DHARM
STRESS DISTRIBUTION IN SOIL 369
B=2a q/unit area
0
a
2a
3a
4a
0.9 q
0.8 q
0.7 q
0.6 q
0.5 q
0.4 q
0.2 q
0.3 q
0.15 q
0.1 q
0.05 q
B=2a q/unit area
0
a
2a
3a
4a
0.2 q
0.275 q
0.3 q
0.275 q
0.25 q
0.225 q
0.2 q
0.125 q
0.10 q
0.075 q
0.05 q
(a) For vertical stress
(b) For shear stress
Fig. 10.13 Pressure bulbs for vertical and shear stress due to uniform
load on a circular area (After Jürgenson, 1934)
10.5.1 Uniform Load on An Annular Area (Ring Foundation)
This case may arise in the case of a foundation for hollow circular bins, silos, etc.
Let an annular area of a inner radius ai and outer radius ao be loaded uniformly at q per
unit area. (Fig. 10.14)
q
Inner circular
boundary
Outer
circular
boundary
Annular
area
loaded
uniformly
ai
ao
Fig. 10.14 Uniformly loaded annular area (Ring loading)
Applying the case of a uniformly loaded circular area just considered, the vertical stress
at a depth z directly beneath the centre of the ring, σz, may be written:
σz = q
a
z
q
a
z
oi
1
1
1
1
1
1
2 32 2 32
−
+F
HG
I
KJ
R
S
|
T|
U
V
|
W|
L
N
M M M M M M
O
Q
P P P P P P
−−
+F
HG
I
KJ
R
S
|
T|
U
V
|
W|
L
N
M M M M M M
O
Q
P P P P P P
//