The 6 th Kwang-Hua Forum, Tongji University, Shanghai, P. R. China, December 12-14, 2014 Numerical Modeling and Collapse Safety Assessment of an Unbonded Post-Tensioned Cast-In-Place Concrete Wall Hao Wu, PhD Student, Tongji University Visiting Research Associate, Lehigh University Richard Sause, Professor, Lehigh University Leary Pakiding, PhD Student, Lehigh University Stephen Pessiki, Professor, Lehigh University Xilin Lu, Professor, Tongji University December 12, 2014
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The 6th Kwang-Hua Forum, Tongji University, Shanghai, P. R. China, December 12-14, 2014
Numerical Modeling and Collapse Safety Assessment of an Unbonded Post-Tensioned Cast-In-Place Concrete Wall
Hao Wu, PhD Student, Tongji University
Visiting Research Associate, Lehigh University
Richard Sause, Professor, Lehigh University
Leary Pakiding, PhD Student, Lehigh University
Stephen Pessiki, Professor, Lehigh University
Xilin Lu, Professor, Tongji University
December 12, 2014
The 6th Kwang-Hua Forum, Tongji University, Shanghai, P. R. China, December 12-14, 2014
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Outline
Background
Lehigh Wall #1
Numerical Modeling
Collapse Safety Assessment
Concluding Remarks
Acknowledgement
The 6th Kwang-Hua Forum, Tongji University, Shanghai, P. R. China, December 12-14, 2014
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Background
Shear failure
Rebar
fracture
Concrete
crushed
2010 Chile Earthquake(From EERI)
From Fahnestock et al 2007
BRB框架
楼层
位移
(m
m,
MC
E)
Building codes use ductility from
inelastic actions to protect structures
against collapse during large
earthquakes. In conventional seismic
systems, however, this leads to:
• Distributed Structural Damage
• Residual Drifts
The 6th Kwang-Hua Forum, Tongji University, Shanghai, P. R. China, December 12-14, 2014
The 6th Kwang-Hua Forum, Tongji University, Shanghai, P. R. China, December 12-14, 2014
5
Elevation
Lehigh Wall (Ms/Mp=2.0)
3 #
7
#3 @2.25"
#4 @ 4.5"4" 4" 4" 5" 7" 7" 3.5" 6"1.5"
1.5
"10"
72"
CL
(2) bundles of
(5) 0.6" dia. strands
3 #
7
2 #
7
2 #
3
2 #
3
2 #
3
2 #
3
Wall 1
4" 4" 4" 5" 7" 7" 3.5" 6"1.5"
1.5
"10"
72"
CL
3 #
5
2 #
5
2 #
3
2 #
3
2 #
3
2 #
3
(2) bundles of
(7) 0.6" dia. strands
3 #
5
#3 @2.25"
#4 @ 4.5"
(1) bundle of
(5) 0.6" dia. strands
Reduced dia. of boundary rebar
(Ms/Mp=0.5) Increase PT
Wall 2
4" 4" 4" 5" 7" 7" 3.5" 6"1.5"
1.5
"10"
72"
CL
3 #
5
2 #
5
2 #
3
2 #
3
2 #
3
2 #
3
(2) bundles of
(7) 0.6" dia. strands
3 #
5
#3 @2.25"
#4 @ 4.5"
(1) bundle of
(5) 0.6" dia. strands
Unbonded boundary rebars
Wall 3
The 6th Kwang-Hua Forum, Tongji University, Shanghai, P. R. China, December 12-14, 2014
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Lehigh Wall #1
Shear
failure Confined
concrete crushed
Bond slip of
long. rebars
Fracture/buckling
of long. rebars
Actu
ato
r h
eig
ht
15
0 in.
Unb
on
ded P
T h
eig
ht
30
0 in.
Test setup Loading protocol (ACI ITG5.1) Lateral force-disp. response
Yielding of
long. rebars
Concrete
spalling Yielding of PT
Concrete
cracking
The 6th Kwang-Hua Forum, Tongji University, Shanghai, P. R. China, December 12-14, 2014
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Numerical modeling: Analytical model
Wall panel: Force-based fiber beam-column element PT: Corotational truss element Shear failure / Bond slip: zero-length element
(Front face) East
bar-slip fiber
section element
0
Shear spring
reaction wall
actuator support
fixture
actuator
load cell
load cell
foundation block
bearing
plate
PT anchorage
actu
ator
hei
ght
= 3
.81 m
wal
l hei
ght
= 6
.35 m
unbonded
hei
ght
= 7
.62 m
strong floor
1.5
2 m
test
specimen
(Front face) East
(c)
0
Compression-only
spring
critical
height, hcr
truss element
(PT)
node kinematic
constraint
fiber beam
column element
(wall panels)
critical height
element
zero-length
element
wall outline
Reference: Ghannoum, W.M., Moehle J.K., 2006, “Dynamic Collapse Analysis of a Concrete Frame Sustaining Column Axial Failures,” ACI Structural Journal, 109 (3), pp. 403–412 LeBorgne et al., 2014, "Analytical Element for Simulating Lateral-Strength Degradation in Reinforced Concrete Columns and Other Frame Members," Journal of Structural Engineering, V140(7), pp403-412.
The 6th Kwang-Hua Forum, Tongji University, Shanghai, P. R. China, December 12-14, 2014
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1. Sample section at the element end where the bending moments are largest in the absence of member loads;
2. Integrate quadratic polynomials exactly to provide the exact solution for linear curvature distributions;
3. Integrate deformations over the specified lengths lpI and lpJ using a single section in each PH region.
Numerical modeling: PH int. method in FBE
Lp
M
My
F
Fy
M
My
F
Fy
Lp=0
Bi-linear model Hardening Softening
My
EI
Curvature
Mom
ent
Lp
Lp=0
Loss of objectivity
01
( ) ( ) ( ( ) ( ) )p
i
NL
x i
i
x x dx x x
T T
v b e b eCompatibility 0
1
( ) ( ) ( ) ( ( ) ( ) ( ) )p
i
NL
e
x i
i
x x x dx x x x
T T
s s
vf b f b b f b
q
Flexibility Matrix
Reference: M.H. Scott, G.L. Fenves. Plastic hinge integration methods for the force-based beam-column elements. J. Struct. Engrg., 132 (2006), pp. 244–252
Do NOT sample int. pt. at the end of the element to allow initial damage to be occurred at
a certain distance from the end of the element.
The 6th Kwang-Hua Forum, Tongji University, Shanghai, P. R. China, December 12-14, 2014