ALL 12 CHAPTERS COVERED
fg fg fg
SOLUTIONS MANUAL
fg
, CONTENTS
Chapter Page
2 .......................................................................................................................... 1
4 9
5 25
6 41
8 ........................................................................................................................ 51
9 ........................................................................................................................ 61
10 ....................................................................................................................... 65
11 ....................................................................................................................... 79
12 ....................................................................................................................... 91
@
@sseeisismmicicisisoolalatitoionn
, Chapter 2 fg
2.1 a. Spring constant, k :
fg fg fg f g The change in the force per unit length change of the spring.
fg fg fg fg fg fg fg fg fg fg fg
b. Coefficient of subgrade reaction, k: fg fg fg fg
k
Spring constant divided by the foundation contact
fg fg fg fg fg fg
k fg f g
area,
fg
A
c. Undamped natural circular fg fg n rad/s
frequency:
fg fg
W
where m = mass =
fg fg fg fg fg
g
d. Undamped natural fg fn
gf
f g
(in Hz) fg
frequency:
2
fg
m
Note: Circular frequency defines the rate of oscillation in term of radians per unit
fg fg fg fg fg fg fg fg fg fg fg fg fg
time; 2π radians being equal to one complete cycle of rotation.
fg fg fg fg fg fg fg fg fg fg fg
e. Period, T: The time required for the motion to begin repeating itself.
fg fg fg fg fg fg fg fg fg fg fg
n
f. Resonance: Resonance occurs when f g fg fg fg
f g
1 gf
g. Critical damping fg cc 2 f g
fg
coefficient:
fg km
W
where k = spring constant; m = mass =
fg fg fg fg fg fg fg fg fg
g
h. c c
f g
Damping ratio: D = fg f g fg f g
cc 2
km
where c = viscous damping coefficient; cc = critical damping coefficient
fg fg fg fg fg fg fg fg fg fg
i. Damped natural frequency: fg fg
d n 1 D2
fg fg gf fg
@ 1
@sseeisism
m icicisisoolalatitoionn
© fg2017 fgCengage fgLearning®. fgMay fgnot fgbe fgscanned, fgcopied fgor fgduplicated, fgor fgposted fgto fga fgpublicly fgaccessible fgwebsite, fgin fgwhole
fgor fgin fgpart.
, fd f g
1 D2 fn
gf fg
@ 2
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m icicisisoolalatitoionn
© fg2017 fgCengage fgLearning®. fgMay fgnot fgbe fgscanned, fgcopied fgor fgduplicated, fgor fgposted fgto fga fgpublicly fgaccessible fgwebsite, fgin fgwhole
fgor fgin fgpart.
fg fg fg
SOLUTIONS MANUAL
fg
, CONTENTS
Chapter Page
2 .......................................................................................................................... 1
4 9
5 25
6 41
8 ........................................................................................................................ 51
9 ........................................................................................................................ 61
10 ....................................................................................................................... 65
11 ....................................................................................................................... 79
12 ....................................................................................................................... 91
@
@sseeisismmicicisisoolalatitoionn
, Chapter 2 fg
2.1 a. Spring constant, k :
fg fg fg f g The change in the force per unit length change of the spring.
fg fg fg fg fg fg fg fg fg fg fg
b. Coefficient of subgrade reaction, k: fg fg fg fg
k
Spring constant divided by the foundation contact
fg fg fg fg fg fg
k fg f g
area,
fg
A
c. Undamped natural circular fg fg n rad/s
frequency:
fg fg
W
where m = mass =
fg fg fg fg fg
g
d. Undamped natural fg fn
gf
f g
(in Hz) fg
frequency:
2
fg
m
Note: Circular frequency defines the rate of oscillation in term of radians per unit
fg fg fg fg fg fg fg fg fg fg fg fg fg
time; 2π radians being equal to one complete cycle of rotation.
fg fg fg fg fg fg fg fg fg fg fg
e. Period, T: The time required for the motion to begin repeating itself.
fg fg fg fg fg fg fg fg fg fg fg
n
f. Resonance: Resonance occurs when f g fg fg fg
f g
1 gf
g. Critical damping fg cc 2 f g
fg
coefficient:
fg km
W
where k = spring constant; m = mass =
fg fg fg fg fg fg fg fg fg
g
h. c c
f g
Damping ratio: D = fg f g fg f g
cc 2
km
where c = viscous damping coefficient; cc = critical damping coefficient
fg fg fg fg fg fg fg fg fg fg
i. Damped natural frequency: fg fg
d n 1 D2
fg fg gf fg
@ 1
@sseeisism
m icicisisoolalatitoionn
© fg2017 fgCengage fgLearning®. fgMay fgnot fgbe fgscanned, fgcopied fgor fgduplicated, fgor fgposted fgto fga fgpublicly fgaccessible fgwebsite, fgin fgwhole
fgor fgin fgpart.
, fd f g
1 D2 fn
gf fg
@ 2
@sseeisism
m icicisisoolalatitoionn
© fg2017 fgCengage fgLearning®. fgMay fgnot fgbe fgscanned, fgcopied fgor fgduplicated, fgor fgposted fgto fga fgpublicly fgaccessible fgwebsite, fgin fgwhole
fgor fgin fgpart.