Q1) a) List three classical methods of optimization in engineering design.
b) Describe the type of finite elements used to solve 3 dimensional problems in solid mechanics. Supply examples of the application.
c) Describe four "engineering attributes" of a skate board.
Q2) Design a steel helical spring for a minimum volume that will carry a static load of 200 lbs with a deflection of 2.0 inches. The adjusted maximum shear strength is 80,000 psi and there are one and half end turns. The shearing modulus for steel is 11.5 E06 psi. Determine:
a) the appropriate wire diameter in inches.
b) the total number of coils.
e) the volume of the material in cubic inches.
Q3) As chief project engineer, part of your responsibility is to chose a material for the design of the rotor for an integral-horsepower induction motor. Gray cast iron has been used successfully for years, but aluminum alloys are now being considered. It has been determined from experience, that order of importance from 'cast important to most importance is: elongation, ultimate tensile strength, shear strength and yield strength. Based on the data shown in the table, determine the best choice of material using a mathematical attribute selection process.
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Comparison of typical mechanical properties
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Material
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Yield strength, ksi
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Ultimate tensile strength, ksi
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Shear strength, ksi
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Elongation in 2 in, percent
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Gray cast iron
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18
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22
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20
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0.5
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Alloy 356 (as cast)
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15
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26
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16
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3.5
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Alloy 360 (as cast)
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25
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26
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26
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3.5
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Alloy 356-T61 (solution heat-treated and artificially aged)
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28
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38
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30
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5
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Q4) A manufacturer of open top thin sheet metal boxes wants to minimize material costs. The box consists of vertical sides and a base. The cost of material is $100 per cubic meters. If the volume of the box is 400 cubic meters and the thickness of the sheet metal is δ using the Method of Lagrangian Multipliers optimization:
a) Determine the relation between b and h for minimum cost for arbitrary.
b) Determine the actual cost per box for δ = 10 mm.