Criteria for design of reinforced concrete bins for storage of granular and powdery materials, Part 1: General requirements and assessment of bin loads

IS 4995 Part 1: Introduction & Scope - Key Formulas, Tables, and Specs

Notations (Clause 3.1)

• A = Horizontal interior cross-sectional area of bin
• a, b = Sides of rectangular bin (a ≤ b)
• D = Internal diameter of circular bin
• d = Max inscribed circle diameter in bin
• h = Height of bin
• Pa = Air pressure for pneumatic emptying
• Px = Horizontal pressure on bin walls
• Ps = Vertical pressure on stored material
• Pw = Vertical load on wall due to friction
• UT = Interior perimeter
• W = Bulk density of material
• Z = Depth below max fill surface
• ϕ = Angle of internal friction of material
• δ = Angle of wall friction
• u = tan δ = Coefficient of wall friction
• K, My = Coefficients during emptying and filling
• À = Pr/P = Pressure ratio

Key Formula (Clause 6.1.1.2)

[ Z P = TDWR \left[ z - z_u \left(1 - e^{-2/2} \right) \right] ]

Table: Angle of Wall Friction (δ) & Pressure Ratio (À) (Clause 5.3.2)

Notes:

• ϕ = Angle of internal friction of stored material
• Units for velocity in notes: m/h
• Pressure ratios vary for filling and

IS 4995 Part 1 - Key Formulas, Tables & Specifications: Scope

1. Scope Overview (Clause 2.0)

Defines terms and parameters for design of silos and bins handling granular and powdery materials.

2. Key Formula (Clause 6.1.1.2)

Pressure at depth ( Z ):

[ Z_P = T D W R \left[ Z - Z_u \left( 1 - e^{-2Z/Z_o} \right) \right] ]

• ( Z_P ): Pressure at depth ( Z )
• ( Z_u ): Upper reference depth
• ( Z_o ): Characteristic depth parameter

3. Appendix A Table (Clause 6.1.1.3)

Values of ( 1 - e^{-Z/Z_o} ) for different ( Z/Z_o ):

Use interpolation for intermediate values.

4. Design Parameters - Wall Friction & Pressure Ratio (Table 2, Clause 5.3.2)

IS 4995 Part 1: Definitions & Classifications — Key Notations and Parameters

Important Formula (Clause 6.1.1.2):

[ Z_P = T D W R \left[z - z_u \left(1 - e^{-2/2} \right) \right] ]

• (Z_P): Pressure at depth (z)
• (T, D, W, R, z_u): Design parameters as per clause 6.1

Notes:

• Use Tables 1 & 2 (Clause 6.2.1) for design parameters during normal filling and emptying.
• Units for velocity (v) in notes: m/h.
• Pressure ratios differ for filling ((\lambda_i)) and emptying ((\lambda_e)).

flowchart LR
    A[Bin Geometry] -->|a,b,D| B[Cross Sectional Area (A)]
    B --> C[Pressure Calculations]
    C --> D[Horizontal Pressure (Px)]
    C --> E[Vertical

IS 4995 Part 1 - General Requirements Summary

• Scope: Storage of dry materials with properties in Table 1; adjustments needed if moisture, temperature vary (see Note under Table 1).

• Material Properties: Refer to Table 1 for bulk density, angle of repose, flow properties.

• Load Assessment:

  • Bin load calculations consider material properties and geometry.
  • Updated formula for pressure distribution (Clause 6.1.1.2):
    [ Z_P = TDWR \left[z - z_u \left(1 - e^{-2/2}\right)\right] ] where:
    • (Z_P) = pressure at depth (z)
    • (T, D, W, R, z_u) = parameters defined in the code (typically thickness, diameter, unit weight, etc.)

• Units: Velocity (v) in informal tables is in m/h (Clause 6.2.3).

• Exclusions:

  • Thermal insulation, joint details, weatherproofing not covered.

• Rounding: Follow revised rules for rounding numerical values (Clause 1.3).

Key Table Snapshot (Example from Table 1)

flowchart TD
    A[Material Properties] --> B[Load Calculation]
    B --> C[Pressure Distribution using Z_P formula]
    C --> D[Structural Design]
    D --> E[Exclusions: Insulation, Joints]

Use IS 4995 Part 1 as baseline; adjust for environmental conditions per Note in Table 1.

Key Formulas and Specifications for Bin Dimensions and Shapes (IS 4995 Part 1):

1. Bin Dimensions (Clause 4.2.1)

• Volume & Height/Diameter Ratio:
  • Governed by storage and functional needs.
  • Prefer height/diameter (h/D) ≥ 2 to reduce lateral pressure over height.

2. Bin Shapes (Clause 4.2.2 & 5.1)

• Plan Shape: Circular or polygonal.
• Roof & Bottom: Flat, conical, or pyramidal.
• Hopper Angle for Gravity Flow Bins:
  [ \theta_{\text{hopper}} \geq \theta_{\text{angle of repose}} + 15^\circ ]
• Shape Factor ( R ) (Clause 5.1):
  • For polygonal/interstice bins, approximate ( R ) by that of an equivalent square bin with the same cross-sectional area.

