Wind pressure on 36 m building, core city

Assumptions (data not given in the question). $V_b$ is not stated; take 47 m/s (Kathmandu region, IS 875 Part 3 Fig. 1). The building is in a core city, so terrain Category 4 (large city centre with obstructions). Height 36 m, so the greatest dimension is 36 m and the structure is Class B (20 m to 50 m). A design life of 50 years gives $k_1 = 1.0$. The roof truss is taken on a plan width $w = 30$ m with a low roof pitch of $\alpha = 10^\circ$, truss spacing 6 m and normal permeability. $k_3 = 1$ (flat site).

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 $k_1 = 1.00$ (design life 50 years, Table 1).
• Terrain, height and size factor $k_2$: Category 4, Class B, at height 36 m, interpolating between 30 m (0.93) and 50 m (1.05): $k_2 = 0.966$ (Table 2).
• Topography factor $k_3 = 1.000$ (flat site, slope less than 3°).

$$\begin{aligned} V_z &= 47\times1.00\times0.966\times1.000 = 45.40\ \text{m/s} \\ p_z &= 0.6V_z^2 = 0.6\times45.40^2 = 1237\ \text{N/m}^2 = 1.237\ \text{kN/m}^2 \end{aligned}$$

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

Height ratio $h/w = 1.20$ (band $1/2 < h/w \le 3/2$), roof angle $\alpha = 10.0^\circ$. The values for $\alpha = 10^\circ$ are read directly from the table.

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 the windward slope EF (wind 0°), with $C_{pe} - C_{pi} = -1.30$, so $p_d = -1608$ N/m² $= -1.608$ kN/m².

Step 3: Wind force on the roof / truss

$F = (C_{pe} - C_{pi})\,A\,p_z$, acting normal to the roof surface. The most severe net coefficient, $-1.30$, is used for the maximum force.

• One slope of a truss (span 30 m, slope length $15/\cos10^\circ = 15.23$ m, spacing 6 m): $A = 91.4$ m², $F = 1.30\times91.4\times1.237 = 147.0$ kN (suction, i.e. acting away from the roof).

Answer

• Design wind speed $V_z = 45.4$ m/s; design wind pressure $p_z = 1237$ N/m² (1.24 kN/m²).
• Net design pressure on the roof: up to $1608$ N/m² (1.61 kN/m²), suction.
• Force on one slope of a truss (span 30 m, slope length 15.23 m, spacing 6 m): 147.0 kN.