Application of strut and tie concepts to prestressed concrete bridge joints in seismic regions

and knee joint forces, and moment and shear force diagrams at column overstrength condition.!” shear force The FTM evolved from experimental and analytical studies of knee exte- rior

Application of Strut-and-Tie

Concepts to Presressed Concrete

Bridge Joints in Seismic Regions

transfer models based on the proposed mechanisms and design

examples are also included to assist structural engineers with the

application of FTM

eginning with the pioneering

Br of Ritter! and Mérsch?

about a century ago, numerous

researchers have examined the appli- cation of strut-and-tie model concepts

to structural design problems.* Typical

applications have been directed at the detailing of deep beams, beam sup-

ports, frame corners or knee joints,

corbels, and membranes with open-

ings, when subjected to static loading

More recently, strut-and-tie model concepts have been applied in order to

understand structural behavior and ap- propriately detail cap beam-to-column bridge joints, bridge footings and other bridge structural systems sub- jected to seismic loading In this re- gard, strut-and-tie models have direct application to prestressed concrete bridges

This paper presents a mcthodology

suitable for design and assessment of

bridge joints subjected to in-plane seis-

mic actions, which hereafter is referred

to as the force transfer method (FTM)

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Table 1 Summary of large-scale in-plane seismic tests on bridge cap beam-to-column joints considered in the

investigation of FTM

with columns having interlocking spirals

having circular columns

As-built tee joint system having a circular column 75 percent 1 tee joint MacRae et al.”

Redesigned tee joint systems having circular columns " Sritharan et al.!°

with varying amounts of cap beam prestressing

with headed reinforcement

A three-column bent with cast-in-place steel shell circular columns 100 percent 2 knee joints and | tee joint Silva et al.!

and knee joint

forces, and moment

and shear force diagrams at column overstrength condition.!”

shear force

The FTM evolved from experimental

and analytical studies of knee (exte-

rior) and tee (interior) joints in con-

crete multiple column bridge bents

The bridge joint studies were moti-

vated by the (a) use of inadequate joint

details in practice and subsequent

damage in earthquakes, and (b) unnec-

essarily congested details of bridge

joints resulting from the building joint

design method

One major objective of the work has

been to find sufficient and less conser-

July-August 2003

vative joint reinforcement details.*°

Encompassing details from as-built, retrofitted, and repaired joints, as well

as joints designed to specific joint force transfer models, the investiga- tion included seismic testing of 20 bridge joints at 33 to 100 percent scale

(see Table 1).”

Circular columns are generally pre-

ferred for bridge structures in seismic regions because they are efficient, easy to construct, and cost effective for confinement requirements Ac-

cordingly, circular columns were used

in most of the test joints; five of them were designed with rectangular shaped columns with interlocking spirals

All of the bridge test joints were

subjected to cyclic loading with full

reversals to satisfactorily simulate seismic effects An extensive instru-

mentation scheme was adopted in cach test

The experimental studies were com- plemented with parallel analytical studies which focused on understand-

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(c) Variation of vertical

shear force

Fig 2 Comparison of maximum and average vertical joint shear forces.'7

ing the observed joint behavior using

experimental data and linear and non-

linear finite element analyses, as well

as establishing or refining joint force

transfer models Results from various

detailed experimental and analytical

studies were used to develop the FTM

presented here

Seismic design procedures for

bridge joints based on force transfer

models have been recommended for

use in design practice.'*!° These docu-

ments provide a prescriptive set of de-

sign steps which are based on one of

several force transfer models pre-

sented by Priestley et al.'’ However,

the selected force transfer model for

use in design practice has been shown

to be inadequate through experimental

and analytical studies.!':'872

Failure to provide a complete treat-

ment of the joint force transfer is the

cause for error in development of the

design steps reported in References 14

to 16 Understanding of the FTM, as

detailed below, will enable both ap-

propriate improvements to be made to the existing, inadequate design mod- els, and the introduction of new mod- els suitable for different joint condi-

tions After selecting a force transfer

model for design in accordance with FTM, a satisfactory set of design steps may be established as illustrated as demonstrated in Reference 19

