H形钢梁考虑有限翘曲约束刚度的扭转效应分析

陈东亮, 张元海

陈东亮, 张元海. H形钢梁考虑有限翘曲约束刚度的扭转效应分析. 力学与实践, 2023, 45(2): 389-394. DOI: 10.6052/1000-0879-22-258
引用本文: 陈东亮, 张元海. H形钢梁考虑有限翘曲约束刚度的扭转效应分析. 力学与实践, 2023, 45(2): 389-394. DOI: 10.6052/1000-0879-22-258
Chen Dongliang, Zhang Yuanhai. Analysis on torsional effect of H-shaped steel beams considering finite warping restraint stiffness. Mechanics in Engineering, 2023, 45(2): 389-394. DOI: 10.6052/1000-0879-22-258
Citation: Chen Dongliang, Zhang Yuanhai. Analysis on torsional effect of H-shaped steel beams considering finite warping restraint stiffness. Mechanics in Engineering, 2023, 45(2): 389-394. DOI: 10.6052/1000-0879-22-258
陈东亮, 张元海. H形钢梁考虑有限翘曲约束刚度的扭转效应分析. 力学与实践, 2023, 45(2): 389-394. CSTR: 32047.14.1000-0879-22-258
引用本文: 陈东亮, 张元海. H形钢梁考虑有限翘曲约束刚度的扭转效应分析. 力学与实践, 2023, 45(2): 389-394. CSTR: 32047.14.1000-0879-22-258
Chen Dongliang, Zhang Yuanhai. Analysis on torsional effect of H-shaped steel beams considering finite warping restraint stiffness. Mechanics in Engineering, 2023, 45(2): 389-394. CSTR: 32047.14.1000-0879-22-258
Citation: Chen Dongliang, Zhang Yuanhai. Analysis on torsional effect of H-shaped steel beams considering finite warping restraint stiffness. Mechanics in Engineering, 2023, 45(2): 389-394. CSTR: 32047.14.1000-0879-22-258

H形钢梁考虑有限翘曲约束刚度的扭转效应分析

基金项目: 国家自然科学基金资助项目(51968040,51468032)。
详细信息
    作者简介:

    张元海,教授,主要从事薄壁箱梁设计理论研究。E-mail:zyh17012@163.com

  • 中图分类号: TU391,TU313.1

ANALYSIS ON TORSIONAL EFFECT OF H-SHAPED STEEL BEAMS CONSIDERING FINITE WARPING RESTRAINT STIFFNESS

  • 摘要:

    为考虑半刚性连接对H形钢梁翘曲变形的有限约束,引入翘曲约束刚度的概念,提出介于简单支承和固定支承之间的半刚性连接H形钢梁约束扭转计算方法。结合数值算例,验证本文方法的正确性,详细分析翘曲约束刚度变化对翘曲正应力和二次剪应力的影响。研究结果表明:翘曲约束刚度引起的双力矩沿跨度呈线性变化,翘曲正应力随翘曲约束刚度的增大而减小,二次剪应力随翘曲约束刚度的增大而增大。

    Abstract:

    In order to consider the finite constraint of semi-rigid connections on the warping deformation of H-shaped steel beams, the concept of warping constraint stiffness is introduced, and a restrained torsion calculation method for semi-rigid connected H-shaped steel beams between simple support and fixed support is proposed. Combined with numerical examples, the correctness of this method is verified, and the effects of the change of warping constraint stiffness on warping normal stress and secondary shear stress are analyzed in detail. The results show that the bi-moment caused by the warping restraint stiffness changes linearly along the span. The warping normal stress decreases with the increase of warping constraint stiffness, and the secondary shear stress increases with the increase of warping constraint stiffness.

