Question

Write a MATLAB function file with the function handle [S, Tm] = principal (Sxy) which takes a matrix input Sxy in the form xx Txy Txz] [Exz Tyz Ozz) and returns the principal stresses in vector form to the variable S and the maximum shear stress in scalar form to the variable Tm. You may find the roots function useful in your calculations. To verify that your function is working correctly, you can use the stress state and answer provided in problem 1. Once working properly, use your function to calculate the principal stresses and maximum shearing stress of the following stress state: Oxx = -18 ksi Oyy = -15 ksi Ozz = -12 ksi Txy = -15 ksi Tyz = 12 ksi Tx = -9 ksi For this problem, turn in a print off of your function file and the resulting command window when calculating the principal stresses and maximum shear stress associated with the stress state above.

Answer 1

For a - Erry byy てりス stren tanson: Say - Gre tu tez 7 blay by Zuz | СТ, Сух ба are given by the moon of the eah. - 6,62 - 126- los 20 .....-0 The principal strenes are given by the " 6 whow, li = 6xx + 6yy + 622 l - Grabey & Syy 622 & Gezona - Tay - , - 66 6 2 4 1 1 6 г - sy, ti - 622 Cum Let 6, 6e and so are the roots of ean ☺ and suppone 6, 7162 763 Then, maximum Shear Stren, Tmax a 7 (6,- 6₂)

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function [S,Tm] = principal(Sxy)
l1=Sxy(1,1)+Sxy(2,2)+Sxy(3,3);
l2=Sxy(1,1)*Sxy(2,2)+Sxy(2,2)*Sxy(3,3)+Sxy(3,3)*Sxy(1,1)-Sxy(1,2)*Sxy(1,2)-Sxy(2,3)*Sxy(2,3)-Sxy(1,3)*Sxy(1,3);
l3=Sxy(1,1)*Sxy(2,2)*Sxy(3,3)+2*Sxy(1,2)*Sxy(2,3)*Sxy(1,3)+Sxy(1,1)*Sxy(2,3)*Sxy(2,3)-Sxy(2,2)*Sxy(1,3)*Sxy(1,3)-Sxy(3,3)*Sxy(1,2)*Sxy(1,2);
S=roots([1 -l1 l2 -l3]);
sigmas=sort(S);
Tm=(1/2)*(sigmas(1,1)-sigmas(3,1));
end

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