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Flanged beam with the neutral axis in the flange

Moment capacity of the flange and design of a T-beam as a rectangular section when the neutral axis lies in the flange. Reference: EN 1992-1-1 3.1.7, 5.3.2.1.

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Flanged beam with the neutral axis in the flange: worked example sheet in Equation Pad with typeset equations and results.

Example only. This sheet shows one way to set out the check. It is not endorsed by the bodies that publish the design codes and does not reproduce them. Check every clause, value and assumption against your own copy of the current edition of Eurocode 2 and its national annex before you use it, and have the result checked by a competent person. See the disclaimer.

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# Materials
f_ck := 30 MPa
f_yk := 500 MPa
gamma_c := 1.5
gamma_s := 1.15
alpha_cc := 1.0
f_cd := alpha_cc*f_ck/gamma_c =
f_yd := f_yk/gamma_s =

# Section and action
b_eff := 1500 mm
b_w := 300 mm
h_f := 150 mm
d := 550 mm
M_Ed := 450 kN*m

# Capacity of the flange
M_Rf := f_cd*b_eff*h_f*(d - h_f/2) = kN*m
M_Ed <= M_Rf =

# Design as a rectangular section b_eff
b := b_eff =
K := M_Ed/(b*d^2*f_ck) =
k_1 := 0.8*alpha_cc/gamma_c =
z := min(d*(0.5 + sqrt(0.25 - 0.4*K/k_1)), 0.95*d) = mm
x := (d - z)/0.4 = mm
0.8*x <= h_f =
A_s := M_Ed/(f_yd*z) = mm^2

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More Eurocode 2 sheets on beams

The same topic in IS 456