Code of practice for design and construction of conical and hyperbolic paraboloidal types of shell foundations
1980 Edition

Overview of IS 9456 Scope

Scope (Clause 1.1):

• Addresses design and construction of conical and hyperbolic paraboloidal shell foundations.
• Applicable for foundations supporting isolated columns.

Essential Design Inputs (Clause 3.1)

• Utilize material and load data as per IS 1080-1962 and IS 2950 (Part I)-1973.
• Include geometric and reinforcement details following Clause 3.1.1.

Core Design Equations (Appendix A, Clauses 5.8 to 5.10.3)

• Formulas cover:
  • Membrane stresses (tensional and compressive) within shells.
  • Bending moments due to column loads.
  • Calculation of shell thickness and reinforcement requirements.
• Detailed equations for conical and hyperbolic paraboloidal shells are in Appendix A.

Soil Compaction Method (Clause 6.4.1, Appendix C)

• Employ centrifugal blast compaction for filling precast shell footings to achieve 80-90% relative density.
• This involves a needle vibrator with centrifugal vane rotor inserted through a hole at the column base.

Typical Shell Shape (Figure 3)

• Hyperbolic paraboloidal shells comprise:
  • Convex parabola representing tension zones.
  • Concave parabola representing compression zones.
  • Straight-line generators acting as ribs.

Summary Table of Design Inputs

Specific stress or reinforcement design formulas can be provided upon request.

Definitions Referenced in IS 9456 (Clause 2.1)

This standard draws from related Indian Standards to clarify terms used in shell foundation design:

• IS 1904-1978: Foundation design code.
• IS 6403-1971: Guidelines for bearing capacity determination.
• IS 2210-1962: Concrete structural code.
• IS 2204-1962: Structural steel code.

Key terms include:

• Bearing Capacity: The maximal soil load per unit area.
• Safe Bearing Capacity: Allowable soil pressure considering safety factors.
• Isolated Column Load: Load applied from a single column.

Important Points from IS 9456

• Focuses on conical and hyperbolic paraboloidal shell foundations under isolated column loads.
• Requires soil and material properties per IS 1080 and IS 2950.
• Design equations are detailed in Appendix A.

Typical Formula (Appendix A)

Soil bearing pressure ( q ) is calculated as:

[ q = \frac{P}{A} ]

Where:

• ( P ) is column load (kilonewtons).
• ( A ) is projected shell foundation area (square meters).

Please specify if particular design formulas or tables are needed.

Design Aspects for Conical and Hyperbolic Paraboloidal Shell Foundations (IS 9456)

Primary Design Criteria (Clause 4.1)

• Net applied load intensity must not exceed allowable soil bearing pressure.
• Allowable pressure is the lesser of:
  • Safe net unit bearing capacity (per IS 6403).
  • Soil pressure corresponding to permissible settlement.
• For sandy soils:
  • Safe bearing capacity increases with foundation width.
  • Soil pressure for settlement decreases as width increases.
• For clayey soils:
  • Safe bearing capacity is independent of width.
• The smaller plan dimension governs bearing capacity and settlement limits.

Shell Foundation Design Formulas (Clause 5.10.1, Appendix A)

• Conical shells: Reinforcement designed for hoop and meridional stresses.
• Hyperbolic paraboloidal shells: Tension along convex parabola, compression along concave parabola, with straight ribs carrying shear.

Reinforcement Placement (Refer Figures 1 & 3)

Soil Compaction Method (Clause 6.4.1, Appendix C)

• Use centrifugal blast compaction with rotating vaned rotor inside hollow footing.
• Achieves 80-90% relative density by radially compacting dry sand.

Design Process Flow

flowchart TD
    A[Calculate Net Load Intensity] --> B{Compare with Allowable Bearing Pressure}
    B -- Within Limits --> C[Determine Foundation Dimensions]
    B -- Exceeds Limits --> D[Increase Foundation Size or Improve Soil]
    C --> E[Design Reinforcement Layout]
    E --> F[Conical: Hoop & Meridional]
    E --> G[Hypar: Parabolic Reinforcement]

This framework supports safe, efficient shell foundation design.

Soil Design Considerations in IS 9456

1. Objective (Clause 4.1)

• Select foundation dimensions ensuring net load intensity does not surpass allowable bearing pressure.
• Allowable bearing pressure equals the minimum of:
  • Safe net unit bearing capacity.
  • Soil pressure corresponding to acceptable settlement.

2. Important Observations

• For sandy soils:
  • Safe bearing capacity rises with foundation width.
  • Soil pressure for a specified settlement decreases as width increases.
• For clayey soils:
  • Safe bearing capacity remains unaffected by width.
• The smaller horizontal plan dimension controls bearing capacity.

