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

IS 9456: Scope Summary & Key Specifications

Scope (Clause 1.1):

• Covers design and construction of conical and hyperbolic paraboloidal shell foundations.
• These foundations support isolated column loads.

Essential Design Inputs (Clause 3.1)

• Use data as per IS 1080-1962 and IS 2950 (Part I)-1973 for materials and loads.
• Additional info per Clause 3.1.1 (e.g., geometry, reinforcement details).

Key Formulae (Appendix A - Clauses 5.8 to 5.10.3)

• Design formulas for shell foundations involve:
  • Membrane stresses in shells (tension/compression).
  • Bending moments due to column loads.
  • Shell thickness and reinforcement calculations.
• Refer to Appendix A for detailed formulae on conical and hyperbolic paraboloidal shells.

Compaction Technique (Clause 6.4.1, Appendix C)

• Centrifugal Blast Compaction for infilling precast shell footings ensures 80-90% relative density.
• Uses a needle vibrator with centrifugal vane rotor inserted through the column base hole.

Typical Shell Geometry (Fig. 3)

• Hyperbolic paraboloidal shell has:
  • Convex parabola (tension zone)
  • Concave parabola (compression zone)
  • Straight line generators (ribs)

Summary Table: Design Inputs

If needed, I can provide specific formulas or diagrams for shell stresses or reinforcement detailing.

IS 9456 - Definitions (Clause 2.1)

This standard references definitions from related IS codes for clarity in shell foundation design:

• IS 1904-1978: Code of practice for foundation design.
• IS 6403-1971: Code for determination of bearing capacity.
• IS 2210-1962: Code for structural use of concrete.
• IS 2204-1962: Code for structural steel.

These provide foundational terminology such as:

• Bearing Capacity: Maximum load per unit area soil can support.
• Safe Bearing Capacity: Allowable pressure considering factor of safety.
• Isolated Column Load: Load from a single column acting on foundation.

Key Notes from IS 9456:

• Applies to conical and hyperbolic paraboloidal shell foundations under isolated column loads.
• Requires soil and material data per IS 1080-1962 and IS 2950 (Part I)-1973.
• Design formulae and parameters are detailed in Appendix A (Clauses 5.8 to 5.10.3).

Typical Formula Reference (from Appendix A):

For shell foundations, bearing pressure ( q ) is related to load ( P ) and shell area ( A ):

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

Where:

• ( P ) = Column load (kN)
• ( A ) = Projected area of shell foundation (m²)

If you need specific formulas or tables for design, please specify which aspect (e.g., thickness, stress, load distribution).

IS 9456: Design Considerations for Conical & Hyperbolic Paraboloidal Shell Foundations

Key Design Principles (Clause 4.1)

• Net Loading Intensity ≤ Allowable Bearing Pressure
• Allowable bearing pressure = Minimum of:
  • Safe net unit bearing capacity (IS 6403)
  • Soil pressure for permissible settlement
• For sand:
  • Safe net unit bearing capacity ↑ with foundation width
  • Soil pressure for given settlement ↓ with foundation width
• For clay:
  • Safe net unit bearing capacity independent of foundation width
• Width = smaller plan dimension (governs bearing capacity and settlement)

Formulas for Shell Foundations (Clause 5.10.1, Appendix A)

• Conical Shell:
  • Hoop and meridional reinforcement designed based on shell stresses
• Hyperbolic Paraboloidal Shell:
  • Tension along convex parabola
  • Compression along concave parabola
  • Straight line generators carry shear

Reinforcement Details (Refer Fig. 1 & 3)

Soil Compaction Technique (Clause 6.4.1, Appendix C)

• Centrifugal Blast Compaction:
  • Rotor with vanes rotates inside hollow footing
  • Sand particles compacted radially outward
  • Achieves 80-90% relative density
  • Improves soil bearing capacity beneath precast shell footings

Summary Diagram

flowchart TD
    A[Determine Net Loading Intensity] --> B{Compare with Allowable Bearing Pressure}
    B -- If ≤ --> C[Design Shell Foundation Dimensions]
    B -- If > --> D[Increase Foundation Size or Improve Soil]
    C --> E[Design Reinforcement]
    E --> F[Conical: Hoop & Meridional]
    E --> G[Hyperbolic Paraboloidal: Parabolic

IS 9456 - Soil Design Key Points

1. Objective (Clause 4.1)

• Determine foundation plan dimensions so that Net Loading Intensity ≤ Allowable Bearing Pressure.
• Allowable Bearing Pressure = Minimum of:
  • Safe Net Unit Bearing Capacity
  • Soil Pressure for permissible settlement

2. Important Notes

• For sand:
  • Safe net unit bearing capacity increases with foundation width.
  • Soil pressure for given settlement decreases with width.
• For clay:
  • Safe net unit bearing capacity is independent of foundation width.
• Width = smaller of the two plan dimensions (controls bearing capacity).

