IF h_f < 0.1*d THEN treat the beam as rectangular.

h_f = MIN(h_f,side1, h_f,side2)

where

h_f,sidei = the depth of the slab on side " i" of the beam

Calculate the value of K from;

K = M_Ed/(f_ck*b_eff*d²)

Calculate the lever arm, z from;

z = MIN(0.5*d*[1 + (1 - 2*K/(η*α_cc/γ_C))^0.5], 0.95*d)

Calculate the depth of the rectangular stress block, λ*x from;

λ*x = 2*(d-z)

IF λ*x ≤ h _f THEN the rectangular compression block is wholly in the depth of the flange and the section can be designed as a rectangular section by setting b_w = b_eff.

IF λ*x > h _f THEN the rectangular compression block extends into the rib of the flanged section and the following design method is to be used.

The design bending strength of the flange, M_f is given by;

M_f = f_cd*h_f*(b_eff-b_w)*(d-0.5*h _f)

The area of reinforcement required to provide this bending strength, A_sf,reqd is given by;

A_sf,reqd = M_f/(f_yd*(d-0.5*h_f))

The remaining design moment, (M_Ed-M_f) is then taken by the rectangular beam section.

Calculate the value of K from;

K = (M_Ed-M_f)/(f_ck*b_w*d²)

Then calculate the limiting value of K, known as K' from;

K' = (2*η*α_cc /γ_C)*(1 - λ*(δ - k₁)/(2*k₂))*( λ*(δ - k₁)/(2*k₂)) for f_ck ≤ 50 N/mm²

K' = (2*η*α_cc /γ_C)*(1 - λ*(δ - k₃)/(2*k₄))*( λ*(δ - k₃)/(2*k₄)) for f_ck > 50 N/mm²

IF K ≤ K' THEN compression reinforcement is not required.

Calculate the lever arm, z from;

z = MIN(0.5*d*[1 + (1 - 2*K/(η*α_cc/γ_C))^0.5], 0.95*d)

The area of tension reinforcement required is then given by;

A_sr,reqd = (M_Ed-M_f)/(f_yd*z)

The total area of tension reinforcement required, A_st,reqd is then given by;

A_st,reqd = A_sf,reqd+A_sr,reqd

The depth to the neutral axis, x_u is given by;

x_u = 2*(d-z)/λ

IF K > K' THEN compression reinforcement is required.

Calculate the depth to the neutral axis from;

x_u = d*(δ-k₁)/k₂ for f_ck ≤ 50 N/mm²

x_u = d*(δ-k₃)/k₄ for f_ck > 50 N/mm²

Calculate the stress in the reinforcement from;

f_sc = MAX(E_s*ε_cu3*(1-(d₂/x_u), f_yd)

where

d₂ = the distance from the extreme fibre in compression to the c of g of the compression reinforcement

Calculate the limiting bending strength, M' from;

M' =K'*f_ck*b_w*d²

Calculate the lever arm from;

z = 0.5*d*[1 + (1 - 2*K'/(η*α_cc/γ_C))^0.5]

The area of compression reinforcement required, A_s2,reqd is given by;

A_s2,reqd = (M_Ed-M_f-M')/(f_sc*(d-d₂))

The area of tension reinforcement required, A_sr,reqd is given by;

A_sr,reqd = M'/(f_yd*z) + A_s2,reqd*f_sc/f_yd

The total area of tension reinforcement required, A_st,reqd is then given by;

A_st,reqd = A_sf,reqd+A_sr,reqd