火灾下空心混凝土楼板内温度场分析模型及算法

计算火灾下空心混凝土楼板内温度场的关键是计算空腔内的热量传递。假设火灾过程中空腔内气体压力为常数,空气流动引起的热量损失忽略不计,空腔内的热量传递通过壁面辐射和空气传导实现。基于奥本海姆网络法,本文提出了计算空心混凝土楼板空腔内辐射热流的算法,推导了矩阵形式的空腔内有效辐射方程,考虑到系数矩阵的对称性,采用LDLT分解法求解有效辐射方程。利用空腔边界上的有效辐射热流,计算空腔边界上单元的温度节点荷载。这种方法已经嵌入作者开发的温度场分析软件TFIELD之中,用TFIELD对底面按ISO834曲线进行加热的空心混凝土楼板进行计算,结果表明,本文算法十分有效,对研究空心混凝土楼板的抗火性能具有积极意义。

Model and Algorithm for Analyzing Temperature Distribution inside Hollow Core Concrete Slabs under Fire

In this paper,an algorithm based on the network method suggested by Oppenheim for calculating the radiative heat flow in a cavity of hollow core concrete slabs exposed to fires is presented.It is assumed that the pressure in a cavity keeps atmospheric pressure during a fire,and the lost heat from the air due to expansion and immediate moving away from a cavity is neglected.The heat in a cavity is transfer via both heat conduction in air and thermal radiation among boundaries,and special regard is paid to modeling heat transfer by radiation.The effective radiative heat flow system of equations is derived and expressed in matrix form.The system of equations features a symmetric coefficient matrix and can be solved using LDLT factorization.Node radiative thermal loads are calculated from effective radiative heat flows at edges of elements located on internal cavities.The nonlinear finite element program TFIELD written by first author has employed the new algorithm.Temperature distribution in a hollow core concrete slab exposed to ISO 834 fire is calculated using TFIELD,and numerical results demonstrate that the new algorithm is very effective and is useful for further study of structural behavior of hollow core concrete slabs in fires.