  • 符拉索夫根据开口薄壁构件的变形特点,针对约束扭转作出刚周边假定和中面无剪应变假定,并采用扇性坐标建立了开口薄壁构件的约束扭转微分方程[1]。樊春雷等[2]指出传统计算方法过于繁琐,致使许多设计师仅在构造上做一些处理,因此他基于变形协调原理提出了一种H型钢梁约束扭转简化计算方法。如今,钢制曲线梁桥在高速公路和铁路中大量使用,在任何情况下,曲线梁都会受到与弯曲相关的扭矩作用,研究人员基于哈密顿原理提出了H形钢梁约束扭转效应的评估方法[3]。通常在解决约束扭转问题时只考虑自由翘曲和完全约束翘曲两种情况,而实际中往往是部分约束翘曲变形的半刚性连接。近几年,对于半刚性连接的受力性能,学者们开展了大量研究工作[4-7]。在大多数情况下,假定刚性连接是不合理的,可能会导致不安全的设计,而假定简单连接又过于保守。AISC设计规范[8]包括半刚性连接类别,该类别比刚性连接和简单连接更具现实意义。Areiza-Hurtado等[9]对弹性地基上具有初始横向挠度和半刚性端部连接的棱柱形梁柱进行了二阶分析。Montoya-Vargas等[10]推导了半刚性连接工字梁的约束扭转计算公式,并与Hunt[11]的理论和试验进行对比。尽管已有科研人员在弯曲分析中考虑了半刚性连接的影响,但鲜有人将半刚性连接纳入结构扭转分析。

    为了考虑半刚性连接对H形钢梁翘曲变形的有限约束,提出翘曲约束刚度的概念,推导半刚性连接H形钢梁约束扭转的广义位移和广义内力计算公式,并分析翘曲正应力和二次剪应力随翘曲约束刚度的变化规律。

    以梁腹板与柱翼缘双角钢加角钢支托的螺栓连接为例,说明半刚性连接H形钢梁计算模型的简化过程。图1(a)~图1(c)均为通过双角钢和螺栓连接到柱翼缘的梁,连接处梁不能发生整体扭转。图1(a)允许梁端翼缘自由翘曲,图1(b)约束梁端下翼缘的部分翘曲变形,图1(c)同时约束梁端上下翼缘的部分翘曲变形。由相容性条件可知,图1(b)和图1(c)梁中受约束的翼缘在面内弯曲的同时必须伴随柱中翼缘的扭转和腹板的变形,但受约束翼缘翘曲变形的发展程度小于图1(a)中自由翘曲的情况。倘若柱的刚度比梁的刚度大得多,则在约束处梁翼缘几乎不会发生翘曲变形。

    图  1  梁腹板与柱翼缘双角钢螺栓连接
    Figure  1.  Double angle steel bolt connection between girder web and column flange

    根据上述变形特点,为考虑半刚性连接有限约束H形钢梁翼缘翘曲变形的情况,用线弹性弹簧简化实际中的半刚性连接。基于图1(c),以左支撑P为原点,取图2所示梁支撑附近无限小的单元。在约束处不允许梁发生整体扭转,但允许翼缘局部变形。若两块翼缘板端部的弹簧刚度为零,则可以考虑图1(a)的情况;若上翼缘板端部的弹簧刚度为零,则可以考虑图1(b)的情况。

    图  2  支承附近梁单元示意图
    Figure  2.  Schematic diagram of girder unit near the support

    在扭矩载荷作用下,梁翼缘发生翘曲位移$u$,从而在梁端连接弹簧的点处产生与翘曲位移相反的反作用力$F$,假设线弹性弹簧的刚度为$k$,则

    $$ F\left( {x,y} \right) = - ku\left( {x,y,z} \right) $$ (1)

    根据符拉索夫的刚周边假定和中面无剪应变假定,开口薄壁梁的翘曲位移为

    $$ u\left( {x,y,z} \right) = - \varphi '\left( z \right)\omega \left( {x,y} \right) $$ (2)

    式中$\omega \left( {x,y} \right)$为主扇形坐标;$\varphi '\left( z \right) = {{{\text{d}}\varphi } \mathord{\left/ {\vphantom {{{\text{d}}\varphi } {{\text{d}}z}}} \right. } {{\text{d}}z}}$为扭率,$\varphi $表示扭转角。

