基于力法的格构梁节点荷载分配方法及悬臂段长度优化设计  

Load distribution method at the node based on the force method and optimum design of cantilever length for lattice beam

作　　者：樊军伟 杨仕教 邓波 孙冰 王东星 FAN Junwei;YANG Shijiao;DENG Bo;SUN Bing;WANG Dongxing(School of Resource Environment and Safety Engineering,University of South China,Hengyang 421001,China;School of Civil Engineering,University of South China,Hengyang 421001,China)

机构地区：[1]南华大学资源环境与安全工程学院,湖南衡阳421001 [2]南华大学土木工程学院,湖南衡阳421001

出　　处：《自然灾害学报》2024年第2期113-121,共9页Journal of Natural Disasters

基　　金：国家自然科学基金项目(52079098,52308356);湖南省自然资源厅科研项目(20230144DZ);衡阳市科技创新计划项目(202250045321)。

摘　　要：格构梁节点荷载简化分配方法的不足在于无法考虑2个方向的梁上其他节点荷载的影响且对文克尔(Winkler)地基上梁的类型进行了主观假定。为克服格构梁节点荷载简化分配方法的上述缺点,提出了一种基于力法的格构梁节点荷载分配方法。根据节点静力平衡条件及变形协调条件,新的格构梁节点荷载分配方法通过构建并求解线性方程组,能够合理地将作用在节点的集中力分别分配给2个方向的纵梁和横梁。进一步地,引入一个格构梁边坡锚固案例并等比例地增加纵梁和横梁的悬臂长度。不同基床系数条件下,基于新的节点荷载分配方法将格构梁节点荷载分配给纵梁和横梁,然后对各梁单独进行弯矩计算。以悬臂最大正弯矩与跨中最大负弯矩比值的绝对值接近1为评价指标,对格构梁最优悬臂长度进行了评价。节点荷载分配结果表明,随着悬臂长度的增加,分配给纵梁和横梁的荷载逐渐趋于稳定。弯矩计算结果表明,随着基床系数的增大,悬臂长度对格构梁弯矩的影响逐渐减弱。不同边坡基床系数条件下,当悬跨比在0.2~0.4之间时,悬臂各梁最大正弯矩与跨中最大负弯矩趋于均衡。因此,基于力法理论的节点荷载分配方法的提出为格构梁内力的精确分析及悬臂长度优化设计提供了可靠的理论依据。The disadvantages of the simplified load distribution method for lattice beam are its inability to consider the effects of loads acting on other nodes of the beam in both directions,and subjective assumptions about the type of beams on Winkler foundation.To overcome the above disadvantages of the simplified load distribution method for lattice beam,a load distribution method is proposed based on the force method.According to the static equilibrium conditions and the deformation compatibility conditions at the nodes,the new load distribution method can distribute the loads acting on the nodes to the vertical beams and the cross beams running in both directions respectively,by constructing and solving a system of linear equations.In addition,this paper introduced a case of a slope reinforced by lattice beams,and the cantilever lengths of the vertical beams and cross beams were proportionally increased.Under the conditions of different subgrade reaction coefficients,the loads acting on the nodes of the lattice beams were assigned to the vertical beams and the cross beams based on the new load distribution method,and the bending moments of each beam were calculated separately.Using the absolute value of the ratio between the maximum positive bending moment of the cantilever and the maximum negative bending moment at the mid-span close to 1 as the evaluation index,the optimum cantilever lengths of the lattice beam were evaluated.The load distribution results show that the loads assigned to the vertical beams and the cross beams gradually become more constant as the cantilever lengths increase.The bending moment results show that the influence of the cantilever lengths on the bending moments gradually decreases as the subgrade reaction coefficient increases.Under the conditions of different subgrade reaction coefficients,the maximum positive bending moment of the cantilever and the maximum negative bending moment at the mid-span of each beam tend to be equal when the cantilever span ratio is between 0.2 and 0.4.Therefo

关 键 词：格构梁 荷载分配方法 力法 悬臂长度 优化设计 文克尔地基模型 边坡工程 

分 类 号：TU318[建筑科学—结构工程]