Stress (σ) Stress. Strain

Transkripsi

1 Stress () Stress () = F/A dimana A=luas permukaan Unit stress yang umum adalah pascal (KPa, MPa, GPa), bar atau dalam skala luas seperti psi (pound per square inch) dan kg/cm Stress untuk batuan didalam bumi: = ρgh (lithostatic stress) Stress pada suatu titik dapat dibagi menjadi normal ( ) dan shear ( ) stress komponen Stress dapat bersifat compressive (+) dan tensile (-) Shear stress dalam system kopel akan positive bila searah jarum jam dan negative bila berlawanan arah jarum jam Stress D disuatu titik digambarkan sebagai stress ellipse Stress 3D disuatu titik digambarkan sebagai stress ellipsoid Principles stress : > > Koordinat sumbu utama stress ( 1,, 3 ) adalah sejajar dengan stress utama Stress-1 BS/3/ Stress- BS/3/ Stress Strain STRESS vs. STRAIN Stress-3 BS/3/ Stress-4 BS/3/

2 Relationship Between Stress and Strain Evaluate Using Eperiment of Rock Deformation Rheology of The Rocks Using Triaial Deformation Apparatus Measuring Shortening Measuring Strain Rate Strength and Ductility Limitation of The Concept of Stress in Structural Geology Stress-5 BS/3/ Stress-6 BS/3/ TECTONICS AND STRUCTURAL GEOLOGY Study of rock Deformation as Response to Forces and Stresses Involving Motion of Rigid Body Deformation = Translation + Rotation + Dilation + Distortion FACTOR CONTROLING DEFORMATION SCALE FACTOR RHEOLOGY TIME FACTOR DESCRIPTIVE ANALYSIS KINEMATIC ANALYSIS DYNAMIC ANALYSIS Stress-7 BS/3/ Stress-8 BS/3/

3 TECTONICS AND STRUCTURAL GEOLOGY NEW CONCEPTS IN TECTONIC AND STRUCTURAL GEOLOGY LINKED FAULT AND FOLD SYSTEMS 1. Geometric. Kinematic 3. Dynamic PROGRESSIVE DEFORMATION SCALE INDEPENDENCE IN BRITTLE DEFORMATION STRUCTURAL INHERITANCE Stress-9 BS/3/ Twiss and Moores, 199 Stress-1 BS/3/ SCALE FACTOR Km-Scale Fold Geologic Cross-Section and Seismic Section 5 Km Plates m-scale Fold Aerial Photograph STRUCTURAL GEOLOGY DATA FOLLOW FRACTAL RELATIONSHIP 1Km Stress-11 BS/3/ Stress-1 BS/3/

4 Deformation of rock in various scale Single Particle EVOLUTION OF STRUCTURE Force history Movement history Particles (Modified from Means, 1976) Stress-13 BS/3/ Stress-14 BS/3/ DESCRIPTIVE ANALYSIS RHEOLOGY THREE TYPES OF STRUCTURES BRITTLE DUCTILE CONTACTS PRIMARY STRUCTURES SECONDARY STRUCTURES Stress-15 BS/3/ Stress-16 BS/3/

5 BASIC CONCEPTS Force Equilibrium FORCES AND VECTORS Force is any action which alters, or tends to alter Newton II law of motion : F = M a Unit force : kgm/s = newton (N) or dyne = gram cm/s ; N = 1 5 dynes (a). Force: vector quantity with magnitude and direction (b). Resolving by the parallelogram of forces (A) Balance (B) Torque (C) Static Equilibrium (D) Dynamic Equilibrium Two Types of Force Body Forces (i.e. gravitational force) Contact Forces (i.e. loading) Modified Price and Cosgrove (199) (Davis and Reynolds, 1996) Stress-17 BS/3/ Stress-18 BS/3/ STRESS Stress defined as force per unit area: = F/A A = area, Stress units = Psi, Newton (N), Pascal (Pa) or bar (1 5 Pa) V R Z W V W (Davis and Reynolds, 1996) Stress-19 BS/3/ Stress- BS/3/

