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IS 875 Part 3 · Wind

Wind Load Calculation as per IS 875 Part 3 — Complete Guide with 3 Examples

⏱ 18 min read📅 June 2026✅ IS 875 Part 3:2015🎓 GATE relevant

Wind is a critical lateral load for structures — especially tall buildings, industrial sheds, signboards, and structures in coastal or hilly areas. IS 875 Part 3 (2015 revision) provides the complete framework for calculating design wind pressure on any structure in India. This guide walks through the entire chain from basic wind speed → design wind speed → design wind pressure → force on building, with three worked examples and 10 GATE MCQs.

1. Introduction

Wind exerts pressure on any surface it hits. For a low-rise building in an interior city, wind forces are usually small compared to earthquake loads. But for a coastal high-rise, a tall chimney, or a large-span industrial shed, wind can be the governing lateral load. IS 875 Part 3 classifies the entire country into six basic wind speed zones (33 to 55 m/s) and provides a systematic procedure to convert this into the actual pressure on any building surface.

The 2015 revision of IS 875 Part 3 introduced significant changes from the 1987 version — including revised wind speed maps, gust factor approach, and terrain roughness categories. GATE questions now increasingly test the new provisions.

2. Concept and Theory

The wind pressure chain

The calculation follows a logical chain: V_b → V_z → p_z → F. Start with the basic wind speed V_b (from the wind map for your city), modify it for terrain, height, topography, and importance to get the design wind speed V_z, convert that to design wind pressure p_z using the kinetic energy formula (½ρV²), and finally apply pressure coefficients (C_p) to get the actual force on each surface of the building.

Think of it like this: the wind map tells you how fast the wind blows in your region (worst case, once in 50 years). But a building at 50m height in an open field experiences much higher wind speed than a building at 10m height in a dense city. The modification factors account for these differences.

Why terrain matters

Wind near the ground is slowed by friction with the surface — trees, buildings, and rough terrain all slow the wind. In a dense urban area (Terrain Category 3), the wind at 10m height is much slower than in an open field (Category 2) or near the sea coast (Category 1). IS 875 accounts for this through the k₂ factor, which varies with both terrain category and height above ground.

3. IS Code Background

Clause	Subject	Plain English
Cl 6.2	Basic wind speed V_b	From the wind map (Appendix A). Based on 50-year return period, 3-second gust at 10m height in Terrain Category 2.
Cl 6.3	Design wind speed V_z	V_z = V_b × k₁ × k₂ × k₃ × k₄. Four modification factors.
Cl 7.2	Design wind pressure p_z	p_z = 0.6 × V_z² (N/m²). The 0.6 comes from ½ × air density (1.2 kg/m³).
Cl 7.3	Force on surface	F = (C_pe − C_pi) × A × p_z. Net pressure = external − internal pressure coefficient × area × pressure.

4. Key Formulas

Design Wind Speed

V_z = V_b × k₁ × k₂ × k₃ × k₄

V_b = basic wind speed from wind map (m/s)
k₁ = risk coefficient (1.0 for normal buildings, 50-year life)
k₂ = terrain roughness and height factor (from Table 2)
k₃ = topography factor (1.0 for flat terrain; > 1.0 for hills/ridges/cliffs)
k₄ = importance factor for cyclonic region (1.0 for non-cyclonic)

Design Wind Pressure

p_z = 0.6 × V_z² (N/m²)

0.6 = ½ × ρ_air = ½ × 1.2 kg/m³
At V_z = 47 m/s: p_z = 0.6 × 47² = 1325 N/m² = 1.325 kN/m²

Force on a Surface

F = (C_pe − C_pi) × A × p_z

C_pe = external pressure coefficient (from tables based on building shape)
C_pi = internal pressure coefficient (±0.2 for buildings with normal openings)
A = surface area tributary to the element being designed

5. Important Tables

Basic Wind Speed for Key Indian Cities

City	V_b (m/s)	Zone
Chennai	50	Very high (coastal cyclone)
Mumbai	44	High
Kolkata	50	Very high
Delhi	47	High
Bangalore	33	Low
Hyderabad	44	High
Ahmedabad	39	Moderate

