Overhanging beam - Uniformly distributed load Calculator
Formula
| Category |
Formula |
| Deflection \( y_{AB} \) |
\[
y_{AB} = \frac{-w_{0}x}{24LEI} \left( L^4 - 2L^2x^2 + Lx^3 - 2a^2L^2 + 2a^2x^2 \right)
\] |
| Deflection \( y_{BC} \) |
\[
y_{BC} = \frac{-w_{0}x_1}{24EI} \left( 4a^2L - L^3 + 6a^2x_1 - 4ax_1^2 + x_1^3 \right)
\] |
| Slope \( \theta_{AB} \) |
\[
\theta_{AB} = \frac{-w_{0}}{24LEI} \left( L^4 - 6L^2x^2 + 4Lx^3 - 2a^2L^2 + 6a^2x^2 \right)
\] |
| Slope \( \theta_{BC} \) |
\[
\theta_{BC} = \frac{-w_{0}}{24EI} \left( 4a^2L - L^3 + 12a^2x_1 - 12ax_1^2 + 4x_1^3 \right)
\] |
| Moment \( M_{AB} \) |
\[
M_{AB} = \frac{w_{0}x}{2L} \left( L^2 - Lx - a^2 \right)
\] |
| Moment \( M_{BC} \) |
\[
M_{BC} = \frac{-w_{0}}{2} \left( a - x_1 \right)^2
\] |
| Shear \( V_{AB} \) |
\[
V_{AB} = \frac{w_{0}}{2L} \left( L^2 - 2Lx - a^2 \right)
\] |
| Shear \( V_{BC} \) |
\[
V_{BC} = w_{0} \left( a - x_1 \right)
\] |
| Reactions \( R_A \), \( R_B \) |
\[
R_A = \frac{w_{0}}{2L} \left( L^2 - a^2 \right), \quad R_B = \frac{w_{0}}{2L} \left( L + a \right)^2
\] |
| Where \( x_1 \) |
\[
x_1 = x - L
\] |
Definitions
| Symbol |
Physical quantity |
Units |
| E·I |
Flexural rigidity |
N·m², Pa·m⁴ |
| y |
Deflection or deformation |
m |
| θ |
Slope, Angle of rotation |
- |
| x |
Distance from support (origin) |
m |
| L |
Length of beam (without overhang) |
m |
| M |
Moment, Bending moment, Couple moment applied |
N·m |
| P |
Concentrated load, Point load, Concentrated force |
N |
| w |
Distributed load, Load per unit length |
N/m |
| R |
Reaction load, reaction force |
N |
| V |
Shear force, shear |
N |
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