A vertical force $P=28kN$ acts on the end of a cantilever beam with a rectangular cross$-$section

width of $28cm$ 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. $L=4m,h_0=30cm,h_L=15cm,E=10$GPa

$1_{?}$

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. Again, divide the system into $20$ equal parts for your calculations.