Mechanism and Mechanical Characteristics of Cable-Catenary Arch Combined Structure

doi:10.12141/j.issn.1000-565X.230566

Abstract

Abstract:

With the increase of traffic volume and overloading of vehicles, the mechanical properties of early arch bridges under live load can no longer satisfy the needs of modern traffic due to low design load grade, lack of effective maintenance and long term operation. To improve the mechanical performance of this kind of arch bridges, this paper proposed a cable-catenary arch combined structure. The cables were symmetrically arranged on both sides of the arch rib to form a new force system, which could change the force transmission path of the catenary arch structure and reduce the internal force of the arch structure. Under the mechanical diagram of cable-arch combined structure, the force equation of the cable-arch combined structure was established based on the elastic center method, and the analytical solution of the internal force of the arch rib was deduced by the approximate curve integration method under the vertical moving load. The reliability of the analytical solution was verified by ANSYS finite element analysis software, and the influences of design parameters such as cable constraint position, arch-axis coefficient, rise-span ratio, and axial stiffness ratio on the internal force of the arch structure under lane loading were analyzed. The mechanical properties and internal variation rules of the cable-arch combined structure were revealed. The results show that the relative error between the analytical solution of the internal force and the finite element result is within 1%. The setting of the cable changes the positive and negative interval distribution of the bending moment influence line value of the arch structure, and effectively reduces the peak value of the bending moment influence line of the arch structure, which can greatly reduce the overall bending moment of the arch structure and make the bending moment distribution more uniform. From the arch foot to the arch crown, the reduction of the bending moment and the growth of the axial force of the arch structure gradually decrease. As the axial stiffness ratio increases from 0.02 to 0.10, the negative bending moment of the arch foot decreases nonlinearly, with the maximum decrease of 63.7%; the increase of the cable force is inversely proportional to its value, and when the cables are set at 0.3L (L is the span of the arch) from the arch crown, the cable force can be increased to 1.9 times that at the axial stiffness ratio of 0.02. The influence of the rise-span ratio on the internal force of the arch structure cannot be ignored. The greater the rise-span ratio is, the greater the change in internal force of the arch structure is. The effect of arch-axis coefficient on the internal force of the arch structure can be neglected.

Key words: cable-arch combined action, arch bridge reinforcement, catenary arch, rise-span ratio, arch-axis coefficient, internal force influence line, analytical solution

CLC Number:

U441

HAO Tianzhi, LI Chunhua, YANG Tao, LONG Xiayi, DENG Nianchun. Mechanism and Mechanical Characteristics of Cable-Catenary Arch Combined Structure[J]. Journal of South China University of Technology(Natural Science Edition), 2024, 52(8): 89-102.

Figures/Tables 13

Fig.1

Fig.2

Fig.3

Table 1

Internal forces of basic structure under redundant force and external load"

内力	$X 1$	$X 2$	$X 3$	$X 4$		单位移动荷载
内力	$X 1$	$X 2$	$X 3$	$x 1 ≥ x$	$x 1 < x$	$x p ≥ x$	$x p < x$
弯矩	$M ¯ 1$ = 1	$M ¯ 2$ = $y - y s$	$M ¯ 3$ = $± x$	$M ¯ 4$ = 0	$M ¯ 4 = y c o s α - L / 2 - x s i n α$	$M p$ = 0	$M p = - x - x p$
轴力	$N ¯ 1$ = 0	$N ¯ 2$ = $c o s φ$	$N ¯ 3$ = $∓ s i n φ$	$N ¯ 4$ = 0	$N ¯ 4 = c o s α + φ$	$N p$ = 0	$N p = s i n φ$
剪力	$Q ¯ 1$ = 0	$Q ¯ 2$ = $± s i n φ$	$Q ¯ 3 =$ $c o s φ$	$Q ¯ 4$ = 0	$Q ¯ 4 = s i n α + φ$	$Q p$ = 0	$Q p = ∓ c o s φ$

Table 1

Table 2

Explicit solution of constant displacement and load displacement"

