考虑剪切滑移效应的叠合梁有限元解

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刘寒冰, 时成林, 谭国金. 考虑剪切滑移效应的叠合梁有限元解.吉林大学学报:工学版, 2016, 46(3): 792-797
LIU Han-bing, SHI Cheng-lin, TAN Guo-jin. Finite element solution of composite beam with effect of shear slip. Journal of Jilin University Engineering and Technology Edition, 2016, 46(3): 792-797 复制到剪切板

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考虑剪切滑移效应的叠合梁有限元解

刘寒冰¹, 时成林^1,², 谭国金¹

1.吉林大学交通学院,长春 130022

2.吉林省交通科学研究所科研开发中心,长春 130012

通讯作者:谭国金(1981-),男,副教授,博士.研究方向:桥梁检测与加固.E-mail:tgj@jlu.edu.cn

作者简介:刘寒冰(1957-),男,教授,博士生导师.研究方向:桥梁检测与加固.E-mail:lhb@jlu.edu.cn

基金:国家自然科学基金项目(51478203); 吉林省科技厅项目(20140520135H); 吉林省交通运输厅项目(2012-1-7); 吉林省重大科技攻关专项项目(20140203002sf)

摘要

为了准确计算叠合梁在荷载作用下的受力、位移,基于弹性力学基本思想和接触理论推导了考虑剪切滑移效应的叠合梁的有限元解。利用该有限元解计算了集中荷载作用下的叠合梁挠度和交界面剪切滑移,并与试验结果进行了对比分析,结果表明:有限元解与试验结果能够较好地吻合,彼此具有较强的相关性,验证了有限元解的准确性和可靠性,为分析叠合梁受力和变形提供了新的计算手段,具有较高的实际推广价值。

关键词: 桥梁工程; 叠合梁; 有限单元法; 剪切滑移; 抗剪刚度

中图分类号:U441 文献标志码:A 文章编号:1671-5497(2016)03-0792-06

Finite element solution of composite beam with effect of shear slip

LIU Han-bing¹, SHI Cheng-lin^1,², TAN Guo-jin¹

1.College of Transportation,Jilin University,Changchun 130022, China

2.Scientific Research and Development Center,Jilin Provincial Transport Scientific Research Institute, Changchun 130012, China

Abstract

In order to accurately calculate the stress and displacement of composite beam under load, based on the elastic mechanics and contact theory, the finite element solution of the beam is derived, in which the effect of shear slip is considered. Using the finite element solution, the deflection and interface shear slip under concentrated loads are calculated. The calculation results are in good agreement with experimental results, which verifies the accuracy and reliability of the finite element solution. This finite element solution provides a new computing tool to analyze the stress and deformation of composite beams with shear slip.

Keyword: bridge engineering; composite beam; the finite element method; shear slip; shear stiffness

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叠合梁是目前逐渐兴起的一种桥梁结构形式, 通常情况下由受拉性能好的钢梁和抗压性能好的混凝土顶板组成^{[1, 2, 3]}, 充分利用钢材和混凝土的优点, 相对于钢梁而言, 叠合梁的稳定、耐久性主要取决于桥梁各部分的协同受力^{[4, 5, 6, 7]}。在组合梁的设计方面, 目前大多采用刚度折减法, 而在受力状态分析方面, 研究成果大多集中在某一特殊受力情况如竖向集中力和竖向均布荷载的受力状态分析, 尚未发现能够适合桥梁工程结构的具体工作状态的普遍适用的设计计算理论^{[8, 9, 10, 11, 12]}。

本文利用接触理论推导了考虑主梁与叠合梁顶梁的剪切滑移特性, 两部分协同受力的叠合梁在受到水平力和竖向力以及平面弯矩等外荷载作用下的有限元刚度方程。并与具体的试验结果进行了对比分析, 验证了本文给出的计算理论的正确性和可靠性。

1 计算公式的推导

1.1 基本假定

考虑钢-混组合梁的实际变形和受力状态。根据叠合梁的基本性质提出以下基本假定:①钢梁和混凝土板各自符合平截面假定; ②钢梁与混凝土板交界面处存在滑移, 交界面处传递的剪力集度与二者的水平位移差成正比; ③忽略钢梁与混凝土板交界面处的竖向掀起现象, 即在外力作用下二者的竖向位移、转角和曲率相同。

