear forces at the pier. The section is pretensioned for shipping andhandling stresses and for a portion of the service negative moment over the pier. Thepier segment also contains ducts for two stages of longitudinal post-tensioning: onefor the beam-only section and one for the beam-deck composite section.

This portion of the system provides for the connection of the precast pier segmentto the column as shown in Figure 15.2.4.2-1. The pier diaphragm is formed and

poured around the precast pier segments and the entire system is connected bymeans of transverse post-tensioning through the complete length of the pier cap.Reinforcing steel in the top slab and in the cap improves the monolithic response ofthe superstructure-column interface. The principal mechanism for developing mono-lithic response is a combination of torsion and shear-friction through the bent cap,which then translates into longitudinal bending of the beams. The correspondingbent cap design procedure is presented in Example 15.5.

This drop-in section traverses the positive moment region of a span and utilizesa standard bulb-tee shape. It is pretensioned for lifting and handling stresses andcontains ducts for the two-stage post-tensioning of the continuous beam and com-

15.2.4.1Precast Concrete

Pier Segment

15.2.4.2Cast-in-Place

Concrete Bent Cap

15.2.4.3Drop-In Precast

Concrete Segment

SEISMIC DESIGN15.2.4.1 Precast Concrete Pier Segment/15.2.4.3 Drop-In Precast Concrete Segment

Elevation

in girders(full length)

for bent cap

Temporary shoring to supportgirders and formwork

Section A-A

CIP closure jointTemporary tie down or shoring

A

A

CIP Closure Joint

Variable length pier segment

40'-0" Standard length

in bent capPost-tensioning

in bent cap connectors

Erectiontension ductsSplice post-

Rebar splice

bracket

Post-tensioning

Continuity tendons

Figure 15.2.4.1-1Details at Integral Cap and CIP Closure Joint


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posite sections. See Figure 15.2.4.3-1. The drop-in segment is supported from thepier segments by erection brackets as shown in Figure 15.2.4.1-1 and described inChapter 11.

SEISMIC DESIGN15.2.4.3 Drop-In Precast Concrete Segment

Typical Section at Pier

Section A-A (beams not shown)

in bent cap

A

Post-tensioning

AFigure 15.2.4.2-1

Longitudinal Section andCross-Section of CIP Pier Cap

Typical drop-in segment

Stage 2 P-T

Longitudinal Section

Section A-A

Stage 1 P-T

CIP splice (typ.)

Sym. about C

A

A

L

P-T ducts

Pretensioningstrands

Pier segment

Figure 15.2.4.3-1Longitudinal Sectionand Cross-Section of

Drop-In Segment


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One of the important features of the integral system is its minimal impact on trafficduring the construction process, compared to CIP box-girder systems. This is of criti-cal interest in regions where bridge construction occurs in urban areas with minimalvertical clearances. The proposed construction sequence using the system for a two-span bridge is illustrated in Figure 15.2.4.3-2. Additional details for spliced beams

are found in Chapter 11.

The goal of a seismic connection at this location is to transfer the plastic momentdemands at the top of the column into the superstructure without yielding eitherthe connection itself or the beam ends. To achieve this, both the connection andthe beam ends must be designed to provide a design strength exceeding the requiredstrength from the forces transferred i.e., capacity must exceed demand. Additionally,the connection should be detailed to ensure adequate distribution of the longitudinalmoment from the top of the column to the various beams.

SEISMIC DESIGN15.2.4.3 Drop-In Precast Concrete Segment/15.2.5.1 Superstructure-to-Bent Cap Connection

15.2.5

Seismic Details

15.2.5.1Superstructure-to-Bent

Cap Connection

Stage 5 (days 39 thru 41): Post-tension bent cap

Stage 6A (days 43 thru 44): Erect left span segments and tie down

Stage 6B (days 45 thru 46): Erect right span segments

Stage 7 (days 49 thru 55): Cast closure joints

Stage 8 (days 56 thru 57): Tension first phase tendons

Stage 9 (days 58 thru 72): Construct cast-in-place deck

Stage 10 (day 73): Tension second phase tendons

Stage 11 (days 74 thru 83): Complete bridge

Stage 4 (days 29 thru 38): Form and cast bent cap

Stage 3 (days 19 thru 28): Erect segments on temporary suppports

Stage 2 ( day 2): Detension strands

Stage 1 (day 1): Pretension strands and cast girder concrete

Figure 15.2.4.3-2Construction Sequence for Bulb-Tee Bridge


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The design procedure involves the following steps:

1. Determination of the plastic moment capacities at the top and bottom of thecolumn.

2. Calculation of the principal stresses in the bent cap due to joint shear.

3. Design of joint reinforcement.4. A torsion-shear friction analysis to verify the ability of the bent cap to transfer the

column plastic moments to the bridge superstructure.

5. A check of the bridge superstructure capacity to ensure that the plastic hingesform in the column rather than the superstructure.

Piles in soft soils supporting bridge structures may be subjected to large horizontaldisplacements due to design earthquakes. These deformations produce significantcurvatures in the piles. The pile-cap interface (end fixity of the pile in the pile cap) isa region of significant curvature. Another region of high curvature is within the soil.These regions of high curvature need to be designed to possess adequate ductility.Ductility is improved by confining the concrete with spiral or hoop reinforcement.In addition to confining the concrete, spiral or hoop reinforcement prevents thebuckling of reinforcing bars and tendons at large deformations and ensures adequateshear resistance.

Gerwick (1982) and Sheppard (1983) reported on the results of lateral load testson prestressed concrete piles conducted in California. They provide specific recom-mendations for the required transverse reinforcement in critical regions of the pile.Park and Falconer (1983), summarize the results of experimental tests conductedon precast, prestressed concrete piles at the University of Canterbury, New Zealand.The objective of these tests was to determine if the requirements for transverse spi-ral reinforcement in concrete columns and piers of the Standard Code of Practice ofNew Zealand(1982) would result in ductile behavior of precast, prestressed concretepiles. The spiral reinforcement in the test specimens was in accordance with the NewZealand Code requirements for potential plastic hinge regions of ductile reinforcedconcrete columns and piers. The tests showed that when there is adequate transversereinforcement, piles subjected to cyclic lateral loading are capable of undergoing largepost-elastic deformations without significant loss of load carrying capacity.

For pile bents in Seismic Performance Categories B, C and D, the Standard Specificationsrequires that the volumetric ratio of spiral reinforcement in potential plastic hinge regionsbe:

sg

c

c

yh

A

A

f

f=

0 45 1. [STD Div. I-A, Eq. 6-4]

or,

sc

yh

f

f=

0 12. [STD Div. I-A, Eq. 6-5]

whichever is greater

15.2.5.2Ductility of Precast

Concrete Piles

SEISMIC DESIGN15.2.5.1 Superstructure-to-Bent Cap Connection/15.2.5.2 Ductility of Precast Concrete Piles


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where

s = ratio of the volume of spiral reinforcement to total volume of concrete core(out-to-out of spiral)

Ag = gross area of the pile

Ac = area of pile core measured to the outside of the transverse spiral reinforcementfc = specified compressive strength of concretefyh = yield strength of hoop or spiral reinforcement

The Standard Specificationsalso requires that center-to-center spacing of the spiralsnot exceed the smaller of 0.25 times the pile diameter, or 4 in. for Categories C andD and 6 in. for Category B. At the top of piles in pile bents, the transverse rein-forcement for confinement must be provided over a length equal to the maximumcross-sectional pile dimension or one-sixth of the clear height of the pile, whicheveris the larger, but not less than 18 in. At the bottom of piles in pile bents, transversereinforcement must be provided over a length extending from three pile diametersbelow the calculated point of moment fixity to one pile diameter, but not less than18 in., above the mud line. Lapping of spiral reinforcement in the transverse confine-ment regions is prohibited; connections of spiral reinforcement in this critical regionmust be full strength lap welds.

