Question#$3(16$ Marks$)$

a$.$ Consider an overhanging beam ABC shown in Figure Q$3.$ For the loading shown, determine:

i$.$ Derive the equation of the elastic curve for the beam.

$[2$ Marks$]$

ii$.$ The deflection at point B by assuming the values of $p,q,$ and $a.$

$[3$ Marks$]$

iii. The slope at point $A.$

$[3$ Marks$]$

b$.$ If the uniformly distributed load is omitted with a concentrated load at $C,$

i$.$ Derive the equation of the elastic curve for the beam.

$[2$ Marks$]$

ii$.$ Determine the deflection at point B$.$ Compare the result with that of Q$3$aii.

$[3$ Marks$]$

c$.$ If the support is only at point A without uniformly distributed load, determine the deflection at point $B.$ Discuss the results with that of Q$3$aii and Q$3$bii.

$[3$ Marks$]$