Criteria for Design of Reinforced Concrete Bins for Storage of Granular and Powdery Materials, Part II: Design Criteria

Scope of IS 4995 Part 2 (Design Criteria for Circular Cement Storage Bins)

This standard provides the design parameters and notation for reinforced concrete circular bins storing bulk materials like cement.

Key Notations & Parameters:

Design Considerations:

• Loads: Dead load, horizontal & vertical pressures, frictional forces.
• Thermal effects: Temperature difference causing moments (MAT).
• Reinforcement: Percentage and area of steel in walls and columns.
• Safety factors: For concrete cracking and strength.
• Thermal properties: Conductivity, surface conductance, and expansion coefficients.

Formula Examples:

• Modular ratio:
  [ m = \frac{E_s}{E_c} ]

• Percentage reinforcement:
  [ p = \frac{A_s}{A_c} \times 100 ]

• Moment due to temperature difference:
  [ M_{AT} = \text{Function of } \Delta T, E_c, t, \text{and geometry} ]

flowchart LR
    A[Stored Material] -->|Horizontal Pressure Ph| B(Bin Wall)

IS 4995 Part 2: Key Definitions & Tables

Important Notations (Clause 3.1)

• A = Horizontal cross-sectional area of stored material
• Ac = Area of columns (cm²)
• Act = Concrete area in tension per unit height of bin wall (cm²/m)
• As = Area of reinforcement in bin wall at height (cm²/m)
• Asc = Area of reinforcement in column (cm²)
• D = Internal diameter of circular bin
• Ec, Es = Modulus of elasticity of concrete and steel respectively
• h = Height of bin wall
• t = Thickness of bin wall
• Wcr = Crack width in bin wall
• Oct, Ocu = Permissible tensile and compressive strength of concrete

Crack Width Control (Clause 5.10.1 & 5.10.2.2)

• Crack width satisfactory if bar diameters chosen per formula using factor β from Table 5.

Table 5: Values of β for Maximum Permissible Crack Width (mm)

Table 4: Max Bar Diameters (mm) for No Crack Width Calculation

Notes:

• Use **geometrical reinforcement % p₀

IS 4995 Part 2: General Requirements of Working Stress Method

1. General Principles (Clause 5.1)

• Design must consider all stress conditions per mechanics and sound engineering practice.
• Monolithic construction effects on bending moments and shear forces must be accounted for.

2. Permissible Stresses in Steel Reinforcement (Clause 5.4.3, Table 2)

Notes:

• For Grade II mild steel, permissible stresses = 90% of Grade I values.
• Yield stress = 0.2% proof stress if no clear yield point.

3. Crack Width Control (Clause 5.10.2.2, Table 5)

Bar diameter selection for crack width control:

[ d \leq \frac{\Phi}{\sigma_{st}} ]

Where (\Phi) values depend on steel stress and max permissible crack width (0.1 mm or 0.2 mm).

IS 4995 Part 2 (1974) — Materials & Construction Key Points

1. Notations (Clause 3.1)

• A = Horizontal cross-sectional area of stored material
• Ac = Area of columns (cm²)
• As = Reinforcement area in bin wall (cm²/m)
• Ec, Es = Modulus of elasticity of concrete and steel
• D = Internal diameter of circular bin
• t = Thickness of bin wall
• Ph, Pp = Horizontal and vertical pressure from stored material
• Wcr = Crack width in bin wall
• Et = Thermal expansion coefficient of concrete
• T, To, Ti = Temperatures inside/outside bin, material temperature

2. Permissible Stresses in Steel Reinforcement (Clause 5.4.3, Table 2)

• Note: For mild steel Grade II (IS 432 Part I), permissible stresses = 90% of Grade I values or increase reinforcement by 10%.