In the New Zealand Standard Code of Practice satisfactory results have been obtained bymultiplying the generally accepted AASHTO volumetric ratios, s, by the expression:

0 5 1 25. .+

P

f Ae

c g

where Pe= axial compression load on the pile

For a perspective on Caltrans state of the practice, the engineer should refer toSeismic Design Criteria SDC V1.3, 2004 and applicable references. In summary,piles with a cap placed in competent soil are not designed explicitly for lateral dis-placements; typical pile standard details (referred to as XS Sheets and downloadedfrom www.dot.ca.gov) are used. For bridges with flexible foundations (i.e. soft ormarginal soil, liquefaction, scour), the piles are explicitly designed for both verticaland lateral load path.

The strength and ductility of the connection between precast, prestressed concretepiles or pile extensions and reinforced concrete pile caps or bent caps is vital to theseismic performance of the piles. Gerwick (1993) describes three types of pile-to-cap

connections that have been successfully employed. The connections are illustrated inFigure 15.2.5.3-1. They are described as follows:

Case 1Pile embedment into the pile cap. The pile is designed to extend into thecap. Prior to concreting the cap, the surface of the pile is cleaned and rough-ened to provide shear transfer.

15.2.5.3Pile-to-Cap Connections

SEISMIC DESIGN15.2.5.2 Ductility of Precast Concrete Piles/15.2.5.3 Pile-to-Cap Connections


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Case 2Break away pile cover concrete and exposed strands. The concrete at the endof the pile is broken back to expose the strands, which are then embeddedin the cast-in-place cap. The spirals are removed and the exposed strands aresplayed to facilitate the development of the full strand strength in the cap.

Case 3Dowel bars embedded in the cap. Holes may be pre-formed in the pile withflexible metal ducts that are held in place during concreting by a mandrel.

The holes may also be drilled in the pile after it is driven, provided the pileis not damaged during driving. The dowels should be embedded a distancesufficient to develop their full strength and the moment in the pile head.Dowel bars are typically grouted with a non-shrink grout.

Tests at the University of Canterbury, New Zealand, (Joen and Park, 1990) onprestressed concrete piles showed that well detailed prestressed concrete piles andpile-pile cap connections are capable of undergoing large post-elastic deformationswithout significant loss in strength when subjected to severe seismic loading. Thethree connection types mentioned above were investigated. All three permitted thepile to reach its full flexural strength and all three were found to have satisfactoryductile behavior.

The tests indicated that spiral steel, similar to that provided in the potential plastic hingeregions should be provided within the region of the pile that is embedded in the pile cap,especially in the broken-back pile head type connection (Case 2) described above. The spi-ral steel improves the bond of the strands and assists in the transfer of the lateral forces tothe surrounding concrete in the cap. The tests showed that the non-prestressed reinforce-ment was not essential to the satisfactory ductile performance of the pile but did permit agreater dissipation of seismic energy by the pile.

SEISMIC DESIGN15.2.5.3 Pile-to-Cap Connections

Case 1 - Pile Embedment Case 2 - Break Pile Cover

Strands Strands

Break pile concreteto expose

Case 3 - Dowel Bars

Dowels incorrugated

tubing

Precast, prestressedconcrete pile

Precast, prestressedconcrete pile

concrete pile

Precast,prestressed

CIP cap CIP cap CIP cap

43/4"clr

Spiral #9 (total of 8)

Section A-A

A A

45

2'-0"

3"

P-S strands

in CapExposed P-S StrandsConcrete and Embed Embedded in Cap

spacing

strands @ equal0.6"-dia. prestressed

metal tubing2 1/4"- dia. corrugated

Figure 15.2.5.3-1Alternative Pile-to-Pile

Cap Connections


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Figure 15.2.5.3-2 details typical monolithic and independent pile extension orbuild-up details for applications where the pile cut-off elevation may be differentfrom that specified on the drawings due to field conditions.

Seismic isolation is gaining increased acceptance in the United States both as a means ofenhancing the seismic performance of existing structures and as a way of reducing the seis-mic force demand on substructures for new bridges. Seismic isolators decouple the super-structure from the substructure, which is the opposite strategy to the integral superstruc-ture-substructure connection. The objective of seismic isolation of bridge superstructuresis to protect the piers, abutments and their foundations by limiting the forces transferredthrough the beams. Besides reducing seismic loads, the isolation design helps distribute theseismic forces to the piers and abutments in relationship to their capacities.

SEISMIC DESIGN15.2.5.3 Pile-to-Cap Connections/15.2.6 Isolation Methods

15.2.6Isolation Methods

W20 @ 21/2" pitch

min

.

Pour monolithic with deck

Independent Pile Build-Up Detail

Monolithic Pile Build-Up Detail

hook ends

concrete pileDriven prestressed

metal tubesCorrugated

pile head (4 total)#5 Ea. side

min.max.

Bottom of pier cap orabutment footing

#5 @ 3 in.

Roughen top of pilesurface to 1/4" amplitude

#9 (total of 8)

Cut-off line

Bottom of pier cap orabutment footing

#9 (total of 8)

Prestressing strands

Roughen top ofpile surfaceto 1/4" amplitude

clr

.5"@

Piers

pile

Top ofdriven

24'-0"max.

clr

.

pile

bu

ild-up

6'-0"ma

x.

3"@

Abutments

6" 4" 2

"

For Pile Driven Up to 6" BelowCut-Off Elevation

11/2"

11/2"

Figure 15.2.5.3-2

Typical Monolithic andIndependent Pile Buildup

Details


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Decoupling the bridge superstructure and substructure from damaging horizontalcomponents of earthquake ground motions reduces the seismic demand on the sub-structure. However, it is essential to limit the seismic displacements of isolated bridgestructures to tolerable levels in order to reduce the problem of supporting trafficacross excessive gaps (typically at the end abutments) and other structural problems

arising from large displacements.

In addition to performing the function of regular bridge bearings, seismic isolationbearings should provide:

1. Additional flexibility in the bearings in order to lengthen the period of vibrationof the structure

2. Additional damping and energy dissipation to control relative displacementsacross the isolator

3. Rigidity under service loads such as wind, braking and centrifugal forces

The required characteristics of the isolation bearing system result in the bilinearforce-deformation characteristics such as shown in Figure 15.2.6-1. Several propri-etary seismic isolation bearing systems are available in the United States.

