645_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

645_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 7.7 Plane Strain 639 Problem 7.7-20 A strain rosette, or delta rosette , consists of three electrical-resistance strain gages arranged as shown in the figure. Gage measures the normal strain in the direction of the axis. Gages and measure the strains and in the inclined directions shown. Obtain the equations for the strains , and associated with the axis. xy g xy P x , P y P c P b C B x P a A 60° Solution 7.7-19 Cantilever beam (plane stress) Beam loaded by a force acting at an angle . Axial force Shear foce (At the neutral axis, the bending moment produces no stresses.) S TRAIN GAGES E LEMENT IN PLANE STRESS â x ± 171 * 10 ² 6 â y ±²³ â x ±² 59.85 * 10 ² 6 t xy ±² 3 V 2 A ±² 3 P cos a 2 bh s x ± F A ± P sin a bh s y ± 0 At u ± 75°: â B ±² 266 * 10 ² 6 At u ± 0°: â A ± â x ± 171 * 10 ² 6 V ± P cos a F ± P sin a h ± 3.0 in. E ± 6.0 * 10 6 psi ³± 0.35 b ± 1.0 in. a P H OOKE SLAW (1) (2) F OR : (3) Substitute into Eq. (3): (4) S OLVE E QS . (1) AND (4): P ± 5000 lb ; tan a ± 0.7813 a ± 38° ; or P cos a ± 3939.8 lb ² (56.25 * 10 ² 9 ) P cos a ² 266 * 10 ² 6 ± 55.575
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Unformatted text preview: * 10 6 99.961 * 10 6 x 1 B 266 * 10 6 2 u 150 x 1 x + y 2 + x y 2 cos 2 u + g xy 2 sin 2 u u 75 (225.0 * 10 9 ) P cos a g xy t xy G 3 P cos a 2 bhG 3(1 + v ) P cos a bhE P sin a bhE x 3078 lb x s x E P sin a bhE y C B A x O 60 60 60 Solution 7.7-20 Delta rosette ( strain rosette) 60 S TRAIN GAGES F OR u 0: x A ; Gage C at u 120 Strain C Gage B at u 60 Strain B Gage A at u 0 Strain A F OR : (1) B A 4 + 3 y 4 + g xy 1 3 4 B A + y 2 + A y 2 (cos 120) + g xy 2 (sin 120) x 1 x + y 2 + x y 2 cos 2 u + g xy 2 sin 2 u u 60 07Ch07.qxd 9/27/08 1:24 PM Page 639...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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