Chapter 3 Rock Mechanics Stress

Slides:



Advertisements
Similar presentations
Normal Force Force on an object perpendicular to the surface (Fn)
Advertisements

Mohr Circle for stress In 2D space (e.g., on the s1s2 , s1s3, or s2s3 plane), the normal stress (sn) and the shear stress (ss), could be given by equations.
Make a sketch Problem: A 10.0 kg box is pulled along a horizontal surface by a rope that makes a 30.0 o angle with the horizontal. The tension in the rope.
Forces applied at an Angle & Inclined Planes
Chapter Outline Shigley’s Mechanical Engineering Design.
CTC / MTC 222 Strength of Materials Chapter 1 Basic Concepts.
Chapter 2 Mechanical Equilibrium
III. Strain and Stress Basics of continuum mechanics, Strain Basics of continuum mechanics, Stress Reading Suppe, Chapter 3 Twiss&Moores, chapter 15 Additional.
Geology 3120 Powerpoint notes available online at:
The stresses that cause deformation
Mechanics of Materials – MAE 243 (Section 002) Spring 2008 Dr. Konstantinos A. Sierros.
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.
Joints and Shear Fractures
Stress, Strain, and Viscosity San Andreas Fault Palmdale.
16 July 2015GLG510 Advanced Structural Geology Force, Traction, and Stress.
Stress II Cauchy formula Consider a small cubic element of rock extracted from the earth, and imagine a plane boundary with an outward normal, n, and an.
IV. Basics of continuum mechanics, Stress Reading Suppe, Chapter 3 Twiss&Moores, chapter 15 Additional References : Jean Salençon, Handbook of continuum.
NEWTON’S SECOND LAW.
Geotechnology Fundamental Theories of Rock and Soil Mechanics.
Chapter 4 Sec 6-8 Weight, Vector Components, and Friction.
Vectors and Scalars Chapter 8. What is a Vector Quantity? A quantity that has both Magnitude and a Direction in space is called a Vector Quantity.
Stress II. Stress as a Vector - Traction Force has variable magnitudes in different directions (i.e., it’s a vector) Area has constant magnitude with.
Force and Stress Earth Structure (2 nd Edition), 2004 W.W. Norton & Co, New York Slide show by Ben van der Pluijm © WW Norton, unless noted otherwise.
Resolving the gravitational forces on an inclined plane
Force Diagrams And Types of Forces. Review Force = push or pull. Measured in Newtons. –1 lb = 4.45 N F net = ma a = F net / m Big force = big acceleration.
CTC / MTC 222 Strength of Materials Chapter 1 Basic Concepts.
Applications & Examples of Newton’s Laws. Forces are VECTORS!! Newton’s 2 nd Law: ∑F = ma ∑F = VECTOR SUM of all forces on mass m  Need VECTOR addition.
This week: PS #1 assigned (due next Tuesday) Lab #1 due tomorrow at 11:00 Lectures: ch. 3- Force and Stress Lab #2: Field trip to Mt Baldy- Will collect.
Lecture 7 Mechanical Properties of Rocks
This is the trace of the strain tensor. In general the trace of the strain tensor gives area change in 2-D and volume change in 3-D The principal axes.
The Laws of Motion. Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting on them Describes.
Friction Ffriction = μFNormal.
Unit 2 Notes. Free Body Diagrams Show an object and the forces acting on it The object is represented by a circle (you can write the object’s name inside.
 Force: A push or a pull Describes why objects move Defined by Sir Isaac Newton.
Chapter 3 Force and Stress. In geology, the force and stress have very specific meaning. Force (F): the mass times acceleration (ma) (Newton’s second.
NB: Uniaxial strain is a type a non-rotational transformation Uniaxial strain.
Stress: Stress tensor Principal stresses and directions Maximum shear stresses and directions Failure theories.
The stresses that cause deformation
Today: Back to stress stress in the earth Strain Measuring Strain Strain Examples Today: Back to stress stress in the earth Strain Measuring Strain Strain.
Outline Force, vectors Units Normal, shear components Pressure
Mechanics 1 Friction.
Push and Pull Newton’s Laws. Newton’s First Law An object at rest remains at rest, and an object in motion continues in motion with constant velocity.
Objects on Inclined Planes I guess you could call them ramps if you want.
REVISION NEWTON’S LAW. Quantity with magnitude and direction. e.g. displacement, velocity, acceleration, force and weight.. VECTOR Quantity having only.
1 Structural Geology Force and Stress - Mohr Diagrams, Mean and Deviatoric Stress, and the Stress Tensor Lecture 6 – Spring 2016.
Force and Stress – Normal and Shear Stress Lecture 5 – Spring 2016
Mohr-Coulomb failure Goal: To understand relationship between stress, brittle failure, and frictional faulting and to use this relationship to predict.
9/30 Friction  Text: Chapter 4 section 9  HW 9/30 “Skier” due Thursday 10/3  Suggested Problems: Ch 4: 56, 58, 60, 74, 75, 76, 79, 102  Talk about.
Physics Section 4.4 Describe various types of forces Weight is a measure of the gravitational force exerted on an object. It depends upon the objects.
Transformation methods - Examples
Principal Stresses and Strain and Theories of Failure
Today: (Ch. 3) Tomorrow: (Ch. 4) Forces and Motion in Two and Three Dimensions Equilibrium and Examples Projectile Motion.
Lecturer: Dr. Frederick Owusu-Nimo
STRESS SUMMARY Stress= amount of force per unit area (units Pa) Force= mass * acceleration (units N)
Dynamics and Relative Velocity Lecture 07 l Problem Solving: Dynamics Examples l Relative Velocity.
Mohr Circle In 2D space (e.g., on the s1s2 , s1s3, or s2s3 plane), the normal stress (sn) and the shear stress (ss), could be given by equations (1) and.
Stress = Force/Area Force is measured in units of mass*acceleration 1 N (Newton) = 1 kg * m * s-2 another common unit for force is the pound.
Vectors and Scalars Chapter 8.
Chapter 3 Force and Stress
Vectors Scalars and Vectors:
Mechanical Principles
Chapter 11.1 Rock Deformation.
Friction.
Aim: How do we explain motion along an inclined plane?
Physics Warm-Up List 15 forces you have applied since you were last in Physics class. Circle the forces that caused an acceleration.
Review from LAB #3.
The Traction Vector and Stress Tensor
Mechanics of Materials Engr Lecture 20 More Mohr’s Circles
Presentation transcript:

