波形钢腹板组合梁弯曲变形的三角级数解

叶华文; 王力武; 张庆; 徐勋; 卫星

doi:10.3969/j.issn.0258-2724.20170277

波形钢腹板组合梁弯曲变形的三角级数解

doi: 10.3969/j.issn.0258-2724.20170277

基金项目: 国家自然科学基金资助项目（51408501）；四川省科技计划资助（2019YJ0223）

详细信息

作者简介:
叶华文（1982—），男，副教授，硕士生导师，研究方向为桥梁工程，E-mail：hwye@swjtu.edu.cn

中图分类号: TU311.4
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- 文章访问数: 514
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- PDF下载量: 18
- 被引次数: 0
出版历程
- 收稿日期: 2017-04-14
- 修回日期: 2017-05-30
- 网络出版日期: 2019-04-25
- 刊出日期: 2019-08-01

Trigonometric Series Solution of Bending Deformation for Composite Beam with Steel Corrugated Webs

摘要

摘要: 为研究波形钢腹板剪切变形对波形钢腹板组合梁弯曲变形行为的影响，采用三角级数拟合简支波形钢腹板组合梁的变形曲线，各构件弯曲变形满足平截面假定，基于最小势能原理，推导了简支和悬臂波形钢腹板组合梁分别在均布荷载和集中荷载作用下的弯曲变形解析解和简化解；基于简化解推导出考虑剪切变形的波形钢腹板组合梁挠度增大系数，并给出对考虑剪切变形影响与否的高跨比界限；采用有限元方法验证了解析解和简化解的正确性和适用性. 研究结果表明：所提方法边界条件明确、推导过程简单、结果可靠、适用性强，可为波形钢腹板组合梁的设计和变形计算提供可靠的依据.
- 波形钢腹板组合梁 /
- 弯曲变形 /
- 最小势能原理 /
- 三角级数解 /
- 剪切变形
Abstract: In order to study the influence of shear deformation on the bending deformation of composite beams with steel corrugated steel webs, trigonometric series solution was introduced to simulate the deformation of the components (web and flange) of the beam according to the plane-section assumption, and a theoretical model was presented on the basis of the principle of minimum potential energy. Then, analytical solutions and respective simplified forms were derived for simply supported and cantilever corrugated steel web girder cases under uniform distribution and mid-span concentrated load. Furthermore, a limit value of depth-span ratio was suggested to estimate the influence of shear deformation with regard to magnifying coefficient of deflection. Validity and usability of the analytical solution and the model were determined by the finite element method. The results show that the presented method has advantages of ease in boundary condition and deduce, high reliability and universal applicability, and can be referred for deflection design of steel corrugated steel web beam.
- composite beam with steel corrugated web /
- bending deformation /
- principle of minimum potential energy /
- trigonometric series solution /
- shear deformation

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图 1 波形钢腹板组合梁弯曲变形分析

Figure 1. Bending deformation of composite beam with steel corrugated web

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图 2 计算梁截面几何尺寸与有限元模型

Figure 2. Cross section and FEM model of the analysis beam

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图 3 简支梁与悬臂梁挠度比较分析

Figure 3. Deflection of simply supported and cantilever beams

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图 4 截面应变分布

Figure 4. Stress distribution in the cross section

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图 5 挠度解析解与简化解比较分析

Figure 5. Comparison of deflections from simplified method and analytical solution

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表 1 挠度计算值与实测值比较

Table 1. Comparison of predicted andexperimental deflections

试验	加载位置及方式	荷载/kN	f_t	f_tr	f_tr/f_t	f_th	f_th/f_t	f_j	f_tr/f_j
李宏江等^[4]	跨中单点加载	15	0.41	0.30	0.72	0.46	1.12	0.60	1.46
		20	0.56	0.40	0.71	0.61	1.09	0.80	1.43
		25	0.70	0.50	0.71	0.77	1.10	1.00	1.43
李宏江等^[12]	跨中单点加载	5	0.22	0.20	0.90	0.22	1.00	0.26	1.18
		10	0.48	0.40	0.83	0.44	0.92	0.52	1.08
		20	1.01	0.80	0.79	0.88	0.87	1.04	1.03
		30	1.41	1.19	0.85	1.33	0.94	1.58	1.12
		40	2.04	1.59	0.78	1.77	0.87	2.11	1.03
李立峰、刘志才、王芳等^{[6, 13-14]}	梁 A 跨中单点加载	11.6	0.53	0.51	0.96	0.56	1.06	0.62	1.16
		15.3	0.69	0.67	0.98	0.74	1.08	0.81	1.18
		20.3	0.92	0.89	0.97	1.04	1.13	1.07	1.16
		25.2	1.14	1.11	0.97	1.29	1.13	1.34	1.17
		30.1	1.36	1.33	0.98	1.54	1.13	1.60	1.18
		35	1.58	1.54	0.98	1.79	1.13	1.86	1.18
李立峰、刘志才、王芳等^{[6, 13-14]}	梁 B 跨中单点加载	10.5	0.47	0.50	1.05	0.56	1.20	0.59	1.26
		15.6	0.67	0.74	1.10	0.84	1.25	0.88	1.31
		20.3	0.88	0.96	1.09	1.09	1.24	1.14	1.30
		25.2	1.13	1.19	1.05	1.35	1.20	1.42	1.26
		30.4	1.38	1.43	1.04	1.63	1.18	1.71	1.24
		35.1	1.61	1.66	1.03	1.88	1.17	1.97	1.22
		40.4	1.85	1.91	1.03	2.22	1.20	2.28	1.23
Huang等^[15]	两点对称加载	50	0.26	0.18	0.68	0.27	1.02	0.28	1.08
Metwally等^[16]	A80 两点对称加载	100	3.39	1.65	0.49	3.08	0.91	3.66	1.08
	A110 两点对称加载	80	2.72	1.32	0.49	2.46	0.90	2.93	1.08
	A175 两点对称加载	60	2.37	0.99	0.42	1.85	0.78	2.19	0.92
	A215 两点对称加载	40	1.67	0.66	0.40	1.29	0.77	1.43	0.86

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文章访问数: 514
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波形钢腹板组合梁弯曲变形的三角级数解

doi: 10.3969/j.issn.0258-2724.20170277

作者简介: 叶华文（1982—），男，副教授，硕士生导师，研究方向为桥梁工程，E-mail：hwye@swjtu.edu.cn

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Trigonometric Series Solution of Bending Deformation for Composite Beam with Steel Corrugated Webs

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作者简介:
叶华文（1982—），男，副教授，硕士生导师，研究方向为桥梁工程，E-mail：hwye@swjtu.edu.cn