IS 875 Part 4 — Code of Practice For Design Loads (Other Than Earthquake) For Buildings And Structures, Part 4: Snow Loads

IS 875 Part 4: Scope & Key Formulas for Roof Snow Loads

Scope (Clause 4.2.1)

• Applies to snow loads on roofs including:
  • Simple flat and monopitch roofs
  • Simple or multiple pitched roofs (positive and negative slopes)
  • Two-span or multispan roofs

Key Formulas for Shape Coefficients (Table 4.2.1)

Additional Shape Coefficient for Multilevel Roofs (Clause 4.2.4)

[ H_w = 1 + \frac{(m_1 + m_2)(4 - 2h)}{l} ]

• (m_1, m_2) depend on roof profile:
  • Plane roofs slope < 20° or vaulted: 0.5
  • Plane roofs slope > 20° or vaulted: 0.3
• (h, l) in meters
• Adjust coefficients for snow transfer conditions (wind, temperature).

Notes:

• Heights and coefficients are used to calculate snow pressure (S_0) in kPa.
• Restrictions: Roof length (l) between 5 m and 15 m.
• Use these coefficients to find design snow load:
  [ p = S_0 \times H ] where (H) is the shape coefficient.

flowchart TD
    A[Start: Determine Roof Type & Slope] --> B{Slope (A)}

IS 875 Part 4 - General Principles for Snow Load (Clause 4.1 & 4.2)

1. General Principles (Clause 4.1)

• Snow load is ideally uniform on roofs in calm weather.
• Wind redistributes snow, causing drift loads on roofs, especially multilevel roofs.
• Shape coefficient (μ) accounts for roof geometry and snow drift.
• Snow distribution parallel to eaves is assumed uniform.
• Nominal shape coefficients are provided due to limited statistical data.

2. Shape Coefficients for Simple Roofs (Clause 4.2.1)

3. Multilevel Roofs (Clause 4.2.4 & Appendix A)

• Total shape coefficient:
  [ \mu = \mu_s + \mu_w ] where:

  • (\mu_s) = snow sliding coefficient (nominal 0.8)
  • (\mu_w = 1 + (m_1 + m_2)(4 - 2h)/l) (wind effect)

• Parameters:

  • (h) = height difference between roofs (m)
  • (l) = horizontal length of upper roof (m), (5 \leq l \leq 15)
  • (m_1 = 0.8) (typical)
  • (m_2 = 0.3) to 0.5 depending on roof slope (<20° or >20°)

• Restrictions:
  [ 0.8

IS 875 Part 4: Snow Load on Roofs - Key Formulas & Specifications

1. Design Snow Load on Roof (Clause 3.1)

[ S = p \times S_0 ]

• S = Design snow load on roof (Pa)
• p = Shape coefficient (dimensionless)
• S₀ = Ground snow load (Pa)

2. Ground Snow Load (S₀)

• Depends on maximum snow depth and average density.
• For Indian regions with snow (Jammu & Kashmir, Himachal Pradesh, Uttarakhand, etc.), consult:
  • Snow and Avalanches Study Establishment (DRDO), Manali
  • Indian Meteorological Department (IMD), Pune

3. Shape Coefficient (p)

• Accounts for roof geometry effects: snow drifts, sliding, accumulation.
• Varies with roof slope, shape, and exposure.
• Values provided in IS 875 Part 4 tables (not included here; refer to the standard).

4. Notes

• Design for max(S, imposed loads per IS 875 Part 2).
• Snow load is considered as uniform pressure on plan area.
• Use 1 Pa = 1 N/m² for units.

flowchart TD
    A[Ground Snow Load S₀] --> B[Apply Shape Coefficient p]
    B --> C[Design Snow Load on Roof S]
    C --> D{Compare with Imposed Loads (IS 875 Part 2)}
    D -->|Greater| E[Design for Snow Load]
    D -->|Lesser| F[Design for Imposed Load]

For detailed shape coefficients and regional snow load data, refer to the official IS 875 Part 4 document or contact the mentioned authorities.

IS 875 Part 4: Shape Coefficients for Roofs (Clauses 4.2 - 4.3)

1. Shape Coefficients for Simple Flat and Monopitch Roofs (Clause 4.2.1)

2. Multilevel Roofs (Clause 4.2.4)

• Total shape coefficient:
  [ M_a = M_s + M_w ] where

  • (M_s) = due to sliding
  • (M_w) = due to wind

• (M_w = 2h_s), with restrictions:
  [ 5,m < l < 15,m, \quad 0.8 < M_w < 4.0 ]

• For slopes (B > 15^\circ), additional load of 50% of max total load on adjacent upper slope is linearly distributed.