3. Reference Standards

• IS 6403 for allowable bearing pressure determination.
• IS 456 for general shallow foundation structural safety.

4. Net Loading Intensity Formula

[ q_{net} = \frac{P}{A} - \gamma D_f ] Where:

• ( P ) = Applied load (kN)
• ( A ) = Plan area (m²)
• ( \gamma ) = Unit weight of soil above foundation base
• ( D_f ) = Depth of foundation

5. Design Workflow

• Compute net loading intensity.
• Verify it is within allowable limits.
• Adjust foundation width if necessary.

Conceptual Diagram of Soil Design

flowchart TD
    A[Determine Applied Loads] --> B[Compute Net Loading Intensity]
    B --> C{Is q_net ≤ Allowable Bearing Pressure?}
    C -- Yes --> D[Foundation Dimensions Approved]
    C -- No --> E[Increase Foundation Width]
    E --> B

This process assures soil safety and serviceability for shell foundations.

Structural Design Guidelines for Conical and Hyperbolic Paraboloidal Shell Foundations (IS 9456)

Fundamental Design Rules (Clause 4.1)

• Foundation size is determined so that net applied load does not exceed allowable soil bearing pressure.
• Allowable bearing pressure is the minimum of:
  • Safe net bearing capacity (per IS 6403).
  • Soil pressure for permissible settlement.
• For sandy soils, bearing capacity increases with width; for clay soils, it is width-independent.
• The smaller plan dimension critically influences bearing capacity.

Key Design Equation

• Ultimate ridge failure moment capacity (Clause 2.2.2):

[ P_u = 4 N_g + 8 N_p ]

Where:

• ( P_u ) = Ultimate axial load capacity
• ( N_g ), ( N_p ) = Membrane stress resultants related to ridge section

Reinforcement Details (Appendix B, Clause 5.10.2)

• Critical reinforcement is necessary in hyperbolic paraboloidal footings to achieve ultimate strength.
• Include circumferential (hoop) and radial (meridional) steel as per design.
• Tension zones correspond to convex parabola ribs; compression zones correspond to concave ribs.

Typical Structural Elements

• Conical footings reinforced with hoop and meridional steel.
• Hypar shells with tension in convex ribs and compression in concave ribs.
• Umbrella footings combining hypar shells with edge and ridge beams.

Bearing Capacity Influence Summary

Structural Design Flow

flowchart TD
    A[Applied Load] --> B[Compute Net Load Intensity]
    B --> C{Compare with Allowable Bearing Pressure}
    C -- ≤ --> D[Select Foundation Size]
    C -- > --> E[Increase Foundation Size]
    D --> F[Design Reinforcement]
    F --> G[Conical: Hoop & Meridional Steel]
    F --> H[Hypar: Parabolic Reinforcement]

This structure ensures safe and efficient shell foundations.

Construction Requirements and Procedures for Shell Foundations (IS 9456)

1. Design Formulae (Appendix A, Clause 5.10.1)

• Applicable to conical and hyperbolic paraboloidal shell footings under isolated column loads.
• Material and load aspects referenced from IS 1080-1962 and IS 2950 (Part I)-1973.

2. Soil Compaction Method (Clause 6.4.1, Appendix C)

• Use centrifugal blast compaction for filling precast shell footings.
• Employ a centrifugal vane rotor attached to a needle vibrator through the footing’s hollow base.
• This method compacts dry sand radially outward to achieve 80-90% relative density.
• Ensures uniform, dense filling and enhanced foundation stability.

3. Shell Reinforcement (Figure 3)

• Hyperbolic paraboloidal shells have:
  • Convex ribs under tension.
  • Concave ribs under compression.
  • Straight-line generators forming ribs.

Summary Table: Compaction Parameters

Compaction Process Flow

flowchart LR
    A[Place Dry Sand in Footing Hollow] --> B[Insert Rotor into Footing Base]
    B --> C[Activate Rotor Motor]
    C --> D[High-Speed Rotor Spins]
    D --> E[Sand Blasts Radially Outward]
    E --> F[Sand Settles Densely Against Footing Walls]
    F --> G[Progressive Filling from Edges to Center]
    G --> H[Manual Compaction at Base Hole]

Detailed design calculations are available in Appendix A and relevant IS codes.

IS 9456 Appendix A: Membrane Stresses and Ultimate Load Capacities

1. Membrane Stress Resultants (Clauses 1.1, 2.1)

• Provides stresses per unit width caused by vertical soil reactions and bending moments for convex and concave paraboloidal shells.
• Includes forces in beams and shell reinforcements (see Figure 21).

