考虑剪切变形影响的开口薄壁梁约束扭转的扭转角分析

Torsion angle analysis of restrained torsion theory for open thin walled beams considering shear deformation

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。

Based on the theory of restrained torsion for an open thin-walled beams, the twist angle of pen thin-walled beam under the action of external torque is derived out through the initial parameter method. The precise calculation formula of channel steel shear stress non-uniform coefficient is obtained. For the purpose to obtain the simplified formula similar to the Timoshenko beam theory, the case of Saint-Venant torque can be ignored is explored. The theoretical solution and the simplified method of error sources are given, this paper gives, and the shear deformation influence parameters are defined. Span through concrete example analysis, the influence of aspect ratio and other parameters on the torsion angle, and Vlasov theory, ANSYS shell element and simplified method of the calculation results are compared, validating the presented method and formulas. Calculation results show that when bending twist coefficient and aspect ratio at constant, the maximum error of suggested method and Vlasov solution from 16.15% to 30 m span to 89.5% span length is 5m. When bending twist coefficient and span at constant, the maximum error of suggested method and Vlasov solution from 6.9% to 1 aspect ratio to 62.44% aspect ratio is 5. Span decreases or aspect ratio increases, shear deformation should not be ignored. When bending twist coefficient and span to a certain value of the product can be ignored, the simplified formula of Saint-Venant torque is obtained. As the aspect ratio increases, the shear stress non-uniform coefficient of channel section decreases first, and then increases.