﻿ 节段预制拼装混凝土桥梁剪力键接缝的抗剪强度
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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (10): 1414-1420.  DOI: 10.11908/j.issn.0253-374x.2019.10.005 0

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SHEN Yin, CAI Peng, CHEN Lisheng, LI Guoping. Shear Strength of Keyed Joints in Segmental Precast Concrete Bridges[J]. Journal of Tongji University (Natural Science), 2019, 47(10): 1414-1420. DOI: 10.11908/j.issn.0253-374x.2019.10.005

文章历史

1. 同济大学 土木工程学院，上海 200092;
2. 上海城建市政工程(集团)有限公司，上海 200065

Shear Strength of Keyed Joints in Segmental Precast Concrete Bridges
SHEN Yin 1, CAI Peng 1, CHEN Lisheng 2, LI Guoping 1
1. College of Civil Engineering, Tongji University, Shanghai 200092, China;
2. Shanghai Urban Construction Municipal Engineering (Group) Co., Ltd., Shanghai 200065, China
Abstract: Based on the stress analysis of a free body with a multi-keyed joint at the web of segmental precast concrete bridge, the shear stress distribution on the root of multi-keys at the joint was analyzed and derived. According to the elastic theoretical analysis, a non-uniform factor of shear stress at the root of multi-keys was proposed and used to modify the AASHTO formula of shear strength of the joint with multi-keys. The comparison with the numerical analysis results shows that the modified formula can accurately reflect the change trend and peak effect of shear stress in multi-keys. Moreover, the differences between the calculation results of the proposed modified formula and the relevant test results are within 5%.
Key words: segmental precast concrete bridges    multi-keyed joints    non-uniform shear stress distribution    shear strength

 $V_{\mathrm{u}}=A_{\mathrm{k}} \sqrt{f_{\mathrm{ck}}}\left(0.2048 \sigma_{\mathrm{n}}+0.9961\right)+0.6 \mathrm{A}_{\mathrm{sm}} \sigma_{\mathrm{n}}$ (1)

1 多齿剪力键剪应力分布理论分析 1.1 脱离体受力分析

 图 1 腹板脱离体 Fig.1 Free body of web

 图 2 上部脱离体应力 Fig.2 Stress of upper free body

(1) 接缝面全程受压，紧密贴合无脱离，接缝面左右侧纤维共同变形，满足平截面假定.

(2) 梁的上下层纤维间剪应力τzy均匀地分布在截面宽度b方向上.

(3) 剪力键根部剪应力τi均匀地分布在剪力键根部面积Ai上.

 $\int_{A^{*}} \sigma_{z} \mathrm{d} A-\int_{A_{i}+A_{\mathrm{sm}}}\left(\sigma_{z}+\mathrm{d} \sigma_{z}\right) \mathrm{d} A+\tau_{z y} b \mathrm{d} z=0$

 $\tau_{z y}=\frac{1}{b \mathrm{d} z} \frac{\mathrm{d} M_{x}}{I_{x}} S_{A^{*}}=\frac{Q}{I_{x} b} S_{A^{*}}$ (2)

 $\begin{array}{l} \sum {{M_L}} = \int_{{A^*}} {{\sigma _z}} \left( {y - {y_{\rm{s}}}} \right){\rm{d}}A + \int_{{A_i}} {{\tau _i}{\rm{d}}z{\rm{d}}A} + \\ \;\;\;\;\;\;\int_{{A_{\rm{m}}}} {{\tau _{{\rm{ma}}}}} {\rm{d}}z{\rm{d}}A - \int_{{A_i} + {A_{\rm{m}}}} {\left( {{\sigma _z} + {\rm{d}}{\sigma _z}} \right)} \left( {y - {y_{\rm{s}}}} \right){\rm{d}}A = \\ \;\;\;\;\;\sum {{\tau _i}} {A_i}{\rm{d}}z + \mu \left( {{\sigma _z} + {\rm{d}}{\sigma _z}} \right){\rm{d}}z{A_{{\rm{sm}}}} - \\ \;\;\;\;\;\;\frac{{{\rm{d}}{M_x}}}{{{I_x}}}\left( {{I_{{A^*}}} - {y_{\rm{s}}}{S_{{A^*}}}} \right) = 0 \end{array}$

