585_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

585_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 1:18 PM Page 579 SECTION 7.2 Plane Stress Solution 7.2-14 579 Biaxial stress STRESS ELEMENT u sx1 sx sy sx + sy sx1 2 0 Find angles u for s 38.66° sy sx tx1y1 50 MPa txy s sy1 32 MPa 0 ; 18 MPa sin 2u + txy cos 2u ; 40 MPa 0. normal stress on plane a-a sx + sy sx1 sy sx + 2 2 cos 2u + txy sin 2u 9 + 41 cos 2u ( MPa) For sx1 2u ‹ 9 41 0, we obtain cos 2u 77.32° and u 38.66° ; Problem 7.2-15 An element in plane stress from the frame of a racing car is y oriented at a known angle u (see figure). On this inclined element, the normal and shear stresses have the magnitudes and directions shown in the figure. Determine the normal and shear stresses acting on an element whose sides are parallel to the xy axes, that is, determine sx, sy, and txy. Show the results on a sketch of an element oriented at u 0˚. 2475 psi 3950 psi u = 40° 14,900 psi O Solution 7.2-15 Transform from u sx txy u sx1 sx1 to u 40° sy 14900 psi 2475 psi 0° 3950 psi tx1y1 tx1y1 40° sy1 sx + sy sy sx + 2 12813 psi 2 ; cos (2u) + txy sin (2u) sy1 sy sx 2 sin (2u) + txy cos (2u) 4962 psi sx + sy 6037 psi ; sx1 ; x ...
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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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