Terrain Categories

Category	Description	Example
1	Open terrain with few obstructions	Sea coast, flat open farmland
2	Open terrain with scattered obstructions (reference)	Airfields, open suburbs
3	Terrain with closely spaced obstructions	Typical city centres, industrial areas
4	Terrain with large and closely spaced obstructions	Dense metro cities with tall buildings

k₂ Values (extract)

Height (m)	Cat 1	Cat 2	Cat 3	Cat 4
10	1.05	1.00	0.91	0.80
15	1.09	1.05	0.97	0.80
20	1.12	1.07	1.01	0.80
30	1.15	1.12	1.06	0.97
50	1.20	1.17	1.12	1.10

6. Step-by-Step Design Procedure

Find V_b from the IS 875 wind map for your location.
Determine k₁ based on design life and risk level (usually 1.0).
Determine k₂ from Table 2 based on terrain category and height.
Determine k₃ based on topography (1.0 for flat, higher for hills).
Calculate V_z = V_b × k₁ × k₂ × k₃ × k₄ at each height zone.
Calculate p_z = 0.6 × V_z² at each height.
Determine C_pe for each surface from IS 875 tables based on building shape, aspect ratio, and roof angle.
Assume C_pi = ±0.2 for normal permeability (use the sign that gives worst case).
Calculate net pressure on each surface: (C_pe − C_pi) × p_z.
Calculate forces on structural elements by multiplying net pressure by tributary area.

7. Worked Examples

Example 1 — Wind Pressure on a Low-Rise Building (Beginner)

A building in Delhi (V_b = 47 m/s), height 10m, Terrain Category 3, flat terrain, normal building.

Step 1 — Modification Factors

k₁ = 1.0, k₂ = 0.91 (Cat 3, 10m), k₃ = 1.0, k₄ = 1.0

Step 2 — Design Wind Speed

V_z = 47 × 1.0 × 0.91 × 1.0 × 1.0 = 42.77 m/s

Step 3 — Design Wind Pressure

p_z = 0.6 × 42.77² = 0.6 × 1829 = 1097.6 N/m² ≈ 1.1 kN/m²

Example 2 — Tall Building in Mumbai (Intermediate)

A 50m tall building in Mumbai (V_b = 44 m/s), Terrain Category 2, flat terrain.

Pressure at Different Heights

At 10m: V_z = 44 × 1.0 × 1.00 = 44 m/s → p = 0.6 × 1936 = 1162 N/m²
At 30m: V_z = 44 × 1.12 = 49.28 m/s → p = 0.6 × 2429 = 1457 N/m²
At 50m: V_z = 44 × 1.17 = 51.48 m/s → p = 0.6 × 2650 = 1590 N/m²

Net Pressure on Windward Wall

C_pe = +0.8 (windward), C_pi = −0.2 (suction inside, worst case)
Net = 0.8 − (−0.2) = 1.0
F at 50m = 1.0 × 1590 = 1590 N/m² = 1.59 kN/m²

Example 3 — Industrial Shed with Roof (Advanced)

An industrial shed in Chennai (V_b = 50 m/s). Roof angle 15°. Height to eaves = 8m. Terrain Category 1 (coastal). Building 30m × 15m.

Step 1 — Design Pressure

k₂ = 1.05 (Cat 1, 10m), k₄ = 1.15 (cyclonic region)
V_z = 50 × 1.0 × 1.05 × 1.0 × 1.15 = 60.4 m/s
p_z = 0.6 × 60.4² = 2189 N/m² = 2.19 kN/m²

Step 2 — Roof Pressure

For θ = 15° on windward slope: C_pe = −0.8 (suction)
Leeward slope: C_pe = −0.4
With C_pi = +0.2 (worst case for uplift):
Net on windward roof = −0.8 − 0.2 = −1.0 (uplift!)
Uplift pressure = 1.0 × 2189 = 2189 N/m² = 2.19 kN/m² uplift

Step 3 — Design Implication

The roof sheeting and purlins must be designed to resist 2.19 kN/m² uplift — this is often more critical than gravity load on industrial roofs. Connections must resist pull-out, not just gravity.

