Code of practice for concrete structures for the storage of liquids, Part 4: Design tables

IS 3370 Part 4 - Scope & Key Design Tables Summary

• Scope:
  Covers design tables for rectangular and cylindrical tanks, enabling design under various loading and support conditions (Clause 3.1). Applicable for tanks built in or on the ground.

• Key Formulas:

  1. Moments in Cylindrical Wall (Fixed Base, Free Top) under Rectangular Load:
     [ M = \text{Coefficient} \times p H^3 \quad \text{(kg·m/m)} ]
     Where:

     • (p) = pressure
     • (H) = height of wall
     • Coefficients from Table 18 based on (H_3/D_i) ratio and location.

  2. Moments in Cylindrical Wall (Fixed Base, Free Top) with Shear (V) at Top:
     [ M = \text{Coefficient} \times V H \quad \text{(kg·m/m)} ]
     Where:

     • (V) = shear per meter
     • (H) = height
     • Coefficients from Table 19 based on (H_2) and point location.

• Tables Provided:

  Table No.	Description	Notes
  18	Moments in cylindrical wall under rectangular load	Coefficients for moment calculation
  19	Moments in cylindrical wall under shear at top	Coefficients for shear-induced moments
  5, 6	Moment coefficients for rectangular tanks (top/bottom edges)	For single-cell tanks, various ratios b/a and c/a

• Notes:

  • Positive moment coefficients indicate tension on the outside face.
  • Use proper combination of tables for complex tank shapes and loadings.

flowchart LR
    A[Tank Type] --> B{Rectangular or Cylindrical?}
    B -->|Rectangular| C[Use Tables 5 & 6]
    B -->|Cylindrical| D[Use Tables 18 & 19]
    D --> E[Calculate Moments: M = Coeff × pH³ or M =

Moment Coefficients for Rectangular Tanks (IS 3370 Part 4, Clause 2.2 & 2.2.1.1)

• For rectangular tanks, moment coefficients for individual panels (with fixed edges) must be adjusted for continuity at common edges, similar to moment distribution in frames.
• The final end moments are the sum of fixed end moments (from Tables 1-3) plus induced moments due to edge rotation.
• Tables 5 & 6 provide moment coefficients for various aspect ratios ( \frac{b}{c} ) (b = larger horizontal dimension, c = smaller) and edge conditions (e.g., free top, hinged bottom).

Key Parameters:

• ( a ) = wall height
• ( b ) = wall width (larger horizontal dimension)
• ( c ) = smaller horizontal dimension
• ( w ) = liquid density

Moment Formulas:

• Horizontal moment:
  [ M_y = \text{My coefficient} \times w a^3 ]
• Vertical moment:
  [ M_x = \text{Mx coefficient} \times w a ]

Typical Moment Coefficients (from Table 5 for walls free at top and hinged at bottom):

Note: Values vary with ( \frac{c}{a} ) and tank geometry; refer to full tables for design.

Summary:

• Use Tables 5 & 6 for moment coefficients based on tank dimensions and edge conditions.
• Apply moment distribution to adjust fixed end moments for continuous rectangular tanks.
• Calculate moments by multiplying coefficients with ( w

Design Data for Cylindrical Tanks (IS 3370 Part 4)

Key Points:

• The code provides design tables for cylindrical tanks considering various boundary conditions.
• Base conditions: Fixed base vs. hinged base affect moments and shear forces significantly.
• For safer design, hinged base assumption is often recommended due to possible subgrade settlements (Clause 3.1.2).

Important Tables (IS 3370 Part 4):

Typical Load & Moment Considerations:

• Triangular liquid pressure distribution on wall height.
• Wall subjected to ring tension (circumferential stress) and bending moments.
• Shear at base depends on wall fixity and load type.

