Multiple constraints: Connecting rods for high performance engines

[PCarson85]

Summary:: How to combine two formulas to find the material index

Attached is the problem I am having trouble understanding.

I have been able to do the first two combinations by transposing for A in the mass equation then subsituting into the stress equation. The next combinations (in red box) are harder to see. Is L isolated and then inserted into the next formula? How is this broken down?

Thanks for any help on this.

 

[BvU]

Hello @PCarson85, !

(10.5) ##\Rightarrow I = L^2 F / (\pi^2 E) ##
##I = b^3 w/12 ## & ##b = \alpha w \ \Rightarrow I = \displaystyle {\alpha^3w^4\over 12} ##
##A = bw ## & ##b = \alpha w \ \Rightarrow A = \alpha w^2 \Rightarrow I = \alpha A^2/12 \Rightarrow A = \sqrt {\displaystyle {12 I\over \alpha}} = \sqrt{\displaystyle {12 L^2F\over \alpha \pi^2E}}##
Rearrange and substitute in (10.1) to get (10.6)

 

[PCarson85]

Of course... b x w is area... much appreciated!