# Question:Analysis and Design of Machine Foundation

## Question:Analysis and Design of Machine Foundation

Maple 17

ANALYSIS AND DESIGN OF MACHINE FOUNDATION

 (1)

 Introduction This document deals with vibration analysis and design of machine foundations subjected to dynamic load.

 (2)

 (3)

 Richart and Lysmer's Model Richart et al. (1970) idealised the foundation as a lumped mass supported on soil which is idealised as frequency independent springs which he described in term of soil parameter dynamic shear modulus or shear wave velocity of the soil for circular footing when footings having equivalent circular radius. The Tables below shows the different values of spring and damping vlaues as per Richart and Lysmer. In which, G = dynamic shar modulus of he soil and is given  ; ν = Piosson's ratio of the soil; ρs = mass density of the soil; Vs = shear wave velocity of the soil obtained from soil testing; g = acceleration due to gravity; m = mass of the machine and foundation; J = mass moment of inertia of the machine and foundation about the appropriate axes; K = equivalent spring stiffness of the soil; C = damping value of the soil; B = interia factor contributing to the damping factor; D = damping ratio of the soil; r = equivalent radius of a circular foundation; L = length of foundation, and B = width of the foundation.

 Sketch

Table : Values of soil springs as per Richart and Lysmer (1970) model

 SI No. Direction Spring value Equivalent radius Remarks 1 Vertical This is in vertical Z direction 2 Horizontal This induce sliding in horizontal X 2.1 Horizontal This induce sliding in horizontal Y 3 Rocking This produces roxking about Y axis 3.1 Rocking This produces roxking about X axis 4 Twisting This produces twisting about vertical Z axis

Table : Values of soil damping as per Richart and Lysmer (1970) model

SI No.

Direction

Mass ratio (B)

Damping ratio and Damping values

Remarks

1

Vertical

This damping value is in vertical Z direction

2

Horizontal

This damping value is in lateral X direction

2.1

Horizontal

 (5.1)
 (5.2)

This damping value is in lateral Y direction

3

Rocking

 (5.3)
 (5.4)

This damping value is for rocking about Y direction

3.1

Rocking

 (5.5)

This damping value is for rocking about X direction

4

Twisting

 (5.6)

This damping value is valid for twisting about vertical Z axis

 (4)

Vertical Motion Considering damping of the Soil

For vertical direction the equation becomes that of a lumped mass having single degree of freedom when

 (6.1)

 (6.2)

 (6.3)

By algebraically manipulating the expression, the form traditionally used by engineers is derived:

 (6.4)

 (6.5)

This form includes the damping ratio , the natural frequency , and the external forcing term .  Consider only free vibration by setting

 (6.6)

 (6.7)