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Feng Xiong PhDProfessor of Civil
Engineering Sichuan University
Nonlinear Finite Element Analysis for Precast Short
Column Connections Under Cyclic Loading
Background and MotivationP03
Seismic Behavior Testing of Precast short columnsP04
Finite Element Analysis of Precast Short ColumnsP18
Comparing of Shear Strength Formulas of Precast Column Joint between Chinese and Japanese Codes
P37
ConclusionP39
CONTENTS
Background and Motivation
With the development of industrialized building, precast concrete structures are currently applied since the advantages in low costing, better quality, and quickly constructing;
The short columns with shear-span ratio less than 2.0 frequently occur in high-rise precast concrete frame structures with increasing of column section size;
The one concern in precast column design is the shear strength of joints in the column bottom. Does the shear failure occur along the joints when using wet connections, i.e. sleeve grouting connection?
In the new Chinese "Technical specification for precast concrete
structures”(JGJ 1-2014), a shear strength formula is first given. But it is quite different from in Japanese codes
No Concrete pouring Rebar connecting Joint configuration
PSC-A-1 Cast-in-place No No joint
PSC-D-2 Cast-in-place Sleeve grouting No joint
PSC-E-3 Precast Sleeve grouting Joint with shear key
PSC-C-4 Precast Sleeve groutingJoint filled in grouting
material
PSC-B-6 Precast Sleeve grouting Joint filled in concrete
Two cast-in-place short columns and three precast short columns were tested under cyclic loading to investigate the effects of sleeve grouting connection and joint configurations on the behaviors of the column 。
Seismic Behavior Testing of Precast Short Columns
• Testing Objective
• Test specimens
Specimen PSC-A-1 Specimen PSC-D-2
Testing specimen elevations
Specimen PSC-E-3 Specimen PSC-C-4 Specimen PSC-B-6
Testing specimen elevations
( 1 ) Concrete
No ConcreteAge ( da
y)Cube Strength
fcu(MPa)Cuboid Strength
fc(MPa)
PSC-A-1
C45
42 45.24 34.39
PSC-D-2 55 46.26 35.16
PSC-E-3 31 50.07 38.06
PSC-C-4 48 45.89 34.88
PSC-B-6 35 51.08 38.82
Materials of testing specimen
( 2 ) Steel rebar
DiameterYield
strength
fy(MPa)
Ultimate strength fst
(MPa)
Elastic modulus
Es(MPa)Remarks
18(1) 432 615 191606 In member PSC-D-2、 PSC-E-3、PSC-C-4、 PSC-B-6
18(2) 517 657 202228 In member PSC-A-1
6 450 583 180304 Stirrups
Testing Equipment
Loading System
The design axial compression ratio of all testing specimens is 0.6. The axial loads calculated as the measured concrete strength were exerted as the table following ;
Horizontal cyclic loading was controlled by the displacement as the figure.
Specimen
Axial Compression Calculated
kN
Axial Compression
Exerted
kN
PSC-A-1 1466 1466
PSC-D-2 1498 1498
PSC-E-3 1629 1460
PSC-C-4 1466 1466
PSC-B-6 1661 1460
Testing process and observation
• Horizontal bending cracks occurred on the top ;
• When loading at displacement of±5.25m, diagonal cracks occurred in the cross shape ;
• When getting to ultimate loading, diagonal cracks distributed in whole column ;
• When loading at displacement of ±21mm concrete began to crush ;
• Finally loading at displacement of±42mm, concrete crushed and rebar exposed , indicated column damage.
Crack at 1.3125mm
Crack at 5.25mm
Crack at 10.5mm
to ultimate loading
Crack at 42mm
when damaging
Specimen PSC-A-1 (cast in place)
• Horizontal bending cracks occurred on the top at ±1.3125mm, with the joint at the bottom cracking ;
• Similar process occurred as the cast in place specimen ;
• Finally loading at displacement of±42mm, concrete crushed and rebar exposed , but the joint crack didn’t go through.
Crackingat 1.3125mm
Diagonal cracks
occurred at 5.25mm
At 10.5mmGot to ultimate
loading
At 42mmSpecimen damaged
Specimen PSC-E-3 (Precast)
Testing process and observation
Hysteretic Curves
PSC-A-1 PSC-D-2 PSC-E-3
PSC-C-4 PSC-B-6 5 specimens including cast-in-place and precast columns have the similar hysteretic behavior and energy absorbed.
Skeleton curve
Comparing with PSC-A-1and PSC-D-2 , it is indicated that the sleeve has few effects on initial stiffness . With loading increases, the stiffness of sleeve column (PSC-D-2) decreases but ultimate strength increases. There is a longer platform at ultimate strength to slow down the stiffness degrading.
PSC-A-1 vs PSC-D-2Sleeve effects
Comparing with PSC-E-3 and PSC-C-4, it shows that the specimen with shear key has lower strength but better deformation and slower stiffness degrading than the specimen with the smooth joint.
PSC-E-3 vs PSC-C-4Shear key effect
Skeleton curve
Comparing with PSC-C-4 and PSC-B-6 , it shows that the specimen filled in high-strength grouting material in the joint has higher strength but less deformation than the specimen filled in concrete in the joint.