In the remainder of this paper, some familiarity with the basic strut-and-tie model framework, such as the method

outlined by Scleich et al.,”° is as-

sumed As a preamble to discussing FTM, the current bridge seismic de- sign philosophy, resulting joint force condition and joint failure modes are first discussed An outline of the force transfer method, with guidelines for joint design and assessment, is then presented Application of strut-and-tie concepts in representing joint force transfer and key joint mechanisms, and joint force transfer models are fi- nally presented, along with examples

in Appendix A

SEISMIC DESIGN PHILOSOPHY Seismic design of concrete bridge structures is currently based on the ca-

pacity design philosophy,'’ in which

the locations of plastic hinges are pre- selected, most conveniently at the col- umn ends, and inelastic actions devel- oping outside these hinges are prevented by using strength hierarchy

in the design Joints and other struc- tural members are, therefore, designed for actions corresponding to develop-

ment of the overstrength moment ca-

pacities of the column plastic hinges

Joint Forces Typical forces acting in the bridge joint regions, consisting of the joint panel and end zones of the cap beam and column, are shown in Figs la to

lc With plastic hinges developing at the column top adjacent to the joint in- terface, an average shear force acting upon the joint panel in the horizontal direction can be approximated assum- ing that the column overstrength mo- ment uniformly diminishes over the full depth of the cap beam as illus- trated in Figs 1d and le:!”

M’-AM_ M?

V =

" d-05a h, (1)

where M? = overstrength moment capac- ity of the column at the joint interface and is obtained from a column section anal- ysis with due consideration

to the column axial force re- sulting from gravity and seismic actions

AM = resultant moment resistance due to beam shear at the joint interfaces [= 0.5h,(V 5,

+ V?,)|

d = effective beam depth

a = depth of the equivalent rect- angular compression block

in the beam

h, = beam depth

h = column section depth (or di-

ameter for circular columns)

in the plane of loading The corresponding average joint shear force in the vertical direction can be approximated by:

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h

The average joint shear forces in

Eqs (1) and (2) are regarded as suit-

able for joint design, rather than using

the maximum shear forces derived

from forces acting upon the joints (see

Figs la to lc).'’?! The maximum

shear force, which is more useful for

describing localized damage such as

the initiation of joint cracking, is com-

pared in Fig 2 with the corresponding

average joint force in the vertical di-

rection for a bridge tee joint

Joint Stresses

Using the average joint shear force,

joint shear stress developed in the hor-

izontal and vertical directions during

in-plane loading can be obtained from:

where 5; is the joint effective width and

is taken as the lesser of /2D or b,, (see

Fig 3) with D and b,, being, respec-

tively, the column diameter and the

beam width.'’ For joints with rectangu-

lar columns, /2D is replaced with (h,

+ b,), where b, is the column width

Using the column and beam axial

forces, the joint normal stresses in the

vertical and horizontal directions may

be estimated A 45-degree dispersion

of forces is assumed for calculating the

vertical stress f, (see Fig 3a), while the

beam gross area is used in estimating

the joint horizontal stress f, With these

estimates, the joint principal compres-

sion and tensile stresses are:

Since the principal stresses have

better correlation to joint damage than

do other parameters such as the joint

shear force, p,; and p, are used as initial

design parameters in FTM

JOINT FAILURE MODES

When subjected to in-plane seismic

loading, the failure of bridge joints

(b) Horizontal shear stress

Fig 3 Effective areas for calculating stresses in joints with circular columns

may occur in four different modes.°®

Each of these failure modes was ob-

served in large-scale testing of joints

and is shown in Fig 4 In each case, despite joint failure, the test unit was able to sustain the simulated gravity

load effects Descriptions of the joint

failure modes are given below

Compression Failure

In general, compression failure oc- curs in bridge joints in a brittle man- ner as a result of crushing of concrete struts in the joint This failure mode is typical in prestressed joints (see Fig

4a), and in reinforced concrete joints detailed with sufficient shear rein- forcement such that they remain elas- tic during seismic response Compres- sion failure of joints will substantially reduce the lateral force resistance of the structure, most likely leading to total structural collapse with sufficient duration of earthquake shaking

Tension Failure Tension failure is typically devel- oped in reinforced concrete joints when shear reinforcement responsible for mobilizing the joint compression

field is subjected to large inelastic

strains Since these inelastic strains are irreversible a growth of the joint panel occurs under seismic loading Consequently, the effective concrete strength of the joint core is signifi- cantly reduced, which often results in crushing of the joint strut at large dis- placement ductilities (Fig 4b) Al-

though significant lateral strength loss

is associated with such a joint failure, which may lead to structural collapse, strength degradation will occur in a gradual manner

In joints with wide cap beams, as currently adopted in practice,!® tension

failure can be triggered by crushing

and spalling of the thick lightly con- fined cover concrete, which partici- pates in joint force transfer at initial

stages.°*? Tension failure is also ex-

pected in older bridge joints detailed with little or no shear reinforcement,

as column longitudinal reinforcement provides some tensile resistance to the

joint at small shear strains.'”

Anchorage Failure For satisfactory seismic perfor- mance of a bridge structure, it is es- sential that the column and cap beam

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(a) Compresssion failure

(c) Anchorage failure

Fig 4 Four different joint failure modes

longitudinal reinforcement be suffi-

ciently anchored into the joint Inade-

quate anchorage will result in bond

slip of the reinforcement, introducing

an additional member end rotation at

the joint interface and thus reducing

the lateral strength of the structure

The bond slip rotation resulting from

anchorage failure can contribute in ex-

cess of 40 percent to the total lateral

đisplacement.”