2. Ultimate Strength via Ridge Failure (Clause 2.2.2)

• Ultimate load capacity expressed as:

[ P_u = 4 N_g + 8 N_p ]

Where:

• ( P_u ): Ultimate axial load capacity
• ( N_g ): Membrane stress resultant from soil pressure
• ( N_p ): Additional stress resultant

3. Reinforcement Detailing (Appendix B, Clause 5.10.2)

• Specifies reinforcement at critical sections to fully achieve ultimate strength in hyperbolic paraboloidal footings.

4. Design Formula Set (Clauses 5.8–5.10.3)

• Comprehensive equations for conical and hyperbolic paraboloidal shell foundations addressing stress and moment distributions.

Summary Table of Parameters

Stress Analysis Flow

flowchart LR
    Soil_Load --> Membrane_Stresses[N_g, N_p]
    Membrane_Stresses --> Ultimate_Load(P_u = 4N_g + 8N_p)
    Ultimate_Load --> Reinforcement_Details
    Reinforcement_Details --> Full_Ultimate_Strength

Refer to IS 9456 Figure 21 and appendices for detailed stress and reinforcement layouts.

IS 9456 Appendix B: Reinforcement Detailing to Achieve Ultimate Strength in Hyperbolic Paraboloidal Footings

Principal Failure Modes (Figure 22)

• Ridge Failure: Characterized by cracking at the principal ridge, yielding of edge beams, and plastic hinges at the column face.
• Diagonal Failure: Identified by principal diagonal cracks, corner yielding, and plastic hinges near the column face.

Ultimate Strength Equation for Ridge Failure (Clause A-2.2.2)

[ P_u = 4 N_g + 8 N_p ] Where:

• (P_u): Ultimate axial load capacity
• (N_g): Soil pressure resistance
• (N_p): Plastic moment capacity related to ridge

(See Figure 22 for failure illustrations.)

Critical Sections and Reinforcement Requirements (Clause B-1.0 & Appendix B)

• Reinforcement must be provided at:
  • Principal ridge areas
  • Yielding edge beams
  • Plastic hinge zones at the column face
• Detailing includes adequate anchorage, lap lengths, continuity, and proper bar sizing per bending demands (see Figure 23).

Summary Table: Reinforcement Zones

Reinforcement Development Flow

flowchart TD
    A[Hypar Footing] --> B[Ridge Section]
    A --> C[Edge Beam]
    A --> D[Column Face]
    B --> E[Principal Ridge Cracking]
    C --> F[Yielding Edge Beam]
    D --> G[Plastic Hinge Formation]
    E & F & G --> H[Achieve Full Ultimate Strength]

Refer to IS 9456 Appendix B for bar diameters, spacing, and anchorage lengths to ensure ductility and strength.

IS 9456 Appendix C: Remote Compaction Methods for Precast Shell Footings

Highlights from Clause 6.4.1:

• Precast footings are set into trenches excavated to a level bottom.
• Dry sand is poured through the column base hole into the hollow cavity beneath the footing.
• The sand must be compacted uniformly to high density.
• For steep conical footings, manual tamping via the hole is feasible.
• For shallow conical or hypar footings with difficult-to-access corners, remote compaction tools are employed to ensure soil core integrity.
• Steel columns connect using embedded bolts and neoprene pads to isolate moments.
• Concrete columns use dowels or socket connections.

Recommended Remote Compaction Practices (Appendix C)

• Use vibratory probes or pneumatic rammers inserted through the base hole.
• Compact sand in layers to avoid voids.
• Ensure uniform density beneath the entire footing.

Design Considerations

• Maintain net loading intensity within allowable bearing pressure (IS 6403).
• Foundation width affects bearing capacity in sandy soils.
• Utilize Appendix A formulas for shell foundation stress and thickness design.

Connection Details Summary

Remote Compaction Process Diagram

flowchart TD
    A[Place Precast Footing in Trench] --> B[Pour Dry Sand Through Hole]
    B --> C{Footing Type}
    C -->|Steep Conical| D[Manual Tamping]
    C -->|Shallow Conical/Hypar| E[Use Remote Compaction Tools]
    E --> F[Vibratory Probe or Pneumatic Rammer]
    F --> G[Compact Sand Evenly]
    G --> H[Ensure Solid Soil Core Under Footing]

Summary: Remote compaction techniques ensure even, dense soil support beneath precast shell footings by filling voids with properly compacted sand through access holes.