纤维增强聚合物加固黏弹性Timoshenko木梁的弯曲变形

假定木梁和纤维增强聚合物(FRP)布分别服从标准线性固体黏弹性本构和弹性本构,且FRP布与木梁紧密粘贴,建立了FRP布加固黏弹性矩形截面Timoshenko木梁弯曲变形的控制方程.在此基础上,利用Laplace变换及其逆变换,给出了突加集中和均布载荷作用下FRP布加固简支黏弹性Timoshenko木梁弯曲变形的轴向位移、转角和挠度解析表达式.根据花旗松(DF)木材标准线性固体本构的材料参数,数值分析了芳纶纤维聚合物(AFRP)含量和梁跨高比对AFRP布加固黏弹性Timoshenko DF梁弯曲蠕变行为的影响.结果表明:Timoshenko DF梁的弯曲蠕变效应显著,AFRP布加固可有效减小Timoshenko DF梁的蠕变挠度;随着DF梁跨高比减小或AFRP含量的提高,AFRP布加固Timoshenko DF梁的最大压应力和最大拉应力减小.     

纤维增强聚合物加固带裂缝矩形截面木梁的弯曲

对具有纵向贯穿裂缝的矩形截面木梁采用侧贴纤维增强聚合物布(FRP布)的方式加固。将FRP布视为正交各向异性材料,在组合梁小挠度变形的假定下,建立了侧贴FRP布加固具有纵向贯穿裂缝矩形截面木梁弯曲变形的控制方程;研究了FRP加固简支木梁在跨中集中力作用下的弯曲行为,得到了木梁挠度的解析表达式,在此基础上通过参数分析,考察了材料参数、几何参数、加固方式等对梁弯曲挠度的影响。数值结果表明:当FRP布纤维方向与梁轴线夹角=0°时,CFRP布的加固效果好于GFRP布的加固效果,而当为10°~15°时,FRP布的加固效果最为显著;当FRP布量纲为一的厚度(FRP布厚度与木梁的宽度之比)<0.02、剪切模量(FRP布OXZ方向的剪切模量与木梁弹性模量之比)<0.5时,和对FRP布加固木梁的挠度有较显著的影响。     

纤维增强聚合物布加固简支木柱的稳定性

考虑加固层中纤维增强聚合物布(FRP布)拉伸与压缩时的双模量性质,基于考虑FRP加固木柱弯曲变形二阶效应的控制方程,研究了轴向压力作用下FRP布加固简支木柱中间部分的稳定性问题,计算了临界载荷的精确值,给出了基于能量法的临界载荷近似表达式,并考察了近似临界载荷与精确临界荷载的误差.数值结果表明:随着FRP布加固层厚度和长度的增加,FRP布加固简支木柱的临界载荷增加;当FRP布加固层长度比例δ=0.7～1.0时,FRP布加固木柱的临界荷载变化较小;而当加固层长度比例δ＜0.7时,增加比例δ可显著提高FRP布加固木柱的临界载荷.因此,为节省FRP材料,并得到较好的加固效应,应重点加固木柱的中间部位.另外,对于工程中的FRP布加固木柱,近似临界载荷与精确临界荷载的误差小于5％,所得近似临界载荷表达式具有一定的工程实用价值.     

集中载荷作用下FRP布加固带裂缝木梁的弯曲

将FRP布视为正交各向异性材料,考虑其拉伸与压缩时的双弹性模量性质,给出了四周粘贴FRP布加固带裂缝木梁四点弯曲的边值问题,得到了FRP布加固木梁挠度的解析解,并验证了其有效性和适用性.参数分析表明:相比于侧面粘贴CFRP布,在木梁受拉侧沿轴向粘贴CFRP布的刚度加固效果更加显著;CFRP布加固木梁的挠度随CFRP加固布厚度和弹性模量的增加而减小,但当侧贴CFRP布厚度增加到某一值时,继续增加厚度对木梁挠度的减少效果已不明显;当受拉侧CFRP布厚度较小时,木梁挠度随CFRP布厚度的增加非线性减小,而当受拉侧CFRP布厚度较大时,木梁挠度随CFRP布厚度几乎呈线性减小.同时,当侧贴CFRP布的剪切模量很大时,此时,CFRP布加固带裂缝木梁的挠度趋于CFRP布加固完整无裂缝木梁的挠度,此时,CFRP加固完全消除了裂缝因素.     

