Criteria for Design of Steel Bins for Storage of Bulk Materials, Part 2: Design Criteria
1979 Edition

Overview & Application Scope - IS 9178 Part 2

1. Purpose and Coverage

• Details design criteria for steel storage bins including silos and bunkers.
• Applies to both circular/polygonal silos and rectangular/square bunkers.
• Utilizes a modified Janssen approach for pressure distribution.
• Addresses flow challenges such as arching and piping, with mass and funnel flow concepts elaborated in Part 3.

2. Symbols and Terminology (Clause 3.1)

3. Important Data Table: Ring Beam Bending and Torsion (Clause 1.3)

IS 9178 Part 2 - Symbols and Definitions (Clauses 3.1 & 2.1)

Formulas for Ring Stiffener Moments (Clause 10.3.6.1)

For a closed rectangular stiffener ring under load P':

[ \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: Negative sign denotes tension on the inner face.

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

Loads Acting on Steel Bins (IS 9178 Part 2)

• Dead and Live Loads: Follow IS 875 (1964) guidelines, including self-weight, imposed loads, wind, and seismic forces.

• Loads from Stored Bulk Material:

  • Utilize bulk density values from Table 2, Part I.
  • Pressure at depth z is assumed uniform.

• Load Computation (Clauses 4.1.1 & Part I, 6): [ p = \gamma \times h ] Where:

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

• Typical Bulk Densities:

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

• Load Application:

  • Walls experience uniform lateral pressure.
  • Vertical load on base accounts for material weight plus bin structure.

graph TD
    A[Bulk Material] -->|Bulk Density \( \gamma \)| B[Pressure at Depth \( p = \gamma \times h \)]
    B --> C[Uniform Lateral Pressure on Walls]
    A --> D[Vertical Load on Base]

Refer to IS 875 for environmental loads and IS 9178 Part 1 for material characteristics.

Material Specifications and Welding Consumables (IS 9178 Part 2)

• Welding Consumables (Clause 5.6):

  • Electrodes, filler wires, and fluxes must comply with relevant IS codes:
    • IS 814 (Parts I & II): Covered electrodes for metal arc welding of 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 of ferritic steels.
    • IS 7280: Base wire electrodes for submerged arc welding.

• Other Materials (Clause 5.7):

  • All materials related to steel fabrication should meet applicable Indian Standards.

• Allowable Stresses (Clause 6.1):

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

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

Openings and Foundation Requirements per IS 9178 Part 2

Foundations (Clauses 7.4 & 7.4.4)

• Must comply with:

  • IS 456-1978 (Plain and Reinforced Concrete Design)
  • IS 1080-1962 (Tank Foundation Design)
  • IS 2911 (Part 1)-1964 (Pile Foundations)
  • IS 2950 (Part 1)-1973 (Tank Foundation Design)

• Design Factors:

  • Confirm soil bearing capacity.
  • Account for loads: dead, live, hydrostatic.
  • Choose footing type (spread, raft, or pile) based on soil and load.

Openings (Clauses 7.2 & 7.2.1)

• For filling, discharging, ventilation, and instrumentation.
• Provide safe manual access.
• Avoid openings in high-stress zones to maintain structural strength.

Basic Foundation Design Formula (IS 456)

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

[ \text{Footing Depth} \geq \text{Minimum Cover} + \text{Effective Depth for Bending} ]

Locations for Openings

flowchart LR
    A[Bin Structure] --> B[Critical Stress Zones]
    A --> C[Non-critical Zones]
    B -->|Avoid openings| D[Preserved Structural Integrity]
    C -->|Allow openings| E[Instrument Access and Ventilation]

Refer to IS 456 and IS 2911 for detailed foundation design and reinforcement norms.

Design Essentials for Silos and Bunkers (IS 9178 Part 2)

Notations (Clause 3.1)

• P1, P2, P3: Horizontal pressure loads
• W1, W2, W3: Vertical pressure loads
• M: Bending moment on stiffeners
• T: Tension in stiffeners
• H, H': Bursting forces
• L, B: Dimensions of stiffeners
• I1, I2: Stiffener moments of inertia
• Ia, ID: Moments of inertia of bin walls
• s: Spacing between stiffeners
• t: Thickness of wall plates
• r1: Hopper radius
• r2: Mean radius of ring beam
• Other symbols define geometry and load conditions.

