A NEW MODEL FOR JOINT SHEAR FAILURE OF REINFORCED CONCRETE INTERIOR BEAM-TO-COLUMN JOINT

8/12/2019 A NEW MODEL FOR JOINT SHEAR FAILURE OF REINFORCED CONCRETE INTERIOR BEAM-TO-COLUMN JOINT

1/30

Journal of the School of Engineering, The University of Tokyo, Vol. XLV (1998)

1

A NEW MODEL FOR JOINT SHEAR FAILURE OF

REINFORCED CONCRETE

INTERIOR BEAM-TO-COLUMN JOINT

by

Hitoshi SHIOHARA *

(Received June 25, 1998 )

ABSTRACT

The primary objective of this study is to point out an irrationality in the joint shear failure

model, which is adopted in the most current design codes of reinforced concrete beam-to-col-

umn joint. To examine this issue, tests of twenty reinforced concrete interior beam-to-column-

joint failed in joint shear are reexamined. The data indicated that joint shear stress had

increased in the most specimens, even after apparent joint shear failure starts, while beam

moment decreases due to decrease of flexural resistance which is caused by reduction of dis-

tance between stress resultants in beam at column face. The cause of the deterioration of story

shear is identified to be a degrading of moment resistance of joint, originated from a finite

upper limit of anchorage capacity of beam reinforcements through the joint core. So a new

mathematical model for joint shear failure is introduced to reflect this fact. The behavior of the

model is investigated and a new approach for the design of beam-to-column joint in seismic

zone is proposed based on the prediction of the model.

Contents

1. INTRODUCTION

2. REVIEW OF DESIGN CONCEPT

3. DEFINITION OF JOINT SHEAR

4. REEVALUATION OF TEST DATA ON JOINT SHEAR

4. 1 Test Program4. 2 Story Shear

4.3 Nonlinear Constitutive Model for Steel

4. 4 Stress in Flexure Reinforcement at Column Face and Joint Shear

4. 5 Joint Shear Stress

4. 6 Shift of the Location of Stress Resultants

4. 7 Change of Stress in Compressive Reinforcement

4. 8 Observed Failure Mode

4. 9 Components of Joint Shear Deformation

Associate ProfessorDepartment of Architecture, School of Engineering


2/30


2

5. A NEW MODEL FOR JOINT SHEAR FAILURE

5. 1 Moment and Shear Resistance of the Connection

5. 2 Assumptions

5. 3 Equilibrium in Segments

5. 4 Comparison of Test and Analysis

6. PARAMETRIC STUDY6. 1 Parameters

6. 2 Story Shear Capacity

6. 3 Pseudo Joint Shear at Moment Capacity of Beam-to-Column Joint

7. DISCUSSION

7. 1 Beam-to-column joint designed by the current code

7. 2 Implication of the new model for design of beam-to-column joint

8. CONCLUSION

1. INTRODUCTION

Beam-to-column joint is an important part for an earthquake resistant design of reinforced con-

crete moment resisting frames. Beam-to-column joints should have sufficient stiffness and

strength to resist and sustain the load induced from adjacent beams and columns. High strength

steel bars or large diameter bars are sometimes preferred in the structural design of a building

which has smaller sectional size of structural member, as a result, the stress level in beam-col-

umn joint is increased. A full care to the increased joint stress is important in the design, other-

wise, it may cause problems such as (1) lower strength than calculated based on the flexural

strength of beams or columns and (2) reduction of stiffness due to premature failure of joint

shear panel accompanied with diagonal cracks and local crushing of concrete. Those kind of

failure are called a joint shear failure and need attention for the structural integrity of members

jointed as rigid and strong as they are assumed in a structural analysis. To call attention to that

problem, increasing number of building codes have provisions for the joint shear failure

recently. Despite of the importance of the issue, no unified theory available for the provision

have not been established.

The first part of this paper deals with the irrationality in the models on joint shear failure

adopted in the most current design codes. The models are unanimously based on a hypothesis

that a joint shear failure occurs when joint shear force input reaches the shear capacity of the

joint, whereas it has not been confirmed by tests. Thus tests of twenty reinforced concrete

beam-to-column joint failed in joint shear are reexamined. The purpose of the rest of this paper

is to develop a new model to explain the mechanism of joint failure which will replace the

existing model, in particular applicable to an interior beam-to-column joint.


3/30


3

2. REVIEW OF DESIGN CONCEPT

In 1969, Hanson et. al. reported a test of beam-to-column joints and they gave a quantitative

definition of joint shear and suggested that it is needed to prevent joint shear failure by setting

a limit corresponding to the stress level at which joint shear failure occurs

1)

. The committee

ACI-ASCE 352 published a proposal of beam-to-column joint design, incorporating the provi-

sions which limit joint shear stress

2)

in 1976. Meinheit and Jirsa reported a series of joint tests

designed to fail in joint shear so as to evaluate the joint shear capacity

3)

. Based on these early

developments, recent concrete codes, such as US 4)

NZ 5)

and Japan

6)

adopt the design provi-

sion supplying limit value to joint shear stress. In these years a significant number of tests of

beam-to-column joint have been carried out. The reliability of this design concept seems to be

supported by those tests.

However, there still remains much ambiguity and no unified model or theory of the joint failure

has not been established. Joint shear failure model of the ACI318-95

4)

, NZ3101

5)

and AIJ

guideline

6)

are different each other. In the AIJ guideline, the joint shear failure is explained as

failure of diagonal concrete compressive strut of joint panel, whereas, NZS 3101 considers that

tensile shear failure of truss mechanism is suitable for joint shear failure. Those models in the

codes are usually only qualitative ones. In addition to that, the limit value of joint shear stress

are empirical one.

