02-04ChapGere.0012 - 2 5 s x [ 2 sin u ] 2 s x 5 s u cos 2...

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Problem 2.6-15 Acting on the sides of a stress element cut from a bar in uniaxial stress are tensile stresses of 10,000 psi and 5,000 psi, as shown in the figure. (a) Determine the angle u and the shear stress t u and show all stresses on a sketch of the element. (b) Determine the maximum normal stress s max and the maximum shear stress t max in the material. Solution 2.6-15 Bar in uniaxial stress SECTION 2.6 Stresses on Inclined Sections 133 = 10,000 psi 5,000 psi 10,000 psi 5,000 psi u t u t u t u t u s u (a) A NGLE u AND SHEAR STRESS t u s u 5 s x cos 2 u s u 5 10,000 psi (1) P LANE AT ANGLE u 1 90 8 (2) Equate (1) and (2): tan 2 u 5 1 2 Ê tan u 5 1 Ï 2 Ê u 5 35.26 8 10,000 psi cos 2 u 5 5,000 psi sin 2 u s x 5 s u 1 90 8 sin 2 u 5 5,000 psi sin 2 u s u 1 90 8 5 5,000 psi 5 s x sin 2 u s u 1 90 8 5 s x [cos( u 1 90 8 )]
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Unformatted text preview: 2 5 s x [ 2 sin u ] 2 s x 5 s u cos 2 u 5 10,000 psi cos 2 u From Eq. (1) or (2): Minus sign means that t u acts clockwise on the plane for which u 5 35.26 8 . N OTE : All stresses have units of psi. (b) M AXIMUM NORMAL AND SHEAR STRESSES t max 5 s x 2 5 7,500 psi s max 5 s x 5 15,000 psi 5 2 7,070 psi 5 ( 2 15,000 psi)(sin 35.26 8 )(cos 35.26 8 ) t u 5 2 s x sin u cos u s x 5 15,000 psi 10,000 psi 5,000 psi 10,000 psi 5,000 psi u t u t u 10,000 5,000 10,000 5,000 u = 35.26 ° 7,070 7,070 y x A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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