| 张文福,方强,历昱秀,黄斌,章丛俊.集中荷载作用下跨中布置侧向支承简支梁临界弯矩[J].安徽建筑大学学报,2022,30(): |
| 集中荷载作用下跨中布置侧向支承简支梁临界弯矩 |
| Critical moment of simply supported beam with lateral support in the middle of span under concentrated load |
| 投稿时间：2021-06-11 修订日期：2021-10-12 |
| DOI： |
| 中文关键词: 简支梁 弯扭屈曲 侧向支承 板-梁理论 有限元法 |
| 英文关键词: Simply supported beam Flexural-torsional buckling Lateral support Plate-beam theory Finite element method |
| 基金项目:国家自然科学(51578120);国家自然科学(51178087) |
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| 中文摘要: |
| 基于板-梁理论,运用双变量的总势能方程,采用无穷项的三角级数表达精确模态函数,运用能量变分法,建立集中荷载作用下跨中布置侧向平移约束支承工字型简支梁弯扭屈曲总势能方程,引入无量纲的参数,依据势能驻值原理,获得简支梁弯扭屈曲的无量纲的临界弯矩解析解。再利用有限元软件验证理论解的正确性。结果表明：无量纲的临界弯矩计算公式得出的理论解与有限元解吻合较好,误差在±5%以内,可为工程设计提供参考,而规范所给的解过于保守。可以依据该理论求得在跨间任意位置侧向支承的简支梁弯扭屈曲的解析解。 |
| 英文摘要: |
| Based on the plate-beam theory, the total potential energy equation of bivariate and the trigonometric series of infinite terms are used to express the exact modal function. The energy variational method is used to establish the total potential energy equation of bending and torsional buckling of I-shaped simply supported beams with lateral translational restrained braces under concentrated load, The analytical solution of the critical moment of dimension one for the flexural torsional buckling of simply supported beams is obtained. The correctness of the theoretical solution is verified by the finite element software. The results show that the theoretical solution of the critical moment formula of dimension one is in good agreement with the finite element solution, and the error is less than 0 ± 5%, which can provide reference for engineering design, But the solution given by the criterion is too conservative. Based on this theory, the analytical solution of the flexural torsional buckling of simply supported beams with lateral supports at any position between spans can be obtained. |
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