﻿ 波形钢腹板单箱多室箱梁横向受力分析
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 哈尔滨工程大学学报  2018, Vol. 39 Issue (6): 1109-1115  DOI: 10.11990/jheu.201610073 0

### 引用本文

ZHAO Pin, YE Jianshu. Transverse force study of single box multi-chamber with corrugated steel webs[J]. Journal of Harbin Engineering University, 2018, 39(6), 1109-1115. DOI: 10.11990/jheu.201610073.

### 文章历史

Transverse force study of single box multi-chamber with corrugated steel webs
ZHAO Pin, YE Jianshu
School of Transportation, Southeast University, Nanjing 210096, China
Abstract: The transverse span of a single-box multi-chamber corrugated steel web is large, while the stiffness of a corrugated steel web is relatively small and its transverse force is more complex than that of a single-box single-chamber box beam. Through a test was carried out for a test beam with a single-box double-chamber corrugated steel web in the elastic stage, the distribution of the beam roof's transversal internal force was analyzed. With consideration to the influence of lateral and distortion bend, an energy method was applied in order to establish a calculation model for the transversal force of the single-box double-chamber box beam with a corrugated steel web. Additionally, the results was obtained by this energy method, test results, and results obtained by the finite element method, were analyzed in order to obtain their parameters. The analytical results showed that the impact of the intermediate web thickness on the roof's transversal internal force cannot be ignored. The roof's transversal internal force in the single-box multi-chamber box beam with the corrugated steel web, decreased with the increase of the linear stiffness ratio between the web and the roof plate.
Key words: bridge engineering    box girders with corrugated steel webs    energy method    bridge deck    transverse internal force    linear stiffness ratio

1 波形钢腹板箱梁横向内力计算模型

1.1 反对称荷载作用下加支撑的结构分析 1.1.1 横向弯曲应变能

1) 外荷载P作用下的内力和位移。

 $\begin{array}{*{20}{c}} {{M_1} = \frac{{\left( {b - d} \right)P}}{2} - \frac{b}{4}{X_1} - {X_2}}\\ {{M_2} = \frac{{\left( {c - d} \right)P}}{2} - \frac{b}{4}{X_1} - {X_2} - h{X_3}}\\ {{M_3} = \frac{b}{4}{X_1} - {X_2} - h{X_3}}\\ {{M_4} = {X_2},{M_5} = \frac{b}{4}{X_1} - {X_2}} \end{array}$ (1)

