MECHANICS (ES2410) SPRING 2013 This is due Wednesday, April 17, by classtime. No working in groups or pairs. Do your own work. Figure 1. Schematic diagram of a beam made of West- ern Hemlock 2x4s glued together. (1) Figure 1 shows a cross section of a beam made of glueing to- gether 2×4s (you‘ll need to look up the dimensions, but 158×358 is probably close enough). Each ten foot-long unsupported sec- tion of this beam might have to support 62% of the design load of 100 lb/ft2 of a floor that is twenty-seven (27) feet wide. The wood is Western Hemlock and the design calls for a factor of safety of 5.0. Find: (a) The required depth of the beam to support this load. (b) The necessary shear strength of the glue holding the lumber together. Date: April 10, 2013. 1
2 MECHANICS (ES2410) SPRING 2013 Figure 2. Tank for storage of oil. The material is like A36 steel. (2) Figure 2 shows a view of an oil storage tank that has a diameter of 30m, and holds oil to a height of 10m. Specific gravity of the oil is 0.85. Ignore the effect of the base. Consider steel with yield stress of 250MPa as the material from which this tank is fabricated. The wall thickness at the base of the tank is 20mm. Find: (a) Mohr’s circle for state of stress at the bottom of the tank, and the maximum shear stress. (b) Whether or not the tank is stable using an appropriate failure criterion, and if so, what is the factor of safety. (c) The wall thickness one-half way up the filled depth that has a safety factor of at least 5.0. (d) By what amount does the tank increase its diameter be- cause of stress at the base? Hint: is the tank holding any pressure in its vertical direction?
MECHANICS (ES2410) SPRING 2013 3 (3) Figure 3 shows a shaft from which a bucket is suspended in a well. Obviously the way the bucket hangs from the shaft places a torque on the shaft that would not be present if the bucket could be suspended from the shaft center. Otherwise these two cases of loading present identical…