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Unformatted text preview: 85. [8.4] Consider the thickwalled cylinder of Hg. P.8.4
constrained by immovable walls at the ends and subject to an .
‘ internal pressure so as to undergo plane strain. It is best here
Etc use cylindrical coordinates. The strains are considered for
fan element shown on a slice in Fig. P.8.4 as follows: a" 5 normal strain in radial direction see 5 normal strain in transverse direction 8’9 E shear strain between line segments dr and r :19 of the
element showu Figure 18.4. If the following data are known for a point in the pipe at 9 =
30", en, = —.002
a” = .00
0:"9 = .001 what are the strains on and a”, at the point? Er ﬁt Redefine axes as shoWn to right in order to use formulations of text. 5‘: i. ' = — “a
. Exx '002 7' 1: = .003 yy 10‘
Exy — .001
_ .002 + .003 + .002  .003 F')(')(' " 2 2 cos(60°) + .001 sin(60°) .0005  (.0025)(.500)  (.001)(.866) = .0005  .00125  .000866 = .001616 ey.y. = .0005 + .00125 + .000866
= .002516 ‘ The desired strains are: .001616 ——.—_ .002616 "8.6. [8.4] In Problem 85, what are the principal strains in
the xy plane at the point of interest? Let err = ex.x. = .002
see = ey.y. = .003
are = exw. = .001
ta" 29 = —.302;?303 = ’ i%%% = "400 29 = '21.8" 6 = 10.9°  002 + .003 .002  .003
.52 """§' * 2'  cos(21.8) + (.001)s1'n(21.8) .0005  (.0025)(.928) + (.001)(—.371) .0005  .00232  .000371 =' = .0005 + .00232 + .000371 = 5.10. [8.4] Given : ex,= —1xmos
.i a” = .0002
ex), = .0001 ‘Using Mohr’s circle as an aid, ﬁnd the principal strains and the
strains {Cir taxes I ’y ’ rotated 30“ counterclockwise from axes xy.‘; _ S x ‘ 5 2 2 1/2
r — [(—X—T—u) +(exy) 1 = [(2'.5)2+12]1/2 x 10'4 = 2.593x10'4
4
tan 29) = ,'.¢ = 21.8cl
2.5x10 .‘ly Ea . 6E  r cos(60°21.8°) =  % x 10'42.693x1o'4 cos(38.2)
= 2.616 x 10'4 ____.~..—.— . 55 + r coé 38.2 =  % x 10‘4 + 2.593x10'4 cos(38.2)
= 1.616 x 10" I = r sin(38.2)
= 2.693x10"sin(3 .2) = 1.665x10'4 4 2.616x1o' 1.616xm'4 yy ——— ('I
II +1.665x1o'4 = 65 + r =  % x 10’4 + 2.693x10'4 = 2,133x10'4 = 66  r =  i x 10'4  2.693x10‘4 2  3.193x10‘4 EEiﬂEiEﬂl_&1§§ @‘k ...
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This note was uploaded on 07/15/2008 for the course ME 311 taught by Professor Pitteressi during the Spring '08 term at Binghamton.
 Spring '08
 PITTERESSI

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