Mulungushi University
School of Engineering and Technology
Department of Civil Engineering
COURSE CODE: CIE 462 COURSE NAME: STRUCTURAL DYNAMICS
Tel: +260777037178
Email: ryanjosephmk.lectmu@gmail.com
QUIZ – SINGLE DEGREE OF MOTION
Given date: 03rd May 2022
Duration: 1h20min
Presentation of Work/Solutions carries with it 1 Mark
Questions:
Question 1 [10 Marks]
A vehicle of mass M=2 tonnes travels from Lusaka to Kabwe on a stretch of a deformed
bituminous road induced by various factors under investigation by a team of civil engineering
students from Mulungushi University.
Figure: Model of car on the deformed section of the road
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The deformed section can be described by a harmonique function given by: 𝑥 = 𝑥𝑔 cos(𝜔𝑡).
Considering that the tires have infinite stiffness and are always in contact with the surface of
the road, find the maximum vertical displacement 𝑥𝑚𝑎𝑥 that the car is subjected to for the
following cases of damping:
a) 𝜉 = 0
b) 𝜉 = 0.4
We are given: 𝐿 = 15𝑚; 𝑉 = 20𝑚/𝑠; 𝑀 = 2 𝑡𝑜𝑛𝑛𝑒𝑠; 𝐾 = 20𝐾𝑁/𝑚; 𝑥𝑔 = 3𝑐𝑚
Question 2 [10 Marks]
The building below is subjected to two different successive impulse loads as shown below.
Considering that, the given structure has the following initial conditions:
𝑥0 = 𝑥̇ 0 = 0
and
𝑀 = 10𝑡𝑜𝑛𝑛𝑒𝑠; 𝐾 = 1000 𝐾𝑁⁄𝑚 ; 𝑃0 = 30𝐾𝑁
a) Show that the displacements:
𝑥(𝑡 = 0.1s) = 1.63𝑐𝑚
𝑥(𝑡 = 1s) = 1.86𝑐𝑚
b) Compute the following displacements:
𝑥(𝑡 = 1.1s)
𝑥(𝑡 = 3.0s)
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