 ${X_3} = \frac{{P \cdot C}}{B}$

 $A = \frac{{6b{c^2}{h^3}{n^2}}}{{{I_c} \cdot I_{\rm{u}}^2}} + \frac{{108bc{h^4}n}}{{I_{\rm{c}}^2 \cdot {I_{\rm{u}}}}} + \frac{{144b{h^5}}}{{I_{\rm{c}}^3}} + \frac{{3b{c^2}{h^3}{n^3}}}{{{I_0} \cdot I_{\rm{u}}^2}} + \\\frac{{6c{b^2}{h^3}{n^2} + 60cb{h^4}{n^2}}}{{{I_0} \cdot {I_c} \cdot {I_{\rm{u}}}}} + \frac{{9n{b^2}{h^4} + 99nb{h^5}}}{{{I_0} \cdot I_{\rm{c}}^2}} + \frac{{3{b^2}c{n^3}{h^3}}}{{I_0^2 \cdot {I_{\rm{u}}}}} + \frac{{6{b^2}{n^2}{h^4}}}{{I_0^2 \cdot {I_{\rm{c}}}}}$
 $\begin{array}{*{20}{c}} {B = \frac{{24{c^2}{h^3}{n^2}}}{{{I_c} \cdot {I_{\rm{u}}}}} + \frac{{432c{h^4}n}}{{I_{\rm{c}}^2}} + \frac{{576{h^5} \cdot {I_{\rm{u}}}}}{{I_{\rm{c}}^3}} + \frac{{12{c^2}{h^3}{n^3}}}{{{I_0} \cdot {I_{\rm{u}}}}} + \frac{{240c{h^4}{n^2} + 24cb{h^3}{n^2}}}{{{I_0} \cdot {I_c}}} + }\\ {\frac{{\left( {396n{h^5} + 36nb{h^4}} \right) \cdot {I_{\rm{u}}}}}{{{I_0} \cdot I_{\rm{c}}^2}} + \frac{{12bc{n^3}{h^3}}}{{I_0^2}} + \frac{{24b{n^2}{h^4} \cdot {I_{\rm{u}}}}}{{I_0^2 \cdot {I_{\rm{c}}}}}} \end{array}$
 $\begin{array}{*{20}{c}} {C = \frac{{3{c^3}{h^3}{n^3}}}{{I_{\rm{u}}^2}} - \frac{{59{c^2}{h^3}{n^2}}}{{{I_{\rm{c}}} \cdot {I_{\rm{u}}}}} - \frac{{48cn{h^4}}}{{I_{\rm{c}}^2}} + \frac{{96{h^5} \cdot {I_{\rm{u}}}}}{{I_{\rm{c}}^3}} + \frac{{\left( {3{c^2}{h^3}{n^3} - 3b{c^2}{h^2}{n^3}} \right)}}{{{I_0} \cdot {I_{\rm{u}}}}} + \frac{{\left( {61c{n^2}{h^4} - 2bc{n^2}{h^3}} \right)}}{{{I_0} \cdot {I_{\rm{c}}}}} + }\\ {\frac{{\left. {90n{h^5} + 6bn{h^4}} \right) \cdot {I_{\rm{u}}}}}{{{I_0} \cdot I_{\rm{c}}^2}} + \frac{{3bc{n^3}{h^3}}}{{I_0^2}} + \frac{{3b{n^2}{h^4} \cdot {I_{\rm{u}}}}}{{I_0^2 \cdot {I_{\rm{c}}}}}} \end{array}$

 $\begin{array}{*{20}{c}} {{I_0} = \frac{{t_0^3}}{{12\left( {1 - {\mu ^2}} \right)}},{I_u} = \frac{{t_u^3}}{{12\left( {1 - {\mu ^2}} \right)}}}\\ {{I_c} = {I_{c1}} = \frac{{2{L_c}{t_c}{{\left( {\frac{{{h_c}}}{2}} \right)}^2} + \frac{{{t_c}h_c^3}}{6}\sin \theta }}{q}} \end{array}$ (2)

 $\begin{array}{*{20}{c}} {{\Delta _q} = \frac{{\left[ {\left( { - 2b + d + c} \right)P + \frac{b}{4}{X_1} + {X_2} - h{X_3}} \right]{h^2}}}{{3nE{I_c}}} + }\\ {\frac{{\left[ {\left( {c - d} \right)P - \frac{b}{4}{X_1} - 3{X_2} - 3h{X_3}} \right]hc}}{{3E{I_u}}}} \end{array}$ (3)

2) 剪力差Ti作用下的内力和位移。

 $\left\{ \begin{array}{l} {{M'}_1} = \frac{b}{4}{X_{11}} + {X_{22}}\\ {{M'}_2} = \frac{{Ph}}{2} - \frac{b}{4}{X_{11}} - {X_{22}} - h{X_{33}}\\ {{M'}_3} = \frac{b}{4}{X_{11}} - {X_{22}} - h{X_{33}}\\ {{M'}_4} = {X_{22}},{{M'}_5} = \frac{b}{4}{X_{11}} - {X_{22}} \end{array} \right.$ (4)

 $\begin{array}{*{20}{c}} {{\Delta _T} = \frac{{\left[ {\frac{{{{T'}_s}h}}{2} - \frac{{3b}}{4}{X_{11}} - 3{X_{22}} - h{X_{33}}} \right]{h^2}}}{{3nE{I_c}}} + }\\ {\frac{{\left[ {{{T'}_s}h - \frac{{3b}}{4}{X_{11}} - {X_{22}} - h{X_{33}}} \right]hc}}{{3E{I_u}}}} \end{array}$ (5)

