STRESS
MECHANICS
study of the action and effect of forces on bodies.
"The Science of Motion"
Newton�s First Law of Motion- (Law of Inertia)
A body at rest will remain at rest and a body of motion will remain in motion unless acted upon by an outside force; i.e., a free body moves without acceleration.
Newton�s Second Law- (Law of Acceleration)-
Force equals the mass times the acceleration. F=ma
Newton�s Third Law-
A directed force is counteracted by an equal force in the opposite direction.
FORCE-
vector quantity with both magnitude and direction.
Force= (mass) (acceleration) F=ma
Body Forces-
forces that result from action of a field at every point within the body. E.g. gravity
Surface Forces-
forces that act on the specific surface area in a body.
STRESS
Stress s Force per unit area or the intensity of Force s=F/A
Stress units: 1 bar= 105 Pa= 1 atm; 1 kbar=108 Pa = 100 MPa
1 pascal = one pascal is one kilogram per meter per second squared;
that is, 1 Pa = 1 kg � m-1 � s-2.
1 MPa= 106 pascals
CLASSIFICATION OF STRESS
Compressive Stress By convention, Geologists consider compressive stress as Positive
(+) (this designation is opposite to that used by engineers)
Tensile Stress By convention, Geologists consider tensile stress as Negative
( - )
Normal Stress sh Stress directed perpendicular to a given plane
Shear Stress st Stress directed parallel to a given plane
Principal Stresses 3 orthogonal stress axes directed perpendicular to
principal planes upon which no shear stress exists.
s 1 >s 2 >s 3
s 1 = maximum compressive stress axis
s 2= intermediate stress axis
s 3= minimum compressive stress axis
Principal Planes Planes with no shear stress.
Contain 2 principal stress axes and normal to 3rd axis
Stress Field Total distribution of stress within a rock body
Components of Stress:
the orientation and magnitude of the stress state of a body can be defined by 9 components within the Cartesian coordinate system, defined by 3 mutually perpendicular axes:
In the direction of:
x y z
Stress on face normal to x: s xx s xy s xz
Stress on face normal to y: s yx s yy s yz
Stress on face normal to z: s zx s zy s zz
Note that we can define the stress state based on 6 independent stress vector components:
s xx , s yy , s zz (Normal stresses) and s xy , s yz , s xz (shear stresses)
ISOTROPIC VS. ANISOTROPIC STRESS
Isotropic Stress
All 3 principal stress axes of equal magnitude (s 1 =s 2 =s 3) defining a sphere.
Non-Deviatric Stress- Stress equal in all directions . s1= s2=s3.e.g. hydrostatic stress.
For any non-deviatric stresses, no shear stresses exist.
s1= s2=s3 can have any orientation, as stress equal in all orientations
Non-Deviatric Stress- Two predictions can be made from non-deviatric (static ) stresses:
1. no change in shape (no shear stress; no shear strain)
2. causes volume (decrease) changes and increases density
Mean Stress sm
Average stress of the three principal axes (s 1 + s 2+ s 3)/3
Hydrostatic Stress= mean stress= s1+ s2+s3
3
Anisotropic Stress Unequal Stress
At least one principal stress has a magnitude not equal to other principal stresses
Deviatric Stress- sdev directed stress;
One or more stress axes are not equal to the other two.
Compressive Stress - denoted as a positive (+) force
Tensile Stress - denoted as a negative (-) force
Normal Stress- (sn) force applied perpendicular to a plane.
Shear Stress- (st ) force applied parallel to a plane (ccw=pos; cw=neg); max at 450.
Transpression- shear plus compressison
Transtension- shear plus tension
Deviatric Stress- two predictions:
1. there will be shear strain as a result of stress
2. shear strain will result in distortion (change in shape)
i.e., Causes Shape Changes
Deviatric Stress- Directed stress;
component of stress that remains after mean stress is removed.
EFFECTIVE STRESS & FLUID PORE PRESSURE-
Effective Stress= normal stress minus the pore fluid pressure.
Fluid Pore Pressure (Pf)-
hydrostatic pressure exerted by interstitial water.
STRESS STATES:
Total Stress stotal= sm + sdev.
General Triaxial Stress s 1 >s 2 >s 3 and not equal to 0
Biaxial Stress one principal stress axis equals 0
Uniaxial Tension s 1 =s 2 =s 3 < 0
Uniaxial Compression s 1 =s 2 =s 3 > 0
Hydrostatic Stress s 1 =s 2 =s 3
Lithostatic Stress s 1 =s 2 =s 3;
stress exerted on a point at depth overlain by a body of rock
Homogeneous Stress
Stress at any point in the body is of equal magnitude and direction.
Magnitude & orientation of the stress ellipsoids are the same throughout the rock body
All principal stresses have same orientation and magnitude; less complex, less common.
s 1 , s 2 , s 3 are not (generally) equal; i.e., homogeneous stress is not necessarily isotropic.
Inhomogeneous Stress
Stress is of different magnitude and/or orientation at different points in a body;
More complex stress conditions within rock body; difficult to analyze; common.
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