mnl-133-97 chapter 15

PCI BRIDGE DESIGN MANUAL CHAPTER 15

JUN 04

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 EXAMPLE—BULB-TEE, TWO SPANS, DESIGNED IN ACCORDANCE WITH STANDARD SPECIFICATIONS DIVISION I-A

15.4.1 Introduction

15.4.1.1 Bridge Geometry

15.4.1.2 Level of Precision

TABLE OF CONTENTSSEISMIC DESIGN

7602 PCI Bridge Manual Ch 15.1-3.indd 1 6/22/04 9:53:26 AM


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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 EXAMPLE—INTEGRAL BENT CAP 15.5.1 Introduction

15.5.1.1 Bent Cap Geometry

15.5.1.2 Reinforcement

15.5.1.3 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 area

A = seismic acceleration coefficient

Ac = area of pile core measured to the outside of the transverse spiral rein-forcement

Ag = gross area of pile

Ah = area of hoop reinforcement

Ai = area of a segment in a bent cap section

Ajv = vertical reinforcement to be placed over a distance of hb/2 from the column face

Aps = area of prestressing steel

ARS = acceleration response spectrum

As = 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 area

bb = bent cap width parallel to the longitudinal axis of the bridge

bje = effective width of bent cap

Cb = compression force

Cc = column compression force

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

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

D = column diameter

D = core diameter of spirally confined column

Di = force in diagonal compression strut within the superstructure/substructure joint where i = 1 through 3

Ecc = modulus of elasticity of deck and column concrete

Ecs = modulus of elasticity of concrete in the beam and bent cap

Es = modulus of elasticity of nonprestressed reinforcement

F = bent cap prestressing force after all losses

Fi = force in each quadrant

f c = specified compressive strength of concrete

foyc = over-strength stress of column reinforcement including strain hardening

fh = average horizontal stress (due to prestress) in the horizontal direction

fv = average joint axial stress in the vertical direction

fy = specified yield strength of non-prestressed reinforcement

fyh = yield strength of hoop or spiral reinforcement

fyv = yield strength of joint vertical reinforcement

g = gravitational acceleration (32.2 ft/sec/sec)

H = average column height in frame

hb = cap beam section depth

hc = column length from top of footing to center of gravity of the superstructure

IC = importance classification



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Ic = moment of inertia of column

Is = moment of inertia of superstructure cross-section about vertical axis through centroid

K = equivalent transverse stiffness

Kc = column shear stiffness

L = span length

L = length of longitudinal frame between expansion joints

la = assumed length of column anchorage reinforcement in joint

M = total contributory mass of superstructure and column

Mobot = column over-strength moment capacity at column bottom

Moi,bentcap = moment at middepth of bent cap

ML = longitudinal moment

MT = transverse moment

Motop = column over-strength moment capacity at column top

N = minimum abutment support length

n = modular ratio

P = axial force

PDL,BOT = axial force due to dead load at bottom of column

PDL,TOP = axial force due to dead load at top of column

Pe = axial compression load on the pile

pt = principal tensile stress

q = uniformly distributed load

R = response modification factor

Rcol = column seismic shear force

RSA = response spectrum analysis

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

S = site coefficient

SPC = seismic performance category

sreqd = required spacing of hoop reinforcement

T = external torsion

Tc = partial tension force in column

Tc = partial tension force in column

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

T(tr) = period of structure in the transverse direction

Vc = column shear force

Voi,column = horizontal shear force at top of column

Vjh = horizontal joint shear force

vjh = nominal horizontal shear stress in the joint

VL = longitudinal shear force

VT = transverse shear force

VT(Abutment) = abutment transverse shear force




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f ci

f c

Tc´–Yb

VV = vertical shear force

W = total contributory weight of superstructure and column

xi, yi = distances defining location of quadrant force, Fi–Yb = distance to centroid of superstructure cross-section from extreme

bottom fiber

Z = 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)

µ = coefficient of friction over the interface

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

ρs,min = minimum required value of ρs

τ = shear friction stress




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The threat of seismic hazard is often thought to be limited to California and a few other western states. However, the discovery of new fault zones and an increased understanding of their activity have prompted many other states to include some form of seismic design requirements in their bridge design specifications. Although most 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 1886 causing loss of life and considerable damage. Small earthquakes still occur in the region and seismologists indicate the potential for another damaging earthquake.

Other notable sources of earthquakes include the New Madrid Seismic Zone, the Central Virginia Seismic Zone; the Giles County, Virginia, Seismic Zone; and the Eastern Tennessee (or Southern Appalachian) Seismic Zone. Low seismic wave attenuation in the Eastern United States has the potential to cause significant shak-ing over broad areas, sometimes covering several states. The 1811-1812 New Madrid earthquakes, for example, caused seismic shaking of Intensity VI on the Modified Mercalli 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 the American Association of State Highway and Transportation Officials (AASHTO). Neither the first edition nor subsequent editions of the standard published prior to 1941 addressed seismic design. The editions published in the 1940s mentioned seismic 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 general requirements for seismic design of bridges were formulated in 1940. Specific force level recommendations for earthquake design were established in 1943.

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

SEISMIC DESIGN

15.1 INTRODUCTION

15.1.1 Seismic Activity

15.1.2 Seismic Design Criteria

15.1.2.1 Background



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SEISMIC DESIGN15.1.2.1 Background

Figu

re 1

5.1.

1-1

Acc

eler

atio

n C

oeffi

cien

t, A

, for

the

Uni

ted

Stat

es (

g’s)



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for seismic design of bridges were based in part on the lateral force requirements for buildings developed by the Structural Engineers Association of California. In 1973, Caltrans developed a specification based on research that considered the relation-ship of the site to active faults, seismic response of the soils at the site and dynamic response characteristics of the bridge. In 1975, AASHTO adopted interim specifica-tions that were slightly modified from the 1973 Caltrans provisions.

