装配式小箱梁桥内力横向分布系数建议公式

doi:10.13229/j.cnki.jdxbgxb.20221079

吉林大学学报(工学版) ›› 2024, Vol. 54 ›› Issue (6): 1688-1700.doi: 10.13229/j.cnki.jdxbgxb.20221079

• 交通运输工程·土木工程 • 上一篇

装配式小箱梁桥内力横向分布系数建议公式

张彦玲^1,²(),贾云飞^1,²,贾晓远^1,²,郑旺^1,²,李运生^1,²()

^1.石家庄铁道大学土木工程学院，石家庄 050043
^2.石家庄铁道大学道路与铁道工程安全保障省部共建教育部重点实验室，石家庄 050043

收稿日期:2022-08-24 出版日期:2024-06-01 发布日期:2024-07-23
通讯作者: 李运生 E-mail:06mzhang@163.com;liysh70@163.com
作者简介:张彦玲（1973-），女，教授，博士.研究方向：桥梁结构分析，组合结构桥梁.E-mail：06mzhang@163.com
基金资助:
国家自然科学基金项目(51778377);河北省大型结构健康诊断与控制重点实验室开放基金项目(KLLSHMC2112)

Proposed formulae for transverse distribution factor of internal forces of prefabricated small box-girder bridge

Yan-ling ZHANG^1,²(), JIAYun-fei^1,²,Xiao-yuan JIA^1,²,Wang ZHENG^1,²,Yun-sheng LI^1,²()

^1.School of Civil Engineering，Shijiazhuang Tiedao University，Shijiazhuang 050043，China
^2.Key Laboratory of Roads and Railway Engineering Safety Control of Ministry of Education，Shijiazhuang Tiedao University，Shijiazhuang 050043，China

Received:2022-08-24 Online:2024-06-01 Published:2024-07-23
Contact: Yun-sheng LI E-mail:06mzhang@163.com;liysh70@163.com

摘要/Abstract

摘要：

为了采用横向分布系数的概念简化多主梁装配式连续梁桥、斜交桥和曲线桥的受力分析过程，基于某多主梁装配式连续小箱梁桥构建了桥梁数据库，采用梁格法建立了每座桥梁的有限元模型，研究了主梁间距、高跨比、斜交角和圆心角对内力横向分布系数的影响规律，并通过统计回归方法给出了内力横向分布系数建议公式。研究结果表明：弯矩和剪力横向分布系数均随主梁间距的增大而增大；随主梁高跨比λ的增大，跨中正弯矩增大，但跨中剪力、支点负弯矩和支点剪力均减小；斜交桥和曲线桥内力横向分布系数可在直线正交桥公式基础上乘以修正因子得到。在本文的计算模型范围内，采用建议公式得到的多主梁装配式连续梁桥、斜交桥和曲线桥的内力横向分布系数均与有限元结果吻合良好，且可通过沿纵向的简化包络图得到任意截面的内力横向分布系数。

关键词: 桥梁工程, 装配式桥梁, 横向分布系数, 连续小箱梁桥, 斜交桥, 曲线桥

Abstract:

In order to simplify the stress analysis process by using the concept of transverse distribution factor （TDF） for the multi-girder fabricated continuous girder bridges， skew bridges and curved bridges， the bridge database based on a multi girder fabricated continuous small box girder bridge was established， and the finite element model of each bridge was built by using the grillage method. The influence of the girder spacing， height span ratio， skew angle and center angle on the transverse distribution coefficient of internal force was investigated， and the formulae of the transverse distribution factor of internal forces were proposed by statistical regression method. The results show that the transverse distribution factors of bending moment and shear force increase with the development of the girder spacing； With the increase of the height span ratio of the main beam λ， the transverse distribution factors for mid-span positive bending moment increases， but decrease for that of the mid-span shear force and the negative bending moment and shear force at the support； The transverse distribution factor of internal force in skew bridges and curved bridges can be obtained by multiplying the modification factor with the formula of straight orthogonal bridges. Within the scope of the calculation model in this paper， the transverse distribution factors of internal forces of multi-girder fabricated continuous girder bridges， skew bridges and curved bridges obtained by the proposed formulae are in good agreement with the finite element results， and the transverse distribution factors of internal forces of any section can be obtained by the simplified envelope diagram along the longitudinal direction.

