Lecture Problem 20'D5

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Lecture Problem 20.D5

• Zane Kealey
• 3/23/07

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Project Statement Summary
Given

• Identify functions, objectives and constraints
• Find expressions for both performance indices
  using free variable
• Select metal alloys with a stiffness performance
  indice above 1.50, a strength performance indice
  above 6.0 and a minimum cost.

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Functions, Objectives and Constraints

• Functions
• Spans distance between to supports
• Supports a distributed load
• Objectives
• Minimize mass, m
• Minimize cost, m(/kg)
• Constraints
• Specified L, F, d and w
• Must not permanently deform

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Performance indices

• Stiffness performance indice, Ps
• Solve for free variable t
• Plug into mass equation because thats what were
  optimizing
• Identify varying parameters
• Invert expression so the performance index can be
  maximized

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Performance indices

• Strength performance index, P
• Same method as stiffness performance index

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Using performance indices

• Need a Psgt1.5
• Take the log of the performance expression
• Slope of 3, y-intercept of 3.375
• Use CES to determine which metal alloys have
  appropriate properties

WATCH UNITS IN CES!! 3.375 GPa/(g/cm3)3
2.01e-6 (106psi/(lb/ft3)3
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CES Stiffness Performance Index
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Strength performance index

• Need a Pgt6.0
• Slope of 2, y-intercept of 36
• For CES
• 36 MPa/(g/cm3)2 1.34e-3 (ksi/(lb/ft3)2)

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CES Strength Performance index
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Minimizing Cost

• A log plot of densityprice versus Youngs
  Modulus can be used to find the most cost
  effective material
• Slope is still 3 since we are just multiplying
  the density by a constant factor
• The material farthest from the line is the lowest
  priced stiffness-per-mass

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CES Best priced stiffness-per-mass
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CES Best priced strength-per-mass
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Material Selection

• To construct this bridge to meet required
  specifications and to minimize cost, an aluminum
  alloy would be the best choice.
• This problem has applications in any design
  problem where you need to choose a material that
  will meet needed specifications and minimize cost.