The 1971 San Fernando earthquake stimulated research activity by the Federal Highway Administration (FHWA), which, in 1978, funded a major research proj-ect headed by the Applied Technology Council (ATC). This effort focused on the development of improved seismic design guidelines for highway bridges that would be applicable to all regions of the United States. It culminated in the publication of Report No. ATC-6 entitled “Seismic Design Guidelines for Highway Bridges” (ATC, 1982). These guidelines incorporated an elastic Response Spectrum Analysis (RSA), with R and Z factors to account for redundancy in the structure, ductility of the structural components and risk. These guidelines emphasized detailing for ductile behavior and prevention of collapse even after significant structural damage occurs.

Acceptable seismic performance criteria for bridge structures must satisfy both safety and economic conditions. Clearly, requiring all bridges to be serviceable immediately after an earthquake may not be economically feasible. At the same time, it is well recognized that preventing bridge collapse and possible loss of life can and must be achieved. The principles used in the development of AASHTO provisions were:

1. The design ground motion must have a low probability of being exceeded during the normal lifetime of the bridge (10% probability of being exceeded in 50 years or a 475-year return period).

2. The bridge must have a low probability of collapse due to the design ground motion.

3. Structural damage is acceptable as long as it does not result in collapse or loss of life; and, where possible, damage that does occur should be readily detectable and accessible for inspection and repair. Small and moderate earthquakes should be resisted within the elastic range of the structural components without significant damage.

4. Functionality of essential bridges must be maintained.

5. The provisions must be applicable to all regions of the United States.

AASHTO adopted the ATC-6 recommendations as a guide specification in 1983, a standard specification in 1990, and incorporated them into the Standard Specifications in 1992. Subsequent to the earthquakes in Loma Prieta in California (1989), Costa Rica (1991) and the Philippines (1991), AASHTO requested that the Transportation Research Board review the provisions and prepare revised specifications as appropri-ate. Funded by the National Cooperative Highway Research Program (NCHRP), the National Center for Earthquake Engineering Research prepared the seismic design provisions that are included in the Standard Specifications.

15.1.2.2 Performance Objectives

15.1.2.3 Current Design Specifications

15.1.2.3.1 Standard Specifications

SEISMIC DESIGN15.1.2.1 Background/15.1.2.3.1 Standard Specifications



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Caltrans bridge engineering practice generally embraced deterministic ground motion hazards as established based on Caltrans 1996 California Seismic Hazard Map. A technical report published with the 1996 Map can be reviewed for further information on the considered seismic sources. Caltrans uses the mean event for standard practice and refers to it as the Maximum Credible Earthquake (MCE). Caltrans Seismic Design Criteria (SDC) V1.3, 2004, documents the current state of the practice. These criteria are intended to achieve a “No Collapse” condition for standard ordinary bridges using one level of Seismic Safety Evaluation.

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

The AASHTO LRFD Specifications incorporates many of the seismic provisions of the 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 response coefficients (response spectra) for soft soil conditions.

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

As more is learned about the effect of soil-structure interaction (SSI), new guidelines and procedures continue to be developed to enhance the accuracy of predictions of the bridge response to seismic loading. However, practical limitations prevent detailed incorporation of 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 be required. On very long bridges, the subsurface conditions may vary to the extent that a single-response spectra is not an accurate representation of the soil conditions. In these cases, multiple-support excitations may be specified. Multiple-support excitation requires the use of time history analysis, i.e., RSA cannot be used.

15.1.2.3.3 LRFD Specifications

15.1.2.4 Effect 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

15.1.2.3.2 Caltrans Specifications



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

In addition to SSI analyses, site stability issues should be addressed. These issues include soil liquefaction, soft-clay sites and slope hazards. Soil liquefaction includes the analysis for lateral spread, loss of support, dynamic settlement, as well as possible means of mitigation (site improvements). Large site amplification effects are usually considered for soft-clay sites. Earthquakes have been recognized as major causes of slope 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 signify an emerging application, which is expected to expand in coming years. Spliced beams provide 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. As a result of continuity, spliced-beam bridges also provide increased redundancy and improved 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 of low to moderate seismicity. However, precast concrete bridge systems developed for some level of seismic resistance may offer certain desirable qualities which can result in better and more economical designs, even when earthquakes are not among the major design considerations.

The most common form of concrete bridge consists of a cast-in-place (CIP) concrete deck 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 rectangular columns 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 connected to the substructure are used to create longitudinal frames with multiple spans. The box girders are, in some cases, supported on single columns. Multi-column bents are usually provided on wider bridges. Unlike the precast concrete beam system of a drop-cap pier, the CIP box girder system with a monolithic connection to the substructure resists longitudinal forces in double curvature bending of the column as 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 construction requires extensive falsework and formwork, which can result in lengthy periods for construction with possible traffic disruptions in roadways below the bridge.

15.2 SEISMIC RESISTANT PRECAST CONCRETE

BRIDGES

15.2.1 Spliced 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, prestressed concrete 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 the foundation supports. This requirement places substantial force demands on the foundations of multi-column bents, particularly in areas of moderate to high seismicity. Developing a moment 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 connection between 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 than the superstructure or footing. This is because plastic hinging is accompanied by a certain degree of damage in the form of inelastic displacements, cracked and spalled concrete and yielded 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 increasing the likelihood of collapse. Damage to a footing or pile system is not easily detected and is extremely difficult to repair. Plastic hinging in the column can be quickly identified by inspection and sometimes repaired. More importantly, a properly confined column will continue 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 dead load and a portion of the column seismic (plastic) moment on one side of the pier, and the difference 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 side where the moments are additive and a smaller, relatively constant positive moment on the

15.2.3 Seismic Response

Characteristics of Precast Concrete 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 CurvatureShape

Force

Force

Moment diagram

Shape Moment diagram

Fixed

Fixed

Fixed

Pinned

Figure 15.2.2-1 Single- versus Double-

Curvature Column



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opposite side. This distribution is reversible depending on the direction of the earthquake force. 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 (see Figure 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 in California to address the requirements of superstructure and substructure continuity, aes-thetics and minimized traffic impact during construction. Cross-sections for both single and two-column bents are shown in Figure 15.2.4-1. The superstructure of this bridge system consists of three basic components as described in the following sections.

