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

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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.

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Abbreviations

A t :

Cross-sectional area of tendon

b :

Beam width

C c :

Compressive resultant force of concrete

C cx :

Distance from extreme compression fiber to compressive resultant force

D :

Beam depth

d t :

Distance from extreme compression fiber to tendon position on tensile side

E c :

Elastic modulus of concrete

E t :

Stiffness of tendon

E t1 :

Elastic stiffness of tendon

E t2 :

Tangent stiffness of tendon between elastic limit and yield points

E t3 :

Tangent stiffness of tendon after yielding point

j d :

Moment arm length from compressive to tensile resultant force

L :

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

L 1 :

Horizontal distance from beam–column interface to point A

L 2 :

Horizontal distance from point A to inflection point

l c0 :

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

M u :

Ultimate bending moment of beam

P b :

Shear force of beam

P u :

Ultimate flexural strength of beam

R :

Story drift angle

R b :

Deflection angle of beam

R ro :

Rotation angle at beam end

R u :

Deflection angle of beam at ultimate flexural state

T t :

Tensile force of tendon

T t0 :

Initial prestressing force of tendon

T ty :

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

X 1 :

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

X 2 :

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

x n :

Neutral axis depth at beam end

x nx :

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

δ d, tp :

Crack opening distance at tendon position on tensile side

δ t :

Elongation of tendon

ε c :

Concrete compressive strain

ε c0 :

Initial compressive strain of concrete due to initial prestressing force

ε cu :

Ultimate compressive strain of concrete

ε n :

Concrete strain at extreme compression fiber of beam end

ε nL1 :

Concrete strain at extreme compression fiber of point A section

ε nL2 :

Concrete strain at extreme compression fiber of inflection point section

ε nx1 :

Concrete strain at extreme compression fiber in region L1

ε nx2 :

Concrete strain at extreme compression fiber in region L2

ε t :

Tensile strain of tendon

ε t0 :

Initial tensile strain of tendon by initial prestressing force

ε te :

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

ε ty :

Yield strain of tendon according to 0.2% offset method

ε x :

Concrete strain at extreme tension fiber of beam in region L2

ξ :

Modification factor for beam deflection angle in ultimate flexural state

σ B :

Concrete compressive strength

σ c :

Concrete compressive stress

σ c0 :

Initial compressive stress of concrete due to initial prestressing force

σ t :

Tensile stress of tendon

σ te :

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

σ ty :

Yield stress of tendon according to 0.2% offset method

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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.

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Authors and Affiliations

  1. Department of Architecture, Meiji University, Kawasaki, Kanagawa, Japan

    Kiwoong Jin

  2. Department of Infrastructure Safety Research, Korea Institute of Civil Engineering and Building Technology, Goyang, Gyeonggi-do, South Korea

    Sunghoon Song

  3. Division of Architecture and Urban Studies, Tokyo Metropolitan University, Hachioji, Tokyo, Japan

    Kazuhiro Kitayama

  4. Earthquake Engineering Research and Test Center, Guangzhou University, Guangzhou, China

    Linfei Hao

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  1. Kiwoong Jin
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  2. Sunghoon Song
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  3. Kazuhiro Kitayama
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  4. Linfei Hao
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Correspondence to Sunghoon Song.

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Jin, K., Song, S., Kitayama, K. et al. Detailed evaluation of the ultimate flexural states of beams in unbonded precast prestressed concrete frames. Bull Earthquake Eng 17, 1495–1519 (2019). https://doi.org/10.1007/s10518-018-0504-8

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