 (7)
 ${X_{22}} = \frac{{{{T'}_s} \cdot F}}{B}$
 ${X_{33}} = \frac{{{{T'}_s} \cdot G}}{B}$

 $\begin{array}{*{20}{c}} {D = \left[ {\frac{{6\left( {c - d} \right){c^2}{h^3}{n^2}}}{{{I_{\rm{c}}} \cdot I_{\rm{u}}^2}} + \frac{{4\left( {15c + 12b - 27d} \right)c{h^4}n}}{{I_{\rm{c}}^2 \cdot {I_{\rm{u}}}}} + \frac{{24{h^5}\left( {3b + 3c - 5d} \right)}}{{I_{\rm{c}}^3}} + \frac{{3\left( {c - d} \right){c^2}{h^3}{n^3}}}{{{I_0} \cdot I_{\rm{u}}^2}} + } \right.}\\ {\frac{{6{{\left( {b - d} \right)}^2}c{n^3}{h^3}}}{{I_{\rm{0}}^2 \cdot {I_{\rm{u}}}}} + \frac{{2\left( {8{b^2} + 18bh - 16bd + 22ch + 13d - 40dh - 5{d^2}} \right)c{h^3}{n^2}}}{{{I_0} \cdot {I_{\rm{c}}} \cdot {I_{\rm{u}}}}} + }\\ {\left. {\frac{{\left( {27{{\left( {b - d} \right)}^2} + 4h\left( {15b - 27d + 12c} \right)n{h^4}} \right.}}{{{I_0} \cdot I_{\rm{c}}^2}} + \frac{{12{{\left( {b - d} \right)}^2}{n^2}{h^4}}}{{I_{\rm{0}}^2 \cdot {I_{\rm{c}}}}}} \right]} \end{array}$
 $\begin{array}{*{20}{c}} {F = \left[ {\frac{{\left( {2c + 4b - 6d} \right){c^2}{h^3}{n^2}}}{{{I_{\rm{c}}} \cdot {I_{\rm{u}}}}} + \frac{{\left( {100c + 8b - 108d} \right)c{h^4}n}}{{I_{\rm{c}}^2}} + \frac{{24{h^5}\left( {5b + c - 6d} \right) \cdot {I_{\rm{u}}}}}{{I_{\rm{c}}^3}} + } \right.}\\ {\frac{{3{{\left( {b - d} \right)}^2}{c^2}{h^2}{n^3}}}{{{I_{\rm{0}}} \cdot {I_{\rm{u}}}}} + \frac{{\left[ {70{b^2} + 66{d^2} - 137bd - bc} \right]c{h^3}{n^2}}}{{{I_{\rm{0}}} \cdot {I_{\rm{c}}}}} + \frac{{\left( {111{b^2} + 105{d^2} - 21bd} \right)n{h^4} \cdot {I_{\rm{u}}}}}{{{I_{\rm{0}}} \cdot I_{\rm{c}}^2}} + }\\ {\left. {\frac{{3{{\left( {b - d} \right)}^2}bc{h^2}{n^2}}}{{I_0^2}} + \frac{{6{{\left( {b - d} \right)}^2}b{h^3}{n^2} \cdot {I_{\rm{u}}}}}{{I_0^2 \cdot {I_{\rm{c}}}}}} \right]} \end{array}$
 $\begin{array}{*{20}{c}} {G = \left( {\frac{{4{c^2}\left( {c - b} \right){c^2}{h^2}{n^2}}}{{{I_{\rm{c}}} \cdot {I_{\rm{u}}}}} + \frac{{96\left( {c - b} \right)cn{h^3}}}{{I_{\rm{c}}^2}} - \frac{{{h^4}\left( {b - c} \right) \cdot I}}{{I_{\rm{c}}^3}} - \frac{{3\left( {{b^2} - 2bd - ch + {d^2} + dh} \right){c^2}h{n^3}}}{{{I_{\rm{0}}} \cdot {I_{\rm{u}}}}} + } \right.}\\ {\frac{{\left[ { - 73{b^2} + 7bc + 135bd + 61ch - 69{d^2} - 63dh + 2bh} \right]c{h^2}{n^2}}}{{{I_{\rm{0}}} \cdot {I_{\rm{c}}}}} + }\\ {\frac{{\left( { - 150{b^2} - 144{d^2} + 288bd + 54bh + 6cb - 144dh + 90ch} \right)n{h^3} \cdot {I_{\rm{u}}}}}{{{I_{\rm{0}}} \cdot I_{\rm{c}}^2}} - }\\ {\left. {\frac{{3\left( {{b^2} - 2bd - ch + {d^2} + dh} \right)bch{n^3}}}{{I_{\rm{0}}^2}} + \frac{{\left( { - 9{b^3} + 18{b^2}d + 8{b^2}h - 9b{d^2} - 18bdh + 6{d^2}h + 4cbh} \right){h^2}{n^2} \cdot {I_{\rm{u}}}}}{{I_{\rm{0}}^2 \cdot {I_{\rm{c}}}}}} \right)} \end{array}$

