基于挠度分析的等截面连续梁合理边中跨跨径比

Reasonable Length Ratio Between Side Span and Middle Span of Continuous Beams with Uniform Section Based on Deflection Analysis

等截面连续梁如边跨和中跨不等跨布置,边中跨跨径比对结构受力影响显著。本文基于奇异函数法推导在不同跨数和不同边中跨跨径比情况下,作用有均布荷载和集中荷载的等截面连续梁挠曲线方程,以各跨内向上挠度极值和向下挠度极值整体最小为目标,找出结构最优边中跨跨径比。综合均布荷载作用情况和集中荷载作用情况分析结果表明:当边中跨跨径比在接近0.82时,连续梁挠度总体最小,且结构挠度基本不随跨数的改变而有较大变化。

As the layout of the side span of continuous beams with uniform section is different from that of the middle span,the length ratio between side span and middle span has a significant influence on the structural mechanical responses.In the paper,in the case of different spans and different length ratios of side span and middle span,the deflection equation of the continuous beam with uniform section affected by uniform load and concentrated load is deduced by singularity function method.The optimal ratio of side span and middle span is determined through minimizing both upward deflection extremum and downward deflection extremum of all spans.Synthesizing the analysis result of beams affected by both uniform load and concentrated load,it shows that when the length ratio of side span and middle span is nearly 0.82,the deflection value of continuous beam is minimum,and the deflection of structure doesn’t change significantly with the number of spans.