soil stresses (ch10) stress assumptions continuous material homogeneous (eng. props. = at all...
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Stress
Assumptions
Continuous material
Homogeneous (eng. props. = at all locations)
Isotropic (Modulus and are = in all directions)
Linear-elastic stress-strain properties
Stress Concept
xz
x
z
normal stresses
xx
xz
zx
zx
z
z
shear stresses
Ten (-), Comp (+)
Clock (+), CC (-)
Stresses in Soils
1. Geostatic Stresses
Due to soil’s self weight
2. Induced Stresses
Due to added loads (structures)
3. Dynamic Stresses
e.g., earthquakes
0.248811
0.241673
ASi
g
81.950 ti
0 10 20 30 40 50 60 70 80 900.4
0.2
0
0.2
0.4
Geostatic Stresses
TOTAL VERTICAL STRESS AT A POINT
z = depth = 5 m
A
Ground surface
Soil , = 18 kN/m3
AA z “total vertical stress at A”
Geostatic Stresses
PORE WATER PRESSURE AT A POINT
z = 5 m
A
Ground surface
Soil , = 18 kN/m3
ApwA hu “pore water pressure at A”
hpA
Lateral Stresses
z
A
Ground surface
Soil , = 18 kN/m3
' = Vertical effective stress = 'v
h' = Horiz. eff. stress = ?
The Mohr Circle
Describes 2-D stresses at a point in a material
Plots and on an = scale
Each point on the MC represents the and on one side of an element oriented at a certain angle
The angle between two points in the MC is = 2 times the angle between the planes they represent
The Mohr Circle
A 1
A 2B 1
B 2
B2
B1
A2
A1
A2
A1
B2
B1
If we change we will get two more points on the same MC.
A
B
The Mohr Circle – Principal Stresses
Planes A and B are called principal planes when there are no shear stresses (only normal stresses) acting on them.
1 = major principal stress
3 = minor principal stress