Given that the bond slip mechanism

does not provide adequate force resis-

tance, nor a profound energy dissipa-

tion system, the structure will exhibit

poor force-displacement hysteresis re-

sponse, characterized by gradual

strength deterioration and escalation

of the loop pinching effect as displace-

(d) Lap splice failure

ment ductility and/or number of load

reversals is increased However, there may be no apparent damage on the joint faces as shown in Fig 4c

The column longitudinal reinforce- ment is typically anchored into the joint with straight bar ends in order to

improve constructability.!*'’ These re- inforcing bars are susceptible to bond

slip as they may be subjected to stresses up to 1.5 times the yield stress Hence, sufficient anchorage

length must be provided for the col- umn longitudinal reinforcement based

on the maximum expected bar stress

Bond slip of the cap beam longitudi- nal reinforcement bars is most likely

to occur in bridge knee joints when

they are terminated within the joint

with straight bar ends,°° although it is

recognized that termination using a 90-degree hook at the bar end, as shown in Figs la and 1b, is typically

used in current practice

In seismic design, beam bars are not spliced within tee joints as this detail

causes additional reinforcement con- gestion Consequently, bond slip of

these bars is not expected in bridge tee joints unless significant inelastic stresses are developed in the beam longitudinal reinforcement at the col- umn faces

Lap Splice Failure Lap splice failure is most likely to occur in bridge knee joints subjected

PE}AJOURNAL

to closing moments As shown in Fig

5a, the column tension force may be

transferred to the top beam reinforce-

ment by bond if adequate confinement

is provided for the lap splice If the

confining pressure is not sufficient to

prevent splitting of concrete between

the reinforcement and straightening

the hook of the beam bars, a failure

may ensue as illustrated in Fig 5b

(also see an example in Fig 4d)

Note that a lap splice failure can

also occur in well-confined joints if

the lap length between the reinforce-

ment is not sufficient to transfer the

column tension force to the beam rein-

forcement

FORCE TRANSFER METHOD

Joint design has traditionally been

performed based solely on the maxi-

mum shear force estimated within the

joint panel, despite potential for the

joint to experience different failure

modes The joint shear is but one force

of the complete force transfer action

that develops in the joint region,

which includes both the joint panel

and the member regions directly adja-

cent to the joint

Therefore, it is conceivable that

when the joint force transfer region is

assumed to be limited to the joint

panel and that shear, which is not di-

rectly correlated to damage, is treated

as an independent force for design

purposes to establish the joint rein-

forcement, unnecessarily conservative

joint details are likely to result This

notion is consistent with observations

that bridge joint design based on the

building code approach, using the

joint shear force as the design parame-

ter, led to congested, impracticable re-

inforcing details.>*!°

In FTM, the necessary joint rein-

forcement is viewed as that required to

support sufficient anchorage of the

column longitudinal reinforcing bars

into the joint, eliminating the joint an-

chorage failure mode and permitting

the plastic hinge capacity of the col-

umn to be fully developed Conse-

quently, the necessary reinforcement

in the joint region is quantified by em-

ploying key mechanisms that satisfac-

torily anchor the column reinforce-

ment into the joint and by estimating

As shown subsequently, in addition

to transverse reinforcement within the

joint panel, the FTM may rely upon

transverse reinforcement placed in the cap beam region adjacent to the joint panel, and top and/or bottom beam longitudinal reinforcement across the joint to support force transfer In con- trast, the conventional building joint design concept assumes that only the shear reinforcement provided within the joint panel is responsible for trans- fer of forces across the joint

In accordance with capacity design principles, the force transfer method

of joint design or joint assessment is performed at the ultimate limit state for forces corresponding to the over- strength capacity of column plastic hinges The average joint principal stresses estimated at the ultimate limit state will be used as the initial design parameters in FTM

At the serviceable limit state, the

joint principal tensile stress is kept

below 0.25.) f’ (MPa) [or 3.0.) £’ (psi) ]

with no special detailing requirement, where f” is the specified unconfined

compressive strength of the joint con-

crete For a typical bridge column hav- ing longitudinal reinforcement content

in the range of 1.0 to 4.0 percent and a regular proportion for the column diam- eter and beam depth dimensions preva- lent in practice, the serviceability de-

sign criterion will be readily accomplished

At higher load levels, the force transfer across the joint initiates crack- ing in the joint region, which activates distinctive joint mechanisms and mo- bilizes reinforcement in the joint re- gion Therefore, using the estimated average joint principal tensile stress to

gauge the extent of joint cracking, a

force transfer model consisting of ap- propriate joint mechanisms is selected and the required reinforcement in the joint region is then quantified consis- tent with this design model

