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Unformatted text preview: Lecture 11 Stress Tensor and Equilibrium Equations Shaofan Li University of California at Berkeley 1. Can we use a scalar field to represent the stress state ? Traction Vector Continuum mechanics definition of stress 2. Can we use a vector field to represent the stress state ? Pass a section through the member forming an angle with the normal plane. cos sin cos sin cos cos cos 2 A P A P A V A P A P A F = = = = = = The average normal and shear stresses on the oblique plane are Stress on an Oblique Plane sin cos P V P F = = Resolve P into components normal and tangential to the oblique section, From equilibrium conditions, the distributed forces (stresses) on the plane must be equivalent to the force P. The maximum normal stress occurs when the reference plane is perpendicular to the member axis, m = = A P The maximum shear stress occurs for a plane at + 45 o with respect to the axis, = = = 2 45 cos 45 sin...
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This note was uploaded on 01/21/2012 for the course C 85 taught by Professor Papadopoulos during the Spring '08 term at University of California, Berkeley.
 Spring '08
 PAPADOPOULOS
 Statics, Stress

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