hydrostatic state of stress as shown in the figure. For no change in the volume to occur, what should be its Poisson's ratio? Oy Ox

The strain components Ex, Ey, and Yxy are given for a point in a body subjected to plane strain. Determine the strain components En Et, and Ynt at the point if the n-t axes are rotated with respect to the x-y axes by the amount and in the direction indicated by the angle 8. Sketch the deformed shape of the element. Ex = -950 μE, Ey = 380 μE, Vxy = 1000 μrad, and 8 = 30% t Answer: En = & = Ynt= με με Hrad n X

A circular bar of magnesium alloy is 390 mm long. The stress-strain diagram for the material is shown in the figure. 70 63 56 49 O (MPa) 42 35 28 21 14 7 0.002 0.004 0.006 0.008 0.01 The bar is loaded in tension to an elongation of 2.34 mm, and then the load is removed. Hint: Use the concepts illustrated in the figures below. (Assume the curve in the figure above is linear between (0, 0) and (0.001, 28), and curves with a gradually decreasing slope otherwise.) F В E F Loading CD Loading Residual Elastic strain recovery (a) What is the permanent set of the bar (in mm)? 2.184 X mm (b) If the bar is reloaded, what is the proportional limit (in MPa)? 55 X MPa

9-10 Determine the equivalent state of stress on an element if it is oriented 30° clockwise from the element shown. Use the stress-transformation equations. 300 psi 950 psi