Shear between flanges and web of flanged beams (concrete beam: EC2)
The shear strength of the interface between the flanges and the web of a flanged beam is checked and, if necessary, transverse reinforcement is provided as shown in the diagram below.^{1}
The calculations for the transverse reinforcement are as follows:  


The lever arm at the point of maximum sagging moment is given by; 

z  =  0.5*d*[1 + (1 – 2*K/(η*α_{cc}/γ_{C}))0.5] 
where 

K 
=  M_{Ed,+max}/(f_{ck}*b_{eff}*d^{2}) 
M_{Ed,+max}  = 
the maximum sagging (+ve) design moment on the beam 
The depth of the compression block, d_{c} is then given by; 

d_{c}  = 
2*(dz) 


The following calculations are then carried out on each side, i of the beam. 

IF d_{c} ≤ h_{fi,min} THEN the stress block is completely within the flange. 

where  
h_{fi,min}  = 
the minimum depth of the flange on each side of the beam 
= 
MIN(h_{f1}, h_{f2}) 

The force in the flange on side i of the beam, F_{i} is then given by; 

F_{i}  = 
η*f_{cd}*d_{c}*b_{eff,i} 
where  
b_{eff,i}  = 
the width of the flange on side i of the beam 
IF d_{c} > h_{fi,min} THEN the force in the flange on side i of the beam, F_{i} is then given by; 

F_{i}  =  η*f_{cd}*h_{fi}*b_{eff,i} 
where 

h_{fi}  = 
the depth of the flange on side i of the beam 
The maximum rate of change of the bending moment for all load combinations in the sagging region of the beam, (dM_{Ed}/d_{x})_{max} (the moment gradient) is then determined. 

The moment gradient is then given by; 

dM_{Ed}/dx  =  ABS(M_{Ed,end0})/interval length 
The length over which the flange force is transferred to the web, L_{T} is given by; 

L_{T}  = 
M_{Ed,+max}/(dM_{Ed}/dx)_{max} 
The design shear stress on side i of the web is then given by; 

v_{Edi}  = 
F_{i}/(h_{fi}*L_{T}) 
The limiting value of the shear stress, v_{Ed,lim} is given by; 

v_{Ed,lim}  = 
k*f_{ctd} 
where  
k  = 
an NDP factor 
For design in accordance with EC2 Recommendations, UK NA, Irish NA, Malaysian NA, Singapore NA, Finnish NA, Norwegian NA and Swedish NA;  
IF v_{Edi} ≤ v_{Ed,lim} THEN no additional transverse reinforcement is required  
ELSE  
A_{sfi,reqd}  =  ((v_{Edi}*h_{fi}/f_{yd})/cotθ_{fi})*1000  mm2 per metre length of beam 
The result for the beam is then given by;  
A_{sfi,reqd}  =  MAX(A_{sf1,reqd}, A_{sf2,reqd})  
where  
θ_{fi}  = 
MIN{θ_{fmax}, MAX(0.5*sin^{1}(2*v_{Edi}/(ν*f_{cd})), θ_{fmin})} 

ν  = 
an NDP value 

θ_{fmax}  = 
an NDP value 

θ_{fmin}  = 
an NDP value 



For design in accordance with EC2 Recommendations, UK NA, Irish NA, Malaysian NA, Singapore NA, Finnish NA and Swedish NA;  
ν  =  0.6*(1(f_{ck}/250))  
θ_{fmax}  =  tan^{1}(1)  
θ_{fmin}  =  tan^{1}(0.5)  


For design in accordance with Norwegian NA;  
ν  =  0.6*(1(f_{ck}/250))  
θ_{fmax}  =  tan^{1}(1)  
θ_{fmin}  =  tan^{1}(0.4)  

Footnotes