ts $>$ Week $11-18$th Nov $>$ Problem Set Week$112021$

em Set Week$112021$

$1$ of $2$

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Select a material for the 'ultimate bicycle', i$.$e$.,$ the lightest possible for a given stiffness.

Assume the tubes of which it is made can be treated as cantilevered beams $($length I$),$ where displacement $$ of one end for a force $F$ is

$=\frac{F{l}^3}{3E{r}^{3}t}$

Consider two situations

The designer fixes the diameter of the tubes that you can use, but you can vary the thickness the tube $t.$

The designer fixes the thickness of the tubes that you can use, but you can vary the diameter the tube.

a$)$ Develop a Merit Index for the two situations, then using the information in the table below, choos the 'best' material.

b$)$ Give $2$ reasons why this Merit Index may be insufficient for material selection purposes.

$\backslash$table$[[$Material$,,$E$[$GPa$],r_{?}$