Solution Manual for Principles of Soil Dynamics 3rd Edition by Braja M. Das – All Chapters Covered

STUDY NOTES & REFERENCE GUIDE

ALL 12 CHAPTERS COVERED




SOLUTIONS MANUAL




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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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Chapter 2

2.1 a. Spring constant, k : The change in the force per unit length change of the spring.

b. Coefficient of subgrade reaction, k:
k
Spring constant divided by the foundation contact area, k =
A


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


d. 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.

e. Period, T: The time required for the motion to begin repeating itself.

n
f. Resonance: Resonance occurs when =1


g. Critical damping coefficient: cc = 2 k
mW
where k = spring constant; m = mass =
g

h. c c
Damping ratio: D = =
cc 2 km

where c = viscous damping coefficient; cc = critical damping coefficient

i. Damped natural frequency:

d = n 1 − D2

fd = 1 − D2 fn


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2.2 Weight of machine + foundation, W = 400 kN
Spring constant, k = 100,000 kN/m
W 400 kN
Mass of the machine + foundation, m = = = 40.77
g 9.81 m s2

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

1 k
fn = = = 7.88 Hz
2 m 2 40.77

1 1
From Eq. (2.18), T = = = 0.127 s
fn 7.88


2.3 Weight of machine + foundation, W = 400 kN
Spring constant, k = 100,000 kN/m

Static deflection of foundation is [Eq. (2.2)]
W
z = =
400
= 4 10−3 m = 4 mm
s
k 100,000


2.4 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 = v0 = 0

W 178 kN
a. Mass of the machine + foundation, m = = = 18.145
g 9.81 m s2

k
n = = = 62.11 rad/s
m
2 2
T= = = 0.101 s
n 62.11

b. The frequency of loading, f = 13.33 Hz

 = 2 f = 2 (13.33) = 83.75 rad/s




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