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Stress_Transform_2D_Symbolic

Stress_Transform_2D_Symbolic - Normal stress in...

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MATLAB Demo: 2D-Stress transformation using symbolic toolbox Example 2.1-2 ........................................................................................................................................... 1 Clear the workspace clear all; clc; Define Variables for Symbolic Calculations syms sigmax sigmay tauxy theta Define given state of Stress sigma=[sigmax tauxy; tauxy sigmay] sigma = [ sigmax, tauxy] [ tauxy, sigmay] Define Transformation Matrix T=[cos(theta) sin(theta); -sin(theta) cos(theta)]; Compute State of Transformed Stress sigmap=T*sigma*T.'; collect function is used to "collect" all the terms tauxy together collect(sigmap,tauxy); Example 2.1-2 (Numerical Values) Given stresses and orientation (Numerical values) Stresses at original co-ordinates

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Unformatted text preview: Normal stress in x-dir (original co-ordinate) sigmax=3; Normal stress in y-dir (original co-ordinate) sigmay=9; Shear stress (original co-ordinate) tauxy=-4; Orientation (counterclockwise positive) theta=-pi/4; Substituting these values in the stress transformation matrices (subs command) State of stress (original co-ordinate) s=subs(sigma) s = 3 -4 9 Transformation matrix subs(T) ans = 0.7071 -0.7071 State of stress (New/Transformed co-ordinate) sp=subs(sigmap) sp = 10.0000 -3.0000 2.0000 Normal stress in x-prime-dir (New/Transformed co-ordinate) sp(1,1) 10 Normal stress in y-prime-dir (New/Transformed co-ordinate) sp(2,2) Shear stress (New/Transformed co-ordinate) sp(1,2)...
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