3. DEFINITION OF JOINT SHEAR

The definition of joint shear V

j

in Eq. (1) was introduced by Hanson et. al.,

1)

and it is widely

accepted. The joint shear V

j

in Eq. (1) means a internal force acting on the free body cut at the

horizontal line at the mid height of the joint core as shown in Fig. 1. Physical meanings is very

clear for this definition. The contribution of steel and concrete are taken into account sepa-

rately. This paper adopted this definition the primary one for joint shear. Strain gage reading is

necessary to monitor tensile force T and T

. Sometimes, inelastic constitutive model of steel is

also necessary when strain in reinforcing steel goes beyond linearly elastic range.

V

j

= T +

C

s

+ C

c

-

V

c

= T + T' V

c

=

a

t

f

s

+

a

t

f

s

V

c

(1)

where, C

s

: compressive force in steel bar, C

c

: compressive force in concrete, , : tensile

force in steel,

a

t

,

a

t

: total sectional area of beam longitudinal reinforcement for positive

moment and negative moment respectively, f

s

, f

s

: tensile stress in beam longitudinal rein-

forcement, and V

c

: column shear force. (see Fig. 1) This definition is not adequate to measure

absolute value of T

or T

with high accuracy because the stress in parallel reinforcing bar usu-


4/30


4

ally does not coincide and it causes error if only the strain of one bar are monitored. To mea-

sure the total force in the section, it is necessary to put strain gages on all longitudinal

reinforcement. But it is an unrealistic instrumentation plan for an ordinary test.

Because of the difficulty in evaluating the absolute value of T

and T

with reliability in an

actual test, joint shear reported in literatures are usually calculated with assumption of a con-

stant value ofjb; the length of moment lever arm at the column face. As the moment of beam at

column faceMbis the product of T; tensile force in tensile reinforcement, andjb(no axial forcein beam is assumed), Eq. (1) is rewritten as Eq. (2)

Vj=Mb/jb+Mb /jb Vc (2)

The estimated joint shear obtained by Eq. (2) is suitable for statistical evaluation of test results

from a literature survey. But it is not suitable for discussing the joint shear failure model,

because the Vjobtained from Eq. (2) is not real joint shear but is just an index for induced force

level. So the joint shear by Eq. (2) is called hereafterpseudo joint shear

to identify the differ-

ence from that by Eq. (1). The most significant problem in using Eq. (2) is that the value of j

b

changes during a test, due to the non-linearity of stress-strain relation of material and of bond-

slip relation. It is obvious that in particular high compressive stress in concrete and poor bond

condition give smaller values forj

b

. Thus the Eq. (1) is adopted to get a true joint shear force in

this study. The magnitude of forces is evaluated based on the strain history measured by strain

gauges attached on the surface of the longitudinal steel bars. In this paper, the change of joint

shear force is focused, while the absolute value for joint shear stress is not focused.

Vc

Vj

T

Dc

'T

'Cc

'Cs

CcCs

beam column joint

column

beam Vj= T+ T' Vc

Joint Shear

Fig. 1 : Definition of horizontal joint shear in R/C beam-to-column joint


5/30


5

4. REEVALUATION OF TEST DATA ON JOINT SHEAR

Test results reported in two references ,8)are reexamined using data not reported in the refer-

ence. The whole test program are briefly summarized.

4. 1 Test Program

The specimens reported in the reference )by the author are listed in Table 1. They are nine R/

C 1/2.5 scale interior beam-to-column joint subassemblages. In this series, nine specimens

from the eleven specimens were chosen because specimens with transverse beam (J-3) and

specimen with slab (J-9) were excluded. The beams were 240 mm wide and 300 mm deep,

while their columns had a 300 mm square cross section in common. The major variables of the

tests were (a) amount of longitudinal reinforcing bar, (b) yield strength of the reinforcing bars,

and (c) concrete compressive strength. The concrete strengths were from 39.2 MPa to 81.2MPa, while tensile yield strength of reinforcing bars were 370 MPa to 1,456 MPa. The bond

index varied from 3.0 to 6.9.

Table 2 lists the eleven specimens tested by Teraoka

8)

. The size of the beam and column sec-

tion is the same with that of the specimens in the reference

7)

. The major variables of the tests

were (a) concrete strength including the effect of light weight concrete, and (b) the amount of

Table 1 : Test parameters of the beam-to-column subassemblage test 7

Specimen J-1 J-2 J-4 J-5 J-6 J-7 J-8 J-10 J-11

Beam

Bars

Top

Bot.

9-D13

7-D13

8-U138-U13

10-D1310-D13

9-D137-D13

9-D137-D13

7-D135-D13

9-D197-D19

9-D137-D13

9-D197-D19

t

(%) Top

Bot.

1.92

1.44

1.66

1.66

2.16

2.16

1.92

1.44

1.89

1.43

1.43

0.98

4.27

3.24

1.89

1.43

4.27

3.24

f

y

(MPa) 638 1 456 515 839 676 370 700 372

B

(MPa) 81.2 72.8 79.2 39.2

3.0 6.9 2.6 4.2 3.2 3.2 2.6 4.7 3.7

v

pu

(MPa) 14.2 15.3 14.5 16.3 15.1 12.0 17.1 10.8 12.7

R

u

(%) 2.7 2.8 3.1 3.0 2.9 3.0 1.8 1.9 2.0

Failure mode BJ J BJ BJ BJ BJ BJ J J

Note

t

: tensile reiforcement ratio, f

y

: yield point strength,

B

: concrete compressive strength,

: bondindex = (

f

y

/ )(

d

B

/

D

c

) (

f

y

and

B

in MPa), d

B

: nominal diamiter of beam bar,D

c: column depth, vpu :maximum joint shear obtained from definition of Eq. (2). Ru: story drift at maximum story shear, BJ :joint shear failure after beam flexural yield, J : joint shear failure without beam flexulal yield.

B


6/30


6

joint hoop. The range of the concrete strength was from 30.5 MPa to 46.7 MPa. The amount

of joint hoop was varied from 0.6% to 1.8%.

In the both series of tests, the upper and lower columns were supported by pin joints. The beam

ends were loaded so as to keep same deflection in opposite direction. The specimens were sub-

jected to reversed cyclic load with increasing amplitude and were loaded to failure. The speci-

mens were loaded at the beam ends by displacement control. In order to monitor the strain of

longitudinal reinforcing bars, strain gages were attached on the surface of the bars. Observed

failure mode were joint shear failure (J or BJ). Some of their failure occurred before beamyields in flexure (J).