 $\sum {{\tau _i}} {A_i} = \frac{Q}{{{I_x}}}\left( {{I_{{A^*}}} - {y_{\rm{s}}}{S_{{A^*}}}} \right) - \mu {\sigma _z}{A_{{\mathop{\rm sm}\nolimits} }}$ (3)

 $\sum \tau_{i} A_{i}=f\left(\frac{2 y_{\mathrm{s}}}{h}\right) Q-\mu \sigma_{z} A_{\mathrm{sm}}$ (4)

 $\sum \tau_{i} A_{i}=f\left(\frac{2 y_{\mathrm{s}}}{h}\right) Q$ (5)

 图 3 ys取值区间 Fig.3 Value interval of ys

(1) 将ys=yi+1+hi/2代入式(4)，得到前i个剪力键上合剪力∑τiAi.

(2) 将ys=yi+hi/2代入式(4)，得到前(i-1)个剪力键上合剪力∑τi-1Ai-1.

(3) 两者相减得到第i个剪力键根部剪应力

 $\tau_{i}=\frac{\sum \tau_{i} A_{i}-\sum \tau_{i-1} A_{i-1}}{A_{i}}$ (6)
1.2 剪应力分布不均匀系数

(1) 典型的剪力键均匀分布的接缝面如图 4所示，其中A面为凸面，B面为凹面.

 图 4 均匀分布剪力键的接缝面 Fig.4 Joint with uniformly distributed keys

 $\left(\tau_{i}\right)_{\max }=\frac{Q}{b h_{i}}\left(f\left(\frac{2 y_{i+1}+h_{i}}{h}\right)-f\left(\frac{2 y_{i}+h_{i}}{h}\right)\right)$

 $\bar{\tau}=\frac{Q}{b \sum h_{i}}$ (7)

 $k=\frac{\left(\tau_{i}\right)_{\max }}{\bar{\tau}}$ (8)

 $\left\{ {\begin{array}{*{20}{l}} {k = N\left( {f\left( {\frac{{ - {h_i} - 2s}}{h}} \right) - f\left( {\frac{{{h_i}}}{h}} \right)} \right), N为奇数}\\ {k = N\left( {f\left( {\frac{{ - s}}{h}} \right) - f\left( {\frac{{2{y_i} + {h_i}}}{h}} \right)} \right), N为偶数} \end{array}} \right.$ (9)

(2) 典型的剪力键靠一侧分布的接缝面如图 5所示.

 图 5 剪力键靠一侧分布的接缝面 Fig.5 Joint with non-uniformly distributed keys

 $\left(\tau_{i}\right)_{\max }=\frac{Q}{b h_{i}} f\left(\frac{2 y_{2}+h_{i}}{h}\right)$

 $k=N f\left(\frac{2 y_{2}+h_{i}}{h}\right)$ (10)

(3) 分别计算(1)、(2)两种情况下的剪应力分布不均匀系数k，取较大值作为最终的剪应力分布不均匀系数k.

1.3 考虑剪应力不均匀分布的抗剪承载力

(1) 施工阶段应力计算时，节段预制拼装混凝土桥梁剪力键接缝面上的剪应力应考虑剪力键中的剪应力不均匀分布效应.施工阶段剪力键中的剪应力峰值可表达为

 $\tau=\bar{\tau}_{\max }$ (11)

(2) 运营阶段承载能力计算时，可沿用AASHTO规范建议公式并进行修正.考虑了剪应力分布不均匀系数修正后的抗剪承载力计算式可表达为

 $V_{\mathrm{u}}=A_{\mathrm{k}} \frac{\sqrt{f_{\mathrm{ck}}}}{k}\left(0.2048 \sigma_{\mathrm{n}}+0.9961\right)+0.6 A_{\mathrm{sm}} \sigma_{\mathrm{n}}$ (12)

k值反映了剪力键中剪应力的峰值效应，由此得到修正后的抗剪承载力为塑性下限解.