3) 横向弯曲应变能。

 ${\mathit{\Pi }_W} = \int_L {\int_S {\frac{{M_q^2}}{{2EI}}{\rm{d}}s{\rm{d}}z} } + \int_L {\int_S {\frac{{{M_q}{M_T}}}{{EI}}{\rm{d}}s{\rm{d}}z} } + \int_L {\int_S {\frac{{M_T^2}}{{2EI}}{\rm{d}}s{\rm{d}}z} }$ (6)

 $\begin{array}{*{20}{c}} {\int_0^l {\int_s {\frac{{M_q^2}}{{2EI}} \cdot {\rm{d}}s{\rm{d}}z} } = \int_0^l {d\left[ {\left( {M_4^2 + M_5^2 + {M_4}{M_5}} \right)/\left( {6E{I_0}} \right) + \\\left( {b - d} \right)\left( {M_4^2 + M_1^2 + {M_4}{M_1}} \right)/\left( {6E{I_0}} \right) + } \right.} }\\ {a\left( {M_1^2 + M_2^2 + {M_1}{M_2}} \right)/\left( {3nE{I_c}} \right) + c\left( {M_2^2 + M_3^2 - {M_2}{M_3}} \right)/\left( {6E{I_u}} \right) + }\\ {\left. {2h\left( {M_3^2 + M_5^2 + {M_3}{M_5}} \right)/\left( {3nE{I_c}} \right)} \right]{\rm{d}}z} \end{array}$
 $\begin{array}{*{20}{c}} {\int_0^l {\int_s {\frac{{M_T^2}}{{2EI}} \cdot {\rm{d}}s{\rm{d}}z} } = \int_0^l {d\left[ {\left( {M{'}_4^2 + M{'}_5^2 + {{M'}_4}{{M'}_5}} \right)/\left( {6E{I_0}} \right) +\\ \left( {b - d} \right)\left( {M{'}_4^2 + M{'}_1^2 + {{M'}_4}{{M'}_1}} \right)/\left( {6E{I_0}} \right) + } \right.} }\\ {a\left( {M{'}_1^2 + M{'}_2^2 - {{M'}_1}{{M'}_2}} \right)/\left( {3nE{I_c}} \right) + c\left( {M{'}_2^2 + M{'}_3^2 - {{M'}_2}{{M'}_3}} \right)/\left( {6E{I_u}} \right) + }\\ {\left. {2h\left( {M{'}_3^2 + M{'}_5^2 - {{M'}_3}{{M'}_5}} \right)/\left( {3nE{I_{\rm{c}}}} \right)} \right]{\rm{d}}z} \end{array}$
 $\begin{array}{*{20}{c}} {\int_0^l {\int_s {\frac{{{M_q}{M_T}}}{{EI}} \cdot {\rm{d}}s{\rm{d}}z} } = \int_0^l {d\left[ {\left( {{M_4}\left( {2{{M'}_4} - {{M'}_5}} \right) +\\ {M_5}\left( {2{{M'}_5} - {{M'}_4}} \right)} \right)/\left( {12E{I_0}} \right) + \left( {b - d} \right)\left( {3{M_4}\left( {{{M'}_4} - {{M'}_1}} \right) + } \right.} \right.} }\\ {\left. {\left( {{M_1} - {M_4}} \right)\left( {{{M'}_4} - 2{{M'}_1}} \right)} \right)/\left( {12E{I_0}} \right) + a\left( {{M_1}\left( {2{{M'}_1} - {{M'}_2}} \right) +\\ {M_2}\left( {2{{M'}_2} - {{M'}_1}} \right)} \right)/\left( {6nE{I_c}} \right) + }\\ {c\left( { - {M_2}\left( {2{{M'}_2} + {{M'}_3}} \right) + {M_3}\left( {2{{M'}_3} + {{M'}_2}} \right)} \right)/\left( {6E{I_u}} \right) + }\\ {\left. {h\left( {{M_5}\left( {2{{M'}_5} + {{M'}_3}} \right) + {M_3}\left( {2{{M'}_3} + {{M'}_5}} \right)} \right)/\left( {6nE{I_c}} \right)} \right]{\rm{d}}z} \end{array}$

