PSEUDO-STATIC TEST AND MOMENT-CURVATURE HYSTERTIC MODEL OF PVC-CFRP CONFINED COLUMN-RC RING BEAM EXTERIOR JOINT
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摘要: 开展11根PVC-CFRP管钢筋混凝土柱-钢筋混凝土环梁T型节点低周反复加载试验，分析环梁尺寸、环筋配筋率、CFRP条带间距、梁纵筋配筋率、轴压比等因素对其破坏形态、滞回性能、骨架曲线等影响。结果表明：节点破坏经历初裂、通裂、极限和破坏四个阶段，节点的弯矩-曲率滞回曲线包括弹性段、弹塑性段和平稳段，节点滞回环饱满，显示出良好的抗震性能。基于软化混凝土本构关系模型，考虑各因素对骨架曲线特征点的影响，提出骨架曲线特征点简化计算公式。基于退化三线型恢复力模型，给出卸载刚度计算公式，提出节点滞回规则，建立预测精度较高的环梁节点弯矩-曲率恢复力模型。Abstract: Eleven PVC-CFRP confined concrete column-reinforced concrete ring beam exterior joints are tested under low cyclic loading. The effects of the ring beam width, reinforcement ratio of ring reinforcement, spacing of CFRP strips, reinforcement ratio of frame beam and axial compression ratio on the failure mode, hysteretic behaviors and skeleton curves are analyzed. The test results show that the failure of typical specimens experiences four stages, i.e., initial crack, crack penetration, limit and failure. The moment-curvature hysteretic curve consists of elastic stage, elastic-plastic stage and stationary stages. The hysteresis loops are full, indicating that the specimens exhibit excellent seismic behaviors. By considering the effects of the above parameters on the characteristic points of moment-curvature skeleton curves, the simplified formulas for predicting the characteristic points are proposed based on the softening constitutive model of concrete. On the basis of the degenerate trilinear hysteretic model, the calculation formula for unloading stiffness and the hysteretic rule are proposed, and a moment-curvature hysteretic model of the joints is established with high accuracy.
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Key words:
- PVC-CFRP confined concrete /
- column /
- beam /
- joint /
- hysteretic behavior /
- restoring force model
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图 8 各因素对弯矩-曲率骨架曲线的影响
Figure 8. Influence of various factors on moment-curvature skeleton curves
图 10 环梁节点弯矩-曲率骨架曲线计算值和试验值比较
Figure 10. Comparison between calculated and experimental results of moment-curvature skeleton curve of ring beam joints
图 11 环梁节点弯矩-曲率关系滞回规则
Figure 11. Hysteretic rule of moment-curvature relationship for the ring beam joints
图 12 环梁节点恢复力模型计算值和试验值对比
Figure 12. Comparison between the calculated and experimental values of restoring force model for ring beam joints
表 1 环梁节点试验参数
Table 1. Experimental parameters of ring beam joints
试件编号 环梁尺寸b×h /mm CFRP条带层数$ {n_{\text{f}}} $/间距$s_{\text{f} }'$/mm 环筋配筋率$ {\rho _{\text{r}}} $ 梁纵筋配筋率$ {\rho _{\text{b} }} $/(%) 轴压比n S1 100×340 2/40 1.51%(4 
