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# I need answers for these 5 questions that i posted Attachment 1 Attachment 2 Attachment 3 ATTACHMENT PREVIEW Download attachment Screen Shot 2019-10-02 at 2.43.40 PM.png The ﬁrst 3 problems are the same three problems of the sample MT#1 posted. 1) 2) (Strain) (l6pt) Start with a given coordinate axes x1 — x2 — x3 , the strain tensor at a given point P in a elastic solid is 0.004 0.001 0 4 1 0 [SI-j]: ? 0.006 ? = ? 6 ? x10‘3, find,a)—d) 4pt each: ? 0.004 0.001 ? 4 1 the eigenvalues and corresponding normalized eigenvectors, using Cardan’s formula the 3 principal strains 81 &gt; 82 &gt; £3 , the orientation of the principal axis of £1 (w.r.t. x1 — x2 — x3 ), the octahedral normal so“ and shearing yo“ strains in the octahedral plane. if, without given [80.] , only 31, Em and you are known, can we find 32 and 33? How? (14pt) (Strain Compatibility, Stress vs Strain) In a region with a Cartesian coordinate system (19,1:2 ,x3) , the small strain components are given by _ 2 _ 2 _ 2 611—351 922—352 333—35 312 = xlxz 323 = x2x3 631 = x1x3 a) (Spt) If E = 32,000ksi and v=0.25, , find the Lamé constants x1 and y , and the corresponding components of stress. b) (5pt) Determine if the strains compatible in the region by checking ALL six compatible equations. ATTACHMENT PREVIEW Download attachment Screen Shot 2019-10-02 at 2.43.51 PM.png 3) (10pt) (Tensor) Given two vectors SE and j? (w.r.t. x1 — x2 — x3 ). In a rotated coordinate system 3:; — x; — x; , the same two vectors take the form i't' and j&quot; . Find out if the scalar dot an, iv, . products 33- 33 and x - y 1n the two coordinate systems are the same. If they are the same, prove it. If not, give a counter—example. ATTACHMENT PREVIEW Download attachment Screen Shot 2019-10-02 at 2.44.07 PM.png 4) L09: (20pt) You learned in your sophomore year the Generalised Hooke's Law as 1 Ex E (0, - V(0, to2)) Kxx 3 2G Xx 2 E (0) - V(ox to2) ) 1 E yz 2G 2 yz E (0, - V(0 * + 0 ,)) 1 E zx 2G .T zx a) (10pt) Write this in matrix form (a 6 X 6 matrix), using the X - X2 - X3 coordinate system, expressing the strains in terms of the stresses. b) (10t) Express the normal stresses -11 , 22, 33 in terms of the normal strains Ell, E22 and 833 , and similarly the shear stresses in terms of the shear strains. I n other words, find the inverse relations. 5) L10: (10pt) Express the shear modulus G (or u) in terms of E and v, Young's Modulus and Poisson's

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