 ${\lambda _{w1}} = \frac{{\int_0^l {\int_s {\frac{{M_q^2}}{{2EI}} \cdot {\rm{d}}s{\rm{d}}z} } }}{P},{\lambda _{w2}} = \frac{{\int_0^l {\int_s {\frac{{M_T^2}}{{2EI}} \cdot {\rm{d}}s{\rm{d}}z} } }}{{\Delta _T^2}},{\lambda _{w3}} = \frac{{\int_0^l {\int_s {\frac{{{M_q}{M_T}}}{{EI}} \cdot {\rm{d}}s{\rm{d}}z} } }}{{P\Delta _T^2}}$ (7)
1.1.2 纵向翘曲应变能计算

 $\Delta \left( z \right) = {\Delta _0}\left( z \right) + {\Delta _u}\left( z \right) = {\Delta _q}\left( z \right) + {\Delta _T}\left( z \right)$ (8)

 ${\mathit{\Pi }_{\rm{q}}} = \int_L {\left\{ {W\left( z \right) \cdot {{\left[ {{{\Delta ''}_q}\left( z \right) + {{\Delta ''}_T}\left( z \right)} \right]}^2}} \right\}{\rm{d}}z}$ (9)

 $\beta ' = \frac{{3 + \alpha _u^3\frac{{b \cdot {t_u}}}{{h' \cdot n \cdot {t_c}}}}}{{3 + \alpha _0^3\frac{{b \cdot {t_0}}}{{h' \cdot n \cdot {t_c}}}}}$
1.1.3 外部荷载势能Πp

 $\begin{array}{l} {\mathit{\Pi }_{\rm{p}}} = - \int_L {P \cdot d \cdot \theta {\rm{d}}z} = \\ - \int_L {{\psi _q}\left( z \right) \cdot {P^2}{\rm{d}}z} + \int_L {{\psi _T}\left( z \right) \cdot P \cdot {\Delta _T}\left( z \right){\rm{d}}z} \end{array}$ (10)