Key words: bridge construction, prefabricated bridge, transverse distribution factor, continuous small box-girder bridge, skewed bridge, curved bridge

中图分类号:

U448.25

张彦玲,贾云飞,贾晓远,郑旺,李运生. 装配式小箱梁桥内力横向分布系数建议公式[J]. 吉林大学学报(工学版), 2024, 54(6): 1688-1700.

Yan-ling ZHANG, JIAYun-fei,Xiao-yuan JIA,Wang ZHENG,Yun-sheng LI. Proposed formulae for transverse distribution factor of internal forces of prefabricated small box-girder bridge[J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(6): 1688-1700.

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内力类型	位置	工况（i）	拟合公式形式	相关系数R²
M_l_/2	边梁	1	m_λ =0.652 8e^{-0.000 2/（}^λ^{-0.038 3）}	0.985 0
M_l_/2	中梁	2	m_λ =0.640 9e^{-0.000 7/（}^λ^{-0.027 3）}	0.986 9
M₀	边梁	3	m_λ =0.644 8e^{0.000 7/（}^λ+^{0.004 5）}	0.988 7
M₀	中梁	4	m_λ =0.622 6e^{0.003 0/（}^λ+^{0.068 8）}	0.989 0
Q₀	边梁	5	m_λ =0.740 5e^{0.020 7/（}^λ^{-0.014 7）}	0.986 8
Q₀	中梁	6	m_λ =0.746 0e^{0.025 1/（}^λ^{+0.000 1）}	0.983 8
Q_l_/2	边梁	7	m_λ =0.639 1e^{0.002 1/（}^λ^{+0.129 8）}	0.991 2
Q_l_/2	中梁	8	m_λ =0.606 6e^{0.000 9/（}^λ^{+0.006 4）}	0.989 7

内力类型	位置	工况（i）	拟合公式	相关系数R²
M_l_/2	边梁	1	m_D =0.268 7D^{1.106 0}	0.999 8
M_l_/2	中梁	2	m_D =0.308 7D^{0.959 0}	0.999 3
M₀	边梁	3	m_D =0.263 1D^{1.136 5}	0.999 6
M₀	中梁	4	m_D =0.309 5D^{0.924 0}	0.998 2
Q₀	边梁	5	m_D =0.682 6D^{0.752 8}	0.994 6
Q₀	中梁	6	m_D =0.742 1D^{0.592 1}	0.999 9
Q_l_/2	边梁	7	m_D =0.255 1D^{1.159 1}	0.999 0
Q_l_/2	中梁	8	m_D =0.350 0D^{0.906 7}	0.999 6

内力类型	位置	工况（i）	主梁间距D		主梁高跨比λ=H/L
内力类型	位置	工况（i）	b_D	R²	b_λ	c_λ	R²
M_l_/2	边梁	1	1.106 0	0.999 8	-0.000 2	-0.038 3	0.985 0
M_l_/2	中梁	2	0.959 0	0.999 3	-0.000 7	-0.027 3	0.986 9
M₀	边梁	3	1.136 5	0.999 6	0.000 7	0.004 5	0.986 7
M₀	中梁	4	0.924 0	0.998 2	0.003 0	0.068 8	0.989 0
Q₀	边梁	5	0.752 8	0.994 6	0.020 7	-0.014 7	0.986 8
Q₀	中梁	6	0.592 1	0.999 9	0.025 1	0.000 6	0.983 8
Q_l_/2	边梁	7	1.159 1	0.999 0	0.002 1	0.129 8	0.991 2
Q_l_/2	中梁	8	0.906 7	0.999 6	0.000 9	0.006 4	0.989 7

