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A cylindrical vessel used for storing water for home in Alaska In very cold night the temperatures drop to -40F and the water in the tank freezes The iced water inserts pressure of 500 KPa uniformly on the cylinder walls when it is completely frozen. Complete freeze happens at -20F. The cylinder has radius of 1m and thickness of 10 mm on both hemisphere and the cylinder section and the radius of the hemisphere the same as the cylinder. The allowable shear and normal stresses of the cylinder are temperature dependent and both decrease as temperature decreases according to the following graph: 90 20 10 -80 -60 -40 -20 20 40 Shear stress -0-Normal Stress (a) At what temperature does the cylinder fail? What the failure mechanism (shear or normal)? (b) How would you modify the design to avoid failure to temperatures as low as 60F given you can only use this type material? Provide your calculations and design ideas by sketching the new design and calculating the new dimensions. 3. A Solid circular bar fixed at point A. The bar subjected to moment M and torque, T= NM The bar has length of 1.5m and diameter of mm. Determine the critical location on the beam ir terms of x, and coordinates If allowable shear stress OMPa and allowable normal stress 50 Mpa, what the maximum moment that can be applied to the beam? y T + A M y 1. Draw the Mohr circle for the following cases? material fails due to shear, which case fails faster? If material fails due to normal stress, which case fails faster? a o (b) t=a (c)

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Solution
The stored vessel is subjected to the rise in the internal pressured due to the freezing of the water in the tank. The projected pressure in the cylindrical vessel is 500kPa.
The complete freeze is expected at -20 Degree Fahrenheit of temperature.
The given radius of the cylinder is 1m.
The thickness of the hemispheres of the tank are 10mm
(Given that the allowable stresses in the material of the tank reduces with the temperature and from the given plot the allowable shear stress at -20 F is 15MPa and the allowable normal stress is 50Mpa.)
The ratio of R/t = 0.5/0.01 = 50>10 hence the given vessel can be considered as thin vessel.
The hoop stress...

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