Stress and the Mohr diagram D

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Stress and the Mohr diagram(DR, 98-122)
1. Why learn about stress? 2. What is
stress?3. Lithostatic stress4. Important
stress tractions and stress ellipse 5. Stress
Mohr circle
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Detailed Structural Analysis

• Descriptive mapping, measurements

• Kinematics Interpreting movements responsible
  for developing structures
• Translation change in position
• Rotation change in orientation
• Distortion change in shape
• Dilation change in size

Dynamics/Mechanics relating deformation to
stresses Break out the math.
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Why study stress?
Dynamic/mechanical analysis Interpret the
stresses that produce deformation- Tectonic
stresses
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- Rock deformation
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• Mass total amount of materialcommonly measured
  in grams, kilograms and the like
• Volume total space occupied by a masscommonly
  expressed as liters, cubic centimeters and the
  like
• Density is the measure of the mass per unit
  volumecommonly expressed as grams per cubic
  centimeter or kilograms per cubic meter.
• r m/v (mass/volume)

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Force vs. Stress
Force That which changes, or tends to change,
body motionNewton's first law of motion
Fma mass in kg acceleration in m/s2 1 Newton
(1N) 1kg m/s2Forces are vector quantities
they have magnitude and direction.
GRAVITY! F mg
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Body forces act on every point within a body
(Gravitational and Electromagnetic)
Surface or Contact forces act on a specific
surface in a body (Gravitational loading, thermal
loading, and displacement loading)
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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!s F/A
(Force/Area)
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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/m2 1 Pa
100 MPa 1 kbar
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lithostatic stress
vertical force rVg rL3g
vertical stress rL3g/L2 rgL
rgL (2700 kg/m3)(9.8m/s2)(1500m) 39690000 Pa
39.69 MPa .397 kbar
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a stress traction is a vector, like force
normal stress (traction) stress perpendicular to
planeshear stress (traction) stress parallel to
plane
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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
s1
s1 axis of greatest principal stresss3 axis of
least principal stress
s3
s3
s1 and s3 always perpendicularand always
perpendicular to planes of no shear stress
s1
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Can also be 3-D
s1
Greatest
s2
intermediate
s3
Least
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What is it?
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The goal of stress analysis determine the normal
and shear stresses on any plane of any
orientation, given the direction and magnitude of
the principal stresses
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Analytical approach Fundamental stress equations
q angle of plane from s1
Equation for a circle!
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Geometric approach Mohr Stress Diagram a plot
of ss vs. sn
first step plot s1 and s3 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 2q, measured from s3.
The plane is at an angle of 55 (q) from s1- we
plot 2q.
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differential stress (s1-s3) diameter of
circle causes distortion
mean stress (s1s3)/2 center of
circle causes dilation
deviatoric stress (s1-s3)/2 radius of
circle causes distortion
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Mohr circles are useful for visualizing states of
stress
s1 s2 s3
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 ( DR,
122-126)
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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