15.2.4 Integral 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 jointor abutment

140' 160' 160'

Reactionfromadjacentframe

Field splice

Dead loadEarthquakeDead load + earthquake

Figure 15.2.3-1 Moment Distribution

along the Superstructure of a Longitudinal Frame Unit

Two-Column Bent

Single-Column Bent

Figure 15.2.4-1 Typical Bridge Cross-Sections with

Single- 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 variable length 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 and handling stresses and for a portion of the service negative moment over the pier. The pier segment also contains ducts for two stages of longitudinal post-tensioning: one for 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 segment to 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 by means 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 of the 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 corresponding bent cap design procedure is presented in Example 15.5.

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

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

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 15.2.4.1-1 Details 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 the pier segments by erection brackets as shown in Figure 15.2.4.1-1 and described in Chapter 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 and

Cross-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 15.2.4.3-1 Longitudinal Section and Cross-Section of

Drop-In Segment



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One of the important features of the integral system is its minimal impact on traffic during 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 minimal vertical 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 moment demands at the top of the column into the superstructure without yielding either the connection itself or the beam ends. To achieve this, both the connection and the beam ends must be designed to provide a design strength exceeding the required strength from the forces transferred i.e., capacity must exceed demand. Additionally, the connection should be detailed to ensure adequate distribution of the longitudinal moment 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

15.2.5.1 Superstructure-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 15.2.4.3-2 Construction 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 the column.

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 hinges form in the column rather than the superstructure.

Piles in soft soils supporting bridge structures may be subjected to large horizontal displacements due to design earthquakes. These deformations produce significant curvatures in the piles. The pile-cap interface (end fixity of the pile in the pile cap) is a 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 the buckling of reinforcing bars and tendons at large deformations and ensures adequate shear resistance.

Gerwick (1982) and Sheppard (1983) reported on the results of lateral load tests on 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 conducted on 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 of New Zealand (1982) would result in ductile behavior of precast, prestressed concrete piles. The spiral reinforcement in the test specimens was in accordance with the New Zealand Code requirements for potential plastic hinge regions of ductile reinforced concrete columns and piers. The tests showed that when there is adequate transverse reinforcement, piles subjected to cyclic lateral loading are capable of undergoing large post-elastic deformations without significant loss of load carrying capacity.

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

ρsg

c

c

yh

A

Aff

= −

′

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

or,

ρsc

yh

ff

=

′

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

whichever is greater

15.2.5.2 Ductility 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

ρs = 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 reinforcement

f c = specified compressive strength of concrete

fyh = yield strength of hoop or spiral reinforcement

The Standard Specifications also requires that center-to-center spacing of the spirals not exceed the smaller of 0.25 times the pile diameter, or 4 in. for Categories C and D 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 maximum cross-sectional pile dimension or one-sixth of the clear height of the pile, whichever is the larger, but not less than 18 in. At the bottom of piles in pile bents, transverse reinforcement must be provided over a length extending from three pile diameters below the calculated point of moment fixity to one pile diameter, but not less than 18 in., above the mud line. Lapping of spiral reinforcement in the transverse confine-ment regions is prohibited; connections of spiral reinforcement in this critical region must be full strength lap welds.

In the New Zealand Standard Code of Practice satisfactory results have been obtained by multiplying the generally accepted AASHTO volumetric ratios, ρs, 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 to Seismic 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 downloaded from www.dot.ca.gov) are used. For bridges with flexible foundations (i.e. soft or marginal soil, liquefaction, scour), the piles are explicitly designed for both vertical and lateral load path.

The strength and ductility of the connection between precast, prestressed concrete piles or pile extensions and reinforced concrete pile caps or bent caps is vital to the seismic performance of the piles. Gerwick (1993) describes three types of pile-to-cap connections that have been successfully employed. The connections are illustrated in Figure 15.2.5.3-1. They are described as follows:

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

15.2.5.3 Pile-to-Cap Connections

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



JUN 04

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

Case 3— Dowel bars embedded in the cap. Holes may be pre-formed in the pile with flexible 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 pile is not damaged during driving. The dowels should be embedded a distance sufficient 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) on prestressed concrete piles showed that well detailed prestressed concrete piles and pile-pile cap connections are capable of undergoing large post-elastic deformations without significant loss in strength when subjected to severe seismic loading. The three connection types mentioned above were investigated. All three permitted the pile to reach its full flexural strength and all three were found to have satisfactory ductile behavior.

The tests indicated that spiral steel, similar to that provided in the potential plastic hinge regions 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 to the 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 a greater 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 incorrugatedtubing

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

spacingstrands @ equal0.6"-dia. prestressed metal tubing

2 1/4"-dia. corrugated

Figure 15.2.5.3-1 Alternative Pile-to-Pile

Cap Connections



JUN 04

Figure 15.2.5.3-2 details typical monolithic and independent pile extension or “build-up” details for applications where the pile cut-off elevation may be different from that specified on the drawings due to field conditions.

Seismic isolation is gaining increased acceptance in the United States both as a means of enhancing 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 superstructures is to protect the piers, abutments and their foundations by limiting the forces transferred through the beams. Besides reducing seismic loads, the isolation design helps distribute the seismic 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

15.2.6 Isolation 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.

pilebuild-up

6'-0"max.

