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Homework-03

# Homework-03 - 2 2 2 2 1 1 o n n n o n Q k Force due to the...

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FLORIDA INTERNATIONAL UNIVERSITY Department of Civil and Environmental Engineering CEG 5065C Soil Dynamics - Earthquake Engineering - Fall Term 2009 Homework No. 3 Due by 2400 hours Wednesday, 07 October 2009 Problem #1. Consider the figure below, describing a vibrating system without damping. The weight of the combined machine and its foundation is 400 kN. Assume that the spring constant is 400,000 kN/m. a) Redo the figure in AutoCAD with pastel colors. b) Determine the natural frequency and natural period of the system. c) What is the static deflection u s of this foundation? Assume that at time t = 0 , u = u o = 0 and the initial velocity = 0. d) Plot the dynamic force on the subgrade of the foundation due to the free part of the response time t = 0 to t = 2T . e) Plot the dynamic force on the subgrade of the foundation due to the forced part of the response time t = 0 to t = 2T . f) Plot the total dynamic force on the subgrade of the foundation due to both (they will be the algebraic sum).

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Unformatted text preview: 2 2 2 2 1 1 o n n n o n Q / k Force due to the free part = k sin t / Q / k Force due to the forced part = k sin t / ϖ - - - Problem #2. Consider the figure below that describes a vibrating system with damping. The foundation weighs 800 kN, where the foundation and the soil mass are idealized as a mass-spring-dashpot system. Assume that the spring constant is 200,000 kN/m, and the dashpot coefficient is 2,340 kN-s/m. The foundation is subject to a vertical earthquake force Q = Q o sinωt where Q o = 25 kN and ω = 100 radians/second. a) Redo the figure in AutoCAD with pastel colors. b) Determine the critical damping coefficient c c . c) Determine the damping ratio. d) Determine the logarithmic decrement. e) The damped natural frequency. f) Determine the amplitude of the vertical vibration. g) Determine the maximum dynamic force transmitted to the subgrade....
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