1. College of Civil Engineering, Hunan University, Changsha 410082, China 2. China Construction Fifth Engineering Bureau Co. Ltd, Changsha 410004, China
A 30 m span simply supported steel plate composite girder bridge with continuous deck was taken as the research object, in order to realize the standardized design of steel plate composite girder and achieve the purpose of further popularization and application. The current design code of steel plate composite girder bridge in China was combined, the cost of bridge and the steel consumption were taken as the objective function, the dimension layout parameters and the number of main beam were taken as the design variables, and the stress, deformation, local stability as well as standard construction requirements were taken as the constraint conditions. The optimization model of the section parameters of the composite steel plate girder was established based on the above conditions, and the genetic algorithm was used for optimization analysis. The optimization results showed that the proposed algorithm was stable, reliable and efficient, and there was a large space for optimization, depending on the structure section layout of the project. Under the condition of keeping the width of the bridge and the layout of the driveway unchanged, the cost of using the six-beam section was the least, which was reduced by about 13% compared with that of the original design. The steel consumption with four-beam section was the least, 123.69 kg/m2, and about 27% of the steel consumption was saved compared with the original design. The optimization results can provide reference for the section design of medium span steel plate composite bridge. Economic analysis showed that, the economic values of the span height ratio of the section were 20?23, 18?21, 14?17, respectively, when the main beam spacing was about 2.3 m, 3.2 m and 4.8 m.
Lifeng LI,Kun HOU,Deqiang ZOU,Hao PENG,Lingxiao LI. Optimization of section layout of steel plate composite beam with medium span. Journal of ZheJiang University (Engineering Science), 2024, 58(3): 510-517.
Fig.1General layout of initial design of steel-concrete composite beam
计算方法
σsmax/MPa
σcmax/MPa
τmax/MPa
y/mm
简化计算公式
249.5
17.9
43.9
35.8
有限元模型
244.9
16.7
45.5
29.3
Tab.1Comparison of results of simplified formulas and finite element calculations for most unfavorable state of dependent project
变量
含义
取值范围/mm
初值/mm
h
钢梁高度
[500, 2 000]
1 500
d
主梁间距
[(B/(N+0.2), B/(N?0.2)]
—
b1
钢梁上翼缘宽度
[360, 800]
400
t1
跨中截面钢梁上翼缘厚度
[16, 40]
20
tw1
跨中截面钢梁腹板厚度
[12, 40]
20
b2
钢梁下翼缘宽度
[450, 1 500]
600
t2
跨中截面钢梁下翼缘厚度
[22, 40]
22
t3
支点截面钢梁上翼缘厚度
[16, 40]
20
tw2
支点截面钢梁腹板厚度
[12, 40]
20
t4
支点截面钢梁下翼缘厚度
[22, 40]
22
Tab.2Design variables for optimized cross section
cs/（元?t?1）
cc/（元?m?3）
c1s/（元?t?1）
c1c/（元?m?3）
14 462
1 200
260
566
c2/（元?m?2）
c3/（元?t?1）
C4/万元
—
56
8 269
13.30
—
Tab.3Prices of components in cost calculation
Fig.2Optimization iterative process with cost as optimization objective
设计
N
$ {t_{\text{c}}} $/mm
d/mm
C/万元
Δ/%
初始设计
8
260
2 400
238.71
—
最优设计
4
321
4 550
211.66
11.3
6
253
3 180
207.69
13.0
8
221
2 370
212.46
11.0
Tab.4Optimization results with cost as optimization objective
Fig.3Layout of cross section of optimization result with cost as optimization objective (N=6)
Fig.4Optimization iterative process with steel consumption as optimization objective
设计
N
$ {t_{\text{c}}} $/mm
d/mm
Ms/(kg?m?2)
Δ/%
初始设计
8
260
2 400
176.11
—
最优设计
4
281
4 860
128.65
27.0
6
235
3 180
142.74
19.0
8
211
2 370
158.13
10.2
Tab.5Optimization results with steel consumption as optimization objective
Fig.5Layout of cross section of optimization result with steel consumption as optimization objective (N=4)
Fig.6Midas finite element model of six-girder steel plate composite girder bridge
目标函数
计算方式
σsmax/MPa
σcmax/MPa
τmax/MPa
y/mm
C（N=6）
简化计算公式
245.1
16.2
68.5
32.8
有限元模型
242.2
16.2
65.7
29.8
Ms（N=4）
简化计算公式
245.4
13.7
66.5
23.4
有限元模型
236.6
13.7
64.9
21.3
规范限值
245.4
20.4
160.0
50.0
Tab.6Comparison of simplified formulas and finite element calculations of most unfavorable state of optimization results
Fig.7Relationship between steel consumption and span
Fig.8Relationship between span-height ratio of section and span
Fig.9Cost components of optimization results with cost as optimization objective
[1]
张凯. 中小跨径钢板组合梁桥快速建造技术与应用研究[D]. 西安: 长安大学, 2016. ZHANG Kai. Research on the accelerated construction technology and the application of composite steel plate girder bridge with medium-small span [D]. Xi'an: Chang'an University, 2016.