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 and

Independent Pile Buildup Details



JUN 04

Decoupling the bridge superstructure and substructure from damaging horizontal components of earthquake ground motions reduces the seismic demand on the sub-structure. However, it is essential to limit the seismic displacements of isolated bridge structures to tolerable levels in order to reduce the problem of supporting traffic across 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 isolation bearings should provide:

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

2. Additional damping and energy dissipation to control relative displacements across 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 bilinear force-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 Seismic Isolation Design (1999). The first is to take advantage of the reduced forces and pro-vide a more economical bridge design than conventional construction. This option uses the same modification factors as the Standard Specifications and hence provides the same level of safety. The second option intends to eliminate or significantly reduce 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 by eliminating the ductility demand on the substructure. The Guide Specifications also

SEISMIC DESIGN15.2.6 Isolation Methods

Displacement

ForceFigure 15.2.6-1

Force-Displacement Characteristics of Bilinear

Isolation Bearings



JUN 04

accounts for a reduction in the post-peak Acceleration Response Spectrum (ARS) curve due to the damping characteristics of the isolation bearings.

Further information on isolation methods is provided by Billings and Kirkcaldie, (1985) and Buckle and Mayes, (1990a and 1990b).

There are two general approaches to evaluate the seismic response of a bridge. The first approach is the conventional force-based analysis while the second involves the use of a displacement criterion. Caltrans uses the displacement method as described in the Seismic Design Criteria V1.3, 2004.

In this method, the bridge analysis is performed and the forces on its various components are determined. Next, the capacities of the components are evaluated. The component demand/capacity (D/C) ratios are then calculated. A particular component is said to have adequate capacity if its D/C ratio is less than a prescribed force reduction factor, R (or Z). This factor allows for limited inelastic behavior and depends on the type of compo-nent considered. The provisions contained in the Standard Specifications, Division I-A, are largely based on this approach. Figure 15.3.1.1-1 is a flow chart of the basic steps of seismic design in the Standard Specifications. The corresponding AASHTO classifications and analysis requirements are given in Table 15.3.1.1-1.

Seismic Acceleration Coefficient

Aa

Importance Classification (IC)

IC = I

(Essential Bridges)

IC = II

(Other Bridges)

SPCb Minimum Analysis Requirements SPCb Minimum Analysis

Requirements

A ≤ 0.09 A Not Required A Not Required

0.09 < A ≤ 0.19 B Regular bridges with 2 through 6

spans:c

Use Procedure

1 or 2d

Not regular bridges with 2 or more

spans:c

Use Procedure

3d

B Regular bridges with 2 through 6

spans:c

Use Procedure

1 or 2d

Not regular bridges with 2 or more

spans:c

Use Procedure

3d

0.19 < A ≤ 0.29 C C

0.29 < A D C

a Acceleration Coefficient, A, is defined in STD Div. I-A, Art 3.2b Seismic Performance Category, SPC, is defined in STD Div. I-A, Art 3.4c Regular bridge requirements are given in Table 4.2B of STD Div. I-A, Art 4.2d Seismic Analysis Procedures are defined in STD Div. I-A, Art 4.3 and 4.4

15.3.1.1 Conventional Force Method

SEISMIC DESIGN15.2.6 Isolation Methods/15.3.1.1 Conventional Force Method

15.3 SEISMIC ANALYSIS

AND DESIGN

15.3.1 Analysis Methods

Table 15.3.1.1-1 AASHTO Seismic

Classifications and Analysis Requirements



JUN 04

SEISMIC DESIGN15.3.1.1 Conventional Force Method

START

Preliminary Design

Applicablility of the SpecificationSTDDiv. I-A, Art. 3.1

Acceleration CoefficientSTDDiv. I-A, Art. 3.2

Importance ClassificationSTDDiv. I-A, Art. 3.3

Site Effects

Seismic Performance Category

STDDiv. I-A, Art. 3.5


Determine Elastic Seismic Forces

Determine Analysis Procedure

Response Modification Factors

STDDiv. I-A, Section 4



and Displacements

Determine Design Forces Design FoundationsDesign Abutments

PerformanceCategory D?

SeismicDesign Approach SlabsSTDDiv. I-A, Art. 7.4.5

Are

Adequate?Components

Seismic Design CompletePrepare Seismic Details

END

Revise Structure

No

No

Yes

Yes

Figure 15.3.1.1-1 Basic Steps in AASHTO

Division I-A Seismic Design



JUN 04

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. Capacity thus takes on a more global meaning since it refers to the entire structure rather than to a given component, as in the force analysis. Displacement is taken as the measure 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 sustain any further increase in rotation. Typically, displacement demand is obtained from a three-dimensional analysis using reduced flexural and torsional section properties. By relying 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 forces and displacements are based on a linear elastic multi-mode Response Spectrum Analysis (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 often requires additional data to describe the behavior of the material.

3. It provides acceptable limit-state solutions. In most cases, there are no real gains in resorting to a higher level of analysis. When discontinuities or other sources of non-linearity exist, an iterative procedure based on the equivalent linear solution may be used to satisfy force and displacement requirements. Limit states are often used 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 boundary conditions or material properties. Examples of the commonly used limit states are the tension and compression models of a bridge with expansion hinges and abut-ment supports. The tension model corresponds to the opening of all expansion hinges and lack of abutment soil springs (stiffness), while the compression model corresponds 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 as proximity 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

15.3.1.2 Displacement Ductility

Method

15.3.2 Computer Modeling



JUN 04

15.3.3.1 Causes of Failures

15.3.3.2 Preliminary Design Recommendations

15.3.3 Seismic Design Issues

Linear elastic solutions often provide adequate accuracy. The extra effort needed to produce 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 where an 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, the demand for improved seismic performance of bridges has been increasing. The gen-eral trend is toward an increase in seismic design requirements and an emphasis on the 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 to insufficient 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 acceleration or 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 large movements 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 components and 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 prevent concentration of load demands on a particular bent or frame. This will also minimize 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 those cases, foundation flexibility should be considered when evaluating the demand.

