Failure Analysis of Dapped-End Cracking in Posttensioned Bridge Girder

Acknowledgments

Notation

E_ci

initial elastic modulus of concrete;

E_cs

secant elastic modulus at the peak stress of concrete;

E_ps

elastic modulus of prestressing steel;

$E_{ps}^{\mathrm{\prime }}$

modulus of prestressing steel in plastic region;

E_s

elastic modulus of reinforcing steel;

$f_c^{\mathrm{\prime }}$

cylinder compressive strength of concrete;

$f_c^{\mathrm{\prime }ef}$

effective compressive strength of concrete;

$f_{cu}^{\mathrm{\prime }}$

cubic compressive strength of concrete;

f_pu

tensile strength of prestressing steel;

f_t

tensile strength of concrete;

$f_t^{ef}$

effective tensile strength of concrete;

f_y

tensile strength of reinforcing steel;

G_f

fracture energy;

L_c

crack band size for compression;

$L_c^{\mathrm{\prime }}$

projection of the finite-element dimension for compression;

L_t

crack band size for tension;

$L_t^{\mathrm{\prime }}$

projection of the finite-element dimension for tension;

r_ec

reduction factor of the compressive strength of concrete;

r_et

reduction factor of the tensile strength of concrete;

w₀

crack opening displacement at the complete release of stress in tension;

w_d

plastic displacement of concrete after peak compressive stress;

γ

orientation factor;

ɛ₀

tensile strain in concrete at the complete release of stress;

ɛ_c

compressive strain in concrete at peak stress;

ɛ_d

limit compressive strain at the zero stress;

ɛ^eq

equivalent uniaxial strain in concrete;

ɛ_ps

strain in prestressing steel;

ɛ_s

strain in reinforcing steel;

ɛ_t

tensile strain in concrete at tensile strength;

σ_c1

maximum principal stress in concrete;

σ_c2

minimum principal stress in concrete;

σ^ef

effective stress in concrete;

σ_ps

stress in prestressing steel;

σ_s

stress in reinforcing steel; and

θ

angle between the direction of the normal to the failure plane and element sides.

References