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## Analysis of transverse separated-block construction effects of steel box girders based on partial shear theory

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Abstract

An analytical method for deformation and stress was established in order to analyze the effect of weakened and uneven shear rigidity caused by the transverse separated-block construction on the mechanical characteristics of separated-block steel box girders. The theory of composite structure considering slip at the interlayer was adopted based on the partial shear connection between the top and bottom plate of the asymmetrical thin-walled, open-section block after partition. The deformation equation based on the key parameters such as the span of the bridge, segment length and shear stiffness was established by analyzing the section design parameters from the typical single-box multi-cell steel box girder with constant sections, obtaining the statistical law and eliminating some geometric parameters. The block construction method, which can be applied to steel box girder with different spans, was proposed by analyzing the impact parameters. Results show that temporary shear braces should be used to increase the shear stiffness, or a temporary pier is required to reduce the deflection and control the construction quality when the segment length exceeds 40 m.

Keywords： steel box girder ; transverse separated-block construction ; partial shear ; parameter analysis ; construction method

WANG Jin-feng, WU Tian-mei, WANG Jian-jiang, WANG Min-quan, XU Rong-qiao. Analysis of transverse separated-block construction effects of steel box girders based on partial shear theory. Journal of Zhejiang University(Engineering Science)[J], 2019, 53(7): 1380-1388 doi:10.3785/j.issn.1008-973X.2019.07.018

### 图 1

Fig.1   Infinitesimal of composite structure

#### 1.2.1. 部分抗剪连接组合结构控制微分方程

$\overline {EI} \frac{{{{\rm{d}}^4}w}}{{{\rm{d}}{x^4}}} - h\overline {EA} \frac{{{{\rm{d}}^3}{u_{\rm{s}}}}}{{{\rm{d}}{x^3}}} - q = 0\;,$

$\overline {EA} h\frac{{{{\rm{d}}^3}w}}{{{\rm{d}}{x^3}}} - \overline {EA} \frac{{{{\rm{d}}^2}{u_{\rm{s}}}}}{{{\rm{d}}{x^2}}} + {k_{\rm{s}}}{u_{\rm{s}}} = 0\;.$

1）两端简支的部分抗剪连接组合结构在均布荷载q作用下挠度的精确解为

$\begin{split} w = & \frac{q}{{24\overline {EI} }}({x^4} - 2{x^3}l + x{l^3}) + \\ & \frac{q}{{{\alpha ^4}\overline {EI} }}({\beta ^2} - 1)[ - \tanh \;({{\alpha l}}/{2})\sinh \;(\alpha x) + \\ & \cosh \;(\alpha x) + {\alpha ^2}(lx - {x^2})/2 - 1]\;. \end{split}$

2）两端简支的部分抗剪连接组合结构在集中荷载P作用下挠度的精确解为

w = \left\{ \begin{aligned} & \frac{P}{{48\overline {EI} }}x(3{l^2} - 4{x^2}) + \frac{P}{{2{\alpha ^3}\overline {EI} }}({\beta ^2} - 1)\bigg[\alpha x - \\ & \qquad \frac{{\sinh \;(\alpha x)}}{{\cosh \;(\alpha l/2)}}\bigg],\;\;\;\;\;0 \leqslant x \leqslant l/2; \\ & \frac{P}{{48\overline {EI} }}(l - x)[3{l^2} - 4{(l - x)^2}] + \\ & \qquad \frac{P}{{2{\alpha ^3}\overline {EI} }}({\beta ^2} - 1)\bigg[\alpha (l - x) - \\ & \qquad \frac{{\sinh \;(\alpha l - \alpha x)}}{{\cosh \;(\alpha l/2)}}\bigg]\;,\;\;\;\;\;l/2 < x \leqslant l . \end{aligned} \right.

### 2.1. 影响参数归并

$w = w(q,l,h,{A_1},{A_2},{I_1},{I_2},{k_{\rm{s}}})\;.$

Tab.1  Calculation parameters of general-span steel box girders

 L/m H/m m h1/m h2/m a1/m ad/m af/m i1/m3 id/m3 if/m3 40 2.2 1/18 0.114 0.053 0.026 0.022 0.013 0.000 28 0.000 17 0.013 50 2.5 1/20 0.111 0.039 0.028 0.026 0.023 0.000 28 0.000 13 0.010 60 2.5 1/24 0.112 0.053 0.027 0.027 0.012 0.000 30 0.000 18 0.008 70 3.2 1/22 0.108 0.053 0.029 0.027 0.022 0.000 32 0.000 19 0.013 80 3.2 1/25 0.107 0.042 0.033 0.035 0.021 0.000 35 0.000 11 0.016 90 3.8 1/24 0.103 0.038 0.031 0.031 0.019 0.000 31 0.000 10 0.011

$m = H/L.$

${A_1} = {a_1}B,\;{A_2} = {a_{\rm{d}}}B + {a_{\rm{f}}}mL,$

$q = \rho ({A_1} + {A_2}),$

$h = H - {h_1} - {h_2},$

${I_1} = {i_1}B,\\ {I_2} = {i_{\rm{d}}}B + {i_{\rm{f}}}mL + \\ {(d - {h_2})^2}{a_{\rm{d}}}B + \frac{{{{(mL - 2d)}^2}}}{4}{a_{\rm{f}}}mL. \\$

B为相邻腹板间距，ρ为钢材容重.