Two design philosophies are utilized in the AASHTO Guide Specifications for SeismicIsolation Design (1999). The first is to take advantage of the reduced forces and pro-vide a more economical bridge design than conventional construction. This optionuses the same modification factors as the Standard Specificationsand hence providesthe same level of safety. The second option intends to eliminate or significantlyreduce damage to the substructure due to the design event. In this option, an R(ductility) factor ranging from 1.5 to 2.5 will ensure an essentially elastic response byeliminating the ductility demand on the substructure. The Guide Specificationsalso

SEISMIC DESIGN15.2.6 Isolation Methods

Displacement

ForceFigure 15.2.6-1

Force-DisplacementCharacteristics of Bilinear

Isolation Bearings


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SEISMIC DESIGN15.3.1.1 Conventional Force Method

START

Preliminary Design

Applicablility of the SpecificationSTD Div. I-A, Art. 3.1

Acceleration CoefficientSTD Div. I-A, Art. 3.2

Importance ClassificationSTD Div. I-A, Art. 3.3

Site Effects

Seismic Performance Category

STD Div. I-A, Art. 3.5


Determine Elastic Seismic Forces

Determine Analysis Procedure

Response Modification Factors

STD Div. I-A, Section 4



and Displacements

Determine Design Forces Design FoundationsDesign Abutments

PerformanceCategory D?

SeismicDesign Approach SlabsSTD Div. I-A, Art. 7.4.5

Are

Adequate?Components

Seismic Design CompletePrepare Seismic Details

END

Revise Structure

No

No

Yes

Yes

Figure 15.3.1.1-1Basic Steps in AASHTO

Division I-A Seismic Design


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In the second approach, a more rational form of ductility assessment is sought by tak-ing the effect of sequential yielding into account when evaluating capacity. Capacitythus takes on a more global meaning since it refers to the entire structure ratherthan to a given component, as in the force analysis. Displacement is taken as themeasure of the capacity of the structure. Failure occurs when enough plastic hinges

have formed to render the structure unstable or when a plastic hinge cannot sustainany further increase in rotation. Typically, displacement demand is obtained from athree-dimensional analysis using reduced flexural and torsional section properties. Byrelying on the reserve strength of the materials involved in constructing the bridge,this method results in considerable savings.

In most cases, the solutions to the equations of motion to determine demand forcesand displacements are based on a linear elastic multi-mode Response SpectrumAnalysis (RSA). This type of analysis is considered acceptable for basic regular struc-tures. RSA offers the following advantages:

1. It is usually simple to use.

2. It eliminates the need for extensive testing. Representing non-linearities oftenrequires additional data to describe the behavior of the material.

3. It provides acceptable limit-state solutions. In most cases, there are no real gainsin resorting to a higher level of analysis. When discontinuities or other sources ofnon-linearity exist, an iterative procedure based on the equivalent linear solutionmay be used to satisfy force and displacement requirements. Limit states are oftenused in conjunction with an iterative process to envelop the behavior of the struc-ture. Each limit state is a worst-case scenario corresponding to a set of boundaryconditions or material properties. Examples of the commonly used limit states arethe tension and compression models of a bridge with expansion hinges and abut-ment supports. The tension model corresponds to the opening of all expansionhinges and lack of abutment soil springs (stiffness), while the compression modelcorresponds to the closing of all gaps and the engaging of the soil at one or both

abutments.4. It uses predefined ARS curves, except when required by the size of the project

and/or the geology of the site. The ARS curves take into account such factors asproximity to fault zone and site geology (primarily the depth to rock).

Typical sources of non-linearity include:

Material:

Soil

Concrete

Soil-structure interaction

Inelastic action (yielding of the reinforcement)Geometric:

P- effects Gap elements

Expansion hinges

Abutments

Support system such as bearings

SEISMIC DESIGN15.3.1.2 Displacement Ductility Method/15.3.2 Computer Modeling

15.3.1.2Displacement Ductility

Method

15.3.2Computer Modeling


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15.3.3.1Causes of Failures

15.3.3.2Preliminary DesignRecommendations

15.3.3Seismic Design Issues

Linear elastic solutions often provide adequate accuracy. The extra effort needed toproduce additional accuracy is rarely justified in the majority of bridge applications.In fact, there are instances where the effort to obtain added accuracy may be coun-terproductive and create misleading results. This is particularly true in cases wherean attempt is made to use non-linear time-history analysis without the proper model

parameters.

As more is learned about earthquake mechanics and its effects on structures, thedemand for improved seismic performance of bridges has been increasing. The gen-eral trend is toward an increase in seismic design requirements and an emphasis onthe mechanics of resistance.

Based on experience learned from major earthquakes, bridge failures during an earth-quake may be attributed to one or more of the following causes:

1. Unseating of the superstructure at abutments, hinges or expansion joints due toinsufficient support width.

2. Inadequate or poor distribution of lap splices of vertical column steel.3. Column failure due to longitudinal bar buckling from inadequate lateral reinforcement.

4. Column failure due to horizontal shear forces and inadequate lateral reinforcement.

5. Joint shear failure at critical superstructure-substructure connections.

6. Columns punching through the superstructure due to large vertical accelerationor inadequate connection details.

7. Footing failure due to lack of a top layer of reinforcement.

A systems approach to seismic design of bridges must be used because of the largemovements usually associated with earthquakes. The ability of the bridge to with-

stand such movements depends not only on the primary system displacement capac-ity but also depends on the displacement compatibility of individual components.The movements of components must be assessed in relation to other componentsand to the overall bridge system. By providing the necessary displacement capacities,the potential for both local and global failures will be minimized.

Several recommendations can be made regarding the preliminary design stages. These guide-lines can help avoid problems during final design and enhance seismic performance.

1. Avoid span arrangements that induce large dead load moments in the columns,thereby reducing column capacity to resist seismic moments.

2. Use continuous frames.

3. Avoid highly irregular or suddenly changing stiffnesses of members to preventconcentration of load demands on a particular bent or frame. This will alsominimize the tendency of the bridge to undergo in-plane rotation.

4. Do not allow plastic hinges to form in the superstructure.

5. Consider a depth of flexibility for piers below the actual ground level.

6. Assume the footings to be fixed except where soft soil conditions exist. In thosecases, foundation flexibility should be considered when evaluating the demand.

7. Avoid skews at the abutments and hinges that are greater than 30 from thenormal to the centerline of the bridge.

SEISMIC DESIGN15.3.2 Computer Modeling/15.3.3.2 Preliminary Design Recommendations


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8. Make the superstructure depth at integral bent caps equal to or greater than themaximum column diameter.

9. Use isolation details at column architectural flares, or if the flares are to be reliedupon structurally, use proper confinement.

10. Consider using integral abutments for shorter bridges.11. Consider using isolation methods.

SEISMIC DESIGN15.3.3.2 Preliminary Design Recommendations


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This design example is of a bridge with two 140-ft-long spans supported by abut-ments at each end and a single column midway between abutments as shown inFigure 15.4.1-1. The superstructure consists of four precast, prestressed concretebulb-tee beams made continuous over the column and bent cap through post-ten-sioning and a cast-in-place deck slab. The column is supported on a pile footing andis therefore considered fixed at its base. The superstructure is integrally connected tothe column through a cast-in-place, post-tensioned bent cap.

It should be noted that superstructure-to-substructure continuity is not a require-ment for seismic design. Introduction of continuity in this example provides aprototype structure for the integral bent design, presented in the following section.The seismic analysis procedure presented here is equally valid for other conventionalprecast bridge systems.