1.2 叠合梁位移函数的建立

1.2.1 基本位移函数

由于钢梁与混凝土板在水平方向不能协调变形, 叠合梁的位移包含三个基本未知函数 $\begin{matrix} u_{p}, v, u_{b} \end{matrix}$ 如图1所示, 其表达式为:

$\begin{matrix} \{\begin{matrix} u_{p} (x, z_{1}) = u_{p 0} (x) + z_{1} φ (x) \\ v (x) = v (x) \\ u_{b} (x, z_{2}) = u_{b 0} (x) + z_{2} φ (x) \end{matrix} \end{matrix}$ (1)

式中: $\begin{matrix} u_{b 0} (x) 、 u_{p 0} (x) \end{matrix}$ 分别为外荷载作用下叠合梁主梁中性轴、顶梁中性轴的轴向位移; $\begin{matrix} v (x) \end{matrix}$ 为叠合梁竖向位移; $\begin{matrix} φ (x) \end{matrix}$ 为叠合梁的转角, $\begin{matrix} φ (x) = dv (x) / dx 。 \end{matrix}$

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	图1 横断面位移状态Fig.1 Displacement state of cross section

1.2.2 叠合梁的物理方程

根据材料力学的基本原理, 叠合梁的内力与位移之间的关系为:

$N_{p} (x) = E_{p} A_{p} ε_{p 0} (x) = E_{p} A_{p} u'_{p 0} (x)$ (2)

$N_{b} (x) = E_{b} A_{b} ε_{b 0} (x) = E_{b} A_{b} u'_{b 0} (x)$ (3)

$M_{0} (x) = E_{p} p I_{p} ρ (x) + E_{b} I_{b} ρ (x) = B_{0} v″ (x)$ (4)

式中: $\begin{matrix} N_{p} (x) 、 N_{b} (x) \end{matrix}$ 分别为叠合梁顶梁和主梁对应的轴向力, 轴力方向以受压为正、受拉为负; $\begin{matrix} E_{p} 、 E_{b} \end{matrix}$ 分别为叠合梁顶梁和主梁的弹性模量; $\begin{matrix} I_{p} 、 I_{b} \end{matrix}$ 分别为叠合梁顶梁和主梁的惯性矩; $\begin{matrix} A_{p} 、 A_{b} \end{matrix}$ 分别为叠合梁顶梁和主梁的横断面面积; $\begin{matrix} ρ (x) \end{matrix}$ 为叠合梁在 $\begin{matrix} x \end{matrix}$ 截面处的曲率, $\begin{matrix} ρ (x) = v ″ (x), B_{0} = E_{p} I_{p} + E_{b} I_{b} 。 \end{matrix}$

叠合梁顶梁与主梁顶面之间的滑移量为:

$\begin{matrix} Δu (x) = u_{bu} (x) - u_{pb} (x) \end{matrix}$ (5)

由式(1)和图1可知:

$\begin{matrix} \begin{matrix} Δu (x) = u_{b 0} (x) - u_{p 0} (x) + φ (x) (z_{1 b} + z_{2 u}) = \\ u_{b 0} (x) - u_{p 0} (x) + v' (x) z_{d} \end{matrix} \end{matrix}$ (6)

式中: $\begin{matrix} Z_{d} = z_{1 b} + z_{2 u} \end{matrix}$

由基本假定可知, 混凝土铺装与主梁交界面处的剪力集度为:

$\begin{matrix} q (x) = kΔu (x) \end{matrix}$ (7)

式中: $\begin{matrix} k \end{matrix}$ 为交界面的剪切刚度。

联立式(6)(7)可解得:

$\begin{matrix} q (x) = k [u_{b 0} (x) - u_{p 0} (x) + v' (x) z_{d}] \end{matrix}$ (8)

叠合梁微元体受力情况如图2所示。

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	图2 交界面微元体受力图Fig.2 Force state sketch of interface

由图2可知:

$\begin{matrix} \{\begin{matrix} q (x) = - \frac{d N_{b}}{dx} = - E_{b} A_{b} u ″_{b 0} (x) \\ q (x) = \frac{d N_{p}}{dx} = E_{p} A_{p} u ″_{p 0} (x) \end{matrix} \end{matrix}$ (9)

1.2.3 叠合梁的平衡方程

根据内外力的平衡条件可知:

