Exam1_Solution - Problem I (33 points) Consider the stress...

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Unformatted text preview: Problem I (33 points) Consider the stress tetrahedron shown in figure at the right where the lengths of the orthogonal sides are: OA is 0.8, OB is 0.4, and OC is 0.5 (consider these lengths to nominally be 1.0 in the uncut case). If the given state of stress on the associated differential volume is: o 1 : 1 0 0 , o 2 2 : 2 0 0 , o 3 3 : - 1 0 0 , T t 2 : 0 , r r r : - 1 0 0 , Tzl : 0. Please determine: a) Unit vectorfi expressed in terms of unit vectors A A ^ i t , i 2 \ ? b) What is the total stress i, c) lf i, = onrfi + rnr.f , where respectively, what is orr? d) What is magnitude r,,, ? A) r" =-o.8il +o,vii / acting on-the face ABC (expressed in terms of basis vectors i,ir?ry h and.i unit vectors *tr'ii"normal to, and lie in plane ABC i3 c tl i2 \'/-1 z a r a , / t f ' - = - O . 8 t , f O . $ r 2 , V 1 AB -7A? '\ r'\ 't f " " x f " " o ' a i , + o . r l i z t - o ' 3 7 i s g =1P'ffi1 o'Eqqqt n : o - 3 6 3 7 t r r o ' 7 2 7 t / t z f a ' E o t l t l l- , il 1i"1, = [z ],, I fiJ, f,f] rool(o,ttyl i l | o llont | =- ,ooJIo,s aa J Il: , ' } 1* 9 D r o 7 o O o B ) c ) u) Cnn =-2 tns t .a -t, -) n - T . ' ^ ,\ -, = rL- Tn {nn tr = t nJ' tt"] [-t'' Bt I {r"rl = [r,]-o;,^4=1rvss I l' vv'rt 1 t" I=o ttJ, = =ff, [ - ^ ' o svzJl';, zf: :11 Tns....
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This note was uploaded on 10/31/2010 for the course MANE 4060 taught by Professor Huang during the Fall '08 term at Rensselaer Polytechnic Institute.

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Exam1_Solution - Problem I (33 points) Consider the stress...

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