变截面两铰拱推力影响线解析解及损伤识别应用

doi:10.13229/j.cnki.jdxbgxb.20230086

吉林大学学报(工学版) ›› 2025, Vol. 55 ›› Issue (2): 664-672.doi: 10.13229/j.cnki.jdxbgxb.20230086

• 交通运输工程·土木工程 • 上一篇

变截面两铰拱推力影响线解析解及损伤识别应用

周宇^1,^2,³(),李萌^2,³,狄生奎¹,石贤增²,陈东²

^1.兰州交通大学土木工程学院，兰州 730070
^2.安徽建筑大学土木工程学院，合肥 230601
^3.安徽建筑大学建筑健康监测与灾害预防技术国家地方联合工程实验室，合肥 230601

收稿日期:2023-02-05 出版日期:2025-02-01 发布日期:2025-04-16
作者简介:周宇（1989-），男，副教授，博士.研究方向：结构健康监测与桥梁性能评估.E-mail：yuzhou923@outlook.com
基金资助:
国家自然科学基金项目(51868045);安徽省高校省级自然科学研究项目-重点项目(2022AH050248);甘肃省建设科技项目(JK2023-03);建筑健康监测与灾害预防国家与地方联合工程实验室开放课题项目(GG22KF002);安徽省高校优秀拔尖人才培育项目(gxgnfx2022021);企业委托技术开发课题项目(HYB20220240)

Analytical solution of thrust influence line of variable section two-hinged arch and application of damage identification

Yu ZHOU^1,^2,³(),Meng LI^2,³,Sheng-kui DI¹,Xian-zeng SHI²,Dong CHEN²

^1.School of Civil Engineering，Lanzhou Jiaotong University，Lanzhou 730070，China
^2.School of Civil Engineering，Anhui Jianzhu University，Hefei 230601，China
^3.National and Local Joint Engineering Laboratory of Building Health Monitoring and Disaster Prevention Technology，Anhui Jianzhu University，Hefei 230601，China

Received:2023-02-05 Online:2025-02-01 Published:2025-04-16

摘要/Abstract

摘要：

针对变截面两铰拱水平推力影响线解析研究仍不完善的现状，围绕变截面两铰拱在抛物线、悬链线两种线型下的推力影响线解析解推导与应用展开研究，利用Ritter公式确立拱圈截面变化规律，对变截面两铰拱进行曲线积分，基于力法原理提出两种线型的变截面两铰拱水平推力影响线解析解，进而提取损伤前后两铰拱结构推力影响线差值曲率损伤识别指标，提出基于推力影响线的变截面两铰拱损伤识别新方法，对比有限元结果表明：推力影响线解析解与有限元计算偏差在8.5％以内，通过有限元算例验证了本文方法可以实现两铰拱结构损伤定位，可作为拱结构在移动荷载作用下的拱座基础强度设计依据与拱桥快速检测应用理论参考。

关键词: 结构工程, 变截面拱, 两铰拱, 推力影响线, Ritter公式, 损伤识别

Abstract:

Analytical research on the horizontal thrust influence line of the variable cross section two-hinged arch is still imperfect， this study focuses on the derivation and application of the analytical solution of the thrust influence line of the variable cross section two-hinged arch under parabola and catenary. Ritter's formula is used to establish the variation rule of the arch ring section， and the curve integration of the variable cross section two-hinged arch is carried out. Put forward on the basis of the principle of force method of two kinds of linear variable cross-section two hinged arch horizontal force influence line analytical solution， compared with the finite element results show that the proposed formula and finite element calculation error within 8.5%， and then extract the two foot arch structure before and after damage force influence line difference curvature damage identification index， based on force influence line， a new method of variable cross-section two hinged arch damage identification， The finite element example verifies that the proposed method can realize the damage location of the two-hinged arch structure， which can be used as the basis for the arch foundation strength design under the action of moving loads and the theoretical reference for the rapid detection application of arch Bridges.

Key words: structural engineering, variable section arch, two-hinged arch, thrust influence line, ritter formula, damage identification

中图分类号:

TU311

周宇,李萌,狄生奎,石贤增,陈东. 变截面两铰拱推力影响线解析解及损伤识别应用[J]. 吉林大学学报(工学版), 2025, 55(2): 664-672.

Yu ZHOU,Meng LI,Sheng-kui DI,Xian-zeng SHI,Dong CHEN. Analytical solution of thrust influence line of variable section two-hinged arch and application of damage identification[J]. Journal of Jilin University(Engineering and Technology Edition), 2025, 55(2): 664-672.

