岩石力学课件基础力学.ppt

Chapter 2 The Fundamental of Elastic Mechanics Divided normal stress and shear stress A stress state is： [?]={?x,?y,?z,?xy,?yz,?zx} Ex. 1 Determing the internal force in each area and their stresses in the following sylinder. Ex.2 If ?1=120MPa,?2=40MPa, and the surface, pls determine the normal stress ?n and shear stress ? ? Normal direction of the surface ? is 30 ° * * * force Outside force Internal force stress normal stress shear stress The sign of the stress spot stress state Stress tensor Stress invariants and deviatoric stress Mohrsstress circle Strain and strain tensor Elastic moduli and Poisson’s ratio poroelasticity force Outside force Internal force Outside force: surface force( point force and distribution force), body force. P point force distribution force body force Act on every mass point of the mass body, so called Quality force. As Gravity, Electromagnetic force Internal force reaction force of outside force Equal but Opposite direction stress normal stress shear stress The sign of the stress stress Cross section Relation between active force and active surface is any orientation. If active force points towards normal surface, it is normal force, otherwise it is shear force, pointing towards tangential surface. Compressive stress + Tension stress _ The sign of the stress positive negative Shear stress -- Shear stress + X Y counterclockwise clockwise ?R ?=?R/?A ?z ?y ?x ?xy?zx spot stress state Unit body matrix ?y ?yz ?yx ?z ?zx ?zy ?x ?xz ?xy spot stress state x y z Stress tensor Stress tensor Stress tensor Stress invariants and deviatoric stress In rock mechanics,we regulate: ?1 ??2 ? ? 3 As ?1 stand for the maximum principal stress, ?3 stand for the minimum principal stress, ? 2 intermediate principal stress. Mohrsstress circle Mohrs stress circle is a tool to analyze the two-dimension spot stress state. We will mainly introduce the mohrs stress circle under two-dimension stress state,that’s to say the plane stress state. Mohrsstr