4. 2 Story Shear

The envelope curves of the relation of story drift and story shear are plotted for the in Fig. 2

and Fig. 3. In all the specimens, the degradation of story shear started when the story drift was

larger than 2 to 3%.

Table 2 : Test parameters of the beam-to-column subassemblage test 8)

Specimen No.1 No2 No.3 No.4 No.5 No.6 No.7 No.8 No.9 No.10 No.11 No.12

BeamBar

Top 2-D22 & 2-D19 4-D22 2-D22&2-D19 4-D22

Bot. 2-D22 & 2-D19 4-D22 2-D22&2-D19 4-D22

t(%) Top 2.16 2.48 2.16 2.48

Bot. 2.16 2.48 2.16 2.48

fy(MPa) 411 406 (D19) 411 411 369 396

h

(%) 1.2 1.8 1.2 1.2 1.8 1.2 1.2 1.8 0.6 1.2 0.6 1.2

B

(MPa) 33.6

(LC)

34.5 36.6 39.6

(SF)

46.7 30.5

(LC)

32.2

5.24.5

5.24.5

5.24.4

5.0 5.0 4.8 4.5 4.5 5.54.3

5.54.3

5.2 5.2

v

pu

(MPa) 10.5 10.1 11.1 12.3 12.4 12.8 13.1 13.2 9.4 9.2 10.3 10.6

R

u

(%) 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0

Failure mode J J J J J BJ BJ BJ J J J J

Note

t

: tensile reiforcement ratio, f

y

: yield point strength,

h

: joint hoop reinforcement ratio,

B

:concrete compressive strength of joint,in which LC and SF mean light weight concrete and steel fibre con-crete respectively,

: bond index = (

f

y

/ )(

d

B

/

D

c

) (fy

and

B

in MPa), d

B

: nominal diamiter of beam bar,

D

c

: column depth, v

pu

: maximum joint shear obtained from definition of Eq. (2). R

u

: story drift atmaximum story shear, BJ : joint shear failure after beam flexural yield, J : joint shear failure without beamflexulal yield.

B


7/30


7

4.3 Nonlinear Constitutive Model for Steel

A nonlinear constitutive model for cyclic loading were used to evaluate the stress from the

strain of the longitudinal reinforcing steel in beams. Ramberg-Osgood curve was incorporated

to the model with linearly elastic stage and yield plateau. Test results of the tensile test of rein-

forcing steel under monotonically increasing load were used to model the skeleton curve. Typ-

ical hysteresis curve predicted by the model is shown in Fig. 4.

350

300

250

200

150

100

50

0

storys

hear

force

(kN)

6 543210

story drift angle (%)

J-1

J-2

J-4

J-5

J-6

J-7

J-8

J-10J-11

/ h: story drift angle

h

Vc

Vc

Fig. 2 : Relation of story shear to story drift observed )

Fig. 3 : Relation of story shear to story drift observed (2)


storyshearforce,k

N

300

250

200

150

100

50

0

0 1 2 3 4 5 6

No. 1

No. 2

No. 3

No. 4

No. 5

No. 6

No. 7

No. 8

No. 9

No. 10

No. 11

No. 12/ h : story drift angle

h

Vc

Vc


8/30


8

4. 4 Stress in Flexure Reinforcement at Column Face and Joint Shear

The steel stress in tensile reinforcement of a beam in the first layer at the column face are plot-

ted against story drift for the specimen J-2, J-7 and J-10 in Fig. 5. Although the story shear

decrease due to cyclic load in these three specimens as shown in Fig. 2, the tensile stress

increased at load peaks.

Joint shear V

j

was calculated using Eq. (1) in the following section, assuming the stress in all

bars including bars without strain gages are identical. All the specimen have the strain gages in

first layer reinforcing bars, while only the specimens from J-6 to J-11 have strain gages for sec-

ond layer reinforcing bars. The strain in the second layer bar for the specimens J-1 to J-5 are

calculated from other strain reading using the Bernouli's assumption that plain section remains

plain.

800

600

400

200

0

-200

-400

calculatedste

el

tensilestress(M

Pa)

2.52.01.51.00.50-5steel tensile strain observed (%)

J-6Ramberg-Osgood Curve

Fig. 4 : Example of stress-strain relation predicted using Ramberg-Osgood model

1000

800

600

400

200

0

-200

-400

-4 0 4

yield

1000

800

600

400

200

0

-200

-400

-4 0 4

yield

1000

800

600

400

200

0

-200

-400

840-4

steeltensilestress(MP

a)


J-2 J-7 J-10

(J) (BJ) (BJ)

Fig. 5 : Typical relation of story drift vs. tensile stress in first layer tensile reinforcing steel


9/30


10/30


10

2.0

1.5

1.0

0.5

0.0

Jointshearstre

ss/(B

1/2)

6543210Story drift angle (%)

J-1J-2J-4J-5J-6J-7J-8

J-10J-11

/ h : story drift angle

h

fc' : concrete compressive strength in MPa

t= 1.4 - 2.0 %

t= 4.0 %

t: tensile reiforcement ratio

Fig. 7 : Relation of story shear vs. joint shear evaluated with Eq. (1) at load peaks7)


jointshearstress/(fc

')1/2

3.0

2.5

2.0

1.5

1.0

0.5

0.00 1 2 3 4 5 6

No. 1No. 2No. 3No. 4No. 5No. 6No. 7No. 8No. 9

No. 10No. 11No. 12

Fig. 8 : Relation of story shear vs. joint shear evaluated with Eq. (1) at load peaks8)

1.0

0.8

0.6

0.4

0.2

0.0543210

story drift (%)

Vj

Vjf

Vj: joint shear capacity

Vjf: joint shear at beam flexural yielss

Bond failure

No bond failure

Fig. 9 : Model for joint shear degradation proposed by Priestley9)


11/30


11

It is noted that the joint shear stress of those with ordinary strength steel longitudinal bars with

high volume (t= 4%) showed high joint shear stress, while the joint shear stress of specimens

with low volume (t = 1.4 2.0%) apparently have lower joint shear stress. This fact suggests

that attained joint shear level are function of amount of longitudinal steel as well as concrete

compressive strength. On the contrary to that, amount of joint hoop seems to be have less effecton the attained joint shear as shown in Fig. 8, in which specimens with different amount of

joint hoop are included.

