ELASTIC MODULUS OF PRESTRESSED AND REINFORCED CONCRETE BEAMS IN TAIWAN UNDER DYNAMIC FLEXURAL LOADING

台灣預力鋼筋混凝土梁受動態撓曲載重作用之彈性模數

10.6652/JoCICHE.202104_33(2).0001

Marco Bonopera；張國鎮(Kuo-Chun Chang)

concrete beam ； elastic modulus ； flexural vibration ； frequency ； 混凝土梁 ； 彈性模數 ； 撓曲振動 ； 頻率

中國土木水利工程學刊

33卷2期（2021 / 04 / 01）

83 - 92

英文

The elastic modulus plays a significant role in the dynamics of Reinforced (RC) and Prestressed Concrete (PC) structures. According to Model B4-TW, the effective elastic modulus of concrete in Taiwan is approximately 80% of that calculated by international standards due to smaller coarse aggregate amount and higher paste volume which reflect its mechanics. This work allowed to verify the influence of such a reduced modulus on the dynamic flexural response of RC and PC beams in Taiwan. Laboratory tests were conducted in distinct days, for a total period of ≈ 2.5 months, on a RC beam made in Taiwan prestressed by a parabolic tendon. The RC beam was short term subjected to free flexural vibrations under prestress losses and different conditions of early-age curing. Simultaneously, its time-dependent daily elastic modulus was determined by Model B4-TW, and experimentally by ASTM C 469/C 469M-14 and the solution proposed by Bonopera et al. tuned on compression test results on cylinders. Subsequently, all test data were compared with prediction formulas based on the beam dynamics of Euler-Bernoulli. The predictions indicated that the fundamental frequency of RC and PC beams in Taiwan is well simulated by the variation of their reduced modulus due to the consolidation/hardening of concrete, according to Model B4-TW. Moreover, the accurate measurement of fundamental frequency was confirmed to be a reliable solution for flexural stiffness evaluation of RC and PC members.

鋼筋混凝土和預力混凝土梁的彈性模數在其結構動態特性扮演很重要的角色。根據B4-TW鋼筋混凝土材料應力應變研究模型顯示，由於台灣相較美國採用較少的粗粒料及較高的漿體體積進行混凝土材料配置，台灣混凝土材料實際有效彈性模數約為美國混凝土設計規範計算值之百分之八十。本研究探討混凝土材料有效彈性模數折減現象對台灣鋼筋混凝和預力混凝土梁之動態撓曲反應的影響。以拋物線型配置鋼腱之預力鋼筋混凝土為實驗試體，試體澆鑄時同步灌注混凝土標準圓柱試體，進行為期約兩個半月，取得混凝土圓柱試體在不同養護齡期天數下之抗壓試驗資料。量測鋼筋混凝土梁試體受短期預力損失和早期養護差異條件之撓曲振動值，同時採用B4-TW模型、ASTM C 469／C 469M-14試驗模型和Bonopera et al.（2018）研究成果，探討每日圓柱試體抗壓試驗所計算得到之混凝土材料彈性模數時變性。接著，將所有試驗資料與Euler-Bernoulli梁動態特性預測計算公式進行比較，結果顯示，台灣鋼筋混凝土和預力鋼筋混凝土梁的基本振動頻率，可有效以B4-TW模型考量混凝土養護過程凝固和硬化，計算得折減的彈性模數進行推估。因此，研究驗證精確量測鋼筋混凝土和預力鋼筋混凝土梁基本振動頻率，是評估其撓曲勁度可靠的方法。