6 STRESS Stress at a point in D Types of stress Normal stress ( N ) Normal Stress ( ) Stress () STRESS on PLANE Shear Stress ( ) (+) Compressive (-) Tensile Shear stress ( S ) (+) (-) Coordinate System Stress-1 BS/3/ Stress- BS/3/ Stress Ellipsoid The State of Two-Dimensional Stress at Point Σ Σ A. Stress elipse a) Triaial stress b) Principal planes of the ellipsoid B. Principal stress components (top) (top) Σ (top) Σ (rt) X 3 X 1 Principal coordinate aes and planes Z Principal Stress: > Σ, Σ = Surface Stress (lft) (lft) Σ (lft) d d (bot) (rt) (rt) X (Modified from Means, 1976) Σ (bot) (bot) C. General stress components Arbitrary coordinate aes and planes Stress-3 BS/3/ Stress-4 BS/3/

7 The State of 3-Dimensional Stress at Point A. Stress elipsoid Principal Stress: > > 3 1 Principal coordinate planes Stress Tensor Notation 1 3 B. Principal stress components y y = y y y yy y C. General stress components y Arbitrary coordinate planes y = 1, 3 = 1, 3 = Geologic Sign Convention of Stress Tensor Stress-5 BS/3/ Stress-6 BS/3/ Mohr Diagram -D Mohr Diagram -D A. Physical Diagram A. Mohr Diagram A. Physical Diagram B. Mohr Diagram n θ n 1 (p) n (p) s 3 (p) s 1 3 sin θ r θ (p) (p) (, s (p) ) n' α α θ p' p (p') ( (p') n, s ) α α θ (, (p) s (p) ) 3 Plane P cos θ Stress-7 BS/3/ Stress-8 BS/3/

8 Mohr Diagram -D A. Physical Diagram B. Mohr Diagram Mohr Diagram -D Planes of maimum shear stress θ 1 A. Physical Diagram B. Mohr Diagram (θ + 9º) α 3 (θ + 9º) α ( ' ) θ n + θ = +45º 1 Planes of maimum shear stress 1 θ' = +45º n - 1 s ma Counter clockwise 3 3 θ = +9º θ ' = 9º ( ' ) ( + ) ( ) Counterclockwise shear stress Clockwise shear stress s ma Clockwise Stress-9 BS/3/ Stress-3 BS/3/ Mohr Diagram 3-D Mohr Diagram 3-D Geometry of a three-dimensional Stress on a Mohr diagram Maimum Shear Stress Stress-31 BS/3/ Stress-3 BS/3/

9 FUNDAMENTAL STRESS EQUATIONS Principal Stress: > > All stress aes are mutually perpendicular Shear stress are ero in the direction of principal stress N = + - cos θ (Davis and Reynolds, 1996) Stress Ellipsoid = Sin θ Mohr diagram is a graphical representative of state of stress Mean stress is hydrostatic component which tends to produce dilation Deviatoric stress is non hydrostatic which tends to produce distortion Differential stress, if greater is potential for distortion Stress-33 BS/3/ Stress-34 BS/3/ Image of Stress Image of Stress Deviatoric Applied 1 = = 3 p = 3 = Δ3 Δ3 p p A. Hydrostatic stress p B. Uniaial compression a C. Uniaial tension -a a G. Pure shear stress -a H. Deviatoric stress (two-dimensional) Δ1 Δ1 = 1 n 3 n Effective Applied E E E D. Aial or confined compression a b b E. Aial etension or etensional stress a a b F. Triaial stress a b c D I. Differential stress (Three eamples) D D D = 1 3 J. Effective stress p f E 1 p f E = p f E 3 p f Stress-35 BS/3/ Stress-36 BS/3/

10 STRESS Body force works from distance and depends on the amount of materials affected (i.e. gravitational force). Surface force are classes as compressive or tensile according to the distortion they produce. Stress is defined as force per unit area. Stress at the point can be divided as normal and shear component depending they direction relative to the plane. Structural geology assumed that force at point are isotropic and homogenous Stress vector around a point in 3-D as stress ellipsoid which have three orthogonal principal directions of stress and three principal planes. Principal stress > > The inequant shape of the ellipsoid has to do with forces in rock and has nothing directly to do with distortions. Mohr diagram is a graphical representative of state of stress of rock Stress-37 BS/3/ Stress-38 BS/3/