4. 6 Shift of the Location of Stress Resultants

In order to show that the story shear degradation at large story drift is attributed to the move-

ment of the location of the stress resultants at beam section, Fig. 10 shows the transition of the

distance of normal stress resultants j

b

at load peaks. They were calculated using the relation

that the beam moment is product of force in longitudinal reinforcement and j

b

. The distancenormalized with effective depth of beam is shown. In all the specimen, the j

b

. decreased as

story drift increased. Hence, the decrease of story shear is caused by the degradation of

moment resistance, which occurred due to the reduction of the distance of stress resultants.

1.2

1.0

0.8

0.6

0.4

0.2

0.0

76543210Story drift angle (%)

J-1J-2J-4J-5J-6J-7J-8J-10J-11

distanceofstre

ssresultants

/effectivedepth

Fig. 10 : Transition of the length jb(moment lever arm length) in beam at critical section

calculated from observed moment and stress in reinforcing steel


12/30


12

4. 7 Change of Stress in Compressive Reinforcement

Decrease of distance between locations of stress resultants were partly because the location of

compressive stress resultants shifted to the center of beam. It is attributed the expansion of con-

crete compressive zone for flexural resistance. But the most significant reason is the change of

stress in compressive reinforcement from compression to tension. These changes are activated

by the anchorage softening; yield or degradation of anchorage capacity, of beam reinforcement

through the joint core as well as volume expansion in horizontal direction due to crack opening

of joint panel. The sequence of beam moment reduction due to poor anchorage is depicted in

T

Cc C

cjba

jba

T

jbb

jbb

(a) good bond (b) poor bond

Cs Cs

Ma Mb

Ma

Mb

>

>

Fig. 11 : Effect of poor bond on moment resistance of beam-to-column joint


13/30


13

Fig. 11. The observed distribution of tensile stress along the longitudinal bar through joint core

are plotted for the specimens J-7, J-10 and J-11 in Fig. 12.

As shown in Fig. 12, the compressive reinforcement have tensile stress. It is noted that the ten-

sile stress in steel bars in the second layer is much larger than that of the first layer. Therefore,

it is presumed that one of the fundamental cause of the degradation of story shear is the upper

limit of anchorage capacity, not the joint shear capacity degradation.

Fig. 12 : Observed stress in beam longitudinal reinforcements

1000

800600

400

200

0

-200

-400

yield

yield

1000

800

600

400

200

0

-200

-400

J-7

J-7

columnbeam beam

2%

2%

2%

tensilesteelstress(MPa)

strain gauge locationain gauge location

strain gauge location

600

400

200

0

-200

J-10

600

400

200

0

-200

J-10

columnbeam beam

3%

3%

3% 3%

yield

yield

columnbeam beam

400

300

200

100

0

-100J-11

J-11

400

300

200

100

0

-100

yield

yield

3%

3%

3%

3%

tensilesteelstress(M

Pa)

story drift = 3%story drift =

3%story drift =

strain gage


14/30


14

4. 8 Observed Failure Mode

In order to show that the specimens used in this study are not unusual ones, the typical crack

pattern after tests are shown in Photo 1 and 2. Joint failure with a diagonal cracks and crushing

concrete are observed. As shown in Fig. 6, in these specimens, no joint shear degradation was

observed in terms of joint shear defined in Eq. (1).

Photo 1 : Observed crack pattern after test (specimen J-7)

Photo 2 : Observed crack pattern after test (specimen J-10)


15/30


15

4. 9 Components of Joint Shear Deformation

Figure 13 compares the two components; contribution of diagonal compression and tension to

the total shear deformation of joint panel. They were measured by a set of displacement trans-

ducers, diagonally located on the surface of the specimen. The compressive component is

smaller than 20% of total shear distortion of the joint panel. In addition to that, no sudden

increase of compressive displacement was observed. In other word, the shrinkage of diagonal

concrete strut is not evident. On the other hand, most of the shear deformation comes from the

diagonal tensile component. These test results contradict the model of Japanese design

guideline

6)

which assumes joint shear failure occur due to compressive failure of diagonal

compressive strut.

5. A NEW MODEL FOR JOINT SHEAR FAILURE

The previous section demonstrated that the joint shear deformation apparently increases

despite the diagonal concrete strut showes no evidence of compressive failure. The two facts

seem to contradict unless a new model is introduced to reconcile the contradictory facts. In thenew model, joint shear will be transferred by diagonal strut like the traditional strut model,

because existence of diagonal strut is supported by tests and analyses. However, cause of joint

shear deformation should not be crush of diagonal strut due to compressive force in strut.

One example of model which satisfy the above condition is shown in Fig. 14. The shear defor-

mation of joint comes from rotational movement of four rigid segments. Thus shear deforma-

tion concentrates at the boundaries which consists of diagonal cracks and flexural cracks,

which had been already formed by shear or flexural stress in previous cyclic loading as

depicted in Fig. 14. Usually beam column joint have such cracks except some special case

4

3

2

1

0

-1

-2

co

mponentofjointshearstrain(rad)

420-2-2 : average joint shear strain (%)

-3

-2

-1

0

1

2

3

-4 0 2

J-10J-7

1%

-1%

-2%

-2%

-3%

-3%

2%

3%

4%

-4%

4% 6

%

-4%

storydrift

storydrift

comp

ression

tension

=a

a

2+ b

b

2

2ab(d

1

d1

+d2

d2

due to diagonal compressiondue to diagonal tension

Fig. 13 : Contributions of tensile and compressive components of joint shear deformation


16/30


16

such as a beam-to-column joint with debonded beam bars. In the model, the rigid segments

rotates around contact points, the movement of which will be detected by an instrumentation as

joint shear deformation during tests. In reality, the rigid segments are not perfectly rigid. Thus

the contact point of the segments is a finite size.

