Code of practice for design and construction of machine foundations, Part 2: Foundations for impact type machines (hammer foundations)

Scope and Key Parameters - IS 2974 (Part 2) - 1980

This part covers dynamic load testing of pile foundations using a two-mass system model (tup + anvil + foundation block).

Key Notations (Clause 2.1 - Table A-2.1)

Important Relations (Clause 2.2.1)

• Total mass on foundation block = Wa + Wb (depending on frame attachment)
• Spring constant of soil or foundation system:
  [ k_y = 1.45 , \text{kg/cm} ]

Cushioning Details (Clause 3.3)

• If resilient pad used:

  • Elastic modulus (Ep)
  • Max allowable deformation
  • Allowable stress intensity

• If springs/dampers used:

  • Max allowable spring deflections (normal/extreme)
  • Details of springs and dampers

Two-Mass System Model (Fig. 3)

graph LR
  Tup(W1)

IS 2974 Part 2 - Definitions and Key Parameters

Key Notations (Clause 2.1, Table A-2.1)

Important Formulas (Clause 2.2.1)

• Effective Mass Addition: [ W = W_a + W_f \quad \text{(if frame attached to anvil)} ] or \

IS 2974 Part 2 - Necessary Data & Key Parameters

Key Parameters (Clause 3.1)

• Masses:
  • Total hammer mass (frame + falling parts)
  • Falling parts mass (tup + top die)
  • Anvil mass (plus frame mass if attached)
• Energy of impact
• Blows per minute (frequency)
• Anvil basic dimensions
• Manufacturer's drawings (cross-section, plan, elevation, anchor bolt details)
• Coefficient of impact of anvil (for extreme die-to-die blows)

Notations & Typical Data (Clause 2.1, Table A-2.1)

Important Formulae (Clause 2.2.1)

• Total mass for dynamic analysis:

  [ W = W_a + W_b + W_f \quad \text{(depending on frame attachment)} ]

• Energy of Impact:

  [ E = W_1 \times g \times h ]

  Where:

  • (W_1) = mass of tup (kg)
  • (g\

IS 2974 Part 2 - Design Criteria for Hammer Foundations

Key Design Requirements (Clause 3.1)

• Alignment: Centres of gravity of anvil, foundation block, and resultants of elastic pad & foundation support forces should align closely with the hammer tup's line of fall.
• Vibration Control: Induced vibrations in nearby structures must be within safe limits.
• Natural Frequency:
  • Avoid natural frequency (f_n) being an integer multiple of impact frequency (f_i).
  • Recommended: ( f_n \geq 2.5 \times f_i ) or
  • If ( f_n < f_i ), then ( f_n \leq 0.7 \times f_i ) (30% below).

Cushioning Details (Clause 3.3)

• Resilient Pad:

  • Elastic modulus ( E_p )
  • Max allowable deformation ( \delta_{max} )
  • Allowable stress intensity ( \sigma_{allow} )

• Springs & Dampers:

  • Max spring deflections for normal/extreme & static/dynamic loads
  • Details of spring constants and damping coefficients

Important Parameters (Clause 2.1 & 2.2.1)

Natural Frequency Calculation for Two-Mass System (Fig. 3)

[ f_n = \frac{1}{2\pi} \sqrt{\frac{K}{M}} ]

• ( K ) =

IS 2974 Part 2: Vibration Analysis Key Points

1. Two-Mass System Model (Clause A-1.1)

• System: Mass ( m_1 ) subjected to velocity ( V_1 ).
• Natural Frequencies ( f_{ni}, f_{na} ): Roots of [ f^2 - (f_{2na} + f_{onb})(1+B) f^2 + (1+B) f_{ans} f_{2b} = 0 ]
• Amplitude of Vibrations: [ a_1 = \frac{(f_{ena} - f_{ong})(f_2 D_s - f_{em}) V_1}{2m f_{na} (f_{on} - f_{ona})} ] [ a_3 = \frac{2m (f_{2nl} - f_{an2}) f_{na} V_1}{(f_{on} - f_{on})} ]

