Menu

Left end guided, right end simply supported for concentrated intermediate load

Concentrated intermediate load W a y A R A M A R B M B l θ B θ A
Concentrated intermediate load
Left end guided, right end simply supported for concentrated intermediate load a W
Left end guided, right end simply supported 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 $

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

Angular displacement $ θ_A $

$$θ_A=0$$

Deflection $ y_A $

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

Vertical end reactions $ R_B $

$$R_B=W$$

Reaction end moment $ M_B $

$$M_B=0$$

Angular displacement $ θ_B $

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

Deflection $ y_B $

$$y_B=0$$

Max. moment

$$M_{max}=M_A$$

Max. angular displacement

$$θ_{max}=θ_B$$

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

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