Question $2$

$($a$)$ With reference to the following support conditions for a beam, draw a neat sketch to show the slope and deflection, when:

$($i$)$ Both ends pinned

$($ii$)$ Both ends fixed

$[12$ marks$]$

$($b$)$ A cantilever beam of length $4$ m is loaded at the free end by a load $W=20kN.$ Determine the maximum deflection of the beam given that the second moment of area of the cross section is $104{10}^{6}m{m}^4$ and $E=100G\frac{N}{m^2}.$ Use the slope deflection method to derive the expression used.

$[13$ marks$]$