2. Hammer Foundation Mass Ratios (Clause 4.4.3)

• Mass of anvil: ~20 × mass of tup.
• Foundation block mass ( W_b ):
  • ≥ 3 × anvil mass (general)
  • 4–5 × anvil mass (stiff clay/compact sand)
  • 5–6 × anvil mass (soft clay/loose sand)

3. Key Parameters (Clause 2.1, Table A-2.1)

IS 2974 (Part 2) - Key Construction Formulas & Specifications

Notations (Clause 2.1)

• W₁ = Mass of frame (kg)
• h = Height of fall of tup (cm)
• N = Frequency of impact (blows/min)
• A = Area of piston (cm²)
• Ab = Area of foundation block (cm²)
• Ep = Elastic modulus of pile material (kg/cm²)
• Ap = Cross-sectional area of pile (cm²)
• G = Dynamic shear modulus of soil (kg/cm²)
• Cu = Coefficient of uniform elastic compression of soil (kg/cm³)
• Kp = Spring coefficient of pile foundations (kg/cm)

Key Formulas (Clause 2.2.1 & 2.2.2)

• Loading intensity on pad:
  [ \sigma_1 = K_1 \cdot \delta_1 \cdot A \quad \text{(kg/cm}^2\text{)} ] where ( K_1 ) is a constant, (\delta_1) is pad deflection.

• Soil loading intensity:
  [ \sigma_2 = \frac{W_a - W_b + W_e + k_2 L_b - A_b}{2 \pi r f_{nb} V_{bs}} \times (1 + k) ] Must be less than allowable soil bearing pressure.

• Maximum deflection of foundation (single impact):
  [ \delta = \frac{2 w f_{nb} V'}{1 + W_a + W_b + W_3} ] (V') = velocity after impact, (f_{nb}) = natural frequency (Hz).

Pad Cushioning (Clause 3.3)

• If resilient pad used:

  • Elastic modulus
  • Max allowable deformation
  • Allowable stress intensity

• If springs/dampers used:

  • Max spring deflections (normal/extreme)
  • Details of springs and dampers

Summary Table of Parameters

| Parameter | Symbol | Unit | |----------------------------------|--------

Vibration Analysis of Two-Mass System (IS 2974 Part 2)

Key Formulas:

• Natural frequencies (fn1, fn2):
  The two natural frequencies are roots of:
  [ f^2 - (f_{na}^2 + f_{nb}^2)(1+B)f + (1+B)f_{na}^2 f_{nb}^2 = 0 ]
  where ( B = \frac{m_2}{m_1} ), ( f_{na} = \frac{1}{2\pi} \sqrt{\frac{k_1}{m_1}} ), ( f_{nb} = \frac{1}{2\pi} \sqrt{\frac{k_2}{m_2}} ).

• Amplitude of vibrations:
  [ x_1 = \frac{(f_{na}^2 - f^2)}{(f^2 - f_{na}^2)(f^2 - f_{nb}^2)} V_1, \quad x_2 = \frac{2m (f_{na}^2 - f_{nb}^2) f_{na}}{(f_{na}^2 - f_{nb}^2)} V_1 ]

• Velocity (V_1) is calculated from the momentum equation of the hammer impact.

Application to Hammer Foundations:

• Masses:

  • (m_1): Anvil + frame (if attached)
  • (m_2): Foundation block + frame (if attached)

• Springs:

  • (k_1): Elastic pad stiffness between anvil and block
  • (k_2): Foundation soil stiffness

Design Specifications:

• Foundation must be deep enough to maintain strength where 'cut-in' by anvil pits (Clause 6.7).
• Centres of gravity and force resultants should align with hammer tup fall line.
• Avoid natural frequency (f_n) being integer multiples of hammer impact frequency (f_i).
  • Prefer (f_n \geq 2.5 f_i) or
  • (f_n \leq 0.7 f_i) (30% below (f_i)).