Design values of shear resistance and torsional resistance moment (concrete beam: EC2)
The design value of the shear resistance of a concrete section with vertical shear reinforcement, V_{Rd,max} is given by; 

V_{Rd,max} 

0.9*α_{cw}*b_{w}*d*ν_{1}*f_{cwd}/(cotθ + tanθ) 
where 

θ 

MIN{θ_{max}, MAX[0.5*sin^{1}[2*V_{Ed,max}/( α_{cw}*b_{w}*0.9*d*ν_{1}*f_{cwd})], θ_{min}]} 
where  
ν_{Ed} 

V_{Ed,max} /(b_{w}*d) 
τ_{Ed} 

T_{Ed,max}/(2*A_{k}*t_{ef}) 
A_{k} 

(ht_{ef})*(b_{w}t_{ef}) 
t_{ef} 

MAX(A/u, 2*(hd_{o})) 
A 

h*b_{w} 
u 

the outer circumference of the crosssection 

2*(h+b_{w}) 

d_{o} 

the effective depth of the outer layer of longitudinal reinforcement 
V_{Ed,max} 

max. absolute value from all the shear regions 
T_{Ed,max} 

max. torsion on the member 


The maximum design value of the torsional resistance moment, Τ_{Rd,max} is given by  
Τ_{Rd,max} 

2*ν_{1}*α_{ccw}*f_{cwd}*A_{k}*t _{ef}*sinθ*cosθ 


For design in accordance with UK NA, Irish NA, Malaysian NA and Singapore NA;  
f_{cwd}^{1} 

α_{ccw}*min (f_{ck},50)/γ_{C} 


For design in accordance with EC2 Recommendations, Finnish NA, Norwegian NA and Swedish NA; 

f_{cwd} 

α_{ccw}*f_{ck}/γ_{C} 


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

α_{cw} 

1.0 
γ_{C} 

1.5 
γ_{1} 

0.6*(1 – f_{ck}/250) 


For design in accordance with EC2 Recommendations, UK NA, Irish NA, Malaysian NA, Singapore NA and Swedish NA;  
α_{ccw} 

1.0 


For design in accordance with Finnish NA and Norwegian NA;  
α_{ccw} 

0.85 


The design value of the torsional resistance moment of a concrete section with no shear reinforcement, Τ_{Rd,c} is given by^{2}; 

Τ_{Rd,c} 

2*A_{k}*t_{ef}*f_{ctd} 
where 

f_{ctd} 

the design tensile strength of the concrete 

α_{ct}*f_{ctk,0.05}/γ_{C}  


For design in accordance with EC2 Recommendations, UK NA, Irish NA, Malaysian NA, Singapore NA, Finnish NA and Swedish NA;  
α_{ct} 

1.0 
γ_{C} 

1.5 


For design in accordance with Norwegian NA;  
α_{ct} 

0.85 
γ_{C} 

1.5 


If the maximum torsional moment acting on the beam, T_{Ed,max} is less than the ignorable torque limit then no further calculations are necessary. 

Otherwise: 

If (Τ_{Ed,max,i}/Τ_{Rd,max}) + (V_{Ed,max,i}/V_{Rd,max}) ≤ 1.0 

then the torsion design process can proceed. 

ELSE the torsion design FAILS since the section size is inadequate for torsion. 
Footnotes