A hanger is made of two bars of different sizes. Each bar has a square cross-section. The hanger is loaded by three-point loads in the mid vertical plane as shown in the figure. Ignore the self-weight of the hanger. What is the maximum tensile stress in N/mm² anywhere in the hanger without considering stress concentration effects? 100 KN 50 mm. 100 mm 50 kN 100 KN

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

Problems: Stress (ksi) 53.2 1. Determine the ductility (u) of the material based on the stress- strain diagram (problem S5.1). 43.6 37.1 0.0013 0.0063 0.163 0.247 Strain (in/in)

GIVEN: Bar has a cross-sectional area of 4 in? and is placed between two rigid immoveable supports when it is 30.00 inches long at a temperature of -20°F. REQ’D: A) The stress in the bar at 90°F if it were made of steel. Esteel = 10 x 10° psi asteel = 13 x 106/°F B) The final length of the aluminum bar

1. If we take the stress function = 2x²y + xy², what are the stress components according to this stress function? What are the stresses on the boundaries of the body below? O y H H L X

Wire BC has a diameter of 0.10 in. And its material has the stress-strain characteristics shown in the figure. Determine the vertical displacement of the handle D if the pull on the handle is slowly increased and reaches the magnitude of P = 655 lb. o (ksi) 40 pulg 80 70 B 50 pulg - 30 pulg € (pulg/pulg) 0.007 0.12

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A 20 m long steel rod is at a temperature of 20°C. The rod is heated so that temperature rises by 50°C. If rod is allowed to expand by 14 mm, what will be the stress induced in rod? Take E = 200 GPa and α = 12 x 10-6/°C.

If the block is subjected to the centrally applied force of 600kN, determine the average normal stress in the material. Show the stress acting on a differential volume element of the material