Q.3// A thin-wall tube with closed ends is subjected to a maximum internal pressure of 35 MPa in service. The mean radius of the tube is 30 cm. (a) If the tensile yield strength (hoop direction) is 700 MPa, what minimum thickness must be specified to prevent yielding? (b) If the material has a yield strength in shear of k 280 MPa, what minimum thickness must be specified to prevent yielding? (c) For (a) only, use von Mises criteria to determine the necessary yield strength to prevent yielding.

The stresses on the surface of a hard bronze component are shown in the figure below. The yield strength of the bronze is σY = 345 MPa.a) What is the factor of safety predicted by the maximum-shear-stress theory of failure for the stress state shown? Does the component fail according to this theory?b) What is the value of the Mises equivalent stress for the given state of plane stress?c) What is the factor of safety predicted by the failure criterion of the maximum-distortion energy theory of failure? Does the component fail according to this theory?

Steel railroad reels 10 m long are laid with a clearance of 3 mm at a temperature of 15°C. (a) At what temperature will the rails just touch? (b) What stress would be induced in the rails at that temperature if there were no initial clearance? Assume a = 11.7 um/(m. C) and E = 200 GPa.

A sheet metal cutting machine cuts the sheet metal via shear force, V as shown in Fig. 1. The crosssection of sheet metal is rectangular with width, b = 3m and thickness, d = 5mm. The sheet metal ishaving yield strength σy = 220 MPa; Young’s modules, E = 200 GPa and Poisson’s ratio, ν = 0.3.Conduct the following analyses at the state of stress when maximum stress reaches σy and beforeshearing commences.  (Need answer Question c) & d) c. Sketch the YIELD LOCI for both cases above. d. As a sheet-metal engineer, which failure criterion in (b) will you use to determine the cuttingshear force? Explain the reason for your answer.

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Problem 15 The compound bar shown below is made of a light, strong material with E= 70,000 N/mm². Two forces are applied to the rigid plates connecting the bars. The yield strength is o, = 200 N/mm². The bar has a rectangular cross section with height H = 12.5 mm and thickness t = 1.0 mm. You may neglect the weight of the bars. (a) Calculate the x-direction internal force in segments AB and BC of the compound bar. Show all work. (b) Calculate the total length change of the compound bar. (c) The plane 1-2 represents a lap joint. Calculate the normal stress on the lap joint. L₂= 625 mm A L₁ = 775 mm H = 12.5 mm X 1800 N B 1 H = 12.5 mm =35° 2 F₂ = 1000 N Cross section H-12 H = 12.5 mm t = 1.0 mm