Curtailment of tension steel in beams

Meaning of curtailment

Curtailment means stopping (cutting off) some of the tension bars of a beam where the bending moment has fallen so much that fewer bars are needed. The main bars are designed for the maximum bending moment at mid-span, but near the supports the moment is small, so the same amount of steel is not needed there. Curtailing the extra bars saves steel and reduces congestion at the supports, but it must be done so that the remaining bars can still carry the moment and the shear, and so that every bar has enough bond length.

Theoretical and actual cut-off points

• Theoretical cut-off point: the section where the bending moment diagram shows that the bar is no longer required, i.e. where the moment of resistance of the remaining bars equals the applied moment $M_u$.
• Actual cut-off point: the bar cannot be stopped exactly at the theoretical point, because the stress in the bar is still being developed there and the real moment diagram may differ from the assumed one (shift due to diagonal cracking, load variations). IS 456 cl. 26.2.3.1 therefore requires every bar to be extended beyond the theoretical cut-off point (towards the support) by a distance not less than the effective depth $d$ or $12\phi$, whichever is greater (except at a simple support or the end of a cantilever).

 Bending moment diagram, left half of a simply supported beam

  M ^
    |                              ______ Mu,max (mid-span):
    |                       ___----        all bars needed
    |                 __--
    |- - - - - - - -*- - - - - - - - - -  MR of continuing bars
    |            _-'  :
    |         _-'     :
    |      _-'   :    :
    |   _-'      :    :
    +--'---------+----+-----------------> x
  support        Q    P              mid-span
                 |<-->|
          PQ >= d or 12 phi (whichever is greater)

  P = theoretical cut-off point (M = MR of continuing bars)
  Q = actual cut-off point (bar is stopped here)

At the theoretical point P the moment of resistance of the remaining bars is just equal to the applied moment. The curtailed bar is carried on to Q, so that it is fully effective up to P.

Conditions to be satisfied (IS 456 cl. 26.2.3)

1. The bar must also have a development length $L_d$ measured from the point of maximum stress, i.e. the length of bar beyond the section of maximum moment must be at least $L_d$.
2. Flexural bars must not be stopped in a tension zone unless one of the following is satisfied at the cut-off point: (a) the shear there does not exceed two-thirds of the permitted shear; or (b) extra stirrups are provided over a distance of $3d/4$ from the cut-off point; or (c) for bars of 36 mm or less, the continuing bars provide double the area needed for flexure and the shear does not exceed three-quarters of the permitted value.
3. At least one-third of the positive moment steel (one-fourth in continuous members) must be carried into the support.
4. At a support, at least one-third of the negative moment steel must extend beyond the point of inflection by at least $d$, $12\phi$ or $l/16$, whichever is greater.
5. Bars are curtailed symmetrically and in stages, never all at one section.