Criteria for Design of Steel Bins for Storage of Bulk Materials, Part 3: Bins Designed for Mass Flow and Funnel Flow

IS 9178 Part 3 - Introduction and Scope: Key Formulas and Tables

This part covers load distribution in bulk material storage bins (mass flow and funnel flow), with detailed procedures in Appendices F and G.

Key Definitions (Clause 3.1)

Load Calculation Procedure (Appendix F - Mass Flow Bins)

1. Define geometry & flow properties (d, h, w, friction angles).
2. Calculate h/d ratio.
3. Calculate max wall pressure ( P_h ) and friction stress ( t_w ) using Fig. 6 and Eq. (3).
4. Calculate vertical force ( P_v ) and circumferential force using Fig. 7 and Eq. (8).
5. Calculate radius of curvature ( R ) (Eq. 2).
6. Determine average vertical pressure ( Q_c/A ) at transition (Fig. 5).
7. Calculate initial hopper pressure (Eqs. 5,6,7).
8. Calculate radial pressure ( P_{atr} ) (Eq. 9, Fig. 9/10).
9. Calculate peak pressure ( P_{nt} ) (Eq. 10, Fig. 11/12).
10. Calculate slant height (0.3 d) for overpressure.

Load Calculation Procedure (Appendix G - Funnel Flow Bins)

1. Define geometry & flow properties.
2. Calculate max wall pressure ( P_h ) and friction stress ( t_h ) using Fig. 14 and Eq. (3).
3. Calculate normal ( P_n ) and shear stresses ( t_h ) on hopper wall (Eqs. 14 or 15).
4. Calculate vertical force ( P_v ) and circumferential force (Fig. 7 and Eq. 13).

IS 9178 Part 3: General Requirements & Assessment of Loads for Bulk Storage Bins

Key Formulas & Procedures

Mass Flow Bins (Appendix F, Clause 12.3)

1. Define bin geometry & material flow properties: diameter (d), height (h), flow properties (m, u, 8h, etc.)
2. Calculate h/d ratio.
3. Calculate:
   • Maximum cylinder wall pressure, ( P_h ), using Fig. 6 for ((P_h/wd)_{max})
   • Friction stress, ( \tau_w ), via Eq. (3)
4. Calculate vertical force ( P_v ) and circumferential force using Fig. 7 and Eq. (8).
5. Calculate radius of curvature ( R ) (Eq. 2).
6. Average vertical pressure at transition ( Q_c/A ) (Fig. 5).
7. Initial hopper pressure (Eqs. 5, 6, 7).
8. Radial pressure component ( P_{atr} ) (Eq. 9, Figs. 9 or 10).
9. Peak pressure at transition ( P_{nt} ) (Eq. 10, Figs. 11 or 12).
10. Slant height for overpressure ≈ 0.3d.

Funnel Flow Bins (Appendix G, Clause 13.4)

1. Define bin geometry and flow properties.
2. Calculate max cylinder wall pressure ( P_h ) and friction stress ( \tau_w ) (Fig. 14, Eq. 3).
3. Calculate normal stress ( P_n ) and shear stress ( \tau_h ) on hopper walls (Eqs. 14 or 15).
4. Calculate max vertical force ( P_v ) and circumferential force (Fig. 7, Eq. 13).

Important Specifications

• Use Appendix E for a recommended calculation sheet (Clause 10.6).
• Material principal stresses < 70 kg/m² for small outlets (<1 m) (Clause 5.2).
• SI units are standard: Pressure in Pascal (Pa = N/m²), Force in Newton (N).

Summary Table: Key Parameters

IS 9178 Part 3: Definitions and Terminology - Key Formulas & Specifications

Key Notations (Clause 3.1)

Important Parameters

• Flow function (FF): Characterizes flowability of bulk solid.
• Pressure terms: Initial, peak, radial pressures on hopper/cylinder walls.
• Forces: Vertical force in cylinder walls, major consolidating force, shearing force.

Design Procedure Highlights (Appendix F & G)

1. Define geometry & material properties: d, h, θ, m, ρ, τw, τh, φ.
2. Calculate dimensionless ratios: h/d, etc.
3. Cylinder wall pressure (P_h) and friction stress (τ_w): [ \tau_w = \mu_w P_h ] where (\mu_w) = coefficient of friction between bulk and wall.
4. Vertical force in walls and pressure at transition from graphs (Figs. 5-12).
5. Radial and peak pressures on hopper walls using: [ P_{tr} = f(\theta, \phi, \delta, \

IS 9178 Part 3: Design Criteria for Funnel or Plug Flow Bins

Key Design Parameters & Formulas (from Clauses 7.8.4, 10.6, Appendix D & E)

1. Bulk Material Properties

• Average Bulk Density, ( w )
• Lump Size, ( d_{max} )
• Shear Cell Area, ( A_g )
• Flow Function, ( f_f ) (from Fig. C-9 & C-10, Appendix C)

2. Hopper Slope Angle, ( \theta )

• Calculated using flow factor ( f ) from bulk material properties.
• Use recommended slope angle ( \theta ) or ( f_p ) (Fig. C-10).
• Typical design: hopper slope ( \theta \geq f_f ) to ensure flow.

