能量法计算无梁板桥结构的理论解及数值分析

Theoretical calculation and numerical analysis of sirderless slab bridge with energy method

由经典的薄板弯曲理论为基础,利用能量原理,首次提出并推导了无梁板桥在均布荷载下的挠度函数,由此还给出了桥面板正应力的表达式,并根据这一系列的公式制成Excel表格,直接在表格中输入数据,使数据的处理更加方便.利用大型空间有限元程序ANSYS对无梁板桥进行建模,分析了其在恒载、车道荷载作用下的挠度和应力的变化规律,结果表明无梁板桥能承受较大的汽车荷载.通过有限元的数值分析,对无梁板桥的受力性能有了一定的认识.为验证所推导的公式的正确性,给出无梁板桥的算例,用推导的理论公式分析了桥面板的挠度和正应力,计算结果和有限元的计算结果吻合得较好,从而验证了该方法的正确性,对这类结构的设计及其工程应用提供参考.

Based on the classical thin plate bending theory,deflection function of girderless slab bridge under uniform load by energy principle is proposed and derived.It also gives the expression of normal stress of bridge deck.The Excel tables are made basis of these formulas,which is more convenient to process the datas.Using the finite element program ANSYS for modeling of girderless slab bridge,the deflection and stress under dead load and lane load is analyzed.The results show that girderless slab bridge can bear a larger vehicle load.Through the finite element analysis of girderless slab bridge,understanding of the mechanical behavior is acquired.To verify the correctness of these formulas,example of girderless slab bridge is given,using the theoretical formulas derived in this paper analyze the deflection and normal stress of bridge deck,and the results agree well with finite element calculations and the calculation results fit in well.It proves that the method is correct,serving as the reference of the design and engineering application of the kind of structure.