15.4SEISMIC DESIGN

EXAMPLEBULB-TEE,TWO SPANS, DESIGNED

IN ACCORDANCE

WITH STANDARDSPECIFICATIONS

DIVISION I-A

15.4.1Introduction

SEISMIC DESIGN15.4 Seismic Design ExampleBulb-Tee, Two Spans, Designed In Accordance With Standard Specifications Division I-A/

15.4.1 Introduction

26'-0"

5'-0"

typ.

Abutment

140'-0"

Typical Section

42'-6"

3 Spaces @ 10'-10"

6'-0" diameter column

Elevation

140'-0"7'-0"

6'-81/2"

Bulb-tee beam

Abutment

A

A

Shear key,typ.

End diaphragm

Bearing pad

Bottom of enddiaphragm

Bearing pad

Shear key

Section A-A

Abutment Elevation

Pier

Field splice, typ.

BearingLC

BearingLCLC

Figure 15.4.1-1Bridge Elevation and Typical Sections


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Because the bridge is a two-span concrete structure, the seismic loads and analysisprocedures of Division I-A of the Standard Specificationsare applicable [STD Div.I-A, Art. 3.1]. The bridge is assumed to be located in an area where the Seismic Acceleration Coefficient, A, is 0.15 [STD Div. I-A, Art. 3.2]. Since the bridgeAcceleration Coefficient, A, is less than 0.29, the assignment of importance classifi-

cation (IC) is not required [STD Div. I-A, Art. 3.3].

Since A falls between 0.09 and 0.19, the Seismic Performance Category (SPC) isB [STD Div. I-A, Art. 3.4].

The soil profile at the site is used to determine the Site Coefficient, S. In this exam-ple, soil profile Type II is assumed. This soil type corresponds to stable deposits ofstiff clay and sand with a depth exceeding 200 ft. From STD Div. I-A, Table 3.5.1,the corresponding S is 1.2.

The Response Modification Factors, R values, for the various components are shown

in Table 15.4.1-1

Component R Value

For a single column 3.0

Superstructure-to-abutment connection (shear key) 0.8

Column-to-superstructure connection 1.0

Column-to-foundation connection 1.0

For design, the bridge has the following dimensions:

Span length = 140.0 ftBent cap width = 7.00 ftBent cap depth = 6.71 ft for structural calculationsColumn height = 26.00 ftColumn diameter = 6.00 ftBeam spacing = 10.83 ftDeck thickness = 8 in. for structural calculationsAbutment diaphragm thickness = 3.00 ft

The calculations in the design example are made using a minimum of three significantfigures.

Beam concrete strength = 6,000 psiBent cap concrete strength = 6,000 psiDeck concrete strength = 4,000 psiColumn concrete strength = 4,000 psiUnit weight of concrete = 144 pcfUnit weight of beams and bent cap = 155 pcf

15.4.1.1

Bridge Geometry

LOADS AND LOAD DISTRIBUTION15.4.1 Introduction/15.4.2 Material Properties

Table 15.4.1-1Response Modification Factors

[STD Div. I-A, Table 3.7]

15.4.1.2Level of Precision

15.4.2Material Properties


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Unit weight of deck, columns, and abutment diaphragms = 150 pcfModulus of elasticity of concrete in the beam and bent cap, Ecs:

E f psi f ksics c c= = 57 000 57,

where fc= concrete strength, psiE ksf cs = =57 6 000 144 635 800, ( ) ,Modulus of elasticity of concrete in deck and column, Ecc:

E ksf cc = =57 4 000 144 519 100, ( ) ,Modular ratio between the two concretes, n:

nE

Ecc

cs

= = =519 100

635 8000 816

,

,.

Procedure 1 (Uniform Load Method) may be used because the SPC of the bridge is B.According to this method, the seismic load is approximated as a uniform static load appliedat the center of gravity of the superstructure, transverse to its axis, as shown in Figure15.4.3-1. The total seismic load (uniform load times bridge length) is taken equal to thetotal dead weight of the superstructure plus the tributary weight of the columns multipliedby the seismic response coefficient. The superstructure is assumed to respond to the uni-form seismic load as a continuous beam supported on a flexible column.

Area of cross-section of precast beam = 7.39 ft2

Overall depth of precast beam = 6.0 ftMoment of inertia about the centroid of the major axis of the non-composite precastbeam = 36.44 ft3

Moment of inertia about the centroid of the minor axis of the non-composite precastbeam = 3.33 ft2

Distance from centroid to the extreme bottom fiber of the non-composite precastbeam = 3.10 ftDistance from centroid to the extreme top fiber of the non-composite precast beam= 2.90 ft

15.4.3Seismic Analysis in

Transverse Direction

15.4.3.1

Section Properties

15.4.3.1.1Beam Properties

SEISMIC DESIGN15.4.2 Material Properties/15.4.3.1.1 Beam Properties

L

L

q

Figure 15.4.3-1

Assumed TransverseResponse According to the

Uniform Load Method


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As a first step, the moment of inertia, Is, of the bridge cross-section about the verti-cal axis through the centroid is calculated. The cast-in-place haunch above the beamcontributes very little to the moment of inertia of the section and may be ignored.However, the deck eccentricity including the haunch thickness is used to determinethe location of the centroid.

Referring to Figure 15.4.3.1.2-1:

Transformed flange width = n(flange width) = 0.816 (42.5) = 34.68 ftTransformed flange area = (transformed flange width)(deck thickness)

=34 68 8

1223 12

..

( )( )= ft 2

Is=( . )( . )0 667 34 68

12

3+ 4(3.33) + 2(7.39)[(5.42)2 + (16.25)2] = 6,669 ft4

The location of the centroid of the superstructure from the extreme bottom fiber is

Y ftb =+ ( )( )

+=

( )( . )( . ) . .

( . ) ( . ).

4 7 39 3 10 23 12 6 38

4 7 39 23 124 54

The moment of inertia of the uncracked circular column is:

Ic= D4

64

6

64

4

=( )

= 63.62 ft4

The total dead load to be included in the seismic analysis is equal to the sum of theweights of the deck slab, four beams with haunches, bent cap, two barriers, futurewearing surface, end diaphragms, and one-half of the column weight. Refer to Figures15.4.1-1 and 15.4.3.1.2-1 for component dimensions and section properties.

Deck slab, haunch and beams:

[(42.5)(0.667) + (4)(4)(0.5/12)]0.150 + (4)(7.39)(0.155) = 8.93 kip/ftBent cap: (7.0)(6.71)(42.5)(0.155) = 309 kipsBarriers (2 barriers at 0.4 kip/ft): 2(0.4) = 0.8 kip/ft

15.4.3.1.2Composite Section Properties

15.4.3.1.3Column Properties

15.4.3.2

Tributary Dead Load

SEISMIC DESIGN15.4.3.1.2 Composite Section Properties/15.4.3.2 Tributary Dead Load

X

8"

0.5"1.

84'

6.

38'

C.G.1.

44'

3.1

0'

Effective width = 42.5 n = (42.5) (0.816) = 34.68'

Y

Girder

Y

X

Y = 4.54'b

4'-0"(typ.)

