摘要
为了合理计算薄壁箱梁约束扭转剪应力,基于乌曼斯基第二理论,根据总扭矩平衡条件和翘曲位移连续性条件,导出了薄壁箱梁约束扭转剪应力的2种计算公式,并论证了2种公式的等价性.在公式推导过程中,对箱梁悬臂板进行了考虑.针对2种公式中广义扇性静矩计算的繁琐性,进一步导出了其实用简化计算公式,并举例说明了其具体应用.数值算例表明:有悬臂板的薄壁箱梁发生约束扭转时,全截面最大剪应力出现在腹板内,在悬臂板内也存在较大的剪应力;顶板和底板内的剪应力非均匀分布程度显著,其中部区域内剪应力很小.如果近似按自由扭转理论计算剪应力,求得的腹板剪应力只有实际最大剪应力的69%,严重低估了腹板内的实际剪应力大小,表明不能忽略翘曲约束效应对剪应力的影响.
In order to reasonably calculate the shear stress in thin-walled box girders under restrained torsion,two sets of formulas for the shear stress were derived according to the total torque equilibrium and the warping displacement continuity condition based on Umansky's second theory.The consistency of the two sets of formulas was demonstrated.The cantilever plate was considered in the formula derivation process.In view of the complication of calculating the generalized sectorial static moment in the two sets of formulas,the practical simplified calculation formula was further derived,and its specific application was illustrated through examples.Numerical examples show that when a thin-walled box girder with cantilever plates undergoes constrained torsion,the maximum shear stress in the whole cross section appears in the webs,and there is also large shear stress in the cantilever plate.The non-uniform distribution of shear stress in the top and bottom plates is significant,and the shear stress in the middle area is very small.If the shear stress is calculated approximately according to the free torsion theory,the obtained shear stress in the webs is only 69%of the actual maximum shear stress,which seriously underestimates the actual shear stress in the webs.It shows that the effect of restrained warping on the shear stress cannot be ignored.
作者
张元海
黄洪猛
梁永永
Zhang Yuanhai;Huang Hongmeng;Liang Yongyong(School of Civil Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)
出处
《东南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2021年第6期942-948,共7页
Journal of Southeast University：Natural Science Edition
基金
国家自然科学基金资助项目(51968040).
关键词
薄壁箱梁
约束扭转
扭转剪应力
二次剪应力
广义扇性静矩
thin-walled box girder
restrained torsion
torsional shear stress
secondary shear stress
generalized sectorial static moment
