Sangjoon
Park,
PhD
Candidate
Khalid
M.
Mosalam,
Professor
UC
Berkeley
PEER Meeting, San Francisco, 10/16/2009
 Motivation and Objectives
 Database and Parameters
 Semi-Empirical Joint Shear Strength Model
 Analytical Joint Shear Strength Model
 Ongoing Experimental Program
 Conclusions
  Seismic performance of old RC beam-column joints
- No seismic design code prior to 1970’s
- No transverse reinforcement in the joint region
  Existing joint strength models
- Inappropriate application from reinforced joints to unreinforced joints
- Overly simplified failure mechanism
- Underestimation of shear strength (ASCE/SEI 41)
Joint geometry
γ
4
6
8
  Dependency of joint shear strengths on beam reinforcement
Walker (2001)
Column Shear [kips]
*: Large number represents
high beam reinforcement ratio
140
*
PEER-4150
120
PEER-2250
100
80
PEER-1450
60
40
PEER-0850
20
0
0
1
2
3
Drift [%]
4
5
6
  Determine controlling parameters for shear strength of
unreinforced exterior beam-column joints
  Develop two rational shear strength models
- Semi-empirical equation for easy application
- Analytical model with consistent procedure for different failure modes
  Explain the dependency on beam reinforcement ratio
  Minimize obscure definition of parameters
e.g. joint aspect ratio, width of diagonal strut, ductility factor, etc.
  Simulate using extension to the element level of joint model
  Unreinforced exterior joint tests w/o or w/ one lateral beam
or
(a)
(c)
(b)
  Anchorage details of selected specimens
Type A
Type B
  Column width (bc)
Type C
Type D
beam width (bb)
  62 test data are collected
  Failure mode:
J (joint shear failure without beam yielding)
BJ (joint shear failure with beam yielding)
1. Joint aspect ratio: hb / hc
J failure
Other failure
Joint aspect ratio, hb / hc
2. Beam reinforcement index:
low aspect ratio,
high aspect ratio
,removed data from high aspect ratio
3. Column axial load:
1. Joint aspect ratio
Cc
Vc
C-C-T
node
A s fs
hb
hs
khc
Vjh
h s
D
C-C-C
node
hc
C b
Cc
 Equilibrium
Equilibrium
 C-C-T node zone
 Constitutive
Vollum (1998)
C-C-T node strength reduction
 Determine principal tensile strain
Strength reduction factor,
■ C-C-T node strength reduction factor
(d)
(a),(f),(i)
(h)
(b),(e)
(c)
(j)
(g)
■ Approximation of principal tensile strain
Concrete compressive strength [psi]
Approximate
 Proposed equation for joint aspect ratio
×
Pantelides et al. (2002)
×
J failure
Other failure
Joint aspect ratio, hb / hc
2. Beam reinforcement
 Equilibrium
If beam reinforcement is yielding, fs = fy
 Normalized form
: Beam reinforcement index = Joint shear demand at fs = fy
3. Proposed model
(11.7)
(5)
(4)
(· ): value at hb/hc=1.0
(11.7)
MEAN = 0.97
COV = 0.16
Vjh,test [kip]
Vjh,test [kip]
Vjh,test [kip]
4. Evaluation
(b) Vollum (1998)
(d) Bakir and Boduroğlu (2002)
(c) Hwang and Lee (1999)
Vjh,test [kip]
Vjh,test [kip]
Vjh,test [kip]
(a) Proposed model
MEAN = 1.09
COV = 0.19
MEAN = 1.37
COV = 0.39
MEAN = 0.83
COV = 0.23
MEAN = 0.60
COV = 0.17
(e) Hegger et al. (2003)
MEAN = 0.85
COV = 0.29
(f) Tsonos (2007)
1. Assumptions
 Two inclined struts mechanism
ac
Vc
lh
Vc
x
As fs
As fs
C-C-T
hb
ST2
ST1
ST1
ST2
ab
C-C-C
hc
ac
 Basis of two inclined struts mechanism
- Tests with different anchorage details
- Crack patterns for different failure modes
High
contribution
of ST2
(a) Beam reinforcement bent-into the joint (Wong, 2005)
(a) J failure (Ortiz, 1993)
Low
contribution
of ST2
(b) Beam reinforcement bent-outside the joint (Wong, 2005)
(b) BJ failure (Wong, 2005)
