Advertisement

Bulletin of Earthquake Engineering

, Volume 17, Issue 3, pp 1495–1519 | Cite as

Detailed evaluation of the ultimate flexural states of beams in unbonded precast prestressed concrete frames

  • Kiwoong Jin
  • Sunghoon SongEmail author
  • Kazuhiro Kitayama
  • Linfei Hao
Original Research
  • 58 Downloads

Abstract

To guarantee the ductile and self-centering behavior of unbonded precast prestressed concrete (PCaPC) frames, a macro-model that accurately reflects the seismic behavior of cruciform unbonded PCaPC subassemblages was built using a theoretical approach in this study. By employing this macro-model, the relation between the strain states of the tendons and concrete in an arbitrary beam section was established. Based on this relation, iterative and simplified evaluation methods for the beam strength and deflection, as well as the strain of the tendons, in the ultimate flexural state were proposed. The accuracy and effectiveness of the proposed methods were verified through comparison of their results with those obtained in previous experiments and with other calculation methods. The proposed methods proved capable of providing more accurate evaluations of not only the ultimate strength and deflection of a beam, but also the corresponding strain of the tendon and are thus more effective than the previous calculation methods. In addition, the proposed simplified methods are sufficiently practical to be employed for design. By using the proposed methods, both the damage tolerance and self-centering performances of unbonded PCaPC frames can be achieved with higher accuracy.

Keywords

Precast prestressed concrete frame Post-tensioned unbonded tendon Macro-model Flexural strength Beam deflection Strain of tendon 

List of symbols

At

Cross-sectional area of tendon

b

Beam width

Cc

Compressive resultant force of concrete

Ccx

Distance from extreme compression fiber to compressive resultant force

D

Beam depth

dt

Distance from extreme compression fiber to tendon position on tensile side

Ec

Elastic modulus of concrete

Et

Stiffness of tendon

Et1

Elastic stiffness of tendon

Et2

Tangent stiffness of tendon between elastic limit and yield points

Et3

Tangent stiffness of tendon after yielding point

jd

Moment arm length from compressive to tensile resultant force

L

Whole length of tendon going through beams and beam–column joint

L1

Horizontal distance from beam–column interface to point A

L2

Horizontal distance from point A to inflection point

lc0

Initial axial shortening of beam concrete by initial prestressing force

l

Horizontal distance from beam–column interface to inflection point

M

Bending moment of beam

Mu

Ultimate bending moment of beam

Pb

Shear force of beam

Pu

Ultimate flexural strength of beam

R

Story drift angle

Rb

Deflection angle of beam

Rro

Rotation angle at beam end

Ru

Deflection angle of beam at ultimate flexural state

Tt

Tensile force of tendon

Tt0

Initial prestressing force of tendon

Tty

Yield strength of tendon

V

Story shear force

X

Horizontal distance from beam-column interface to arbitrary point between beam–column interface and inflection point

X1

Horizontal distance from beam-column interface to arbitrary point between beam–column interface and point A

X2

Horizontal distance from point A to arbitrary point between point A and inflection point

xn

Neutral axis depth at beam end

xnx

Neutral axis depth at arbitrary beam section

γ

Ratio of neutral axis depth to beam depth

Δc,ex

Beam axial shortening at extreme compression fiber

Δc,tp

Beam axial shortening at tendon position on compressive side

δd, tp

Crack opening distance at tendon position on tensile side

δt

Elongation of tendon

εc

Concrete compressive strain

εc0

Initial compressive strain of concrete due to initial prestressing force

εcu

Ultimate compressive strain of concrete

εn

Concrete strain at extreme compression fiber of beam end

εnL1

Concrete strain at extreme compression fiber of point A section

εnL2

Concrete strain at extreme compression fiber of inflection point section

εnx1

Concrete strain at extreme compression fiber in region L1

εnx2

Concrete strain at extreme compression fiber in region L2

εt

Tensile strain of tendon

εt0

Initial tensile strain of tendon by initial prestressing force

εte

Elastic-limit strain of tendon according to 0.01% offset method

εty

Yield strain of tendon according to 0.2% offset method

εx

Concrete strain at extreme tension fiber of beam in region L2

ξ

Modification factor for beam deflection angle in ultimate flexural state

σB

Concrete compressive strength

σc

Concrete compressive stress

σc0

Initial compressive stress of concrete due to initial prestressing force

σt

Tensile stress of tendon

σte

Elastic-limit stress of tendon according to 0.01% offset method

σty

Yield stress of tendon according to 0.2% offset method

Notes

Acknowledgements

The financial support of the JSPS (Japanese Society for the Promotion of Science) Grant-in-Aid for Scientific Research (Category (C), Grant No: 15K06302, Principal Investigator: Kazuhiro Kitayama) is greatly appreciated.

