Fatigue evolution of natural frequency for prestressed concrete beam

doi:10.3785/j.issn.1008-973X.2022.10.012

Journal of ZheJiang University (Engineering Science)

2022, Vol. 56

Issue (10): 2007-2018 DOI: 10.3785/j.issn.1008-973X.2022.10.012

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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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

Received: 14 November 2021 Published: 25 October 2022

CLC:

TU 311

Fund: 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)

Corresponding Authors: Jun WEI E-mail: 2396370613@qq.com;juneweii@126.com

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Cite this article:

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.

URL:

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

预应力混凝土梁自振频率的疲劳演变

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

Fig.1 Calculation diagram of unbonded PC simply supported beam with quadratic parabolic reinforcement

Fig.2 Force diagram of micro beam unit under static balance state

Fig.3 Force diagram of micro beam unit under vibration balance state

Fig.4 Fatigue evolution comparison of first three order frequencies for three types of beams

Fig.5 Frequency degradation curves comparison of first three order frequencies for three types of beams

Fig.6 Development law of frequency correction coefficient for Timoshenko beam

Fig.7 Development curve of first and third order frequency correction coefficient for prestressed beam

Fig.8 Geometric dimension and reinforcement diagram

Fig.9 Acceleration versus time data of modal test

Tab.1 Test parameters setting of model beams

Fig.10 Stiffness degradation of model beam

N/10⁴	w_e(N)/Hz			w_E(N)/Hz
N/10⁴	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	w_T(N)/Hz			w_P(N)/Hz
N/10⁴	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%)

Tab.2 Summary of theoretical frequencies and measured frequencies of beam PCB-MPD-CFL-1

Fig.11 Measured frequency degradation curves and development surface of frequency correction coefficient

Fig.12 First order frequency degradation curves of test beams


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