参数	物理意义	参数表达式
$δ 11$	常变位	$L E I ∑ i = 1 4 1 2 i - 1 λ i - 1$
$δ 22$		$L E I ∑ i = 1 4 f 2 λ i - 1 m - 1 2 ∑ j = 1 3 1 2 i + 4 j - 1 n j 2 + 2 n 1 n 2 n 3 ∑ j = 1 3 1 n j 1 2 i - 2 j + 11 - 2 y s f λ i - 1 m - 1 ∑ j = 1 3 1 2 i + 2 j - 1 n j + b ω i - 1 + y s 2 λ i - 1 2 i - 1$
$δ 33$		$L E I ∑ i = 1 4 L 2 4 2 i + 1 λ i - 1 + b 2 i - 1 λ i - 1 - ω i - 1$
$δ 44$		$L 2 E I ∑ i = 1 4 L 2 λ i - 1 s i n 2 α 4 ∑ j = 1 3 1 - ξ 1 2 i + j - 2 2 i + j - 2 - 1 - ξ 1 2 i 2 i / 3 + L f λ i - 1 s i n 2 α 4 m - 1 ∑ j = 1 3 n j 1 - ξ 1 2 i + 2 j i + j - 2 - 2 ξ 1 2 i + 2 j - 1 2 i + 2 j - 1 + f 2 λ i - 1 c o s 2 α m - 1 2 ∑ j = 1 3 1 - ξ 1 2 i + 4 j - 1 2 i + 4 j - 1 n j 2 + 2 n 1 n 2 n 3 ∑ j = 1 3 1 n j 1 - ξ 1 2 i - 2 j + 11 2 i - 2 j + 11 + b 1 - ξ 1 2 i - 1 2 i - 1 ω i - 1 c o s 2 α + λ i - 1 s i n 2 α - ω i - 1 s i n 2 α - 1 - ξ 1 2 i 2 i ρ i - 1 s i n 2 α + b L c t E I$
$δ 14$ / $δ 41$	常变位	$L 2 E I ∑ i = 1 4 f λ i - 1 c o s α m - 1 ∑ j = 1 3 1 - ξ 1 2 i + 2 j - 1 2 i + 2 j - 1 n j - L λ i - 1 s i n α 2 1 - ξ 1 2 i - 1 2 i - 1 - 1 - ξ 1 2 i 2 i + 1 - ξ 1 b c o s α - b η s i n α c o s h k - c o s h k ξ 1 k$
$δ 24$ / $δ 42$		$L 2 E I ∑ i = 1 4 L y s λ i - 1 s i n α 2 1 - ξ 1 2 i - 1 2 i - 1 - 1 - ξ 1 2 i 2 i + L f λ i - 1 s i n α 4 m - 1 ∑ j = 1 3 1 - ξ 1 2 i + 2 j i + j n j - f λ i - 1 c o s α m - 1 L 2 t a n α + y s ∑ j = 1 3 1 - ξ 1 2 i + 2 j - 1 2 i + 2 j - 1 n j + f 2 λ i - 1 c o s α m - 1 2 ∑ j = 1 3 1 - ξ 1 2 i + 4 j - 1 2 i + 4 j - 1 n j 2 + 2 n 1 n 2 n 3 ∑ j = 1 3 1 n j 1 - ξ 1 2 i - 2 j + 11 2 i - 2 j + 11 + b 1 - ξ 1 2 i - 1 2 i - 1 ω i - 1 c o s α - 1 - ξ 1 2 i 2 i ρ i - 1 s i n α$
$δ 34$ / $δ 43$		$L 2 E I ∑ i = 1 4 L 2 λ i - 1 s i n α 4 1 - ξ 1 2 i + 1 2 i + 1 - 1 - ξ 1 2 i 2 i + L f λ i - 1 c o s α 4 m - 1 ∑ j = 1 3 1 - ξ 1 2 i + 2 j i + j n j - b 1 - ξ 1 2 i 2 i ρ i - 1 c o s α + 1 - ξ 1 2 i - 1 2 i - 1 s i n α λ i - 1 - ω i - 1$
$Δ 1 p$	载变位	$L 2 4 E I ∑ i = 1 4 ξ p 1 - ξ p 2 i - 1 2 i - 1 λ i - 1 - 1 - ξ p 2 i 2 i λ i - 1$
$Δ 2 p$		$L 2 4 E I ∑ i = 1 4 y s λ i - 1 1 - ξ p 2 i 2 i - 1 - ξ p 2 i - 1 2 i - 1 ξ p - f λ i - 1 2 m - 1 ∑ j = 1 3 1 - ξ p 2 i + 2 j i + j n j + f ξ p λ i - 1 m - 1 ∑ j = 1 3 1 - ξ p 2 i + 2 j - 1 2 i + 2 j - 1 n j + b ρ i - 1 L i 1 - ξ p 2 i$
$Δ 3 p$		$L 2 4 E I ∑ i = 1 4 L λ i - 1 2 1 - ξ p 2 i 2 i ξ p - 1 - ξ p 2 i + 1 2 i + 1 + 2 b 1 - ξ p 2 i - 1 L 2 i - 1 λ i - 1 - ω i - 1$
$Δ 4 p$		$L 2 4 E I ∑ i = 1 4 L λ i - 1 s i n α 2 1 + ξ p 1 - ξ p 2 i 2 i - ξ p 1 - ξ p 2 i - 1 2 i - 1 - 1 - ξ p 2 i + 1 2 i + 1 - f λ i - 1 c o s α 2 m - 1 ∑ j = 1 3 1 - ξ p 2 i + 2 j i + j n j + f ξ p λ i - 1 c o s α m - 1 ∑ j = 1 3 1 - ξ p 2 i + 2 j - 1 2 i + 2 j - 1 n j + b L 1 - ξ p 2 i i ρ i - 1 c o s α - 2 1 - ξ p 2 i - 1 s i n α 2 i - 1 λ i - 1 - ω i - 1$

