chapter 9: Stresses in soil mass 1- Stresses caused by...
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1 chapter 9: Stresses in soil mass 1- Stresses caused by point load:
Transcript of chapter 9: Stresses in soil mass 1- Stresses caused by...
1
chapter 9: Stresses in soil mass
1- Stresses caused by point load:
2
Problem 1) 9.6 Text book
Consider concentrated loads of
15kN, 20kN and 30kN acts at
A, B and C respectively.
Determine the increase in stress below
point D at depth of 5 m.
22
12
yxr
IZ
PZ
CZBZAZZ
Point r (m) Z (m) r/Z I1
A 2.5 5 0.5 0.2733 B 2.5 5 0.5 0.2733
C 2 5 0.4 0.3294
2
222
/78.0
3294.05
302733.0
5
202733.0
5
15
mkNZ
Z
CZBZAZZ
x
y
z
Table 9.1 P230 text book
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2- Stresses caused by line load:
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Problem 2) 9.7 text book
Apoint at find
5.1,1,2
00.0
/75
z
21
2
1
mZmxmx
q
mkNq
2
z
1
2
2
/25.15.1
75025.0
025.0/
P.232 9.2 tablefrom25.1
3
5.1,312 :For
00.01
1
mkN
zqz
x
mzmxq
z
qzzqz
qzqzz
5
3- Vertical stress caused by strip load:
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Problem 3) 9.12 text book
Determine the vertical stress
increase at point A.
5.112
922
833.012
522
B
x
B
z
From table 9.3 P 235 – 236
psf
qB
z
qB
z
qB
z
Z
Z
Z
Z
11.6335018.0
18.0833.02
@:ioninterpolatBy
195.09.02
@
173.08.02
@
q = 350psf
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4- Vertical stress due to embankment:
2Iqoz
هثلث أ يجة لرطثيق ر العالقح أى يكى الجزء هي السدم الوساد حساب اإلجاداخ الاذجح ه عثازج عي هسرطيل أ
.هسرطيل هثلث
I 2
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Problem4) 9.15 text book
Determine the vertical added stress
At points A, B and C due to the embankment load.
At point A:
psfq
z
B
z
B
o
AzAzz
345030115
415
60
5.015
5.7
:AFor
2
1
1
21
From figure 9.11, P238:
psfIAz 158746.0345046.0
12
From symmetry, psfpsfAzAzAz 3174158721587
12
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At point B:
psfq
z
B
z
B
o
BzBzz
345030115
415
60
015
0
:BFor
2
1
1
21
From figure 9.11, P238:
psfIBz 144942.0345042.0
12
psfq
z
B
z
B
o 345030115
415
60
115
15
:BFor
2
1
2
From figure 9.11, P238:
psfIBz 165648.0345048.0
22
psfBz 310516561449
10
At point C:
psfq
z
B
z
B
o
CzCzz
345030115
415
60
515
75
:CFor
2
1
1
21
From figure 9.11, P238:
psfICz 17255.034505.0
12
psfq
z
B
z
B
o 345030115
415
60
015
0
:CFor
2
1
2
From figure 9.11, P238:
psfICz 144942.0345042.0
22
psfCz 27614491725
Solve example 9.5 P.239 Text book (هن جدا).
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5- Added vertical stress below center of loaded circular area:
6- Added vertical stress below any point of loaded circular area:
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7- Added vertical stress caused by rectangular loaded area:
.يشرسط أى ذكى القطح الوساد حساب االجاداخ عدا ذقع في طسف الوسرطيل
:هالحظح، اك حالح خاصح اذا كاد القطح في هرصف الوسرطيل يرن حساب االجاداخ عدا تالعالقح
B
zn
B
Lm
qI
21
1
4
Look table 9.8 P 249 to find I4.
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Problem 5) 9.20 text book:
Determine the added vertical
Stress at depth 2m below
Point B.
Point B is neither corner nor center, we have to divide the rectangle to sub
rectangles at which point B represent corner as follow:
kpa
II
I
n
m
mmLmB
I
I
n
m
mmLmB
I
IIIIq
z
z
048.421063.00931.01431.01247.090
1063.0 0.0931,:mannersimilar By
0.1431
2.12
4.2
0.62
2.1
2 z , 4.2 , 2.1
:For
0.1247
0.82
6.1
0.62
2.1
2 z , 6.1 , 2.1
:For
3433
32
32
31
31
34333231
2/90 mkNq
