Criteria for Design of Steel Bins for Storage of Bulk Materials, Part 2: Design Criteria

IS 9178 Part 2: Introduction & Scope - Key Points, Formulas, and Tables

1. Scope & Purpose

• Covers design criteria for steel bins (silos and bunkers) storing bulk materials.
• Applies to both circular/polygonal (silos) and rectangular/square (bunkers) bins.
• Based on modified Janssen's theory for pressure distribution.
• Addresses flow problems like arching and piping by considering mass flow and funnel flow designs (covered in Part III).

2. Key Notations (Clause 3.1)

3. Important Table: Bending & Torsional Moments in Ring Beams (Clause 1.3)

IS 9178 Part 2 — Key Notations & Definitions (Clause 3.1 & 2.1)

Important Formulae for Ring Stiffener Moments (Clause 10.3.6.1)

For load ( P' ) on a closed rectangular ring stiffener:

[ \begin{aligned} T_A &= P' \frac{B}{2} \ T_O &= -P' \frac{L}{2} (X + Y^2) \ M_O &= 2T_A - P' \frac{L^2}{12} \ M_B &= \frac{L}{2}(X+1) P' \frac{L^2}{12} \left[ \frac{12(3X+1) - 2X}{(X+1)(X+Y^2)(X+1)} \right] \end{aligned} ]

Note: Minus sign indicates tension on the inside face.

Table 1: Coefficients for Moment Calculation ( M = A P' L^2 )

| (I_2/I_1) | Y=1

IS 9178 Part 2: Loads on Bins - Key Points

• Dead & Live Loads: As per IS 875 (1964), consider self-weight, superimposed loads, wind, seismic, etc.

• Stored Material Loads:

  • Use bulk densities from Table 2, Part I for common materials.
  • Load intensity at depth ( z ) is uniform (Clause 9.0).

• Load Calculation (Clause 4.1.1 & Part I, Clause 6):
  For a bin storing bulk material:
  [ p = \gamma \times h ] where:

  • ( p ) = pressure at depth ( h ) (kN/m²)
  • ( \gamma ) = bulk density of material (kN/m³)
  • ( h ) = depth of material (m)

• Typical Bulk Densities (from Table 2, Part I):

  Material	Bulk Density (kN/m³)
  Wheat	7.5
  Rice	7.8
  Coal	8.0
  Cement	14.0

• Load Application:

  • Uniform lateral pressure on bin walls.
  • Vertical load on bin base equals weight of stored material + bin structure.

graph TD
    A[Stored Material] -->|Bulk Density γ| B[Pressure at depth p = γ × h]
    B --> C[Uniform Lateral Load on Walls]
    A --> D[Vertical Load on Bin Base]

For detailed design, refer to IS 875 for environmental loads and IS 9178 Part 1 for material properties.

IS 9178 Part 2 - Materials and Components Key Points

Welding Consumables (Clause 5.6)

• Electrodes, filler materials, flux must conform to relevant IS standards:
  • IS 814 (Part I & II): Covered electrodes for metal arc welding (structural steel)
  • IS 1278: Filler rods and wires for gas welding
  • IS 3613: Wire-flux for submerged-arc welding
  • IS 6419: Filler rods for inert gas welding (ferritic steels)
  • IS 7280: Base wire electrodes for submerged arc welding

Other Materials (Clause 5.7)

• Materials associated with steel work must comply with applicable Indian Standards.

Permissible Stresses (Clause 6.1)

• Follow IS 800-1962 for permissible stress values in structural steel design.

Table: Bending and Torsional Moments in Supporting Ring Beams (Clause 1.3)

IS 9178 Part 2: Openings and Foundations – Key Points

Foundations (Clause 7.4 & 7.4.4)

• Design Standards: Foundations must comply with:

  • IS 456-1978 (Plain and Reinforced Concrete)
  • IS 1080-1962 (Foundations for tanks)
  • IS 2911 (Part 1)-1964 (Pile Foundations)
  • IS 2950 (Part 1)-1973 (Design of foundations for tanks)

• Design Considerations:

  • Ensure soil bearing capacity is adequate.
  • Account for tank loads: dead load, live load, hydrostatic pressure.
  • Use standard footing types (spread footing, raft, or pile) based on soil and load conditions.

