Wind pressure on sloping roof, Delhi

Data. Span 10 m, pitch $1/4$ (rise/span), so rise $= 2.5$ m and $\tan\alpha = 2.5/5 = 0.5$, $\alpha = 26.57^\circ$. Eaves height $h = 5$ m; take the lesser plan dimension $w = 10$ m, so $h/w = 0.5$. Delhi: $V_b = 47$ m/s (IS 875 Part 3, Appendix A). Given: $k_1 = 1$, $k_2 = 0.8$, $k_3 = 1$. Permeability normal.

Step 1: Design wind speed (IS 875 Part 3:1987, cl. 5.3)

$$V_z = V_b\,k_1k_2k_3$$

• Basic wind speed $V_b = 47$ m/s.
• Risk coefficient $k_1 = 1.00$ (given).
• Terrain, height and size factor $k_2 = 0.8$ (given).
• Topography factor $k_3 = 1.000$ (given).

$$\begin{aligned} V_z &= 47\times1.00\times0.800\times1.000 = 37.60\ \text{m/s} \\ p_z &= 0.6V_z^2 = 0.6\times37.60^2 = 848\ \text{N/m}^2 = 0.848\ \text{kN/m}^2 \end{aligned}$$

Step 2: Pressure coefficients (Table 5, pitched roof of rectangular clad building)

Height ratio $h/w = 0.50$ (band $h/w \le 1/2$), roof angle $\alpha = 26.6^\circ$. Values are interpolated between $\alpha = 20^\circ$ and $30^\circ$.

Internal pressure coefficient $C_{pi} = \pm0.2$ (normal permeability), cl. 6.2.3.

Design pressure normal to the roof: $p_d = (C_{pe} - C_{pi})\,p_z$ (positive = towards the surface, negative = suction). The most severe case is slope EG (wind 90°), with $C_{pe} - C_{pi} = -0.90$, so $p_d = -763$ N/m² $= -0.763$ kN/m².

Answer (design wind pressure)

• Design wind speed $V_z = 37.6$ m/s; design wind pressure $p_z = 848$ N/m² (0.85 kN/m²).
• Net design pressure on the roof: up to $763$ N/m² (0.76 kN/m²), suction.