The joint shear deformation will occure in conjunction with expansion of joint panel.

Because the joint expansion is accompanied by joint shear deformation, axial force in column

and the transverse reinforcement in joint are effective for decreasing the joint shear deforma-

tion. Total story drift consists of joint shear deformation (Fig. 15(a)) and beam (Fig. 15(b))

deformation. If sufficient amount of hoops are provided, the opening of the diagonal cracks is

restrained, which keeps the joint stiffness high, and the percentage of beam deformation occu-

pying in the total story drift increase, because the springs for two deformation modes are cou-

pled in serial. In this case, the failure mode of joint becomes beam yielding.

rotation

ro

tation

rotation

flexural crackat beam end

diagonalshear crack

rotation

diagonal strut

hoop and axial force incolumn restrain theexpansion of jointpanel

Fig. 14 : Joint failure mechanics and force flow among adjacent members

Fig. 15 : Joint failure mechanics model

(a) joint deformation mode (b) beam end deformation mode

center of rotation


17/30


18/30


18

The parameter to describe the problem, geometry and the dimensions, the external force, and

the boundary stresses need to be defined. In this paper, the following notations are used, j

: dis-

tance between tensile reinforcement and compressive reinforcement on the cross section of

beam and column to depth of beam, t

: thickness of beam-to-column joint panel, N

c : column

axial force divided by

t

, t

: the product of joint sectional area, and effective concrete

compressive strength,N

b

: beam axial force divided by t

, L

b

: the length of beam L : the

length of column and : L /L b.

Unknown variables describing the set of the internal forces are also introduced. The tensile

forces T

1

, T

2

, T

3

, T

4

, T

5 (positive in tension) in reinforcement are shown in Fig. 16(a), where,

tensile force T

5 in distributed hoop in height direction assumed to concentrate at the mid

height. The compressive force C

1

, C

2

(positive in compression) in concrete are shown in Fig.16(b). They are considering thex

andy

component of forces acting perpendicular to the seg-

T1

T3 T3

T4 T4

T4

T5 T5

T4

T3T3

T1

T1

T1T2

T2

T2

T2

column

column

rightbeam

rightbeam

leftbeam

leftbeam

column

column

45

45

C1

C1

C1

C1

C2

C2

C1

C1

C1

C1C2

C2

C2

C2

C2

C2A

A'

O

O

O

O

B

C

C'

D

D'

B'

c

c

C

C

O

O

O

O

Fig. 16 : Internal forces and their notations

Vc

Vb=Vc

Vb=Vc

Vc

columnsection

beamsection

LB/2LB/2

1

1

j

j

Nc

NB

NB

Nc

Lc/2

Lc/2

beam

column

Fig. 17 : Geometry of beam-column-joint and external forces

fc fc

fc


19/30


19

ment boundary. Column shear V

c

is identical to story shear and Beam shear is V

b

. All the

forces considered in this paper are normalized by t

. By this unit convention, the width of

compressive zone is coincident with the magnitude of the concrete forces.

5. 3 Equilibrium in Segments

To define equilibrium of forces acting on one rigid body in two-dimension, three equations are

necessary, taking into consideration three degrees of freedom of the rigid body. In this system

shown in Fig. 16, twelve equations are necessary because it consist of four rigid bodies. How-

ever, considering the symmetric condition, number of required equations becomes six. In

addition to that, in this system the column shear V

c and the beam shear V

b is dependent. There-

fore the independent equations to represent the equilibrium is estimated to be five. They are as

follows.

The equilibrium ofx

andy

directional forces on the right beam are expressed as,

(3)

(4)

respectively. The equilibrium of moment with respect to the center point O on the right beam is

given.

(5)

The equilibrium of x and y directional forces on the right beam are

(6)

(7)

respectively. The simultaneous equations of second order from Eq. (3) to Eq. (7) give solution

to five unknown variables, provided other variables are confirmed.

5. 4 Comparison of Test and Analysis

The new model and its equations of equilibrium are applied to the test results to check the reli-

ability of model. Test data were used for T

1

T

2

and T

5

, the unknown valuables T

3

and T

4

, the

concrete stress C

1

and C

2

, and Column Shear V

c

were calculated by solving the set of equa-

tions. The value for tensile stress T

5

is assumed to be equal to the total tensile strength of hoop,

fc

T1 T2 T5 C+ 1 C2 Nb+ 0=

T3 T4 C2 C1 Vc+ 0=

12--V

c

12j T3 T4( )

12j T1 T2( ) C2 1 C2( ) C1C1+ + + 0=

T1 T2 C2 C1 Vc+ 0=

T3 T4 C1 C2 Nc+ + 0=


20/30


20

based on the description of strain in hoops in the reference7). Fig. 18 show the calculated forces

acting on the right beam segment, as well as comparison with the stress in column steel and

column shear observed in the test. To get the solutions for the simultaneous equation, Maple V;

a software package for symbolic mathematical tool, and its solve function is used.

In specimen No. 1, calculated values for column shear Vcshows good correlation, while the

forces T4and T5in column rebars do not show good correlation. It is partly because, the col-

umn section have multi layered longitudinal bars, which is different from the model, where

only one layer of steel is assumed. In the specimen No.2 and No.6, predicted Vcunderestimate

the test value in particular in the case where, tensile force in compressive bars is very large

value.

In the Fig. 19, the calculated column shear Vcare plotted against the test result. In this calcula-

tion, the force in joint hoops T5is assumed zero due to lack of the data of strain history for

hoops, while the stress in the hoops increase according to the joint shear deformation. As the

result of the neglects, the calculated shear Vcis smaller than test results in all the specimens.

