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579_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 579_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 573 SECTION 7.2 Plane Stress 573 Solution 7.2-4 sx u sx1 sx1 sy 40 MPa 160 MPa txy 54 MPa 52° sx + sy sy sx + 2 2 sin (2u) + txy cos (2u) ; 84.0 MPa sy1 sx + sy sy1 ; 136.6 MPa 2 tx1y1 cos(2u) + txy sin(2u) sy sx tx1y1 sx1 16.6 MPa ; Problem 7.2-5 Solve the preceding problem if the normal and shear stresses acting on element A are 6500 psi, 18,500 psi, and 3800 psi (in the directions shown in the figure). Determine the stresses acting on an element oriented at a counterclockwise angle of 30˚ from the horizontal. Show these stresses on a sketch of an element oriented at this angle. 18,500 psi 6500 psi A A 3800 psi Side View Cross Section Solution 7.2-5 sx u sy 6500 psi txy 30° sx1 sx1 sx + sy 18500 psi sy sx + 2 3041 psi 2 ; 3800 psi tx1y1 tx1y1 cos (2u) + txy sin (2u) sy1 sy1 sy sx 2 sin (2u) + txy cos (2u) ; 12725 psi sx + sy sx1 8959 psi Problem 7.2-6 An element in plane stress from the fuselage of an airplane is subjected to compressive stresses of magnitude 27 MPa in the horizontal direction and tensile stresses of magnitude 5.5 MPa in the vertical direction (see figure). Also, shear stresses of magnitude 10.5 MPa act in the directions shown. Determine the stresses acting on an element oriented at a clockwise angle of 35˚ from the horizontal. Show these stresses on a sketch of an element oriented at this angle. ; 5.5 MPa 27 MPa 10.5 MPa ...
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