 Definition of joint shear failure: when the demand of ST1 reaches its capacity
from Hakuto et al. (2000)
 Horizontal width of ST1 and ST2
- Constant value independent of column axial load, failure modes, or ductility
Hwang and Lee (1999)
Vollum (1998)
2. Formulation
 Equilibrium
Vc
As fs
: Bond strength
ST1
ST2
Lehman & Moehle (2000)
CEB-FIP (1990)
fy fp
fs : tensile stress of beam reinforcement
 Fraction factor
of ST1
 Fraction factor
curve
1.0
: Fraction factor of ST1
fo
fy
fr
fp
fs : tensile stress of beam reinforcement
3. Solution algorithm
Input:
Calculate:
fo
,
fp
,
fr
,
α1 ,
α2 ,
Vjh,ST1,max Assume:
fs,i
Determine:
αi
Define:
Vjh,i =As fo(1-0.85hb/H)
Calculate:
Vjh,i ,
Vjh,ST1,i Yes
Check:
fs,i< fo
No
Yes
Check:
Vjh,ST1,i ≥Vjh,ST1,max
Define:
Vjh = Vjh,i
End
No
4. Evaluation
0.985
0.955
0.927
COV
0.149
0.149
0.150
0.147
Vjh,test [kip]
MEAN = 0.98
COV = 0.15
Vjh,model [kip]
(a) Proposed Model
Vjh,test [kip]
1.016
Vjh,test [kip]
Mean
MEAN = 1.37
COV = 0.39
Vjh,model [kip]
(b) Hwang and Lee (1999)
MEAN = 0.85
COV = 0.29
Vjh,model [kip]
(c) Tsonos (2007)
4. Evaluation
4. Evaluation
5. Two joint shear strengths of a specific joint
Vjh,high
Vjh,low
(b) Joint with low reinforcement ratio
(a) Joint with high reinforcement ratio
Vjh,ST1=
Vjh
Vjh,ST1,max
Joint shear failure point
(c) Joint shear demand of ST1
1. Moment vs. Rotation of the joint
J mode
BJ mode
Rotational spring with rigid links
J mode
J mode
BJ mode
BJ mode
(a) Joint shear stress versus strain
(b) Joint shear stress versus slip
2. Simulations using proposed model
Force [kN
]
Force [kN
]
Wong (2005)
150
100
Beam capacity = 138kN
Beam capacity = 79kN
100
50
50
-60
-40
-20
0
40
20
80
100
center to center analysis
Proposed rotational spring
Beam capacity = 138kN
-40
-20
0
Displacement (mm)
-50
-100
60
-150
(a) J failure (BS-L)
20
40
60
80
100
Displacement (mm)
-50
-100
center to center analysis
Proposed rotational spring
(b) BJ failure (JA-NN03)
1. Specimen design
Reinforcement Ratio
Aspect Ratio
For All Specimens,
Concrete Strength : fc = 3.5 ksi
Reinforcing bars
: Grade 60
2. Construction
3. Setup
Papplied
Allow vertical translation
for column axial load variation
Vb,T
Vb,L
Preact
Target B/C
Sliding vertically
4. Loading
+
+
+
TR
-
Papplied
+
-
LN
-
- Pre-defined equation for column axial loading
SP 1&3 : Papplied=-95 + 2Vb,x + 2Vb,y
SP 2&4 : Papplied=-95 + 4Vb,x + 4Vb,y
5. Test movies
6. Test-SP4
ASCE/SEI 41
Transverse direction
Prediction by
Semi-empirical model
Prediction
by Analytical model
Beam tip displacement [in]
Beam shear [kips]
Beam shear [kips]
Longitudinal direction
Beam tip displacement [in]
6. Test-SP4
1. Main parameters
  Joint aspect ratio (hb / hc)
  Beam reinforcement index
2. Shear strength models of unreinforced exterior joints
  Semi-empirical model
  Analytical model
- Accurate prediction of beam reinforcement tensile stress at shear failure
3. Application of analytical model to simulation
  Single rotational spring with rigid link
  Successful capture of force and displacement at shear failure
4. Experimental verification
  Accurate prediction of joint shear failure following beam yielding
  Further verification of proposed models
  Initial stiffness and post-failure behavior of joint
  High column axial load effect
  Interaction behavior under bi-directional loading
  Extension to unreinforced interior joints
  Progressive collapse analysis using developed joint element
within the framework of “direct element removal”
Questions?
Comments?