$\begin{matrix} \begin{matrix} M_{p} (x) = M_{0} (x) - N_{b} (x) \times z_{d} = \\ B_{0} v ″ (x) - E_{b} A_{b} u'_{b 0} (x) \times z_{d} \end{matrix} \end{matrix}$ (10)

式中: $\begin{matrix} M_{p} (x) \end{matrix}$ 为外荷载产生的弯矩。

由式(8)(9)可得:

$\begin{matrix} u_{p 0} (x) = u_{b 0} (x) + v' (x) z_{d} + \frac{E_{b} A_{b}}{k} u ″_{b 0} (x) \end{matrix}$ (11)

由于弯曲梁单元轴力为零:

$\begin{matrix} N_{p} (x) = - N_{b} (x) \end{matrix}$ (12)

由式(11)(12)得:

$\begin{matrix} \begin{matrix} v ″ (x) = - \frac{1}{z_{d}} [\frac{E_{b} A_{b}}{k} u ‴_{b 0} (x) + \\ (1 + \frac{E_{b} A_{b}}{E_{p} A_{p}}) u'_{b 0} (x)] \end{matrix} \end{matrix}$ (13)

由式(10)(13)可得:

$\begin{matrix} αu ‴_{b 0} (x) + βu'_{b 0} (x) = - \frac{z_{d}}{B_{0}} M_{p} (x) \end{matrix}$ (14)

式中: $\begin{matrix} α = \frac{E_{b} A_{b}}{k}; β = 1 + \frac{E_{b} A_{b}}{E_{p} A_{p}} + \frac{E_{b} A_{b} z_{d}^{2}}{B_{0}} 。 \end{matrix}$

解微分方程(14)可得:

$\begin{matrix} u'_{b 0} (x) = a_{1} \cos (Rx) + a_{2} \sin (Rx) - \frac{z_{d}}{B_{0}} M_{p} (x) \end{matrix}$ (15)

式中: $\begin{matrix} R = \sqrt[]{\frac{β}{α}}; a_{1}, a_{2} \end{matrix}$ 为待定系数。

1.3 叠合梁的有限元解

1.3.1 单元位移函数的建立

由式(15)可知, 在位移函数中含有 $\begin{matrix} \cos (Rx) 、 \sin (Rx), \end{matrix}$ 根据有限元基本理论, 可以将叠合梁中主梁的轴向位移函数设为:

$\begin{matrix} \{\begin{matrix} u ″_{b 0} (x) = a_{1} R^{2} \cos (Rx) + a_{2} R^{2} \sin (Rx) \\ u ″_{p 0} (x) = - k_{A} [a_{1} R^{2} \cos (Rx) + a_{2} R^{2} \sin (Rx)] \end{matrix} \end{matrix}$ (16)

式中: $\begin{matrix} k_{A} = \frac{E_{b} A_{b}}{E_{p} A_{p}} 。 \end{matrix}$

由式(16)可得:

$\begin{matrix} \{\begin{matrix} u'_{b 0} (x) = a_{1} Rsin (Rx) - a_{2} Rcos (Rx) + a_{3} \\ u'_{p 0} (x) = - k_{A} a_{1} Rsin (Rx) + k_{A} a_{2} Rcos (Rx) + a_{5} \\ u_{b 0} (x) = - a_{1} \cos (Rx) - a_{2} \sin (Rx) + a_{3} x + a_{4} \\ u_{p 0} (x) = k_{A} a_{1} \cos (Rx) + k_{A} a_{2} \sin (Rx) + a_{5} x + a_{6} \\ u ‴_{b 0} (x) = - a_{1} R^{3} \sin (Rx) + a_{2} R^{3} \cos (Rx) \end{matrix} \end{matrix}$ (17)

由式(13)(17)可得:

$\begin{matrix} \{\begin{matrix} v ″ (x) = a_{1} n_{1} Rsin (Rx) - a_{2} n_{1} Rcos (Rx) - \\ \frac{a_{3}}{z_{d}} + \frac{a_{5}}{z_{d}} \\ v' (x) = - a_{1} n_{1} \cos (Rx) - a_{2} n_{1} \sin (Rx) - \\ \frac{x a_{3}}{z_{d}} + \frac{x a_{5}}{z_{d}} + a_{7} \\ v (x) = - a_{1} \frac{n_{1}}{R} \sin (Rx) + a_{2} \frac{n_{1}}{R} \cos (Rx) - \\ \frac{x^{2} a_{3}}{2 z_{d}} + \frac{x^{2} a_{5}}{2 z_{d}} + a_{7} x + a_{8} \end{matrix} \end{matrix}$ (18)