[2]
刘永健, 高诣民, 周绪红, 等 中小跨径钢-混凝土组合梁桥技术经济性分析[J]. 中国公路学报, 2017, 30 (3): 1- 13 LIU Yongjian, GAO Yimin, ZHOU Xuhong, et al Technical and economic analysis in steel-concrete composite girder bridges with small and medium span[J]. China Journal of Highway and Transport, 2017, 30 (3): 1- 13
doi: 10.3969/j.issn.1001-7372.2017.03.001
[3]
邬沛, 李玉顺, 许达, 等 基于遗传算法的钢-竹组合工字形梁截面优化设计[J]. 建筑结构学报, 2020, 41 (1): 149- 155 WU Pei, LI Yushun, XU Da, et al Multi-objective optimal section design of I-shaped section steel-bamboo composite beam using genetic algorithm[J]. Journal of Building Structure, 2020, 41 (1): 149- 155
朱劲松, 秦亚婷, 刘周强 预应力UHPC-NC组合梁截面优化设计[J]. 吉林大学学报:工学版, 2023, 53 (11): 3151- 3159 ZHU Jingsong, QIN Yating, LIU Zhouqiang Section optimization design of prestressed uhpc-nc composite beams[J]. Journal of Jilin University: Engineering and Technology Edition, 2023, 53 (11): 3151- 3159
[6]
刘齐茂, 李微, 李暾, 等 钢-混凝土组合梁的截面优化设计[J]. 兰州理工大学学报, 2006, (3): 115- 118 LIU Qimao, LI Wei, LI Tun, et al Optimization design of cross section of steel concrete composite beams[J]. Journal of Lanzhou University of Technology, 2006, (3): 115- 118
doi: 10.3969/j.issn.1673-5196.2006.03.033
[7]
MELA K, HEINISUO M Weight and cost optimization of welded high strength steel beams[J]. Engineering Structures, 2014, 79: 354- 364
doi: 10.1016/j.engstruct.2014.08.028
[8]
SKOGLUND O, LEANDER J, KAROUMI R Optimizing the steel girders in a high strength steel composite bridge[J]. Engineering Structures, 2020, 221: 110981
doi: 10.1016/j.engstruct.2020.110981
SENOUCI A, AIANSARI M Cost optimization of composite beams using genetic algorithms[J]. Advances in Engineering Software, 2009, 40: 1112- 1118
doi: 10.1016/j.advengsoft.2009.06.001
[12]
中华人民共和国交通运输部. 公路钢结构桥梁设计规范[S]. 北京: 人民交通出版社, 2015.
[13]
刘明慧. 钢板-混凝土组合梁桥截面优化研究[D]. 西安: 西安科技大学, 2019. LIU Minghui. Research on section optimization of steel plate-concrete composite girder bridge [D]. Xi’an: Xi’an University of Science and Technology, 2019.
STORN R, PRICE K Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces[J]. Journal of Global Optimization, 1997, 11 (4): 341- 359
doi: 10.1023/A:1008202821328
