Q1) A fixed-fixed steel beam, of length 5 m, width 0.5 m, and thickness 0.1 m, carries an electric motor of mass 75 kg and speed 1200 rpm at its mid-span, as shown in the figure. A rotating force of magnitude Fo- 5000 N is developed due to the unbalance in the rotor of the motor. a) Find the amplitude X of steady-state vibrations by disregarding the mass of the beam. b) Identify the difference in this amplitude X, if we introduced damping of a damping ratio ( = 0.3 c) What will be the amplitude if the mass of the beam is considered? d) Identify the difference in this amplitude X, if we introduced damping of a damping ratio = 0.3 e) Name the damping cases, (<1,5 = 1 and (>1 aut Fo mm.
Q1) A fixed-fixed steel beam, of length 5 m, width 0.5 m, and thickness 0.1 m, carries an electric motor of mass 75 kg and speed 1200 rpm at its mid-span, as shown in the figure. A rotating force of magnitude Fo- 5000 N is developed due to the unbalance in the rotor of the motor. a) Find the amplitude X of steady-state vibrations by disregarding the mass of the beam. b) Identify the difference in this amplitude X, if we introduced damping of a damping ratio ( = 0.3 c) What will be the amplitude if the mass of the beam is considered? d) Identify the difference in this amplitude X, if we introduced damping of a damping ratio = 0.3 e) Name the damping cases, (<1,5 = 1 and (>1 aut Fo mm.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![Q1) A fixed-fixed steel beam, of length 5 m, width 0.5 m,
and thickness 0.1 m, carries an electric motor of mass 75 kg
and speed 1200 rpm at its mid-span, as shown in the figure.
A rotating force of magnitude Fo- 5000 N is developed due
to the unbalance in the rotor of the motor.
a) Find the amplitude X of steady-state vibrations by
disregarding the mass of the beam.
b) Identify the difference in this amplitude X, if we
introduced damping of a damping ratio = 0.3
c) What will be the amplitude if the mass of the beam is
considered?
d) Identify the difference in this amplitude X, if we
introduced damping of a damping ratio = 0.3
to
1/20
e) Name the damping cases, < < 1,5 = 1 and (>1
Formulas:
I
1-2b h³, where I is area moment of inertia, b is beam cross section width and h is cross section thickness
192 EI
K
where K is beam stiffness, I is beam length, E is modulus of elasticity (for steel E-2.07 *10¹¹ Pa)
1³
1
{-AT-K]}}
√(1-2)²
+(25r)²
+ 25-
X
8gt
Where 8st =, r=
Fo](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0280cc21-8041-4b35-83af-094302e775e5%2F83456c75-58df-45f1-9d2e-1b307b5d3189%2F6gs13zj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1) A fixed-fixed steel beam, of length 5 m, width 0.5 m,
and thickness 0.1 m, carries an electric motor of mass 75 kg
and speed 1200 rpm at its mid-span, as shown in the figure.
A rotating force of magnitude Fo- 5000 N is developed due
to the unbalance in the rotor of the motor.
a) Find the amplitude X of steady-state vibrations by
disregarding the mass of the beam.
b) Identify the difference in this amplitude X, if we
introduced damping of a damping ratio = 0.3
c) What will be the amplitude if the mass of the beam is
considered?
d) Identify the difference in this amplitude X, if we
introduced damping of a damping ratio = 0.3
to
1/20
e) Name the damping cases, < < 1,5 = 1 and (>1
Formulas:
I
1-2b h³, where I is area moment of inertia, b is beam cross section width and h is cross section thickness
192 EI
K
where K is beam stiffness, I is beam length, E is modulus of elasticity (for steel E-2.07 *10¹¹ Pa)
1³
1
{-AT-K]}}
√(1-2)²
+(25r)²
+ 25-
X
8gt
Where 8st =, r=
Fo
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