Complete Solutions Manual for Essentials of Structural Dynamics Hector Estrada Luke S. Lee 1st Edition Full Chapters solutions are included for end of chapters problems chapter 1 Introduction chapter 2 Free Vibration of Single-Degree-of-Freedom Systems chapter 3 Forced Vibration Response of SDOF ...
1.1 Consider a rigid column having mass m, length L, and constrained to move horizontally at
mid-height by a spring having a stiffness k as shown below. Draw a free-body diagram
(FBD) of the column after a time-dependent vertical force is applied and formulate the
equation of motion using D’Alembert’s Principle.
p(t)
m L
k
Answer
i) Draw the FBD including inertial force and moment
= L
p(t)
L/2
W
I G k
G müx
1.2 Consider a rigid column having mass m, length L, and constrained to move horizontally at
the base by a rotational spring having a stiffness k as shown below. Draw a free-body
diagram (FBD) of the column after a time-dependent vertical force is applied and formulate
the equation of motion using D’Alembert’s Principle.
p(t)
m L
k
Answer
i) Draw the FBD including inertial force and moment
= L
p(t)
L/2
W
I G
G müx
1.3 Consider a rigid beam having mass m, span L, and constrained to move vertically at the right
support by a linear spring having a stiffness k and constrained at the left support by a
rotational spring having a stiffness k as shown below. Draw a free-body diagram (FBD) of
the beam after a time-dependent vertical force is applied and formulate the equation of
motion in terms of the rotation of the beam using D’Alembert’s Principle.
p(t)
k m
k
50ft
Answer
i) Draw the FBD including inertial force and moment
p(t)
W I G
𝑀𝐴 = 𝑘𝜃 𝜃
G
Ax
Ay = L
L/2 L/2 k
müy
1.4 Determine the effective weight at the roof and floor levels for a 60ft by 150ft, three-story
office building with equal story heights of 10ft and the following loading:
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