The design value of the shear resistance of a concrete section with no shear reinforcement, V_Rd,c is given by;¹

V_Rd,c = ν_min * b_w * d

For design in accordance with UK NA, EC2 Recommendations, Irish NA, Malaysian NA and Singapore NA;

C_Rd,c = 0.18/γ_C

γ_C = 1.5

ν_min = 0.035 * k^1.5 * f_ck^0.5

where

k = MIN(1 + √(200/d), 2.0) d in mm

For design in accordance with UK NA, EC2 Recommendations, Irish NA, Malaysian NA and Singapore NA;

α_ct = 1.0

γ_C = 1.5

If (Τ_Ed,max/Τ_Rd,c) + (V_Ed,max/V_Rd,c) ≤ 1.0

THEN no additional longitudinal reinforcement for torsion is required.

IF (Τ_Ed,max/Τ_Rd,c) + (V_Ed,max/V_Rd,c) > 1.0

THEN additional longitudinal reinforcement for torsion, A _slT,reqd is required in some or all regions.

The additional longitudinal reinforcement is given by;

A_slT,reqd = (Τ_Ed * u_k* cotθ)/(2 * A_k * f_yd)

where

u_k = 2*((h-t_ef)+(b_w-t_ef))

This reinforcement is in addition to that required for bending and tension arising from vertical shear and it is distributed in each of the four faces of the beam in proportion to the length of the face of the cross-section.

The area of the additional link reinforcement that is required to resist torsion is given by;

A_swt/s = (Τ_Ed)/(2 * A_k * 0.9 * f_ywd* cotθ) per leg