式中: $\begin{matrix} n_{1} = \frac{E_{b} A_{b}}{k z_{d}} R^{2} - \frac{1 + k_{A}}{z_{d}}; a_{1} ~ a_{8} \end{matrix}$ 为待定系数。

设单元左结点为 i右结点为j则单元两端的结点位移分别为 $\begin{matrix} {\bar{u}}_{bi} 、 {\bar{u}}_{pi} 、 {\bar{φ}}_{i} 、 {\bar{v}}_{i}; {\bar{u}}_{bj} 、 {\bar{u}}_{pj} 、 {\bar{φ}}_{j} 、 {\bar{v}}_{j}, \end{matrix}$ 由解式(17)(18)可得:当x=0时, $\begin{matrix} {\bar{u}}_{bi} = u_{b} (0) 、 {\bar{u}}_{pi} = u_{p} (0) 、 {\bar{φ}}_{i} = v' (0) 、 {\bar{v}}_{i} = v (0); 当 x = l \end{matrix}$ 时, $\begin{matrix} {\bar{u}}_{bj} = u_{b} (l) 、 {\bar{u}}_{pj} = u_{p} (l) 、 {\bar{φ}}_{j} = v' (l) 、 {\bar{v}}_{l} = v (l), \end{matrix}$ 写成矩阵形式可表示为:

$\begin{matrix} [\begin{matrix} - 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ k_{A} & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ - n_{1} & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & n_{1} / R & 0 & 0 & 0 & 0 & 0 & 1 \\ - \cos (Rl) & - \sin (Rl) & l & 1 & 0 & 0 & 0 & 0 \\ k_{A} \cos (Rl) & k_{A} \sin (Rl) & 0 & 0 & l & 1 & 0 & 0 \\ - n_{1} \cos (Rl) & - n_{1} \sin (Rl) & - \frac{l}{z_{d}} & 0 & \frac{l}{z_{d}} & 0 & 1 & 0 \\ - \frac{n_{1}}{R} \sin (Rl) & \frac{n_{1}}{R} \cos (Rl) & - \frac{l^{2}}{2 z_{d}} & 0 & \frac{l^{2}}{2 z_{d}} & 0 & l & 1 \end{matrix}] [\begin{matrix} a_{1} \\ a_{2} \\ a_{3} \\ a_{4} \\ a_{5} \\ a_{6} \\ a_{7} \\ a_{8} \end{matrix}] = [\begin{matrix} {\bar{u}}_{bi} \\ {\bar{u}}_{pi} \\ {\bar{φ}}_{i} \\ {\bar{v}}_{i} \\ {\bar{u}}_{bj} \\ {\bar{u}}_{pj} \\ {\bar{φ}}_{j} \\ {\bar{v}}_{j} \end{matrix}] \end{matrix}$ (19)

式(19)可简写为:

$\begin{matrix} Aa = {\bar{δ}}^{e} \end{matrix}$ (20)

式中: $\begin{matrix} A \end{matrix}$ 为8阶方阵; $\begin{matrix} a \end{matrix}$ 为待定系数列阵; $\begin{matrix} {\bar{δ}}^{e} \end{matrix}$ 为结点位移列阵。

由式(20)可解得:

$\begin{matrix} a = C \cdot {\bar{δ}}^{e} \end{matrix}$ (21)

式中: $\begin{matrix} C = A^{- 1} \end{matrix}$ 为试探函数系数矩阵。

这样, 单元内任意点的位移可以表示为:

$\begin{matrix} \{\begin{matrix} u_{b 0} (x) \\ u_{p 0} (x) \\ v' (x) \\ v (x) \end{matrix}\} = [\begin{matrix} - \cos (Rx) & - \sin (Rx) & x & 1 & 0 & 0 & 0 & 0 \\ k_{A} \cos (Rx) & k_{A} \sin (Rx) & 0 & 0 & x & 1 & 0 & 0 \\ - n_{1} \cos (Rx) & - n_{1} \sin (Rx) & - \frac{x}{z_{d}} & 0 & \frac{x}{z_{d}} & 0 & 1 & 0 \\ - \frac{n_{1}}{R} \sin (Rx) & \frac{n_{1}}{R} co s (Rx) & - \frac{x^{2}}{2 z_{d}} & 0 & \frac{x^{2}}{2 z_{d}} & 0 & x & 1 \end{matrix}] \times C \times {\bar{δ}}^{e} = N {\bar{δ}}^{e} \end{matrix}$ (22)