$w = w(L,{l_{\rm{f}}},{k_{\rm{s}}})\;.$

### 图 2

Fig.2   Relationship between wP and lf

### 图 3

Fig.3   Variation of deflection due to partial shear connection

### 图 4

Fig.4   Relationship between wP and ks

### 2.3. 应力的影响参数分析

$w''{\rm{ = }}\frac{{{M_1}}}{{{M_2}}} = \frac{{E{I_1}}}{{E{I_2}}} = \frac{{M - Nh}}{{EI}}\;.$

${\sigma ^{{\rm{P}}i}} = {N}/{{{A_i}}} + {{{M_i}{h_i}}}/{{{I_i}}}\;.$

### 图 5

Fig.5   Relationship between σPi and lf

### 图 6

Fig.6   Variation of stress due to partial shear connection

### 图 7

Fig.7   Relationship between σP2 and ks

## 3. 分块施工技术讨论

### 图 8

Fig.8   Flow chart of block construction design

### 图 9

Fig.9   Section of（40+65+40）m steel box girder after transverse blocking

L= 65 m，lf=27 m时，可以从图3中预测 (wPwT)小于15 mm，即不超过[w]，不需要采用加固措施. 分块后节段的挠度结果如图10所示，(wPwT)为9 mm，与预测值相符. 由于lf较小，吊装节段wP最大仅为12.2 mm. 由2.3节的讨论可知，σP2σP1更不利，σP2理论及实测结果如图11所示. σP2最大值为12.9 MPa，|σP2σT2|最大为1.5 MPa，在工程允许范围内. 综合考虑分块节段的挠度与应力影响，可以直接吊装而无需额外采用加固措施，如图12所示. 施工过程中的变形和应力实测值与理论值对比显示，两者吻合较好.

### 图 10

Fig.10   Comparison of theoretical deflection result and practical data of 27 m hoisting segment

### 图 11

Fig.11   Comparison of theoretical stress result and practical data of 27 m hoisting segment

### 图 12

Fig.12   Field hoisting of transverse block construction

### 图 13

Fig.13   Section of（40+60+40）m steel box girder after transverse blocking

L=65 m，lf=38 m时，由图3可以预测(wPwT)达到25 mm，需要采用加固措施. 分块后节段挠度和应力的理论和实测结果如图1415所示. 在没有任何加固措施时，wP为46 mm，(wPwT)为31 mm，与预测值相符并且超过允许值. σP2的最大值为25.2 MPa，在工程允许范围内，应力增大效应不明显. 由于分块后的箱梁块端部滑移明显，可以在端部设置抗剪临时撑来改善受力变形特性，如图16所示. X型抗剪临时撑的构造及连接方式如图17所示. 通过抗剪支撑加固，增大了部分抗剪连接钢箱梁的ks，可以利用两端简支的部分抗剪连接组合结构在均布荷载q作用下的挠度计算公式（4），通过改变ks来计算加固后分块钢箱梁的挠度，并结合式（13）、（14）计算应力. 支撑后σP2略有减小，而wP=24 mm，减小47.8%，可见抗剪临时支撑对减小挠度的效果十分明显.

### 图 14

Fig.14   Comparison of theoretical deflection result and practical data of 38 m hoisting segment

### 图 15

Fig.15   Comparison of theoretical stress result and practical data of 38 m hoisting segment

### 图 16

Fig.16   Block of steel box girder strengthened by X-type brace

### 图 17

Fig.17   Structural map of X-type brace

### 图 18

Fig.18   Section of (55+65) m steel box girder after transverse blocking

L=65m，lf=55m时，由图3可以确定(wPwT)将超过[w]，预测需要采用加固措施. 分块后节段挠度和应力的理论和实测结果如图1920所示. 理论分析表明，横向分块后wP达到144.0 mm，(wPwT)为78.4 mm，远超工程允许范围. σP2的最大值为47.8 MPa，与完全抗剪连接相比，|σP2σT2|最大为9.8 MPa，未超出工程允许范围，应力增大效应不明显. 由于部分抗剪连接引起的挠度过大，采用在跨中设置临时支点的方法，如图21所示. 跨中临时支墩加固相当于作用一个竖向集中力，可以由式（4）、（5）计算挠度，根据叠加原理和临时支墩处挠度为零解得竖向集中力，进而得到边跨各截面挠度，结合式（13）、（14）计算应力. 结果表明，在跨中临时墩处会产生压应力，但较小；整体挠度的减小效果十分明显，满足施工线形要求，且与实测值吻合良好.

### 图 19

Fig.19   Comparison of theoretical deflection result and practical data of 55 m hoisting segment

### 图 20

Fig.20   Comparison of theoretical stress result and practical data of 55 m hoisting segment

### 图 21

Fig.21   Supported by mid-span temporary pier

## 5. 结　论

（1）根据部分抗剪连接组合结构的分析理论，考虑实际工程的设计特点和变形规律，对影响钢箱梁横向分块施工效应的参数进行归并，建立分块施工结构形状尺寸参数与结构挠度之间的关系式，分析影响规律，为横向分块施工提供了理论支撑.

（2）对横向分块施工技术进行探讨，给出施工方法的设计流程，并将该方法应用于实例工程，解决了多座不同跨径城市高架钢箱梁桥的快速施工问题，可以为同类工程提供参考.

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