摘要
求解等跨等截面连续梁的变形和内力是土木工程领域的典型问题.基于Euler–Bernoulli梁理论,利用位移法和辅助数列推导出任意跨数的等跨等截面连续梁梁端转动刚度的解析表达式,进而得到连续梁支点转角、弯矩在跨中集中荷载、满跨均布荷载、竖向温差作用下的通用计算公式.研究表明:当跨数趋于无穷大时,等跨等截面连续梁的梁端转动刚度上限值为单跨梁抗弯线刚度的2√3倍.不同跨数的等跨等截面连续梁可采用形式统一的解析公式计算支点转角和弯矩,不同静力荷载作用结果的区别仅由单跨梁的固端弯矩决定.所得公式形式简洁、通用性强、应用方便,能揭示跨数对连续梁力学特性的影响规律,亦可用于分析顶推施工导梁参数优化等实际工程问题.
Solving the deformation and internal force of a prismatic multispan continuous beam of equal spans is a fundamental and classic problem in the area of civil engineering.Based on the Euler–Bernoulli beam theory,this paper presents unified analytical formulas to calculate the member-end rotation and bending moment of prismatic continuous beams of equal spans.First,simple closed-form expressions to determine the beam-end rotational stiffness of an equal-span prismatic continuous beam comprising any number of spans are derived using the displacement method in structural mechanics and the auxiliary series in mathematics.Furthermore,the rotational stiffness formulas are used to derive the analytical formulas for determining the joint rotation and bending moment at the supports of continuous beams subjected to various types of static loads and actions,such as a single point load applied at mid-span,distributed load applied over the span length,and differential temperature change between the top and bottom surfaces of the beam.Moreover,the implications of the proposed formulas on some interesting academic problems are thoroughly discussed.It is observed that as the number of spans goes infinity,the beam-end rotational stiffness of an equal-span prismatic continuous beam approaches the upper 2√3 limit of i0,where i0 denotes the linear stiffness,which is the product of the modulus of elasticity(E)and the moment of inertia(I)divided by the length(l0)of the member of single-span beams.For equal-span prismatic continuous beams with various spans,the analytical formulas of the joint rotation and bending moment at the supports have unified expressions,while the difference between formulas for different static loads and actions is solely dependent on the fixed-end bending moment of single-span beams.This set of formulas reveals the advantages of concise form,general applicability,and convenient calculation.They can reveal the influence of the number of spans on the mechanical characteristics of continuous beams and analyze r
作者
周毅
岳清瑞
潘旦光
兰成明
ZHOU Yi;YUE Qingrui;PAN Danguang;LAN Chengming(School of Civil and Resource Engineering,University of Science and Technology Beijing,Beijing 100083,China;Research Institute of Urbanization and Urban Safety,University of Science and Technology Beijing,Beijing 100083,China)
出处
《工程科学学报》
EI
CSCD
北大核心
2023年第11期1970-1976,共7页
Chinese Journal of Engineering
基金
国家自然科学基金资助项目(52192662)
佛山市科技创新专项资金资助项目(BK20BE008,BK21BE014)。
关键词
连续梁
转角
弯矩
解析公式
结构力学
continuous beams
rotation
bending moment
analytical formula
structural mechanics
