Wind load on industrial truss, 40 m span

Assumptions (data not fully given). $V_b = 47$ m/s (given). Terrain is an open industrial area: Category 2 ("open terrain with scattered obstructions"); Class A (as stated). Life 50 years: $k_1 = 1.0$; flat site: $k_3 = 1$. The roof slope is not given, so $\alpha = 20^\circ$ is assumed (rise $= 20\tan20^\circ = 7.3$ m). Eaves height 10 m, so $h/w = 10/40 = 0.25$; mean roof height $= 10 + 7.3/2 = 13.6$ m. Normal permeability ($C_{pi} = \pm0.2$); GI sheeting. Truss spacing is assumed to be 5 m.

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 $k_1 = 1.00$ (50-year life; Table 1).
• Terrain, height and size factor $k_2$: Category 2, Class A, at height 13.6 m: interpolating between 10 m (1.00) and 15 m (1.05): $k_2 = 1.036$ (Table 2).
• Topography factor $k_3 = 1.000$ (flat site).

$$\begin{aligned} V_z &= 47\times1.00\times1.036\times1.000 = 48.71\ \text{m/s} \\ p_z &= 0.6V_z^2 = 0.6\times48.71^2 = 1424\ \text{N/m}^2 = 1.424\ \text{kN/m}^2 \end{aligned}$$

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

Height ratio $h/w = 0.25$, roof angle $\alpha = 20.0^\circ$. The values are read directly from the $\alpha = 20^\circ$ row, so no interpolation is needed.

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 $p_d = -1281$ N/m² $= -1.281$ 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, $-0.90$, is used for the maximum force.

• One truss (both slopes, slope length 21.28 m each, spacing 5 m): $A = 212.8$ m², $F = 0.90\times212.8\times1.424 = 272.7$ kN (suction, i.e. acting away from the roof).

• Whole roof, 40 m × 100 m plan: $A = 4256.7$ m², $F = 0.90\times4256.7\times1.424 = 5454.0$ kN (suction, i.e. acting away from the roof).

Answer

• Design wind speed $V_z = 48.7$ m/s; design wind pressure $p_z = 1424$ N/m² (1.42 kN/m²).
• Net design pressure on the roof: up to $1281$ N/m² (1.28 kN/m²), suction.
• One truss (both slopes, slope length 21.28 m each, spacing 5 m): 272.7 kN.
• Whole roof, 40 m × 100 m plan: 5454.0 kN.