Q1 - The pressure vessel consists of 2 cylinders and a spherical dome that are bolted together at end flanges. Flange connection 1 consists of ½ inch diameter steel bolts on a 50" bolt circle. Flange 2 consists of ½ inch diameter aluminum bolts on a 50" bolt circle.
Use the following properties:
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Aluminum
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Steel
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E, 106 lbs/in2
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10.5
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30
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Yield stress, ksi
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20
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30
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Ultimate stress, ksi
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40
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60
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Ultimate shear stress, ksi
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15
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25
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Poisson Ratio
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0.3
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0.3
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A. Pressurize assembly to 100 psi. Calculate hoop and axial stress in each section. Design both bolt patterns (number and spacing) for safe operation. Justify your design. Ignore stress concentrations.
B. A torque of 5000 ft. lbs is applied to the steel cylinder at its midpoint. The pressure is removed. Develop a plot of shear stress from the base to the top of the cap. Will the bolts from the design in A work. If not fix it. Calculate the angular rotation at the top of the spherical cap.
C. Remove the torque and internal pressure. Apply an axial load F as shown. Assume that the cap is very thick and will not fail and that 6 bolts are used in teeth flange. What force F is necessary to fail each of the elements of the design (the bolts, the cylinders), i.e., what is the sequence of failures as the load F continues to increase (What fails first, what fails next, etc).
Q2 - The three little pigs are building a woks-proof house out of gingerbread. You are their structural engineer. The house will be built as shown. The bottom 25 ft is made of concrete but the upper 25 ft is made of gingerbread. There are steps leading up to a ledge made of cheese, above which is the entry door. So to get in, one must climb up the ladder and walk along the cheese ledge to the door. The pigs each weigh 50 Ibs and the big bad wolf weighs 200 lbs so the key is to design the pins and the cheese ledge sections to the gingerbread so that the pigs can get to the door but the wolf cannot.
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Potential pin material
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Shear strength psi
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Bearing strength psi
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Carrots
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25
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20
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Celery sticks
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50
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40
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Zucinni sticks
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75
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20
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Breadsticks
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100
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40
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Potential cheese materials
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Shear str psi
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Bearing str psi
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Tension str psi
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American
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2
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15
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1
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Cheddar
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4
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10
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5
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Provolone
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6
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20
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30
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Jack
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8
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5
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10
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Potential gingerbread materials
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Shear psi
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Bearing psi
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Tension psi
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Comp psi
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Standard
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0.5
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3
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1
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2
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Stale
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1.0
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6
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2
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4
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Overbaked
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1.5
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12
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3
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6
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The cheese blocks are 24" x 24" x 10" thick. The gingerbread walls are 6" thick. Assume that the pigs and the wolf can stand on only one cheese block at a time.
Design the system. You will have to specify pin, cheese and gingerbread materials, number of pins per cheese block and their location, and pin and hole diameter. Prove your solution works.
Q3 - Lets design 2 structures, one out of wood and one from aluminum. The rectangular pieces of wood (or aluminum) are pinned together using 1" diameter steel pins. The geometry of the structure is shown in the figure. Point A is pinned to the abutment and Point E is free to translate at the opposite abutment. Available wood stock is Southern Pine in 11 ft lengths with cross sections shown in the chart. There are 7 pieces of each cross section. Available 2024 T4 aluminum stock includes 11 ft pieces of the cross sections shown below (7 pieces each). You also have the use of a 1" drill and a power saw, good for cutting wood and aluminum.
(1) For the given loading and geometry, determine the required piece cross sections (i.e. choose the wood and aluminum pieces). Justify your choices.
(2) Design the pin joints. Provide a sketch showing where the pin holes are drilled. Justify dimensions.
(3) What does each structure weigh?
(4) Calculate the induced thermal stresses in the wood and aluminum pieces on a day where (delta)T = 100 deg F. Use CTE of Southern pine to be 20 x 10-6/degF.
(5) For the same (delta)T = 100F, calculate the thermal strain in A-B. Calculate the axial and cross sectional growth of the wood ant aluminum pieces.