The degradation of story shear after the maximum column attained at about 2% of story drift is

show good correlation, except at very large story drift such as 6% or more. The unreliable mea-

surement of strain history may be attributed to the discrepancy.

(0.227)

Story shear = 0.085(0.087)

(0.093)

(0.079)

No. 01

(0.227)

Story shear = 0.066(0.067)

(0.212)

No. 01

0.1

93(0.0

69)

0.2

07(0.0

34)

0.0

62(-0.0

22)

0.1

89(0.0

70)

(0.227)

(0.114)

Story shear = 0.0071(0.089)

(0.075)

No. 02

(0.203)

Story shear = 0.044(0.071)

(0.135)

No. 02

(0.219)

Story shear = 0.069(0.084)

(0.197)

No. 06 0.0

90(0.0

38)

0.0

79(0.0

72)

0.0

54(0.0

17)

0.1

69(0.0

78)

0.1

47(0.0

83)

0.1

11(0.0

02)

No. 2No. 1 No. 6

No. 2No. 1 No. 6

(b) Story drift is 5 %

(a) Story drift is 2 %

T1

T2

T5

T3

T4

(0.079) (0.114) (0.071)

(0.204)

Story shear = 0.085(0.095))

(0.045)

No. 06-0.0

62(-0.0

13)

0.0

63(0.0

57

)

(0.071)

Fig. 18 : Predicted column shear by the model (number in parentheses is observed value)


21/30


21

300

250

200

150

10050

0

No. 01

observed

analysis

0.020.00 0.04 0.06 0.08

300

250

200

150

10050

0

No. 02

0.020.00 0.04 0.06 0.08

300

250

200

150

10050

0

No. 03

0.020.00 0.04 0.06 0.08

300

250

200

150

100

50

0

No. 04

0.020.00 0.04 0.06 0.08

300

250

200

150

100

50

0

No. 05

0.020.00 0.04 0.06 0.08

300

250

200

150

100

50

0

No. 06

0.020.00 0.04 0.06 0.08

300

250

200

150

100

50

0

No. 07

0.020.00 0.04 0.06 0.08

Storyshear,

kN

300

250

200

150

100

50

0

No. 08

0.020.00 0.04 0.06 0.08

300

250

200

150

100

50

0

No. 09

0.020.00 0.04 0.06 0.08

300

250

200

150

10050

0

No. 10

0.020.00 0.04 0.06 0.08

300

250

200

150

100

50

0

No. 11

0.020.00 0.04 0.06 0.08

300

250

200

150

10050

0

No. 12

0.020.00 0.04 0.06 0.08

Story drift , rad

Fig. 19 : Comparison of analysis and


22/30


22

6. PARAMETRIC STUDY

6. 1 Parameters

A parametric study was carried out using the model discussed in the previous section. The

varying parameters include (a) the size of beam and (b) ratio of column length to beam length.

Table 3 lists the parameters.

The value ofj; distance of stress resultant in beam is assumed to be 80% of column depth for

all the cases. The case 2 represents the connection, where the size of beam is 20% larger than

case 1. By comparing the case 1 and case 2, the effect of section size could be evaluated. The

case 3 represents the connection with longer column. By comparing the case 1 and case 3, the

effect of column shear could be examined. In this parametric study, VcT3T4C1and C2are

chosen as an unknown variables, whereas, the T1T2andT5is given.

6. 2 Story Shear Capacity

By solving the equations from Eq.(3) to Eq.(7), the story shear Vcis calculated. as shown in

Fig. 18. The primary valuable govern the story shear Vcis T1 + 0.5(Nb+ T5), and the differ-

ence of T2and T1, i. e. T1T2. The value of T1T2 is regarded as the anchorage resistance of

beam bar through joint. Because the obtained solution Vcdoes not contain the term of column

axial force Nc, Nchas no effect of Vc. On the other hand, the beam axial force Ncand joint

hoops tensile force T5is equivalent to the effect of T1.

In all the cases shown in Fig. 18, in condition T1T2is fixed, the increase of T1lead to increase

the moment resistance of joint and the excessive increase of T1cause decrease of Vc. It is

because, the increase of C1and C2causes reduction of moment lever arm length in the moment

resistant mechanism.

Table 3 : Parameters for a parametric study

parameters Case 1 Case 2 Case 3

length of beamLB 10 8.33 10

length of columnLC=L 5 4.17 20

(=LB/LC) 0.5 0.5 2.0


23/30


23

0.1 0.2 0.3 0.4 0.5 0.6 0

0.02

0.04

0.06

0.08

0.1

0.12

0.1 0.2 0.3 0.4 0.5 0.6 0

0.005

0.01

0.015

0.02

0.025

T1

-T

2

T1

-T

2

T1

-T

2

0.2

0.3

0.4

0.5

0.5

0.4

0.4

0.5

0.3

0.3

0.2

0.2

T1 + 0.5 (T5+ Nb)

T1 + 0.5 (T5+ Nb)

T1 + 0.5 (T5+ Nb)

T1

T2

T5+ N

bT5 + Nb

(a) control condition (Case1)

(b) Effect of depth (Case 2)

(c) effect of distance betweeninflection points in columns (Case 3)

Case 3LB=10LC=20

Case 2LB= 8.33LC= 4.17

Vc

Vc

Vb

Vb

Storyshea

r(columnshear)V

c

Storyshear(columnshear)V

c

Storyshear(columnshear)V

c

0.10.2

0.30.4

0.50.6

0.1

0.2

0.3

0.40.5

0.60

0.005

0.010

0.015

0.020

0.025

T1+0

.5(T5

+Nb)

T1-T

2

Vc

Column shear

0.10.2

0.30.4

0.50.6

0.1

0.2

0.3

0.4

0.5

0.60

0.02

0.04

0.06

0.08

0.10

0.12

T1+0

.5(T5

+Nb)

T1-T

2

Vc

Column shear

0.10.2

0.30.4

0.50.6

0.1

0.2

0.3

0.40.5

0.60

0.02

0.04

0.06

0.08

0.10

T1+0

.5(T5

+Nb)

