Practical Examples in Soil-Structure Interaction

Machine Foundations

Structural Engineering Simplified

Chapter 1. Soil Structure Interaction

Chapter 1

1.1 What is Soil-Structure-Interaction (SSI)?1.2 Dynamic Vs Static Impedance 1.3 Notations and Sign Conventions 1.4 Degrees of Freedom Animation 1.5 Why Dynamic Stiffness is Frequency Dependent?1.6 Foundation and Soil Design Parameters 1.7 Examples

1.7 Examples

Figure 1.7.1 Example 1.7.1

Example 1.7.1

During the start up of a machine, its angular frequency is ramped from 0 to 50 rad/s. Assuming that the vertical static stiffness of the soil foundation was found to be equal to 6000 kip/in, damping for vertical motion is equal to 60 kip.s/in, and that the effective mass of the soil column is equal to 3 kip.s²/in. Construct a graph to show how the dynamic stiffness and damping of the soil changes with the angular frequency of the vibrating machine.

Observations

Notice that the dynamic stiffness changes with the frequency according to $k = k_{st} - m \omega^2$

And that the viscous damping changes with the frequency according to $c = c_{st} \omega$