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

SEISMIC DESIGN15.3.2 Computer Modeling/15.3.3.2 Preliminary Design Recommendations



JUN 04

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

9. Use isolation details at column architectural flares, or if the flares are to be relied upon 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



JUN 04

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 in Figure 15.4.1-1. The superstructure consists of four precast, prestressed concrete bulb-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 and is therefore considered fixed at its base. The superstructure is integrally connected to the 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 a prototype structure for the integral bent design, presented in the following section. The seismic analysis procedure presented here is equally valid for other conventional precast bridge systems.

15.4 SEISMIC DESIGN

EXAMPLE—BULB-TEE, TWO SPANS, DESIGNED

IN ACCORDANCE WITH STANDARD SPECIFICATIONS

DIVISION I-A

15.4.1 Introduction

SEISMIC DESIGN15.4 Seismic Design Example—Bulb-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 15.4.1-1 Bridge Elevation and Typical Sections

7602 PCI Bridge Manual Ch 15.4.indd 1 6/22/04 9:57:39 AM


JUN 04

Because the bridge is a two-span concrete structure, the seismic loads and analysis procedures of Division I-A of the Standard Specifications are 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 bridge Acceleration 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) is B [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 of stiff 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 ft

Bent cap width = 7.00 ft

Bent cap depth = 6.71 ft for structural calculations

Column height = 26.00 ft

Column diameter = 6.00 ft

Beam spacing = 10.83 ft

Deck thickness = 8 in. for structural calculations

Abutment diaphragm thickness = 3.00 ft

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

Beam concrete strength = 6,000 psi

Bent cap concrete strength = 6,000 psi

Deck concrete strength = 4,000 psi

Column concrete strength = 4,000 psi

Unit weight of concrete = 144 pcf

Unit 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 15.4.1-1 Response Modification Factors

[STD Div. I-A, Table 3.7]

15.4.1.2 Level of Precision

15.4.2 Material Properties



JUN 04

Unit weight of deck, columns, and abutment diaphragms = 150 pcf

Modulus of elasticity of concrete in the beam and bent cap, Ecs:

E f psi f ksics c c= =′ ′57 000 57,

where f c = concrete strength, psi

E ksfcs = =57 6 000 144 635 800, ( ) , Modulus of elasticity of concrete in deck and column, Ecc:

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

nEE

cc

cs

= = =519 100635 800

0 816,,

.

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 applied at the center of gravity of the superstructure, transverse to its axis, as shown in Figure 15.4.3-1. The total seismic load (uniform load times bridge length) is taken equal to the total dead weight of the superstructure plus the tributary weight of the columns multiplied by 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 ft

Moment of inertia about the centroid of the major axis of the non-composite precast beam = 36.44 ft3

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

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

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

15.4.3 Seismic Analysis in

Transverse Direction

15.4.3.1 Section Properties

15.4.3.1.1 Beam Properties

SEISMIC DESIGN15.4.2 Material Properties/15.4.3.1.1 Beam Properties

L

Lq

∆Figure 15.4.3-1 Assumed Transverse

Response According to the Uniform Load Method



JUN 04

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 beam contributes 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 determine the 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 ft

Transformed 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 = π πD4

64

6

64

4

=( )

= 63.62 ft4

The total dead load to be included in the seismic analysis is equal to the sum of the weights of the deck slab, four beams with haunches, bent cap, two barriers, future wearing surface, end diaphragms, and one-half of the column weight. Refer to Figures 15.4.1-1 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/ft

Bent cap: (7.0)(6.71)(42.5)(0.155) = 309 kips

Barriers (2 barriers at 0.4 kip/ft): 2(0.4) = 0.8 kip/ft

15.4.3.1.2 Composite Section Properties

15.4.3.1.3 Column 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'

3.10'

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

Y

Girder

Y

XY = 4.54'b

4'-0"(typ.)

C. G. ofcompositesection

c

Bulb-tee beam:A = 7.39 ft2I = 36.44 ft4 (Major axis)I = 3.33 ft4 (Minor axis)f = 6,000 psi'

Deck slab:A = 23.12 ft2I = 0.86 ft4f = 4,000 psic'

Figure 15.4.3.1.2-1 Bridge Cross-Section Geometric Properties



JUN 04

Future wearing surface at 35 psf: (0.035)(42.5) = 1.49 kip/ft

Abutment diaphragm: (3)(6.71)(42.5)(0.150) = 128 kips per diaphragm

Column: π 62

0 150 4 242

( ) =. . 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 kips

Total dead load: 3,591 + 55.1 = 3,646 kips – Use 3,700 kips.

In the transverse response mode, the superstructure is assumed to provide negligible restraint against column-top rotations. Hence, the column is assumed to undergo single-curvature bending (i.e., it acts like a cantilever). The column length, hc, used for calculating shear stiffness is measured from the top of footing to the center of gravity 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 q

q = uniformly distributed load

L = length of one span

∆2 =( )R 2L

48E Icol

3

cs s (Eq. 15.4.3.3-2)

where

∆2 = lateral displacement caused by a column force of Rcol

Rcol = column force

∆ = ∆1 − ∆2 (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 IR (8)L48E I

4

cs s

col3

cs s

(Eq. 15.4.3.3-5)

15.4.3.3 Equivalent Transverse

Stiffness

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 EffectRcol

q = 1.0 kip/ft

∆

∆

∆

Figure 15.4.3.3-1 Column Reaction Due to a Uniform Transverse Load



JUN 04

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

∆ ∆ ∆= − = −(5)(1.0)(16)L384E I

24E I L

48h E I

80L384E 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) (4.240 x10 )

4

9

7 3

3 9∆ ∆0 0189 0 3752. .

