i$)$ A vertical force $P=$akN acts on the end of a cantilever

beam with a rectangular cross$-$section width of $cm$ and

a height that changes linearly. Divide the beam length

into $20$ equal parts and calculate the deflection and

rotation at the midpoint of the beam using the finite

difference method. $(20$ points$)L=4m,h_o=30cm,$

h $-15$nmE$-1RD.$

$a=36$

ii$)$ When the loading and support conditions are as shown

in the figure $($uniformly distributed load and simply

supported at the right end$),$ find the values and locations

of the maximum deflection, maximum positive rotation,

maximum positive moment, and maximum positive shear

force. $(30$ points$)$ Again, divide the system into $20$ equal

parts for your calculations.

You may use electronic spreadsheets for your

calculations. However, you must also write clearly in

your assignment what you did, how you did it$,$ and why

you did it$.$