3. Steel Types (Clause 4.2.2)

• Mild steel or medium tensile steel bars per IS 432 (Part I & II)
• Deformed bars per IS 1139
• Cold twisted bars per IS 1786

Summary Diagram: Reinforcement & Stress Flow

graph TD
    A[Stored Material Pressure] -->|Horizontal (Ph),

IS 4995 Part 2 — Design Criteria: Key Points

• Design Foundations as per relevant IS codes:
  • IS 456: Plain and Reinforced Concrete (latest edition recommended)
  • IS 1080: Code of Practice for Foundations in Soil
  • IS 2911 Part 1 & 3: Pile Foundations
  • IS 2950: Design of Foundations for Transmission Line Towers

Key Design Considerations:

• Loadings: Self-weight, wind, seismic, and live loads as per IS 875 & IS 1893.
• Soil Parameters: Bearing capacity, settlement criteria from site investigation.
• Safety Factors: As specified in relevant IS codes for materials and load combinations.
• Material Strengths: Use characteristic strengths per IS 456 and IS 2911.

Typical Foundation Design Formulae:

• Safe Bearing Capacity (q_safe): [ q_{safe} = \frac{q_{ult}}{FS} ] where (q_{ult}) = ultimate bearing capacity, (FS) = factor of safety (usually 3).

• Pile Capacity (Q): [ Q = Q_s + Q_b ] where (Q_s) = skin friction, (Q_b) = base resistance.

Summary Table: Design Codes for Foundations

flowchart TD
    A[Loadings] --> B[Foundation Design]
    B --> C[Soil Parameters]
    B --> D[Material Strength]
    B --> E[Safety Factors]
    C --> F[IS 1080, IS 2911]
    D --> G[IS 456]
    E --> H[Load Combinations IS 875]

Note: Always refer to the latest IS code editions for updated provisions.

IS 4995 Part 2 (1974) – General Design Considerations: Key Formulas & Specifications

Key Notations:

• A = Horizontal cross-sectional area of stored material
• Ac = Area of columns (cm²)
• Act = Concrete area in tension per unit height of bin wall (cm²/m)
• As = Area of reinforcement in bin wall at height considered (cm²/m)
• Ec, Es = Modulus of elasticity of concrete and steel
• D = Internal diameter of circular bin
• h = Height of bin wall
• t = Thickness of bin wall
• Ph = Horizontal pressure on wall due to stored material
• Po = Vertical load on unit wall area due to friction
• Wcr = Crack width in bin wall
• K, K1, K2, K3 = Coefficients for bending and torsion moments in ring girder
• Ar = Temperature difference across bin wall
• Et = Coefficient of thermal expansion of concrete

Important Design Parameters:

• Modular ratio:
  [ m = \frac{E_s}{E_c} ]
• Pressure on wall:
  Horizontal pressure ( P_h ) and vertical pressure ( P_p ) must be calculated considering material properties and bin geometry.
• Reinforcement percentage:
  [ p = \frac{A_s}{A_c} \times 100 ]
• Thermal stresses:
  Moment due to temperature difference ( M_{AT} ) must be accounted for in design.

Design Checks:

• Ensure crack width ( W_{cr} ) is within permissible limits.
• Use safety factor ( K ) for concrete cracking.
• Calculate bending moments using coefficients ( K_1, K_2 ) for ring girders.
• Account for wall friction coefficients during filling and emptying.

Summary Table (Example):

IS 4995 Part 2 - Permissible Stresses Summary

1. Permissible Stresses in Concrete (Table 1)

Note: Permissible tensile stress in bending = Permissible shear stress (inclined tension).

2. Permissible Stresses in Steel Reinforcement (Table 2)

Design of Bin Walls as per IS 4995 Part 2

1. Walls of Polygonal Bins (Clause 5.5.2)

• Consider walls as slabs spanning vertically/horizontally or two-way slabs for horizontal loads.
• For vertical loads, design as beams with combined bending + axial forces.
• Check for:
  • Vertical loads (stored material + frictional loads)
  • Horizontal loads (wind, seismic)
  • Temperature-induced bending moments
  • Restraints at top/bottom edges

2. Walls of Circular Bins (Clause 5.5.1)

• Design primarily for hoop stresses due to internal pressure from stored material.
• Use: [ \sigma_h = \frac{p \cdot r}{t} ] where:
  • ( \sigma_h ) = hoop stress
  • ( p ) = lateral pressure
  • ( r ) = radius of bin
  • ( t ) = wall thickness