 $\left\{ \begin{array}{l} {\psi _q} = - \frac{{{{\left( {b - d} \right)}^2}}}{{12PE{J_s}}}\left( {2{M_1} + {M_4}} \right) + \frac{{h\left( {b - d} \right)\left( {{M_1} - {M_2}} \right)}}{{2PE{J_h}}} + \\ \;\;\;\;\;\;\;\frac{{c\left( {b - d} \right)\left( {{M_3} + 2{M_2}} \right)}}{{12PE{J_x}}}\\ {\psi _T} = \left( {\left( {{{M'}_2} - {{M'}_1}} \right)h\left( {b - d} \right)/\left( {2nE{J_h}} \right) - } \right.\\ \left( {b - d} \right)\left( {{{M'}_3} + 2{{M'}_2}} \right)/\left( {12cE{J_x}} \right) - \\ \left. {\left( {b - d} \right)2\left( {{M_4} + 2{M_1}} \right)/\left( {12E{J_s}} \right)} \right)/{\Delta _T}\\ {J_s} = \frac{1}{{12}}{b^3}{t_0} + \frac{1}{6}b_{os}^3{t_o} + \frac{1}{2}{b_{os}}{t_o}{\left( {b + {b_{os}}} \right)^2} \end{array} \right.$
 ${J_x} = \frac{1}{{12}}{c^3}{t_u}$
 ${J_h} = \frac{1}{{12}}{h^3}{t_c} + \frac{1}{4}{h^3}{t_c}{\left( {\frac{{1 - \beta '}}{{1 + \beta '}}} \right)^2}$

 $\mathit{\Pi } = {\mathit{\Pi }_{\rm{w}}} + {\mathit{\Pi }_{\rm{q}}} + {\mathit{\Pi }_{\rm{p}}}$ (11)

 $\begin{array}{*{20}{c}} {\frac{{{{\rm{d}}^2}}}{{{\rm{d}}{z^2}}}\left[ {2W\left( z \right) \cdot {{\Delta ''}_T}\left( z \right)} \right] + 2{\lambda _2}\left( z \right) \cdot {\Delta _T}\left( z \right) = }\\ { - {\lambda _1}\left( z \right) \cdot q\left( z \right)} \end{array}$ (12)

1.2 反对称荷载作用下支撑释放后的结构分析

2 试验验证

3 腹板线刚度比对桥面板横向内力的影响

 Download: 图 7 中腹板厚度增加后不同线刚度比条件下顶板横向内力变化图 Fig. 7 Transversal internal force change under different line stiffness ratio after the increase in web thickness

4 结论

1) 采用能量法可以较好地计算波形钢腹板单箱双室箱梁桥面板的横向内力，与试验结果及有限元结果吻合较好。

2) 对于波形钢腹板箱梁，其腹板对顶板的约束程度直接影响到顶板的横向受力，顶板横向应力值随腹板与顶板线刚度比变化基本呈线性变化；中腹板厚度变化对箱梁顶板横向内力的影响不可忽略。

