Define balanced, under, over-reinforced sections

• Balanced section: a section in which the steel and concrete reach their limiting strains together, i.e. concrete reaches the ultimate strain 0.0035 just when steel reaches its yield strain. Here $x_u=x_{u,max}$ and $A_{st}=A_{st,lim}$.
• Under-reinforced section: the steel area is less than for the balanced section, so steel yields first while concrete is not yet crushed ($x_u<x_{u,max}$). Failure is ductile with warning, and this type is preferred.
• Over-reinforced section: the steel area is more than for the balanced section, so concrete crushes (strain 0.0035) before steel yields ($x_u>x_{u,max}$). Failure is sudden and brittle, and it is not permitted in design.

Limiting values of $x_{u,max}/d$ (IS 456): 0.53 for Fe250, 0.48 for Fe415, 0.46 for Fe500.