工程科学与技术   2018, Vol. 50 Issue (5): 77-86

Calculation Method of the Plastic Hinge Length for the Reinforced Concrete Frame Joint Based on Energy Dissipation
FENG Bo, XIONG Feng, CHEN Jiang, CHEN Wen
College of Architecture & Environment, Sichuan Univ., Chengdu 610065, China
Abstract: Plastic hinge length is an important parameter when the elastic-plastic analysis is carried out on a structure and it has an important influence on the analysis result. The calculation method for the plastic hinge length is mainly the equivalent plastic length method at present and the plastic hinge length is calculated based on the deformation of a structure. While the plastic hinge length has a close relationship with the energy dissipation of a structure, but it is not considered in the equivalent plastic hinge length method. And the plastic hinge length should not be a constant and it should vary with the loading level of a structure. However, the empirical equation used to calculate the plastic hinge length only give the final length of the plastic hinge at present, and do not provide the relationship between the plastic hinge length and the loading level. Thus, it would lead to the reduction of analysis accuracy when this kind of plastic hinge length is adopted. Hence,a plastic hinge length calculation method based on energy dissipation for the reinforced concrete beam-column joint was established, and the influence of the loading level at the beam end on the plastic hinge length was taken into account. Comparison with the analysis result, it was found that the plastic hinge length calculated by the method proposed in this paper agrees well with the range of the plastic development. At last, the relationship between the plastic hinge length and the rotation at the beam end, the reinforcement ratio as well as the effective depth of the cross section was established by means of analysis of the 18 first-grade frame joints.
Key words: plastic hinge length    energy dissipation    frame joint    finite element

1 塑性铰长度计算方法

1）结构的塑性变形均发生在塑性铰范围内；

2）塑性铰内截面塑性曲率相等；

3）不考虑结构的剪切变形和钢筋滑移的影响，仅考虑弯曲变形。基于以上3个假设，可以建立起加载端位移与塑性较长度的关系，如式（1）所示：

 ${\varDelta _{\text{p}}} = {\varDelta _{\max }} - {\varDelta _{\text e}} = ({\varphi _{\text u}} - {\varphi _{\text e}}){L_{\text p}}(L - \frac{1}{2}{L_{\text p}})$ (1)

1）结构的能量耗散只发生在塑性铰长度内；

2）塑性铰范围内各个截面耗散的能量相等；

3）不考虑结构的剪切变形和钢筋滑移的影响，仅考虑弯曲变形。通过与等效塑性铰计算方法比较可以发现，两种方法的假定3）完全相同。虽然两种方法的假定1）表述上略有不同，但是由于只有结构的塑性变形才能耗散能量，因此两种方法的假定1）是等价的。对于假定2），两种方法在大剪跨比情况下差异不大，因为截面的耗能情况主要与弯矩和塑性曲率有关，在大剪跨比情况下塑性铰的长度相对于梁或柱的跨度较短，因此在塑性铰内弯矩的变化不大，如果塑性铰内的塑性曲率相等，则在塑性铰内的耗能也就基本相当。通过比较可以认为，采用的3个假定是合理的。

 $E = \int {F(\varDelta ){\rm d}\varDelta } = {E_{\rm {lp}}}$ (2)

 ${E_{\rm {lp}}}{\text{ = }}\iint {M(\varphi ,l){\rm d}\varphi {\rm d}l}$ (3)

 $\varphi = \frac{{{\varepsilon _1} - {\varepsilon _2}}}{h}$ (4)

 $\int {F(\varDelta )} {\text d}\varDelta = \iint {M(\varphi ,l)}{\text d}\varphi {\text d}l$ (5)

 $\int {F(\varDelta ){\rm d}\varDelta } = {l_{\rm p}}\int {\overline M(\overline \varphi )} {\rm d}\overline \varphi$ (6)

 ${l_{\rm p}} = \frac{{\int {F(\varDelta ){\text d}\varDelta } }}{{\int {\overline M(\overline \varphi )} {\text d}\overline \varphi }}$ (7)

 图1 试件基本信息 Fig. 1 Basic information of the specimen

2 试验概况

 图2 加载装置 Fig. 2 View of the set up

3 有限元模型的建立与验证 3.1 模型建立

 图3 数值模型 Fig. 3 FE model

3.2 材料本构

 ${E_{\rm d}} = {E_0}{(1 - {D_k})^2},k ={t},{c}$ (8)

 ${D_k} = 1 - {(1 - {d_k})^{1/2}},k = {t},{c}$ (9)

3.3 模型验证

 图4 等效塑性拉应变云图 Fig. 4 Contours of the PEEQT

 图5 滞回曲线对比 Fig. 5 Comparison of the hysteretic curves

 图6 塑性铰长度随梁端转角的变化 Fig. 6 Change of the plastic hinge length with the ration at the beam end

 图7 不同加载水平下的等效塑性应变云图 Fig. 7 Contours of the PEEQ under different loading level

4 塑性铰长度计算结果

5 参数分析

5.1 单参数对塑性铰长度的影响

 图8 截面高度对塑性铰长度的影响 Fig. 8 Influence of the section height on the plastic hinge length

 图9 配筋率对塑性铰长度的影响 Fig. 9 Influence of the reinforcement ratio on the plastic hinge length

 图10 加载水平对塑性铰长度的影响 Fig. 10 Influence of the loading level on the plastic hinge length

5.2 塑性铰长度计算模型

 $\frac{{{l_{\rm p}}}}{{{h_0}}} = 13.349{(\theta \rho )^{0.572\;2}}$ (10)

 图11 塑性铰长度变化规律 Fig. 11 Change rule of the plastic hinge length

6 结　论

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