 [1] 陈宜言. 波形钢腹板预应力混凝土桥设计与施工[M]. 北京: 人民交通出版社, 2009: 1-10. CHEN Yiyan. Design and construction of prestressed concrete bridge with corrugated steel webs[M]. Beijing: China Communications Press, 2009: 1-10. (0) [2] 刘玉擎. 组合结构桥梁[M]. 北京: 人民交通出版社, 2005: 35-50. LIU Yuqing. Composite structure bridge[M]. Beijing: China Communications Press, 2005: 35-50. (0) [3] ELGAALY M, SESHADRI A. Girders with corrugated webs under partial compressive edge loading[J]. Journal of the Structural Division, ASCE, 1997, 122(4): 783-791. (0) [4] 聂建国, 朱力, 唐亮. 波形钢腹板的抗剪强度[J]. 土木工程学报, 2013, 46(6): 97-109. NIE Jianguo, ZHU Li, TANG Liang. Shear strength of trapezoidal corrugated steel webs[J]. China civil engineering journal, 2013, 46(6): 97-109. (0) [5] 彭鲲, 李立峰, 肖小艳, 等. 波形钢腹板组合箱梁疲劳性能试验与理论分析[J]. 中国公路学报, 2013, 26(4): 94-101. PENG Kun, LI Lifeng, XIAO Xiaoyan, et al. Experimental and theoretical analysis of fatigue performance of composite box girder with corrugated steel webs[J]. China journal of highway and transport, 2013, 26(4): 94-101. (0) [6] 张阳, 邱俊峰, 唐重玺. 部分波形钢腹板预应力连续组合梁性能分析[J]. 湖南大学学报, 2013, 40(12): 14-20. ZHANG Yang, QIU Junfeng, TANG Chongxi. Analysis of behaviors of prestressed steel-concrete continuous composite beam with partial corrugated steel webs[J]. Journal of Hunan University, 2013, 40(12): 14-20. (0) [7] 贾慧娟, 戴航, 张建东. 波形钢腹板组合梁桥横向受力研究[J]. 工程力学, 2014, 31(12): 76-82. JIA Huijuan, DAI Hang, ZHANG Jiandong. Research on transverse internal forces in box-girder bridge with corrugated steel webs[J]. Engineering mechanics, 2014, 31(12): 76-82. (0) [8] 袁卓亚, 李立峰, 刘清, 等. 波形钢腹板组合箱梁横向内力分析及试验研究[J]. 中国公路学报, 2015, 28(11): 73-81. YUAN Zhuoya, LI Lifeng, LIU Qing, et al. Analysis and experimental study of transverse internal force in composite box-girder with corrugated steel webs[J]. China journal of highway and transport, 2015, 28(11): 73-81. (0) [9] 赵品, 荣学亮, 叶见曙. 波形钢腹板组合箱梁横向受力有效分布宽度研究[J]. 湖南大学学报, 2016, 43(7): 105-110. ZHAO Pin, RONG Xueliang, YE Jianshu. Research on the lateral effective width of composite box-girders with corrugated steel webs[J]. Journal of Hunan University, 2016, 43(7): 105-110. (0) [10] 方志, 郑辉, 刘双阳. 基于塑性分析的钢筋混凝土箱梁悬臂板横向受力有效分布宽度[J]. 土木工程学报, 2012, 45(3): 35-41. FANG Zhi, ZHENG Hui, LIU Shuangyang. Plastic analysis of the lateral effective width of cantilever slabs of reinforced concrete box-girders[J]. Journal of China civil engineering, 2012, 45(3): 35-41. (0) [11] 李立峰, 侯立超, 孙君翠. 波形钢腹板抗剪性能的研究[J]. 湖南大学学报, 2015, 42(11): 56-63. LI Lifeng, HOU Lichao, SUN Juncui. Research on shear mechanical property of corrugated steel webs[J]. Journal of Hunan University, 2015, 42(11): 56-63. DOI:10.3969/j.issn.1674-2974.2015.11.008 (0) [12] 李立峰, 王芳, 刘志才. 体外预应力波形钢腹板组合箱梁徐变性能研究[J]. 湖南大学学报, 2008, 35(5): 1-5. LI Lifeng, WANG Fang, LIU Zhicai. Study on the creep behavior of externally prestressed composite beam with corrugated steel webs[J]. Journal of Hunan University, 2008, 35(5): 1-5. (0) [13] 聂建国. 钢-混凝土组合梁结构:试验、理论与应用[M]. 北京: 科学出版社, 2005: 43-99. NIE Jian-guo. Steel concrete composite bridges[M]. Beijing: China Communications Press, 2005: 43-99. (0) [14] 徐向锋, 张峰, 韦成龙. 预应力混凝土箱梁开裂后的刚度损伤评估[J]. 工程力学, 2015, 32(7): 95-102. XU Xiangfeng, ZHANG Feng, WEI Chenglong. Stiffness damage assement of prestressed concrete box-girder after cracking[J]. Engineering mechanics, 2015, 32(7): 95-102. (0) [15] 郭金琼, 房贞政, 郑振. 箱形梁设计理论[M]. 2版. 北京: 人民交通出版社, 2008: 138-175. GUO Jinqiong, FANG Zhenzheng, ZHENG Zhen. Design theory of box girder[M]. Beijing: China Communications Press, 2008: 138-175. (0)