火灾作用下混凝土双向简支板的挠度计算

Determination of deflection of two-way simply supported reinforced concrete slabs in fire

小挠度薄板理论可以用来确定混凝土双向板正常使用时的挠度,当用于计算火灾作用下处于大挠度的双向混凝土板挠度时则会带来很大误差。在引入弹性板的大挠度微分控制方程后,考虑外加荷载与高温的共同作用,并计及高温下材料特性的变化,对火灾作用下钢筋混凝土双向简支板的挠度随温度的变化进行了分析。引入无量纲量,对大挠度微分控制方程进行无量纲化处理,并以无量纲板均布荷载为摄动参数,结合Galerkin方法提出了钢筋混凝土双向简支板火灾作用下挠度的计算式,计算结果与试验结果吻合较好,可为火灾作用下板的大挠度分析提供依据。研究结果表明：火灾作用下混凝土板的挠度与外加荷载和热弯矩均有关,与热弯矩成线性关系,,而与外荷载则成非线性关系;当没有热弯矩时,挠度主要由外加荷载确定;当外加荷载恒定时,挠度则主要由热弯矩引起。

The small deflection theory of thin slabs is suitable to determine the deflection of reinforced concrete two- way slabs at ambient temperatures, but not for determining the deflection at elevated temperatures. Introducing some dimensionless coefficients, the formulations based on the governing equations for large deflections of elastic plates are transformed to be dimensionless, and the dimensionless loading is applied as the perturbation coefficient. Based on the Galerkin method, the formula to determine the deflection of the two-way simply supported reinforced concrete slab is presented. The analytical results are in good agreement with the experimental results, and the formula can provide the basis for the large deflection analysis of reinforced concrete slabs in fire. The analytical results indicate that the deflection is related to the applied loading and the thermal moment, and the deflection of the slab is linearly related to the thermal moment but non-linearly to the applied loading. When the thermal moment is vanished, the deflection is caused mainly by the applied loading. If the applied loading varies slightly, the deflection is caused by the thermal moment.