3. Notes on Wind Pressure Coefficients (Clause 4.3)

• Wind coefficients vary with exposure and shape.
• For detailed wind pressure (u_w), refer to Appendix A of IS 875 (Part 4).

Summary Table for Simple Roof Slopes

| Slope (A) | M1 (Positive slope)          | M2 (Negative slope)                     |
|-----------|-----------------------------|----------------------------------------|
| 0°-30°    | 0.8                         | 0.8                                    |
| 15

IS 875 Part 4: Shape Coefficients for Simple Flat and Monopitch Roofs (Clause 4.2.1)

Key Formulas for Roof Slope Angle ( A ):

• For negative roof slope or multispan roofs, coefficients are similarly defined with (M_1) and (M_2) adjusted accordingly.
• For asymmetrical roofs, treat each side as half of a symmetrical roof.

Additional Notes:

• (H_a = H_s + H_w), where (H_s) is snow load and (H_w) is wind load.
• Restrictions on roof height and wind load coefficient (u) apply: (0.8 \leq u \leq 4.0).
• For slopes (B > 15^\circ), an additional load of 50% of the maximum load on the adjacent upper slope is considered.
• For slopes (B < 15^\circ), this additional load is zero.

Summary Table for Shape Coefficients

IS 875 Part 4: Simple Curved Roofs (Clause 4.2.3)

For Simple Curved Roofs, wind pressure coefficients must be derived considering roof slope and curvature. Two key cases are examined:

Key Points from Clause 4.2.3:

• Cases to examine:

  1. Curved roofs with positive slope
  2. Curved roofs with negative slope

• Use shape coefficients similar to those for simple pitched roofs (Clause 4.2.1).

From Clause 4.2.1 (Roof Slope Coefficients):

Application for Curved Roofs:

• Approximate the curved roof slope by an equivalent slope angle ( A ).
• Use the above coefficients ( M_1 ) and ( M_2 ) for external pressure calculations.
• For multispan or complex roofs, refer to Clause 4.25.

Summary Formula:

[ M_1 = \begin{cases} 0.8 & 0^\circ < A \leq 30^\circ \ 0.8 \times \frac{60 - A}{30} & 30^\circ < A < 60^\circ \ 0 & A > 60^\circ \end{cases} ]

[ M_2 = \begin{cases} 0.8 & 0^\circ < A \leq 30^\circ \ 1.2 \times \frac{60 - A}{30} & 30^\circ < A < 60^\circ \ 0 & A >

IS 875 Part 4 - Shape Coefficients for Areas Exposed to Wind (Clause 4.3 & 4.2)

Key Points:

• Shape Coefficients (C_s) depend on roof type, slope, and exposure.
• Coefficients from Clause 4.2 and Appendix A can be reduced by 25% if:
  • Roof is fully exposed (open terrain, no shielding within 10× obstruction height).
  • No significant projections (e.g., parapets) that trap snow.
• Special considerations apply in calm valleys or warm areas where snow removal by wind is minimal.

Important Formula & Restrictions for Multilevel Roofs (Clause 4.2.4):

[ H_a = H_s + H_w ]

• (H_a): Total snow load on roof
• (H_s): Load due to sliding snow
• (H_w): Load due to wind drift

Restrictions:

• (5,m < l < 15,m)
• (0.8 < u_w < 4.0)
• (H_w = 2 h S_0), where (S_0) is ground snow load (kN/m²), (k=2,kN/m^3)
• For roof slope (\beta > 15^\circ), additional load = 50% of max load on adjacent upper slope, distributed linearly.
• For (\beta < 15^\circ), (H_w = 0).