Basic formula for hoop (ring) tension, ( T ):

[ T = p \times r ] Where:

• ( p ) = liquid pressure at depth
• ( r ) = radius of cylindrical tank

Moment at base (hinged base assumption):

[ M = \frac{p \times h^2}{6} ] Where:

• ( h ) = height of liquid

Shear force at base:

[ V = \frac{p \times h}{2} ]

Diagram: Cylindrical Tank Wall with Hinged Base Under Triangular Load

graph TD
  A[Top of Wall] -->|Free| B[Wall]
  B -->|Triangular liquid pressure| C[Base (Hinged)]
  C -->|Shear V, Moment M, Ring Tension T| D[Foundation]

Summary:

• Use Tables 11-13 for shear, tension, and moment values.
• Prefer hinged base assumption for safer design.
• Apply triangular pressure distribution for liquid load.
• Calculate hoop tension, moment, and shear using above formulas and verify with tables.

For detailed values and coefficients, refer directly to IS 3370 Part 4 Tables 11-13.

Shear at Edges and Base of Tank Walls
As per IS 3370 (Part 4), 1967

Key Formula:

[ \text{Shear per unit length} = \text{Coefficient} \times w \times a^2 ]

• (w) = density of liquid (kN/m³)
• (a) = width of the wall panel (m)
• Coefficients depend on position along edges and boundary conditions.

Shear Coefficients (Selected from Table 7):

Note: Negative shear at corners indicates reaction opposite to load direction; often neglected for bond stress checks.

Important Notes:

• Shear at vertical edges causes axial tension in adjacent walls; combine with bending moments for tensile reinforcement design.
• Coefficients apply even if vertical edges are not fully fixed (Clause 2.3.6).
• Shear varies with (\lambda = \frac{\text{height}}{\text{width}}) of the wall panel.
• For cylindrical

IS 3370 Part 4: Ring Tension & Moments in Circular Walls

Key Formulas:

• Ring Tension with Shear at Top (Clause 3.1.4):

[ T = - k \times H \times V \times R ]

Where:

• (T) = Ring tension at height (H)
• (k) = Coefficient from Table 15 (depends on (H/R) ratio)
• (V) = Shear force at top
• (R) = Radius of cylindrical wall
• (H) = Height from base

Important Tables:

Notes:

• When the top is fixed (dowelled), ring tension at top = 0 (cannot expand).
• Use Table 15 coefficients to find shear distribution along height.
• Moments and stresses should be checked using Tables 18 & 19 for walls, and 20-23 for slabs.

flowchart LR
    A[Shear V at Top] --> B[Use Table 15 for k]
    B --> C[Calculate Ring Tension T = -k * H * V * R]
    C --> D[Check Moments from Table 18 or 19]
    D --> E[Design Reinforcement]

This approach ensures correct tension and moment evaluation in circular walls per IS 3370 Part 4.

IS 3370 Part 4: Adjustment of Moments for Continuous Walls

Key Points from Clause 3.1.6:

• When the roof slab and wall top are continuous, the roof deflection induces a moment at the top of the wall.
• Tables 16 & 17 (not fully provided here) give moments for one-end moment application with the other end free, hinged, or fixed.
• These tables can be used to estimate moments in continuous walls with reasonable accuracy.

Moment Calculation (Clause 2.1.2):

• Wall dimensions:

  • a = height of wall
  • b = width of wall
  • w = density of liquid

• Moments due to liquid pressure:

  • Horizontal moment: ( M_y = w a b^2 )
  • Vertical moment: ( M_x = w a^2 b )

Moment Coefficients Table (Excerpt):

Mg and My are moment coefficients for moments about x and y axes respectively.

Moment Adjustment for Continuous Walls:

• Use moment coefficients from Tables 1-3 (edge conditions) to find moments at wall ends.
• Apply moment factors from Tables 16 & 17 for the effect of roof slab continuity.
• Adjust moments by multiplying with these factors to account for rotation and restraint at the top.

