Solution Manual for Principles of Soil Dynamics (3rd Edition) by Braja M. Das and Zhe Luo

ALL 12 CHAPTERS COVERED
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SOLUTIONS MANUAL
d

, CONTENTS
Chapter Page

2.................................................................................................................................. 1

4 9

5 25

6 41

8................................................................................................................................ 51

9................................................................................................................................ 61

10 ............................................................................................................................... 65

11 ............................................................................................................................... 79

12 ............................................................................................................................... 91




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, Chapter2 d




2.1 a. Spring constant, k: The change in the force per unit length change of the spring.
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b. Coefficient of subgrade reaction, k: d d d d




k
Spring constant divided by the foundation contact area,
d d d d d d d
k = d d




A


c. Undamped natural circular frequency: d d d n = d rad/s
W
where m = mass = d d d d d




g


d. Undamped natural frequency: fn = (in Hz)
2
d d d d


m
d




Note: Circular frequencydefinestherateofoscillationintermofradians per unit time;
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2π radians being equal to one complete cycle of rotation.
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e. Period,T: Thetimerequiredfor the motiontobeginrepeating itself.
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n
f. Resonance: Resonance occurs when d d d d
d

=1 d






g. Critical damping coefficient: cc =2 km
d d
d
d




W
where k = spring constant; m = mass =
d d d d d d d d d




g

h. c c
Damping ratio: D = =
d


d d d d




cc 2
km
where c = viscous damping coefficient; cc = critical damping coefficient
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i. Damped natural frequency: d d




d =n 1− D2
d d d d




fd = 1− D2 fn
d
d d




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© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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, 2.2 Weightofmachine+ foundation,W=400 kN d d d d d d d d




Spring constant, k = 100,000 kN/m
d d d d d d




W 400 kN
= = 40.77
d d



Massofthemachine +foundation,m= d d d d d d d
d d




g 9.81 m s2d d




Natural frequency of undamped free vibration is [Eq. (2.19)]
d d d d d d d d




1 k
fn = = = 7.88 Hz
2 2
d d d



m 40.77
d




1 1
= = 0.127 s
d d d



From Eq. (2.18), T = d d d d
d d




fn d 7.88


2.3 Weightofmachine+ foundation,W=400 kN d d d d d d d d




Spring constant, k = 100,000 kN/m
d d d d d d




Static deflection of foundation is [Eq. (2.2)]
d d d d d d




z = 400
d
= = 410−3m = 4 mm
W
d d d d d d




d
100,000
s
k


2.4 External force to which the foundation is subjected, Q = 35.6sint kN
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f = 13.33 Hz
d d d




Weightofthemachine +foundation,W= 178kN d d d d d d d d d




Spring constant, k = 70,000 kN/m
d d d d d d




For thisfoundation, lettimet=0, z = z0 =0, zɺ=v0 = 0
d d d d d d d d d d
d
d d d d
d
d




W 178 kN
a. Mass of the machine + foundation, m= = = 18.145
d d


d d d d d d d d d




g 9.81 m s2
d d




k
n = d = = 62.11 rad/s d d



m
2 2
T= = = 0.101 s
d d d d


d d d d d




n 62.11

b. The frequencyof loading, f = 13.33 Hz
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= 2f = 2(13.33) = 83.75rad/s
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© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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