References

  1. American Concrete Institute (ACI) (2014) Building code requirements for structural concrete, ACI 318-14. Farmington Hills, MIGoogle Scholar
  2. Architectural Institute of Japan (AIJ) (2015) Guidelines for structural design and construction of prestressed concrete buildings based on performance evaluation concept (draft). Tokyo, JapanGoogle Scholar
  3. Chou C, Tsai K, Yang W (2009) Self-centering steel connections with steel bars and a discontinuous composite slab. Earthq Eng Struct Dyn 38:403–422Google Scholar
  4. Christopoulos C, Tremblay R, Kim H, Lacerte M (2008) Self-centering energy dissipative bracing system for the seismic resistance of structures: development and validation. J Struct Eng 134:96–107Google Scholar
  5. Eatherton MR, Hajjar JF (2014) Hybrid simulation testing of a self-centering rocking steel braced frame system. Earthq Eng Struct Dyn 43:1725–1742Google Scholar
  6. El-Sheikh MT, Sause R, Pessiki S, Lu LW (1999) Seismic behavior and design of unbonded post-tensioned precast concrete frames. PCI J 44:54–71Google Scholar
  7. Hassanli R, El-Gawady MA, Mills JE (2015) Experimental investigation of in-plane cyclic response of unbonded posttensioned masonry walls. J Struct Eng.  https://doi.org/10.1061/(ASCE)ST.1943-541X.0001450 Google Scholar
  8. Ho T, Dao T, Aaleti S, van de Lindt JW, Rammer (2016) Hybrid system of unbonded post-tensioned CLT panels and light-frame wood shear walls. J Struct Eng.  https://doi.org/10.1061/(ASCE)ST.1943-541X.0001665 Google Scholar
  9. Imamura S, Miao S, Jin K, Kitayama K (2016) Seismic performance estimation of unbonded precast prestressed concrete frame focusing on different steel indices. Part 1: experiment outlines and results. In: Summaries of technical papers of annual meeting, C-2, Structures IV, Architectural Institute of Japan (AIJ), Fukuoka, Japan, pp 763–764 (in Japanese) Google Scholar
  10. Kim H, Christopoulos C (2008) Seismic design procedure and seismic response of post-tensioned self-centering steel frames. Earthq Eng Struct Dyn 38:355–376Google Scholar
  11. Kim K, Shiohara H, Kusuhara H (2008) Seismic test of unbonded precast prestressed concrete cruciform subassemblage aimed at improvement of workability and reparability. Proc Jpn Concr Inst 30(3):343–348 (in Japanese) Google Scholar
  12. Kishida S, Kitayama K, Maruta M, Moriyama K (2004) Earthquake resistant performance and failure mechanism of precast prestressed concrete beam-column joints assembled by post-tensioning steel bars. In: Proceeding of 13th world conference on earthquake engineering, Vancouver, BC, Canada, Paper ID1763Google Scholar
  13. Kurama YC (2002) Hybrid post-tensioned precast concrete walls for use in seismic regions. PCJ J 47:36–59Google Scholar
  14. Kurama YC, Shen Q (2004) Posttensioned hybrid coupled walls under lateral loads. J Struct Eng 130:297–309Google Scholar
  15. Kurama YC, Sause R, Pessiki S, Lu LW (2002) Seismic response evaluation of unbonded post-tensioned precast walls. ACI Struct J 99:641–651Google Scholar
  16. Lee WK, Billington SL (2011) Performance-based earthquake engineering assessment of a self-centering, post-tensioned concrete bridge system. Earthq Eng Struct Dyn 40:887–902Google Scholar
  17. Lu X, Cui Y, Liu J, Gao W (2015) Shaking table test and numerical simulation of a 1/2-scale self-centering reinforced concrete frame. Earthq Eng Struct Dyn 44:1899–1917Google Scholar
  18. Maguire M, Collings WN, Halbe KR, Roberts-Wollmann CL (2016) Multi-span members with unbonded tendons: ultimate strength behavior. ACI Struct J 113:195–204Google Scholar
