User:Eas4200c.f08.WIKI.E/hw1

 Case one:  σ reaches σallowable first therefore τ < τallowable

The first case is for tau less than or equal to tau allowable. Using the following formulas, you can find the optimal cross section.

Recall: $$ \displaystyle \tau$$ = {T}/{2·B·A·t}


 * σ = M·Z/I

M = Bending Moment

Z = Ordinate of a point on the axis perpendicular to bend of neutral axis

I = 2nd Area Moment of Inertia

$$I = \iint_{A}^{} \Z^2 dx\,dy$$