Table 2

Fig.4

Table 3

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

References 34

1	陈少林，伍锐，张娇，等．地形和土-结相互作用效应对三维跨峡谷桥梁地震响应的影响分析［J］．力学学报，2021，53（6）：1781-1794.
	CHEN Shaolin， WU Rui， ZHANG Jiao，et al ．Topo-graphy and soil-structer interaction effects on the seismic response of three dimensional canyon-crossing bridge ［J］．Chinese Journal of Theoretical and Applied Mechanics，2021，53（6）：1781-1794.
2	谢肖礼，勾文鑫，庞木林，等．RC刚架拱桥的板桁组合加固及动力特性［J］．华南理工大学学报（自然科学版），2023，51（4）：31-43.
	XIE Xiaoli， GOU Wenxin， PANG Mulin，et al ．Dynamic characteristics of RC rigid frame arch bridge strengthened by plate-truss combination［J］．Journal of South China University of Technology （Natural Science Edition），2023，51（4）：31-43.
3	陈旭勇，胡海棠，高兵勇．非概率可靠性在拱桥评估与加固中的应用［J］．桥梁建设，2016，46（2）：60-64.
	CHEN Xu-yong， HU Hai-tang， GAO Bing-yong ．Application of non-probabilistic reliability theory to assessment and reinforcement of arch bridges［J］．Bridge Construction，2016，46（2）：60-64.
4	陈增顺，周建庭，张承，等．体外预应力加固钢筋混凝土拱桥关键技术研究［J］．重庆交通大学学报（自然科学版），2013，32（Sup1）：823-826.
	CHEN Zengshun， ZHOU Jianting， ZHANG Cheng，et al ．Key technology of external prestressing reinforced concrete arch bridge［J］．Journal of Chongqing Jiaotong University （Natural Science），2013，32（Sup 1）：823-826.
5	SHAO X D， HE G， SHEN X J，et al ．Conceptual design of 1000 m scale steel-UHPFRC composite truss arch bridge ［J］．Engineering Structures，2021，226：111430/1-12.
6	WANG Z S， YANG J， ZHOU J T，et al ．Strengthening of existing stone arch bridges using UHPC：theoretical analysis and case study［J］．Structures，2022，43：805-821.
7	王宗山，周建庭，杨俊，等. UHPC在圬工拱桥加固中的应用［J］．世界桥梁，2022，50（2）：105-111.
	WANG Zong-shan， ZHOU Jian-ting， YANG Jun，et al ．Application of UHPC to reinforcement masonry arch bridges［J］．World Bridge，2022，50（2）：105-111.
8	YANG J， CHEN R， ZHANG Z Y，et al ．Experimental study on the ultimate bearing capacity of damaged RC arches strengthened with ultra-high performance concrete ［J］．Engineering Structures，2023，279：115611/1-13.
9	VARRO R， BÖGÖLY G， GÖRÖG P ．Laboratory and numerical analysis of failure of stone masonry arches with and without reinforcement［J］．Engineering Failure Analysis，2021，123：105272/1-10.
10	XIE X Q， CHEN Z F， GUO S S ．Bridge bearing capacity test and the application research carbon fiber reinforcement technology［J］．Advanced Materials Research. 2015，1065：860-864.
11	马兴林，杨俊，周建庭，等．UHPC与石材的粘结界面抗剪性能试验研究［J］．材料导报，2022，36（24）：21070133/1-7.
	MA Xinglin， YANG Jun， ZHOU Jianting，et al ．Experimental study on shear properties of UHPC and stone［J］．Materials Reports，2022，36（24）：21070133/1-7.
12	陈磊，丁鹏，周建庭，等．基于UHPC套箍与预应力相结合的肋拱桥加固技术研究［J］．混凝土，2019，362（12）：173-176.
	CHEN Lei， DING Peng， ZHOU Jianting，et al ．Research on reinforcement technology of ribbed arch bridge based on UHPC hoop and prestress［J］．Concrete，2019，362（12）：173-176.
13	彭凯，乔奋义，贾小飞．预应力折线形铰接钢拱加固拱桥技术试验研究［J］．重庆交通大学学报（自然科学版），2017，36（4）：12-17.
	PENG Kai， QIAO Fenyi， JIA Xiaofei ．Strengthening technique of prestressing hinged piecewise steel arches for arch bridges［J］．Journal of Chongqing Jiaotong University （Natural Science），2017，36（4）：12-17.
14	何劲，徐温，宋丹青，等．FBG自感知预应力碳纤维板在桥梁加固中的应用［J］．公路，2023（1）：129-134.
	HE Jin， XU Wen， SONG Dan-qing，et al ．Research on the application of FBG self-sensing prestressed carbon fiber plates in bridge strengthening［J］．Highway，2023（1）：129-134.
15	KAREEM M M， YASER A A ．Experimental investigation on the transform the simply supported girders to continuous girder by using the UHPC cast in place joint ［J］．KSCE Journal of Civil Engineering，2023，27（4）：1697-1707.
16	QIN X， PANG M L， XIE X L，et al ．A new deck arch bridge and a study on its mechanical properties by FE and experiment methods［J］．Advances in Structural Engineering，2022，25（1）：63-82.
