2 Basic Physics Force Stress that which changes the state of rest or the state of motion of a body F=maStressforce applied to an area σ=F/A
3 Basic PhysicsScalarPossesses only a magnitude at some point in time or spaceVectorPossesses both magnitude and directionTensorA field of data with magnitudes and directions
4 Basic PhysicsTensorsZero-order tensor is a scalar like temperature and has only 1 componentFirst-order tensor is a vector like wind direction and is described by 3 components (time, magnitude, direction)Second-order tensor relates sets of tensors to each other and has 9 componentsThe number of components may be determined from 3nwhere n in the order of the tensor
5 Basic Physics Stress can be Tensional - Pulling apart Compressional - Pushing together
6 Basic PhysicsStress on a surface can be broken into two vector componentsNormal Stress (σn) - acts perpendicular to the reference surfaceShear Stress (τ)- acts parallel to the surface
7 Basic Physics Principal normal stress components (σ1, σ2, and σ3) These are oriented perpendicular to each other and σ1 σ2 σ3Differential stress is the difference between the maximum (σ1) and the minimum (σ3)Mean stress is (σ1 + σ2 + σ3)/3If the differential stress exceeds the strength of the rock, permanent deformation occurs
8 Basic Physics Lithostatic state of stress Occurs where the normal stress is the same in all directionsHydrostatic PressureConfining stress acting on a body submerged in waterLithostatic PressureConfining stress acting on a body under ground
9 Stress on a plane Horizontal plane F = ma = volume x density x accelerationF = 104 m3 x 2,750 kg m-3 x 9.8 ms-2Plane is 1 x 1 m, A = 1 m2What is the Stress?
10 Stress on a plane σ=F/A F = (2.7 x 108 kg ms-2)/1m2 2.7 x 108 kg m-1s-2 or 2.7 x 108 Pa or 269.5MPa
11 Stress on a plane Inclined Plane at 45º Through the same 1m x 1m space, actually has a larger surface area, now 1.41 m2Still F = 2.7 x 108 kg m s-2So σ=F/Aσ= (2.7 x 108 kg m s-2)/1.41 m2or 191 MPaHow does that compare to the stress on the horizontal plane?
12 Stress on a planeStress can be broken down into components of normal and shear stress.σn = σ cos 45º= 191 MPa x 0.707= 135 MPaτ = σ sin 45º
13 Stress EllipsoidA Shear Ellipsoid is a graphical means of showing the relationship between the principal stressesThe axes represent the principle normal stress components σ1, σ2, and σ3The planes of maximum shear stress are always parallel to σ2 and at 45º to σ1 and σ3.