15-34 - 15-34 Mohr’s circle tor the state of sum in...

Unformatted text preview: 15-34. Mohr’s circle tor the state of sum in Fig.15-v13a is shown in mas—155. Show that the coordinates of point Hay, 5-,.) on the circle gives” the sum value as the stress-- transformation Eqs. 15-1 and 154. Comtructtoa of tho Cit-etc : a", :- $Ifl the worm for mfmnoe point“ and C It: m. 1”) c("*—;”’L. o) Theradiua ofdsecimleis 03-1-6 3 d,- _ +113): (.2—1) {If}, Stress on The Rotated Elem»: : The. nomallnd shear stress componenm( 6,. and 1“,.) are moment! by the coordirm of point? on weirdo. a". m bed-amnion! by calculating III: coordinate: of flora Ihc circh 1 . g..—£-—J_+[ [J—L) +r}, cow [1} 1 1,,- =[ [fi—L) +1},]sinlr [2] However, V8 i — 26 m (9—29) 2 cos tacos 29+sinosin 28 [3] shto—Zm-sin coo; ZO-sin 29mg [4] Frommccircle. ¢.-¢ m5" —3—: I 0,-0 JU—‘Ffl ”E, 2 (flfifni. 1' sin 1’ ‘ ’ z {6] (a?) + :3, Substima Eqs.[3] and {5] into [6] into [1] rich F +0 01-0 63' =-—xz—L+—z-—L¢DI 29+T”Sil129 (9.3.0.) Subsliluls Eq.[4] and [S] into [6] lnln [2} yield 5.1. . .Eféflsh 29+ rum :5 (g. a. n.) ...
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