2 数值分析 2.1 分析参数及有限元模型

 图 6 多剪力键接缝面几何参数(单位：mm) Fig.6 Geometries of multi-keyed joints(unit:mm)

 图 7 有限元模型(单位：mm) Fig.7 Finite element model(unit:mm)
2.2 数值分析结果 2.2.1 剪力键数量影响

 图 8 剪力键数量的影响 Fig.8 Effect of key's number

2.2.2 剪力键布置形式影响

 图 9 剪力键布置形式影响 Fig.9 Effect of keys' layout

2.2.3 轴力剪力比影响

 图 10 轴力剪力比影响 Fig.10 Effect of axial force to shear ratio
3 修正抗剪承载力计算公式的验证 3.1 与Jiang等[4]试验结果比较

 $V_{\mathrm{u}}=0.14 f_{\mathrm{c}} A_{\mathrm{k}}+0.65 \sigma_{\mathrm{n}} A_{\mathrm{joint}}$ (13)
 图 11 试件尺寸[4](单位：mm) Fig.11 Dimension of specimen[4] (unit: mm)

3.2 与Alcalde等[3]的有限元结果比较

Alcalde等[3]以Zhou等[2]的试验模型为基础建立有限元模型(见图 12)，取剪力键数量为主要参数，研究了从单齿到七齿剪力键接缝面的受力性能.通过对有限元结果进行系数回归给出了考虑剪力键数量影响的抗剪承载力计算公式，该公式仅适用于混凝土标准抗压强度为50 MPa、接缝面压应力水平为3 MPa的情况, 如下所示：

 \begin{aligned} V_{\mathrm{u}}=& 7.118 {A}_{\mathrm{k}}\left(1-0.064 N_{\mathrm{k}}\right)+\\ & 2.436 {A}_{\mathrm{sm}} \sigma_{\mathrm{n}}\left(1+0.127 N_{\mathrm{k}}\right) \end{aligned} (14)
 图 12 有限元模型[3](单位：mm) Fig.12 Finite element model[3](单位:mm)

4 结论

(1) 通过对单腹板剪力键接缝面脱离体的受力分析，从理论上阐释了剪力键接缝面上剪应力不均匀分布的受力机理，提出了多齿剪力键接缝面上剪力键根部剪应力的计算方法以及考虑剪应力不均匀分布的抗剪承载力计算方法.

(2) 多剪力键接缝面剪应力及抗剪承载力的计算中均应考虑剪应力在剪力键中的不均匀分布效应.本研究采用剪应力分布不均匀系数k来反映剪力键中剪应力分布的峰值效应，并给出了k的简化计算方法.

(3) 通过数值分析方法，讨论了轴力剪力比、剪力键数量及剪力键分布形式对剪力键根部剪应力的影响.结果表明:剪力键数量增多会增加剪力键根部剪应力分布的不均匀程度，当剪力键靠一侧分布时，剪应力峰值由梁中心向剪力键稀疏侧转移，而轴力剪力比对剪应力分布的影响较小.所提出的剪应力分布计算公式可准确反映剪力键中剪应力的变化趋势和峰值效应.

(4) 将考虑剪应力不均匀分布的抗剪承载力计算结果分别与文献[4]的试验结果及文献[3]的有限元结果进行比较.结果表明：AASHTO规范建议公式对三齿剪力键接缝面抗剪承载力的计算结果比试验结果偏大10%左右，对七齿剪力键接缝面抗剪承载力的计算结果比有限元结果偏大35%左右；所提出的考虑了剪应力不均匀分布的修正公式对抗剪承载力的计算结果与试验、有限元结果相比，误差均在5%以内.

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