Consider the shaft shown in $($Figure $1).$ EI is constant

Determine the equation of the elastic curve of the shaft.

$v=\frac{P}{2EI}[x^2+($:$x-a$:${)}^2+($:$x-3a{)}^2+ax]$

$v=\frac{P}{6EI}[-x^3-($:$x-a$:${)}^3+($:$x-3a$:${)}^3+15a^{2}x-14a^3]$

$v=\frac{P}{6EI}[-x^3-($:$x-a$:${)}^3+($:$x-3a$:${)}^3+12a^{2}x-11a^3]$

$v=\frac{P}{6EI}[-x^3+($:$x-a$:${)}^3+($:$x-3a$:${)}^3+12a^{2}x-11a^3]$

$v=\frac{P}{6EI}[-x^3+($:$x-a$:${)}^3-($:$x-2a$:${)}^3+8a^{2}x-9a^3]$

$v=\frac{P}{6EI}[-x^3+($:$x-a$:${)}^3+($:$x-3a$:${)}^3+9a^{2}x-8a^3]$

$v=\frac{P}{6}[x^3+($:$x-a$:${)}^3+($:$x-3a$:${)}^3+9a^{2}x-8a^3]$

$v=\frac{P}{6EI}[x^3+($:$x-a$:${)}^3+($:$x-3a$:${)}^3-15a^{2}x+14a^3]$

Figure

$1$ of $1$

Part B

Determine the maximum deflection in region $BC$ of the shaft.

Express your answer in terms of some or all of the variables $a,E,$I, and $P.$ Enter positive value if the deflection is upward and negative value if the deflection is downward.

Determine the deflection of end $A$ of the shaft

Express your answer in terms of some or all of the variables $a,E,$I, and $P.$ Enter positive value if the deflection is upward and negative value if the deflection is downward.