Reinforcement quantities in the joint

region will depend on the efficiency of

the adopted force transfer model However, when compared with the more traditional approach based di- rectly on joint shear forces, the FTM

is expected to provide joint reinforce-

ment with reduced congestion regard- less of the choice of the design model This expectation for FTM is a direct consequence of considering all actions

in the joint region for quantifying the reinforcement

It is the authors’ opinion that the most efficient force transfer models for seismic joint design are those pro- ducing satisfactory joint performance while requiring the least amount of re- inforcement within the joint panel Bearing this in mind, the remainder of this article addresses a formulation of the most efficient force transfer mod- els for different joint conditions

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Guidelines for Joint Design

The following guidelines are sug-

gested for designing joints in new

bridges using FTM:

1 At the overstrength capacity of

the plastic hinge, the column tension

force may be represented by: #1

T„=0.5A./ (5)

where A, and iG are, respectively, the

total area and overstrength stress in the

column longitudinal reintorcement

The column overstrength stress may be

taken as 1.3 times the measured value

of f, or 600 MPa (87 ksi) for Grade 60

reinforcing bar Alternatively, an accu-

rate estimate of 7, may be obtained

from a section analysis of the column

2 Since the joint design procedure,

which is aimed at protecting joints

from any significant inelastic actions,

is based on the overstrength moment

capacity of the column plastic hinge

and on conservative material proper-

ties, a strength reduction factor of @ =

1.0 may be satisfactory

3 Using the principal tensile stress

obtained at the ultimate limit state [from

Eq (4)], the joint design is approached

in the following manner:

(a) If p, < 0.25 f/(MPa) [or

3.0.) f’ (psi) ], only limited insignifi-

cant joint cracking is expected Appli-

cation of FTM is not required and the

following nominal reinforcement is

provided within the joint paucl for sat-

isfactory force transfer:!”19

Total area of vertical joint reinforce-

The requirement in Fq_ (A) is in-

tended to assist bond transfer of top beam reinforcement and formation of joint diagonal struts while Eq (7) is based on providing hoop reinforce- ment sufficient to support a tension force equivalent to 50 percent of the

principal tension strength of 0.29,) £’ (MPa) [or 3.54) £7 (psi) ]."”

The nominal joint reinforcement in Eqs (6) and (7) may be viewed as equivalent to supporting a column ten- sion force of (0.12 + B)T., where the first part of the expression is obtained

by combining Eqs (5) and (6)

The second part of the expression is based on column tension force that can be supported by p, as in Eq (7) with:

B= 0.22.) f2 (MPa) 1?/Ascfy [or 8= 0.22x103.//7 (psi) U7/Aschy |]

where /, is the anchorage length as de- fined in Eq (12)

(b) If p, > 0.42Vf0 (MPa) [or

5.0.) f’ (psi) ] joint design should be based on a force transfer model that supports the total column tension force, T The joint region is detailed identifying tension demands imposed

by the joint force transfer model

(c) For joint principal tensile stresses between the above limits, sat- isfactory joint force transfer may be achieved by providing supplementary reinforcement to the nominal require- ments in Eqs (6) and (7) The supple-

mentary reinforcement should be de-

termined using a force transfer model

to anchor the unsupported component

of the column tension force equal to

(0.88 — B)T., i.e., [1 — (0.12 + Ø)7,]

The advantage of this approach is that

a suitable force transfer model may be

found using a single joint mechanism

A higher limit of p, = 0.29) f” (MPa)

[or 3.5 ,/ f” (psi) ], was recommended in the past as a threshold value for detail- ing joints with nominal reinforce-

ment.*:!°!7 The more conservative ap-

proach suggested herein is due to the approximation made in Eq (1) for cal- culating the joint shear force, which in- fluences the value of p,

4 For joints with p, > 0.25) f7 (MPa)

[or 3.0,/ f’ (psi) ], nominal reinforce- ment will be adequate if it is shown that the column bars can be satisfacto- rily anchored into the joint main strut without the need for any special rein-

forcement.® This will often be satisfied

in joints designed with a fully pre- stressed cap beam The potential for satisfying this condition may be estab- lished using simple beam theory as il- lustrated for a tee joint in Fig 6 It will

be necessary to show that for the over- strength condition, the beam neutral axis depth at the tension face of the of the column is equal to or greater than (g + la eg); where g is the distance be- tween the end of the column bars and

the beam top surface, and /, vis the ef-

fective anchorage length as defined in

Eq (13) The joint mechanism sup- porting force transfer in these joints is depicted in Fig 13b and its description