Openings (Clause 7.2 & 7.2.1)

• Purpose: For filling, emptying, aeration, instrumentation.
• Manual Access: Must be provided safely.
• Stress Zones: Avoid openings in critical stress zones to maintain structural integrity.

Typical Foundation Design Formula (IS 456 basics)

[ \text{Area of footing} = \frac{\text{Total Load}}{\text{Allowable Soil Bearing Pressure}} ]

[ \text{Depth of footing} \geq \text{Minimum cover + effective depth for bending} ]

Summary Table: Openings Location

flowchart LR
    A[Tank Structure] --> B[Critical Stress Zones]
    A --> C[Non-critical Zones]
    B -->|Avoid Openings| D[Structural Integrity Maintained]
    C -->|Allow Openings| E[Access & Instrumentation]

Note: Refer to IS 456 and IS 2911 for detailed footing design calculations and reinforcement requirements.

IS 9178 Part 2: Design of Silos and Bunkers - Key Formulas & Specifications

Notations (Clause 3.1)

• P1, P2, P3 = Total horizontal loads due to pressure (P_h)
• W1, W2, W3 = Total vertical loads due to pressure (P_v)
• M = Moment in stiffener
• T = Tension in stiffener
• H, H' = Bursting forces
• L, B = Stiffener dimensions
• I₁, I₂ = Moment of inertia of stiffener
• I_a, I_b = Moment of inertia of shorter and longer bin walls
• s = Spacing between stiffeners
• t = Thickness of wall plate
• r₁ = Radius of hopper section
• r₂ = Mean radius of ring beam
• Other symbols define bunker/hopper geometry and loads.

Moment at Corners for Rectangular Bunkers (Clause 9.1)

When moments of inertia of walls differ:

[ M = \frac{P a^2}{12} \left[ \frac{6 I_a + 3 I_b}{b I_a + a I_b} \right] + \frac{P a^2}{12} \left[ \frac{2 I_b}{b I_a + a I_b} \right] ]

• (P) = horizontal wall load intensity (varies with height)
• (a), (b) = breadth and length of bin
• (I_a), (I_b) = moments of inertia of shorter and longer walls

For square bins ((a=b)):

[ M = -0.083 P a^2 ]

Typical Structural Details (Figures 11-16)

• Use main vertical ISMB stiffeners with secondary horizontal plate stiffeners.
• Support bunkers on box girders or main beams without transferring torque.
• Provide lining at hopper bottom to prevent wear/corrosion.
• Use riveted or bolted connections for stiffeners and plates.

Design Considerations

• Horizontal and vertical stiffeners spaced based on wall thickness and load.
• Thickness

Design of Skin Plates and Stiffeners (IS 9178 Part 2)

Key Points from Clauses:

• Skin Plate Design (Clause 10.2 & 10.2.1):

  • Skin plates span between stiffeners and are mainly designed for bending.
  • Shear stresses in the skin plate are usually neglected.
  • Longitudinal tension is carried by stiffeners, sometimes including a part of the plate.
  • Skin plate acts as a beam (simply supported or continuous) between stiffeners.

• Composite Width for T-type Stiffeners (Clause 10.4.2):

  • Define spacing to thickness ratio: ( \frac{s}{t} )
  • If ( \frac{s}{t} < 40 ), width for composite action = ( s )
  • If ( \frac{s}{t} \geq 40 ), width ≤ ( 40t )
  • Maximum spacing between stiffeners: ( \leq 80t )

Typical Design Steps:

1. Calculate bending moment on skin plate between stiffeners.
2. Select thickness ( t ) and spacing ( s ) such that:
   • ( s \leq 80t )
   • Composite width as per above rules.
3. Check bending stress in skin plate:
   [ f_b = \frac{M}{Z} \leq f_{allow} ] where ( M ) = bending moment, ( Z ) = section modulus of plate strip.
4. Design stiffeners to carry longitudinal tension and support skin plate.