17	ZAMPIERI P， PIAZZON R， FERRONI R，et al ．The application of external post-tensioning system to a damage masonry arch［J］．Procedia Structural Inte-grity，2023，44：605-609.
18	陈齐风，徐赵东，郝天之，等．设置反拱加固的拱结构力学性能研究［J］．应用力学学报，2020，37（2）：666-673.
	CHEN Qifeng， XU Zhaodong， HAO Tianzhi，et al ．Mechanical performance of arch structure with anti arch reinforcement［J］．Chinese Journal of Applied Mechanics，2020，37（2）：666-673.
19	董越，霍文营，孙海林．中铁青岛世界博览城展廊屋盖索拱结构设计［J］．建筑结构，2022，52（1）：12-16.
	DONG Yue， HUO Wenying， SUN Hailin ．Structural system design of cable arch structure on exhibition gallery roof of China Railway Qingdao World Expo City ［J］．Building Structure，2022，52（1）：12-16.
20	康厚军．索拱结构的稳定与振动研究［D］．长沙：湖南大学，2007.
21	刘利，康厚军，苏潇阳，等．拱暨索拱面内稳定性研究的传递矩阵法［J］．计算力学学报，2020，37（1）：98-107.
	LIU Li， KANG Hou-jun， SU Xiao-yang，et al ．Transfer matrix method for studying the in-plane stability of arch and cable-arch［J］．Chinese Journal of Computational Mechanics，2020，37（1）：98-107.
22	刘迎春，薛素铎，李雄彦，等．上承式拉索组合拱桥动力特性研究［J］．公路，2013（5）：15-19.
	LIU Ying-chun， XUE Su-duo， LI Xiong-yan，et al ．Study on dynamic characteristics of deck type arch bridge with diagonal cables［J］．Highway，2013（5）：15-19.
23	李双蓓，梁睿，梅国雄．考虑弹性压缩的弹性支承抛物线拱内力解析解［J］．工程力学，2023，40（11）：1-10.
	LI Shuang-bei， LIANG Rui， MEI Guo-xiong. Analytical solution of internal force of parabolic arch with elastic supports considering elastic compression［J］．Engineering Mechanics，2023，40（11）：1-10.
24	KANG H J， ZHAO Y Y， ZHU H P ．Analytical and experimental dynamic behavior of a new type of cable-arch bridge［J］．Journal of Constructional Steel Research，2014，101：385-394.
25	KANG H J， ZHAO Y Y， ZHU H P ．Stability of cable-arch structure［J］．Applied Mechanics and Materials，2012，204/205/206/207/208：3061-3067.
26	周宇，许成超，赵青，等．变截面悬链线无铰拱应变影响线的解析解［J］．计算力学学报，2022，39（5）：551-556.
	ZHOU Yu， XU Cheng-chao， ZHAO Qing，et al ．Practical analytical expression to strain influence line of varying cross section catenary fixed arch［J］．Chinese Journal of Computational Mechanics，2022，39（5）：551-556.
27	胡常福，陆小雨，甘慧慧，等．基于近似积分的悬链线拱实用解析解［J］．中南大学学报（自然科学版），2015，46（3）：1058-1065
	HU Changfu， LU Xiaoyu， GAN Huihui，et al ．Practical analytical solution of catenary arch based on approximate integration method［J］．Journal of Central South University （Science and Technology），2015，46（3）：1058-1065.
28	胡常福，何兵兵，石萃佳，等．复杂轴线拱结构实用解析解研究［J］．中南大学学报（自然科学版），2018，49（1）：217-225.
	HU Changfu， HE Bingbing， SHI Cuijia，et al ．Research on approximate analytical solution of arch structure with complex arch axis［J］．Journal of Central South University （Science and Technology），2018，49（1）：217-225.
29	程红光．实腹式圬工拱桥简化计算图式研究［D］．武汉：华中科技大学，2011.
30	WANG J， MELBOURNE C ．Mechanics of MEXE method for masonry arch bridge assessment［J］．Proceedings of the Institution of Civil Engineers-Engineering and Computational Mechanics，2010，163（3）：187-202.
31	顾懋清，石绍甫．公路桥涵设计手册——拱桥（上册）［M］．北京：人民交通出版社，1994.
32	徐福旺，胡清，袁长春，等．钢管混凝土悬链线深拱单点加载试验研究［J］．建筑结构学报，2021，42（S2）：373-381.
	XU Fuwang， HU Qing， YUAN Changchun，et al ．Experimental investigation on concrete-filled steel tubular catenary arches under single-point concentrated load ［J］．Journal of Building Structures，2021，42（S2）：373-381.
33	侯春辉，宋顺心．基于APDL语言的拱轴线优化及立柱布置研究［J］．铁道工程学报，2017，34（10）：55-59.
	HOU Chun-hui， SONG Shun-xin ．Research on the optimization of arch-axis and column layout based on APDL language［J］．Journal of Railway Engineering Society，2017，34（10）：55-59.
34	叶伟，王雷，孙向东，等．中承式钢管混凝土拱桥拱肋关键参数影响分析［J］．桥梁建设，2023，53（3）：79-86.
	YE Wei， WANG Lei， SUN Xiang-dong，et al ．Key parameter influence analysis of half-through concrete-filled steel tubular arch bridge［J］．Bridge Construction，2023，53（3）：79-86.

