Question

A rectangular RCC machine foundation of size 3.0 x 3.0 x 0.8m thick is supporting a machine of weight is 10kN. The machine transmits an unbalanced vertical load passing through the combined CG of the machine and foundation whose amplitude is 8[1-sin/4t]kN Soil medium has the following properties: Young’s modulus, E=1.2 x10^5 kN/m^2. Poisson’s ratio, v=0.3. Unit weight of soil and concrete, s=17 kN/m^3. c=17 kN/m^3 Find the response of the system and natural frequency using Elastic half-space approach for vertical and sliding vibration.

a) 1.2 Hz, 5 mm
b) 2.5 Hz, 8 mm
c) 0.8 Hz, 10 mm
d) 3.0 Hz, 6 mm

Answer 1

To calculate the response of the system and the natural frequency using the Elastic half-space approach for vertical and sliding vibration, we need to first calculate the stress and strain in the foundation based on the given information.

Step-by-step explanation:

To calculate the response of the system and the natural frequency using the Elastic half-space approach for vertical and sliding vibration, we need to first calculate the stress and strain in the foundation based on the given information. The stress can be calculated using the formula:

Stress = Load/Area

The strain can be calculated using the formula:

Strain = Stress/Young's Modulus

Using the calculated stress and strain values, we can determine the response of the system and the natural frequency. Plug in the values into the relevant formulas to find the answer.