Problem $1-$

A horizontal beam ABCDE of thickness $18$ mm $,$ and depth $80$ mm is

supported by a fixed support at A$,$ and roller supports at C$,$ and E$.$

The beam is made of two parts that are connected together by a

frictionless pin at D of diameter $20$ mm $.$ The beam is loaded as

shown. Determine:

i$-$ The external reactions at $A,C,$ and E $,$ and the force

transmitted through the pin at D$.$

ii$-$ Plot the variations of the internal reaction diagrams for the

two parts of the rod ABCDE $,$ and hence determine the maximum

absolute values of the shearing forces, and bending moments and

their locations.

iii$-$ Determine the bearing pressure acting on the pin B $.$