02-05ChapGere.0001

02-05ChapGere.0001 - 5 2 s x sin u cos u t u 5 2 s x sin u...

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Problem 2.6-16 A prismatic bar is subjected to an axial force that produces a tensile stress s u 5 63 MPa and a shear stress t u 5 2 21 MPa on a certain inclined plane (see figure). Determine the stresses acting on all faces of a stress element oriented at u 5 30° and show the stresses on a sketch of the element. Solution 2.6-16 Bar in uniaxial stress 134 CHAPTER 2 Axially Loaded Members 21 MPa 63 MPa u s u 5 63 MPa t u 52 21 MPa I NCLINED PLANE AT ANGLE u s u 5 s x cos 2 u 63 MPa 5 s x cos 2 u (1) (2) Equate (1) and (2): or From (1) or (2): s x 5 70.0 MPa (tension) tan u 5 21 63 5 1 3 Ê u 5 18.43 8 63 MPa cos 2 u 5 21 MPa sin u cos u s x 5 21 MPa sin u cos u 2 21 MPa
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Unformatted text preview: 5 2 s x sin u cos u t u 5 2 s x sin u cos u s x 5 63 MPa cos 2 u S TRESS ELEMENT AT u 5 30 8 Plane at u 5 30 8 1 90 8 5 120 8 N OTE : All stresses have units of MPa. 5 30.31 MPa t u 5 ( 2 70 MPa)(sin 120 8 )(cos 120 8 ) s u 5 (70 MPa)(cos 120 8 ) 2 5 17.5 MPa 5 2 30.31 MPa 5 ( 2 70 MPa)(sin 30 8 )(cos 30 8 ) t u 5 2 s x sin u cos u 5 52.5 MPa s u 5 s x cos 2 u 5 (70 MPa)(cos 30 8 ) 2 u 30 17.5 30.31 52.5 30.31 52.5 y x A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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