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浙江大学学报(工学版)
浙江大学学报(工学版)  2022, Vol. 56 Issue (10): 2007-2018    DOI: 10.3785/j.issn.1008-973X.2022.10.012
土木工程、交通工程、海洋工程     
预应力混凝土梁自振频率的疲劳演变
杜永潇1,2,4(),卫军3,4,*(),孙晓立1,2
1. 广州市市政工程试验检测有限公司，广东 广州 510520
2. 广州建筑股份有限公司，广东 广州 510030
3. 武昌首义学院 城市建设学院，湖北 武汉 430064
4. 中南大学 土木工程学院，湖南 长沙 410075
Fatigue evolution of natural frequency for prestressed concrete beam
Yong-xiao DU1,2,4(),Jun WEI3,4,*(),Xiao-li SUN1,2
1. Guangzhou Municipal Engineering Testing Limited Company, Guangzhou 510520, China
2. Guangzhou Construction Engineering Limited Company, Guangzhou 510030, China
3. School of Urban Construction, Wuchang Shouyi University, Wuhan 430064, China
4. School of Civil Engineering, Central South University, Changsha 410075, China
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摘要：

为了研究预应力混凝土（PC）梁自振频率的疲劳演变规律，理论推导了抛物线型布筋的后张无黏结预应力梁疲劳历程自振频率的计算公式. 针对Euler梁、Timoshenko梁和预应力梁等3类梁，分析剪转效应、预应力效应对梁自振频率的疲劳演变规律的影响. 通过对预应力混凝土模型T梁的疲劳试验和动力测试，对比分析3类梁理论频率计算公式的适用性. 研究结果表明，抛物线型布筋的预应力不影响整个疲劳历程中梁的偶数阶频率. 梁的第1阶频率退化速率随着疲劳荷载幅值的增大而增大，随着预应力的增大而减小. 在实际工程应用中，对于偏心布筋无黏结预应力梁结构，须考虑预应力对基频的增强效应.
关键词： 自振频率;  疲劳试验;  预应力混凝土梁;  频率修正系数;  频率退化    
Abstract:

The calculation formula of natural frequency during fatigue process for post tensioned unbonded prestressed beam with quadratic parabolic reinforcement was theoretically derived in order to analyze the fatigue evolution law of natural frequency for prestressed concrete (PC) beams. The effects of shear-rotation and prestress on the fatigue evolution law of natural frequency for beams were analyzed for Euler beams, Timoshenko beams and prestressed beams. The applicability of the theoretical frequency calculation formulas of three types of beams was compared and analyzed through the fatigue test and dynamic test on the prestressed concrete model T-beams. Results show that the prestress with quadratic parabolic reinforcement does not affect the even order frequencies during fatigue process of the beam. The first-order frequency degradation rate of the beam increases with the increase of fatigue load amplitude and decreases with the increase of the prestress. The strengthening effect of prestress on the fundamental frequency should be considered for the unbonded prestressed beam structure with quadratic parabolic reinforcement in practical engineering application.
Key words: natural frequency    fatigue test    prestressed concrete beam    frequency correction coefficient    frequency degradation
收稿日期: 2021-11-14 出版日期: 2022-10-25
CLC:  TU 311  
基金资助: 国家自然科学基金资助项目(51578547，51778628)；广州市建筑集团有限公司科技计划资助项目([2022]–KJ023，[2021]-KJ010)；广东省住房和城乡建设厅2020年科技计划资助项目(2020-K9-594664)
通讯作者: 卫军     E-mail: 2396370613@qq.com;juneweii@126.com
作者简介: 杜永潇（1992—），男，博士，从事混凝土结构疲劳性能的研究. orcid.org/0000-0002-4269-2127. E-mail： 2396370613@qq.com
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引用本文:

杜永潇,卫军,孙晓立. 预应力混凝土梁自振频率的疲劳演变[J]. 浙江大学学报(工学版), 2022, 56(10): 2007-2018.

