MODULUS OF ELASTICIITY

Modulus of Elasticiity

Modulus of Elasticiity

Elastic properties of cushion materials are used to determine elastic properties of composite hammer cushions. Equivalent stiffness of the composite hammer cushion depends mostly on the characteristics of soft cushion material and only the thickness of a soft material, not the total cushion thickness, should be taken for calculations. Equivalent modulus of elasticity of the composite hammer cushion depends on the modulus of elasticity of a soft material and a ratio of stiff to soft layers thicknesses. A change of soft and stiff layers thicknesses and their ratio may be used as a tool to increase force transmitted to the pile.

1 INTRODUCTION

Hammer cushion is installed in a well on a top of the drive cap (helmet) under the anvil which is struck by the hammer ram. The drive cap is employed to hold the pile head in position under hammer and to transfer impact energy to the pile.

The hammer cushion is used for two opposite purposes. On the one hand the hammer cushion must transfer the hammer energy to the pile without excessive energy losses, but on the other hand the hammer cushion has to prevent pile and hammer damage from driving.

Various materials such as wood, rope, polymers, fibers, aluminum and others are placed in the hammer cushion well. Combination of materials, like aluminum with Conbest or micarta, are frequently used for hammer cushions (Practical guidelines 1984; GRL Manual 1997; SPS 1999; Penn State Fabricators 1999).

Laminated materials such as aluminum and Conbest or aluminum and micarta have a relatively constant elasticity during relatively long life, consistent and predictable energy transfer and more uniform driving results.

The transfer of hammer energy to the pile and protection of pile and hammer from possible damage during pile driving depend on the moduli of elasticity and the stiffness of the materials used to composite hammer cushions.

The purpose of this paper is to show how moduli of elasticity and stiffness of different laminated cushion materials effect equivalent modulus of elasticity and equivalent stiffness of the composite hammer cushions.

2 TWO CUSHION MATERIALS

A composite hammer cushion has alternate layers of soft materials like Conbest or micarta and layers of stiff materials like aluminum or steel.

Stiffness of a soft layer, ksoft, and a stiff layer, kstf, may be written

(1)

where

Esoft = modulus of elasticity of soft material;

Estf = modulus of elasticity of stiff material;

A = cross-section of cushion materials;

tsoft = thickness of soft material layer;

tstf = thickness of stiff material layer.

It is common that Estf is considerably greater than Esoft and tstf is equal or less than tsoft.

2.1 Equal number of layers

Soft and stiff material layers are in series. Therefore equivalent stiffness of the composite hammer cushion, keq, is

(2)

where

n = number of layers of each material;

remaining parameters are the same as defined previously.

Equation (2) may be rewritten as

(3)

Relationship between equivalent stiffness and equivalent modulus of elasticity is

(4)

Equating the right pars of equations (3) and (4), we obtain

(5)

Equation (3) can be simplified to analyze a contribution ...