3. Referenced IS Codes

• IS 6403: Determination of allowable bearing pressure.
• IS 456: Structural safety of shallow foundations.

4. Formula for Net Loading Intensity (q_net)

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

• (P) = Load on foundation
• (A) = Plan area of foundation
• (\gamma) = Unit weight of soil above foundation base
• (D_f) = Depth of foundation

5. Design Steps

• Calculate net loading intensity (q_{net}).
• Check (q_{net} \leq) allowable bearing pressure from IS 6403.
• Adjust foundation width accordingly.

Conceptual Diagram: Soil Design Process

flowchart TD
    A[Determine Loads] --> B[Calculate Net Loading Intensity]
    B --> C{Compare with Allowable Bearing Pressure}
    C -- q_net ≤ Allowable --> D[Foundation Dimensions OK]
    C -- q_net > Allowable --> E[Increase Foundation Width]
    E --> B

This concise framework ensures safe, serviceable foundations per IS 9456 soil design requirements.

IS 9456 — Structural Design of Conical & Hyperbolic Paraboloidal Shell Foundations

Key Design Principles (Clause 4.1)

• Foundation sizing ensures net loading intensity ≤ allowable bearing pressure.
• Allowable bearing pressure = min {
  (a) safe net unit bearing capacity (IS 6403),
  (b) soil pressure for permissible settlement
  }
• For sand, safe net bearing capacity ↑ with foundation width; for clay, it is independent of width.
• Width = smaller plan dimension → critical for bearing capacity.

Important Formulas

• Ultimate ridge failure moment capacity (Clause 2.2.2):

[ P_u = 4 N_g + 8 N_p ]

Where:

• (P_u) = ultimate load capacity
• (N_g), (N_p) = forces related to the ridge section

Reinforcement Detailing (Appendix B, Clause 5.10.2)

• Critical sections of hyperbolic paraboloidal footings require careful reinforcement detailing to achieve full ultimate strength.
• Use hoop reinforcement (circumferential) and meridional reinforcement (radial) as per figures.
• Shell reinforcement follows tension/compression zones:
  • Convex parabola → tension
  • Concave parabola → compression

Typical Structural Elements (Figures)

• Conical footing: hoop + meridional reinforcement
• Hyperbolic paraboloid shell: tension in convex, compression in concave parabolas
• Umbrella footing: hypar shell + edge & ridge beams

Summary Table: Bearing Pressure Influence

flowchart TD
    A[Load on Foundation] --> B[Net Loading Intensity]
    B --> C{Compare with Allowable Bearing Pressure}
    C -->|≤| D[Safe Foundation Dimensions]
    C -->|>| E[Increase Foundation Size]
    D --> F[Design Reinforcement]
    F --> G[Hoop & Meridional for Conical]
    F --> H[Shell

IS 9456: Key Construction Formulas and Specifications for Shell Foundations

1. Design Formulae (Appendix A, Clause 5.10.1)

• Applies to conical and hyperbolic paraboloidal shell foundations.
• Design considers isolated column loads.
• Refer to IS 1080-1962 and IS 2950 (Part I)-1973 for additional data.

2. Compaction Technique (Appendix C, Clause 6.4.1)

• Centrifugal Blast Compaction for infilling precast shell footings.
• Uses a centrifugal vane rotor attached to a needle vibrator.
• Achieves relative density of 80-90% by blasting dry sand radially outward inside hollow footing.
• Ensures dense, uniform filling, improving foundation stability.

3. Shell Reinforcement (Fig. 3)

• Hyperbolic paraboloidal shell has:
  • Convex parabola ribs (tension)
  • Concave parabola ribs (compression)
  • Straight line generators

Summary Table: Compaction Parameters

flowchart LR
    A[Pour Dry Sand Batch] --> B[Insert Rotor into Hollow Space]
    B --> C[Switch On Motor]
    C --> D[Vaned Rotor Spins at High Speed]
    D --> E[Sand Particles Blast Radially Outwards]
    E --> F[Particles Settle Densely Against Footing Walls]
    F --> G[Progressive Filling from Periphery to Center]
    G --> H[Manual Compaction at Center Hole]

For detailed design calculations, consult Appendix A and related IS codes mentioned.

