For the stepped cantilever beam shown, using Interval Finite Element Analysis, obtain the bounds of the vertical displacement at the free end, as well as the bounds of the fundamental natural circular frequency.

For this project, the modulus of Elasticity, $E,$ possesses interval uncertainty

The modulus of Elasticity of each of the four beam segments should be considered as separate independent interval variables.

The interval for each segment should be: $0\mathrm{.}9E,1\mathrm{.}1E.$

To perform interval finite element analysis, perform deterministic analyses for all combinations of upper and lower bounds for each interval variable. The interval bounds will be the maximum and minimum results found from the evaluation of all such combinations.

Structural Notes:

The stepped Cantilever Beam is made of cross laminated timber $($CLT$)$

The species of wood is Douglas Fir: $E=1,720,000$ psi

Douglas Fir has a density: $=33pcf$

The shallowest section has an area of $A=16i{n}^2$

The shallowest section has a moment of inertia $I=85$ in ${?}^4$