Summary Formula:

[ M_{\text{adjusted}} = M_{\text

IS 3370 Part 4: Design Tables for Wall Panels with Various Edge Conditions

Key Moment Coefficients (Clause 2.1)

• Moment coefficients assume wall panels as thin plates fixed on vertical edges.
• Tables 1 to 3 provide moments for:
  • Table 1: Top hinged, bottom hinged
  • Table 2: Top free, bottom hinged
  • Table 3: Top free, bottom fixed

Shear at Edges for Panels Free at Top & Hinged at Bottom (Clause 2.3.6)

Note: Negative shear indicates reaction in direction of load.

Shear at Edges for Panels Hinged at Top and Bottom (Clause 2.3.4.1)

IS 3370 Part 4: Design Tables for Slabs Subjected to Uniform Loads

Key Points from IS 3370 Part 4:

• Clause 2.1.2:

  • Moment coefficients for uniformly loaded rectangular plates hinged on all four sides are provided in Table 4.
  • Useful for cover and bottom slabs of rectangular tanks with a single cell.
  • For continuous slabs over intermediate supports, refer to Appendix C of IS 456-1964 for design procedure.

• Clause 3.2:

  • Moments in circular slabs under various edge conditions and loads are tabulated in Tables 20 to 23.

Typical Moment Coefficients for Rectangular Slabs (from Table 4):

• Mx, My = Moments per unit width = ( \alpha \times w \times a^2 )
  where:
  • ( \alpha ) = Moment coefficient from table
  • ( w ) = Uniform load (kN/m²)
  • ( a ) = Shorter span (m)

Design Formula for Moments in Rectangular Slabs:

[ M_x = \alpha_x \times w \times a^2 ] [ M_y = \alpha_y \times w \times a^2 ]

Notes:

• Use hinged boundary conditions for conservative design unless continuity is provided.
• For continuous slabs, moments reduce and require IS 456 methods.
• Circular slab moments depend on edge restraint; consult Tables 20-23 for detailed coefficients.

flowchart LR
    A[Uniform Load (w)] --> B[Rectangular Slab (a x b)]
    B --> C{Boundary Condition}
    C -->|Hinged Sides| D[Use Table 4 Moment Coefficients]
    C -->|Continuous| E[Use IS 456 Appendix C]

IS 3370 Part 4: Effects of Hydrostatic Pressure Distributions

Key Formulas & Tables:

1. Tension in Circular Ring Wall (Fixed Base, Free Top, Triangular Load)
   [ T = \text{Coefficient} \times w H R \quad (\text{kg/m}) ]

   • w: Density of liquid
   • H: Liquid height
   • R: Radius of ring
   • Coefficients from Table 9 vary with height ratio ( H_2/D_i ) and position along the wall.

2. Moments in Cylindrical Wall (Fixed Base, Free Top, Triangular Load)
   [ M = \text{Coefficient} \times w H^3 \quad (\text{kgm/m}) ]

   • Coefficients from Table 10 depend on height ratio ( H_3/D_i ) and position.

3. Shear at Base of Cylindrical Wall (Hinged Base, Free Top, Trapezoidal Load)

   • Use coefficients from Table 11 for shear force calculations.
   • Applicable when load is a combination of uniform + triangular (trapezoidal distribution).

Notes on Load Distribution:

• Triangular load approximates hydrostatic pressure increasing linearly with depth.
• Trapezoidal load occurs with additional uniform pressure (e.g., vapour pressure or earth pressure).
• For underground tanks, consider both internal and external pressures; external may be trapezoidal or earth pressure distributions.
• Approximate trapezoidal load by equivalent triangular load with same area and mid-depth intensity for simplicity.

Practical Use:

• Select coefficients based on ( H/D_i ) ratio and wall height fraction.
• Calculate tension, moment, and shear using the respective coefficients.
• Combine effects for trapezoidal loads by superposition (triangular + uniform).

