Home
BackOverhanging beam - Concentrated load at end of overhang Calculator
Formula
| Category | Formula |
|---|---|
| Deflection \( y_{AB} \) | \[ y_{AB} = \frac{Pax}{6LEI} \left( L^2 - x^2 \right) \] |
| