Max wind force on roof truss, 50 yr, hill crest

Assumptions (data not fully given). Kathmandu: $V_b = 47$ m/s. A "highly dense city" is terrain Category 4. Plan 20 m × 30 m, so the largest dimension is 30 m: Class B. Life 50 years: $k_1 = 1.0$. Roof: span 20 m, rise 2 m, so $\tan\alpha = 2/10$, $\alpha = 11.3^\circ$ and $h/w = 5/20 = 0.25$. Normal permeability ($C_{pi} = \pm0.2$). Height for $k_2$: eaves 5 m plus half the rise = 6 m, which is below 10 m, so $k_2$ is the value at 10 m. The site is 15 m above the mean ground level and 100 m from the crest of a ridge 200 m high. The slope of the ridge is not given and is assumed steeper than 17°, so (Appendix C) $C = 0.36$ and $L_e = Z/0.3 = 667$ m. The site is upwind of the crest: $X/L_e = -100/667 = -0.15$; $H/L_e = 15/667 = 0.022$; from Fig. 15, $s \approx 0.7$ (read from the chart, approximate). Truss spacing is not given; 5 m is assumed (6 bays along 30 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 4, Class B, at height 6 m (use 10 m): $k_2 = 0.76$ (constant up to 10 m) (Table 2).
• Topography factor $k_3 = 1 + Cs = 1 + 0.36\times0.7 = 1.252$ (ridge).

$$\begin{aligned} V_z &= 47\times1.00\times0.760\times1.252 = 44.72\ \text{m/s} \\ p_z &= 0.6V_z^2 = 0.6\times44.72^2 = 1200\ \text{N/m}^2 = 1.200\ \text{kN/m}^2 \end{aligned}$$

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

Height ratio $h/w = 0.25$, roof angle $\alpha = 11.3^\circ$. Values are interpolated between $\alpha = 10^\circ$ and $20^\circ$.

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 the windward slope EF (wind 0°), with $C_{pe} - C_{pi} = -1.295$ (shown as $-1.30$ in the table), so $p_d = -1554$ N/m² $= -1.554$ 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, $-1.295$, is used for the maximum force.

• Whole roof, 20 m × 30 m plan (slope length 10.20 m, both slopes): $A = 611.9$ m², $F = 1.295\times611.9\times1.200 = 951.0$ kN (suction, i.e. acting away from the roof).

• One truss at 5 m spacing (both slopes): $A = 102$ m², $F = 1.295\times102\times1.200 = 158.5$ kN (suction, i.e. acting away from the roof).

Answer

• Design wind speed $V_z = 44.7$ m/s; design wind pressure $p_z = 1200$ N/m² (1.20 kN/m²).
• Net design pressure on the roof: up to $1554$ N/m² (1.55 kN/m²), suction.
• Whole roof, 20 m × 30 m plan (slope length 10.20 m, both slopes): 951.0 kN.
• One truss at 5 m spacing (both slopes): 158.5 kN.