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Math · Advanced Math
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1 n the following, a repeated index in any of i, j or k only indicates that the summation convention is to be used. Given the stress state, defined in MPa Oxx-: 6,0000, Ơxy-1.2247, Ơxz-1.2247, Ơyy-4.5000, Ơyz -0.5000 and Ơzz 4.5000 together with the transformation matrices cos0 0-sin y 0 0 sina cosa sin ey 0 cos y cos ez-sin ez 0 zsin cose 0 0 then · find the new stress state (to the nearest K Pa) corresponding to the rota- tion θ,-π/2 followed by θy-π/4 and finally by θ,-π/3. Remember that, after a rotation described by the rotation matrix T, then the new stress state is related to the old stress state by o(new) To(old)T where T denotes transpose; Find -the mean (average) stress ơvew)/3; - the deviatoric stresses defined by 3 where oy represents the usual 3 x 3 unit matrix; and Snew)

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