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Strand bond stress–slip relationship for prestressed concrete members at prestress release

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Abstract

The transfer of prestress force from prestressing strands to the surrounding concrete is dependent on the bond between the two materials. Understanding the actual bond stress distribution along the transfer length results in optimized design of the transfer zone of prestressed concrete members. Equations of estimating the transfer length in ACI 318 code and AASHTO LRFD bridge design specifications simply take into account the effect of the strand diameter only. The objective of this study is to provide a generalized procedure for determining the bond stress–slip relationship accurately by incorporating the effects of additional parameters, such as concrete compressive strength at prestress release, center-to-center strand spacing, and concrete bottom cover. First, the bond stress distribution along the transfer length of a prestressed concrete member is formulated based on longitudinal slip–strain compatibility, force equilibrium and invariable bond stress–slip relationship along the transfer length. Second, a generalized Inverse Problem-Solving approach is introduced to determine best parameter coefficients through minimizing the discrepancy between the calculated and measured results. Two types of measurements (i.e., transfer length and end slip) reported in the literature are utilized to demonstrate the proposed approach. Predicted transfer length and end slip values using the calibrated bond stress–slip relationship show better agreement with the test data compared to those predicted by ACI 318 code and AASHTO LRFD bridge design specifications. Third, a computational procedure is developed and an example is presented to assist engineers using the developed formulae for determining the bond stress distribution along the transfer length of prestressed concrete members.

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Abbreviations

A ps :

Area of a strand

A c :

Area of the concrete cross-section

A tot :

Total area of strands

C tot :

The total circumference of all strands in a prestressed concrete member

c bc :

Clear bottom cover

d ps :

Diameter of a strand

E ci :

Concrete elastic modulus at prestress release

E ps :

Elastic modulus of strands

f′ ci :

Concrete compressive strength at prestress release

f pe :

Effective prestress in strands

f pj :

Jacking stress in strands

f ps.z :

Prestress in strands at z-coordinate location

f pu :

Ultimate strength of prestressing strand

I x :

Moment of inertia of the concrete cross-section

l t :

Transfer length of strands

M c.z :

Moment in the concrete cross-section at z-coordinate location

M c.0 :

Moment in the concrete cross-section at the transfer length location

M sw.0 :

Moment due to self-weight at the transfer length location

M sw.z :

Moment due to self-weight at z-coordinate location

m n,i :

Measured values corresponding to the measurement type n

N :

Total types of measurements

N c.z :

Axial force in the concrete cross-section at z-coordinate location

N e.0 :

Axial force in the concrete cross-section at the transfer length location

N ps.z :

Prestress force in strands at z-coordinate location

N :

Measurement type

n ps :

Number of strands in a member cross-section

OF n :

Discrepancy of the measurement type n

P j :

Jacking force in strands

p n,i :

Predicted values corresponding to the measurement type n

R tot.n :

Total number of records for the measurement type n

S :

Slip of strand to concrete

s z :

Slip of strand to concrete at z-coordinate location

s end :

Slip of strand to concrete at the ends of a specimen

s cc :

Center-to-center strand spacing

w n :

Weighting factor for the measurement type n

v i (i = 3, 4, …, k):

Other parameters except the slip and the strand diameter

\(\overline{y}\) :

Distance from the centroid to the bottom fiber of the concrete cross-section

y tot :

Distance from the centroid of strands to the bottom fiber of the concrete cross-section

Δσ ps :

Change of stress in strand

α lt :

Ratio of predicted transfer length to test results

α s,end :

Ratio of predicted end slip to test results

β j (j = 3, 4, …, k):

Coefficients related to parameters of the bond stress–slip relationship

ε c.z :

Strain in the concrete fiber at the centroid of strands at z-coordinate location

τ :

Bond stress along the slip direction

τ z :

Bond stress on the interface at z-coordinate location

χ :

Effects of other parameters except the slip and the strand diameter

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Authors and Affiliations

  1. Bridge Engineering Center, Institute for Transportation, Iowa State University, 2711 South Loop Drive, Suite 4700, Ames, IA, 50010, USA

    Yaohua Deng

  2. Durham School of Architectural Engineering and Construction, Peter Kiewit Institute, University of Nebraska-Lincoln, 1110 S. 67th St., Omaha, NE, 68182, USA

    George Morcous

  3. Department of Civil and Environmental Engineering, University of Tennessee, Knoxville, 223 Perkins Hall, Knoxville, TN, 37996, USA

    Zhongguo John Ma

Authors
  1. Yaohua Deng
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  2. George Morcous
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  3. Zhongguo John Ma
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Correspondence to Yaohua Deng.

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Deng, Y., Morcous, G. & Ma, Z.J. Strand bond stress–slip relationship for prestressed concrete members at prestress release. Mater Struct 49, 889–903 (2016). https://doi.org/10.1617/s11527-015-0546-1

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