T1-T

2

Vc

Column shear

0.1 0.2 0.3 0.4 0.5 0

0.02

0.04

0.06

0.08

0.1Case 1LB= 10LC= 5

Case 1LB= 10LC= 5

Case 2LB= 8.33LC= 4.17

Case 3LB=10LC=20

Fig. 20 : Example solution for story shear Vc calculated by the new model


24/30


25/30


25

0.1 0.2 0.3 0.4 0.5 0.6 0

0.1

0.2

0.3

0.4

0.5

0.1

0.3

0.4

0.5

0.2

0.1

0.3

0.4

0.5

0.2

T1

-T

2

T1

-T

2

T1

-T

2

0.1

0.2

0.3

0.4

0.5

0.1 0.2 0.3 0.4 0.5 0.6 0

0.1

0.2

0.3

0.4

0.5

0.1 0.2 0.3 0.4 0.5 0.6 0

0.1

0.2

0.3

0.4

0.5

Case 1LB= 10LC= 5

T1 + 0.5 (T5+ Nb)

(c) effect of distance betweeninflection points in columns (Case 3)

T1

T2

T5

+ NbT5 + Nb

Vc

Vc

Vb

Vb

T1 + 0.5 (T5+ Nb)

(a) control condition (Case 1)

T1 + 0.5 (T5+ Nb)

(b) Effect of depth (Case 2)

jointshearstressdefinedinEq.

(3)

jointshearstressdefinedinEq.

(3)

0.10.2

0.30.4

0.5

0.6

0.1

0.2

0.3

0.4

0.5

0.60

0.1

0.2

0.3

0.4

0.5

T1+0

.5(T5

+Nb)

T1-T

2

Pseudo joint shear

0.10.2

0.30.4

0.50.6

0.1

0.2

0.3

0.4

0.5

0.60

0.1

0.2

0.3

0.4

0.5

T1+0

.5(T5

+Nb)

T1-T

2

Vj

Pseudo joint shear

0.10.2

0.30.4

0.50.6

0.1

0.2

0.3

0.4

0.5

0.60

0.1

0.2

0.3

0.4

0.5

T1+0

.5(T5

+Nb)

T1-T

2

Vj

Pseudo joint shear

Case 1LB= 10LC= 5

Case 2LB= 8.33LC= 4.17

Case 2LB= 8.33LC= 4.17

Case 3LB= 10LC= 20

Case 3LB= 10LC= 20

Fig. 21 : Example solution for pseudo joint shear calculated by the new model


26/30


26

7. DISCUSSION

7. 1 Beam-to-column joint designed by the current code

Although the existing design methods5, 6, 7)set limit value for the induced joint shear stress so

as to prevent joint shear failure, this method have been effective empirically. It is partly

because by the limiting the joint shear stress, the amount of beam reinforcement is restricted as

well as the ratio of diamiter of the bar is restricted. As a result bond stress is usually kept lower

as a side effect. Thus, the anchorage capacity is sufficient. This is one reason because the

design provisions in current codes seem to work properly despite of their irrational model for

joint shear failure.

But another issue could be identified on the model considering compressive failure of diagonal

strut explaining the joint shear failure. There is few test reported in references that the columndid not sustain constant axial load after the joint failure. The exceptions is only one specimen

reported by Kimura in 1997, where a exterior joint panel was crushed under combination of

joint shear and extremely high axial force level in column with approximately 60% of concrete

compressive strength, in which resistance to the axial load diminished. Maybe this specimen

was exceptional case, in which diagonal strut in joint actually crushed. Because the diagonal

strut formed in joint panel is a on the path of axial force in beam column joint, strut compres-

sive failure should cause the loss of axial force resistance. Therefore, in the most cases,

observed joint shear failure is not associated with strut compressive failure, but the expansion

of diagonal cracks.

It is concluded from the discussion above that the design based on the limiting of joint shear

capacity is effective if it is applied to beam-to-column joint with conventional reinforcing

detail, while it have no rational basis. If the design is applied to special reinforcing detail or

special configuration of joint, such as prestress concrete beam-to-column joint, the current

design may be conservative for one joint, while it is dangerous for another joint. Therefore it is

recommend to reexamine the test of joint shear failure based on the real stress in the longitudi-

nal reinforcement to develope more rational model for joint shear failure.

7. 2 Implication of the new model for design of beam-to-column joint

The new model for a moment resisting capacity of beam-to-column joint leads to a new

approach for the design for joint shear failure. To prevent the joint failure of beam-to-column

joint designed for weak beam-strong column philosophy, it is effective to increase the moment

capacity of joint relative to the induced moment at beam ends which yield in flexure. However,

in conventional reinforcement detail, increasing of longitudinal reinforcement in joint core

inevitably also increase the beam moment capacity because the longitudinal reinforcement for

joint and beam is common. The method to overcome the problem is to arrange aditional longi-


27/30


27

tudinal bar only in joint panel and joint hoops to make joint moment capacity larger than that

of beams using reinforcing detail as shown in Fig. 21(a). By the additional reinforcement in the

joint, joint deformation depicted by Fig. 15(a) will be significantly diminished, while the beam

deformation in Fig. 15(b) will be increased. However no experimental works on this kind of

special reinforcement in beam-to-column joint have not been reported before. By this counter-measure, failure mode of joint is presumed to be changed to more favorable ductile failure

mode by preventing the plastic deformation concentrated in joint shear panel. So the change of

failure mode will be easily achieved, not by limiting the joint shear.

Fig. 22 : Probable reinforcing detail to prevent joint shear failure

Although the proposed reinforcing method may be effective to get favorable failure mode, it

will have no effect on increasing absolute moment joint capacity, because poor anchorage of

beam reinforcement going through the joint make moment resisting capacity lower as pre-

dicted by the new model as shown in Fig. 20. It is in particular important theoretical important

for the design of beam-to-column joint after the beams yielding. Cyclic reversal loading after

beam yield imposes high demand for anchorage capacity, which accelerate deterioration of

anchorage due to bond

It sometimes causes joint shear failure after beam yield and it is well known fact. To prevent

the deterioration of the moment capacity of the joint, some special mechanical anchorage

device or spiral will be effective as shown in Fig. 21(b).

8. CONCLUSION

The joint shear input of twenty interior beam-to-column joint, which showed failure mode of

joint shear, subjected to cyclic loading simulating earthquake load are investigated. It is con-

cluded as follows;

1. In the specimens failed in joint shear in the tests, joint shear force did not degrade for themost specimens, although the story shear degraded due to cyclic load.

(a)

increase the area of beam

bar only in joint

additional joint hoops

detail to increase the

moment capcity of joint

column

beam

(b)

anchorage plate

additional spiral

detail to enhance anchorage

capacity of beam longitudinal rebar

column

beam

diagonal cracks

causing joint deformation


28/30


28

2. The cause of the degradation of story shear was attributed to the finite upper limit of

anchorage capacity of beam longitudinal reinforcement through the joint. It makes the

tensile stress in compressive reinforcement shift to tension. The lost compressive resis-

tance of the compressive force also causes the location of stress resultant of compression

shift to the mid-height of the section. As a result, the moment resistance of beamdecreased.

3. For a significant number of joint shear failure specimens, joint shear failures may not be

a compressive failure of diagonal concrete strut as assumed in some current design code.

It is rather the joint shear failure occurred due to expansion of diagonal cracks. In other

word, the direct relation between joint shear input and joint shear deformation does not

exist in those specimens.

4. Quite a large number of experiments on joint shear failure have been accumulated, whilethe joint shear data based on the stress in the longitudinal reinforcement are scarce. More

investigation of test data is urged to derive more reliable general conclusion.

5. The hypothesis of joint shear failure which assumes that the joint shear failure is the

result of diagonal compressive failure of joint panel does not have rational basis as far as

the test observed test data concerns.

Based on the examination of test, the necessity of a mathematical model which accounts the

mechanism of moment resistance of joint panel was emphasized. To explain the behavior ofjoint failure, a new model was proposed, which consists of divided segments by diagonal

cracks in joint shear panel. They rotates due to bending moment from beams and columns. The

equilibrium of internal stress in steel and concrete at the boundary and external forces acting

on beam ends and column ends is taken into account to predict the moment resisting capacity

of joint shear panel. It is concluded from the analysis using the model.

. The reliability of the model and its assumptions were verified. The prediction of model

showed good correlation with the effects of parameters including the concrete compres-

sive strength, amount of beam reinforcement, and amount of joint hoop.

7. The prediction of behavior of the new model for the moment resisting capacity of beam-

to-column joint leads to a new approach to prevent from joint shear failure. To modify

the joint failure into more ductile beam yield failure mode, it is effective to increase the

moment capacity of joint, relative to the induced moment at beam ends yield in flexure,

but joint shear resisting capacity.


29/30


29

9. ACKNOWLEDGEMENT

Dr. M. Teraoka, senior researcher of Fujita Corp. is greatly acknowledged for his offering of

detailed test data including strain history obtained in his research project. Mr. F. Kusuhara and

Mr. S. Kishikawa, graduate students, School of Engineering, the University of Tokyo, are sin-cerely appreciated for their work on test data reduction and drawing some of the figures used in

this paper.

10. REFERENCES

1. Hanson, Norman W. and Harold W. Connor : Seismic Resistance of Reinforced Concrete

Beam-Column Joint, Journal of the Structural Division, Vol. 93, ST5, Oct.1967, pp. 533-

560.

2. ACI-ASCE Committee 352 : Recommendations for Design of Beam-Column Joints in

Monolithic Reinforced Concrete Structures, ACI Journal, No. 73-28, July 1976, pp. 375-

387.

3. Meinheit, Donald F. and James O. Jirsa : Shear Strength of R/C Beam-Column Connec-

tions, Journal of the Structural Division, ASCE, Vol. 107, No. ST11, Nov. 1981, pp.

2227-2244.

4. ACI 318-95: Building Code Requirements for Structural Concrete and Commentary

,

ACI, Farmington Hills, Michigan, pp. 367.

5. Standards New Zealand:NZS3101Concrete Structures Standard :Part1 - The Design of

Concrete Structure:1995

, 1995.

6. Architectural Institute of Japan :AIJ Structural Design Guidelines for Reinforced Con-

crete Buildings , Tokyo, 1994, 168 pp..

7. Oka, Koji and Hitoshi Shiohara : Tests of high-strength concrete interior beam-to-columnjoint subassemblages, Proceedings of the Tenth World Conference on Earthquake Engi-

neering, Balcelona, 1992, pp. 3211-3217.

8. Masaru Teraoka, A study on seismic design of R/C beam-to-column joint in high rise

frame structure, Research Report of Fujita Institute of Technology, Extra Issue No. 5,

1997, (in Japanese)

9. Priestley, M. J. N., : Displacement-based Seismic Assessment of Existing Reinforced

Concrete Building, Proceedings of the Pacific Conference on Earthquake Engineering,

Volume 3, Australia, 20-22 November, 1995, pp. 225-244.


30/30


10. Kashiwazaki, T., T. Nagai and H. Noguchi : Parametric Study on the Shear Strength of R/

C Interior Beam-Column Joints using Finite Element Method, Transactions of Japan

Concrete Institute, Vol. 18, 1996, pp. 275-282

11. Hideki Kimura, Taku Kawai, Masayuki Iwata and Tokio Watai, Experimental study onbehavior of R/C External Beam-to-Column Joint under high axial load, Proceedings of

AIJ Annual Convention, Vol. C-2, September 1997, pp. 389-390 (in Japanese)

A NEW MODEL FOR JOINT SHEAR FAILURE OF REINFORCED CONCRETE INTERIOR BEAM-TO-COLUMN JOINT

Documents

Transcript of A NEW MODEL FOR JOINT SHEAR FAILURE OF REINFORCED CONCRETE INTERIOR BEAM-TO-COLUMN JOINT