THE FAILURE MODES OF CONCRETE BEAMS STRENGTHENED WITH NEAR SURFACE MOUNTED FRP BARS

为研究不同参数下表面内嵌纤维筋加固后T 形混凝土梁的破坏模式, 对5 根不同梁端锚固、FRP(fiber reinforced polymer) 筋表面特征和FRP 筋类型的T 形混凝土梁进行受弯性能试验. 结果表明, 无梁端锚固、光圆GFRP (glass fiber reinforced polymer) 筋和CFRP (carbon fiber reinforced polymer) 筋加固梁试件发生粘结破坏. 梁端锚固和FRP 筋表面特征影响加固梁试件的极限载荷, CFRP 筋加固梁试件的屈服载荷和极限载荷较大. 螺纹FRP 筋和有梁端锚固加固梁试件FRP 筋利用率较高. 因此, 有梁端锚固的表面内嵌螺纹GFRP 筋加固是最为有效的加固方式.     

CFRP布加固具有边缘裂纹板条的疲劳性能

将碳纤维增强复合材料(CFRP)布在板条两表面双面粘贴加固具有边缘穿透裂纹的板条,研究了加固板条在两端循环拉伸载荷作用下的断裂和疲劳性能.首先建立了CFRP布加固板条粘结层与CFRP布/板条的界面剪应力控制方程,并求得两端均布拉力作用下CFRP布加固具有边缘穿透裂纹的板条的界面剪应力解析解.其次,利用叠加原理推导了CFRP加固板条裂纹尖端的应力强度因子表达式,分别给出了其Paris和Elber模型疲劳寿命公式,通过与相关实验结果的比较,发现Elber模型的疲劳寿命公式与试验结果较吻合.最后的参数研究表明:CFRP布刚度对应力强度因子范围有显著的影响,且应力强度因子范围随CFRP布长度或粘贴层剪切模量的增加而减小,并趋于定值.同时,粘贴胶厚度对应力强度因子范围几乎没有影响.     

基于裂纹诱导弦挠度的简支外伸梁裂纹损伤识别

基于梁横向开裂纹的线性扭转弹簧模型，给出了具有任意裂纹数目的简支外伸梁弯曲挠度的显式解析解，研究了集中载荷作用下简支外伸梁裂纹诱导弦挠度函数的性质，给出了裂纹位置和裂纹等效扭转弹簧柔度的近似表达式，从而实现了梁横向裂纹位置及裂纹损伤程度的识别．在此基础上，为利用裂纹梁的测量挠度识别裂纹损伤，提出了分段线性函数的最佳拟合法，实现了简支外伸梁裂纹的损伤参数识别．通过数值试验验证了该识别方法的适用性和可靠性，考察了识别结果对梁挠度测量误差和裂纹深度的敏感性，结果表明随着挠度测量误差的增大，裂纹损伤参数识别误差增大，但裂纹损伤识别方法具有较强的鲁棒性，在工程实际中具有一定的应用性．     

基于等效弹簧模型的裂纹Euler-Bernoulli梁弯曲变形分析

考虑裂纹的缝隙效应,研究了开闭裂纹Euler-Bernoulli梁的弯曲变形．首先,将裂纹等效为内部旋转弹簧,利用广义函数,给出了考虑裂纹缝隙影响的Euler-Bernoulli梁的等效抗弯刚度,推导了具有任意数目开闭裂纹梁弯曲变形的显式通解．在此基础上,研究了均布载荷作用下上侧单裂纹简支梁以及裂纹处承受集中力和集中力偶共同作用的固支梁的弯曲变形,分析了梁长细比、裂纹深度和位置以及载荷等对裂纹开闭状态和梁弯曲变形的影响。结果表明：梁挠度分布在裂纹处存在尖点,而转角分布存在跳跃;梁挠度与载荷的响应关系一般为双折线形式,分别对应于裂纹的张开和闭合状态;且裂纹张开时,裂纹梁的柔度随着梁长细比的增加和裂纹深度的减小而减小。这些结果对梁裂纹无损检测具有指导意义．     

考虑界面滑移效应的组合裂纹梁弯曲解析解

将上部子梁的裂纹等效为线性扭转弹簧,考虑组合梁连接面的滑移位移,建立了以组合裂纹梁挠度和滑移位移为基本未知量的组合裂纹梁弯曲变形一维数学模型．利用Laplace变换及其逆变换,给出了组合裂纹梁弯曲变形一维数学模型的解析通解．在此基础上,研究了均布载荷作用下简支组合裂纹梁的弯曲变形问题,数值分析了连接面剪切刚度、裂纹深度、数目和位置等参数对组合裂纹梁弯曲变形的影响,结果表明：在裂纹处,组合裂纹梁挠度曲线存在尖点,而横截面转角曲线存在跳跃,且随着裂纹数目和深度的增加,挠度和横截面转角跳跃值增大;随着连接面剪切刚度的增加,挠度和横截面转角减小,并最终趋于定值．并且,随着组合梁跨高比的增加,连接面剪切刚度对梁挠度影响逐渐减弱．     

