---
title: "Wind pressure on roof truss, 20 m span, 30 deg"
subject: "Design of Steel and Timber Structure"
chapter: 8
key: "semester_6/design_of_steel_and_timber_structure:wind-roof-truss-20m-span-30deg"
source: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/wind-roof-truss-20m-span-30deg
site: BCT Engineering
---

# Wind pressure on roof truss, 20 m span, 30 deg

Design of Steel and Timber Structure · Chapter 8: Design of Roof Trusses

- Asked in: 2076 Bhadra, 10 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/wind-roof-truss-20m-span-30deg
- Whole chapter: https://www.bctengineer.com/md/semester_6/design_of_steel_and_timber_structure/chapter-8

## Question

Find the wind pressure for design of roof truss of span 20 m and slope 30°. The height of the truss roof is 10m above the support. The building is in Kathmandu.

## Short answer

Using IS 875 with Category 3, Class B, Vz = 47 x 1.0 x 0.915 x 1.0 = 43.0 m/s and pz = 0.6Vz^2 = 1.11 kN/m^2. For alpha = 30 degrees, h/w = 0.5 and Cpi = +/-0.2, the worst net pressure is 0.998 kN/m^2 suction; the largest downward pressure is +222 N/m^2 on the windward slope.

## Answer

**Assumptions.** Span 20 m, roof slope $30^\circ$ (rise $= 10\tan30^\circ = 5.77$ m). The height "of the truss roof above the support" is taken as the eaves height $h = 10$ m, so $h/w = 10/20 = 0.5$ and the mean roof height $= 10 + 5.77/2 = 12.9$ m. Kathmandu: $V_b = 47$ m/s; town terrain with closely spaced obstructions: **Category 3**; greatest dimension 20 m, so **Class B** (20 m to 50 m) is taken. Life 50 years ($k_1 = 1$), flat site ($k_3 = 1$), normal permeability.

#### 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 3, Class B, at height 12.9 m: interpolating between 10 m (0.88) and 15 m (0.94): $k_2 = 0.915$ (Table 2).
- Topography factor $k_3 = 1.000$ (flat site).

$$
\begin{aligned} V_z &= 47\times1.00\times0.915\times1.000 = 42.99\ \text{m/s} \\ p_z &= 0.6V_z^2 = 0.6\times42.99^2 = 1109\ \text{N/m}^2 = 1.109\ \text{kN/m}^2 \end{aligned}
$$

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

Height ratio $h/w = 0.50$, roof angle $\alpha = 30.0^\circ$. The values are read directly from the $\alpha = 30^\circ$ row, so no interpolation is needed.

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

| Surface | $C_{pe}$ | $C_{pe} - C_{pi}$ ($C_{pi}=+0.2$) | $C_{pe} - C_{pi}$ ($C_{pi}=-0.2$) | $p_d$ (N/m²), $C_{pi}=+$ | $p_d$ (N/m²), $C_{pi}=-$ |
|---|---|---|---|---|---|
| Windward slope EF (wind 0°) | +0.00 | -0.20 | +0.20 | -222 | +222 |
| Leeward slope GH (wind 0°) | -0.40 | -0.60 | -0.20 | -665 | -222 |
| Slope EG (wind 90°) | -0.70 | -0.90 | -0.50 | -998 | -554 |
| Slope FH (wind 90°) | -0.60 | -0.80 | -0.40 | -887 | -444 |

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 $p_d = -998$ N/m² $= -0.998$ kN/m².

#### Answer

- Design wind speed $V_z = 43.0$ m/s; design wind pressure $p_z = 1109$ N/m² (1.11 kN/m²).
- Net design pressure on the roof: up to $998$ N/m² (1.00 kN/m²), suction. The largest downward (positive) pressure is $+222$ N/m², on the windward slope with $C_{pi} = -0.2$.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why is Class B chosen?
   A. The greatest dimension is between 20 m and 50 m
   B. It is under 20 m
   C. It is over 50 m
   D. The slope is 30 degrees
   Answer: A. A greatest dimension of 20 m falls in Class B (20 to 50 m). (Key point: Building class)

2. How is the height for k2 decided?
   A. Eaves height only: 10 m
   B. Eaves height plus half the rise: 10 + 5.77/2 = 12.9 m
   C. Full ridge height: 15.8 m
   D. The span: 20 m
   Answer: B. k2 is read at the mean roof height, giving 0.915 for Category 3 Class B. (Key point: Mean roof height)

3. What are Vz and pz?
   A. Vz = 47 m/s; pz = 1325 N/m^2
   B. Vz = 43.0 m/s; pz = 25.8 N/m^2
   C. Vz = 43.0 m/s; pz = 1109 N/m^2
   D. Vz = 41.4 m/s; pz = 1028 N/m^2
   Answer: C. Vz = 47 x 0.915 = 43.0 m/s and pz = 0.6 x 43.0^2 = 1109 N/m^2. (Key point: Design wind pressure)

4. At 30 degrees with h/w = 0.5, Cpe on the windward slope is 0.00. What does the sign of net pressure depend on?
   A. It is zero in both cases
   B. It is always suction
   C. It is always pressure
   D. On Cpi: pressure of +0.2 pz with Cpi = -0.2 (towards the roof) and suction of 0.2 pz with Cpi = +0.2
   Answer: D. Net = Cpe - Cpi = 0 -/+ 0.2, so the sign flips with the internal pressure; the severe design case is EG at 90 degrees. (Key point: Pressure on windward slope)

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