考虑剪切变形影响的开口薄壁梁约束扭转的扭转角分析

发布时间：2018-02-13 15:19

本文关键词： 约束扭转剪切变形简化方法开口截面圣维南扭矩　出处：《应用力学学报》2016年04期 　论文类型：期刊论文

【摘要】：以开口薄壁梁约束扭转分析理论为基础,通过初参数法推导开口薄壁梁在外扭矩作用下产生的扭转角;推导了槽钢扭转剪应力不均匀系数的精确计算公式;为得到与Timoshenko梁理论类似的简化公式,探讨圣维南扭矩可以忽略时的情形,阐述了简化方法与理论解之间的误差来源,定义了剪切变形影响参数。通过具体算例分析跨度、高宽比等参数对扭转角的影响,并与符拉索夫理论、ANSYS壳单元、简化方法的计算结果进行对比。计算结果表明:当弯扭系数、高宽比恒定时,本文方法的解与符拉索夫解的最大误差从跨径为30m的16.15%到跨径为5m的89.5%;当弯扭系数、跨径恒定时,本文方法的解与符拉索夫解的最大误差从高宽比为1的6.9%到高宽比为5的62.44%;随跨径减小或高宽比增大,剪切变形不容忽略。当弯扭系数与跨径的乘积减小到一定值时可以忽略圣维南扭矩从而得到简化公式;高宽比增大,扭转剪应力不均匀系数先减小后增大。
[Abstract]:Based on the theory of constrained torsion analysis of thin-walled open beam, the torsion angle of thin-walled open beam under external torque is deduced by the initial parameter method, and the accurate calculation formula of non-uniform coefficient of torsional shear stress of channel steel is derived. In order to obtain a simplified formula similar to that of Timoshenko beam theory, and to discuss the case in which San Venan torque can be neglected, the error source between the simplified method and the theoretical solution is expounded, and the influence parameters of shear deformation are defined. The span is analyzed by an example. The effect of the aspect ratio on the torsion angle is compared with that of the simplified method, which is based on the Flasov theory and ANSYS shell element. The results show that when the coefficient of bending and torsion and the ratio of height to width are constant, The maximum error between the solution of this method and that of Frasov solution is from 16.15% with span of 30 m to 89.5 with span of 5 m, when the coefficient of bending and torsion is constant and the span is constant, The maximum error between the solution of this method and that of Frasov solution is from 6.9% with aspect ratio 1 to 62.44 with aspect ratio 5, with the span decreasing or the aspect ratio increasing. When the product of bending and torsional coefficient and span is reduced to a certain value, the simplified formula can be obtained by ignoring Saint Venant torque, and when the aspect ratio increases, the non-uniform coefficient of torsional shear stress decreases first and then increases.
【作者单位】：中南大学土木工程学院;长沙理工大学土木与建筑学院;广东省公路工程质量监测中心;
【基金】：国家重点基础研究发展计划(973计划)项目(2015CB057701) 国家自然科学基金(51278072)
【分类号】：O342

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