IS 9456: Stress Resultants & Ultimate Strength Theories

1. Membrane Stress Resultants (Clauses 1.1, 2.1)

• Per unit width stresses due to vertical soil reactions and moments are given for convex and concave paraboloid shells.
• Forces in beams and shell reinforcement are considered (see Fig. 21).

2. Ultimate Strength by Ridge Failure (Clause 2.2.2)

• Simplified formula for ultimate load capacity at ridge failure:

  [ P_u = 4 N_g + 8 N_p ]

  where:

  • ( P_u ) = ultimate load capacity,
  • ( N_g ) = membrane stress resultant due to soil pressure,
  • ( N_p ) = additional stress resultant,
  • ( M'_r ) = ultimate moment capacity of the ridge section.

3. Detailing for Ultimate Strength (Appendix B, Clause 5.10.2)

• Reinforcement detailing at critical sections ensures full utilization of ultimate strength.
• Applies specifically to hyperbolic paraboloidal footings.

4. Design Formulae (Appendix A, Clauses 5.8–5.10.3)

• Provides comprehensive formulae for conical and hyperbolic paraboloidal shell foundations considering stresses and moments.

Summary Table: Key Parameters

flowchart LR
    Soil_Load --> Membrane_Stress_Resultants[N_g, N_p]
    Membrane_Stress_Resultants --> Ultimate_Load_Capacity(P_u = 4N_g + 8N_p)
    Ultimate_Load_Capacity --> Reinforcement_Detailing
    Reinforcement_Detailing --> Full_Ultimate_Strength

Note: Refer to IS 9456 Fig. 21 and Appendices for detailed stress diagrams and reinforcement layouts.

IS 9456: Detailing for Full Ultimate Strength of Hypar Footings

Key Failure Modes (Fig. 22)

• Ridge Failure: Principal ridge cracking, yielding edge beam, plastic hinge at column face.
• Diagonal Failure: Principal diagonal cracking, corner yielding, plastic hinge at column face.

Ultimate Strength Formulas (Clause A-2.2.2)

For Ridge Failure: [ \boxed{ P_u = 4 N_g + 8 N_p } ]

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

(Refer Fig. 22 for failure mechanism details.)

Critical Sections & Detailing (Clause B-1.0 & Appendix B)

• Reinforcement must be provided at:
  • Principal ridge sections
  • Edge beams (yielding zones)
  • Column face (plastic hinge zones)
• Detailing ensures full development of ultimate strength by:
  • Providing adequate anchorage and lap lengths
  • Ensuring continuity and sufficient reinforcement at critical sections (Fig. 23)
  • Using proper bar diameters and spacing as per bending moment demands

Summary Table: Reinforcement Zones

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

Note: Refer IS 9456 Appendix B for detailed bar sizes, spacing, and anchorage lengths to ensure ductility and strength.

IS 9456 - Remote Compaction Techniques for Precast Footings

Key Points from Clause 6.4.1:

• Precast footings are installed in a trench cut to level bottom.
• After levelling, dry sand is poured through a hole in the column base into the hollow space below the footing.
• This sand must be compacted to high and uniform densities.
• For steep conical footings, manual tamping through the hole is possible.
• For shallow conical and hypar footings with inaccessible corners, remote compaction techniques (Appendix C) are used to ensure a sound core.
• Steel column connections use embedded bolts and neoprene pads to avoid moment transfer.
• Concrete columns connect via dowels or socket arrangements.

Recommended Remote Compaction Method (Summary from Appendix C):

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

Design Considerations (from Clauses 4.1 & 5.10.1):

• Ensure net loading intensity ≤ allowable bearing pressure (IS 6403).
• Foundation width influences bearing capacity in sand.
• Use formulas from Appendix A for conical/hyperbolic paraboloidal shell design.

Typical Connection Details:

Visualization: Remote Compaction Process

flowchart TD
    A[Install 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[Remote Compaction Tools]
    E --> F[Vibratory Probe / Pneumatic Rammer]
    F --> G[Compact Sand Uniformly]
    G --> H[Sound Soil Core Under Footing]

Summary:
For precast footings, remote compaction ensures full contact and load transfer by filling voids with compacted sand via holes in the footing base. Manual tamping suits steep cones; remote tools are necessary