1. Chin, W. Y.,Chern, J. C.(2018)。Establishment of B4-TW prediction model for concrete deformation in Taiwan (II): Drying shrinkage, autogenous shrinkage and total shrinkage。Structural Engineering，33(3)，65-86。
   連結：
2. Hu, W. H.,Liao, W. C.(2019).Study of influences of reduced elastic modulus of concrete in Taiwan on the seismic and collapse evaluation of RC structures.Journal of the Chinese Institute of Civil and Hydraulic Engineering,31(3),239-251.
   連結：
3. Liu, T. K.,Chern, J. C.(2018)。Establishment of B4-TW prediction model for concrete deformation in Taiwan (I): Basic creep, drying creep and total creep。Structural Engineering，33(3)，43-64。
   連結：
4. ACI=American Concrete Institute(2019).Building code requirements for structural concrete and commentary.Farmington Hills, MI, U.S.A.:ACI.
5. ASTM=American Society for Testing and Materials(2016).Annual Book of ASTM standards, Section 4: Construction vol. 04.02, Concrete & Aggregates.West Conshohocken, PA, U.S.A.:
6. Bazant, Z. P.,Cedolin, L.(1991).Stability of Structures.New York, NY, U.S.A.:Oxford University Press.
7. Bažant, Z. P.,Jirásek, M.,Hubler, M. H.,Carol, I.(2015).RILEM draft recommendation: TC-242-MDC multi-decade creep and shrinkage of concrete: material model and structural analysis. Model B4 for creep, drying shrinkage and autogenous shrinkage of normal and high-strength concretes with multi-decade applicability.Materials and Structures,48(4),753-770.
8. Bonopera, M.,Chang, K. C.,Chen, C. C.,Lee, Z. K.,Sung, Y. C.,Tullini, N.(2019).Fiber Bragg grating-differential settlement measurement system for bridge displacement monitoring: Case study.Journal of Bridge Engineering, ASCE,24(10),1-12.
9. Bonopera, M.,Chang, K. C.,Chen, C. C.,Lee, Z. K.,Tullini, N.(2018).Axial load detection in compressed steel beams using FBG-DSM sensors.Smart Structures and Systems,21(1),53-64.
10. Bonopera, M.,Chang, K. C.,Chen, C. C.,Lin, T. K.,Tullini, N.(2018).Bending tests for the structural safety assessment of space truss members.International Journal of Space Structures,33(3-4),138-149.
11. Bonopera, M.,Chang, K. C.,Chen, C. C.,Lin, T. K.,Tullini, N.(2018).Compressive column load identification in steel space frames using second-order deflection-based methods.International Journal of Structural Stability and Dynamics,18(7),1-16.
12. Bonopera, M.,Chang, K. C.,Chen, C. C.,Sung, Y. C.,Tullini, N.(2019).Experimental study on the fundamental frequency of prestressed concrete bridge beams with parabolic unbonded tendons.Journal of Sound and Vibration,455,150-160.
13. Bonopera, M.,Chang, K. C.,Chen, C. C.,Sung, Y. C.,Tullini, N.(2018).Prestress force effect on fundamental frequency and deflection shape of PCI beams.Structural Engineering and Mechanics,67(3),255-265.
14. Bonopera, M.,Chang, K. C.,Chen, C. C.,Sung, Y. C.,Tullini, N.(2018).Feasibility study of prestress force prediction for concrete beams using second-order deflections.International Journal of Structural Stability and Dynamics,18(10),1-19.
15. Bonopera, M.,Chang, K. C.,Lee, Z. K.(2020).State-of-the-art review on determining prestress losses in prestressed concrete girders.Applied Sciences,10(20),7257.
16. CEB(1993).CEB-FIP Model Code 1990.Lausanne, Switzerland:Comité Euro-International du Béton.
17. Deák, G.(1996).Discussion on prestress force effect on vibration frequency of concrete bridges.Journal of Structural Engineering, ASCE,458-459.
18. Gan, B. Z.,Chiew, S. P.,Lu, Y.,Fung, T. C.(2019).The effect of prestressing force on natural frequencies of concrete beams ⎯ A numerical validation of existing experiments by modelling shrinkage crack closure.Journal of Sound and Vibration,455,20-31.
