Bent-up bars in shear strength

Bent-up bars are part of the main tension bars that are bent upwards at 45$^\circ$ (or 30$^\circ$ to 60$^\circ$) near the supports, where the bending moment is small but shear is large. They carry the diagonal tension across the inclined cracks, as well as serving as flexural steel at mid-span.

   crack
     \       bent-up bar (alpha = 45 deg)
 ====o\=====o=====
        \        \
         \_______/ stirrup

Contribution to shear

The tension $T = 0.87f_yA_{sb}$ in a bar inclined at angle $\alpha$ to the beam axis has a vertical component:

$$V_{us}=0.87f_yA_{sb}\sin\alpha$$

Here $A_{sb}$ is the total area of the bent-up bars in one plane. For $\alpha=45^\circ$, $V_{us}=0.615f_yA_{sb}$.

Code provisions (IS 456 cl. 40.4)

• Bent-up bars should not carry more than 50% of the total shear to be resisted by shear reinforcement; the rest is carried by vertical stirrups.
• For a single bar or a single group of parallel bars all bent at the same cross-section, $V_{us}$ is as above; for a series of bars bent at different sections, spacing is also considered.
• Bent-up bars must be properly anchored and bent at gradual radius; bends are placed where they are no longer needed for flexure.

Total shear resistance: $V_u=V_c+V_{us}(\text{stirrups})+V_{us}(\text{bent-up})$, with $V_c=\tau_cbd$.