Yong-xiao DU,Jun WEI,Xiao-li SUN. Fatigue evolution of natural frequency for prestressed concrete beam. Journal of ZheJiang University (Engineering Science), 2022, 56(10): 2007-2018.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.10.012    或    https://www.zjujournals.com/eng/CN/Y2022/V56/I10/2007

图 1  二次抛物线型布筋无黏结PC简支梁的计算简图
图 2  静力平衡状态下微梁段的受力示意图
图 3  振动平衡状态下微梁段的受力示意图
图 4  3类梁前3阶频率的疲劳演变对比
图 5  3类梁前3阶频率退化曲线的对比
图 6  Timoshenko梁频率修正系数发展规律
图 7  预应力梁第1、3阶频率修正系数的发展曲线
图 8  模型梁尺寸及配筋图
图 9  模态测试加速度信号时程曲线
梁编号 σcon/MPa Npt/kN E/MPa 试验种类 Pmin/kN Pmax/kN ΔP/kN Pu/kN Nf /104
PCB-MPD-SL-1 0.70fptk 250.21 33 475 静载试验 — — — 241.8 —
PCB-MPD-CFL-1 0.70fptk 250.21 34 143 等幅疲劳试验 40 82 42 — 248.3
PCB-MPD-CFL-2 0.70fptk 250.21 33 408 等幅疲劳试验 40 90 50 — 160.1
PCB-LPD-SL-1 0.60fptk 207.44 32 594 静载试验 — — — 234.6 —
PCB-LPD-CFL-1 0.60fptk 207.44 31 673 等幅疲劳试验 40 92 52 — 63.2
表 1  模型梁的试验参数设置
图 10  模型梁的刚度退化
N/104 we(N)/Hz wE(N)/Hz
第1阶 第2阶 第3阶 第1阶 第2阶 第3阶
0 27.344 75.543 141.933 26.240(?4.04%) 104.961(38.94%) 236.161(66.39%)
1 26.137 72.591 138.184 25.798(?1.30%) 103.190(42.15%) 232.178(68.02%)
5 26.344 73.242 139.039 25.183(?4.41%) 100.733(37.53%) 226.650(63.01%)
9 25.996 72.429 137.207 24.975(?3.93%) 99.898(37.93%) 224.771(63.82%)
40 25.943 72.266 136.719 24.650(?4.98%) 98.602(36.44%) 221.854(62.27%)
60 25.855 71.777 136.067 24.501(?5.24%) 98.003(36.54%) 220.508(62.06%)
100 25.557 71.435 135.742 24.406(?4.50%) 97.624(36.66%) 219.654(61.82%)
150 25.367 71.289 134.440 23.286(?8.20%) 93.144(30.66%) 209.575(55.89%)
200 24.879 69.824 131.673 22.760(?8.52%) 91.041(30.39%) 204.842(55.57%)
240.6 24.414 69.513 130.964 21.916(?10.23%) 87.664(26.11%) 197.243(50.61%)
248.3 23.958 68.271 128.654 20.416(?14.78%) 81.665(19.62%) 183.747(42.82%)
N/104 wT(N)/Hz wP(N)/Hz
第1阶 第2阶 第3阶 第1阶 第2阶 第3阶
0 25.279(?7.55%) 89.586(18.59%) 158.329(11.55%) 26.249(?4.01%) 104.961(38.94%) 236.161(66.39%)
1 24.885(?4.79%) 88.581(22.03%) 158.218(14.50%) 25.806 (?1.27%) 103.190(42.15%) 232.178(68.02%)
5 24.334(?7.63%) 87.143(18.98%) 157.848(13.53%) 25.192 (?4.37%) 100.733(37.53%) 226.650(63.01%)
9 24.146(?7.12%) 86.643(19.63%) 157.666(14.91%) 24.983(?3.90%) 99.898(37.93%) 224.771(63.82%)
40 23.854(?8.05%) 85.856(18.81%) 157.328(15.07%) 24.659 (?4.95%) 98.602(36.44%) 221.854(62.27%)
60 23.719(?8.26%) 85.488(19.10%) 157.149(15.49%) 24.510 (?5.20%) 98.003(36.54%) 220.508(62.06%)
100 23.633(?7.53%) 85.254(19.34%) 157.029(15.68%) 24.415 (?4.47%) 97.624(36.66%) 219.654(61.82%)
150 22.615(?10.85%) 82.400(15.59%) 155.181(15.43%) 23.295 (?8.17%) 93.144(30.66%) 209.575(55.89%)
200 22.133(?11.04%) 81.008(16.02%) 154.051(16.99%) 22.770 (?8.48%) 91.041(30.39%) 204.842(55.57%)
240.6 21.356(?12.53%) 78.706(13.23%) 151.897(15.98%) 21.925 (?10.19%) 87.664(26.11%) 197.243(50.61%)
248.3 19.964(?16.67%) 74.424(9.01%) 147.087(14.33%) 20.426 (?14.74%) 81.665(19.62%) 183.747(42.82%)
表 2  梁PCB-MPD-CFL-1疲劳过程理论频率及实测频率的汇总表
图 11  实测频率退化曲线及频率修正系数发展曲面
图 12  试验梁的第1阶频率退化曲线
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