ALL 12 CHAPTERS COVERED
SOLUTIONS MANUAL
,
2 ................................................ ...................................................
............ 1
4 ................................................ ...................................................
........... 9
5 ................................................ ...................................................
.......... 25
6 ................................................ ...................................................
.......... 41
8 ................................................ ...................................................
.......... 51
9 ................................................ ...................................................
.......... 61
10 ...................................................................................................
.......... 65
11 ...................................................................................................
.......... 79
12 ...................................................................................................
.......... 91
,
Chapter 2
Spring constant, k The change in the force per unit length change of the spring.
Coefficient of subgrade reaction, k :
k
Spring constant divided by the foundation contact area, k
A
k
Undamped natural circular frequency: n
rad/s
m
W
where m = mass =
g
1 k
Undamped natural frequency: f n (in Hz)
2 m
Note: Circular frequency defines the rate of oscillation in term of radians per unit
time; 2π radians being equal to one complete cycle of rotation.
Period, T: The time required for the motion to begin repeating itself.
Resonance: Resonance occurs when n 1
Critical damping coefficient: cc 2 km
W
where k = spring constant; m = mass =
g
c c
Damping ratio: D =
cc 2 km
where c = viscous damping coefficient; cc = critical damping coefficient
Damped natural frequency:
n1 D
2
d
fd 1 D 2n f
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
,
Weight of machine + foundation, W = 400 kN
Spring constant, k = 100,000 kN/m
W 400
Mass of the machine + foundation, m = = = 40.77 kN
g 9.81 m s2
Natural frequency of undamped free vibration is [Eq. (2.19)]
k = 1 100,000 =
f m 40.77
1 2
n
2
1 1
From Eq. (2.18), T = = =
fn 7.88
Weight of machine + foundation, W = 400 kN
Spring constant, k = 100,000 kN/m
Static deflection of foundation is [Eq. (2.2)]
z 400 4 10 3
m=
W 100,000
s
k
External force to which the foundation is subjected, Q 35.6sin t kN
f = 13.33 Hz
Weight of the machine + foundation, W = 178 kN
Spring constant, k = 70,000 kN/m
For this foundation, let time t = 0, z = z0 = 0, zɺ = v 0 = 0
W 178
Mass of the machine + foundation, m = = = 18.145 kN
g 9.81 m s2
k 70,000
n = 62.11 rad/s
m 18.145
T 2
=
2 62.11
n
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
SOLUTIONS MANUAL
,
2 ................................................ ...................................................
............ 1
4 ................................................ ...................................................
........... 9
5 ................................................ ...................................................
.......... 25
6 ................................................ ...................................................
.......... 41
8 ................................................ ...................................................
.......... 51
9 ................................................ ...................................................
.......... 61
10 ...................................................................................................
.......... 65
11 ...................................................................................................
.......... 79
12 ...................................................................................................
.......... 91
,
Chapter 2
Spring constant, k The change in the force per unit length change of the spring.
Coefficient of subgrade reaction, k :
k
Spring constant divided by the foundation contact area, k
A
k
Undamped natural circular frequency: n
rad/s
m
W
where m = mass =
g
1 k
Undamped natural frequency: f n (in Hz)
2 m
Note: Circular frequency defines the rate of oscillation in term of radians per unit
time; 2π radians being equal to one complete cycle of rotation.
Period, T: The time required for the motion to begin repeating itself.
Resonance: Resonance occurs when n 1
Critical damping coefficient: cc 2 km
W
where k = spring constant; m = mass =
g
c c
Damping ratio: D =
cc 2 km
where c = viscous damping coefficient; cc = critical damping coefficient
Damped natural frequency:
n1 D
2
d
fd 1 D 2n f
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
,
Weight of machine + foundation, W = 400 kN
Spring constant, k = 100,000 kN/m
W 400
Mass of the machine + foundation, m = = = 40.77 kN
g 9.81 m s2
Natural frequency of undamped free vibration is [Eq. (2.19)]
k = 1 100,000 =
f m 40.77
1 2
n
2
1 1
From Eq. (2.18), T = = =
fn 7.88
Weight of machine + foundation, W = 400 kN
Spring constant, k = 100,000 kN/m
Static deflection of foundation is [Eq. (2.2)]
z 400 4 10 3
m=
W 100,000
s
k
External force to which the foundation is subjected, Q 35.6sin t kN
f = 13.33 Hz
Weight of the machine + foundation, W = 178 kN
Spring constant, k = 70,000 kN/m
For this foundation, let time t = 0, z = z0 = 0, zɺ = v 0 = 0
W 178
Mass of the machine + foundation, m = = = 18.145 kN
g 9.81 m s2
k 70,000
n = 62.11 rad/s
m 18.145
T 2
=
2 62.11
n
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
