简介概要

贴片加固混凝土梁界面粘结剪应力的分析与计算

来源期刊:中南大学学报(自然科学版)2005年第2期

论文作者:贺学军 周朝阳

文章页码:340 - 343

关键词:混凝土梁;加固片材;剪切变形;粘结剪应力

Key words:reinforced concrete beam; strengthened plate; shear deformation; bonding shear stress

摘    要:以弹性理论为基础,根据贴片加固混凝土梁的截面变形协调条件和静力平衡条件,推导出了任意线性荷载作用下贴片加固梁的界面粘结剪应力及片材端部界面最大粘结剪应力的计算公式,并给出了均布荷载和集中荷载2种情况下的具体表达式。研究结果表明:由于表达式考虑了混凝土梁、粘结胶层和加固片材性能对界面粘结剪应力的影响,因而具有更高的计算精度;采用这些公式可以对不同荷载作用、不同粘结长度和宽度及不同梁截面形式的贴片加固梁片材端部界面最大粘结剪应力进行验算,以防止加固梁片材端部出现界面剥离破坏。关键词:混凝土梁;加固片材;剪切变形;粘结剪应力

Abstract: Based on the linear elastic theory, a new analytical solution is developed for a platestrengthened reinforced concrete beam under a linear distributed load using the cross-sectional equilibrium and compatible conditions. The interfacial shear stress distribution along the bond line and its maximum value at the cut-off point of the plate were given. And direct analytical expressions were presented for the cases of concentrated loading as well as uniform loading. The comparative results show that the present solution has better accuracy because the influences of the behaviors of reinforced concrete beam, adhesive and strengthening plate on the interfacial shear stress are all considered. For a plate-strengthened reinforced concrete beam under different loading,plate length and width and different cross section, the solution can be used to check the maximum bonding shear stress to prevent the plate debonding in the beam at the cut-off point of the plate.



详情信息展示

贴片加固混凝土梁界面粘结剪应力的分析与计算

贺学军,周朝阳

(中南大学 土木建筑学院,湖南 长沙,410075)

摘要: 以弹性理论为基础,根据贴片加固混凝土梁的截面变形协调条件和静力平衡条件,推导出了任意线性荷载作用下贴片加固梁的界面粘结剪应力及片材端部界面最大粘结剪应力的计算公式,并给出了均布荷载和集中荷载2种情况下的具体表达式。研究结果表明:由于表达式考虑了混凝土梁、粘结胶层和加固片材性能对界面粘结剪应力的影响,因而具有更高的计算精度;采用这些公式可以对不同荷载作用、不同粘结长度和宽度及不同梁截面形式的贴片加固梁片材端部界面最大粘结剪应力进行验算,以防止加固梁片材端部出现界面剥离破坏。
关键词: 混凝土梁; 加固片材; 剪切变形; 粘结剪应力
中图分类号:TU746.3 文献标识码:A 文章编号: 1672-7207(2005)02-0340-04

Analysis and Calculation of Interfacial Bonding Shear Stress of Reinforced Concrete Beams Strengthened with Plates

HE Xue-jun, ZHOU Chao-yang

(School of Civil and Architectural Engineering, Central South University, Changsha 410075, China)

Abstract: Based on the linear elastic theory, a new analytical solution is developed for a plate-strengthened reinforced concrete beam under a linear distributed load using the cross-sectional equilibrium and compatible conditions. The interfacial shear stress distribution along the bond line and its maximum value at the cut-off point of the plate were given. And direct analytical expressions were presented for the cases of concentrated loading as well as uniform loading. The comparative results show that the present solution has better accuracy because the influences of the behaviors of reinforced concrete beam, adhesive and strengthening plate on the interfacial shear stress are all considered. For a plate-strengthened reinforced concrete beam under different loading,plate length and width and different cross section, the solution can be used to check the maximum bonding shear stress to prevent the plate debonding in the beam at the cut-off point of the plate.
Key words: reinforced concrete beam; strengthened plate; shear deformation; bonding shear stress
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   在受拉区表面粘贴片材(如钢板、FRP片材等)是加固混凝土梁的一种有效方法。片材和混凝土梁通过胶层传递粘结剪应力和正应力,达到共同工作的目的。但是,在片材端部界面由于应力集中而产生较大的粘结剪应力和粘结正应力[1-9]。当界面粘结剪应力超过混凝土的抗拉强度时,将引起加固体系提前发生片材剥离的脆性破坏[10-13],从而影响结构的安全使用和加固效果。 目前,关于界面粘结剪应力的计算方法主要有两类:一类是近似计算法[1-5]。该方法适当简化界面粘结剪应力的计算模型并忽略某些参数对剪应力的影响,其计算过程简单、直观,但计算结果随参数忽略的数量不同而变化,误差较大。另一类是数值分析法[7-9],需借助计算机编程进行计算,计算结果精确,但该方法计算过程复杂,计算参量无具体表达式。在此,作者在弹性理论的基础上,考虑混凝土梁、胶层及加固片材性能对界面粘结剪应力的影响,对任意线荷载作用下的贴片加固梁界面粘结剪应力进行分析,并推导出加固梁在均布和集中荷载2种情况下的界面粘结剪应力及片材端部界面最大粘结剪应力计算的具体表达式。

1 界面粘结剪应力分析模型

界面粘结剪应力分析模型如图1所示。任意线荷载作用下片材加固梁胶层的剪切变形可由混凝土梁的中和轴转角Ψ与加固梁中混凝土梁和加固片材中和轴连线的转角Φ来确定[14],即

对式(1)关于x进行2次求导,得:


图 1   贴片加固混凝土梁截面应力分析模型
Fig. 1   Model in cross section of plate-strengthening reinforced concrete beam

Φ由加固片材和混凝土梁截面中和轴处的相对轴向位移来确定,即

令EBAB和EBIB分别为混凝土梁的轴向刚度和抗弯刚度,EPAP和EPIP分别为加固片材的轴向刚度和抗弯刚度,由材料力学理论可知:

假定界面粘结剪应力τ(x)由胶层的剪应变γ及其剪切模量Ga确定,则根据加固梁截面的静力平衡条件(见图1(c)和图1(d))可得:

其中:bP为加固片材的宽度。将式(2)~(5)进行适当变换后,即可得到贴片加固梁界面粘结剪应力计算的基本微分方程:

式中:

当荷载q(x)呈线性分布,即q(x)=b1(L0+x)+b2时,由图1(a)可知,贴片加固梁截面产生的弯矩为:

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