Damage evaluation of hinged joints by method of orthotropic plates with hinged joints
Xiao-jing NI1,2(),Yuan XING2,Rong-qiao XU1,*()
1. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China 2. Huahui Engineering Design Group Co. Ltd., Shaoxing 312000, China
A two-dimensional shear force calculation model for hinged joint (HJSFM) taking damage position, cracking length and degree of hinged joints into account was established, in order to quantitatively evaluate the damage degree of hinged joint in the hollow slab girder bridge and provide decision-making basis for subsequent maintenance and reinforcement. In this model, single hollow slab was compared to an orthotropic plate, and the bridge was formed by multiple orthotropic plates laterally connected through hinged joints. The relationship between shear force of the hinged joint and relative displacement occurring across the hinged joint was introduced as the force transfer equation between orthotropic plates. The analytical solution for HJSFM under loads was derived based on Fourier series expansion. Based on the evolution of damage state of hinged joints under design load and overload, a three-level damage rating scheme of light, medium and heavy for hinged joints (HJDRS) was put forward. HJSFM and HJDRS composed the core of damage assessment model for hinged joint (HJDAM). Finally, a finite element model was established to verify accuracy of the shear force calculated by the HJSFM, and the HJDAM was applied to a hollow slab girder bridge with damaged hinged joints. Results show that the accuracy of shear force obtained by the HJSFM can meet the engineering needs and the HJDAM is feasible.
Xiao-jing NI,Yuan XING,Rong-qiao XU. Damage evaluation of hinged joints by method of orthotropic plates with hinged joints. Journal of ZheJiang University (Engineering Science), 2022, 56(5): 920-929.
Fig.1Load and boundary conditions for single orthotropic plate
Fig.2Shear force-relative displacement curves for hinged joint
Fig.3Flow chart for shear force of hinged joint
项目
单位
取值
车辆重力标准值
kN
550
前轮重力标准值
kN
30
中轮重力标准值
kN
2×120
后轮重力标准值
kN
2×140
轮距
m
1.8
前轮着地宽度及长度
m
0.3×0.2
中、后轮着地宽度及长度
m
0.6×0.2
轴距
m
3.0+1.4+7.0+1.4
Tab.1Main technical indexes of vehicle load
Fig.4Illustration of vehicle load
Fig.5Illustration of vehicle load arrangement on hollow slab girder bridge
Fig.6Illustration of cross-section of hollow slab and hinged joint
部位
D1/(N·m)
Dx/(N·m)
Dy/(N·m)
Dxy/(N·m)
Dyx/(N·m)
a/m
b/m
E/(N·m?2)
ν
Kc/(N·m?2)
空心板
2.14×108
1.07×109
1.07×109
7.46×108
2.05×108
20.0
1.0
3.25×1011
0.2
?
铰缝
?
?
?
?
?
?
?
3.25×1011
0.2
2.57×1011
Tab.2Calculation parameters of hollow slab and hinged joint
Fig.7Illustration of finite element model for calculating shear force at hinged joints of hollow slab bridge
Fig.8Variation of shear force with number of Fourier expansion terms at F~J
Fig.9Comparison of shear force at hinged joint 1 resulted from finite element method and proposed shear calculation model
方法
J
I
H
G
F
Vmax/(kN·m?1)
Er/%
Vmax/(kN·m?1)
Er/%
Vmax/(kN·m?1)
Er/%
Vmax/(kN·m?1)
Er/%
Vmax/(kN·m?1)
Er/%
有限元模型
?25.0
0.0
?23.7
0.0
?21.8
0.0
?20.9
0.0
?6.3
0.0
本研究方法(m=200)
?25.8
3.2
?26.0
9.7
?22.7
4.1
?22.7
8.6
?6.7
6.3
Tab.3Shear force at hinged joint 1 resulted from finite element method and proposed shear calculation model
Fig.10Illustration of cross section of hollow slab girder bridge
参数
数值
参数
数值
Kc/(N?m?2)
3.75×109
?wu/mm
0.5
Kp/( N?m?2)
1.00×108
Vc/(N?m?1)
1.1×105
?wc/mm
0.0293
Vu/( N?m?1)
5.0×104
Tab.4Calculation parameters of hinged joint
Fig.11Evolution of damage area of hinged joints with movement of vehicle queue
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