2.17(4 
0.2 S2 100×340 2/40 1.27%(4 2.17(4 0.2 S3 100×340 2/40 0.98%(4 2.17(4 0.2 S4 100×340 2/20 0.98%(4 2.17(4 0.2 S5 100×340 2/60 0.98%(4 2.17(4 0.2 S6 100×340 2/40 1.51%(4 1.76(3 0.2 S7 125×340 2/40 1.05%(4 2.17(4 0.2 S8 75×340 2/40 1.04%(4 2.17(4 0.2 S9 100×340 2/40 1.51%(4 1.39(3 0.2 S10 100×340 − 0.98%(4 2.17(4 0.2 S11 100×340 2/40 0.98%(4 2.17(4 0.4 注：1)环筋配筋率${\rho _{{ {\rm{r} } } } } = { { {A_{ {\text{rs} } } } } / {bh} }$，其中：$ {A_{{\text{rs}}}} $为环梁环形钢筋的总面积；$ b $和$ h $分别为环梁截面宽度和高度；2)梁纵筋配筋率${\rho _{\text{b} } } = { { {A_{ {\text{bs} } } }}/ { {b_{\text{b} } }{h_{\rm{b}}} } }$，其中：$ {A_{{\text{bs}}}} $为纵向受拉钢筋的截面面积；$ b_{\text{b}}^{} $和$ {h_{\text{b}}} $分别为梁截面宽度和高度；3)柱体积配箍率$ {\rho _{{\text{vc}}}} = {{4{A_{{\text{svc}}}}} / {{s_{\text{c}}}{d_{\text{c}}}}} $，其中：$ {A_{{\text{svc}}}} $、$ {s_{\text{c}}} $和$ {d_{\text{c}}} $分别为箍筋截面积、间距和所围成圆直径；4)—表示PVC管表面不缠绕CFRP条带。 
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表 2 钢筋的基本性能
Table 2. Basic mechanical properties of reinforcement
钢筋种类和直径/mm 屈服强度/MPa 极限强度/MPa 弹性模量/GPa HPB300/6 323 542 197 HPB300/8 308 426 201 HPB300/10 313 432 197 HRB400/16 451 620 195 HRB400/18 465 633 195 HRB400/20 446 611 199
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表 3 环梁节点屈服弯矩和曲率试验值与计算值比较
Table 3. Comparison of experimental and calculated yield moment and curvature of ring beam joints
试件编号 $屈服弯矩试验值M_{\rm{y} }^{\rm{t } }/{\rm{kN} }$ $ 屈服曲率试验值\phi_{\rm{y} }^{\rm{t} } /{\rm{mm} } $ $屈服弯矩计算值M_{\rm{y} }^{\rm{c} } /{\rm{kN} }$ $ 屈服曲率计算值\phi_{\rm{y} }^{\rm{c} } /{\rm{mm} } $ $ M_{\rm{y}}^{\rm{t}}/M_{\rm{y}}^{\rm{c}} $ $\phi_{\rm{y}}^{\rm{t}}/\phi_{\rm{y}}^{\rm{c}} $ 式(3) 式(6) 式(5) 式(7) 式(3) 式(6) 式(5) 式(7) S1 57.5 0.014 110.5 50.0 0.008 0.013 0.520 1.150 1.750 1.077 S2 45.8 0.015 110.5 50.0 0.008 0.013 0.414 0.916 1.875 1.154 S3 51.4 0.013 110.5 50.0 0.008 0.013 0.465 1.028 1.625 1.000 S4 47.7 0.015 110.5 50.0 0.008 0.013 0.432 0.954 1.875 1.154 S5 40.5 0.013 110.5 50.0 0.008 0.013 0.367 0.810 1.625 1.000 S6 53.5 0.013 90.6 49.4 0.007 0.014 0.591 1.083 1.857 0.929 S7 49.0 0.014 110.5 50.0 0.008 0.013 0.443 0.980 1.750 1.077 S8 44.6 0.012 110.5 50.0 0.008 0.013 0.404 0.892 1.500 0.923 S9 50.5 0.016 72.5 45.5 0.007 0.015 0.697 1.110 2.286 1.067 S10 49.9 0.012 110.5 50.0 0.008 0.013 0.452 0.998 1.500 0.923 S11 53.6 0.014 110.5 50.0 0.008 0.013 0.485 1.072 1.750 1.077 均值 0.479 0.999 1.763 1.035
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表 4 不同曲率幅值下的卸载刚度
Table 4. Unloading stiffness under different curvature amplitudes
