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Limiting moment of resistance of a singly reinforced beam

Depth of the neutral axis at the balanced point, limiting moment and limiting steel of a rectangular beam to IS 456. Reference: IS 456:2000 Cl. 38.1 and Annex G.

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# Section and materials
f_ck := 25 MPa
f_y := 415 MPa
E_s := 200 GPa
b := 300 mm
d := 500 mm

# Limiting depth of the neutral axis
# The steel reaches its design yield strain when the concrete reaches 0.0035.
k_x := 0.0035/(0.0055 + 0.87*f_y/E_s) =
x_u.max := k_x*d =

# Limiting moment and steel
M_u.lim := 0.36*f_ck*b*x_u.max*(d - 0.42*x_u.max) = kN*m
p_t.lim := 0.36*f_ck*k_x/(0.87*f_y)*100 =
A_st.lim := p_t.lim/100*b*d = mm^2
R_lim := M_u.lim/(b*d^2) = MPa

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