Summary Table for Composite Width:

graph LR
A[Skin Plate] -- spans between --> B[Stiffeners]
B -- carry --> C[Longitudinal Tension]
A -- designed for --> D[Bending]
E[T-type Stiffener] -- composite width --> F{Width b}
F -- if s/t < 40 --> G[b = s]

Key Structural Design Recommendations for Silos (IS 9178 Part 2)

1. Loads on Hopper Skin Plate (Clause 10.4.3)

• Skin plate carries entire load due to vertical pressure (Pv) and horizontal pressure (Pw).
• Design for combined load + bending moment between stiffeners.
• Connections to top beams must resist these loads.

2. Notations & Forces (Clause 3.1)

3. Stiffener Design (Clause 11.3)

• Use circular and vertical stiffeners to prevent local buckling (wrinkling).
• Stiffeners carry moments (M) and tension (T) due to silo pressures.
• Spacing (s) and dimensions (L, B, t) must be chosen to ensure stability.

Essential Formulas (from typical silo design principles aligned with IS 9178):

• Circumferential tension (hoop stress):
  [ T_H = \frac{P_v \times r}{t} ]

• Longitudinal tension:
  [ T_L = \frac{P_h \times r}{2t} ]

• Moment in stiffener:
  [

IS 9178 Part 2: Minimum Thickness Requirements for Plates

• Minimum Thickness (Clause 12.1):

  • Skin plates: Minimum 6 mm (excluding corrosion allowance)
  • Stiffeners: Minimum 5 mm (excluding corrosion allowance)

• Corrosion Allowance (Clause 18.2):

  • Increase plate thickness by 1.5 to 5 mm if no lining is provided, to compensate for corrosion and wear.

• Thickness Calculation Considerations (Clause 11.3.3 & 11.2):

  • Thickness must consider stiffener effects.
  • Ensure stresses (direct and longitudinal) in the wall plate are within permissible limits per IS 800-1962.

Summary Table

Thickness Design Formula (conceptual)

[ t = \max \left( t_{min}, \frac{\sigma \times L}{f_y} \right) + \text{corrosion allowance} ]

Where:

• ( t ) = required thickness
• ( t_{min} ) = minimum thickness from code
• ( \sigma ) = calculated stress in plate
• ( L ) = relevant load length or dimension
• ( f_y ) = yield strength of steel

This ensures safe, durable plates considering loading, stiffening, and environmental effects.

Corrosion Allowance as per IS 9178 Part 2

Key Specifications (Clause 13.1 & 12.1)

• Minimum plate thickness excluding corrosion allowance:
  • Skin plate: 6 mm
  • Stiffeners: 5 mm

Important Notes

• Corrosion allowance is not considered in stress calculations (Clause 13.2).
• If no lining is provided, increase plate thickness by 1.5 to 5 mm based on exposure (Clause 18.2).

Summary formula for total plate thickness:

[ t_{total} = t_{min} + t_{corrosion} ]

Where:

• ( t_{min} ) = minimum thickness (6 mm for skin plate, 5 mm for stiffeners)
• ( t_{corrosion} ) = corrosion allowance from table above

flowchart TD
    A[Exposure Condition] -->|No Lining, Exposed| B[Corrosion Allowance = 5 mm]
    A -->|Lined Inside, Exposed| C[Corrosion Allowance = 4 mm]
    A -->|No Exposure, No Lining| D[Corrosion Allowance = 1.5 mm]
    A -->|No Exposure, Lined Inside| E[Corrosion Allowance = 0 mm]

IS 9178 Part 2: Corner Plates Key Points

• Definition (2.1.3):
  Corner plates are quadrant-shaped steel plates at bin wall junctions, ensuring smooth material flow.

• Design Considerations:

  • Plates span in two directions; if length/width < 3, design as two-way bending (Clause 10.2.2).
  • Plates mainly resist bending; shear is usually neglected (Clause 10.2.1).
  • Longitudinal tension is carried by stiffeners, possibly including plate portions.

• Material & Corrosion (13.4):
  Use special linings if stored material causes wear or chemical corrosion.