Chapter 3 Rock Mechanics Stress

Basic Physics Force Stress that which changes the state of rest or the state of motion of a body F=ma Stress force applied to an area σ=F/A

Basic Physics Scalar Possesses only a magnitude at some point in time or space Vector Possesses both magnitude and direction Tensor A field of data with magnitudes and directions

Basic Physics Tensors Zero-order tensor is a scalar like temperature and has only 1 component First-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 components The number of components may be determined from 3n where n in the order of the tensor

Basic Physics Stress can be Tensional - Pulling apart Compressional - Pushing together

Basic Physics Stress on a surface can be broken into two vector components Normal Stress (σn) - acts perpendicular to the reference surface Shear Stress (τ)- acts parallel to the surface

Basic Physics Principal normal stress components (σ1, σ2, and σ3) These are oriented perpendicular to each other and σ1  σ2  σ3 Differential stress is the difference between the maximum (σ1) and the minimum (σ3) Mean stress is (σ1 + σ2 + σ3)/3 If the differential stress exceeds the strength of the rock, permanent deformation occurs

Basic Physics Lithostatic state of stress Occurs where the normal stress is the same in all directions Hydrostatic Pressure Confining stress acting on a body submerged in water Lithostatic Pressure Confining stress acting on a body under ground

Stress on a plane Horizontal plane F = ma = volume x density x acceleration F = 104 m3 x 2,750 kg m-3 x 9.8 ms-2 Plane is 1 x 1 m, A = 1 m2 What is the Stress?

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

Stress on a plane Inclined Plane at 45º Through the same 1m x 1m space, actually has a larger surface area, now 1.41 m2 Still F = 2.7 x 108 kg m s-2 So σ=F/A σ= (2.7 x 108 kg m s-2)/1.41 m2 or 191 MPa How does that compare to the stress on the horizontal plane?

Stress on a plane Stress can be broken down into components of normal and shear stress. σn = σ cos 45º = 191 MPa x 0.707 = 135 MPa τ = σ sin 45º

Stress Ellipsoid A Shear Ellipsoid is a graphical means of showing the relationship between the principal stresses The axes represent the principle normal stress components σ1, σ2, and σ3 The planes of maximum shear stress are always parallel to σ2 and at 45º to σ1 and σ3.

Triaxial Test Apparatus

Mohr Circle Diagram Created by Otto Mohr, a german engineer, in 1882 Enables us to determine the normal and shear stress across a plane

Mohr Circle Diagram τ τ, P

Mohr Circle Diagram

Mohr Circle Diagram

Measuring Present-Day Stress

Stress in the United States