CEE 502 Problem Set 4 Winter 2008
(Due 5:00 PM, Friday, Feb 8, in 233 More)
(YOU MAY WORK IN GROUPS OF TWO ON THIS ASSIGNMENT)
Reading: Chopra Sections 3.1-3.7, 4.1 – 4.9
1. Solve Chopra Problem 3.2.
2. Solve Chopra Problem 3.10.
3. The undamped, single-degree-
of-freedom cantilever system
shown is subjected to a blast
loading, F(t), with the following
magnitude.
2
max 1
() 1 4 2
b
t
Ft F T
⎡⎤
⎛⎞
⎢⎥
=−−
⎜⎟
⎢⎥
⎝⎠
⎣⎦
where Tb is the duration of the
blast loading.
a) Using the method of undetermined coefficients, determine the displacement history of
the mass for twice the blast length, if the blast duration is equal to:
(i) Tn/2, where Tn is the natural period of the oscillator
(ii) Tn
(iii) 2 Tn
b) Neatly plot the normalized displacement (u(t)/ustatic) solution versus t/Tb for t/Tb = 0
to 2.
c) For the three blast length, determine the maximum displacement response during the
time period t/Tb = 0 to 2.
d) Which of the pulse lengths resulted in the largest maximum displacement? Is this
reasonable? Explain.
F(t)
t
Tb
Fmax
F(t)
L
m
E, I