∆ = =0 01891 3752

0 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 500π π πM

KWgK

= = ,. ( , )

= 0.470 seconds

where

T(tr) = period of structure in the transverse direction

M = total contributory mass of superstructure and column

W = total contributory weight of superstructure and column

g = gravitational acceleration

Cs(tr) = 1.2AS

T2.5A

(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 3573 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

15.4.3.5 Elastic Seismic

Response Coefficient

15.4.3.6 Column Forces in the Transverse Direction

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



JUN 04

The Uniform Load Method may also be used to calculate the longitudinal seismic forces on the structure. The superstructure is assumed to displace as a rigid unit as the supporting 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 restrained against rotation. Therefore, the column undergoes double-curvature bending, as opposed to single-curvature bending, which occurs in the transverse direction. The column length used for calculating shear stiffness, H, is measured from the top of footing to the bottom of the bent cap. In this example, H = 26 ft.

Column shear stiffness = 12E I

H

xcc c3

= =12 3 303 10

2622 550

7

3

( . )

( ), kip/ft

In general, the abutments and soil behind them may contribute to the longitudinal stiffness. Their contribution depends on the abutment type (i.e., integral vs. seat abutment) and the longitudinal displacement of the structure. Several iterations may be needed to evaluate the abutment effect on the stiffness. Additionally, a minimum displacement 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 thus the abutment contribution to stiffness is ignored.

T(long) = 2 2 2π π πMK

WgK

3,70032.2(22,550)

= = = 0.449 seconds

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

Cs(long) = 1.2AS

T2.5A

long2/3( )

≤ [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

15.4.4 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

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

Elevation

Figure 15.4.4-1 Assumed Seismic Response in

the Longitudinal Direction



JUN 04

Column shear = (0.368)(3,700) = 1,362 kips

Column 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 LongitudinalMoment 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-kips

ML = (1.0)(0) + (0.30)(17,706) = 5,312 ft-kips

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

VL = (1.0)(0) + (0.30)(1,362) = 409 kips

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

15.4.4.4 Column Forces in the Longitudinal Direction

15.4.5 Combination of

Orthogonal Forces

Table 15.4.5-1 Summary of Column Forces

15.4.6 Abutment Design Forces

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



JUN 04

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 kips

Design 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 by the 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 factors such as the bearing size may control the final seat width.

LIST OF FIGURES—15.4:

Figure 15.4.1-1 Bridge Elevation and Typical Sections

Figure 15.4.3-1 Assumed Transverse Response According to the Uniform Load Method

Figure 15.4.3.1.2-1 Bridge Cross-Section Geometric Properties

Figure 15.4.3.3-1 Column Reaction Due to a Uniform Transverse Load

Figure 15.4.4-1 Assumed Seismic Response in the Longitudinal Direction

Figure 15.4.6-1 Transverse Shear at the Abutments

Figure 15.4.7-1 Minimum Abutment Seat Width

15.4.7 Minimum 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 15.4.6-1 Transverse Shear at the

Abutments



JUN 04

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 15.4.7-1 Minimum Abutment

Seat Width



JUN 04

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

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

Bent cap width = 84 in.

Bent cap depth, hb = 87 in.

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

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

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

Cast-in-place concrete strength, f c = 4 ksi

Reinforcing steel yield strength, fy = 60 ksi

Modulus of elasticity of tendons, Es = 29,000 ksi

15.5 SEISMIC DESIGN

EXAMPLE—INTEGRAL BENT CAP

15.5.1 Introduction

15.5.1.1 Bent Cap Geometry

15.5.1.2 Reinforcement

15.5.1.3 Material Properties

SEISMIC DESIGN15.5 Seismic Design Example—integral Bent Cap/15.5.1.3 Material Properties

Figure 15.5.1.1-1 Column Cross-Section 72 in.

#11(30 total)

#6 @ 4" pitch

Section

7602 PCI Bridge Manual 15.5-7.indd 1 6/22/04 10:02:26 AM


JUN 04

Axial load: Top of column, PDL,TOP = 2,225 kips Bottom 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 plastic moment capacities.

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

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 for column bars with the reinforcement being extended as close as possible to the top reinforcement in the bent cap.

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

Horizontal joint shear force, Vjh, is given by:

Vjh = M

h

14,115 x1287

1,947 kips topo

b

= =

Effective width of bent cap, bje, by the geometry shown in Figure 15.5.3-1 is

f ci

f c

Mobot

Moi,bentcap

Motop

Tc´–Yb

15.5.1.4 Forces

15.5.1.5 Precision

15.5.2 Design Procedure

15.5.3 Principal Stresses

in the Bent Cap

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

Figure 15.5.3-1 Effective Joint Width for Joint

Shear Stress Calculations

Cap beam

=jeb

D bbje b

Bridge axis

Web

2D



JUN 04

bje = 2 D ( for circular sections ) ≤ bb

where

D = column diameter

bb = 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 D1,947

(84)(72)0.322 ksi jh

b

= =

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

fP

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, no significant 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

2f f

2v t

y h2

v hjh2=

+− −

+

= + − −

+ = −(0.167) (0)2

0.167 02

(0.322) 0.249 ksi2

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 need to be provided. However, for the purpose of this design example, the cap will be designed for the full joint shear requirement.

SEISMIC DESIGN15.5.3 Principal Stresses in the Bent Cap

7602 PCI Bridge Manual 15.5-7.indd 3 7/2/04 12:28:37 PM


JUN 04

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). The assumed joint force transfer mechanism is shown in Figure 15.5.4-1. The assumed mechanism reduces congestion by placing the joint reinforcing steel outside the column 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 diagonal compression strut D1 (see Figure 15.5.4-1).

2. The remaining 25% of the total longitudinal column reinforcement at appropriate strain 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 stirrups allow 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/2 from the column face on each side of the column in accordance with the following equation:

A 0.125 Af

fjv scyco

yv

=

where

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

f oyc = material over-strength stress of column reinforcement allowing for strain

hardening

fyv = yield strength of joint vertical reinforcement

Taking f oyc = 1.4fyv for Grade 60 reinforcement:

15.5.4 Joint Reinforcement Design

SEISMIC DESIGN15.5.4 Joint Reinforcement Design

Figure 15.5.4-1 Assumed Mechanism for Joint

Force Transfer in Pier Cap1D

stirrupsJoint shear

cC c'T Tc

cV

D3

2D

Cb

Integral bent capColumn



JUN 04

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 of hb/2 = 87/2 = 43.5 in. from the column face.