19. Hamed, E.,Frostig, Y.(2006).Natural frequencies of bonded and unbonded pre-stressed beams pre-stress force effects.Journal of Sound and Vibration,295(1-2),28-39.
20. Hu, W. H.,Liao, W. C.(2020).Study of prediction equation for modulus of elasticity of normal strength and high strength concrete in Taiwan.Journal of the Chinese Institute of Engineers,43(7),638-647.
21. Hubler, M. H.,Wendner, R.,Bažant, Z. P.(2015).Comprehensive database for concrete creep and shrinkage: analysis and recommendations for testing and recording.ACI Materials Journal,112(4),547-558.
22. Jain, S. K.,Goel, S. C.(1996).Discussion on prestress force effect on vibration frequency of concrete bridges.Journal of Structural Engineering, ASCE,459-460.
23. Jaiswal, O. R.(2008).Effect of prestressing on the first flexural natural frequency of beams.Structural Engineering and Mechanics,28(5),515-524.
24. Jang, J. B.,Lee, H. P.,Hwang, K. M.,Song, Y. C.(2010).A sensitivity analysis of the key parameters for the prediction of the prestress force on bonded tendons.Nuclear Engineering and Technology,42,319-328.
25. Jerath, S.,Shibani, M. M.(1984).Dynamic modulus for reinforced concrete beams.Journal of Structural Engineering, ASCE,110(6),1405-1410.
26. Kee, S. H.,Kang, J. W.,Choi, B. J.,Kwon, J.,Candelaria, M. D.(2019).Evaluation of static and dynamic residual mechanical properties of heat-damaged concrete for nuclear reactor auxiliary buildings in Korea using elastic wave velocity measurements.Materials,12,2695.
27. Law, S. S.,Lu, Z. R.(2005).Time domain responses of a pre-stressed beam and pre-stress identification.Journal of Sound and Vibration,288(4-5),1011-1025.
28. Limongelli, M. P.,Siegert, D.,Merliot, E.,Waeytens, J.,Bourquin, F.,Vidal, R.,Le Corvec, V.,Gueguen, I.,Cottineau, L. M.(2016).Damage detection in a post tensioned concrete beam - Experimental investigation.Engineering Structures,128,15-25.
29. Liu, T. K.(2017).Department of Civil Engineering, National Taiwan University.
30. Lu, Z. R.,Law, S. S.(2006).Identification of pre-stress force from measured structural responses.Mechanical Systems and Signal Processing,20(8),2186-2199.
31. MATLAB(2019).MATLAB, Introduction to GUIDE, The Mathworks, Inc., 2019a (2019).
32. Mehta, P. K.,Monteiro, P. J. M.(2006).Concrete: Microstructure, Properties, and Materials.New York, NY, U.S.A.:McGraw-Hill.
33. Musiał, M.,Grosel, J.(2016).Determining the Young’s modulus of concrete by measuring the eigenfrequencies of concrete and reinforced concrete beams.Construction and Building Materials,121,44-52.
34. Palanisamy, S. P.,Maheswaran, G.,Annaamalai, M. G. L.,Vennila, P.(2015).Steel slag to improve the high strength of concrete.International Journal of ChemTech Research,7(5),2499-2505.
35. Saiidi, M.,Douglas, B.,Feng, S.(1994).Prestress force effect on vibration frequency of concrete bridges.Journal of Structural Engineering, ASCE,120(7),2233-2241.
36. Song, Y.(2000).Dynamics of Highway Bridges.Beijing, China:China Communications Press.
37. STRAND7(2010).STRAND7, Release 2.4.6. Pty Ltd. Copyright (2010).
38. Timoshenko, S. P.,Gere, J. M.(1961).Theory of Elastic Stability.New York, NY, U.S.A.:McGraw-Hill.
39. Wang, T. H.,Huang, R.,Wang, T. W.(2013).The variation of flexural rigidity for post-tensioned prestressed concrete beams.Journal of Marine Science and Technology,21(3),300-308.
40. Young, W.C.(Ed.),Budynas, R.G.(Ed.)(2002).Roark’s Formulas for Stress and Strain.New York, NY, U.S.A.:McGraw-Hill.