3. Outlet Dimensions

• Minor dimension (e.g., width ( b_o )):
  [ b_o \geq 6 \times d_{max} ]

• Major dimension (e.g., diameter ( d_o ) for circular outlets):
  [ d_o = A_g \times W ] where ( A_g ) = shear cell area, ( W ) = width factor.

• For rectangular outlets:
  [ b_o = \frac{A_s}{W}, \quad l_o = \text{major dimension} ]

• Adopted outlet size must prevent arching/blockage.

4. Recommended Calculation Sheet (Appendix D & E)

• Includes:
  • Material & flow properties input
  • Estimation of hopper slope angle ( \theta )
  • Determination of outlet size based on flow function and shear cell data
  • Check for interaction of flow function ( f_f ) with bulk material flow function (FF)

Summary Table for Outlet Design

IS 9178 Part 3: Design Procedures for Mass Flow Bins

Key Design Steps (Appendix D, Clause 7.8.4)

1. Bulk Material Properties:

   • Average Bulk Density, w (kg/m³)
   • Lump Size (max dimension)
   • Flow Properties: Shear Cell Area, Ag

2. Hopper Wall:

   • Material and surface finish (affects friction)

3. Flow Properties:

   • Flow factor, f_f (from shear tests, Fig. C-13)
   • Hopper slope angle, θ (recommended to stay 5° within boundaries, Fig. A-8)

4. Outlet Dimensions:

   • Major dimension (circular diameter or square side), d₀ or b₀
   • Minor dimension ≥ 6 × maximum lump size
   • Calculated using:

   [ b_0 = A_g \times w ]

   where ( A_g ) = shear cell area, ( w ) = bulk density

   • For rectangular outlets, minor and major sides are calculated separately.
   • Hopper slope angle ( \theta ) should be ≥ flow function angle ( f_f ) for mass flow.

Recommended Hopper Slope and Outlet Size (Summary)

Design Formulae:

• Outlet cross-section area:

  [ A_o = A_g \times w ]

• Minimum outlet dimension:

  [ b_0 \

Flow Properties of Stored Bulk Solids (IS 9178 Part 3)

The flow properties critically influence bin design, especially outlet size, hopper slope, and wall load. They must be determined under actual storage conditions considering:

• Particle size & shape
• Bulk density & consolidation
• Moisture content
• Temperature
• Surface finish of bin walls
• Storage duration

Key Parameters and Their Role

Typical Flow Property Determinations (Clause 10.2 & 7.3)

• Angle of Repose (α): Indicates flowability; lower angle = better flow.
• Wall Friction Angle (δ): Between bulk solid and bin wall; used for hopper slope design.
• Internal Friction Angle (φ): Governs shear strength and arching potential.
• Bulk Density (γ): Used for load calculations.

Hopper Slope Design Guideline

• Hopper half-angle (θ) ≥ wall friction angle (δ) + safety margin.
• For mass flow bins, ensure θ is steep enough to avoid stagnant zones.

Simplified Formula for Minimum Hopper Half-Angle (θ):

[ \theta \geq \delta + 5^\circ ]

where δ = wall friction angle between bulk solid and bin wall.

Summary Diagram of Flow Factors

graph TD
    A[Flow Properties] --> B[Particle Size & Shape]
    A --> C[Bulk Density & Consolidation]
    A --> D[Moisture Content]
    A --> E[Temperature]
    A --> F[Surface Finish]
    A --> G[Storage Period]

Note: Actual values for angles and densities must be measured in lab or field tests simulating bin conditions per Clauses 7.3 & 10.2. These parameters guide outlet sizing, hopper design, and structural load calculations.

