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
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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 andprocesses
- Rock deformation
Force vs. Stress
Force: That which changes, or tends to change, body motion
Newton's first law of motion: F=mamass in kg; acceleration in m/s2
1 Newton (1N) = 1kg m/s2
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), = F/A
1N/m2 = 1 Pa
what about units of stress?
100 MPa = 1 kbar
lithostatic stress
vertical force = Vg = L3g
vertical stress = L3g/L2 = gL
gL = (2700 kg/m3)(10m/s2)(1500m) = 40500000 Pa
= 40.5 MPa = .405 kbar
normal stress (traction): stress perpendicular to planeshear stress (traction): stress parallel to plane
a stress traction is a vector, like force
A complete definition of Stress = a description of tractions at a given point on all possible surfaces going through the point
1: Principal axis of greatest compressive stress
3: Principal axis of least compressive stress
1
1
33
1 and 3 always perpendicularand always perpendicular to planes of no shear stress
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
2sin2
2cos22
31
3131
S
N
= angle of plane from 1
2
3122
31
22
SN
Equation for a circle!
Geometric approach: Mohr Stress Diagram a plot of s vs. n
first step: plot 1 and 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 3.
mean stress: (1+3)/2 center of circlecauses dilation
differential stress: (1-3) diameter of circlecauses distortion
deviatoric stress: (1-3)/2 radius of circlecauses distortion