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.

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

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/N can be used to evaluate if failure is going to occur!