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Assignment_7 - Problem 3 A thin-walled hollow sphere 2 m in...

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1 MAE157 – Lightweight structures (Winter 08) Homework Assignment #7 Due in class on Tuesday, Mar 4 th Solve the following four problems. For each problem, provide a detailed explanation of all the steps involved. Problem 1 The state of stress in a body is uniform and is given by: ! xx = 4 MPa ! xy = 2 MPa ! xz = 0 ! yy = 3 MPa ! yz = 0 ! zz = 0 Find the three components of the traction vector t on the surface ABCD as shown in the figure. Find the component ! n of the traction vector normal to the surface. Problem 2 A state of hydrostatic stress is given by: ! = ! 0 0 0 0 ! 0 0 0 0 ! 0 " # $ $ $ % & Show that on any surface the traction vector is always perpendicular to the surface and that the magnitude of the traction vector is equal to
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Unformatted text preview: . Problem 3 A thin-walled hollow sphere 2 m in diameter is subjected to internal pressure, p .The wall thickness is 5mm and the yield stress of the material is 250 MPa. Use Von Mises criterion to determine the maximum internal pressure p that does not cause yielding. Problem 4 An Aluminum alloy ( Y = 415 MPa ) panel is subjected to biaxial loading as shown in the figure. Assume that 1 = 300 MPa and 2 can be either tensile or compressive. Find 2 the range of ! 2 that the panel can withstand without yielding according to the Von Mises criterion....
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