16 July 2015GLG510 Advanced Structural Geology Force, Traction, and Stress.
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Transcript of 16 July 2015GLG510 Advanced Structural Geology Force, Traction, and Stress.
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April 22, 2023 GLG510 Advanced Structural Geology
Force, Traction, and Stress
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April 22, 2023 GLG510 Advanced Structural Geology
Physical quantities
• Force, F = m a; [=]kg m s-2 = N (newton)
• Stress, s[=](kg m s-2)m-2 = N m-2 = Pa
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April 22, 2023 GLG510 Advanced Structural Geology
Force: Newton’s Laws of Motion
• Law I: Every body continues in its state of rest, or in uniform motion in a straight line, unless it is compelled to change its state by forces impressed upon it.
• Law II: The rate of change of momentum is proportional to the impressed force and is made in the direction in which the force is impressed.
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April 22, 2023 GLG510 Advanced Structural Geology
Force: Newton’s Laws of Motion
m = massv = velocity vectort = timea = acceleration vector
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April 22, 2023 GLG510 Advanced Structural Geology
Force: Newton’s Laws of Motion
Dimensional analysis: fundamental units
Mass = amount of material in a bodyWeight = Force due to gravity action on a body1 liter of water has a mass of
on earth it weighson the moon it weighs
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April 22, 2023 GLG510 Advanced Structural Geology
What does a Newton feel like?
-Davis and Reynolds, p. 101
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April 22, 2023 GLG510 Advanced Structural Geology
Force: Newton’s Laws of Motion
• Law III: To every action there is always opposed an equal reaction, or the mutual actions of two bodies on each other are always equal in magnitude and opposite in direction
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April 22, 2023 GLG510 Advanced Structural Geology
Stress simply
• Simple definition of stress (for the moment) = pressure
-D+
R, p
. 105
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April 22, 2023 GLG510 Advanced Structural Geology
Stress and deformation
• Rheology: relationship between stress and deformation
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April 22, 2023 GLG510 Advanced Structural Geology
Stress and deformation
• Use your stress and deformation words correctly:
• Stress Deformation (strain)• Tension Extension• Compression Contraction or
shortening-watch out for Art Sylvester!
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April 22, 2023 GLG510 Advanced Structural Geology
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April 22, 2023 GLG510 Advanced Structural Geology
Tractions and stress
• A more strict definition of stress
• Traction is stress relative to a surface through a point p.
• Stress tensor is the field of tractions acting over a point p.
• Stress field is the entire collection of stress tensors in a body.
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April 22, 2023 GLG510 Advanced Structural Geology
Tractions and stress
• Start with equilibrium (Newton’s 3rd Law):
• Resolve each into its components in the coordinate directions
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April 22, 2023 GLG510 Advanced Structural Geology
Tractions and stress
• Total torque must vanish
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April 22, 2023 GLG510 Advanced Structural Geology
Tractions and stress
Rock quarried from the earth
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April 22, 2023 GLG510 Advanced Structural Geology
Tractions and stress
• Sign Conventions: compression positive
-Fundamentals of Rock Mechanics by Jaeger and Cook (3rd ed., p. 10)
In many engineering situations, we consider tension as positive and compression negative. This is not usually the case in structural geology.
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April 22, 2023 GLG510 Advanced Structural Geology
Tractions and stress
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April 22, 2023 GLG510 Advanced Structural Geology
Tractions and stress
(a) “Traction” or “Stress vector”
(b) Equilibrium“Cauchy’s relationship
(c) Components of the Traction Vector
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April 22, 2023 GLG510 Advanced Structural Geology
Stress tensor
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April 22, 2023 GLG510 Advanced Structural Geology
Stress tensor
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April 22, 2023 GLG510 Advanced Structural Geology
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April 22, 2023 GLG510 Advanced Structural Geology
3D Stress tensor
Note that the opposite sides have the stress components too!
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April 22, 2023 GLG510 Advanced Structural Geology
Stress tensor
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April 22, 2023 GLG510 Advanced Structural Geology
Andersonian Faulting Theory
• Key assumptions: – Earth’s surface is a free surface (so it has no
shear tractions acting along it). Therefore, 1, 2, 3 must be either parallel or perpendicular to it.
– A fault will slip in the direction of maximum resolved shear traction
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April 22, 2023 GLG510 Advanced Structural Geology
Andersonian Faulting Theory
Davis and Reynolds, p. 306
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April 22, 2023 GLG510 Advanced Structural Geology
Andersonian Faulting Theory
Davis and Reynolds, p. 306
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April 22, 2023 GLG510 Advanced Structural Geology
Andersonian Faulting Theory
Rowland and Duebendorfer
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April 22, 2023 GLG510 Advanced Structural Geology-Engelder, 1993, Stress regimes in the lithosphere, Princeton Univ. Press
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April 22, 2023 GLG510 Advanced Structural Geology
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April 22, 2023 GLG510 Advanced Structural Geology
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April 22, 2023 GLG510 Advanced Structural Geology
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April 22, 2023 GLG510 Advanced Structural Geology
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April 22, 2023 GLG510 Advanced Structural Geology
World Stress Map
http://www.world-stress-map.org/
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April 22, 2023 GLG510 Advanced Structural GeologyNorth America Stress Map
http://www.world-stress-map.org/