试件编号 曲率/屈服曲率卸载刚度/屈服曲率 各级曲率卸载刚度 S1 $ \phi /{\phi _{\text{y}}} $ 0.83 0.93 1.04 1.14 1.25 1.87 2.49 2.90 3.11 3.73 4.35 4.97 $ k_{\text{u}}'/k_{\text{0}}' $ 5.73 5.48 5.30 4.69 3.87 4.12 3.30 2.86 2.25 1.40 1.13 0.83 S2 $ \phi /{\phi _{\text{y}}} $ 0.42 0.52 0.63 0.73 0.84 1.25 1.67 2.09 2.50 2.92 3.34 3.76 $ k_{\text{u}}'/k_{\text{0}}' $ 1.77 1.76 1.74 1.72 1.69 1.56 1.29 1.12 0.98 0.90 0.80 0.77 $ \phi /{\phi _{\text{y}}} $ 4.17 4.59 − − − − − − − − − − $ k_{\text{u}}'/k_{\text{0}}' $ 0.77 0.75 − − − − − − − − − − S3 $ \phi /{\phi _{\text{y}}} $ 0.69 0.81 0.92 1.27 1.58 2.30 2.87 3.45 3.59 4.11 4.61 5.13 $ k_{\text{u}}'/k_{\text{0}}' $ 1.80 1.77 1.75 1.50 1.41 0.88 0.73 0.61 0.64 0.56 0.54 0.51 S4 $ \phi /{\phi _{\text{y}}} $ 0.13 0.25 0.38 0.50 0.63 0.76 0.88 1.01 1.51 2.01 2.52 3.02 $ k_{\text{u}}'/k_{\text{0}}' $ 8.63 8.44 8.42 8.29 4.52 5.15 5.72 7.43 2.40 1.73 1.53 1.34 $ \phi /{\phi _{\text{y}}} $ 3.53 4.03 4.54 − − − − − − − − − $ k_{\text{u}}'/k_{\text{0}}' $ 1.21 1.18 0.99 − − − − − − − − − S5 $ \phi /{\phi _{\text{y}}} $ 0.74 0.85 0.84 1.26 1.69 2.11 2.53 2.95 3.80 4.21 4.64 − $ k_{\text{u}}'/k_{\text{0}}' $ 8.84 8.52 8.16 6.92 4.20 2.20 1.68 1.36 1.10 1.08 1.00 − S6 $ \phi /{\phi _{\text{y}}} $ 0.72 0.84 0.97 1.44 1.92 2.41 2.89 3.37 3.85 4.33 4.82 − $ k_{\text{u}}'/k_{\text{0}}' $ 3.11 3.05 2.85 1.59 1.17 0.98 0.83 0.73 0.66 0.67 0.59 − S7 $ \phi /{\phi _{\text{y}}} $ 0.61 0.72 0.82 1.23 1.63 2.05 2.45 2.86 3.27 3.68 4.08 4.49 $ k_{\text{u}}'/k_{\text{0}}' $ 3.65 3.58 3.27 1.70 1.27 1.09 0.90 0.80 0.77 0.72 0.68 0.65 $ \phi /{\phi _{\text{y}}} $ 4.91 − − − − − − − − − − − $ k_{\text{u}}'/k_{\text{0}}' $ 0.63 − − − − − − − − − − − S8 $ \phi /{\phi _{\text{y}}} $ 0.89 1.00 1.11 1.67 2.23 2.78 3.34 3.89 − − − − $ k_{\text{u}}'/k_{\text{0}}' $ 2.19 2.14 2.11 1.29 1.01 0.88 0.79 0.70 − − − − S9 $ \phi /{\phi _{\text{y}}} $ 0.10 0.39 0.49 0.59 0.69 0.78 0.88 0.98 1.18 1.76 2.35 2.93 $ k_{\text{u}}'/k_{\text{0}}' $ 3.02 2.85 2.54 2.16 2.13 2.09 2.00 1.96 1.92 1.84 1.72 1.65 $ \phi /{\phi _{\text{y}}} $ 3.52 4.69 5.28 − − − − − − − − − $ k_{\text{u}}'/k_{\text{0}}' $ 1.61 0.94 0.76 − − − − − − − − − S10 $ \phi /{\phi _{\text{y}}} $ 0.94 1.06 1.18 1.30 1.41 2.12 2.82 3.52 4.23 4.94 5.64 − $ k_{\text{u}}'/k_{\text{0}}' $ 2.51 2.49 2.48 2.47 2.18 1.31 1.02 0.83 0.75 0.72 0.62 − S11 $ \phi /{\phi _{\text{y}}} $ 0.66 0.77 0.88 0.99 1.10 1.65 2.20 2.75 3.30 0.66 − − $ k_{\text{u}}'/k_{\text{0}}' $ 1.52 1.53 1.48 1.43 1.36 1.26 0.95 0.89 0.75 1.52 − −
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