式中: $\begin{matrix} N \end{matrix}$ 为试探函数矩阵。

1.3.2 单元的几何和物理方程

叠合梁单元的广义应变包括:顶板形心处的应变 $\begin{matrix} ε_{b} (x) 、 \end{matrix}$ 底板形心处的应变 $\begin{matrix} ε_{p} (x) 、 \end{matrix}$ 单元上任意一点的曲率 $\begin{matrix} ρ (x) \end{matrix}$ 和交界面上的滑移量 $\begin{matrix} Δu (x), 其中 ρ (x) = \frac{d^{2} v (x)}{d x^{2}} 。 \end{matrix}$ 由式(7)(17)(18)(22)可得单元上任意一点的广义应变为:

$\begin{matrix} \{\begin{matrix} ε_{b} (x) \\ ε_{p} (x) \\ k (x) \\ Δu (x) \end{matrix}\} = [\begin{matrix} R \sin (Rx) & - Rcos (Rx) & 1 & 0 & 0 & 0 & 0 & 0 \\ - k_{A} Rsin (Rx) & k_{A} Rcos (Rx) & 0 & 0 & 1 & 0 & 0 & 0 \\ n_{1} Rsin (Rx) & - n_{1} Rcos (Rx) & - 1 / z_{d} & 0 & 1 / z_{d} & 0 & 0 & 0 \\ - z_{d} k_{1} R^{2} \cos (Rx) & - z_{d} k_{1} R^{2} \sin (Rx) & 0 & 1 & 0 & - 1 & z_{d} & 0 \end{matrix}] \times C \times {\bar{δ}}^{e} = ε {\bar{δ}}^{e} \end{matrix}$ (23)

式中: $\begin{matrix} ε \end{matrix}$ 为应变矩阵; $\begin{matrix} k_{1} = \frac{E_{b} A_{b}}{k z_{d}} 。 \end{matrix}$

叠合梁单元的广义内力包括:上层梁的轴力、下层梁的轴力、弯矩和交界面剪力 $\begin{matrix} q (x) 。 \end{matrix}$ 叠合梁单元的广义内力用矩阵形式可表示为:

$\begin{matrix} \{\begin{matrix} E_{b} A_{b} ε_{b} (x) \\ E_{p} A_{p} ε_{p} (x) \\ (E_{b} A_{b} + E_{p} A_{p}) k (x) \\ q (x) \end{matrix}\} = Dε {\bar{δ}}^{e} \end{matrix}$ (24)

式中: $\begin{matrix} D = [\begin{matrix} E_{b} A_{b} & 0 & 0 & 0 \\ 0 & E_{p} A_{p} & 0 & 0 \\ 0 & 0 & E_{b} I_{b} + E_{p} I_{p} & 0 \\ 0 & 0 & 0 & k \end{matrix}] 。 \end{matrix}$

1.3.3 单元的刚度方程

设叠合梁单元结点列阵为:

$\begin{matrix} \begin{matrix} {\bar{F}}^{e} = \\ {[\begin{matrix} {N_{bi}}^{e} & {N_{pi}}^{e} & {M_{i}}^{e} & {Q_{i}}^{e} & {N_{bj}}^{e} & {N_{pj}}^{e} & {M_{j}}^{e} & {Q_{j}}^{e} \end{matrix}]}^{T} \end{matrix} \end{matrix}$ (25)

单元的总势能可表示为:

$\begin{matrix} π = \int_{0}^{l} \frac{1}{2} {\bar{δ}}^{eT} ε^{T} Dε {\bar{δ}}^{e} dx - {\bar{δ}}^{eT} {\bar{F}}^{e} \end{matrix}$ (26)

根据弹性力学理论, 对总势能函数进行一阶变分, 可得到单元的刚度方程为:

$\begin{matrix} δπ = δ {\bar{δ}}^{eT} {\bar{K}}^{e} {\bar{δ}}^{e} - δ {\bar{δ}}^{eT} {\bar{F}}^{e} = 0 \end{matrix}$ (27)

由式(26)可得:

$\begin{matrix} {\bar{K}}^{e} {\bar{δ}}^{e} - {\bar{F}}^{e} = 0 \end{matrix}$ (28)