is given under the clamping mecha- nism

5 The average joint principal com- pression stress should always be main-

tained below 0.3f; in order to prevent

compression failure as shown in Fig 4a For larger p, values, a study should

be conducted to verity that the average

stress demand does not exceed the ca- pacity for all critical joint struts

6 Column bars should be anchored

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into the cap beam with straight bar

ends The force transfer method ac-

commodates the use of headed longi-

tudinal reinforcement in columns, pro-

ducing acceptable joint details (see

distributed strut mechanism) How-

ever, employing column bars with

hooks or tails should be avoided as

this detail causes reinforcement con-

gestion in the joint

7 A minimum anchorage length for

the beam and column longitudinal rein-

forcement into the joint should be pro-

vided assuming a uniform bond stress of

1.17, f/ (MPa) [or 14.) £7 (psi) ] along

the embedded portion of the bar.'”

8 Column bars should be extended

as close as practicable to the height of

the top beam reinforcement to maxi-

mize embedment conditions for the

extreme column tension bars into the

joint diagonal strut

9 The last two guidelines described

above should be used to dimension the

minimum cap beam depth

Guidelines for Joint Assessment

When compared to the design of

joints in modern bridges, less conser-

vative guidelines can be adopted in

seismic assessment of joints for

retrofit purposes This is consistent

with recommendations by Priestley et

al.'” for joint assessment, who advo-

cate allowing limited joint damage to

occur as long as the damage does not

lead to total collapse of the structure

or punching of columns through the

deck In light of this philosophy, the

following guidelines are recom-

mended:

1 Considering the column and cap

beam retrofit measures, a plastic col-

lapse mechanism for the bridge bent

should first be established Using Eq

(1), estimate the joint shear demand

based on the expected overstrength

column moment at the joint interface

2 An estimate of the column ten-

sion force, 7., required to be anchored

into the joint should be based on the

expected column overstrength mo-

ment Eq (5) may be used for this pur-

pose when the column plastic moment

capacity is expected to be fully devel-

oped adjacent to the joint Assessment

of the joint should then follow assum-

ing a strength reduction factor of @ =

July-August 2003

1.0

3 As part of the joint retrofit, joint dimensions may be increased This should be considered when estimating joint shear demand and principal

stresses

4 As with the design of new joints,

the principal tensile stress is used as

an initial assessment parameter as fol- lows:

(a) If p, < 0.29J/(MP4) [or

3.5 7 (psi) |, the presence of nominal

reinforcement as given by Eqs (6) and 7) is adequate

th If p, > 0.42Vf/ (MPa) [or

0.42 / ¢’ (psi) ], the adequacy of the joint reinforcement must be estab- lished based on an efficient joint force transfer model supporting the column tension force T

(c) For joint principal tensile stresses between the above limits, ade- quacy of the existing joint reinforce- ment may be demonstrated by using a force transfer model Accordingly, the reinforcement in excess of the nominal requirements should be sufficient to

anchor the column tension force of (0.88 — B)T, into the joint

5 As discussed in the previous sub-

section, if 1t 1s Shown that the column

bars can be anchored into the joint

main strut without the need for any special reinforcement, then nominal joint reinforcement may be considered

adequate even if p; > 0.29.) f’ (MPa) [or 3.5.) f’ (psi) ]

6 The joint principal compression stress should always be maintained

below f/ unless it can be shown that

the demand on joint struts is not ex-

cessive This requirement is critical

when cap beam prestressing is used to improve joint and/or cap beam perfor-

mance

7 Premature termination of column bars is commonplace, particularly in

older bridge joints in California.°*? In-

creasing the column reinforcement embedment length will often be re- quired as part of the retrofit procedure, for example, by haunching the joint, which should be reflected in the force transfer model

8 If necessary, permit limited in-

elastic action to take place in the cap

beam adjacent to the joint at larger

displacement ductilities (u, = 3 — 4)

Also, permitting tensile strains of up

to 0.01 in the joint shear reinforcement may be acceptable when determining the capacity of joint ties

9 As discussed below, a realistic representation of concrete tension car- rying capacity can be included in the force transfer model

Influence of Repeated Loading

In FTM, design is performed for the maximum possible forces that the joint can be subjected to during a repeated

or seismic loading This is implied in

Eys (1), (4) and (5), in which joint

shear force, principal stresses and T, are obtained using estimated strain hardening and yield overstrength of the column longitudinal reinforce-

ment

The influence of seismic or cyclic type loading is not directly taken into account in FTM Strength deteriora- tion of concrete struts resulting from such repeated loading is conveniently incorporated by defining appropriate permissible stress limitations These limitations were established empiri- cally and are presented in the follow-

ing section

Since no significant hardening is ex-

pected for the joint reinforcement and cyclic inelastic excursions will be in the tension range, the stress-strain re- sponse envelope of steel under re- peated loading is assumed to be the same as that obtained for monotonic

loading Therefore, for an estimated

strain in the joint reinforcement, the corresponding stress can be readily obtained