3. Stability Checks (Clause 5.11)

• Case a: Bin Full
  • Consider all vertical loads (including frictional wall load)
  • Lateral loads (wind or earthquake, whichever is critical)
• Case b: Bin Empty
  • Consider vertical loads excluding stored material frictional load
  • Maximum lateral load (wind or earthquake)

Additional Notes:

• For deep beams, refer to PCA curves (ST-66, 1951).
• Always consider combined effects of bending, axial forces, temperature, and restraint.

flowchart TD
    A[Bin Walls] --> B{Type of Bin}
    B --> C[Circular Bin]
    B --> D[Polygonal Bin]
    C --> E[Design for Hoop Stress]
    D --> F[Design as Slabs/Beams]
    F --> G[Vertical Loads: Beam Action]
    F --> H[Horizontal Loads: Slab Action]
    A --> I[Stability Checks]
    I --> J[Full Bin: Vertical + Lateral Loads]
    I --> K[Empty Bin: Vertical (no friction) + Lateral Loads]

Summary: Design polygonal bin walls as beams/slabs with combined bending and axial

Design of Ring Girders and Supports (IS 4995 Part 2, Clause 5.6)

Key Formulas (Clause 5.6.2)

For a ring girder simply supported on n equidistant columns:

• Maximum negative bending moment at supports: [ M_{neg} = K_1 W_r ]

• Maximum positive bending moment at mid-span: [ M_{pos} = K_2 W_r ]

• Maximum torsional moment at angular distance (\theta) from support: [ T_{max} = K_3 W_r r ]

Where:

• (W_r) = Total load on ring girder (including self-weight)
• (r) = Mean radius of ring girder
• (K_1, K_2, K_3) = Coefficients from Table 3
• (\theta) = Angular distance from support (degrees)

Table 3: Coefficients for Ring Girder Moments

Design of Bin Bottoms and Hopper Bottoms (IS 4995 Part 2)

1. Bin Bottom Design (Clause 5.7.1 & 5.7.1.1)

• Vertical Load: As per 6.1.1.2 (a) & (b) of Part I; minimum load not less than 6.1.1.2(b).
• Level Bottom: Treat as a horizontal slab monolithically cast with supporting structure.
• Additional Loads: Include weight of conveying machinery + impact loads.

2. Ring Girder Design (Table 3)

• For circular bins, bending and torsional moments are computed using coefficients (K_1, K_2, K_3) based on the number of supports.

• (W): Total vertical load on the ring girder.

3. Hopper Bottoms (Clause 5.7.2 & 5.7.2.4)

• Design for loads in Clauses 5.3.0 and 5.7.2.1.
• For non-standard shapes (sloping sides, special emptying), use mechanics principles and sound engineering judgment.

Summary Diagram: Load Path in Bin Bottom

graph TD
    Load[Vertical Load W]
    Conveying[Conveying Machinery Load + Impact]
    BinBottom

Temperature Effects and Thermal Stresses (IS 4995 Part 2)

Key Formula for Bending Moment due to Temperature Change (Clause 5.8.2):

[ M_{AT} = E_t \Delta T E_c I ]

• (E_t = 11 \times 10^{-8} , / ^\circ C ) (Coefficient of thermal expansion of concrete)
• (\Delta T) = Temperature difference (°C)
• (E_c = 18000 \sqrt{f_{cu}} , \text{kg/cm}^2) (Modulus of elasticity of concrete)
• (I) = Moment of inertia of bin wall section

Assumptions for Thermal Stresses (Clause 5.8):

• Tensile strength of concrete is neglected.
• Temperature variation is radial or horizontal only.
• Effects of wind and elevation differences are neglected.

Calculating Thermal Stresses:

• Compute bending moment (M_{AT}).
• Apply mechanics of materials principles to find stresses in concrete and steel.
• Add required reinforcement for thermal stresses to the bin walls.