式中: $\begin{matrix} {\bar{K}}^{e} \end{matrix}$ 为叠合梁的单元刚度, 它可表示为:

$\begin{matrix} {\bar{K}}^{e} = \int_{0}^{l} ε^{T} Dεdx \end{matrix}$ (29)

2 叠合梁有限元解的验证

为了验证本文给出的有限元解的正确性, 将本文方法得到的图3所示组合梁的有限元解与文献^[7]中的试验结果进行了对比, 结果如图4和图5所示。从图4和图5可以看出:当跨径为4 m, 横断面如图3所示的组合梁在距离跨中60 cm处对称作用有50 kN的竖向集中力时, 本文的有限元解与试验值有较好的一致性, 而且与解析解的计算结果几乎完全一致, 说明该数值解是可靠、合理的, 能够对叠合梁在竖向荷载作用下的抗弯性能进行合理的分析和计算。

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	图3 组合梁横断面(单位:mm)Fig.3 Cross section of composite beam

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	图4 试验梁的挠曲Fig.4 Deflection curve

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	图5 剪切滑移应变差Fig.5 Strain difference curve

3 叠合梁有限元解的应用

由于目前我国公路桥涵钢结构设计规范中有关组合梁的规定仍然采用容许应力法, 这就需要对钢-混凝土组合梁在线弹性范围内进行精确的分析和计算。为了说明叠合梁有限元解的应用推广价值, 本文以跨径为30 m+40 m+30 m的连续组合梁(横断面如图6所示)的典型特征截面的挠度和交界面的剪切力影响线进行了设计计算。

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	图6 连续组合梁横断面Fig.6 Cross section of composite continue beam

图7和图8分别为采用本文给出的有限元解计算得到的组合梁特征截面的挠度影响线和剪切力影响线。

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	图7 挠度影响线Fig.7 Deflection influence lines

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	图8 交界面剪切力影响线Fig.8 Interface shear influence lines

从图7可以看出:采用本文方法计算的钢-混凝土组合梁挠度影响线与单一梁的曲线形状一致, 只是在数值上有所差别。

本文首次给出了钢-混凝土组合梁交界面处的由于剪切滑移效应引起的交界面剪力影响线(见图8), 通过该影响线可以方便地计算汽车荷载作用下的交界面最大剪力, 为组合梁剪力连接件的设计提供了可靠的理论依据和设计手段, 为组合梁的进一步应用和推广奠定了良好的理论基础。

4 结论

(1)结合叠合梁的受力特性, 利用接触理论推导了外力作用下在考虑剪切滑移效应时叠合梁的有限元解, 该有限元解适于各种变化截面、不同受力状态、叠合梁交界面不同的抗剪刚度条件下叠合梁计算, 包括挠度、位移、转角、曲率、剪切滑移应变差以及各部分内力等计算指标。

(2)经过在竖向荷载作用下叠合梁挠曲线和层间剪切滑移应变差有限元解计算值与试验值的对比分析, 证明了该算法是合理、准确的。

(3)给出了钢-混凝土组合梁交界面剪力影响线, 为组合梁的进一步推广提供了良好的技术设计手段。

(4)本文提出的叠合梁有限元解适合各种层间抗剪刚度条件, 可用此解计算桥梁钢桥面, 也可计算钢筋混凝土桥面的混凝土铺装层, 还可计算桥面沥青铺装层与混凝土层之间的力和位移, 只需要通过试验确定层间的抗剪刚度即可, 因此该有限元解可解决广义的叠合梁的内力计算, 具有更广的应用空间。

The authors have declared that no competing interests exist.

参考文献

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[1]	聂建国, 余志武. 钢-混凝土组合梁在我国的研究及应用[J]. 土木工程学报, 1999, 32(2): 3-7. Nie Jian-guo, Yu Zhi-wu. Research and practice of composite steel-concrete beams in China[J]. China Civil Engineering Journal, 1999, 32(2): 3-7. [本文引用:1]
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[6]	周勇超, 李亮亮, 李子青. 钢-混凝土组合梁界面滑移效应变分法求解[J]. 长安大学学报: 自然科学版, 2013, 33(1): 39-44. Zhou Yong-chao, Li Liang-liang, Li Zi-qing. Solution of slip effect of steel-concrete composite beam with variational principless[J]. Journal of Chang'an University (Natural Science Edition), 2013, 33(1): 39-44. [本文引用:1]
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[9]	Dimitrios P, Jean-Paul L. Design and experimental verification of an innovative steel-concrete composite beam[J]. Journal of Constructional Steel Research, 2014, 93(6): 9-19. [本文引用:1]
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1999

0.0

. 1999, 32(2):3-7 DOI:doi:10.3321/j.issn:1000-131X.1999.02.001

Research and practice of composite steel-concrete beams in China

钢-混凝土组合梁在我国的研究及应用

Nie Jian-guo , Yu Zhi-wu.