Columns with High Longitudinal

Steel Ratio The force transfer method of design and assessment is applicable to all bridge joints, regardless of the longitu- dinal reinforcement ratio of the adja-

cent column As will be discussed

later, the required reinforcement for joint force transfer is determined as a function of the total area of column longitudinal reinforcement Therefore, high longitudinal column steel ratios

will result in larger reinforcement

quantities in the joint region

The higher column steel ratios also mean larger demand on the struts sup- porting the joint mechanisms Since

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(a) Arch: activ aud curved cracks

(b) Parallel sut mechanism and straight cracks

Fig 7 Different compression force paths in knee joints subjected to opening moments

the effective strength of struts is not

increased proportionally, a high col-

umn longitudinal steel ratio will result

in high demand to capacity ratios for

the struts in the joint region

If the demand is kept below capac-

ity in all critical struts, forces across

the joint will be transferred satisfacto-

rily For column steel ratios in the 1 to

4 percent range typically adopted in

practice,'’ satisfactory force paths for

the joint forces can be established

using FTM

STRUT-AND-TIE CONCEPTS

The fundamentals and application

of strut-and-tie concepts to structural

members subjected to static loading

can be found in the literature [e.g., see

References 20, 24 and 25] Due to dif-

ferences in the design philosophy and

the repetitive nature of seismic loads,

some changes to the application pro-

cedure are necessary for successful

modeling of bridge joint regions using

struts and ties

These changes, as applicable to

bridge joints subjected to seismic ac-

tions, are presented below Since the

application of strut-and-tie concepts is

here focused on bridge joints only, the

procedure is simplified wherever pos-

sible

Compression Force Flow

Determining a suitable path for

compression force flow across the

joint is the most critical step in FTM

as this procedure essentially deter-

10

mines the node locations and orienta- tion of struts Elastic analysis of the system using a finite element method- ology, observed crack patterns and past experience are generally consid- ered as appropriate means for identify- ing the force paths in structural mem- bers subjected to static loading

Further, for simplicity, identical models for the ultimate limit state and for the cracked state of serviceability condition have been recommended in the literature (see, for example Refer- ence 20) However, a similar approach

is not applicable to seismic design of bridge joints

Joints in a bridge bent are typically

subjected to axial, shear and flexural actions whose relative magnitudes and thus dominant action can be different

at the service and ultimate limit states

As demonstrated by Bhide and

Collins?® on shear panels with and

without an axial force, the force path and orientation of cracks in the joint region can be considerably different at the two limit states Also, elastic anal- ysis ignores the force redistribution that occurs progressively with the de-

velopment of tensile cracks.”°

Therefore, the joint reinforcement

derived using a force path established

from an elastic analysis will be often unnecessarily conservative; failure of such joints is also possible since the joint behavior at the ultimate limit

state was not modeled Although it is

not required in FTM, it is acknowl- edged that force paths of the critical joint struts can be satisfactorily estab- lished using results from an elastic

analysis conducted at the onset of yielding of the column main reinforce- ment and good engineering judgment

In this case, concrete cracking and strain penetration along the column bars into the joint must be accurately

modeled

The force paths identified for bridge joints in this paper as part of FTM are based on observed crack patterns, ex- perimental data, linear and nonlinear finite element analyses, and the au-

thors’ experience Some issues rele-

vant to establishing force paths in

bridge joints are discussed below

Reinforcement layout and geometric constraints may significantly influence the compression force path in cracked joints This is illustrated in Fig 7 where two knee joints subjected to opening moments are compared In the first joint, with no stub, arch action

is expected to develop within the joint

and consequently curved cracks should result on the joint faces

In the second joint, with a stub and continuous cap beam longitudinal re- inforcement detail as shown in Fig 7b, broadening of the joint diagonal

strut is possible by anchoring a joint

strut against the left bottom corner of the beam reinforcement Since this ac- tion reduces stresses in the critical struts of the joint, this mechanism, in- volving parallel struts, is likely to de- velop in the joint shown in Fig 7b in- stead of an arch mechanism A consequence of the parallel strut mechanism would be the formation of straight cracks on the joint faces

This argument, which is consistent with the cracked pattern observed on the joint faces during testing (see Fig 8), is in accordance with a suggestion

made by Collins and Mitchell? that

when cracking occurs and concrete tension carrying capacity is lost across the crack, the orientation of struts should be towards stiffer reinforce- ment so that the magnitudes of forces and deformations developed in the D- region are minimized