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

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

A 0.0625Af

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 at the top of the joint, these stirrups need not extend to the base of the joint. They are extended at least two-thirds of the bent cap depth or 2/3(87) = 58 in. Figure 15.5.4-2 indicates the locations for the placement of vertical joint reinforcement.

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

SEISMIC DESIGN15.5.4 Joint Reinforcement Design

Figure 15.5.4-2 Locations for Vertical

Joint Reinforcement

1 2

2

≤ 2D

in each area, andjA v

1

Bridge axis Avi = 0.5Ajv within core



JUN 04

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

ρsyh a

sc yco

a

3.3Df l

0.09A f D

lF=

−

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:

ssc yc

o

a2

yh

0.3A f

l fρ =

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

(80) f0.00307yh

2yh

However, minimum horizontal hoop reinforcement, ρs,min, must be provided according to the following:

s,minc

yh

f

f 60,000ρ = = = >

′3 5 3 5 40000 00369 0 00307

. ( . ). .

Use ρs = 0.00369

sreqd = 4A

D

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

6.99 in. h

s′ = =ρ

where

sreqd = required spacing of hoop reinforcement

Ah = area of hoop reinforcement

D = core diameter of spirally confined column = 68.25 in.

Provide #6 stirrups @ 6 in. spacing. If the hoop reinforcement ratio provided is less than the required ratio, the difference could be made up with split hairpins as described 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 shears are 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, spiral cracks 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 illustrated in Figure 15.5.5-1.

15.5.5 Shear-Friction Analysis

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



JUN 04

Assumptions:

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

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

The bent cap section is subjected to a vertical shear force, VV, a horizontal shear force, 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 as parallel to the outer edge, and the shear-friction stress, τ, is taken as:

τ = µ P/A

where

A = total section area

µ = coefficient of friction over the interface

SEISMIC DESIGN15.5.5 Shear-Friction Analysis

Figure 15.5.5-1 Torsional Shear-Friction

Mechanism

T

V

P

VL

V

Figure 15.5.5-2 Conceptual 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



JUN 04

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

Fi = τAi

where Ai = area of the segment.

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

VV = F1 − F3 = τ(A1 − A3)

VL = F2 − F4 = τ(A2 − A4)

T = F1x1 + F2y2 + F3x3 + F4y4 = τ(A1x1 + A2y2 + A3x3 + A4y4)

where

T = external torsion

x1, 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 checking that the implied value of the friction coefficient, µ, is reasonable. Alternatively, a limit design value of µ = 1.4 can be used with F1 to F4 selected to satisfy the first two equations shown above. The torque predicted by the third equation must then be checked to ensure that it exceeds the applied torque. The latter alternative is utilized in this design solution.

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

P = F + As(0.0005)Es

where

F = prestressing force after all losses

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

τ µ= =( )( )( )( ) =P

A

1.4 4,553

7.25 7.00125.6 kips /ft 2

Horizontal shear force at top of column, VM M

Hi,columno bot

otopo

=+




JUN 04

V14,340 14,115

25.751,105 kipsi,column

o = +

=

Moment at middepth of bent cap, M M Vh2

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 are as follows:

Torsion: M 1.1

2

18,120 1.1

2i,bentcapo ( )

=( )( )

= 9,966 ft-kips

Longitudinal shear: V 1.1

2

1,105 1.1

2i,columno ( )

=( )( )

= 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 ascertain the ability of the bent cap to transfer the column plastic moment capacity to the bridge superstructure. The assumed dimensions of each segment are shown in Figure 15.5.5-3.

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

Assumed

X-Coordinate = 4.90 ftY-Coordinate = 2.90 ft

SegmentArea, ft2 Distance from

Centroid, ft

First Moment about 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 y2 = 2.175 33.11

3 7.25 x 2.10 A3 = 7.613 x3 = 2.800 21.32

4 7.00 x 2.90 A4 = 10.150 y4 = 2.658 26.98

Total 50.750 114.57

Capacity Required

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

14,390 9,966

VV = τ (A1 − A3), kips 1,275 1,224

VL = τ (A2 − A4), kips 637 608

Table 15.5.5-1 Torsional Shear-Friction

Computations




JUN 04

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


Figure 15.5.5-3 Assumed Dimensions for Shear-

Friction Computations

A4

A3

7.25'

4.90'

4.35'

A2

7.00'

2.10'

2.90'

A1

Figure 15.5.5-4 Integral 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. strandtendon (total of 6)

#6@6"



JUN 04

Bridges in California have been predominantly CIP box girder systems due to the requirements for high seismic resistance. The examples presented in Sections 15.4 and 15.5, show that spliced beams with integral bent caps can provide a viable solution 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, and lower 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 new system.

Research conducted at the University of California at San Diego (UCSD) included constructing 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. The objective of the testing program was to verify the structural adequacy of newly devel-oped integral column-superstructure details under simulated seismic loads, and to allow Caltrans engineers to evaluate the constructibility of these details via large-scale models. The following sections describe the tests and results.

The focus of this research was to study the effects of longitudinal seismic forces on the column-superstructure continuity. The prototype structure for the bulb-tee beam system is shown in Figure 15.6.1-1. The dimensions and forces of the model test unit were scaled directly from the prototype structure. The region selected for study included the column, bent cap and full-width superstructure extending from mid-span to midspan. Two horizontal actuators placed on either side of the unit applied load 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

15.6.1 Test Model Set-Up

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

Figure 15.6.1-1 Prototype Structure for Bulb-

Tee System Testing Program

42'-6"

Bent 2 Bent 3 Bent 4Abutment 5Abutment 1

585'-0"BB EB132'-6" 132'-6"160'-0" 160'-0"

Region modeled

Earthquake force direction studied

26'-0

"

7'-0" dia.



