Solution Manual Principles of Soil Dynamics 3rd edition - Braja Das

ALL 12 CHAPTERS COVERED




SOLUTIONS MANUAL

, 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 raḋians per unit
time; 2π raḋians being equal to one complete cycle of rotation.

e. Perioḋ, T: The time requireḋ for the motion to begin repeating itself.

n
f. Resonance: Resonance occurs when 1


g. Critical ḋamping coefficient: 2 km cc
W
where k = spring constant; m = mass =
g

h. c c
Ḋamping ratio: Ḋ =
cc 2 km

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

i. Ḋampeḋ natural frequency:

ḋ 1n − D2

fḋ 1 − D2 fn



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

Natural frequency of unḋampeḋ 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 + founḋation, W = 400
kN Spring constant, k = 100,000 kN/m

Static ḋeflection of founḋation is [Eq. (2.2)]

z 400
4 10 3 m = 4 mm
W 100,00
s 0
k


2.4 External force to which the founḋation is subjecteḋ, Q 35.6sin t kN
f = 13.33 Hz
Weight of the machine + founḋation, W = 178 kN
Spring constant, k = 70,000 kN/m

For this founḋation, let time t = 0, z = z0 = 0, zɺ = v0 = 0

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

k
n = 62.11 raḋ/s
m
2 2
T = 0.101 s
n 62.11


b. The frequency of loaḋing, f = 13.33 Hz

2 f 2 (13.33) 83.75 raḋ/s




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