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Limiting neutral axis depth for different steel grades

x_u,max/d and the limiting moment factor for Fe 250, Fe 415 and Fe 500 steel. Reference: IS 456:2000 Cl. 38.1 (note).

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Limiting neutral axis depth for different steel grades: 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 IS 456 before you use it, and have the result checked by a competent person. See the disclaimer.

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# Steel
E_s := 200 GPa
f_y1 := 250 MPa
f_y2 := 415 MPa
f_y3 := 500 MPa

# Limiting depth ratio
k_1 := 0.0035/(0.0055 + 0.87*f_y1/E_s) =
k_2 := 0.0035/(0.0055 + 0.87*f_y2/E_s) =
k_3 := 0.0035/(0.0055 + 0.87*f_y3/E_s) =

# Limiting moment factor M_u,lim/(f_ck b d^2)
Q_1 := 0.36*k_1*(1 - 0.42*k_1) =
Q_2 := 0.36*k_2*(1 - 0.42*k_2) =
Q_3 := 0.36*k_3*(1 - 0.42*k_3) =

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