聂建国, 余志武

近年来,钢-混凝土组合梁结构在我国发展很快,在建筑和桥梁结构等领域已经得到越来越多的应用,取得了显著的技术经济效益和社会效益.本文较为系统地阐述组合梁在我国的研究和应用情况,并指出了有关钢-混凝土组合梁方面值得进一步研究的问题.

... 叠合梁是目前逐渐兴起的一种桥梁结构形式,通常情况下由受拉性能好的钢梁和抗压性能好的混凝土顶板组成^[1,2,3],充分利用钢材和混凝土的优点,相对于钢梁而言,叠合梁的稳定、耐久性主要取决于桥梁各部分的协同受力^[4,5,6,7] ...

2015

0.0

2015

0.0

2009

0.0

2011

0.0

. 2011, 28(11):45-51

Practical design method for steel-concrete composite beam considering shear lag effect

钢-混凝土组合梁考虑剪力滞效应实用设计方法

Nie Jian-guo , Li Fa-xiong , Fan Jian-sheng

聂建国, 李法雄, 樊健生

Shear lag effect has significant effect on stress and deflection of composite beams. According to the elastic analytical model of composite beams, stress and deflection analytical solutions for the cases of simply supported composite beams and cantilever composite beam under uniform distribution load and concentrated load are derived by ignoring slip effect in the interface. By introducing effective flange width and effective sectional rigidity, practical design methods for considering shear lag effect of composite beam are presented, and the results calculated by these methods have good agreement with those obtained from analytical solutions. By comparing different design methods for composite beam considering shear lag effect from different countries, the simple practical design method presented in this research is found to have high accuracy despite of its simplicity.

钢-混凝土组合梁翼板剪力滞效应对组合梁截面应力和变形产生重要影响。基于组合梁弹性理论分析模型，忽略界面滑移效应，推导了简支和悬臂组合梁在均布和集中荷载作用下的应力和变形解析解。通过引入翼板有效宽度和截面有效刚度的两种简化设计方法分别考虑翼板剪力滞效应对组合梁截面应力和变形的影响。用该文提出的简化设计方法计算考虑剪力滞效应时组合梁截面应力和变形与解析结果吻合良好。通过比较分析各国规范关于组合梁剪力滞效应的设计方法，该文提出的简化设计方法具有精度高、计算方法简单等优点。

2013

0.0

. 2013, 33(1):39-44

Solution of slip effect of steel-concrete composite beam with variational principless

钢-混凝土组合梁界面滑移效应变分法求解

Zhou Yong-chao , Li Liang-liang , Li Zi-qing.

周勇超, 李亮亮, 李子青

为了求解钢-混凝土组合梁的界面滑移效应,以弹性理论为基础,建立平衡方程;利用最小势能原理,结合变分方法,分别推导了简支钢-混凝土组合梁在受均布荷载和集中荷载时,组合梁的界面相对滑移、组合梁挠度以及附加弯矩的计算方法。结果表明:此方法使相对滑移微分方程基本形式得到统一;附加弯矩与相对滑移趋势成正比,而与相对滑移量无关;界面相对滑移量与抗滑移刚度、截面剪力有关,并且会增加组合梁挠度;简支组合梁相对滑移在梁两端部达到最大值,而向跨中减小。最后通过算例验证了给出的解析解的正确性。

2005

0.0

... 2 叠合梁有限元解的验证为了验证本文给出的有限元解的正确性,将本文方法得到的图3所示组合梁的有限元解与文献^[7]中的试验结果进行了对比,结果如图4和图5所示 ...

2012

0.0

... 在组合梁的设计方面,目前大多采用刚度折减法,而在受力状态分析方面,研究成果大多集中在某一特殊受力情况如竖向集中力和竖向均布荷载的受力状态分析,尚未发现能够适合桥梁工程结构的具体工作状态的普遍适用的设计计算理论^{[8,9,10,11,12]} ...