When joints are subjected to in- plane loading, struts are developed in

three dimensions The components of

the struts perpendicular to the loading plane can influence the crack pattern

on the joint faces.° Therefore, it is noted that the observed or expected

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(a) Curved cracks Fig 8 Observed joint cracks in bridge knee joints indicating different force paths under opening moments (b) Straight cracks

crack pattern alone is not always suffi-

cient to establish the compression

force path in bridge joints

Furthermore, when establishing

suitable force paths for bridge joints, a

basic rule of strut-and-tie concepts

should not be forgotten That is, the

force transfer model resulting from the

compression force path should not re-

quire excessive deformation in any re-

inforcement ties supporting the joint

mechanism(s) in order to fully develop

the plastic state of the structure If this

condition were not met, premature

tension failure of joints and poor duc-

tile performance for the bridge bent

would be inevitable under seismic ac-

tions

Struts, Ties and Nodes

Compression forces in concrete

structural members are transferred

through three types of stress fields

known as the “prism,” “fan” and “bot-

tle” as shown in Fig 9.2° The prism is

expected in B-regions (beam regions),

while fan and bottle-shaped stress

fields typically develop in D-regions

(disturbed regions), with the struts in

beam-to-column connections gener-

ally being bottle-shaped When the

joint compression force is transferred

between two nodes through a bottle-

shaped stress field, in-plane and out-

of-plane tensile stresses are developed

perpendicular to the force transfer di-

Fig 9 Different stress fields identified in concrete struts (after Schlaich et al.?°)

rection, which reduce the strut capac-

ity

For simplicity, the struts in the joint region can be represented with single straight lines or with zones bounded

by straight lines in 2D, ignoring the

in-plane and out-of-plane tensile

stresses (see Figs 10a and 10b) Fur- thermore, a uniform stress across the in-plane depth and in the out-of-plane direction at any section along the strut

is assumed

These assumptions, which simplify

the estimation of the demand on the

struts, are deemed satisfactory as long

as the allowable compression stresses

in the struts are defined appropriately, taking the transverse tension field into

account This is dealt with in a subse- quent section

The tensile resistance of the rein- forcement or concrete is represented

by ties in single or multiple one-di- mensional layers The tensile resis- tance of concrete can be adversely af- fected by microcracks induced by previous loads, thermal stresses and

shrinkage.’ Consequently, concrete

tension capacity is generally ignored

in structural design

Nonetheless, it has been found that the tensile resistance of cracked con- crete has a significant influence on joint force transfer, and that modeling its role is essential for accurately char- acterizing the seismic behavior of

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Fig 10 Dimensioning struts and nodes, and identifying strut critical sections ina

bridge tee joint

bridge joints.°!*8

Several other researchers have also

promoted the influence of concrete

ties in structural response.”°??3° When

the contribution of the concrete ties is

appropriately accounted for in the

force transfer model, a reduced

amount of joint reinforcement will be

required

Clearly, a designer can still choose

to conservatively neglect the contribu-

tion of concrete ties Incorporating

concrete ties in the assessment of

joints is especially encouraged as this

can avoid unnecessary and expensive

retrofit of bridge joints A procedure

for estimating the joint concrete ten-

sion contribution is presented under

“Contribution of Ties.”

Nodes represent the intersection

points of three or more struts and/or

ties, where change in direction of

forces takes place It should be appre-

ciated that such changes in a rein-

forced concrete structure typically

occur over a zone, except where a

strut or tie delineates a concentrated

stress field.“’ A node with gradual

changes over a zone is identified as a

smeared node, with its dimensions

being determined by the effective

12

widths of struts and ties forming the

node A node having a concentrated stress field is generally referred to as a

joint regions, CCC, CCT and CTT

nodes are commonplace, but TTT nodes are not expected

Dimensioning Struts and Nodes and Identifying Critical Sections Consistent with the discussion pre- sented above, the concepts of simple and detailed strut-and-tie joint models, different node types, the dimensioning

of struts and nodes, and identifying

the critical sections in joint struts are illustrated in Fig 10

Suppose that the anchorage of col- umn tension force 7; in a tee joint is modeled with a simple mechanism as shown in Fig 10a The stress field

within the joint can be identified as

shown in Fig 10b, with strut dimen- sions dictated by the effective anchor- age length of column reinforcement (discussed later) and by the depth of

equivalent beam flexural compression stress blocks

Adjacent to the tension face of the column, the equivalent stress block is required at the interface between the B- and D-region, located at a distance

of h, from the column face Assuming that each stress field is bounded by straight lines, the node and strut di- mensions can then be readily estab- lished

The Zones ABC and DEFG in Fig 10b, respectively, represent CCC and CCT nodes (identified in Figs 10a and 10c) while the joint strut is formed by stress field BDGC The nodal zones can be isolated as shown in Fig 10c and their stress state can be examined

if necessary Also given consideration

in Fig 10b is a multi-layer representa- tion for column tension force 7; and the need for sufficient anchorage of each tie into the CCT nodal zone