IS 9178 Part 3: Testing & Evaluation of Bulk Material Flow Properties

Key Points from Clauses 7.3 & 10.2

• Test Method: Use a shear tester (flow factor tester) to determine flow properties.
• Sample Conditions: Material sample must represent actual storage conditions (size, moisture, temperature, age).
• Parameters to Obtain:
  • Major Consolidating Force, V
  • Flow Function, FF
  • Distribution curves of flow properties under various consolidation stresses
  • Wall Yield Loci (WYL) — from Clause 7.3.1

Important Formulas

• Flow Function (FF):
  [ FF = \frac{\sigma_1}{\sigma_c} ] where
  (\sigma_1) = major principal consolidation stress
  (\sigma_c) = unconfined yield strength (shear stress at zero normal stress)

• Wall Yield Loci (WYL):
  Defines the shear stress at the wall interface, critical for hopper design.

Summary Table (from Appendix C)

Practical Notes

• Perform tests at multiple consolidation stresses to plot flow function curve.
• Use results to classify bulk materials as free-flowing, cohesive, or very cohesive.
• Critical for silo/hopper design to avoid flow obstructions or arching.

flowchart LR
    A[Bulk Material Sample] --> B[Shear Tester]
    B --> C[Measure Major Consolidation Stress (V)]
    B --> D[Measure Unconfined Yield Strength (\sigma_c)]
    B --> E[Determine Wall Yield Loci (WYL)]
    C & D --> F[Calculate Flow Function (FF)]
    F --> G[Plot Flow Function Curve]
    E --> H[Assess Wall Shear for Hopper Design]
``

Load Distribution on Bin Walls (IS 9178 Part 3)

Key Points from IS 9178 Part 3:

• Initial and Flow Pressures (Clause 11.1):

  • Initial load when filling (discharge closed) causes vertical "peaked" pressure distribution.
  • Cylindrical part pressure: Janssen's method applies.
  • Hopper pressure: Linear variation assumed.
  • Consider impact and wear if materials drop from height or charged at high rate.

• Janssen’s Formula for Vertical Pressure, ( p_v ):
  [ p_v = \frac{\gamma \cdot K \cdot R}{4 \mu} \left(1 - e^{-\frac{4 \mu z}{D}}\right) ] where:

  • ( \gamma ) = bulk density
  • ( K ) = lateral pressure coefficient
  • ( \mu ) = wall friction coefficient
  • ( R ) = radius of bin
  • ( D ) = diameter ( (D = 2R) )
  • ( z ) = depth of material

• Load Distribution Characteristics (Clause 4.1.2):

  • Governs structural design and feeder selection.
  • Load varies between initial fill and flow stages.

• Design for Mass Flow (Clause 11.4 & Section 12):

  • Load distribution procedure applies to both mass and funnel flow bins.
  • Appendix E provides a recommended calculation sheet for funnel flow bin design.

Summary Table: Load Distribution

flowchart TD
    A[Bulk Material Filling] --> B[Initial Stage: Peaked Vertical Pressure]
    B --> C[Janssen's Pressure in Cylinder]
   

IS 9178 Part 3: Load Distribution in Mass Flow Bins

Key References:

• Clause 11.4: Load distribution procedure applies to both mass and funnel flow bins.
• Clause 12.3: Refer to Appendix F for detailed calculation steps for mass flow bins.
• Clause 4.1.2: Load distribution governs wall and outlet loads, critical for structural and feeder design.

Calculation Procedure (Summary from Appendix F & Section 12):

1. Determine Initial Pressure:

   • Based on bulk density (γ) and material height (H).
   • Initial vertical pressure, ( P_v = \gamma \times H ).

2. Flow Pressure Distribution:

   • Pressure decreases from top to outlet due to flow.
   • Use Janssen’s equation or code-specific relations for wall pressure ( P_w ).

3. Wall Load Calculation:

   • Horizontal pressure, ( P_h = K \times P_v ), where ( K ) is lateral pressure coefficient (typically 0.4 to 0.6 for mass flow).

4. Load on Outlet:

   • Consider flow channel shape and friction effects.

Typical Formula (Janssen’s Equation Adapted):

[ P_h = \frac{\gamma \cdot D}{4 \mu} \left(1 - e^{-\frac{4 \mu K H}{D}}\right) ]

Where:

• ( P_h ) = horizontal pressure on wall
• ( \gamma ) = bulk density
• ( D ) = bin diameter
• ( \mu ) = wall friction coefficient
• ( K ) = lateral pressure coefficient
• ( H ) = height of material

Important Tables (from Appendix F):

Summary Flow Diagram:

flowchart TD
    A[Material Height H & Bulk Density

IS 9178 Part 3: Load Distribution in Funnel Flow Bins

Key References:

• Clause 10.6 & Appendix E: Calculation sheet for funnel flow bin design.
• Clause 12.3 & Appendix F: Procedure for load distribution in mass flow bins.
• Clause 11.4: Load distribution procedure applicable to funnel flow bins.
• Clause 7.8.4 & Appendix D: Mass flow bin design (for comparison).