Summary Table Snippet (Tension Coefficients Example):

| (H_2/D_i) | 0.0H | 0.1H | 0.2H | 0.3H | 0.4H | 0.5H | 0.6H | 0.7H | 0.8H | 0.9H | |-------------|-------|-------|-------|

IS 3370 Part 4: Shear & Moment Coefficients for Walls

1. Moment Coefficients for Individual Wall Panels (Clause 2.1)

• Panels fixed on vertical edges, with varying top/bottom edge conditions.
• Refer to Tables 1-3 for:
  • Top hinged, bottom hinged
  • Top free, bottom hinged
  • Top free, bottom fixed

2. Shear Coefficients (Clause 2.3.2)

• Walls fixed on vertical edges, hinged at bottom, free at top.
• Shear coefficients given in Fig. 2 and Table 8.

3. Cylindrical Wall Moments and Shear (Clause 3.1.7 & 2.3.3)

• Table 18: Moments for fixed base, free top, under rectangular load
  Moment = Coefficient × pH³ (kg·m/m)

• Table 19: Moments for fixed base, free top, with shear V applied at top
  Moment = Coefficient × VH (kg·m/m)

• Table 17: Moments for hinged base, free top, with moment M applied at base
  Moment = Coefficient × M (kg·m)

Sample Table Format (Table 18 excerpt):

Notes:

• Positive coefficient → tension on outside face.
• Use relevant table based on support conditions and loading.
• For moment/shear at top or base, interpret 0.0H as bottom and 1.0H as top (or vice versa as per note).

flowchart LR
    A[Wall Panel] --> B{Vertical Edges Fixed?}
    B -->|Yes| C[Use Tables 1-3 for Moments]
    B -->|No| D[Check other clauses]
   

Design Considerations for Walls with Shear Applied at Base (IS 3370 Part 4)

Key Points from Clause 3.1.5

• Shear applied at base causes radial displacement at the base.
• Base hinged: zero displacement, inward reaction.
• Base sliding: maximum displacement, zero reaction.
• Table 15 data can be approximately applied for shear at base.

Shear Calculation (Clauses 2.3.3.1, 2.3.4)

• Shear per unit length at any depth ( z ) below top:

[ \text{Shear/unit length} = \text{Coefficient} \times w \times a ]

where:

• ( w ) = density of liquid,
• ( a ) = height of wall,
• Coefficients from Fig. 1 & 2 depend on boundary conditions (fixed/hinged/free edges).

Shear Distribution Highlights (Table 7)

• Negative shear at corners can be neglected for design.

Summary Table for Shear Coefficients (Simplified)

Practical Notes:

• Use Table 15 (IS 3370 Part 4) for approximate values when shear is at base.
• For base sliding, design for displacement; for hinged base, design for inward reaction.
• Shear at corners is theoretically high but can be ignored in shear/bond checks.

flowchart LR
    A[Shear Applied at Base

IS 3370 Part 4: Moment Distribution Method for Rectangular Tanks

Key Points from Clause 2.2 & 2.2.1.1

• Moment coefficients for rectangular tanks require adjustment due to rotation at common edges.
• Artificial restraint (no rotation) is assumed initially; fixed end moments from Tables 1-3 are used.
• Differences in fixed end moments cause edge rotation; removing restraint induces additional moments.
• Final moments = Fixed end moments + Induced moments; must be equal on both sides of the edge.
• Tables 5 & 6 provide moment coefficients for various b/c and c/a ratios with top free and bottom hinged edges.

Important Parameters:

• a = wall height
• b = larger horizontal dimension
• c = smaller horizontal dimension
• w = liquid density

Moment Formulas:

• Horizontal moment, ( M_y = M_y \times w a^3 )
• Vertical moment, ( M_x = M_x \times w a )

Sample from Table 5 (Walls free at top, hinged at bottom):

Note: Values are moment coefficients; use interpolation for intermediate ratios.

