Bending-Induced Stresses in Parallel Seven-Wire Strand Stay Cables

Data Availability Statement

Acknowledgments

Notation

A_s

cross-sectional area of a single strand (mm²/in²);

d

vertical distance between the centroid of a strand and the center of the cable (mm/in);

d_i1 and d_i2

vertical distances between the ith strand and the centroid of the cable cross section at the anchor head and the tension ring, respectively (mm/in);

d_s1

distance between strand s and the centroid of the cable at the anchor head (mm/in);

d_s2

distance between strand s and the centroid of the cable at the tension ring (mm/in);

E

young’s modulus of the stay cable (GPa/ksi);

f_UTS

ultimate tensile strength of the cable material (MPa/ksi);

I

moment of inertia of the cable (mm⁴/in⁴);

I_s

moment of inertia of a single strand (mm⁴/in⁴);

L

cable length (m/ft);

L_T

length of the transition zone (m/ft);

M_FE

fixed-end moment (kN·m/kips·ft);

M_G

bending moment at the guide deviator (kN·m/kips·ft);

M_max

maximum bending moment in the cable (kN·m/kips·ft);

M_si

bending moments in the ith strand (kN·m/kips·ft);

M₁ and M₂

in-plane bending moments developed at the anchor head and at the tension ring, respectively (kN·m/kips·ft);

n

number of strands in the cable;

P

concentrated force (kN/kips);

r

distance between the extreme fiber and the neutral axis (mm/in);

r_g

radius of gyration of the section (mm/in);

T_s

axial cable force (kN/kips);

T_si

tension force in the ith strand (kN/kips);

W

distributed load (kN/m or kips/ft);

ΔL_sb1

change of length of strand s at the anchor head (m/ft);

ΔL_sb2

change of length of strand s at the tension ring (m/ft);

α

rotation angle of the cable (rad);

β_G

coefficient such that M_G = β_GM_max;

γ

inclination angle of the stay cable;

δ

maximum displacement at the cable midlength (mm/in);

ε_s

total strain in strand s due to bending action of the cable (transverse loads);

ε_sa

axial force-induced strain in strand s due to bending action of the cable (transverse load);

ε_sb

moment-induced strain in strand s due to bending action of the cable (transverse loads);

${\epsilon }_{s\cdot \max }$

maximum bending strain;

θ

angle change at the transition zone (rad);

λ

axial loading parameter (fraction of ultimate strength);

${\sigma }_B^{max}$

maximum bending stress of the cable (MPa/ksi);

σ_s

bending stress (MPa/ksi);

σ_s·max

maximum bending stress (MPa/ksi); and

ϕ

total angular deviation (rad).

References