    $\varphi '\left( 0 \right) = {\varphi '_{{p}}}$,则P截面弹簧的反作用力${F_{{P}}}$

    $$ {F_{{P}}}\left( {x,y} \right) = k{\varphi '_{{P}}}\omega \left( {x,y} \right) $$ (3)

    P截面弹簧反作用力产生的双力矩${B_{{P}}}$

    $$ {B_{{P}}} = \sum\limits_{i = 1}^n {{F_i}{\omega _i}} = \sum\limits_{i = 1}^n {{k_i}\omega _i^2{\varphi'_P}} \left( {i = 1,2,\cdots,n} \right) $$ (4)

    式中,${k_i}$表示第$i$个弹簧的刚度,${\omega _i}$表示第$i$个弹簧所在位置的主扇性坐标。

    定义翘曲约束刚度$S$等于每单位扭转角的双力矩,即

    $$ S = \sum\limits_{i = 1}^n {{k_i}\omega _i^2} \left( {i = 1,2,\cdots,n} \right) $$ (5)

    式中$S$的量纲为$ {{\text{L}}^4}{\text{M}}{{\text{T}}^{ - 2}} $(角度没有量纲)。

    式(5)能够通过考虑连接件的位置和刚度,确定螺栓或点焊等离散连接件的翘曲约束刚度。值得注意的是,由于$S$$\omega $的函数,所以可通过改变连接元件的位置提高翘曲约束刚度。

    由于壁厚$t$较小,可以认为翘曲正应力和二次剪应力沿壁厚均匀分布。由式(2)得,约束扭转翘曲正应力${\sigma _\omega }$和相应的双力矩B分别为

    $$ {\sigma _\omega } = - E\varphi ''\omega $$ (6)
    $$ B = \int_s {{\sigma _\omega }\omega t{\text{d}}s} = - E{I_\omega }\varphi '' $$ (7)

    式中$E$为弹性模量。所以翘曲正应力又可以写成

    $$ {\sigma _\omega } = \frac{B}{{{I_\omega }}}\omega $$ (8)

    式中${I_\omega }$为主扇性惯性矩,${I_\omega } = \displaystyle\int_s {{\omega ^2}t{\text{d}}s} $

    将曲线坐标起始点$s = 0$置于上翼缘形心处,在翼缘上任取一个${\text{d}}z \times {\text{d}}s$的微元体,其受力情况如图3所示。由微元体$z$方向的平衡可得

    图  3  H形钢梁微元体受力简图
    Figure  3.  Simplified diagram of micro-body force of H-shaped steel beam
    $$ \frac{{\partial {q_\omega }}}{{\partial s}} + \frac{{\partial {\sigma _\omega }}}{{\partial z}}t = 0 $$ (9)

    将式(6)代入式(9)并积分,可以得到约束扭转剪力流${q_\omega }$和相应的二次扭矩${M_\omega }$分别为

    $$ {q_\omega } = E\varphi '''{S_\omega } $$ (10)
    $$ {M_\omega } = \int_S {{q_\omega }} \rho {\text{d}}s = - E{I_\omega }\varphi ''' $$ (11)

    式中${S_\omega }$为主扇性静面矩,${S_\omega } = \displaystyle\int_0^s {\omega t{\text{d}}s} $$\rho $为扭转中心至壁厚中心线任一点处切线的垂直距离。

    联立式(10)和式(11)可得二次剪应力${\tau _\omega }$

    $$ {\tau _\omega } = \frac{{{q_\omega }}}{t} = - \frac{{{M_\omega }}}{{{I_\omega }t}}{S_\omega } $$ (12)

    根据开口薄壁梁约束扭转经典理论[6],关于扭转角$\varphi $的约束扭转微分方程为

    $$ \frac{{{{\text{d}}^4}\varphi }}{{{\text{d}}{z^4}}} - {p^2}\frac{{{{\text{d}}^2}\varphi }}{{{\text{d}}{z^2}}} = - \frac{1}{{E{I_\omega }}}\frac{{{\text{d}}{M_z}}}{{{\text{d}}z}} $$ (13)