C. G. ofcompositesection

c

Bulb-tee beam:A= 7.39 ft2

I = 36.44 ft4 (Major axis)I = 3.33 ft4 (Minor axis)f = 6,000 psi'

Deck slab:A = 23.12 ft2

I = 0.86 ft4

f = 4,000 psic'

Figure 15.4.3.1.2-1Bridge Cross-SectionGeometric Properties


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Future wearing surface at 35 psf: (0.035)(42.5) = 1.49 kip/ftAbutment diaphragm: (3)(6.71)(42.5)(0.150) = 128 kips per diaphragm

Column: 6

2

0 150 4 24

2

( ) =. . kip/ft

Total dead weight of superstructure:

(8.93)[(2)(140) 7.00 (2)(3.00)] + 309 + (2)(140)(0.80 + 1.49) + (2)(128) = 3,591 kips

Tributary dead load of column: (4.24)(26/2) = 55.1 kipsTotal dead load: 3,591 + 55.1 = 3,646 kips Use 3,700 kips.

In the transverse response mode, the superstructure is assumed to provide negligiblerestraint against column-top rotations. Hence, the column is assumed to undergosingle-curvature bending (i.e., it acts like a cantilever). The column length, h c, usedfor calculating shear stiffness is measured from the top of footing to the center ofgravity of the superstructure.

In this example, hc= 26 +Yb = 26 + 4.54 = 30.54 ft.By referring to Figure 15.4.3.3-1, the following equations may be written:

1 =5q(2L)

384E I

4

cs s

(Eq. 15.4.3.3-1)

where

1 = lateral displacement from a uniformly distributed load of qq = uniformly distributed load

L = length of one span

2 =( )R 2L

48E I

col

3

cs s(Eq. 15.4.3.3-2)

where

2 = lateral displacement caused by a column force of RcolRcol = column force

=12 (Eq. 15.4.3.3-3)

where = net displacement

R K3E I

hcol c

cc c

c

= = 3

(Eq. 15.4.3.3-4)

where Kc= column shear stiffness

Substituting Eq. (15.4.3.3-1 and Eq. (15.4.3.3-2) in Eq. (15.4.3.3-3):

= 5q(16)L

384E I

R (8)L

48E I

4

cs s

col3

cs s

(Eq. 15.4.3.3-5)

15.4.3.3

Equivalent TransverseStiffness

SEISMIC DESIGN15.4.3.2 Tributary Dead Load/15.4.3.3 Equivalent Transverse Stiffness

1

q = 1.0 kip/ft

a) Applied Transverse Unit Load

R

2

col

b) Applied Restoring ForceFrom Column

c) Combined Effect

Rcol

q = 1.0 kip/ft

Figure 15.4.3.3-1Column Reaction Due to aUniform Transverse Load


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Substitute q = 1.0 k/ft and Rcol from Eq. (15.4.3.3-4):

= = (5)(1.0)(16)L

384E I

24E I L

48h E I

80L

384E I

24E I L

48h E I

4

cs s

cc c3

c3

cs s

4

cs s

cc c3

c3

cs s

( )(Eq. 15.4.3.3-6)

EcsIs (superstructure) = (635,800)(6,669) = 4.240x109 kip-ft2

EccIc (column) = (519,100)(63.62) = 3.303x107 kip-ft2

= = (80)(140)

(384)(4.240 x10 )

(24)(3.303 x10 )(140)

48(30.54) (4.240x10 )

4

9

7 3

3 9 0 0189 0 3752. .

= =0 0189

1 37520 0137

.

.. ft

Equivalent transverse stiffness, K=1 0 2 140

0 013720 440 20 500

.

., ,

( )( )( )= kip/ft kip/ft

T(tr)= 2 2 23 700

32 2 20 500

M

K

W

gK= =

,

. ( , )= 0.470 seconds

where

T(tr)= period of structure in the transverse directionM = total contributory mass of superstructure and columnW = total contributory weight of superstructure and columng = gravitational acceleration

Cs(tr)= 1.2AST 2.5A(tr)2/ 3 [STD Div. I-A, Eq. 3-1]

where Cs(tr)= elastic seismic response coefficient in the transverse direction

Substituting:

Cs(tr)=( . )( . )( . )

( . ). . . .

/

1 2 0 15 1 2

0 4700 357 2 5 0 15 0 375

2 3= = ( )( ) =2.5A

Therefore, Cs(tr)= 0.357

Equivalent uniform static load = Cs(tr) W2L

=

0 357 3 7002 140

. ,( )

= 4.72 kip/ft

= (4.72)(0.0137) = 0.0647 ft

Rcol=3E I

h

xcc c

c3

=

( )( . )( . )

( . )

3 3 303 10 0 0647

30 54

7

3= 225 kips

Column seismic moment at bottom of column: (225)(30.54) = 6,872 ft-kips

15.4.3.4

Period of Structure in the

Transverse Direction

15.4.3.5Elastic Seismic

Response Coefficient

15.4.3.6

Column Forces in theTransverse Direction

SEISMIC DESIGN15.4.3.3 Equivalent Transverse Stiffness/15.4.3.6 Column Forces in the Transverse Direction


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The Uniform Load Method may also be used to calculate the longitudinal seismicforces on the structure. The superstructure is assumed to displace as a rigid unit as thesupporting column undergoes bending deformations as shown in Figure 15.4.4-1.Thus, the longitudinal stiffness is assumed equal to the shear stiffness of the column.The total dead load that contributes to the seismic load in the longitudinal direction,

W, is equal to 3,700 kips (the same as the dead load used in the transverse direction).

The assumption of a rigid superstructure implies that the top of the column is restrainedagainst rotation. Therefore, the column undergoes double-curvature bending, as opposedto single-curvature bending, which occurs in the transverse direction. The column lengthused for calculating shear stiffness, H, is measured from the top of footing to the bottomof the bent cap. In this example, H = 26 ft.

Column shear stiffness = 12E IH

xcc c3

= =12 3 303 10

2622 550

7

3

( . )

( ), kip/ft

In general, the abutments and soil behind them may contribute to the longitudinalstiffness. Their contribution depends on the abutment type (i.e., integral vs. seat

abutment) and the longitudinal displacement of the structure. Several iterations maybe needed to evaluate the abutment effect on the stiffness. Additionally, a minimumdisplacement in the range of 2 to 4 in. is typically required to mobilize the soil stiff-ness. In this example, the total longitudinal displacement is small (0.75 in.), and thusthe abutment contribution to stiffness is ignored.

T(long)= 2 2 2 M

K

W

gK

3,700

32.2(22,550)= = = 0.449 seconds

where T(long)= period of structure in the longitudinal direction

Cs(long)=1.2AS

T

2.5A

long

2/3

( )

[STD Div. I-A, Eq. 3.1]

where Cs(long)= elastic seismic response coefficient in the longitudinal direction

Cs(long)=( . )( . )( . )

( . ) /1 2 0 15 1 2

0 449 2 3= 0.368 < 2.5A= 0.375

Therefore, Cs(long)= 0.368

15.4.4Seismic Analysis in

Longitudinal Direction

15.4.4.1Equivalent Longitudinal

Stiffness

15.4.4.2

Period of Structure in theLongitudinal Direction

15.4.4.3

Elastic Seismic ResponseCoefficient

SEISMIC DESIGN15.4.4 Seismic Analysis in Longitudinal Direction/15.4.4.3 Elastic Seismic Response Coefficient

Elevation

Figure 15.4.4-1Assumed Seismic Response in

the Longitudinal Direction


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Column shear = (0.368)(3,700) = 1,362 kipsColumn moment = (1,362)(26/2) = 17,706 ft-kips

A summary of the moments and shear forces are shown in Table 15.4.5-1.