Summary Table (Typical Shape Coefficients for Roofs):

flowchart TD
    A[Ground Snow Load \(S_0\)] --> B[Calculate Sliding Load \(H_s\)]
    A --> C[Calculate Wind Drift Load \(H

IS 875 Part 4: Multilevel Roofs Key Points

1. Shape Coefficients for Multilevel Roofs (Clause 4.2.4)

• Total wind pressure, Ha = Hs + Hw
  • Hs: Basic wind pressure
  • Hw: Additional pressure due to height difference and wind sliding effect
• Height difference: ( h_t = 2h_t ), restricted as:
  • ( 5,m < l < 15,m )
  • ( 0.8 < u_w < 4.0 ) (wind pressure coefficient limits)
• Wind pressure coefficient ( u_w ) depends on roof slope angle ( \beta ):
  • For ( \beta > 15^\circ ), additional load = 50% of max load on adjacent upper slope, linearly distributed.
  • For ( \beta < 15^\circ ), additional load = 0.

2. Roof Slope Coefficients (Clause 4.2.1 Table 4.2.1)

3. Important Formula Summary:

[ u_w = \text{wind pressure coefficient, limited as } 0.8 < u_w < 4.0 ]

[ h_t = 2h_t \quad \text{(height difference factor, restricted by clause)} ]

Notes:

• For complex multilevel roofs

IS 875 Part 4: Roofs with Local Projections and Obstructions (Clause 4.2.6)

Key Points & Formulas:

• Local projections and obstructions on roofs affect wind pressure distribution.
• Use shape coefficients (μ) from Clause 4.2 for roof slopes and configurations.
• For multilevel roofs (Clause 4.2.4), wind pressure is combined from:
  • Ha = Hs + Hw
    • Hs: pressure due to sliding
    • Hw: pressure due to wind, calculated as: [ H_w = 2h_s \quad \text{with} \quad 0.8 \leq \mu_w \leq 4.0 ]
    • Height restrictions: (5,m < l < 15,m)
• For simple pitched roofs (Clause 4.2.1), shape coefficients depend on slope angle (A):

• For obstructions, an additional load of 50% of the max total load on the adjacent upper slope is added and distributed linearly.

Summary:

• Use shape coefficients (M_1, M_2) based on roof slope.
• Add wind pressure effects from local projections using (H_w = 2 h_s).
• For obstructions, increase load by 50% on adjacent slopes.
• Refer to Appendix A of IS 875 Part 4 for detailed (u_w) formula.

flowchart LR
    A

IS 875 Part 4 — Ice Load on Wires (Clause 5.1)

• Ice thickness (t): 3 to 10 mm (location dependent)

• Ice density (ρ): 0.9 g/cm³ = 900 kg/m³

• Increase in wire diameter: Consider original diameter ( d ) plus twice the ice thickness ( t ):

  [ d_{ice} = d + 2t ]

• Ice load per unit length on wire:

  [ w = \pi \times d_{ice} \times t \times \rho \times g ]

  Where:

  • ( w ) = ice load (N/m)
  • ( d_{ice} ) = diameter including ice (m)
  • ( t ) = ice thickness (m)
  • ( \rho ) = density of ice (kg/m³)
  • ( g ) = acceleration due to gravity (9.81 m/s²)

• Wind force on iced wires: Use increased diameter ( d_{ice} ) for drag calculations.

Summary Table

flowchart TD
    A[Original Wire Diameter (d)] --> B[Add Ice Thickness (t)]
    B --> C[Calculate Diameter with Ice: d_ice = d + 2t]
    C --> D[Calculate Ice Load per unit length]
    D --> E[Use d_ice for Wind Load Calculations]

Note: Always verify local climate conditions and use appropriate ice thickness based on site-specific data.

IS 875 Part 4 — Shape Coefficients for Multilevel Roofs (Clause 4.2.4)

Key Formulas and Specifications

• Height parameters:

  • ( H_a = H_s + H_w )
  • ( H_w = 2h ) (restricted by ( 5,m < l < 15,m ))
  • ( H_w = 2h \leq k_h H_w ) where ( k = 2,kN/m^2 )

• Shape coefficient ( \mu_w ) limits: [ 0.8 \leq \mu_w \leq 4.0 ]

• Roof slope considerations:

  • For slope ( \beta > 15^\circ ), an additional load = 50% of max total load on adjacent upper slope, linearly distributed.
  • For ( \beta < 15^\circ ), ( \mu_w = 0 ).

• Interpolation:

  • If ( l/s < 13 ), interpolate ( \mu ) between ( \mu_1 ) and ( \mu_w ).

Table Extract (Clause 4.2.1 for Simple Roofs Slopes (\beta)):

Summary:

• Use height (H_a) as sum of static and wind heights.
• Restrict wind height (H_w = 2h) within limits.
• Shape coefficients (\mu_w) vary