Moment Calculation at Rectangular Bin Corners (Clause 9.1)

For differing wall inertias:

[ 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) ]

Where:

• P = horizontal wall load intensity
• a, b = bin dimensions
• Ia, Ib = moments of inertia for short and long walls

For square bins (a = b):

[ M = -0.083 P a^2 ]

Structural Details

• Employ vertical ISMB stiffeners and horizontal plate stiffeners.
• Support bunkers on box girders or main beams without transmitting torsion.
• Provide wear-resistant lining at hopper base.
• Use riveted or bolted connections for stiffeners and plates.

Design Principles

• Stiffener spacing and thickness chosen based on wall thickness and applied loads.

Skin Plate and Stiffener Design Guidelines (IS 9178 Part 2)

Skin Plate Design (Clauses 10.2 & 10.2.1)

• Plates span between adjacent stiffeners and mainly resist bending.
• Shear stresses in the plate are generally disregarded.
• Longitudinal tension is primarily carried by stiffeners, potentially including portions of the skin plate.
• Plates behave structurally like beams (simply supported or continuous).

Composite Width for T-Shaped Stiffeners (Clause 10.4.2)

• Define spacing-to-thickness ratio ( s/t ).
• If ( s/t < 40 ), composite width ( b = s ).
• If ( s/t \geq 40 ), composite width limited to ( b \leq 40 t ).
• Maximum stiffener spacing restricted to ( \leq 80 t ).

Design Procedure Summary

1. Calculate bending moment on plate between stiffeners.
2. Select plate thickness (t) and spacing (s) ensuring ( s \leq 80 t ) and composite width as above.
3. Verify bending stress ( f_b = M / Z ) does not exceed allowable limit.
4. Design stiffeners to carry longitudinal tension and support skin plate.

Composite Width Summary

graph LR
A[Skin Plate] -- spans --> 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]

Structural Design Recommendations for Silos (IS 9178 Part 2)

Loads on Hopper Skin Plate (Clause 10.4.3)

• Skin plate must resist vertical pressure (Pv) and horizontal pressure (Pw).
• Design must consider combined load and bending moments between stiffeners.
• Connections to top ring beams should withstand these forces.

Notations and Parameters (Clause 3.1)

Stiffener Design (Clause 11.3)

• Employ circular and vertical stiffeners to avoid local plate buckling.
• Stiffeners must accommodate bending moments and tension from silo pressures.
• Select spacing (s) and dimensions (L, B, t) ensuring structural stability.

Essential Formulas

• 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: [formulas as per detailed design]

Minimum Thickness Guidelines for Plates (IS 9178 Part 2)

• Minimum Thickness (Clause 12.1):

  • Skin plates: at least 6 mm (excluding corrosion allowance).
  • Stiffeners: at least 5 mm (excluding corrosion allowance).

• Corrosion Allowance (Clause 18.2):

  • Add 1.5 mm to 5 mm thickness if lining is absent, to allow for corrosion and wear.

• Thickness Selection (Clauses 11.3.3 & 11.2):

  • Consider stiffener effects on effective thickness.
  • Ensure direct and longitudinal stresses comply with IS 800-1962 permissible limits.

Thickness Summary Table

Conceptual Thickness Formula

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

Where:

• ( t ): required thickness
• ( t_{min} ): minimum code thickness
• ( \sigma ): calculated stress
• ( L ): relevant load dimension
• ( f_y ): steel yield strength

This ensures durability and safety against loads and environmental effects.

Corrosion Allowance Requirements (IS 9178 Part 2)

Allowance Based on Exposure (Clauses 13.1 & 12.1)

• Minimum thickness ignoring corrosion allowance:

  • Skin plates: 6 mm
  • Stiffeners: 5 mm

• Corrosion allowance thickness is excluded from stress computations (Clause 13.2).

• If lining is absent, plate thickness must be increased by 1.5 to 5 mm depending on exposure severity (Clause 18.2).

Total Plate Thickness Calculation:

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

Where:

• ( t_{min} ): minimum plate thickness
• ( t_{corrosion} ): corrosion allowance as above

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

Corner Plate Design (IS 9178 Part 2)

• Definition (Clause 2.1.3): Quadrant-shaped steel plates located at bin corner junctions to facilitate smooth material flow.

