113_2009_HW2_final

# 113_2009_HW2_final - with the longitudinal axis The maximum...

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UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science and Engineering Assigned 09/15/09 Due 09/22/09 Fall 2009 MSE 113 Prof. Ritchie Mechanical Behavior of Materials PROBLEM SET 2 Consider an infinite plate. The plate is loaded so that the stress state in the plate is given by Problem 1 𝜎𝜎 𝑖𝑖𝑖𝑖 = 375 80 0 80 120 0 0 0 0 𝑀𝑀𝑀𝑀𝑀𝑀 a) Where are the principal axes and what are the principal stresses? b) The yield stress of the material under uniaxial tension is σ y = 250 MPa. Use both the Tresca and von Mises yielding criteria to determine if yielding occurs in the plate Determine the principal stresses and their orientation relative to the x, y axes for the following sets of applied stresses, and illustrate your answer with a reasonably accurate Mohr’s circle for each case. Problem 2 a) σ 11 = 185 MPa σ 22 = –35 MPa σ 12 = 60 MPa b) σ 11 = 15 MPa σ 22 = –275 MPa σ 12 = 0 c) σ 11 = 100 MPa σ 22 = 20 MPa σ 12 = 125 MPa

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A thin-walled cylindrical pressure vessel is constructed with a helical weld that makes an angle of 60°
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Unformatted text preview: with the longitudinal axis. The maximum internal pressure is 800 kPa, and the inside radius is 2.0 m with a wall thickness of t = 10 mm. Problem 3 a) Find σ θθ and σ zz b) Determine the maximum shear stress, as well as the normal stress and the shear stress acting on the weld. c) Use the von Mises and Tresca criteria to determine at what internal pressure the vessel yields ( σ y = 50 ksi). Comment. Is one of the criteria more conservative than the other? Forces (F1, F2 and F3) are applied to the faces of a rectangular block of material, as shown below. The dimensions of the block are x 1 = 15 cm, x 2 =9 cm and x 3 =3 cm. Calculate the fractional change in x 1 due to the resulting elastic deformation. The Young's modulus is 225 GPa; the Poisson's ratio ν is 0.33 Problem 4 (F 1 = 70 kN, F 2 = 25 kN, F 3 = 45 kN)...
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