Typical Design Formulae:

• Two-way bending moment capacity:

[ M = \frac{f_y \times t^2}{k} ]

Where:

• ( f_y ) = yield strength of plate steel

• ( t ) = plate thickness

• ( k ) = factor depending on boundary conditions and aspect ratio

• Stress due to bending:

[ \sigma = \frac{6M}{t^2} ]

Design Checklist for Corner Plates:

• Thickness ( t ) per bending requirements
• Length-to-width ratio ( < 3 ) for two-way bending assumption
• Stiffener design to carry longitudinal tension
• Protective lining if corrosive materials are stored

flowchart TD
    A[Corner Plate at Bin Corner] --> B{Length/Width < 3?}
    B -- Yes --> C[Two-way Bending Design]
    B -- No --> D[One-way Bending Design]
    C --> E[Calculate bending moments]
    D --> E
    E --> F[Check shear (usually neglected)]
    F --> G[Design stiffeners for longitudinal tension]
    G --> H[Apply corrosion protection if needed]

This summarizes corner plate design per IS 9178 Part 2. For detailed thickness and stiffener sizing, refer to bending moment tables and steel design codes.

Supporting Structures as per IS 9178 Part 2

• Design Codes:

  • Columns and beams must be designed per IS 800:1962 (Structural steel code).
  • Consider forces from filled material + wind and seismic loads (Clause 1.1).

• Permissible Stresses:

  • Use stresses specified in IS 800:1962 for steel members (Clause 6:1).

• Material Standards:

  • All associated materials should conform to relevant Indian Standards (Clause 5.7).

• Insulation:

  • Bin walls must be insulated if stored material temperature > ambient (Clause 18.9).

Key Formula for Design Load on Column/Beam:

[ P_{total} = P_{material} + P_{wind} + P_{seismic} ]

Where:

• (P_{material}) = Load due to stored material
• (P_{wind}) = Wind load (as per IS 875)
• (P_{seismic}) = Seismic load (as per IS 1893)

Reference Table: Permissible Stresses (IS 800:1962 excerpt)

graph TD
A[Load from Stored Material] --> B[Supporting Beam]
C[Wind Load] --> B
D[Seismic Load] --> B
B --> E[Supporting Column]
E --> F[Foundation]

Summary: Design supporting structures considering combined loads per IS 800, use appropriate materials per IS standards, and insulate bin walls if required.

IS 9178 Part 2: Insulation and Lining Key Points

1. Insulation (Clause 18.9)

• Required when stored material temperature > ambient.
• Insulation must also function as lining.
• Commonly applied on bin walls to reduce heat loss.

2. Lining (Clause 18.1 & 18.4)

• Mild steel skin plates usually uninsulated except hopper bottom.
• Lining prevents corrosion and wear from moisture and corrosive materials.
• Mild steel lining plates:
  • Thickness: 5 mm
  • Size: manageable by one person for easy replacement.
• Lining plates are fixed over skin plates; replaced as worn.

3. Supporting Structures & Typical Details (Clauses 17.8, Figs 11-16)

• Use vertical and horizontal stiffeners (ISMB or plate stiffeners).
• Main supporting beams may be box girders or ISMB sections.
• Lining and insulation integrated with support details.
• Typical bunker and silo details shown in Fig. 15 (Sulphur bunker) and Fig. 16 (Rock phosphate silo).

Summary Table: Lining Specification

flowchart TD
    A[Stored Material Temperature > Ambient] --> B[Insulation Required]
    B --> C[Insulation Acts as Lining]
    C --> D[Mild Steel Lining Plates (5 mm thick)]
    D --> E[Fixed over Skin Plates]
    E --> F[Replaced when worn]

Note: Always refer to IS 9178 Part 2 for detailed drawings and exact stiffener/support dimensions.

IS 9178 Part 2 — Ring Beam Design (Annexure Key Points)

1. Ring Beam Load & Equilibrium (Clause 10.3.6.1)

• Load on ring per stiffener spacing:
  [ P' = \text{average pressure} \times \text{distance between stiffeners} ]
• Analyze one quadrant due to symmetry (Fig. 4B).

2. Key Formulas for Moments and Tensions

Note: Minus sign indicates tension on the inside face.

3. Moment Coefficients (Table 1)

• Moments expressed as:
  [ M = A \times P' s L^2 ]
• Coefficients (A) depend on the ratio (I_2/I_1), (Y), and (r) (see Table below excerpt):

(Refer IS 9178 Part 2 Table 1 for full values)

4. Ring Compression Force (Clause

IS 9178 Part 2 - Key Design Tables & Formulas for Supporting Ring Beams

Table 3: Bending & Torsional Moments in Supporting Ring Beams (Clause 1.3)