Load Distribution Calculation - Funnel Flow Bins

1. Load Components:

   • Vertical pressure due to bulk material weight.
   • Lateral pressure on bin walls from material.
   • Flow channel pressure in the hopper region.

2. Basic Formula for Vertical Pressure ( p_v ):

[ p_v = \gamma \cdot h ]

• (\gamma) = bulk density (kN/m³)
• (h) = height of material above section (m)

3. Lateral Pressure ( p_h ):

[ p_h = K \cdot p_v ]

• (K) = lateral pressure coefficient (depends on material and bin surface)

4. Flow Channel Load:
   • Concentrated load in hopper outlet region.
   • Requires hopper slope and outlet dimension consideration (Appendix E).

Typical Calculation Procedure (Appendix E):

Design Considerations:

• Outlet size and hopper slope critical for flow channel load.
• Use Appendix E for funnel flow bin design sheets.
• Load distribution varies from mass flow bins (Appendix F).

flowchart TD
    A[Bulk Material] --> B[Vertical Pressure \(p_v = \gamma h\)]
    B --> C[Lateral Pressure \(p_h = K p_v\)]
    C --> D[Bin Walls Load]
    A --> E

Limitations of Jenike’s Theory (IS 9178 Part 3, Appendix A)

• Overdesign of Critical Outlet Widths: Jenike’s method often leads to conservative (larger) outlet sizes because it ignores sliding arches and the weight of powder above the arch (A-1).

• Arching Below Transition Zone: Arch formation just below the hopper-silo transition is not well predicted (A-2).

• Stress Deviations: Actual stresses near the transition zone deviate significantly from Jenike’s radial stress theory (A-3).

• Impact Loading Ignored: Jenike’s theory does not consider impact loads during filling, which can cause flow discontinuities and arching (A-4).

• Shear Cell Limitations: Jenike’s shear cell test is valid only for particles sized 1-6 mm and requires assumptions on slip planes, limiting accuracy (A-5, A-5.4).

• Ongoing Research: Alternative theories (Walkar, Walters, Enstad) attempt to address these limitations but remain approximate (A-6).

Key Notes for Designers:

• Use Jenike’s method as a guideline, not an absolute.
• Consider arch sliding, impact loads, and transition zone stresses.
• Refer to Appendix G for funnel-flow load calculations.
• Consult referenced literature for advanced understanding.

Typical Formula Reference (from Jenike’s shear theory):

[ W_c = K \times \sigma_c \times A ]

Where:

• (W_c) = Critical arching load
• (K) = Flow factor (from shear cell tests)
• (\sigma_c) = Cohesive strength of bulk material
• (A) = Cross-sectional area of outlet

flowchart TD
    A[Bulk Material] --> B[Shear Cell Test]
    B --> C[Flow Factor & Cohesion]
    C --> D[Jenike's Design Method]
    D --> E[Outlet Size & Wall Pressure]
    E --> F{Limitations?}
    F -->|Yes| G[Consider Arch Sliding, Impact Loads]
    F -->|No| H[Design Accepted]

References: IS 9178 Part 3 (1980), Appendix A & B.

IS 9178 Part 3: Flow Factor (ff) and Flow Function (FF) Charts

Key Points & Formulas:

• Flow Factor (ff):

  • Determined from contours for conical/plane flow channels (Fig. C-13 to C-15, Appendix C).
  • Corresponds to average internal friction angle (φ) and wall friction angle (δ).
  • Minimum value: ff ≥ 1.7 (Clause 10.3.1).
  • Plot of V (velocity) vs D (dimension), with D on ordinate.

• Flow Function (FF):

  • Plot of V (velocity) vs F (flow function value), with F on ordinate.
  • Represents bulk solid flow characteristics.

• Intersection Principle (Clauses 7.5.1 & 10.4.1):

  • Plot ff (V vs D) and FF (V vs F) on same scale.
  • Intersection point (V, V) gives design velocity and flow parameters.

Summary Table:

graph LR
A[Determine φ & δ] --> B[Estimate ff from contours (Fig. C-9, C-13 to C-15)]
B --> C[Plot ff: V vs D]
D[Obtain FF from bulk material] --> E[Plot FF: V vs F]
C & E --> F[Find intersection point (V, V)]
F --> G[Design velocity and flow parameters]

Use these charts to select flow velocity ensuring reliable bulk solid flow in hoppers/chutes.

