stress - I Introduction and Basic Concepts A B Stress force...

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91 I. Introduction and Basic Concepts A. Stress: force applied to rock unit, that results in deformation (strain) B. Definitions 1. Force: vector with magnitude and direction a. compressional vs. tensional forces in geology (1) squeezing vs. pulling apart b. magnitude = how much force? c. direction = direction of force? d. Force = Mass x Acceleration 2. Traction = force distributed per unit area a. given a constant magnitude... (1) > area, < traction (lesser concentration of force) (2) < area, > traction (greater concentration of force b. Stress = "traction" = Force / Area (1) e.g. force applied to a fracture plane or bedding plane 3. Force Components a. 2-D Analysis (1) Force may be broken into 2 vector components oriented at right angles b. 3-D Analysis (1) Force may be broken into 3 vector components oriented at right angles c. Force distributed over an area (1) Force component normal to surface ("normal stress) (2) Force component parallel to surface ("shear stress") 4. Surface Stress Equilibrium a. Traction force applied to surface (1) Equilibrium condition: a pair of equal and opposite tractions acting across a surface of given orientation 5. Vector Review
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92 a. Vector: quantity with magnitude and direction (1) e.g. Velocity, Force (a) e.g. car travels 40 mi/hr in east direction (2) Graphical depiction (a) arrow shows direction (b) length of arrow scaled to magnitude b. "Scalar Quantity": magnitude only (a) e.g. area, temperature, density c. Vectors in 2-D (1) Parallelogram method of vector resolution (a) Vector addition: V + W = R d. Vectors in 3-D (1) Orthogonal Cartesian Coordinate System (a) x-y-z axes mutally perpendicular (also known as x 1 , x 2 and x 3 respectively) (2) Resolution of force F in 3-D (a) F = F1+F2+F3 where F1, F2 and F3 = force components parallel to x,y,z reference axes respectively 6. Remember Your Trigonometry!!! a. Triangles (1) All interior angles of any triangle must = 180 degrees (2) Right Triangle: one of the angles of triangle = 90 degrees b. Right Triangles and Trig. Functions (1) theta = θ = given interior angle of right triangle, not the 90 degree angle (2) "hypotenuse" = line opposite right angle of right triangle (3) "adjacent" = line forming ray of angle θ (4) "opposite" = line opposite angle θ (5) 2 θ = 2 times the angle of θ c. Basic Trig. Functions (1) Sin θ = length opposite / length hypotenuse
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93 (2) Cos θ = length adjacent / length hypotenuse (3) Tan θ = Sin θ /Cos θ = length opposite / length adj. (4) CSC θ = 1/Sin θ = hyp/opp. (5) Sec θ = 1/Cos θ = hyp./adj. (6) Cot θ = 1/Tan = adj./opp. = cos θ /sin θ 7. Units of Force and Stress a. Force Units (F = Mass x Acceleration) (1) Newton = amount of force required to accelerate 1 kilogram of mass at 1 meter per second per second (2) 1 N = 1 kg m/sec 2 = 0.225 lb (in english system) b. Stress Units (Stress = Force / Area) (1) Units = N/m 2 (a) 1 N/m 2 = 1 Pascal (Pa) (b) 1 MPa = 1 megapascal = 10 6 Pa = 10 6 N/m 2 (c) 1MPa = 10 bars = 0.01 kb (2) E.g. atmospheric pressure at sea level = ~ 1000 mb = 1 bar = 0.1 MPa = 10 5 Pa II. More on Force, Traction and Stress...
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