PSC-C-4 vs PSC-B-6Grouting material effect
Skeleton curve
Ultimate Strength
No fc(MPa) Vu+(kN) Vu
-(kN) Vu+/fcbh0 Vu
-/fcbh0 Failure
PSC-A-1 34.39 472.7 -406.9 0.112 0.097 Shear
PSC-D-2 35.16 504.2 -396.1 0.117 0.092 Shear
PSC-E-3 38.06 520.6 -493.3 0.112 0.106 Shear
PSC-C-4 34.88 517.7 -438.8 0.121 0.103 Shear
PSC-B-6 38.82 520.3 -472.5 0.109 0.099 Shear
It is shown that the precast specimens have the similar strength and failure modes as the cast-in-place specimens.
Testing Conclusion
The rebar connected by the sleeve can insure the loading transfer, and the sleeve has no bad effect on the columns;
The precast columns using three horizontal joint configurations have the similar seismic behavior as the cast-in-place columns;
Since the limit specimens, the shear behavior and failure mode along the joints can not be obtained. The test just proves that the precast column has the behavior equal to cast-in-place column.
To investigate if the shear failure occurs along the joint for precast short columns, numerical analysis is employed.
Finite Element Analysis of Precast Short Columns
Attaching the material property Concrete: Damaged plastic model
Reinforcement: Bi-linear model
• Finite element modeling
Modeling componentsas the dimension
Finite Element Modeling
1.划分网格,指定单元类型。
Defining interface and assembling each component
Tie
Tie (Cast-in-place) orFriction contact (Precast)
Embedded region
Specifying boundary condition
Encastre
Constraining Z translation and three rotations
Exerting loadings
Loading• Finite element modeling
Modeling componentsas the dimension
Attaching the material property
Meshing and specifying element
Concrete: three-dimensional linear brick elements
Reinforcement: truss elements
• Finite element modeling
Finite Element Modeling
Defining interface and assembling each component
Specifying boundary condition
Exerting loadings
Modeling componentsas the dimension
Attaching the material property
Verifying the finite element model
Taking the PSC-A-1 as a example. When observing the equivalent plastic tension strain ( PEEQT ), it shows the process of“bending cracks occurring—diagonal cracks occurring—diagonal cracks developing—damaging in shear mode” , and has a good agreement with the testing observation 。
1.3125mm 5.25mm 10.5mm 42mm
( 1 ) Failure process and mode
The contact elements specified in the interface of joint indicates that cracks occurred along the joints of specimens PSC-E-3、 PSC-C-4、 PSC-B-6, but didn’t go through the joints. It states that the damage was not resulted by the shear sliding of the joints and agrees with the test observation.
( 2 ) Cracking in the joints of precast column
PSC-E-3 PSC-C-4 PSC-B-6
Verifying the finite element model
( 3 ) Skeleton Curves
Verifying the finite element modelSince the sleeve and shear key are not modeled In order to simplify the numerical analysis, a few errors can be observed from numerical results.
( 4 ) Ultimate Strength
Specimen PSC-A-1 PSC-D-2 PSC-E-3 PSC-C-4 PSC-B-6
Testing( kN) 472.70 504.20 520.60 517.70 520.30
FE results( kN) 446.09 447.37 480.19 453.50 488.40
Relative Errors(%) 5.63 11.27 7.76 12.40 6.13
Testing ( kN ) -406.90 -396.10 -493.30 -438.80 -472.50
FE results ( kN ) -423.29 -428.69 -421.02 -411.06 -418.24
Relative errors( % ) 4.03 8.23 14.65 6.32 11.48
Testing ( kN ) 439.80 450.15 506.95 478.25 496.40
FE results ( kN ) 434.67 438.03 450.60 432.28 453.32
Relative errors( % ) 1.16 2.69 11.12 9.61 8.68
uV
-uV
uV
Verifying the finite element model
The comparing between numerical analysis and testing results indicates that the finite element models work well. It can be used to stimulate the precast short columns
Parameter Analysis To extend the test study, finite element parameter analysis is conducted. For precast short columns the two important parameters to effect joint shear behaviors are the axial compression ratio and shear-span ratio. By use of the verified model, 9 numerical models are defined as the changes of axial compression ratio and shear-span ratio.
Model shear-span ratio
Column height ( m
m )
axial compression
ratio
Axial compression
( kN )n0.6-1.5 1.5 1050 0.6 1290
n0.3-1.5 1.5 1050 0.3 645
n0.1-1.5 1.5 1050 0.1 215
n0.6-1.0 1.0 700 0.6 1290
n0.3-1.0 1.0 700 0.3 645
n0.1-1.0 1.0 700 0.1 215
n0.6-0.5 0.5 350 0.6 1290
n0.3-0.5 0.5 350 0.3 645
n0.1-0.5 0.5 350 0.1 215
Equivalent plastic strain
Comparing of columns with fixed shear-span ratio of 1.5 and different axial compression ratiosn0.6-1.5
n0.1-1.5
n0.3-1.5
With the decrease of axial compression ratio, the plastic strains increases and implies that cracks develop quickly and damages occur early.
n0.6-1.5
n0.6-0.5
n0.6-1.0
With the decrease of shear-span ratio, the cracks occur from the middle column and develop diagonally in a cross shape. But the final failure modes are similar and all in the shear damage.