• Design Principles:

  • When length-to-width ratio is less than 3, plates are treated as two-way bending members (Clause 10.2.2).
  • Bending resistance is primary; shear stresses typically neglected (Clause 10.2.1).
  • Longitudinal tension is carried by stiffeners, possibly including some plate area.

• Material and Corrosion Protection (Clause 13.4): Use protective linings when materials cause abrasion or chemical corrosion.

Typical Design Equations:

• Two-way bending moment capacity:

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

Where:

• ( f_y ): plate yield strength

• ( t ): plate thickness

• ( k ): factor dependent on boundary and aspect ratio

• Bending stress:

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

Design Checklist

• Plate thickness per bending requirements.
• Ensure length-to-width ratio < 3 for two-way bending assumption.
• Stiffener design to carry longitudinal tension.
• Apply corrosion protection where required.

flowchart TD
    A[Corner Plate] --> B{Length/Width < 3?}
    B -- Yes --> C[Design as Two-way Bending]
    B -- No --> D[Design as One-way Bending]
    C --> E[Calculate Bending Moments]
    D --> E
    E --> F[Shear Check (Usually Neglected)]
    F --> G[Design Stiffeners for Longitudinal Tension]
    G --> H[Add Corrosion Protection if Needed]

Supporting Framework Design (IS 9178 Part 2)

• Design Codes:

  • Structural members (columns, beams) are designed per IS 800:1962.
  • Loads include those from stored material plus wind and seismic forces (Clause 1.1).

• Allowable Stresses:

  • Follow IS 800:1962 stress limits for steel elements (Clause 6:1).

• Material Compliance:

  • All materials related to steelwork must adhere to relevant Indian Standards (Clause 5.7).

• Insulation Requirements:

  • Bins storing materials at temperatures higher than ambient must have insulated walls (Clause 18.9).

Design Load Calculation:

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

Where:

• (P_{material}): Load from stored bulk material
• (P_{wind}): Wind pressure as per IS 875
• (P_{seismic}): Earthquake forces as per IS 1893

Permissible Stress Table (Extract from IS 800:1962)

graph TD
A[Stored Material Load] --> B[Beams]
C[Wind Load] --> B
D[Seismic Load] --> B
B --> E[Columns]
E --> F[Foundations]

Ensure combined loading compliance and material standards per IS codes.

Insulation and Lining Guidelines (IS 9178 Part 2)

Insulation (Clause 18.9)

• Mandatory when stored material temperature exceeds ambient.
• Insulation should also function as an internal lining.
• Typically applied on bin walls to minimize heat loss.

Lining (Clauses 18.1 & 18.4)

• Mild steel skin plates generally uninsulated except at hopper base.
• Linings protect against corrosion and abrasion from moisture and aggressive materials.
• Mild steel lining plates typically 5 mm thick and sized for easy manual handling.
• Linings are fixed over skin plates and replaced when worn.

Supporting Structure & Details (Clause 17.8, Figs 11-16)

• Use vertical and horizontal stiffeners (ISMB or plate stiffeners).
• Main supports can be box girders or ISMB sections.
• Lining and insulation integrated with support design.
• Examples include sulphur bunkers and rock phosphate silos.

Lining Specification Table

flowchart TD
    A[High Material Temperature] --> B[Insulation Required]
    B --> C[Insulation as Lining]
    C --> D[5 mm Mild Steel Plates]
    D --> E[Fixed Over Skin Plates]
    E --> F[Replace When Damaged]

Consult IS 9178 Part 2 for detailed drawings and dimensions.

Ring Beam Design Summary (IS 9178 Part 2 Annexure)

Load and Equilibrium (Clause 10.3.6.1)

• Load per stiffener spacing: [ P' = \text{average pressure} \times \text{stiffener spacing} ]
• Analysis often conducted on one quadrant due to symmetry.

Key Moment and Tension Formulas

Negative values represent tension on inner faces.

Moment Coefficients (Table 1)

Moments expressed as:

[ M = A \times P' s L^2 ]

Coefficients depend on ratios ( I_2/I_1 ), ( Y ), and radius parameters.

(Refer full table in IS 9178 Part 2 for detailed coefficients.)

Essential Design Tables for Supporting Ring Beams (IS 9178 Part 2)

Table 3: Bending and Torsional Moments (Clause 1.3)