3. Notations (Clause 3.1)

4. Design Recommendations

• Use circular bins for uniform pressure distribution.
• Maintain hopper slope ≥ angle of repose + 15° for smooth gravity discharge.
• For polygonal bins, convert to equivalent circular or square bin for pressure calculations.

flowchart TD
    A[Bin Plan Shape] -->|Circular| B[Use Diameter D]
    A -->|Polygonal| C[Equivalent Square Bin]
    C --> D[Calculate Side a for same area A]
    B --> E[Height h]
    D --> E
    E --> F[Height/Diameter Ratio ≥ 2]
    F --> G[Reduced

IS 4995 Part 1 — Material Properties & Load Parameters

1. Bulk Density (W) & Angle of Internal Friction (φ)

Note: Values vary with moisture, particle size, temperature; testing recommended.

2. Angle of Wall Friction (δ) & Pressure Ratio (A)

Key Formulas

• Horizontal pressure, ( p_h = A \times p_v )

  Where:

  • ( A ) = pressure ratio (from table)
  • ( p_v = W \times h ) (vertical pressure at depth ( h ))

• Wall friction angle, ( \delta = k \times \phi )

IS 4995 Part 1: Assessment of Bin Loads

Key Aspects for Bin Load Assessment (Clause 6.0)

• Load Types Considered:
  • Static load due to stored material weight.
  • Dynamic load from filling/emptying operations.
  • Impact load from material drop.
  • Wind and seismic loads (if applicable).

Important Formulas:

1. Static Load (W):
   [ W = \rho \times V ]

   • (\rho) = Bulk density of material (kN/m³)
   • (V) = Volume of material in the bin (m³)

2. Pressure on Bin Walls (P):
   Using Janssen’s formula for lateral pressure:
   [ P = \frac{\rho \cdot g \cdot K \cdot h}{1 - e^{-\mu K h / r}} ]

   • (K) = lateral pressure coefficient
   • (\mu) = wall friction coefficient
   • (h) = height of material
   • (r) = radius or half-width of bin

Typical Bulk Density Values (IS 4995 reference or standard tables):

Specifications:

• Design for maximum fill height.
• Use safety factors as per IS 4995.
• Consider load combinations with wind/seismic loads.
• Account for impact factors (usually 10-20% increase on static load).

flowchart TD
    A[Material Bulk Density] --> B[Calculate Static Load]
    B --> C[Calculate Lateral Pressure on Walls]
    C --> D[Assess Dynamic and Impact Loads]
    D --> E[Combine Loads for Structural Design]

Summary: Use bulk density and volume to find static loads, Janssen’s formula for lateral pressure, and include dynamic/impact loads per IS 4995 Part 1 for safe bin design.

IS 4995 Part 1: Bin Loads Due to Granular Materials

Key Points from Clauses:

• Clause 6.1: Covers bin loads from granular materials (e.g., sand, gravel).
• Clause 2.4: Defines bin loads as pressures exerted by stored materials on bin walls.
• Clause 5.3.2: Introduces pressure ratio ( A = \frac{\text{horizontal pressure}}{\text{vertical pressure}} ) from Table 2.
• Table 1: Provides bulk density and angle of internal friction for various granular materials.

Important Formulas:

1. Vertical Pressure at depth ( z ):

[ P_v = \gamma \times z ]

• ( \gamma ) = bulk density (kN/m³)
• ( z ) = depth of material (m)

2. Horizontal Pressure:

[ P_h = A \times P_v ]

• ( A ) = pressure ratio from Table 2 (depends on internal friction angle)

3. Pressure Ratio ( A ):

From Table 2 (typical values):

Table 1 (Example Extract):

Summary:

• Use bulk density and internal friction angle from Table 1.
• Compute vertical pressure ( P_v ) by depth.
• Calculate horizontal pressure ( P_h = A \times P_v ) using pressure ratio ( A ).
• Design bin walls for ( P_h ) to ensure structural safety.

flowchart TD
    A[Stored Granular Material] --> B[Bulk Density \(\gamma\)]
    A --> C[Internal Friction Angle \(\phi\)]

IS 4995 Part 1 - Bin Loads Due to Powdery Materials

Key Formulas (Clause 6.2.3)

• Rapid Filling Lateral Pressure (PA):

[ P_A = 0.8 \times W \times Z_n ]

Where:

• (W) = bulk density of material (kN/m³)

• (Z_n) = height up to which material flows like fluid during rapid filling (m)

• Calculation of (Z_n):

[ Z_n = \left( \frac{v}{v_0} \right) \times t ]

Where:

• (v) = actual filling speed (m/h)
• (v_0) = minimum filling speed (m/h)
• (t) = time lapse (1 hour)

Minimum Filling Speeds (v_0) (m/h)

Additional Notes:

• Use bulk density (W) and angle of internal friction from Table 1 (Clause 5.3.2) for pressure calculations.
• Horizontal to vertical pressure ratio (A) is given in Table 2 (Clause 5.3.2).