算例	关键截面内力	ξ	悬链线拱			索-拱联合结构
算例	关键截面内力	ξ	文中解析解	有限元解	相对误差/%	文中解析解	有限元解	相对误差/%
算例1（f /L=1/5）	M/（N·m）	0.0	-0.305	-0.305	0.000	-0.111	-0.111	0.000
	M/（N·m）	1.0	-1.312	-1.316	0.304	-0.178	-0.182	2.198
	N/N	0.0	0.673	0.674	0.149	0.395	0.395	0.000
	N/N	1.0	1.059	1.065	0.563	1.189	1.199	0.834
算例2（f /L=1/6）	M/（N·m）	0.0	-0.291	-0.291	0.000	-0.131	-0.131	0.000
	M/（N·m）	1.0	-1.369	-1.372	0.219	-0.382	-0.385	0.779
	N/N	0.0	0.799	0.799	0.000	0.517	0.518	0.193
	N/N	1.0	1.143	1.147	0.349	1.320	1.327	0.528
算例3（f /L=1/7）	M/（N·m）	0.0	-0.275	-0.275	0.000	-0.144	-0.144	0.000
	M/（N·m）	1.0	-1.421	-1.424	0.211	-0.566	-0.568	0.352
	N/N	0.0	0.921	0.921	0.000	0.644	0.644	0.000
	N/N	1.0	1.225	1.226	0.082	1.441	1.443	0.139

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