r - The Hong Kong Polytechnic University

fatigue life of steel columns. Xiao invented methods to transversely confine the plastic hinge region of a steel
column, and test results validated the concept to have superior seismic behavior [Xiao et al. 2009]. Figure 6
shows the concept of transversely confined steel columns. Cyclic lateral loading test results of full-scale
columns without and with transverse confinement are compared in Fig.7, demonstrating the significantly
improved seismic behaviour of confined steel column.
1.5
1.5
1.0
0.5
HWW
N/N y =0.3
1.0
0.5
HWW-RCC
N/N y =0.3
V/Vp
0.0
V/Vp
0.0
-0.5
-0.5
-1.0
-1.0
-1.5
-10 -8 -6 -4 -2 0 2 4 6 8 10
Drift Ratio(%)
-1.5
-10 -8 -6 -4 -2 0 2 4 6 8 10
Drift Ratio(%)
(a)
(b)
Figure 7 Lateral force and drift ratio hysteretic responses of (a) steel H column, and (b) confined steel H column
MODELLING OF CONFINED CONCRETE
The author also devoted significant efforts on fundamental studies aimed to develop rational mechanical models
of confined concrete. In his Doctor of Engineering thesis defended in 1989, the author conducted carefully
designed axial loading tests on more than thirty concrete stub columns confined by steel tubes with different
thickness and concrete strength. Through the instrumentation of strains and analysis of stresses, an octahedral
stress and strain relationship, as shown in Fig.8, along with failure criterion and plastic flow potential were
proposed [Xiao 1989].
For
σ − 3 ε
c
oct c oct
relationship
⎧ ⎛ f ⎞⎫
a = ⎨ − ⎜ ⎟⎬×
⎩ ⎝35.3
⎠⎭
c B
−4
14.60 3.65 10
⎧ ⎛ f ⎞⎫
b = ⎨ + ⎜ ⎟⎬×
⎩ ⎝35.3
⎠⎭
c B
−4
8.27 11.60 10
⎧
⎛ f ⎞⎫
c = ⎨− + ⎜ ⎟⎬×
⎩
⎝35.3
⎠⎭
c B
−4
1.57 5.04 10
For
c
τ
−
γ
oct c oct
relationship
⎧ ⎛ f ⎞⎫
a = ⎨ + ⎜ ⎟⎬×
⎩ ⎝35.3
⎠⎭
c B
−4
8.19 2.03 10
⎧ ⎛ f ⎞⎫
b = ⎨ + ⎜ ⎟⎬×
⎩ ⎝35.3
⎠⎭
c B
−4
7.25 5.85 10
⎧
⎛ f ⎞⎫
c = ⎨− + ⎜ ⎟⎬×
⎩
⎝35.3
⎠⎭
c B
−4
2.82 11.13 10
Figure 8 Octahedral stress-strain relationship for confined concrete proposed by Xiao [1989]
This model was recently used satisfactorily in analyses of CFT and CCFT columns under axial loading [Choi
and Xiao 2010a, b], as shown in Fig.9.
The author also carried out axial loading tests on FRP confined concrete stub columns and established a data set
widely used by other researchers [Xiao and Wu 2000]. Based on the test results, stress strain models for FRP
confined concrete were developed [Xiao and Wu 2000; Xiao and Wu 2003].
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