图/表 11

图1

表1

水平推力影响线实用解析解"

抛物线	悬链线
$[25 L 5 + 7 L 4 (n - 1) x p - 30 L 3 x p 2 - 10 L 2 (n - 1) x p 3 + 5 L x p 4 + 3 (n - 1) x p 5] / 64 f L 4$	$- 2 (m 2 - 2 m + 1) {- [(k + 2 n - 2) L + k x p (n - 1)] L 2 e - k x p / L - [(k - 2 n + 2) L + k x p (n - 1)] L 2 e k x p / L + [k L + x p (n - 1) (k + 2)] L 2 e - k + [k L + x p (n - 1) (k - 2)] L 2 e k - k 3 m (L - x p) (x p + L) (L + n x p / 3 - x p / 3)} / f L 2 k 2 (m - 1) (8 k m 2 + 8 e - k m - 8 e k m - e - 2 k + e 2 k + 4 k)$

表1

图2

表2

图3

图4

表3

损伤时的自变位和载变位的计算式"

变位	计算式
$δ 11'$	$∫ - L b - ε (y - f) 2 E I c o s φ d x + ∫ b - ε b + ε (y - f) 2 E' I c o s φ d x + ∫ b - ε L (y - f) 2 E I c o s φ d x$
$Δ 1 p'$	$- L ≤ x p < b - ε$	$∫ - L x p (y - f) M p E I c o s φ d x + ∫ x p b - ε (y - f) M p E I c o s φ d x + ∫ b - ε b + ε (y - f) M p E' I c o s φ d x + ∫ b + ε L (y - f) M p E I c o s φ d x$
	$b - ε ≤ x p ≤ b + ε$	$∫ - L b - ε (y - f) M p E I c o s φ d x + ∫ b - ε x p (y - f) M p E' I c o s φ d x + ∫ x p b + ε (y - f) M p E' I c o s φ d x + ∫ b + ε L (y - f) M p E I c o s φ d x$
	$b + ε < x p ≤ L$	$∫ - L b - ε (y - f) M p E I c o s φ d x + ∫ b - ε b + ε (y - f) M p E' I c o s φ d x + ∫ b + ε x p (y - f) M p E I c o s φ d x + ∫ x p L (y - f) M p E I c o s φ d x$

表3

表4

图5

图6

图7

参考文献 16

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矢跨比	荷载作用位置x_p	抛物线			悬链线
矢跨比	荷载作用位置x_p	公式解/kN	有限元/kN	相对误差/%	公式解/kN	有限元/kN	相对误差/%
1/4	±l/8	0.270 7	0.295 6	-8.425	0.266 0	0.289 0	-7.934
	±2l/8	0.512 7	0.553 8	-7.425	0.502 6	0.541 6	-7.192
	±3l/8	0.693 3	0.732 1	-5.296	0.678 3	0.718 8	-5.640
	4l/8	0.781 3	0.797 5	-2.042	0.763 9	0.784 6	-2.637
1/5	±l/8	0.338 3	0.365 3	-7.377	0.332 5	0.361 0	-7.874
	±2l/8	0.640 9	0.686 7	-6.668	0.628 3	0.676 6	-7.136
	±3l/8	0.866 7	0.913 8	-5.153	0.847 8	0.898 0	-5.590
	4l/8	0.976 6	0.998 4	-2.189	0.954 9	0.980 2	-2.587
1/6	±l/8	0.406 0	0.438 0	-7.304	0.399 0	0.432 8	-7.807
	±2l/8	0.769 0	0.823 4	-6.598	0.753 9	0.811 3	-7.071
	±3l/8	1.040 0	1.095 7	-5.087	1.017 4	1.076 9	-5.524
	4l/8	1.171 9	1.197 3	-2.122	1.145 8	1.175 5	-2.520
1/7	±l/8	0.473 7	0.510 5	-7.221	0.465 5	0.504 6	-7.731
	±2l/8	0.897 2	0.959 8	-6.517	0.879 6	0.945 7	-6.994
	±3l/8	1.213 3	1.277 3	-5.008	1.187 0	1.255 3	-5.446
	4l/8	1.367 2	1.395 7	-2.042	1.336 8	1.370 2	-2.440
1/8	±l/8	0.541 3	0.582 9	-7.129	0.532 1	0.576 1	-7.643
	±2l/8	1.025 4	1.095 8	-6.425	1.005 3	1.079 8	-6.906
	±3l/8	1.386 7	1.458 3	-4.915	1.356 5	1.433 3	-5.356
	4l/8	1.562 5	1.593 5	-1.947	1.527 8	1.564 5	-2.346

损伤工况	损伤位置	损伤单元	损伤程度
单点损伤	1/2跨	54#	20%、30%、40%、50%、60%、70%、80%、90%
多点损伤	1/4跨	27#、28#	20%、30%、40%、50%、60%、70%、80%、90%
多点损伤	3/4跨	81#、82#	20%、30%、40%、50%、60%、70%、80%、90%

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变截面两铰拱推力影响线解析解及损伤识别应用

Analytical solution of thrust influence line of variable section two-hinged arch and application of damage identification

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