stress and the mohr diagram (d&r, 98-122)
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- PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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Why study stress?Dynamic/mechanical analysis: Interpret the stresses that produce deformation
- Tectonic stresses andprocesses
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- Rock deformation
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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.
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Body forces: act on every point within a body
GRAVITY! F = mg
Surface forces: act on a specific surface in a body
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Stress: that which tends to deform a body how is it different than force?
Deformation depends on how force is distributed!
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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
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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
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normal stress (traction): stress perpendicular to planeshear stress (traction): stress parallel to plane
a stress traction is a vector, like force
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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
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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
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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!
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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
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second step: Draw a line representing the plane at 2, measured from 3.
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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
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Mohr circles are useful for visualizing states of stress
hydrostatic: equal stress magnitude in all directions
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pore fluid pressure: serves to decrease confining pressure
effective stress = confining pressure – fluid pressure
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Next Lecture
Stress and Deformation
( D&R, 122-126; 226-252)
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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
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Ratio of S/N can be used to evaluate if failure is going to occur!