Types of rectangular beam sections

Rectangular RC beam sections are classified by the way reinforcement is provided and by the failure mode.

1. Singly reinforced sections (steel in tension zone only)

• Under-reinforced ($x_u<x_{u,max}$): steel yields first, ductile failure; used in design.
• Balanced ($x_u=x_{u,max}$): steel and concrete reach limits together; $M_{u,lim}=0.138f_{ck}bd^2$ (Fe415).
• Over-reinforced ($x_u>x_{u,max}$): concrete crushes first, brittle failure; not allowed.

2. Doubly reinforced section

Steel is provided in both the tension and compression zones. Used when $M_u>M_{u,lim}$ with a restricted depth, when moment reverses, or to reduce long-term deflection.

  Singly reinforced      Doubly reinforced
  +-----------+          +-----------+
  |           |          | o  o  Asc |  <- d'
  |           |          |           |
  |           |          |           |
  | o  o  o   |          | o  o  o   |
  +-----------+          +-----------+
     Ast                    Ast

Moment of a doubly reinforced section: $M_u=M_{u,lim}+f_{sc}'A_{sc}(d-d')$, where $f_{sc}'=f_{sc}-f_{cc}$.