地基沉降对弹性地基梁的影响

摘要

Considering the effect of shear deformation, Timoshenko beam theory and initial parameter method were used to analyze the settlement influences of elastic foundation beam with two fixed-edges and two simply-supported edges. The transcendent equation of hanging length was established. The solutions of deformations and internal forces were presented. The changing relationship between hanging length and load was studied by examples. Deflections, slopes, shear forces and moments of Bernoulli-Euler beam theory and Timoshenko beam theory were compared for locally hanged beams on Winkler foundation under distributing load. Deflections and internal forces of different settlements were compared. The results show that hanged length derived by Bernoulli-Euler beam theory is relatively large. Deflection, slope, shear force and moment calculated by Bernoulli-Euler beam theory are larger than those by Timoshenko beam theory. Shear deformation influence must be considered for the analysis of foundation settlement.%考虑剪切变形的影响，采用Timoshenko梁理论和初参数法分析两端固结、两端简支的弹性地基梁由于地基沉降造成的影响，建立确定悬空长度的超越方程，导出变形和内力的解析解。通过算例分析悬空长度随荷载的变化，比较局部悬空Winkler地基梁在均布荷载作用下挠度、转角、剪力、弯矩的Bemoulli-Euler梁理论结果和Timoshenko梁理论结果，比较地基不同沉降下的变形与内力。研究结果表明：采用Bemoulli-Euler梁理论计算的悬空长度偏大，采用Bemoulli-Euler梁理论计算的局部悬空弹性地基梁的挠度、转角、剪力、弯矩比相应的Timoshenko梁的理论结果大，地基沉降分析中应考虑剪切变形的影响。