Equivalent plastic strain
Comparing of columns with fixed axial compression ratio of 0.6 and different shear-span ratios
Joint states at failure stage
n0.6-1.5 n0.3-1.5 n0.1-1.5
n0.6-1.0 n0.3-1.0 n0.1-1.0
n0.6-0.5 n0.3-0.5 n0.1-0.5
• When the axial compression ratio changes from 0.6 to 0.3, no sliding is observed along the bottom joints. It indicates that precast columns fail as the cast-in-place columns;
• When axial compression ratio decreases to 0.1, the obvious sliding occurs along the joints. The failure of precast column is resulted by Insufficient shear strength of joints. The failure belongs to connection failure.
Rebar stresses at failure stage
n0.6-0.5 n0.3-0.5 n0.1-0.5
Stirrups yield but vertical rebar is in low stress when columns damage. It indicates that the column damage is the shear failure and dowel action of rebar through joints doesn’t indicate.
Stirrups and rebar through the joint yield. The column damage comes from the shear failure of the joint .
Hysterical Curves
When axial compression ration decreasing to 0.1, the deformation decreases and the areas covered by hysterical curve decrease. It implies that the shear damage of joint is less ductile than shear damage of whole column.
With the decrease of shear-span ratio, the stiffness increases but plastic deformation decreases.
Under low axial compression ratio and shear-span ratio ( n0.1-0.5 ), joint sliding occurs in the first loading cycle.
Hysterical Curves
Skeleton curves
The ultimate strength decreases with the axial compression ratio deceasing. The ultimate deformation under axial compression ratio of 0.1 is more less than that of 0.3 to 0.6
Under the same axial compression ratio, the ultimate strength increases and deformation capacity decreases with the shear-span decreasing.
Skeleton curves
Ultimate strength
The ultimate strength deceases with the axial compression ratio deceasing; and increases with the shear-span ratio deceasing.
Ultimate strength
Numerical analysis conclusion
The axial compression ratio is the key factor to effect the shear failure of joints. It decides if the precast short column fails in the connection or in the column self equal to the cast-in-place column.
For the precast short columns the shear failure will occur along the joints when the axial compression ratio is low, i.e. 0.1. The failure is very brittle with less deformation. Therefore when designing the precast short columns with low axial compression ratio, it is necessary to check the shear capacity for the joints.
The shear-span ratio affects the initial stiffness, deformation ability and ultimate strength for precast short columns. With the decrease of shear-span ratio, the initial stiffness and ultimate strength will enhanced, but deformation will reduce.
Comparing of Shear Strength Formulas of Precast Column Joint between Chinese and Japanese Codes
• Japanese code
docuE VVV , max
2165.1 ycsddo ffAV
NVc
docuE VVV
• Chinese codeShear resistance from friction along joint:
Shear resistance from rebar dowel action force:
Friction coefficient:
Area of dowel rebar:
Tensile rebar is neglected 。
Friction coefficient :
0.8 for all
Area of dowel rebar:
All the rebar through the joint is considered.
Calculating the shear strength of 9 models as the Chinese code and Japanese code respectively ( taking the same friction coefficient of 0.8 ) , the results are shown in the table following :
No.Axial
compression ratio
Shear-span ratio
Numerical results(kN)Calculations as
Japanese code(kN)Calculations as
Chinese code(kN)
n0.1-1.50.1
1.5 277.03 228.46 537.54n0.1-1.0 1.0 293.70 228.46 537.54n0.1-0.5 0.5 345.26 228.46 537.54n0.3-1.5
0.31.5 310.17 516.00 881.54
n0.3-1.0 1.0 333.49 516.00 881.54n0.3-0.5 0.5 387.93 516.00 881.54n0.6-1.5
0.61.5 339.02 1032.00 1397.54
n0.6-1.0 1.0 378.67 1032.00 1397.54n0.6-0.5 0.5 425.26 1032.00 1397.54
Comparing of Shear Strength Formulas of Precast Column Joint between Chinese and Japanese Codes
When axial compression ratios are 0.3 and 0.6, the calculation results are higher than numerical predictions for two codes. It indicates that the failure occurs in the columns. When axial compression ratio is 0.1, Japanese code has a good agreement with numerical results.
Conclusion
The test of 5 specimens indicates that the precast columns with wet connections have the similar strength, deformation and Energy consumption ability as the cast-in-place columns.
Numerical analysis indicates that shear failure occurs along the joint when axial compression is low. This damage is very brittle with less deformation. To avoid the shear failure along the joint, the shear strength of horizontal joints has to be checked when designing.
By comparing with Chinese code and Japanese code of precast structures, the shear strength formula of Chinese code is overestimate by considering both contact friction and rebar dowel action together.
THANKS谢谢聆听