2014

0.0

2002

0.0

. 2002, 35(4):1-5,11 DOI:doi:10.3321/j.issn:1000-131X.2002.04.001

Methods for analysis of composite steel-concrete beams with profiled sheet

钢-压型钢板混凝土组合梁计算的修正折减刚度法

Nie Jian-guo , Wang Ting , Fan Jian-sheng.

聂建国, 王挺, 樊健生

由于滑移效应的影响,采用栓钉剪力连接件的钢-压型钢板混凝土组合梁的刚度和抗弯承载力均有所降低.本文在折减刚度法的基础上,建立了适用于钢-压型钢板混凝土组合梁的修正折减刚度计算公式,并进一步建立了考虑滑移效应影响的弹性抗弯承载力计算公式.公式计算结果与试验梁的实测值吻合良好.

2011

0.0

. 2011, 46(4):541-546 DOI:10.3969/j.issn.0258-2724.2011.04.003

Effective stiffness method for calculation of deflection of composite beams

组合梁挠度计算的新方法#cod#x02014;#cod#x02014;有效刚度法

Zhou Dong-hua , Sun Li-li , Fan Jiang

周东华, 孙丽莉, 樊江

Construction Engineering College, Kunming University of Science and Technology, Kunming 650224, China

Accurate calculation of deflection of composite beams with elastic shear connections is difficult because of difficultly getting an analytical solution under an arbitrary load, and analytical solutions in common load cases are quite complicated. For these reasons, a simplified calculation method called “method of reduction of stiffness” was provided in Chinese Code for Design of Steel Structures. However, the results obtained by the method are not accurate enough and its application is limited under some circumstances. In order to solve the above problem, a new method called “effective stiffness method” was proposed. Calculations with this method are simple and accurate, and the proposed method has a clear mechanic background and can give a composite factor showing the actual effect of shear connections. It can be used to composite beams with an arbitrary stiffness of shear connections, i.e., from near zero to infinity. The calculation results show that the relative error between its solutions and analytical solutions is less than 1.0%.

要精确计算弹性剪切连接时组合梁的挠度较为复杂,因而很难得到任意荷载作用下的解析解,一些常用荷载作用下的解析解冗长,计算繁琐.为此,GB50017—2003《钢结构规范》中提供了一种较为简便的计算方法———抗弯刚度折减法,但用该方法计算时,精度不高,适用范围有局限.为此,提出了组合梁挠度计算的一种新方法———有效刚度法.该方法计算简便、力学概念清晰,且计算精度很高,与精确解析解的误差不超过1.0%;此外,还能给出组合系数的值,能非常直观地评价组合梁组合作用的大小;该方法对剪切连接件的刚度无任何限制,其变化范围可以从趋近于0到无穷大.

2010

0.0

. 2010, 23(4):39-44

Analytical solution of a steel-concrete composite beam under vertical loads

竖向集中荷载作用下钢-混凝土组合梁的解析解

Liu Han-bing , Ma Hui , Liu Tian-ming

刘寒冰, 马辉, 刘天明

In order to accurately analyze the flexural behavior of steel-concrete composite beam, based on contact theory and basic idea of elastic mechanics and considering the shear-slip effect, differential equation of the structure under vertical load was deduced and analytical solution was given. The strain and displacement conditions of composite beam under vertical load were calculated by the analytical solution. Shear-slip strain difference of interface of steel beam and concrete top slab was also analyzed. The results calculated by this method were compared with test result. Result shows that test value has a good agreement with calculated value obtained from a simple beam experiment, and the deflection error is less than 2%. It is concluded that this equation is rational, believable and practical. The method can be used as a simple and convenient analytical method for construction design.

为了准确分析钢-混凝土组合梁的抗弯性能,基于接触理论和弹性力学基本思想推导了钢-混凝土组合梁在竖向荷载作用下考虑剪切滑移效应的微分方程,给出了解析解。计算了竖向集中力作用下组合梁的各部分应变和位移状态,分析了钢梁和混凝土顶板交界面处的剪切滑移应变差,并与试验结果进行了对比。结果表明:计算值与试验值有较好的一致性,挠度相对误差不超过2%;该计算公式是合理的、可信的,为工程设计提供了一种简便的计算方法,具有较强的实用价值。