Shear Friction and Strut-and-Tie Modeling Verification for Pier Caps

Data Availability Statement

Acknowledgments

Notation

A_b

area of reinforcing bars, mm²;

A_h

area of secondary horizontal reinforcement, mm²;

A_s

area of main longitudinal tension reinforcement, mm²;

A_v

area of secondary vertical reinforcement, mm²;

a

shear span measured from the vertical face of the pier to the load center, mm;

b

width of pier cap, mm;

d

effective depth of pier cap, distance from the centroid of longitudinal tension reinforcement to the extreme compression fiber, mm;

E_c

modulus of elasticity of concrete, MPa;

E_s

modulus of elasticity of steel reinforcement, MPa;

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

cylinder compressive strength of concrete, MPa;

f_ct

indirect tensile strength (splitting tensile strength), MPa;

f_r

modulus of rupture, MPa;

f_y

yield stress of main steel reinforcement, MPa;

f_yh

yield stress of secondary horizontal reinforcement, MPa;

f_yv

yield stress of secondary vertical reinforcement, MPa;

h

overall depth of pier cap, mm;

j_d

distance between the centers of the top and bottom nodes, mm;

L

total length of pier cap, mm;

L_b

length of the load-bearing block, mm;

P

ultimate load failure, kN;

P_cr-diag

first diagonal cracking load, kN;

P_cr-flex

first flexural cracking load, kN;

P_SF

theoretical load according to Chapter 16.5 and Chapter 22.9, shear friction, ACI 318M-14, kN;

P_STM

theoretical load according to Chapter 23, ACI 318M-14, strut-and-tie method, kN;

S_h

secondary horizontal reinforcement spacing, mm;

S_v

secondary vertical reinforcement spacing, mm;

θ

angle between the axis of strut, compression diagonal, or compression field and the tension chord of the members;

μ

coefficient of friction;

Δ

displacement corresponding to the ultimate of pier cap, mm;

Δ_diag.crack

displacement corresponding to the first diagonal crack load, mm;

Δ_flex.crack

displacement corresponding to the first flexural crack load, mm;

ρ

main reinforcement ratio;

ρ_h

secondary horizontal reinforcement ratio;

ρ_v

secondary vertical reinforcement ratio;

a/d

shear span to effective depth ratio; and

c/c

center to center, mm.

References