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i) Derive the equation of motion for the one-story building shown in Figure 1.1 and determine the natural frequency (in Hz). Assume the columns are axially rigid and the mass m can only translate horizontally, so that the columns undergo no rotation at the top. (10%) i) Suppose now the structure is built on slope such that one of the columns is shortened as shown in Figure 1.2. What is the percentage increase in the natural frequency? (5%) Jus EI EI EI EI

i) Derive the equation of motion for the one-story building shown in Figure 1.1 and determine the natural frequency (in Hz). Assume the columns are axially rigid and the mass m can only translate horizontally, so that the columns undergo no rotation at the top. (10%) i) Suppose now the structure is built on slope such that one of the columns is shortened as shown in Figure 1.2. What is the percentage increase in the natural frequency? (5%) Jus EI EI EI EI

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question 1 a) The one-story building shown in Figure 1.1 can be modelled in the first approximation as a SDOF system by regarding the columns as massless and the roof as rigid. i) Derive the equation of motion for the one-story building shown in Figure 1.1 and determine the natural frequency (in Hz). Assume the columns are axially rigid and the mass m can only translate horizontally, so that the columns undergo no rotation at the top. (10%) ii) Suppose now the structure is built on slope such that one of the columns is shortened as shown in Figure 1.2. What is the percentage increase in the natural frequency? (5%) m m Tua El EI El EI Figure 1.1 Figure 1.2 Hint: Use the information of the assumptions given in the question and the stiffness of the structural members with different boundary conditions discussed in class to find out the stiffness of each column. b) The damped spring-mass system shown in Figure 3.1 has a mass m= 100 kg, a stiffness k = 4x10° N/m, and a damping coefficient e = 6100 Ns/m. if the mass is subject to an initial displacement of x(0) = 30 mm and suddenly released with zero initial velocity, determine the amplitude of free vibration of the mass after 8, 16 and 24 oscillations. (10%) Figure 3.1 m
Transcribed Image Text:Question 1 a) The one-story building shown in Figure 1.1 can be modelled in the first approximation as a SDOF system by regarding the columns as massless and the roof as rigid. i) Derive the equation of motion for the one-story building shown in Figure 1.1 and determine the natural frequency (in Hz). Assume the columns are axially rigid and the mass m can only translate horizontally, so that the columns undergo no rotation at the top. (10%) ii) Suppose now the structure is built on slope such that one of the columns is shortened as shown in Figure 1.2. What is the percentage increase in the natural frequency? (5%) m m Tua El EI El EI Figure 1.1 Figure 1.2 Hint: Use the information of the assumptions given in the question and the stiffness of the structural members with different boundary conditions discussed in class to find out the stiffness of each column. b) The damped spring-mass system shown in Figure 3.1 has a mass m= 100 kg, a stiffness k = 4x10° N/m, and a damping coefficient e = 6100 Ns/m. if the mass is subject to an initial displacement of x(0) = 30 mm and suddenly released with zero initial velocity, determine the amplitude of free vibration of the mass after 8, 16 and 24 oscillations. (10%) Figure 3.1 m
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