STAAD INPUT FOR SUPPORT CONDITION
VERTICAL STIFFNESS
Allowable vertical settlement = 12 mm
Allowable vertical load (2000*1.5) = 3000 kN Cl. 6.1.5, IS:2911 (Part 4)-1985
Vertical stiffness = 3000×103/12
= 250000 kN/m
Horizontal STIFFNESS
Allowable lateral deflection = 5 mm
Allowable lateral force = 120 kN Cl. 7.4, IS:2911 (Part 4)-1985
Horizontal stiffness = 120×103/5
= 24000 kN/m
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Calculating pile stiffness is crucial for analyzing the load-displacement behavior of piles in soil. While IS codes and ACI codes don’t explicitly give a single formula for pile stiffness, they provide frameworks for pile analysis, including elastic behavior, interaction with soil, and load transfer. Here’s how pile stiffness is calculated according to Indian (IS) and American (ACI/related) standards:
🔹 What is Pile Stiffness?
Pile stiffness refers to the resistance a pile offers to deformation under load. It is generally expressed as:
- Axial Stiffness: k = EA / L
- Lateral Stiffness: Depends on soil-pile interaction, typically derived from p–y curves or subgrade modulus models.
Where:
- E = Modulus of elasticity of pile material
- A = Cross-sectional area of pile
- L = Length of pile
🇮🇳 1. As per IS Codes (India)
Relevant IS codes:
- IS 2911 (Part 1/Sec 1 & 4) – Design and construction of pile foundations
- IS 2950 (Part 1) – Structural design of raft foundations
- IS 456:2000 – General concrete design provisions
🔸 (a) Axial Stiffness (Compression or Tension):
Formula: kaxial=E⋅A / L
Where:
- E: Modulus of elasticity of concrete (as per IS 456: E=5000 sqrt(fck)
- A: Cross-sectional area of pile
- L: Length of pile
Example (for M25 concrete):
- E= 5000 sqrt(25) = 25000 MPa
🔸 (b) Lateral Stiffness (Horizontal Loads):
IS 2911 recommends using modulus of subgrade reaction kh or p–y method for lateral load behavior.
For lateral stiffness: klateral=p / y
Where:
- p: Soil reaction per unit length of pile
- y: Lateral deflection at depth z
Alternatively, use the Winkler spring model: kh=Es / B
- Es: Modulus of subgrade reaction (varies with depth and soil type)
- B: Pile width or diameter
🇺🇸 2. As per ACI / American Practices
ACI does not directly provide pile stiffness equations but defers to geotechnical analysis methods for axial and lateral pile behavior.
Relevant documents:
- ACI 543R – Design, manufacture and installation of concrete piles
- FHWA – Design and construction of driven pile foundations
- API RP 2A / AISC manuals for offshore pile stiffness
🔸 (a) Axial Stiffness:
Same elastic formula used: k=E⋅A / L
Use concrete modulus E=57000 sqrt(fc′) psi for normal weight concrete.
🔸 (b) Lateral Stiffness:
Typically uses p–y curves:
- Soil behavior is modeled using nonlinear springs
- Stiffness is depth-dependent
Software like LPILE, PLAXIS, or SAP2000 uses these models.
✅ Summary Table:
| Type | Formula | Code Reference |
| Axial Stiffness | k=EA / L | IS 456, ACI 318, IS 2911 |
| Lateral Stiffness | Winkler: k=p / y | IS 2911, ACI + FHWA Methods |
| Subgrade modulus | kh≈Es / B | IS 2950, FHWA |
| E (Concrete) | IS: 5000 sqrt(fck) ACI: 57000 sqrt(fc′) | IS 456, ACI 318 |
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