Wind pressure on sloping roof, Madras

Data and assumptions. Span 10 m, pitch $1/4$: rise 2.5 m, $\alpha = 26.57^\circ$. Eaves height $h = 6$ m, $w = 10$ m, $h/w = 0.6$. Madras: $V_b = 50$ m/s (IS 875 Part 3, Appendix A). Terrain Category 2, Class A (building below 20 m); mean roof height $= 7.25$ m, below 10 m. $k_1 = 1$, $k_3 = 1$ (not given). Normal permeability: $C_{pi} = \pm0.2$.

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

$$V_z = V_b\,k_1k_2k_3$$

• Basic wind speed $V_b = 50$ m/s.
• Risk coefficient $k_1 = 1.00$ (50-year life; Table 1).
• Terrain, height and size factor $k_2$: Category 2, Class A, at height 7.25 m: $k_2 = 1.00$ (constant up to 10 m) (Table 2).
• Topography factor $k_3 = 1.000$ (flat site).

$$\begin{aligned} V_z &= 50\times1.00\times1.000\times1.000 = 50.00\ \text{m/s} \\ p_z &= 0.6V_z^2 = 0.6\times50.00^2 = 1500\ \text{N/m}^2 = 1.500\ \text{kN/m}^2 \end{aligned}$$

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

Height ratio $h/w = 0.60$, 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 $C_{pe} - C_{pi} = -1.00$, so $p_d = -1500$ N/m² $= -1.500$ kN/m².

Answer

• Design wind speed $V_z = 50.0$ m/s; design wind pressure $p_z = 1500$ N/m² (1.50 kN/m²).
• Net design pressure on the roof: up to $1500$ N/m² (1.50 kN/m²), suction.