IS 9178 Part 3: Recommended Calculation Sheets for Mass Flow Bin Design

Key Points from Clause 7.8.4 & Appendix D

1. Bulk Material Data

• Material & Size
• Condition
• Average Bulk Density (w)

2. Hopper Wall

• Material & Finish

3. Flow Properties of Bulk Material

• Shear Cell Area, ( A_g )
• Estimated flow function ( f_f ) at hopper wall & outlet

4. Hopper Slope Angle, ( \theta )

• Estimated from Fig. C-13 & Fig. A-8 (usually stay within ±5° boundary)
• ( \theta_c ) or ( \theta_f ) recommended for mass flow

5. Outlet Dimensions Calculation

• Use Fig. C-12 for height ( H(0%) )
• For conical (square/circular) outlet:
  • Minor dimension ( b_o = A_g \times w )
  • Circular outlet diameter ( d_o = b_o \sqrt{\pi/4} )
  • Ensure minor outlet dimension > 6 × maximum lump size
• Select lower flow factor ( f ) if intersection of flow functions occurs

Summary Table for Outlet Dimensions

Hopper Slope Angle

• Recommended slope ( \theta_c ) or ( \theta_f ) from flow function charts (Fig. C-13, A-8)
• Typical slope range: 45° to 70° depending on material flowability

Additional Notes

• Use Appendix D for mass flow bin design calculation sheet.
• For funnel flow design, refer to Appendix E (Clause 10.6).
• Ensure outlet size and hopper slope are compatible with bulk material flow properties to avoid arch

Stepwise Procedure for Load Distribution Calculations (IS 9178 Part 3)

1. Identify Flow Type

• Mass Flow or Funnel Flow bin (Clause 11.4)

2. Initial and Flow Stage Pressures (Clause 11.1 & 12.3)

• Initial load: Use Janssen's method for cylindrical section.
• Hopper: Linear pressure distribution.
• Flow stage: Pressure distribution changes; refer to Appendix F for mass flow bins.

3. Janssen’s Formula for Vertical Pressure ( p_v ) at depth ( z ):

[ p_v = \frac{\gamma \cdot K \cdot D}{4 \mu} \left(1 - e^{-\frac{4 \mu z}{D}}\right) ] Where:

• (\gamma) = bulk density
• (K) = lateral pressure coefficient
• (D) = diameter of bin
• (\mu) = wall friction coefficient
• (z) = depth from surface

4. Load Distribution in Hopper

• Linear variation of pressure from top to bottom (assumed).

5. Funnel Flow Bins

• Use minimum recoverable strain energy principle (Clause 11.1).
• Refer to Appendix A for limitations.
• Design for dynamic loads due to arch collapse.

6. Recommended Calculation Tools

• Use Appendix E for funnel flow design sheet.
• Use Appendix F for mass flow load distribution procedure.

Summary Table

flowchart TD
    A[Start] --> B{Bin Type?}
    B -->|Mass Flow| C[Use Janssen's formula + Appendix F]
    B -->|Funnel Flow| D[Use strain energy method + Appendix E]
    C --> E[Calculate initial & flow pressures]
    D --> E
    E --> F[Design bin walls

Load Distribution Calculation for Funnel Flow Bins (IS 9178 Part 3)

Key References:

• Clause 10.6 & Appendix E: Calculation sheet for funnel flow bin design.
• Clause 11.4: Procedure applies to both funnel and mass flow bins.
• Section 4 & Clause 12.3 / Appendix F: Load distribution method for mass flow bins (similar approach can be adapted).
• Section 3: Design considerations specific to funnel or plug flow.

Load Distribution Procedure Highlights:

1. Pressure Components:

   • Initial Pressure (Static Pressure): Due to the weight of the stored material.
   • Flow Pressure: Additional pressure during discharge, varies with funnel flow patterns.

2. Pressure Calculation:

   • Vertical pressure at depth ( z ): [ P_v = \gamma z ] where (\gamma) = bulk density of material.

   • Radial pressure distribution is non-uniform; funnel flow causes higher pressures near the outlet.

3. Load Distribution:

   • Funnel flow bins have flow channels with active flow and stagnant zones.
   • Load on hopper walls varies; max near outlet, decreases upward.
   • Use pressure diagrams or tabulated values from Appendix E.

4. Typical Steps (Appendix E):

   • Calculate outlet size & hopper slope.
   • Determine vertical and horizontal pressures at key points.
   • Compute resultant forces on hopper walls.
   • Check for sliding, buckling, and structural adequacy.

Example Table (Simplified from Appendix E):

• (K) = lateral pressure coefficient (depends on flow and material).

Summary:

• Use Appendix E for funnel flow bin load calculation sheet.
• Calculate vertical and horizontal pressures based on bulk density and