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AE304_fall09_HW2_solution - Due:Wednesday,September9,2009 H...

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Homework 2 - Solution AE304 – Aircraft Structures I – Fall 2009 Due: Wednesday, September 9, 2009 Exercise 1: The state of stress at a critical point of an aircraft component is given by The tensile yield strength of the material is 82 MPa and the factor of safety is 1.2. Determine whether failure takes place at the point, according to (a) maximum shearing stress theory and (b) maximum energy distortion theory Solution: The applied stresses: The invariant: The equation and the corresponding roots or principal stresses: a. Maximum shearing stress (Tresca) theory: Based on Tresca theory, failure takes place at this point b. maximum energy of distortion (Von Mises) theory: Based on Von Mises theory, failure takes place at this point
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Exercise 2: Simple tension and compression tests on a brittle material reveal that failure occurs by fracture at σ ut = 260 MPa and σ uc = 420 MPa, repectively. In actual application, the material is subjected to perpendicular tensile and compressive stresses, σ 1 and σ 2
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