    式中${M_z}$为扭矩,以力矢指向截面外侧为正;$p = \sqrt {GJ{\text{/}}(E{I_\omega })} $$G$为剪切模量,$J$为抗扭惯性矩。

    ${{{\text{d}}{M_z}} \mathord{\left/ {\vphantom {{{\text{d}}{M_z}} {{\text{d}}z}}} \right. } {{\text{d}}z}} = 0$,即不考虑外载荷作用,可得

    $$ \frac{{{{\text{d}}^4}\varphi }}{{{\text{d}}{z^4}}} - {p^2}\frac{{{{\text{d}}^2}\varphi }}{{{\text{d}}{z^2}}} = 0 $$ (14)

    引入四个初参数,分别为坐标原点处($z = 0$)的扭转角${\varphi _0}$、扭率${\varphi '_0}$、双力矩${B_0}$和总扭矩${T_0}$。则用四个初参数表达的任意横截面的扭转角$\varphi (z)$,扭率$\varphi '(z)$,双力矩$B(z)$及总扭矩$M(z)$分别为

    $$ \begin{split} & \varphi (z) = {\varphi _0} + \frac{{{{\varphi '}_0}}}{p}\sinh \left( {pz} \right) + \frac{{{B_0}}}{{GJ}}\left[ {1 - \cosh \left( {pz} \right)} \right] + \\ &\qquad \frac{{{T_0}}}{{pGJ}}\left[ {pz - \sinh \left( {pz} \right)} \right] \\ \end{split} $$ (15)
    $$ \varphi '(z) = {\varphi '_0}\cosh \left( {pz} \right) - \frac{{p{B_0}}}{{GJ}}\sinh \left( {pz} \right) + \frac{{{T_0}}}{{GJ}}\left[ {1 - \cosh \left( {pz} \right)} \right] $$ (16)
    $$ B(z) = - \frac{{{\varphi _0}^\prime GJ}}{p}\sinh \left( {pz} \right) + {B_0}\cosh \left( {pz} \right) + \frac{{{T_0}}}{p}\sinh \left( {pz} \right) $$ (17)
    $$ M(z) = {T_0} $$ (18)

    图4所示,长度为$l$的半刚性连接H形钢梁承受满跨均布扭矩载荷$m$$m$作用于剪切中心。分别用${S_{{P}}}$${S_{{Q}}}$表示P端和Q端的翘曲约束刚度。

    图  4  半刚性连接H形钢梁受均布扭矩载荷作用
    Figure  4.  H-shaped steel beam with semi-rigid connections subjected to uniform torque load

    根据边界条件,显然有${\varphi _0} = 0$$\varphi (l) = 0$。由于P端弹簧在负面上,Q端弹簧在正面上,所以由式(4)和式(5)得

    $$ {B_0} = - {B_{{P}}} = - {S_{{P}}}{\varphi '_{\text{0}}} $$ (19)
    $$ B\left( l \right) = {B_{{Q}}} = {S_{{Q}}}\varphi '\left( l \right) $$ (20)

    其中正面指的是外法线指向$z$轴正方向的截面。

    根据上述边界条件可以得到

    $$ {T_0} = \frac{1}{2}ml + \frac{{{S_{{P}}}{{\varphi '}_0} + {S_{{Q}}}\varphi '\left( l \right)}}{l} $$ (21)

    ${T_0} \ne {1 /(2ml)}$是因为${B_{{P}}}$${B_{{Q}}}$会引起跨内变化的双力矩。不难看出,${B_{{P}}}$${B_{{Q}}}$引起的二次扭矩${M_{l\omega }}$

    $$ {M_{l\omega }} = \frac{{{\text{d}}{B_l}\left( z \right)}}{{{\text{d}}z}} = - \frac{{{B_{{P}}} - {B_{{Q}}}}}{l} $$ (22)

    所以${B_l}(z)$沿跨度呈线性变化

    $$ {B_l}(z) = {B_{{P}}}\left( {1 - \frac{z}{l}} \right) + {B_{{Q}}}\frac{z}{l} $$ (23)