Earthquake

Direction

Transverse Longitudinal

Moment Shear Moment Shear

ft-kips kips ft-kips kips

Transverse 6,872 225 0 0

Longitudinal 0 0 17,706 1,362

Seismic combination 1:

100% longitudinal force + 30% transverse force [STD Div. I-A, Art 3.9]

Transverse moment, MT:

MT= (1.0)(0) + (0.30)(6,872) = 2,062 ft-kips

Longitudinal moment, ML:

ML= (1.0)(17,706) + (0.30)(0) = 17,706 ft-kips

Transverse shear force, VT:

VT= (1.0)(0) + (0.30) (225) = 68 kips

Longitudinal shear force, VL:

VL= (1.0)(1,362) + (0.30)(0) = 1,362 kips

Seismic combination 2:

100% transverse force + 30% longitudinal force [STD Div. I-A, Art. 3.9]

MT= (1.0)(6,872) + (0.30)(0) = 6,872 ft-kipsML= (1.0)(0) + (0.30)(17,706) = 5,312 ft-kips

VT= (1.0)(225) + (0.30)(0) = 225 kipsVL= (1.0)(0) + (0.30)(1,362) = 409 kips

Reinforced concrete shear keys, such as those shown in Figure 15.4.1-1, will resistseismic transverse forces at the abutments. From statics, the total abutment reac-tions are equal to the equivalent uniform static load minus the column reaction (SeeFigure 15.4.6-1):

15.4.4.4Column Forces in the

Longitudinal Direction

15.4.5

Combination ofOrthogonal Forces

Table 15.4.5-1Summary of Column Forces

15.4.6Abutment Design Forces

SEISMIC DESIGN15.4.4.4 Column Forces in the Longitudinal Direction/15.4.6 Abutment Design Forces


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Abutment transverse shear force, VT(Abutment):

V4.72 2 140 225

2T(Abutment) =

( )( )( ) = 548 kips

The elastic seismic force per shear key= 548/3 = 183 kipsDesign shear per key= 183/R= 183/0.8 = 229 kips

The shear key design is typically based on the shear friction method. [STD Art. 8.15.5.4]

[STD Div. I-A, Art. 6.3.1]

The minimum support length N (in.), shown in Figure 15.4.7-1, is calculated bythe following equation:

N = (8 + 0.02L + 0.08H)(1 + 0.000125S2) [STD Div. I-A, Eq. 6-3A]

where

L = length (ft) of the longitudinal frame between expansion joints (2 x 140 = 280 ft)

S = skew angle (degrees) measured from a line normal to the span (0 degrees)

N = [8 + (0.02)(280) + (0.08)(26)][1 + (0.000125)(0)2] = 15.7 in. Use 16 in.

The seat width provided should be the larger of N and the elastic seismic displace-ment in the longitudinal direction = column shear/longitudinal stiffness = (1,362/22,550)(12) = 0.72 in. While in this example, N clearly controls, additional factorssuch as the bearing size may control the final seat width.

15.4.7Minimum Abutment

Seat Width

SEISMIC DESIGN15.4.6 Abutment Design Forces/15.4.7 Minimum Abutment Seat Width

q = 4.72 kip/ft

225 kipsIsTVT

V

Plan

(Abutment)(Abutment)

Figure 15.4.6-1Transverse Shear at the

Abutments


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SEISMIC DESIGN15.4.7 Minimum Abutment Seat Width

Abutment seat

backwallAbutment

or end of bridge deckL = Distance to next expansion joint

[STD Div. I-A, Art. 6.3.1]

N

Figure 15.4.7-1Minimum Abutment

Seat Width


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This design example illustrates the procedure for integral bent cap design in splicedI-beam bridges. The design procedure evolved from successful experimental testing ofa scale model of the Florida-type bulb-tee beam at the University of California at SanDiego. The results of this testing, which verified the longitudinal seismic response ofprecast spliced-beam bridges, are reported in Holombo, et al (2000).

The integral bent cap is designed to provide force transfer from the spliced I-beambridge superstructure to the foundation through the development of column plasticmoments in a ductile manner.

Bent cap width = 84 in.Bent cap depth, h

b= 87 in.

Column cross-section: Circular with a 6.00-ft diameter, see Figure 15.5.1.1-1

Column reinforcement: Longitudinal: 30 #11 barsTransverse: #6 spirals @ 4-in. pitch

Bent cap post-tensioning: Six 19x0.6-in.-dia strand tendons

Cast-in-place concrete strength, fc= 4 ksiReinforcing steel yield strength, fy= 60 ksiModulus of elasticity of tendons, Es= 29,000 ksi

15.5

SEISMIC DESIGN

EXAMPLEINTEGRAL

BENT CAP

15.5.1Introduction

15.5.1.1Bent Cap Geometry

15.5.1.2

Reinforcement

15.5.1.3

Material Properties

SEISMIC DESIGN15.5 Seismic Design Exampleintegral Bent Cap/15.5.1.3 Material Properties

Figure 15.5.1.1-1Column Cross-Section 72 in.

#11(30 total)

#6 @ 4" pitch

Section


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Axial load: Top of column, PDL,TOP= 2,225 kipsBottom of column, PDL,BOT.= 2,350 kips

Column over-strength moment capacity at the top, Motop= 14,115 ft-kips

Column over-strength moment capacity at the bottom, Mobot= 14,340 ft-kips

The over-strength moment capacities are taken as 20% greater than the plasticmoment capacities.

The calculations in the design example are made using a minimum of three significantfigures.

The design procedure involves the following steps:

1. Calculate principal stresses in the bent cap.

2. Design joint shear reinforcement and ensure minimum embedment length forcolumn bars with the reinforcement being extended as close as possible to the topreinforcement in the bent cap.

3. Perform a torsional shear-friction analysis to verify the ability of the bent cap totransfer column plastic moments to the bridge superstructure.

Horizontal joint shear force, Vjh, is given by:

Vjh=M

h

14,115 x12

871,947 kips

topo

b

= =

Effective width of bent cap, bje

, by the geometry shown in Figure 15.5.3-1 is

15.5.1.4Forces

15.5.1.5Precision

15.5.2Design Procedure

15.5.3Principal Stresses

in the Bent Cap

SEISMIC DESIGN15.5.1.4 Forces/15.5.3 Principal Stresses in the Bent Cap

Figure 15.5.3-1Effective Joint Width for Joint

Shear Stress Calculations

Cap beam

=jeb

D bbje b

Bridge axis

Web

2D


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bje= 2 D ( for circular sections ) bbwhere

D = column diameterbb= bent cap width parallel to the longitudinal axis of the bridge

bje= 1.414(72) = 101.8 in. > bb= 84 in. Therefore, use bb= 84 in.

