Pasternak地基上连续裂纹Euler梁的弯曲  

Bending of Continuous Cracked Euler Beam on Pasternak Foundation

作　　者：孔婷婷 郑超引 杨骁 KONG Tingting;ZHENG Chaoyin;YANG Xiao(Zhejiang Industry Polytechnic College,Shaoxing 312000,Zhejiang,China;Shanghai Customs College,Shanghai 201204,China)

机构地区：[1]浙江工业职业技术学院,浙江绍兴312000 [2]上海海关学院,上海201204

出　　处：《力学季刊》2023年第4期978-989,共12页Chinese Quarterly of Mechanics

基　　金：上海市自然科学基金(18ZR1414500)。

摘　　要：基于梁中开裂纹的等效线性扭转弹簧模型,并将梁跨内支座约束解除,代之以未知约束反力,给出了Pasternak地基上具有任意裂纹数目的多跨连续梁静力弯曲的解析通解.在此基础上,利用梁边界条件及跨内支座处挠度约束条件,得到了Pasternak地基上两等跨简支连续裂纹梁的弯曲挠度,数值考察了地基反力系数、裂纹数目、深度和位置等参数对连续裂纹梁弯曲变形的影响,结果表明:在裂纹处,Pasternak地基上连续裂纹Euler梁挠度存在尖点,而横截面转角存在跳跃,并且随着裂纹深度的增加和地基反力系数的减小,裂纹梁挠度和转角增加;当裂纹深度较小时,裂纹位置对连续地基裂纹梁挠度的影响有限,但随着裂纹深度的增加,裂纹位置对连续地基裂纹梁挠度影响逐渐显著.这些结论对地基梁健康检测和安全评估具有一定指导意义.Based on the linear torsional spring model of a beam with cracks,through removing the constraints of internal supports and replacing them with unknown reaction forces,the general analytical solution of continuous multi-span Euler beam with arbitrary number of open cracks on Pasternak foundation was given.Based on this,the bending deflection of two equi-span continuous cracked beam on Pasternak foundation was obtained utilizing the boundary conditions and the deflection constraints at internal supports of the beam,and the influences of the foundation reaction coefficients,the numbers of crack,as well as the depth and location of the cracks on the bending deformation of the continuous cracked beam were analyzed numerically.It indicates that,there exist deflection cusps and rotation angle jumps in the cracked Euler beam on Pasternak foundation at the crack location,and the deflection and rotation angle increase with the increase of crack depth or the decrease of the foundation reaction coefficients.When the crack depth is small,the influence of crack location on the deflection of the cracked beam on continuous foundation is not evident.With the increase of the crack depth,the influence of the crack location becomes more remarkable.These conclusions can provide certain guidance for the health detection and the safety evaluation of the beams on foundation.

关 键 词：Pasternak基础 连续裂纹Euler梁 广义函数 解析解 参数研究 

分 类 号：TU223[建筑科学—建筑设计及理论] TU317