    由上述边界条件可得,初参数满足的方程组为

    $$ \left[ {\begin{array}{*{20}{c}} {{C_{11}}}&{{C_{12}}}&{{C_{13}}}&{{C_{14}}} \\ {{C_{21}}}&{{C_{22}}}&{{C_{23}}}&{{C_{24}}} \\ {{C_{31}}}&{{C_{32}}}&{{C_{33}}}&{{C_{34}}} \\ {{C_{41}}}&{{C_{42}}}&{{C_{43}}}&{{C_{44}}} \end{array}} \right]\left\{ {\begin{array}{*{20}{c}} {{\varphi _0}} \\ {{{\varphi '}_0}} \\ {{B_0}} \\ {{T_0}} \end{array}} \right\} = \left\{ {\begin{array}{*{20}{c}} {{D_1}} \\ {{D_2}} \\ {{D_3}} \\ {{D_4}} \end{array}} \right\} $$ (24)

    其中 ${C_{11}} = {C_{23}} = 1$

    $$\begin{split} & {C_{12}} = {C_{13}} = {C_{14}} = {C_{21}} = {C_{24}} = {C_{31}} = {C_{41}} = 0\\ & {C_{22}} = {S_{{P}}}\text{;}{C_{32}} = pGJ\sinh \left( {pl} \right)\\ & {C_{33}} = {p^2}\left[ {1 - \cosh \left( {pl} \right)} \right]\text{;} {C_{34}} = p\left[ {pl - \sinh \left( {pl} \right)} \right] \\ & {C_{42}} = - pGJ\left[ {GJ\sinh \left( {pl} \right) + p{S_{{Q}}}\cosh \left( {pl} \right)} \right]\\ & {C_{43}} = {p^2}\left[ {GJ\cosh \left( {pl} \right) + p{S_{{Q}}}\sinh \left( {pl} \right)} \right]\\ & {C_{44}} = p\left[ {GJ\sinh \left( {pl} \right) - p{S_{{Q}}} + p{S_{{Q}}}\cosh \left( {pl} \right)} \right]\\ & {D_1} = {D_2} = 0\text{;}{D_3} = m\left[ {{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}{p^2}{l^2} + 1 - \cosh \left( {pl} \right)} \right] \\ & {D_4} = - m\left[ {GJ + {p^2}l{S_{{Q}}} - GJ\cosh \left( {pl} \right) - p{S_{{Q}}}\sinh \left( {pl} \right)} \right] \end{split}$$

    当结构对称载荷对称时,显然可得${S_{{P}}} = {S_{{Q}}} = S$$\varphi '\left( l \right) = - {\varphi '_0}$,进而四个初参数的解可以简化为

    $$ \left. {\begin{gathered} {{\varphi _0} = 0} \\ {{{\varphi '}_0} = \frac{{m\left[ {2\cosh \left( {pl} \right) - pl\sinh \left( {pl} \right) - 2} \right]}}{{2{p^2}S\left[ {1 - \cosh \left( {pl} \right)} \right] - 2pGJ\sinh \left( {pl} \right)}}} \\ {{B_0} = \frac{{mS\left[ {2 + pl\sinh \left( {pl} \right) - 2\cosh \left( {pl} \right)} \right]}}{{2{p^2}S\left[ {1 - \cosh \left( {pl} \right)} \right] - 2pGJ\sinh \left( {pl} \right)}}} \\ {{T_0} = \frac{1}{2}ml} \end{gathered}} \right\} $$ (25)

    显然,$S$等于0时,${B_0} = 0$,等于简支端的初参数;$S$趋于∞时,$ {\varphi '_0} = 0 $,等于固定端的初参数。说明半刚性连接介于简单支承和固定支承之间。

