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October 16th, 2018, 12:09 PM   #1
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Joined: Feb 2018
From: England

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Merit Index.

Hi All,

Really struggling with the following question, been trying to research to no avail!

Any help would be much appreciated.



Function: To support a hanging load

Constraints: Minimise cost cap C

Objectives: Must carry load without failure, σ ≤ σ y ; Length L

Free variables: Cross-sectional area A ; Material used

i.
The objective is to minimise the actual cost C of the support rod. However, the material supplier can only provide the price per unit volume Pv of the material chosen.

Show that the objective equation is given C = PvAL.

Note: To answer this question you will need to derive an equation linking the actual cost of the material used to the price per unit volume provided by the supplier.

Include the equation with all your workings in your answer.

ii.
Derive an equation defining the strength constraint.
Include the equation with all your workings in your answer.

iii.
By combining the objective and constraint equations to eliminate the free variables, show that the final combined equation is C = Pv FL / σ y.
Include the equation with all your workings in your answer.

iv.

Separate the variables of the combined equation into functional F, geometric G and materials M groupings. In your answer, show the combined equation clearly identifying the F, G and M groupings.

v.
In your answer, show the merit index you derived for this problem is Pv / σ y. Define the axes you would adopt on an Ashby chart to be able to use your merit index and state, with a reason, whether the merit index should be maximised or minimised.

Thank you.
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