MecE_380-W09-Sample I

MecE_380-W09-Sample I - ._1_. __ . __ _ i 2.. CD ~A Ex) ®...

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II Strains & Displacements Strain Transformation & Principal Strains Example I In a delta rosette three strain gages are arranged in the orientation shown in the figure. (a) Determine the strains Cx . C;' and Cxy in terms of &'4, cs, and Ce· (,) Determine the principal strains and the principal directions in terms of &'4, c8, and Ce. v 0A = 0" 9/1=12()O OC = 240 0 x
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/ , I ':} S jr\ e 1\ ( wS6 n= - Sine CDS6 _ •. ,'\ 1 I \ £x , - Sj~9 [(~]) [~''j I ] (~-Sj~ £ "x' E y' - SIne CoS (9 d sa Z)( Case + 2yx Sit") e £)(j c<>se T £"1 Sj", e c..o.sQ 0 $i"e 0 _ _ €'C ( [f" ) ( I <: 3 E7::::-/2.o· £"I{'-£a- T + 2o -;.- --z)c'tJ+T<i j , q,se-= - Z _ ~~ J3 3 ~8 - "4 - 7 EI')J + "4 EJ $;" 9 -:. Ii 'l. . EB = { (cf" - 2 J3 ~J(.1 + 3 ~ )
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; J ~-------'---.I.
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Unformatted text preview: ._1_. __ . __ _ i 2.. CD ~A Ex) ® <is = =f (f)( -:2 J3 ~)(1 t<~ f J ) CD ~c:. == ~ (fx +.2 J3 E.x'j t 3 Ey) 3-t (J?}( + jf) ) == £8 t-fc. 2. ~ f", J fc -£8 -= 4" ' 4 IT ~KJ =1 E<J == -k (E<-~8)] 'Ii (') co + ~ .::-£ bE.' -ex 2' + c:;x -y I )(-2. .2 , ; ~-t ~ .Ex -, OOS~p -2..'1 Sirs ~~ 2. 2. j ~-£, n ~'I(/~I == -4. Si,,\::aP + Ei. j Q>S~,. . J> rh1 C1r c..1 Jlre.ct/~ at +L. ~/e (3 ftJ Juts E./C'J' = e ::!:> ~ pt)~Cj q.( w ,.f~ 1~kh'Jr\ Ex~ £, '~JJ , ~ ~ J,~ df!te,.,;~ {rol1t £x'y' =0 prp1Cir~ str~ £~ M 4 ~/e ~p(iY)ctr".e t -,~~ £ .. = k (£,-1 Hs "t £'C: ) -i [ (€~ -€a )2_1-cr, -:. ):_~-~] J{ LA I ~' I ~ I ,-lAX SI\.ee\( str~ eXj;mt1~ = "'S ~ ma.)( ~ '-;: l~1 -2.1.)...
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This note was uploaded on 01/05/2010 for the course SA sa taught by Professor Sa during the Spring '09 term at A.T. Still University.

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MecE_380-W09-Sample I - ._1_. __ . __ _ i 2.. CD ~A Ex) ®...

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