内力类型	位置	工况（i）	拟合公式形式	k_i
M_l_/2	边梁	1	m₁=k₁D^{1.106 0}e^{-0.000 2/（}^λ^{-0.038 3）}	0.271 9
M_l_/2	中梁	2	m₂=k₂D^{0.959 0}e^{-0.000 7/（}^λ^{-0.027 3）}	0.313 8
M₀	边梁	3	m₃=k₃D^{1.136 5}e^{0.000 7/（}^λ^{+0.004 5）}	0.260 6
M₀	中梁	4	m₄=k₄D^{0.924 0}e^{0.003 0/（}^λ^{+0.068 8）}	0.321 9
Q₀	边梁	5	m₅=k₅D^{0.752 8}e^{0.020 7/（}^λ^{-0.014 7）}	0.425 1
Q₀	中梁	6	m₆=k₆D^{0.592 1}e^{0.025 1/（}^λ^{+0.000 6）}	0.543 0
Q_l_/2	边梁	7	m₇=k₇D^1.1591e^{0.002 1/（}^λ^{+0.129 8）}	0.259 0
Q_l_/2	中梁	8	m₈=k₈D^{0.906 7}e^{0.000 9/（}^λ^{+0.006 4）}	0.329 5

编号	跨度/m	主梁宽度/m	主梁片数	主梁高度/m	高跨比
1	4×10	1.875	8	0.9	0.090
2	4×12	1.875	8	0.9	0.075
3	4×20	1.875	8	1.0	0.050
4	4×20	2.220	5	1.8	0.090
5	4×24	2.220	5	1.2	0.050
6	4×16	2.500	6	1.6	0.100
7	4×20	2.500	6	1.5	0.075
8	4×28	2.500	6	1.6	0.057
9	4×10	3.000	5	0.9	0.090
10	4×14	3.000	5	0.9	0.064
11	4×22	3.000	5	1.1	0.050
12	4×20	5.000	3	1.8	0.090
13	4×20	5.000	3	1.7	0.085
14	4×24	5.000	3	1.8	0.075
15	4×28	5.000	3	1.8	0.064
16	4×32	5.000	3	1.8	0.056

装配式小箱梁桥内力横向分布系数建议公式

Proposed formulae for transverse distribution factor of internal forces of prefabricated small box-girder bridge

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内力类型	位置	工况（i）	拟合公式形式
M_l_/2	边梁	1	1.019 6-0.019 2（cos θ）^10.83
M_l_/2	中梁	2	1.180 8-0.099 7（cos θ）^0.96
M₀	边梁	3	1.015 8+0.034 5（cos θ）^3.94
M₀	中梁	4	1.000 7+0.210 2（cos θ）^1.96
Q₀	边梁	5	0.880 9+0.479 9（cos θ）^0.55
Q₀	中梁	6	1.191 3+0.039 4（cos θ）^2.15
Q_l_/2	边梁	7	0.902 6+0.023 0（cos θ）^0.62
Q_l_/2	中梁	8	1.002 6+0.056 4（cos θ）^2.67

内力类型	位置	工况（i）	拟合公式形式
M_l_/2	边梁	1	1.004 2-0.010 3（cos φ）^1.64
M_l_/2	中梁	2	1.004 6-0.062 7（cos φ）^1.54
M₀	边梁	3	0.994 5+0.002 6（cos φ）^1.15
M₀	中梁	4	0.920 7+0.003 2（cos φ）^1.11
Q₀	边梁	5	1.057 2-0.395 8（sin φ）^0.64
Q₀	中梁	6	0.900 8-0.201 9（sin φ）^0.78
Q_l_/2	边梁	7	0.979 0-0.001 7（sin φ）^1.84
Q_l_/2	中梁	8	0.894 0-0.001 0（sin φ）^4.67

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