Transcript Slide 1
Announcements Next week lab:
1-3 PM Mon. and Tues. with Andrew McCarthy.
Please start on lab before class and come prepared with specific questions Cottonwood wash ex. Due on Mon. in lecture
There will be NO lecture next Wed., Oct. 2.
Please use the time to: 1) Study important terms/concepts at end of Powerpoint lectures 2) Work on practice problems (perhaps as a group in this room) 3) Fault project
Stress and the Mohr diagram (D&R, 98-122)
1. Why learn about stress? 2. What is stress?
3. Lithostatic stress 4. Important stress tractions and stress ellipse 5. Stress Mohr circle
Why study stress?
Dynamic/mechanical analysis:
Interpret the stresses that produce deformation - Tectonic stresses and processes
-
Rock deformation
Force vs. Stress
Force:
That which changes, or tends to change, body motion
Newton's first law of motion:
F=ma mass in kg; acceleration in m/s 2 1 Newton (1N) = 1kg m/s 2 Forces are vector quantities; they have magnitude and direction.
Body forces: act on every point within a body GRAVITY! F = mg Surface forces: act on a specific surface in a body
Stress:
that which tends to deform a body how is it different than force?
Deformation depends on how force is distributed!
Stress may be thought of as a description of force concentration
Stress on a plane (traction),
s
= F/A
what about units of stress?
1N/m 2 = 1 Pa 100 MPa = 1 kbar
lithostatic stress vertical force =
r
Vg =
r
L 3 g vertical stress =
r
L 3 g/L 2 =
r
gL
r
gL = (2700 kg/m 3 )(10m/s 2 )(1500m) = 40500000 Pa = 40.5 MPa = .405 kbar
a stress traction is a vector, like force normal stress (traction):
stress perpendicular to plane
shear stress (traction):
stress parallel to plane
s
3
A complete definition of
Stress =
a description of tractions at a given point on
all
possible surfaces going through the point s
1
s
1:
Principal axis of greatest compressive stress s
3:
Principal axis of least compressive stress s
3
s
1 and
s
3 always perpendicular and always perpendicular to planes of no shear stress
s
1
The
goal
of stress analysis is to determine the normal and shear stresses on any plane of any orientation, given the directions and magnitudes of the principal stresses
Analytical approach: Fundamental stress equations
s
N
s
S
s 1 s 1 s 3 2 s 3 2 sin s 1 2 s 3 2 cos 2
=
angle of plane from s 1 s
N
s 1 s 3 2 2 s
S
2 s 1 s 3 2 2
Equation for a circle!
Geometric approach: Mohr Stress Diagram a plot of
s
s vs.
s
n first step:
plot s 1 and s 3 recalling that they are in directions of no shear stress; draw Mohr circle
second step:
Draw a line representing the plane at 2 , measured from s 3.
differential stress: (
s
1 -
s
3 ) diameter of circle
causes distortion
mean stress: (
s
1 +
s
3 )/2 center of circle
causes dilation
deviatoric stress: (
s
1 -
s
3 )/2 radius of circle
causes distortion
Mohr circles are useful for visualizing states of stress hydrostatic:
equal stress magnitude in all directions
pore fluid pressure:
serves to decrease confining pressure
effective stress
= confining pressure – fluid pressure
Next Lecture
Stress and Deformation
( D&R, 122-126; 226-252)
Important terminology/concepts
force vs. stress static vs. dynamic equilibrium body forces vs. contact forces lithostatic stress definition of stress greatest/least principal stress directions normal stress (traction) shear stress (traction) Mohr circle stress diagram mean stress differential stress deviatoric stress effective stress pore fluid pressure hydrostatic state of stress dynamic/mechanical analysis
Ratio of s S / s N can be used to evaluate if failure is going to occur!