parameter: $a=21$

i$)$ A vertical force $P=$akN acts on the end of a cantilever beam with a rectangular cross$-$section

width of acm 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$)L=4m,h_n=30cm,h_{}=15cm,E=10$GPa

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$.$