FRP加固金属裂纹板的断裂力学分析

传统的金属结构加固方法会形成新的疲劳源,而粘贴FRP加固则具有明显的优势．提出了“三维实体-弹簧-壳元”有限元模型,金属板采用三维实体单元, FRP采用壳单元,用弹簧单元来模拟FRP与金属板之间的胶层,对金属裂纹板粘贴FRP加固后的性能进行了线弹性断裂力学分析,并对影响金属板裂纹前缘应力强度因子的参数进行了讨论．分析结果表明,采用高弹性模量的FRP和增加FRP的厚度对改善加固效果非常明显．     

Bending of simply-supported circular timber beam strengthened with fiber reinforced polymer简

The bending behavior of the circular cross-section timber beam strengthened with a fiber reinforced polymer (FRP) sheet is investigated. The tight bonding is on the interface between the surface of a timber beam and the reinforcement layer of the FRP sheet. An analytical expression for the bending moment-curvature relation is presented, and its failure modes are analyzed. The governing equation for nonlinear small deflection of the FRP-strengthened circular timber beam is established, and the corresponding numerical method is given. The bending deformation of the simply-supported circular timber beam strengthened with the carbon fiber reinforced polymer (CFRP) sheet subject to a uniform load is studied numerically. The influence of the angle and thickness of the CFRP layer as well as the timber strength on the bending deflection of the FRP-strengthened circular timber beam is examined. It is revealed that, with the increases of the thickness and angle, the deflection of the CFRP-strengthened circular timber beam is decreased, and its carrying capacity and ductility are increased. However, when the angle of the layer reaches a certain value, the deflection will no longer decrease with the increase of the angle. At the same time, the nonlinear bending moment-curvature relation of the CFRP-strengthened circular timber beam is simplified as an approximate bilinear constitutive model. The approximate deflections of the simply-supported circular timber beam strengthened with the CFRP sheet are obtained. The results are compared with the linearly elastic bending and nonlinear bending models, showing that the mid-span deflections of a CFRP-strengthened circular timber beam with the approximate bilinear constitutive model are greater than those with the nonlinear constitutive model. The results of its stiffness analysis are on the safe side.     

Nonlinear stability of timber column strengthened with fiber reinforced polymer

By taking into account the effect of the bi-modulus for tension and compression of the fiber reinforced polymer (FRP) sheet in the reinforcement layer, a general mathematical model for the nonlinear bending of a slender timber beam strengthened with the FRP sheet is established under the hypothesis of the large deflection deformation of the beam. Nonlinear governing equations of the second order effect of the beam bending are derived. The nonlinear stability of a simply-supported slender timber column strengthened with the FRP sheet is then investigated. An expression of the critical load of the simply-supported FRP-strengthened timber beam is obtained. The existence of postbuckling solution of the timber column is proved theoretically, and an asymptotic analytical solution of the postbuckling state in the vicinity of the critical load is obtained using the perturbation method. Parameters are studied showing that the FRP reinforcement layer has great influence on the critical load of the timber column, and has little influence on the dimensionless postbuckling state.     

Nonlinear stability of timber column strengthened with fiber reinforced polymer

By taking into account the effect of the bi-modulus for tension and compression of the fiber reinforced polymer (FRP) sheet in the reinforcement layer, a general mathematical model for the nonlinear bending of a slender timber beam strengthened with the FRP sheet is established under the hypothesis of the large deflection deformation of the beam. Nonlinear governing equations of the second order effect of the beam bending are derived. The nonlinear stability of a simply-supported slender timber column strengthened with the FRP sheet is then investigated. An expression of the critical load of the simply-supported FRP-strengthened timber beam is obtained. The existence of postbuckling solution of the timber column is proved theoretically, and an asymptotic analytical solution of the postbuckling state in the vicinity of the critical load is obtained using the perturbation method. Parameters are studied showing that the FRP reinforcement layer has great influence on the critical load of the timber column, and has little influence on the dimensionless postbuckling state.     