Nominal horizontal shear stress in the joint, vjh:

vjh=V

b D

1,947

(84)(72)0.322 ksi

jh

b

= =

Calculate average joint axial stress, fv, in the vertical direction at middepth of thebent cap:

f

P

b D h

2,225

(84)(72 87) 0.167 ksivDL,TOP

b b= +( ) = + =

The average joint axial stress in the horizontal direction, fh= 0 (I-beam superstructure, nosignificant axial stress transferred to bent cap at middepth of bent cap)

The principal tensile stress, pt, in the bent cap/column connection is given by:

pf f

2

f f

2vt

y h

2

v hjh2=

+

+

=+

+ =

(0.167) (0)

2

0.167 0

2 (0.322) 0.249 ksi

2

2

0.249 ksi 249 psi 3.94 f 3.94 4,000 3.5 f psic c= = = >

According to Priestley, et al (1996):

If the principal tension stress 3.5 fc psi, only nominal joint reinforcement is

required.

If the principal tension stress > 5 fc psi, all requirements for joint reinforcement must

be met in accordance with a force-transfer mechanism.

If the principal tension stress is > 3.5 fc psi and 5 fc

psi, linear interpolation

between full and nominal requirements for joint reinforcement must be met.

The principal tension stress is between 3.5 fc psi and 5 fc

psi, so a linear inter-polation between full and nominal joint reinforcement requirement would needto be provided. However, for the purpose of this design example, the cap will bedesigned for the full joint shear requirement.

SEISMIC DESIGN15.5.3 Principal Stresses in the Bent Cap


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The joint design is in accordance with the procedure described in Priestley, et al(1996) and verified by experimental results reported by Holombo, et al (2000). Theassumed joint force transfer mechanism is shown in Figure 15.5.4-1. The assumedmechanism reduces congestion by placing the joint reinforcing steel outside thecolumn core region. The joint reinforcing steel facilitates the transfer of the column

tension force to the top of the joint.

Assumptions:

1. 75% of all column reinforcement providing Tc is clamped by the main diagonalcompression strut D1 (see Figure 15.5.4-1).

2. The remaining 25% of the total longitudinal column reinforcement at appropriatestrain hardening stress, Tc, is clamped by the diagonal compression struts, D2 and D3.The vertical components of D2 and D3 are assumed equal. External joint stirrupsallow the development of strut, D2, which helps redirect the compression force,Cb, into the middle of the joint.

The external vertical reinforcement, Ajv, should be placed over a distance of hb/2from the column face on each side of the column in accordance with the followingequation:

A 0.125 A f

fjv sc

yco

yv

=

where

Asc = total area of longitudinal reinforcement in column section = (30)(1.56)= 46.8 in.2

foyc = material over-strength stress of column reinforcement allowing for strainhardening

fyv = yield strength of joint vertical reinforcement

Taking foyc= 1.4fyv for Grade 60 reinforcement:

15.5.4Joint Reinforcement Design

SEISMIC DESIGN15.5.4 Joint Reinforcement Design

Figure 15.5.4-1Assumed Mechanism for Joint

Force Transfer in Pier Cap1D

stirrupsJoint shear

cC c'T Tc

cV

D3

2D

Cb

Integral bent capColumn


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A (0.125)(46.8)1.4f

f8.19 in.jv

yv

yv

2= =

The number of #6 stirrup legs required = Ajv/0.44 = 8.19/0.44 = 18.6, say 20 legs.

Provide 10 #6 two-legged stirrups on each side of the column face over a distance ofhb/2 = 87/2 = 43.5 in. from the column face.

An additional amount of vertical reinforcement equal to half of this amount shouldbe placed within the joint confines to help stabilize top beam reinforcement andassist in the transfer of column tension force by bond.

Interior vertical joint stirrup area, Avi, is determined by:

A 0.0625A f

f(0.0625) (46.8)

1.4 f

f4.10 in.vi sc

yco

yv

yv

yv

2= = =

The number of #6 stirrups required = Avi/0.44 = 4.10/0.44 = 9.3, say 10 legs. Provide(10) #6 single leg stirrups within the column core. As the clamping action occurs atthe top of the joint, these stirrups need not extend to the base of the joint. They areextended at least two-thirds of the bent cap depth or 2/3(87) = 58 in. Figure 15.5.4-2indicates the locations for the placement of vertical joint reinforcement.

Note: The reinforcement placed outside the column core over a length of hb/2 is inaddition to the shear reinforcement required for conventional shear transfer in thebeam.

SEISMIC DESIGN15.5.4 Joint Reinforcement Design

Figure 15.5.4-2Locations for VerticalJoint Reinforcement

1 2

2

2D

in each area, andjA v

1

Bridge axis Avi = 0.5Ajv within core


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Horizontal hoop reinforcement must be provided to resist a force of one-quarter of thetension force in the column steel due to the plastic moment (0.25Tc) in accordance withthe following equations:

syh a

sc yco

a

3.3

Df l

0.09A f D

l

F=

where

la= assumed length of column anchorage reinforcement in joint = 80 in.F = bent cap prestressing force after all losses

Assuming F = 0, the simplified equation is:

s

sc yco

a2

yh

0.3A f

l f =

= =(0.3)(46.8)(1.4f )(80) f

0.00307yh2

yh

However, minimum horizontal hoop reinforcement, s,min, must be provided accordingto the following:

s,min

c

yh

f

f 60,000 = = = >

3 5 3 5 40000 00369 0 00307

. ( . ). .

Use s= 0.00369

sreqd= 4AD

(4)(0.44)(68.25)(0.00369)

6.99 in.h

s

= =

where

sreqd = required spacing of hoop reinforcementAh = area of hoop reinforcementD = core diameter of spirally confined column = 68.25 in.

Provide #6 stirrups @ 6 in. spacing. If the hoop reinforcement ratio provided isless than the required ratio, the difference could be made up with split hairpins asdescribed in Holombo, et al (2000).

Note: The hoop spacing could be decreased if the cap beam prestress force, F, is considered.

In the absence of the bottom slab in spliced I-beam bridges, column moments and shearsare transferred into the beams through the cap completely through torsional mechanisms.Due to the limited length available between the face of the column and the beam, spiralcracks typically associated with torsion cannot fully develop. Therefore, conventional tor-sion design methodologies that are primarily based on this cracking pattern are not appli-cable. Instead, the torsional capacity is calculated using a plastic friction model as illustratedin Figure 15.5.5-1.

15.5.5Shear-Friction Analysis

SEISMIC DESIGN15.5.4 Joint Reinforcement Design/15.5.5 Shear-Friction Analysis


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Assumptions:

1. Shearing stress is assumed constant over the cross-section and proportional to thenormal force, P.

2. Shear-friction contribution of each segment is assumed proportional to the areaof each segment.

The bent cap section is subjected to a vertical shear force, VV, a horizontal shearforce, VL, a torsion, T, and an axial clamping force, P. The cap is divided, conceptu-ally, into four unequal segments of areas, A1 to A4, as shown in Figure 15.5.5-2.

The direction of shear-friction resistance within each of the four segments is taken asparallel to the outer edge, and the shear-friction stress, , is taken as:

= P/A

where

A= total section area = coefficient of friction over the interface

SEISMIC DESIGN15.5.5 Shear-Friction Analysis

Figure 15.5.5-1Torsional Shear-Friction

Mechanism

T

V

P

VL

V

Figure 15.5.5-2Conceptual Force Diagram For

Resisting Torque In Bent Cap

V2

A1F1 A3

F4

A4

VL

F3

h

x

y

4y

V A2

F2

1 3x

b

bb

T


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The force, Fi, in each segment, is then given by:

Fi=Aiwhere Ai= area of the segment.

