Additional reinforcement for torsion (concrete beam: EC2)
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 EC2 Recommendations, UK NA, Irish NA, Malaysian NA, Singapore NA, Finnish NA and Swedish NA;  
C_{Rd,c} 

0.18/γ_{C} 
γ_{C} 

1.5 
v_{min} 

0.035*k^{1.5}*f_{ck}^{0.5} 
where  
k 

MIN(1 + √(200/d), 2.0) 


For design in accordance with Norwegian NA;  
C_{Rd,c} 

0.15/γ_{C} 
γ_{C} 

1.5 
v_{min} 

0.035*k^{(2/3)}*min(f_{ck},65N/mm^{2})^{0.5} 


where  
k 

MIN(1 + √(200/d), 2.0) 


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*((ht_{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 crosssection. 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 
Footnotes