摘要
为方便利用不同位移函数进行箱梁剪力滞效应分析,针对荷载对称作用于腹板位置的剪力滞问题,以抽象函数作为位移函数形式,采用基于最小势能原理的变分法,推导了箱梁剪力滞的控制微分方程及其解析解;同时,利用编制的箱梁剪力滞分析程序,大致分析了不同位移函数对箱梁剪力滞效应的影响。结果表明:采用抽象位移函数推导得到的剪力滞控制微分方程与采用具体位移函数得到的控制微分方程,形式上是一致的,但前者得到的Reissner参数不仅跟截面特性参数有关,还与位移函数形式相关,而后者由于采用的是特定的位移函数形式,因而只与截面特性有关;将二次、三次及四次抛物线函数作为具体的位移函数代入到有关公式中得到的剪力滞控制微分方程及Reissner参数,与直接采用相应位移函数进行变分法分析得到的结果完全一致;简支梁受集中荷载作用及悬臂梁受均布荷载作用下,采用不同的位移函数计算得到的正应力或剪力滞系数分布结果与实测值吻合较好,采用不同的位移函数形式分析得到的最大剪力滞系数比较接近,但是在顶板悬臂部分和顶板中心附近,剪力滞系数差异较大,即剪力滞分析精度受所选取的位移函数的影响。
In order to analyze the shear lag effect of the box girder by different displacement functions conveniently,taking the shear lag effect of a box girder web which is subjected to symmetric loads as an example,regarding the abstract function as the displacement function,the shear lag governing differential equations and its analytical solutions were deduced by the variational method based on the principle of minimum potential energy. Meanwhile,the influences of different displacement functions on the shear lag effect of box girders were generally analyzed by using a self-compiled program.The results show that the form of the governing differential equation of the shear lag deduced by the abstract displacement function is similar with that deduced by the specific displacement function.However,the Reissner parameters obtainedfrom the former are related to not only the characteristic parameters of the cross section,but also the form of the displacement function.Since the latter adopts the form of a particular displacement function,and the Reissner parameters are only related to the cross section characteristics.And second,third and fourth-order parabolic functions are substituted into relative equations as specific displacement functions to obtain the governing differential equation and the Reissner parameters,which are in good agreement with the results deduced directly by the variational method using corresponding displacement functions.By adopting different displacement functions,the calculated normal stress or shear lag coefficient distribution of the simply-supported beam which is subjected to concentrated load and that of the cantilever beam under uniformly distributed load are in good agreement with measured values.It shows that the maximum shear lag coefficients obtained by using different displacement functions are relatively close.But there are some differences of the shear lag coefficients at the cantilever part of the top plate and around the center of it,which means that the accuracy of the shear lag effe
出处
《中国公路学报》
EI
CAS
CSCD
北大核心
2016年第9期90-96,共7页
China Journal of Highway and Transport
基金
国家自然科学基金项目(51308467)
关键词
桥梁工程
剪力滞效应
能量变分法
位移函数
解析解
bridge engineering
shear lag effect
energy variational method
displacement function
analytical solution
