Left end free, right end fixed (cantilever) for concentrated intermediate load

Values for calculation

$l$ $\mathrm{mm}$
$a$ $\mathrm{mm}$
$W$ $\mathrm{N}$
$E$ $\mathrm{MPa}$
$I$ $\mathrm{mm^4}$
$x$ $\mathrm{mm}$

Calculation

Vertical end reactions $R_A$

$$R_A=0$$

Reaction end moment $M_A$

$$M_A=0$$

Angular displacement $θ_A$

$$θ_A=\cfrac{W\cdot\left(l-a\right)^2}{2\cdot E\cdot I}$$

Deflection $y_A$

$$y_A=\cfrac{-W}{6\cdot E\cdot I}\cdot\left(2\cdot l^3-3\cdot l^2\cdot a+a^3\right)$$

Vertical end reactions $R_B$

$$R_B=W$$

Reaction end moment $M_B$

$$M_B=-W\cdot\left(l-a\right)$$

Angular displacement $θ_B$

$$θ_B=0$$

Deflection $y_B$

$$y_B=0$$

Max. moment

$$M_{max}=M_B$$

Max. angular displacement

$$θ_{max}=θ_A$$

Max. deflection

$$y_{max}=y_A$$

Transverse shear

$\text{if }\ x\le a$
$$V=R_A$$
$\text{else}$
$$V=R_A-W$$

Bending moment

$\text{if }\ x\le a$
$$M=M_A+R_A\cdot x$$
$\text{else}$
$$M=M_A+R_A\cdot x-W\cdot\left(x-a\right)$$

Slope

$\text{if }\ x\le a$
$$θ=θ_A+\cfrac{M_A\cdot x}{E\cdot I}+\cfrac{R_A\cdot x^2}{2\cdot E\cdot I}$$
$\text{else}$
$$θ=θ_A+\cfrac{M_A\cdot x}{E\cdot I}+\cfrac{R_A\cdot x^2}{2\cdot E\cdot I}-\cfrac{W}{2\cdot E\cdot I}\cdot\left(x-a\right)^2$$

Deflection

$\text{if }\ x\le a$
$$y=y_A+θ_A\cdot x+\cfrac{M_A\cdot x^2}{2\cdot E\cdot I}+\cfrac{R_A\cdot x^3}{6\cdot E\cdot I}$$
$\text{else}$
$$y=y_A+θ_A\cdot x+\cfrac{M_A\cdot x^2}{2\cdot E\cdot I}+\cfrac{R_A\cdot x^3}{6\cdot E\cdot I}-\cfrac{W}{6\cdot E\cdot I}\cdot\left(x-a\right)^3$$