    由于${B_{{P}}}$${B_{{Q}}}$仅表示弹簧反作用力产生的双力矩,沿跨内并未施加双力矩,所以任一横截面的广义位移和广义内力为

    $$ \begin{gathered} \varphi (z) = {\varphi _0} + \frac{{{{\varphi '}_0}}}{p}\sinh \left( {pz} \right) + \frac{{{B_0}}}{{GJ}}\left[ {1 - \cosh \left( {pz} \right)} \right] + \\ \frac{{{T_0}}}{{pGJ}}\left[ {pz - \sinh \left( {pz} \right)} \right] - \frac{m}{{{p^2}GJ}}\left[ {\frac{1}{2}{p^2}{z^2} + 1 - \cosh \left( {pz} \right)} \right] \\ \end{gathered} $$ (26)
    $$ \begin{split} &\varphi '(z) = {{\varphi '}_0}\cosh \left( {pz} \right) - \frac{{p{B_0}}}{{GJ}}\sinh \left( {pz} \right) + \\ & \frac{{{T_0}}}{{GJ}}\left[ {1 - \cosh \left( {pz} \right)} \right] - \frac{m}{{pGJ}}\left[ {pz - \sinh \left( {pz} \right)} \right] \\ \end{split} $$ (27)
    $$ \begin{split} & B(z) = - \frac{{{\varphi _0}^\prime GJ}}{p}\sinh \left( {pz} \right) + {B_0}\cosh \left( {pz} \right) + \\ & \frac{{{T_0}}}{p}\sinh \left( {pz} \right) + \frac{m}{{{p^2}}}\left[ {1 - \cosh \left( {pz} \right)} \right] \\ \end{split} $$ (28)
    $$ M(z) = {T_0} - mz $$ (29)

    H形钢梁的约束情况及受载荷情况与图4相同,取$l = 16\;{\text{m}}$$m = 4\;{\text{kN}} \cdot {\text{m/m}}$图5为H形钢梁的横截面尺寸与扭转特性,以及梁端用来约束翘曲位移的线弹性弹簧在横截面中的投影位置。假设弹簧刚度$k = 4000\;{\text{kN/m}}$,则$S = 100\;{\text{kN}} \cdot {{\text{m}}^{\text{3}}}{\text{/rad}}$

    图  5  H形钢梁横截面尺寸与扭转特性(单位: m)
    Figure  5.  Cross-section size and torsional characteristics of H-shaped steel beam (unit: m)

    按照本文所述理论求得距P$1\;{\text{m}}$处正面上的翘曲正应力和二次剪应力的分布曲线如图6所示。

    图  6  翘曲正应力与二次剪应力分布图
    Figure  6.  Distribution of warping normal stress and secondary shear stress

    为了验证本文的正确性,再使用有限元软件ANSYS中的SHELL181壳单元计算该H形钢梁距左支撑$1\;{\text{m}}$处正截面上各板元的翘曲正应力和二次剪应力,并与图6中相应计算点的应力作比较,计算结果见表1。因为H形钢梁自由扭转时不会形成剪力流,中面自由扭转的剪应力为0,所以可直接提取中面剪应力作为本文二次剪应力的ANSYS解,由表1可知,本文解与ANSYS解吻合良好。

    表  1  数值分析结果比较
    Table  1.  Comparisons of numerical analysis results
    StressCalculationpointsSolution of this paper/MPaSolution of ANSYS/MPaRelative error/%
    ${\sigma _\omega }$13.80323.9981–4.9
    27.60648.0390–5.4
    ${\tau _\omega }$11.44221.4440–0.1
    20.90140.87822.6
    Note: relative error =(solution of this paper−solution of ANSYS) / solution of ANSYS × 100%。
    下载: 导出CSV 
    | 显示表格

    为研究翘曲约束刚度对不同截面翘曲正应力和二次剪应力的影响,令翘曲约束刚度从$0$起始以$ 3000\;{\text{kN}} \cdot {{\text{m}}^{\text{3}}}{\text{/rad}} $为步长逐渐增大至 60000$ \;{\text{kN}} \cdot {{\text{m}}^{\text{3}}}{\text{/rad}} $,计算$z = 1\;{\text{m}}$$z = 3\;{\text{m}}$$z = 5\;{\text{m}}$$z = 7\;{\text{m}}$四个横截面上计算点1处的翘曲应力,变化曲线如图7图8所示。

