两点加载翼缘纵向变厚度工型截面简支梁变形的解析解法

Theoretical deformation solution of I-section beam with longitudinally variable thickness flange under two point loading

为充分发挥钢板强度和利用纵向变厚度钢板的厚度变化特性,根据简支梁两点加载情况下的内力分布,使用翼缘纵向变厚度工型截面梁。由于梁截面沿梁纵向变化,其刚度与等厚度工型截面梁有较大差异,需要对其进行深入研究。本文采用单位荷载法,运用积分方法推导得到考虑剪切变形影响的变形计算公式;并且结合具体算例,建立有限元计算模型进行对比分析,得出理论解与有限元解相对误差不超过3%,验证了理论解的正确性。分析结果表明:两点加载时采用翼缘厚度变化率为8mm/m的工型截面梁,在承载力相同且满足变形条件时,可节约11%的钢材,大大减少用钢量,并且降低剪切变形影响。此种形式的梁为结构优化设计提供了一种可行性方案。

Longitudinally profiled steel plate is a new kind of steel-saving plate which is under advanced rolling technology. According to the stress distribution of simply supported beam under two point loading, longitudinally profiled steel plate is proposed for the flanges of I-section beam to give full play of steel strength. In consideration of the rigidity difference between this special beam and the normal beam, further study is imperative. In this paper, the unit load method is taken and theoretical deformation solution considering the influence of shear deformation is deduced with integral methods. The derivation process is complex, but the results are convenient and easy to be used. The finite element models are established, and specific examples are analyzed to verify the theoretical results. The results show that adopting this kind of beam is capable of reducing the amount of steel to reach the same capacity with the normal beam and decreasing the influence of shear deformation. Furthermore, I-section beam with longitudinally variable thickness flanges is better for saving cost. Longitudinally profiled(LP) plate has provided a feasible proposal for structural optimization.