| 张文福,方强,刘迎春,历昱秀,黄斌.集中荷载作用下跨中布置侧向支承简支钢梁的临界弯矩分析[J].安徽建筑大学学报,2023,31(1):10-17 |
| 集中荷载作用下跨中布置侧向支承简支钢梁的临界弯矩分析 |
| Critical Moment Analysis of Simply Supported Steel Beam With Lateral Support in the Middle of Span Under Concentrated Load |
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| 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:国家自然科学基金项目（52178143） |
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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来表达精确模态函数，建立集中荷载作用下跨中布置侧向支承工字形简支梁弯扭屈曲的无量纲总势能方程。依据能量变分法，获得简支梁弯扭屈曲的无量纲的临界弯矩方程解析解，并利用 ANSYS 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，最大误差为 4.26%，可为工程设计提供参考；对于侧向支承布置在下翼缘情况，规范解与有限元解误差较大，要么过于保守（最大误差为 90.03%），要么过于不安全（最大误差为 -45.13%）。此问题需要引起工程师和规范编制者的足够重视。 |
| 英文摘要: |
| Based on the plate beam theory， using the bi-variable total potential energy equation and using the infinite trigonometricseries to express the accurate modal function，the dimensionless total potential energy equation for the flexural-torsional buckling（LTB）of simply supported I-beams with lateral supports in the midspan under concentrated load is established. Based on the energy variationmethod，the dimensionless analytical solution of the critical moment equation for LTB of simply supported beams is obtained， and thecorrectness of the theoretical solution is verified by ANSYS finite element software. The results show that：(1) the theoretical solution ofthe dimensionless critical bending moment formula is in good agreement with the finite element solution，with a maximum error of 4.26%，which can provide reference for engineering design；(2) when the lateral support is arranged at the lower flange，the error between thespecification solution and the finite element solution is large，either too conservative（maximum error is 90.03%）or too unsafe（maximumerror is -45.13%）. This problem needs to be paid enough attention by engineers and specification compilers. |
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