Summary Diagram (Pressure Distribution during Rapid Filling)

graph TD
    A[Top Layer] -->|Rapid Filling| B[Fluid-like flow zone up to Zn]
    B -->|Pressure PA = 0.8 W Zn| C[Bin Walls]
    C --> D[Structural Load]

Use these formulas and tables to compute governing lateral pressures for powdery materials during rapid filling in silos.

IS 4995 Part 1: Effects of Discharge and Aeration Devices

Key Formulas

• Pressure at height z during discharge:

[ Z_P = TDWR \left[ z - z_u \left( 1 - e^{-\frac{2}{2}} \right) \right] ]

Where:

• (Z_P) = pressure at height z
• (TDWR) = Total Design Wall Resistance
• (z_u) = height of outlet or aeration device
• (e) = base of natural logarithm

Design Parameters (Clause 5.3.2, Table 2)

Specifications & Notes

• Units: Velocity (v) in aeration devices is expressed in m/h (meters per hour).
• Normal Filling and Emptying Pressures: Use Tables 1 & 2 for design parameters; compute max pressures per Clause 6.1.
• Discharge Promoting Devices (Clause 6.3.4):
  • Devices like inserts or bridge structures reduce effective cross-section, causing locally increased wall pressures.
  • Designer must perform experimental investigations due to lack of reliable predictive models.

Summary Diagram: Pressure Variation During Discharge

graph LR
A[Outlet / Aeration Device at z_u] --> B[Pressure decreases exponentially above z_u]
B --> C[Pressure at height z: Z_P = TDWR[z

IS 4995 Part 1: Load Reduction Effects Summary

Key Points from Clauses:

• Clause 6.3: Addresses effects that increase bin loads (e.g., filling, impact).

• Clause 6.4: Specifies load reduction near the bin bottom during emptying:

  • Horizontal pressure reduces linearly from the emptying pressure at height min(1.2d, 0.75h) to the filling pressure at the bin bottom.
  • Here,
    • d = bin diameter
    • h = height of granular material
  • This reduction accounts for the bin bottom's influence on pressure distribution.

Important Formula (Clause 6.1.1.2):

[ Z_P = T D W R \left[z - z_u \left(1 - e^{-2/2}\right)\right] ]

• Where variables correspond to load parameters (refer IS 4995 for definitions).

Load Variation Diagram (Fig. 3 Concept):

graph LR
A[Filling Pressure at Bin Bottom] -->|Linearly increases| B[Pressure at height h or 1.2d]
B -->|Emptying Pressure| C[Bin Top]

Units Correction (Clause 6.2.3 Note):

• Velocity v is expressed in m/h (meters per hour).

Summary:

• Use linear pressure reduction from filling to emptying pressure near bin bottom (up to height = min(1.2d, 0.75h)).
• Apply updated formula for load calculation (Clause 6.1.1.2).
• Refer to Fig. 3 for pressure variation visualization.
• Ensure velocity units are consistent (m/h).

This approach ensures safe and economical bin design by accounting for load reductions during emptying.

IS 4995 Part 1: Design Considerations for Structural Adequacy of Reinforced Concrete Bins

Key Design Aspects (Clause 6.2.1 & Tables 1, 2)

• Design Pressure for Normal Filling/Emptying:

  [ p = k \cdot \gamma \cdot h ]

  Where:

  • ( p ) = lateral pressure at depth ( h )
  • ( k ) = lateral pressure coefficient (from Table 1)
  • ( \gamma ) = bulk density of stored material (kN/m³)
  • ( h ) = depth of material (m)

• Tables 1 & 2 provide:

  • Table 1: Values of lateral pressure coefficients ( k ) for different materials and flow conditions.
  • Table 2: Design parameters including bulk density, angle of repose, and friction angles for granular and powdery materials.

Additional Specifications:

• Consider hydrostatic and dynamic pressures during filling/emptying.
• Use partial safety factors as per IS 456 for concrete and steel.
• Account for pressure variations due to bin shape and outlet conditions.

Summary Table (Example):

graph LR
A[Stored Material Depth (h)] --> B[Calculate Lateral Pressure p = k * γ * h]
B --> C[Design Reinforced Concrete Walls]
C --> D[Check Structural Adequacy]

For detailed values, refer to Tables 1 & 2 in IS 4995 Part 1.

IS 4995 Part 1 — Supplementary Data & Tables Summary

1. Key Formula (Clause 6.1.1.2)

[ Z_P = TDWR \left[ 1 - e^{-\frac{Z}{Z_0}} \left( 1 - \frac{Z}{Z_0} \right) \right] ]

• Z = depth or height coordinate
• Z₀ = reference height
• TDWR = total design wall pressure

2. Table: Values of (1 - e^{-Z/Z_0}) for Different (Z/Z_0) (Clause 6.1.1.3)

(Refer to the full table in Clause 6.1.1.3 for intermediate values.)

3. Design Parameters - Angle of Wall Friction ( \delta ) & Pressure Ratio ( A ) (Table 2, Clause 5.3.2)