Bending of Timoshenko beam with effect of crack gap based on equivalent spring model

Considering the effect of crack gap,the bending deformation of the Timoshenko beam with switching cracks is studied.To represent a crack with gap as a nonlinear unidirectional rotational spring,the equivalent flexural rigidity of the cracked beam is derived with the generalized Dirac delta function.A closed-form general solution is obtained for bending of a Timoshenko beam with an arbitrary number of switching cracks.Three examples of bending of the Timoshenko beam are presented.The influence of the beam’s slenderness ratio,the crack’s depth,and the external load on the crack state and bending performances of the cracked beam is analyzed.It is revealed that a cusp exists on the deflection curve,and a jump on the rotation angle curve occurs at a crack location.The relation between the beam’s deflection and load is bilinear,each part corresponding to an open or closed state of crack,respectively.When the crack is open,flexibility of the cracked beam decreases with the increase of the beam’s slenderness ratio and the decrease of the crack depth.The results are useful in identifying non-destructive cracks on a beam.     

基于等效黏性弹簧的黏弹性Timoshenko裂纹梁弯曲解析解

考虑裂纹的缝隙和黏性效应,将梁中横向裂纹等效为黏弹性扭转弹簧,利用广义Delta函数,给出了Laplace变换域内裂纹梁的等效抗弯刚度,得到了具有任意开闭裂纹数目且满足标准线性固体黏弹性本构的Timoshenko梁在时间域内的弯曲变形显式解析通解．在此基础上,通过两个数值算例,分析了时间、梁跨高比和裂纹深度等参数对黏弹性Timoshenko开裂纹梁弯曲变形的影响．结果表明：裂纹黏性对Timoshenko裂纹梁的弯曲具有显著的影响．相比于裂纹的弹性扭转弹簧模型,考虑裂纹黏性效应的黏弹性Timoshenko裂纹梁在裂纹处挠度尖点和转角跳跃现象十分明显．另外,由于横向剪切引起的附加变形,Timoshenko裂纹梁的稳态挠度与Euler-Bernoulli梁挠度的差值为常数,其大小与裂纹模型、梁跨高比或裂纹深度无关,这些结果对梁裂纹无损检测具有指导意义．     

基于均匀荷载面曲率的简支裂纹梁损伤识别

为了采用模态参数对结构裂纹进行定位与定量,基于集中柔度模型,采用无质量的扭转弹簧模拟裂纹,建立简支裂纹梁的振动微分方程。针对现有柔度曲率指标仅能判断裂纹的大致范围,基于线性插值理论,建立裂纹位置与相邻测点均匀荷载面曲率差的关系,提出裂纹进一步定位公式,实现裂纹位置的精确定位。针对现有大多数损伤识别方法无法实现裂纹的损伤定量,基于位移曲率与结构刚度和弯矩的关系,理论推导了均匀荷载面曲率的结构刚度损伤程度识别方法,基于弹簧串联原理和线刚度思想,首次提出串联等效线刚度模型,建立裂纹深度与均匀荷载面曲率的关系,实现裂纹深度的定量。通过简支裂纹梁数值算例,考虑多裂纹的损伤情况,验证了新方法对裂纹定位与定量的有效性。     

基于裂纹诱导弦挠度的梁开闭裂纹损伤识别

考虑裂纹缝隙效应,建立了Euler-Bernoulli梁中开闭裂纹位置、深度和初始张开角等损伤参数的识别方法．首先,基于梁中开闭裂纹的等效单向扭转弹簧模型,给出了开闭裂纹Euler-Bernoulli梁静力弯曲挠度的显式闭合解．在此基础上,证明了裂纹诱导弦挠度函数由分段三次多项式组成,并基于其构造特征,建立了基于测量挠度的梁中开闭裂纹位置、裂纹等效扭转弹簧柔度、裂纹初始张开角和裂纹上下侧属性等参数的数值识别方法．最后,通过数值实验考察了挠度测量误差和裂纹位置等对裂纹识别结果的影响,结果表明：裂纹位置、裂纹等效扭转弹簧柔度和裂纹初始张开角等的识别误差随挠度测量误差增大而增大,但裂纹识别结果具有较强的鲁棒性,在工程实际中具有一定的应用前景．     

Prediction of bond failure and deflection of carbon fiber-reinforced plastic reinforced concrete beams

Carbon fiber-reinforced plastic (CFRP) reinforced concrete beams can fail due to interface debonding, due to the high tensile strength of such rebars. A set of 16 concrete beams reinforced with different amounts of CFRP reinforcement was subject to static three-point bending. The beam dimensions and CFRP reinforcements used were selected to demonstrate a transition from compression failure to bond failure with decreasing reinforcement ratio. It is shown that accurate bond strength data to predict such failures can be obtained from a “hinged-beam” test configuration, rather than the conventional direct “pull-out” tests. Deflection under service loads can also be predicted more accurately using a proposed equation that includes the reinforcement ratio and the elastic modulus of the reinforcement.