Ductility requirements of RC beam with sketch

Ductility is the ability of a member to undergo large inelastic deformation without significant loss of strength. In a beam it is obtained by making the tension steel yield before the concrete crushes and by preventing early shear failure. IS 13920 gives the following detailing rules.

Geometry

• Width $b \ge 200$ mm and $b/D \ge 0.3$.
• Depth $D \le \tfrac14$ of clear span.

Longitudinal steel

• At least two bars (12 mm or more) continuous at top and at bottom.
• $\rho_{min} = 0.24\sqrt{f_{ck}}/f_y$ and $\rho_{max} = 2.5\%$ on any face.
• Positive steel at a joint face is not less than 50% of the negative steel there.
• Along the span, neither positive nor negative capacity is less than 25% of the maximum capacity at either joint face.
• Lap splices only in the middle half of the span, never within the joint or within $2d$ of a joint face. Not more than 50% of bars are spliced at one section and the splice is enclosed by closely spaced hoops (spacing $\le 150$ mm).

Transverse steel (stirrups)

• Closed hoops with $135^\circ$ hooks and a tail of $10\phi$ (not less than 75 mm) so that they stay effective after the cover spalls.
• Diameter $\ge 6$ mm (8 mm if clear span exceeds 5 m).
• Over a length $2d$ from each joint face the spacing is the least of $d/4$, $8\phi_{min}$ and 100 mm, with the first hoop at 50 mm. Elsewhere the spacing is $\le d/2$.
• Stirrups are designed for the shear that develops when plastic hinges form at both ends (capacity design).

  Column |<-- 2d -->|<------ L/2 ------>|<- 2d ->| Column
  -------+-+-+-+-+-+---------------------+-+-+-+-+-------
         | | | | | |  hoops at d/2       | | | | | |
         | | | | | |                     | | | | | |
  -------+-+-+-+-+-+---------------------+-+-+-+-+-------
   50 mm, then s <= min(d/4, 8phi, 100)      lap splice only
                                              in middle half