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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