火灾及爆炸共同作用下平面约束钢梁的非线性分析理论

采用非线性铁木辛柯梁单元,结合一种新的温度-率相关本构方程,推导了单元切向刚度矩阵,并编制了有限元程序。该程序可用于进行火灾或爆炸冲击过程中梁的响应分析,亦可用于两者共同作用下梁的耦合响应分析。基于弹性铁木辛柯梁挠曲线方程构造三次插值位移场,同时考虑了梁变形的几何非线性效应并采用了Green-Lagrangian应变,再结合非线性的本构关系,该理论能较完整地考虑火灾及爆炸诸多工况组合下平面约束钢梁可能发生的多种效应。通过对工字型等截面直梁火灾升温及爆炸3种荷载组合形式下的响应分析,验证了理论模型的合理性。

Study on Response of Restricted Steel Beam under Load Combinations of Fire and Blast Using Nonlinear Timoshenko Beams

Using the nonlinear Timoshenko beams and a new temperature-rate dependent constitu- tive relation, we proposed a finite element model which can be used to analyze the nonlinear re- sponse of restricted steel beam under different load combinations of fire and blast impact. Based on the analysis of the Timoshenko-beam elastic deflection curves, we built the 3rd-order interpolation displacement field of the beam element. Using Green-Lagrangian strain and omitting the large strain terms but retaining the Von Karman term, the model can consider the geometrical nonlinear effects in the loads increments. In order to avoid the element locking, the paper ignored the Von Karman term or other high order terms when the strain was substituted into constitutive equation. The new constitutive relation was built on the data of Split Hopkinson Bar tests of Q345 and Q235B steel at elevated temperature. Because of the considering of material and geo- metrical nonlinearity, the proposed model can be used to analyze the response of restricted beam under most of the load combinations. By using the proposed model to analyze a straight beam with uniform cross-section bearing the action of fire and blast, we validated the correctness and rationality of the model.