As a result of the tension force in- creasing from Section EF to Section

DG in the CCT node (Fig 10b), the resultant compression force in the di- rection of the joint strut gradually in- creases within the nodal zone and at- tains the maximum value at the

strut-to-node interface

Once the strut boundaries are estab- lished, the critical section(s) of the joint strut should be identified so that stability of the strut may be examined For the example in Fig 10b, the strut depth increases from DG to BC with

no change in the magnitude of the compression force, and thus Plane DH perpendicular to the direction of the strut is a critical section

Further, due to the absence of sig- nificant confining stress along the sides (i.e., BD and CG in Fig 10b), the main strut in the joint typically has

a bottle-shaped stress field, with the most adverse effects of the in-plane and out-of-plane tension field being present at the center of the joint Therefore, examining the stress state across the plane at the joint center is always essential This is consistent with experimental observations that crushing of struts typically develops at

the joint center

If two struts are identified within the

joint, the area bounded by the struts is

assumed to be participating in force transfer in proportion to the magni-

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tudes of the struts as illustrated in Fig

10d Furthermore, the effective width

of each strut at the joint center is taken

as 2w, and 2w3, respectively

The procedure described above for

dimensioning struts and nodes and

identifying critical sections in tee

joints can also be applied to bridge

knee joints subjected to opening mo-

ments For knee joints under closing

moments, critical sections can be iden-

tified as shown in Fig 11 using a simi-

lar concept

A critical section in a reinforced

concrete knee joint, incorporating a

stub and continuous top and bottom

beam reinforcement (Fig 11a), is cho-

sen such that the highest strut stress is

at the section with the minimum

depth, as for the tee joint in Fig 10b

In addition, the stress state at the joint

center should also be checked For a

knee joint with a prestressed cap beam

such as in Fig 11b, only one critical

section at the center of the joint is se-

lected

From the above, it can be observed

that although the strut depth is small

close to the CCC node, with the joint

strut force continuously increasing to-

wards this node (Fig 11b), the strut

capacity is significantly higher in this

region due to the confinement pro-

vided by the CCC node

For reinforced and prestressed con-

crete bridge joints, where the column

tension force is modeled with a single

tie such as in Fig 10a, there is a ten-

dency to select the critical section at

the center of the joint This is satisfac-

tory based on the discussion presented

above However, in critical cases (e.g.,

assessment of joints with little or no

reinforcement), the designer is encour-

aged to perform checks at three sec-

tions along the strut; at the center,

midway between the joint center and

CCC node, and midway between the

joint center and CCT node

In all joints, the width of the joint

strut in the out-of-plane direction is

taken as b; as defined in Eq (3)

Allowable Stresses in

Cuncretle Struts

In order to preclude compression

failure of joints resulting from crush-

ing of struts, it should be ensured that

to closing moments

Table 2 Permissible stresses suggested for critical bridge joint struts under

seismic conditions

Permissible stress Strut description

such as that expected in prestressed joints

not subjected to significant strain hardening (¢, < 0.01)

Struts in unreinforced joints or in joints with potential for initiation of

0.34/⁄ tension failure following development of high inelastic strains in the

umn ends adjacent to the joint re-

vealed that the struts bounded or anchored in the joint panel are most critical Therefore, limiting examina- tion of the stress state to these struts is sufficient

The strength of a concrete strut de- pends on its multi-axial stress state, confinement, damage caused by cracking, uniformity of cracking, dis- turbances from reinforcement and the influence of aggregate interlocking

As noted previously, in-plane loading induces joint dilation in the out-of- plane direction, which, in turn, can re- duce the strut capacity significantly

below the unconfined concrete

strength.”923931

Several different recommendations,

based either on beain/shear panel tests

or on engineering judgment, are found

in the literature for estimating strut ca- pacities They range from simple for-

mulas, in which the strut capacity is represented by the effective uncon- fined compressive strength, to detailed equations which account for the state

of strain in the strut Among these rec- ommendations, which are intended for monotonic loading, appreciable dis- crepancies exist between the permissi- ble stresses suggested by different re- searchers for struts subjected to

similar conditions.°

From the seismic tests of bridge joints listed in Table 1 and subsequent analytical investigations, the stress limits shown in Table 2 are recom- mended for seismic design and assess- ment of bridge joints These limits were made to resemble those recom-

mended by Schlaich et al.”° for struts

in structural members subjected to static loads

In a recent study aimed at perform- ing push-over analyses of bridge bents based on strut and tie models, defining

suul Capacities using the permissible

stress values in Table 2 was found to

be satisfactory.*

Recall that in “Design and Assess-

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