8. GATE MCQs

Q1. The basic wind speed in IS 875 Part 3 is defined as:

(a) 1-hour mean wind at 10m height
(b) 3-second gust at 10m height in Terrain Category 2
(c) 10-minute mean at 50m height
(d) Maximum ever recorded wind speed

Answer: (b)
IS 875 Part 3 (2015) defines V_b as a 3-second gust speed at 10m height in Terrain Category 2, with 50-year return period.

Q2. The design wind pressure formula p_z = 0.6 V_z² gives pressure in:

(a) kN/m²
(b) N/m²
(c) kg/m²
(d) MPa

Answer: (b)
When V_z is in m/s and ρ = 1.2 kg/m³, the result is in N/m² (Pascals).

Q3. The constant 0.6 in the wind pressure formula represents:

(a) A safety factor
(b) Half the density of air (½ × 1.2)
(c) An aerodynamic coefficient
(d) A reduction factor

Answer: (b)
p = ½ρV². With ρ_air = 1.2 kg/m³, ½ × 1.2 = 0.6.

Q4. Which terrain category would apply to a building in central Mumbai?

(a) Category 1
(b) Category 2
(c) Category 3
(d) Category 4

Answer: (c) or (d)
Central Mumbai is a dense urban area. Category 3 (closely spaced obstructions) is appropriate for most city locations. Category 4 for very dense areas with tall buildings like Nariman Point.

Q5. As height above ground increases, the k₂ factor generally:

(a) Decreases
(b) Increases
(c) Remains constant
(d) First increases then decreases

Answer: (b)
Wind speed increases with height because surface friction has less effect higher up. Hence k₂ increases with height.

Q6. Internal pressure coefficient C_pi for a building with normal permeability is:

(a) ±0.2
(b) ±0.5
(c) ±0.7
(d) 0

Answer: (a)
IS 875 specifies C_pi = ±0.2 for buildings with normal openings (5–20% of wall area). Large openings on one side can increase this to ±0.7.

Q7. For wind load calculation on a signboard, the net pressure coefficient is typically:

(a) 0.8
(b) 1.0
(c) 1.2
(d) 1.4

Answer: (c)
For isolated signboards, IS 875 specifies a force coefficient of 1.2 (combining windward pressure and leeward suction).

Q8. Wind pressure is proportional to:

(a) V
(b) V²
(c) V³
(d) V⁰·⁵

Answer: (b)
p = 0.6V². Pressure is proportional to the square of wind speed. Doubling wind speed quadruples the pressure.

Q9. The risk coefficient k₁ for a building with 100-year design life is:

(a) Less than 1.0
(b) 1.0
(c) Greater than 1.0
(d) 0.5

Answer: (c)
Longer design life means higher probability of encountering extreme winds. k₁ > 1.0 for lives exceeding the standard 50 years.

Q10. On an industrial shed roof with θ = 10°, the windward slope typically experiences:

(a) Positive pressure (downward)
(b) Suction (uplift)
(c) Zero pressure
(d) Depends on building height only

Answer: (b)
For low roof angles (θ < 20°), the windward slope typically has negative C_pe (suction). Wind separates from the surface at the eaves and creates uplift on the roof.

9. Common Mistakes

Mistake 1: Using p_z in kN/m² when the formula gives N/m². p_z = 0.6 V² gives N/m². Divide by 1000 for kN/m². Many students forget the unit conversion.

Mistake 2: Ignoring internal pressure. C_pi = ±0.2 can add 20% to the net pressure on a surface. Always consider both signs and use the worst case.

Mistake 3: Using same k₂ for entire building height. k₂ varies with height. For a 30m building, different floors experience different wind pressures.

Mistake 4: Forgetting k₄ for cyclonic regions. Coastal cities like Chennai, Visakhapatnam, and Bhubaneswar are in cyclonic zones and need k₄ > 1.0.

10. Quick Revision Summary

Memorise:

V_z = V_b × k₁ × k₂ × k₃ × k₄
p_z = 0.6 × V_z² (N/m²)
F = (C_pe − C_pi) × A × p_z
0.6 = ½ × 1.2 (half air density)
4 terrain categories: 1 (open coast) to 4 (dense metro)
k₂ increases with height, decreases with terrain roughness
C_pi = ±0.2 for normal openings
Pressure ∝ V² — double speed = 4× pressure

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