Equilibrium under external torsion, T, longitudinal shear force, VL, and vertical shearforce, VV, requires that:

VV= F1 F3=(A1 A3)VL= F2 F4=(A2 A4)T = F1x1+ F2y2+ F3x3+ F4y4=(A1x1+ A2y2 +A3x3+ A4y4)

where

T = external torsionx1, x3, y2 and y4 are distances defined in Figure 15.5.5-2

The equations can be solved through trial and error by dividing the section into seg-ments and trying different values until all three equations are satisfied, then checkingthat the implied value of the friction coefficient, , is reasonable. Alternatively, alimit design value of= 1.4 can be used with F1 to F4 selected to satisfy the first twoequations shown above. The torque predicted by the third equation must then bechecked to ensure that it exceeds the applied torque. The latter alternative is utilizedin this design solution.

The normal force, P, is calculated assuming a dilation strain of 0.0005 developed onthe shear plane.

P = F + As(0.0005)Es

where

F = prestressing force after all lossesAs = area of reinforcing steel passing through shear plane including the pre-

stressing steel

= three layers of ten #10 bars = (3)(10)(1.27) = 38.1 in.2 (ignore prestressing steel to be conservative)

Aps = area of prestressing steel = (6)(19)(0.217) = 24.7 in.2

F = (202.5)(0.8)(24.7) = 4,001 kips (A 20% loss is assumed)P = 4,001 + (38.1)(0.0005)(29,000) = 4,553 kips

Assume = 1.4 because surface of beam in joint region is roughened (Caltrans, 2000)

= =( )( )( )( )

=P

A

1.4 4,553

7.25 7.00125.6 kips /ft2

Horizontal shear force at top of column, VM M

Hi,columno bot

otopo

=+



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V14,340 14,115

25.751,105 kipsi,column

o =+

=

Moment at middepth of bent cap, M M Vh

2

i,bentcapo

topo

i,columno b= +

M 14,115 1,10587

(2)(12)18,120i,bentcap

o = +

= ft-kips

PDL,TOP= 2,225 kips

Using a factor of safety of 1.1 for shear-friction analysis, the required resistances areas follows:

Torsion:M 1.1

2

18,120 1.1

2

i,bentcapo ( )

=( )( )

= 9,966 ft-kips

Longitudinal shear: V 1.12

1,105 1.12

i,column

o

( ) = ( )( ) = 608 kips

Vertical Shear:P

2

2,225 1.1

2DL,TOP =

( )( )= 1,224 kips

Table 15.5.5-1 summarizes the torsional shear-friction computations to ascertainthe ability of the bent cap to transfer the column plastic moment capacity to thebridge superstructure. The assumed dimensions of each segment are shown in Figure15.5.5-3.

Given

Bent Cap Depth = 7.25 ftBent Cap Width = 7.00 ftAxial Force = 4,553 kipsFriction Coefficient = 1.4= 125.6 kips/ft2

Assumed

X-Coordinate = 4.90 ftY-Coordinate = 2.90 ft

SegmentArea, ft2

Distance fromCentroid, ft

First Momentabout Centroid,

ft3No. Size, ft

1 7.25 x 4.90 A1= 17.763 x1= 1.867 33.16

2 7.00 x 4.35 A2= 15.225 y 2= 2.175 33.11

3 7.25 x 2.10 A3= 7.613 x3= 2.800 21.324 7.00 x 2.90 A4= 10.150 y 4= 2.658 26.98

Total 50.750 114.57

Capacity Required

T =(A1x1+ A2y2+ A3x3+ A4y4),ft-kips

14,390 9,966

VV= (A1 A3), kips 1,275 1,224

VL= (A2 A4), kips 637 608

Table 15.5.5-1

Torsional Shear-FrictionComputations



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The bridge superstructure moment capacity must also be checked to ensure that theplastic hinges form in the column and not in the superstructure. Figure 15.5.5-4depicts the reinforcement details for the integral bent cap.


Figure 15.5.5-3Assumed Dimensions for Shear-

Friction Computations

A4

A3

7.25'

4.90'

4.35'

A2

7.00'

2.10'

2.90'

A1

Figure 15.5.5-4Integral Bent Cap

Reinforcement Details

& 20-#10 Top

#6 Stirrups

C BentL

Bottom of beam

Bent Cap Detail at Column

8-#10 Bott.

#6"

6"

7'-3"

6" 6'-0"

7'-0"

6"

(Ea.

Side)

19 x 0.6"-dia. strand

tendon (total of 6)

#6@

6"


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Bridges in California have been predominantly CIP box girder systems due to therequirements for high seismic resistance. The examples presented in Sections 15.4and 15.5, show that spliced beams with integral bent caps can provide a viablesolution for highway bridges in moderate to high seismic areas. The precast beam,integral-cap system was tested and has proven to provide levels of seismic resistance

comparable to CIP box girders. With minimal shoring and forming requirements,the new system will shorten construction time, reduce interruption to traffic, andlower the environmental impact. Other benefits of precast beams are reduced crack-ing due to better quality control and efficient utilization of higher concrete strengths.As a result, significant initial and long term cost savings are possible with the newsystem.

Research conducted at the University of California at San Diego (UCSD) includedconstructing and testing two 40% scale models under fully-reversed longitudinal seis-mic loading. The first model utilized a modified version of the Florida bulb-tee beam.The second model, of similar scale, incorporated trapezoidal U-shaped beams. Theobjective of the testing program was to verify the structural adequacy of newly devel-

oped integral column-superstructure details under simulated seismic loads, and toallow Caltrans engineers to evaluate the constructibility of these details via large-scalemodels. The following sections describe the tests and results.

The focus of this research was to study the effects of longitudinal seismic forces onthe column-superstructure continuity. The prototype structure for the bulb-tee beamsystem is shown in Figure 15.6.1-1. The dimensions and forces of the model testunit were scaled directly from the prototype structure. The region selected for studyincluded the column, bent cap and full-width superstructure extending from mid-span to midspan. Two horizontal actuators placed on either side of the unit appliedload to model the seismic inertia forces acting along the bridge. Four vertical actua-tors located at the corners of the test unit applied seismic shear into the beams. The

test setup is shown schematically in Figure 15.6.1-2 (Holombo, et al, 2000).

15.6

CALTRANS RESEARCH

15.6.1Test Model Set-Up

SEISMIC DESIGN15.6 Caltrans Research/15.6.1 Test Model Set-Up

Figure 15.6.1-1Prototype Structure for Bulb-

Tee System Testing Program

42'-6"

Bent 2 Bent 3 Bent 4Abutment 5Abutment 1

585'-0"BB EB

132'-6" 132'-6"160'-0" 160'-0"

Region modeled

Earthquake force direction studied

26'-0"

7'-0" dia.


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The response of the superstructure to the simulated longitudinal seismic loading wasessentially elastic; only minor cracking was observed. Due to prestressing, the crack-ing in the bent cap and the beams closed upon removal of the seismic loads, mak-ing p

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