Crack Width Control (Clause 5.10.2.2 & Table 5):

Summary:

• Use (M_{AT} = E_t \Delta T E_c I) to find bending moments from temperature changes.
• Neglect concrete tension; consider only radial/horizontal temperature gradients.
• Calculate thermal stresses in steel and concrete from (M_{AT}).
• Use Table 5 to select bar diameters to control crack widths.

flowchart

Effects of Shrinkage (IS 4995 Part 2 - Clauses 5.9 & related)

Key Points:

• Shrinkage effect in concrete is equivalent to a temperature drop of 15℃ for structures with >0.5% reinforcement.
• Shrinkage stresses are significant near edges with restraint; elsewhere, they can be ignored.
• Additional vertical reinforcement is required near edges to resist shrinkage stresses.

Simplified Crack Width Check (Clauses 5.10.1 & 5.10.2.2)

• Crack width control depends on bar diameter, steel stress, and bar type.
• For reinforcement percentage ( p_0 \leq 0.4% ) and bar diameters below limits (Table 4), crack width checks may be waived.

Important Tables:

Table 4: Max Bar Diameters (mm) for No Crack Width Calculation

Table 5: Values of (\beta) for Crack Width Formula

Crack Width Formula (Clause 5.10.2.2)

[ d \leq \frac{\beta}{\sigma_{os}} ]

• (d) = Bar diameter (mm)
• (\beta) = Value from Table 5

IS 4995 Part 2: Crack Width Control Key Points

1. Simplified Crack Width Check (Clause 5.10.2)

• Applicable if:
  • Geometrical reinforcement % ( p_0 \leq 0.4% ) (Clause 5.10.1)
  • Bar diameters ≤ max values in Table 4

2. Table 4: Max Bar Diameters (mm) for No Crack Width Calculation

3. For Other Cases (Clause 5.10.2.2)

• Bar diameter (d) chosen by:

[ d \leq \frac{\phi}{\beta} ]

where (\beta) values are from Table 5.

4. Table 5: Values of (\beta) for Crack Width Control

Summary:

• Use **Table 4

IS 4995 Part 2 - Stability Checks (Clause 5.11)

Stability Check Loading Cases:

• Case a) Bin Full:

  • Consider all vertical loads including frictional wall load.
  • Include lateral loads due to wind or earthquake (whichever governs).

• Case b) Bin Empty:

  • Consider vertical loads excluding stored material frictional load.
  • Include maximum lateral load due to wind or earthquake.

Key Parameters & Notations (Clause 3.1):

Stability Check Formula (Typical):

[ \text{Factor of Safety (FS)} = \frac{\text{Resisting Moment or Force}}{\text{Applied Moment or Force}} \geq 1.5 \quad \text{(typical minimum)} ]

• Calculate overturning moments due to lateral loads.
• Calculate resisting moments from self-weight and vertical loads.
• Check sliding using frictional resistance between bin base and foundation.

Crack Width Control (Clause 5.10.2.2):

Bar diameter ( \phi ) selection formula:

[ \phi = \frac{K}{\sigma_{sa}} ]

Where ( \sigma_{sa} ) = steel stress from Table 5, based on max permissible crack width (0.1 mm or 0.2 mm).

Tables Summary:

Table 5: Steel Stress ( \sigma_{sa} ) (kg/cm²) for permissible crack widths

IS 4995 Part 2 (1974) — Minimum Requirements Summary

Key Notations (Clause 3.1)

• A = Horizontal cross-sectional area of stored material
• Ac = Area of columns (cm²)
• As = Reinforcement area in bin wall (cm²/m)
• Asc = Reinforcement area in column (cm²)
• D = Internal diameter of circular bin
• h = Height of bin wall
• t = Thickness of bin wall
• Ec, Es = Modulus of elasticity of concrete and steel
• p₀ = Geometric percentage of tensile reinforcement in bin wall
• Wcr = Crack width in bin wall
• σ_oc, σ_cu = Permissible tensile and compressive strength of concrete

Crack Width Control (Clause 5.10.1 & Table 5.10.2)

• Crack width checks can be simplified if:
  • Geometric reinforcement percentage p₀ ≤ 0.4%
  • Bar diameters ≤ values in Table 4 (below)

Important Formulae

• Modular ratio:
  [ m = \frac{E_s}{E_c} ]

• Geometric reinforcement percentage:
  [ p_0 = \frac{A_s}{A_{ct}} \times 100 ]

• Crack width control:
  Use the above table to decide if detailed crack width calculations are necessary based on bar size and