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817_Mechanics Homework Mechanics of Materials Solution

817_Mechanics Homework Mechanics of Materials Solution -...

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Unformatted text preview: 7.64 The Mohr circle shown mmds tothe state of am given in Fig. m and b, PROBLEM 7-64 pagemr- Notingthat on. = 06 + (cm ms (26, — 26) andum fxy-=(CX') sin (23., - 20), derive the expressions for 0;,- and 1:”. given in Eqs. (1.5) and(7.6), mpcctivcly. [Hint Usesin(A +B)=sinA cosB+cosA sinB mdm(A+B)=oosAoosB+sinA sinB.] SOLUTION 56 = i(6‘g+6}) E? = 631 E? (:05 29F = E (202529? 3 5%Q Cu—X‘ Sn'n 26p :' E; SW} 29’: 7 Ta 6,. c; + 7’ cas (Rep-26) '-'-‘ at, + 56 ( COS'IQQPCOSQQ + Sin 26,, 3M 29) = 5E. + 61' cos 26,. c0529 + "5(7an 29,, Sin 29 =§5;-—(il+-§5:;—6'1c.9529+ 213 513429 “'3 same,— as) = 52’ (sin 29,“:29 .. Cos 29,, side-33 Co; 2,9 - géég su‘n 26 Ex' (51' sin 29' Cos 2.9 - “CT—X220: '29P sin 29 7%: ...
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