All Chapters Covered
SOLUTIONS
, Solving
@Seismicisolation
chapter 2
@Seismicisolation
, تمرین سئواالت زوج فصل دوم
91 مهر دینبمیک خبک: درس
.سواالت زوج آخر فصل دوم را حل کنید
2.2 A machine foundation can be idealized to a mass-spring system, as shown in Figure
2.4.
Given
Weight of machine + foundation = 400 kN
Spring constant = 100,000 kN/m
Determine the natural frequency of undamped free vibration of this foundation and the
natural period.
: حل
√ √
2.3 Refer to Problem 2.2, What would be the static deflection zs of this foundation?
:حل
2.4 Refer to Example 2.3. For this foundation let time t = 0, z = z0 = 0.z0 = u0 = 0.
a. Determine the natural period T of the foundation.
b. Plot the dynamic force on the subgrade of the foundation due to the forced part of the
response for time t =0 to t = 2T.
c. Plot the dynamic force on the subgrade of the foundation due to the free part of the
response for t = 0 to 2T.
d. Plot the total dynamic force on the subgrade [that is, the algebraic sum of (b) and (c)].
Hint: Refer to Eq. (2.33)
: a حل
ُ ًوَدار ّب در اکسل رسن شد، 3.2 در کتبة ٍ تببع ارائِ شدُ در هتي سَال3.2 بب تَجِ بِ دادُ ّبی حبصل اس هثبل: b حل
.ٍ در ایٌجب قزار گزفتِ است
( )
( )
. رسن شدُ استt = 2T تبt = 0 ًوَدار در اس سهبى
T = 0.1012 s , 2T = 0.2024 s
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@Seismicisolation
Page | 1
, تمرین سئواالت زوج فصل دوم
91 مهر دینبمیک خبک: درس
Force due to forced part
50
40
30
dynamic force (KN)
20
10
0
-10 0 0.05 0.1 0.15 0.2 0.25
-20
-30
-40
-50
Time , t(s)
ٍ ُ ًوَدار ّب در اکسل رسن شد، 3.2 در کتبة ٍ تببع ارائِ شدُ در هتي سَال3.2 بب تَجِ بِ دادُ ّبی حبصل اس هثبل: c حل
.در ایٌجب قزار گزفتِ است
( )
( )
. رسن شدُ استt = 2T تبt = 0 ًوَدار در اس سهبى
T = 0.1012 s , 2T = 0.2024 s
Force due to free part
80
60
40
dynamic force (KN)
20
0
0 0.05 0.1 0.15 0.2 0.25
-20
-40
-60
-80
Time , t(s)
@Seismicisolation
@Seismicisolation
Page | 2
SOLUTIONS
, Solving
@Seismicisolation
chapter 2
@Seismicisolation
, تمرین سئواالت زوج فصل دوم
91 مهر دینبمیک خبک: درس
.سواالت زوج آخر فصل دوم را حل کنید
2.2 A machine foundation can be idealized to a mass-spring system, as shown in Figure
2.4.
Given
Weight of machine + foundation = 400 kN
Spring constant = 100,000 kN/m
Determine the natural frequency of undamped free vibration of this foundation and the
natural period.
: حل
√ √
2.3 Refer to Problem 2.2, What would be the static deflection zs of this foundation?
:حل
2.4 Refer to Example 2.3. For this foundation let time t = 0, z = z0 = 0.z0 = u0 = 0.
a. Determine the natural period T of the foundation.
b. Plot the dynamic force on the subgrade of the foundation due to the forced part of the
response for time t =0 to t = 2T.
c. Plot the dynamic force on the subgrade of the foundation due to the free part of the
response for t = 0 to 2T.
d. Plot the total dynamic force on the subgrade [that is, the algebraic sum of (b) and (c)].
Hint: Refer to Eq. (2.33)
: a حل
ُ ًوَدار ّب در اکسل رسن شد، 3.2 در کتبة ٍ تببع ارائِ شدُ در هتي سَال3.2 بب تَجِ بِ دادُ ّبی حبصل اس هثبل: b حل
.ٍ در ایٌجب قزار گزفتِ است
( )
( )
. رسن شدُ استt = 2T تبt = 0 ًوَدار در اس سهبى
T = 0.1012 s , 2T = 0.2024 s
@Seismicisolation
@Seismicisolation
Page | 1
, تمرین سئواالت زوج فصل دوم
91 مهر دینبمیک خبک: درس
Force due to forced part
50
40
30
dynamic force (KN)
20
10
0
-10 0 0.05 0.1 0.15 0.2 0.25
-20
-30
-40
-50
Time , t(s)
ٍ ُ ًوَدار ّب در اکسل رسن شد، 3.2 در کتبة ٍ تببع ارائِ شدُ در هتي سَال3.2 بب تَجِ بِ دادُ ّبی حبصل اس هثبل: c حل
.در ایٌجب قزار گزفتِ است
( )
( )
. رسن شدُ استt = 2T تبt = 0 ًوَدار در اس سهبى
T = 0.1012 s , 2T = 0.2024 s
Force due to free part
80
60
40
dynamic force (KN)
20
0
0 0.05 0.1 0.15 0.2 0.25
-20
-40
-60
-80
Time , t(s)
@Seismicisolation
@Seismicisolation
Page | 2