  19. Matsumora M, Koshikawa T, Kikuchi M (2014) Evaluation of ultimate strength and rotation angle for unbonded post-tensioned precast concrete beams by using section analysis. J Struct Constr Eng AIJ 701:1005–1013 (in Japanese) Google Scholar
  20. Naaman AE, Alkhairi FM (1991) Stress at ultimate in unbonded post-tensioning tendons. Part 2: Proposed methodology. ACI Struct J 88:683–692Google Scholar
  21. Nakaki SD, Stanton JF, Sritharan S (1999) An overview of the PRESSS five-story precast test building. PCI J 44:26–39Google Scholar
  22. Nishimura T, Tani M, Nishiyama M (2008) Damage evaluation of prestressed concrete assemblage. Proc Jpn Concr Inst 30(3):511–516 (in Japanese) Google Scholar
  23. Nishiyama M, Muguruma H, Watanabe F (1988) On the unbonded prestressed concrete member in seismic structures. In: Proceeding of 9th world conference on earthquake engineering, Tokyo–Kyoto, Japan, pp 743–748Google Scholar
  24. Pampanin S, Priestley MN, Sritharan S (2001) Analytical modeling of the seismic behavior of precast concrete frames designed with ductile connections. J Earthq Eng 5:329–367Google Scholar
  25. Priestley MN, MacRae GA (1996) Seismic tests of precast beam-to-column joint subassemblages with unbonded tendons. PCI J 41:64–81Google Scholar
  26. Priestley MN, Tao JR (1993) Seismic response of precast prestressed concrete frames with partially debonded tendons. PCI J 38:58–69Google Scholar
  27. Priestley MN, Sritharan S, Conley JR, Pampanin S (1999) Preliminary results and conclusions from the PRESSS five-story precast concrete test building. PCI J 44:42–67Google Scholar
  28. Rahman MA, Sritharan S (2007) Performance-based seismic evaluation of two five-story precast concrete hybrid frame buildings. J Struct Eng 133:1489–1500Google Scholar
  29. Ricles JM, Sause R, Garlock MM, Zhao C (2001) Posttensioned seismic-resistant connections for steel frames. J Struct Eng 127:113–121Google Scholar
  30. Song L, Guo T, Chen C (2014) Experimental and numerical study of a self-centering prestressed concrete moment resisting frame connection with bolted web. Earthq Eng Struct Dyn 43:529–545Google Scholar
  31. Stanton JF, Stone WC, Cheok GS (1997) A hybrid reinforced precast frame for seismic regions. PCI J 42:20–32Google Scholar
  32. Suzuki D, Song S, Jin K, Kitayama K (2015) Seismic performance of unbonded precast prestressed concrete frame considering column-to-beam flexural strength ratio. Part 1: test outlines and results. In: Summaries of technical papers of annual meeting, C-2, Structures IV, Architectural Institute of Japan (AIJ), Yokohama, Japan, pp 713–714 (in Japanese) Google Scholar
  33. Tsuda K (2015) A study on the calculation method for flexural behavior of unbonded pre-stressed concrete beam. J Struct Constr Eng AIJ 710:659–668 (in Japanese) Google Scholar
  34. Weldon BD, Kurama YC (2012) Analytical modeling and design validation of posttensioned precast concrete coupling beams for seismic regions. J Struct Eng 138:224–234Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of ArchitectureMeiji UniversityKawasakiJapan
  2. 2.Department of Infrastructure Safety ResearchKorea Institute of Civil Engineering and Building TechnologyGoyangSouth Korea
  3. 3.Division of Architecture and Urban StudiesTokyo Metropolitan UniversityHachiojiJapan
  4. 4.Earthquake Engineering Research and Test CenterGuangzhou UniversityGuangzhouChina

Personalised recommendations