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

Abstract

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

CLC Number:

TU311

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.

Figures/Tables 11

Fig. 1

Table 1

Practical analytical solution of horizontal thrust influence line"

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

Table 1

Fig. 2

Table 2

Fig. 3

Fig. 4

Table 3

Calculation formulas of self-displacement and load-displacement of damage"

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

Table 3

Table 4

Fig. 5

Fig. 6

Fig. 7

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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%

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

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