Moment Distribution Procedure Summary:

1. Calculate fixed end moments for each panel using Tables 1-3.
2. Assume common edges fixed (no rotation).
3. Determine unbalanced moments at edges (difference between adjacent panels).
4. Apply moment distribution to balance moments and find induced moments.
5. Sum fixed and induced moments for final moments at edges.

flowchart LR
    A[Calculate Fixed End Moments] --> B[Assume Edge Fixed]
    B --> C[Find Unbalanced Moments at Edges]
    C --> D[Distribute Moments (Moment Distribution)]
    D --> E[Calculate

IS 3370 Part 4 - Moments in Circular Slabs (Clause 3.2)

The code provides moment coefficients for circular slabs under various edge conditions and loadings in Tables 20 to 23. These tables give moments for slabs:

• With centre support
• Without centre support

Key Points:

• Moments are calculated assuming slabs act as thin plates.
• Edge conditions vary: fixed, hinged, or free.
• Loadings include uniform pressure and concentrated loads.

Typical Moment Formulas (from IS 3370 Part 4):

[ M = \text{Coefficient} \times w \times R^2 ]

Where:

• (M) = Moment at a point (kg-m/m or kNm/m)
• (w) = Uniform load intensity (kg/m²)
• (R) = Radius of the circular slab (m)
• Coefficient = From relevant table based on support & load conditions.

Example: Moment Coefficients for Circular Slabs (Summary)

Refer to Tables 20-23 for exact coefficients.

Additional Reference: Moments in Cylindrical Walls (Clause 2.3.3, Table 17)

• Moments are given as:

[ M = \text{Coefficient} \times M_0 ]

Where (M_0) is moment per meter applied at base/top.

• Coefficients vary along height (0 to 1H).
• Positive coefficients indicate tension outside.

Visualization of Moment Variation in Circular Slab:

graph LR
A[Centre Support] --> B[Moment Coefficient Low]
C[No Centre Support] --> D[Moment Coefficient High]
B --> E[Moment at Centre]
D --> F[Moment at Edge]

Summary: Use Tables 20-23 for circular slab moments with/without centre support. Apply:

[ M = \text{Coefficient} \times w \times R^2 ]

Coefficients depend on slab support and loading

IS 3370 Part 4: Notes on Sign Conventions & Load Effects

1. Sign Conventions:

• Positive moment/tension: Tension on the outside face of the wall or slab.
• Positive shear: Shear acting inward.
• Negative signs indicate compression or shear acting outward.

2. Key Formulas:

3. Load Types:

• Triangular load: Varies linearly with height.
• Rectangular load: Uniform pressure.
• Trapezoidal load: Combination of triangular and rectangular.

4. Sample Coefficients (from Table 18 & 19):

5. Shear at Edges (Table 7):

| Location | Shear Coefficient Range (w a²) | |

IS 3370 Part 4 (Design Tables) - Key Points

• Purpose: Provides design tables for moments and stresses in concrete tanks (rectangular & cylindrical) under various loading and edge conditions.

• Moment Coefficients:

  • Tables 5 & 6: Moment coefficients for single-cell rectangular tanks.
  • Parameters: Ratios of larger dimension b to smaller dimension c.
  • Edge conditions: Top and bottom edges (fixed, free, or simply supported).

• Circular Slabs:

  • Tables 20 to 23: Moments in circular slabs with different edge constraints and loadings.

• Design Application:

  • Combine tables to design tanks with complex geometry or boundary conditions.
  • Applicable to tanks built in-ground or above-ground.

Typical Moment Coefficient Table Structure (Example)

Design Approach Summary

flowchart LR
    A[Determine Tank Geometry] --> B[Select Edge Conditions]
    B --> C[Identify b/c Ratio]
    C --> D[Refer to Tables 5 & 6 for Rectangular Tanks]
    C --> E[Refer to Tables 20-23 for Circular Slabs]
    D & E --> F[Calculate Moment Values]
    F --> G[Design Reinforcement & Section]

References: IS 3370 Part 4 (1967) Tables 5, 6, 20-23 for detailed moment coefficients and design data.