Design shear reinforcement of flanged beam

In flanged beams (T- and L-beams), the web carries almost all the shear; the flange contributes little. IS 456 therefore uses the web width $b_w$ in all shear calculations.

Procedure

1. Factored shear force: find $V_u$ at the support; the critical section is taken at $d$ from the face of the support (when the support reaction compresses the end region).
2. Nominal shear stress: $$\tau_v=\frac{V_u}{b_wd}$$ Check $\tau_v\le\tau_{c,max}$ (Table 20); else enlarge the web.
3. Percentage of steel: $p_t=\dfrac{100A_{st}}{b_wd}$ (tension steel continuing to the support). Find design shear strength $\tau_c$ of concrete from Table 19.
4. Decide reinforcement:
   • If $\tau_v\le\tau_c$: provide minimum shear reinforcement, $\dfrac{A_{sv}}{b_ws_v}\ge\dfrac{0.4}{0.87f_y}$.
   • If $\tau_v>\tau_c$: design for $V_{us}=V_u-\tau_cb_wd$ and
   $$s_v=\frac{0.87f_yA_{sv}d}{V_{us}}$$
5. Spacing limits: $s_v\le0.75d$ and $\le300$ mm, and not more than $\dfrac{0.87f_yA_{sv}}{0.4b_w}$.
6. Bent-up bars (optional): $V_{us}=0.87f_yA_{sb}\sin\alpha$, at most half of the total shear reinforcement.
7. Detailing: stirrups are closed (two-legged vertical), carried into the flange top and anchored around the top bars. Vary spacing along the span: closer near supports, up to the maximum where $V_u\le\tau_cb_wd$.

  bf
 +------------------+
 |       flange     |  Df
 +-----+      +-----+
       |  bw  |   <- shear area = bw x d
       |      |
       | o  o |   stirrups around bars