JUN 04

The prototype structure for the second test used precast U-beams. The U-beam seg-ments were spliced at the bent cap and at the midpoint of each span. A single-pour, monolithic bent cap is possible with this system because it is not feasible to make the U-beams continuous over the bent. A setup similar to the one shown in Figure 15.6.1-2 was used for the second test.

Performance of the model bridge structures exceeded the design requirements during the tests (Holombo, et at, 2000).

Ductile plastic hinges formed at the top and bottom of the column with little strength degradation up to a displacement ductility of eight and six for bulb-tee and U-beam models, respectively. Both models exceeded the design ductility capacity of four. The force-displacement loop for the bulb-tee model is shown in Figure 15.6.2.1-1.

15.6.2 Test Results

15.6.2.1 Columns

SEISMIC DESIGN15.6.1 Test Model Set-Up/15.6.2.1 Columns

Figure 15.6.1-2 Test Setup

Reaction frame

tensioningCG post-

Hold-down

Horizontal actuator

spliceBeam

Vertical actuatorstotal (2) each side

66'-6"18'-0" 32'-0"

Reaction wall

floorTest laboratory

2'-9

1 /8"

Figure 15.6.2.1-1 Hysteresis Loop from Testing

of the Bulb-Tee System

Hor

izon

talf

orce

(kN

)

Displacement (mm)

Prediction Vi

Hor

izon

talf

orce

(kip

)

Displacement (in.)

Vi



JUN 04

The response of the superstructure to the simulated longitudinal seismic loading was essentially 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 potential repair of the superstructure after a design level earthquake, essentially cosmetic.

These tests demonstrate the versatility and flexibility of precast spliced-beam systems. Specifically, the tests proved that an integral connection between the superstructure and substructure can be achieved with or without beam continuity through the bent cap. They also proved that, with proper design and detailing, the beam splice points could be placed anywhere in the span or over the supports without any measurable reduction in performance of the system.

AASHTO LRFD Bridge Design Specifications, Second Edition, American Association of State Highway and Transportation Officials, Washington, DC, 1998

ATC, Seismic Design Guidelines for Highway Bridges, Report No. ATC-6, Applied Technology Council, Redwood City, CA, 1982, 210 pp.

ATC, Improved Seismic Design Criteria for California Bridges, Report No. ATC-32, Applied Technology Council, Redwood City, CA, 1996, 214 pp.

Billings, I.J. and Kirkcaldie, D.K., “Base Isolation of Bridges in New Zealand,” Proceedings of the US-NZ Workshop on Seismic Resistance of Highway Bridges, Report No. ATC 12-1, Applied Technology Council, Redwood City, CA, 1985

Bridge Design Specifications, California Department of Transportation, Division of Structures, Sacramento, CA, 2000

Buckle, I.G. and Mayes, R.L., “The Application of Seismic Isolation to Bridges,” Proceedings, ASCE Structures Congress: Seismic Engineering-Research and Practice, May 1990a, pp. 633-642

Buckle, I.G. and Mayes, R.L., “Seismic Isolation – History, Application and Performance – A World View” Earthquake Spectra, EERI, May 1990b

Budek, A.M., Benzoni, G. and Priestley, M.J.N., Precast Pile Tests Indicate High Ductility – Preliminary Report on Prestressed Pile Shaft Test Units, Prestressed Concrete Manufacturers Association of California (PCMAC), Technical Update, 1996

Gerwick, B.C. Jr., “Seismic Design of Prestressed Concrete Piles,” Proceedings, 9th FIP Congress, Federation Internationale de la Precontrainte, Stockholm, Sweden, V.2, 1982, pp. 60-69

Gerwick, B.C., Jr., Construction of Prestressed Concrete Structures, Second Edition, John Wiley & Sons, New York, NY, 1993, 591 pp.

15.6.2.2 Superstructure

15.7 REFERENCES

SEISMIC DESIGN15.6.2.2 Superstructure/15.7 References



JUN 04

Guide Specifications for Seismic Isolation Design, 2nd Edition, American Association of State Highway and Transportation Officials, Washington, DC, 1999, 80 pp.

Holombo, J., Priestley, M.J.N. and Seible, F., “Continuity of Precast Prestressed Spliced-Girder Bridges under Seismic Loads”, PCI JOURNAL V. 45, No. 2, March-April 2000, pp. 40-63

Joen, P. H. and Park, R., “Simulated Seismic Load Tests on Prestressed Concrete Piles and Pile-Pile Cap Connections,” PCI JOURNAL, V. 35, No. 6, November-December 1990, pp. 42-61

Park, R. and Falconer, T.J., “Ductility of Prestressed Concrete Piles Subjected to Simulated Seismic Loading,” PCI JOURNAL, V.28, No.5, September-October 1983, pp. 122-144

Priestley, M.J.N., Seible, F. and Calvi, G.M., Seismic Design and Retrofit of Bridges, John Wiley & Sons, New York, NY, 1996, 704 pp.

SDC, Seismic Design Criteria, California Department of Transportation, Sacramento, CA, V1.3, 2004 (available at www.dot.ca.gov)

Sheppard, D.A., “Seismic Design of Prestressed Concrete Piling,” PCI JOURNAL, V. 28, No. 2, March-April 1983, pp. 20-49 and discussion by Gerwick, B.C. and Sheppard, D.A., V. 29, No. 2, March-April 1984, pp. 172-173

Standard Code of Practice for the Design of Concrete Structures, NZS 3101, Part 1, Standards Association of New Zealand, Wellington, 1982, 127 pp. and Commentary on NZS 3101, NZS 3101, Part 2, 1982, 156 pp.

Standard Specifications for Highway Bridges, 17th Edition, American Association of State Highway and Transportation Officials, Washington, DC, 2002

SEISMIC DESIGN15.7 References


mnl-133-97 chapter 15

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