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ProblemSet10

# ProblemSet10 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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M ASSACHUSETTS I NSTITUTE OF T ECHNOLOGY Department of Mechanical Engineering 2.001-Mechanics and Materials I Spring, 2006 Problem Set 10 Distributed: Monday, May 8, 2006 Due: Friday, May 12, 2006 Æ Please place in collection bin in 1-307 Due to the concomitance of the physics exam on Thursday night, you can have an extension of the due date to Monday 11:am. Reading Assignment: Hibbeler, sections 10.1, 10.3, 10.4, 10.5, 10.6 10.7 Problem 1: Draw the Mohr’s circle for the following stress states: i) σ XX =10MPa σ XY =0 MPa σ YY =0 MPa ii) σ XX =13MPa σ XY =-4 MPa σ YY =7 MPa iii) σ XX =11MPa σ XY =3MPa σ YY =19MPa iv) σ XX =-11MPa σ XY =8 MPa σ YY = 1 MPa v) σ XX = 4 MPa σ XY = -12 MPa σ YY = 36 MPa vi) σ XX =-25MPa σ XY =15 MPa σ YY =-9MPa For each case: a) Draw a (square) element along the X-Y axes and draw the state of stress on this element. b) Draw an element along X’-Y’ axes at 45º from the X-Y axes, obtain and draw the stresses acting on this element. c) Obtain the maximum and minimum principal stresses σ 1 and σ 2 , and the maximum shear stress τ max . Obtain the orientation of the principal ( 1-2 ) axes

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ProblemSet10 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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