    图  7  翘曲正应力随翘曲约束刚度变化曲线
    Figure  7.  Variation curve of warping normal stress with warping constraint stiffness
    图  8  二次剪应力随翘曲约束刚度变化曲线
    Figure  8.  Variation curve of secondary shear stress with warping constraint stiffness

    图7图8中,当翘曲约束刚度$S$等于0时,梁端约束相当于简单支承,翘曲应力与相应简支梁相同;当翘曲约束刚度$S$趋于∞时,梁端约束相当于固定支承,翘曲应力如图中点划线所示。当计入应力的正负号时,翘曲正应力随翘曲约束刚度的增大而减小,二次剪应力随翘曲约束刚度的增大而增大,且翘曲正应力较二次剪应力受翘曲约束刚度的影响更显著。当$S \geqslant 20000\;{\text{kN}} \cdot {{\text{m}}^{\text{3}}}{\text{/rad}}$后,随着翘曲约束刚度增大,翘曲应力变化不再明显。

    比较$z = 1\;{\text{m}}$$z = 7\;{\text{m}}$的应力变化曲线不难得出,越靠近支点截面,翘曲约束刚度对翘曲正应力和二次剪应力的影响越显著;越靠近跨中截面,翘曲约束刚度对翘曲正应力和二次剪应力的影响越小。在全跨范围内不能忽略翘曲约束刚度对翘曲正应力的影响;而在大约距跨中$l{\text{/}}4$的范围内可以忽略翘曲约束刚度对二次剪应力的影响。

    (1)本文引入翘曲约束刚度考虑半刚性连接对翘曲变形的有限约束,在自由翘曲的简单支承和完全约束翘曲的固定支承之间建立了平滑的过渡,为半刚性连接H形钢梁约束扭转提供了计算方法。

    (2)弹簧反作用力产生的双力矩沿跨度呈线性变化。在实际工程中,可以适当改变螺栓或点焊等连接件的位置提高翘曲约束刚度,改善构件的受力性能。

    (3)翘曲正应力随翘曲约束刚度的增大而减小,二次剪应力随翘曲约束刚度的增大而增大。在H形钢梁全跨范围内不能忽略翘曲约束刚度对翘曲正应力的影响;而在距跨中大约$l{\text{/4}}$的范围内可以忽略翘曲约束刚度对二次剪应力的影响。

  • 图  1   梁腹板与柱翼缘双角钢螺栓连接

    Figure  1.   Double angle steel bolt connection between girder web and column flange

    图  2   支承附近梁单元示意图

    Figure  2.   Schematic diagram of girder unit near the support

    图  3   H形钢梁微元体受力简图

    Figure  3.   Simplified diagram of micro-body force of H-shaped steel beam

    图  4   半刚性连接H形钢梁受均布扭矩载荷作用

    Figure  4.   H-shaped steel beam with semi-rigid connections subjected to uniform torque load

    图  5   H形钢梁横截面尺寸与扭转特性(单位: m)

    Figure  5.   Cross-section size and torsional characteristics of H-shaped steel beam (unit: m)

    图  6   翘曲正应力与二次剪应力分布图

    Figure  6.   Distribution of warping normal stress and secondary shear stress

    图  7   翘曲正应力随翘曲约束刚度变化曲线

    Figure  7.   Variation curve of warping normal stress with warping constraint stiffness

    图  8   二次剪应力随翘曲约束刚度变化曲线

    Figure  8.   Variation curve of secondary shear stress with warping constraint stiffness

    表  1   数值分析结果比较

    Table  1   Comparisons of numerical analysis results

    StressCalculationpointsSolution of this paper/MPaSolution of ANSYS/MPaRelative error/%
    ${\sigma _\omega }$13.80323.9981–4.9
    27.60648.0390–5.4
    ${\tau _\omega }$11.44221.4440–0.1
    20.90140.87822.6
    Note: relative error =(solution of this paper−solution of ANSYS) / solution of ANSYS × 100%。
    下载: 导出CSV
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  • 收稿日期:  2022-04-26
  • 修回日期:  2022-05-27
  • 录用日期:  2022-06-30
  • 网络出版日期:  2023-01-03
  • 刊出日期:  2023-05-09

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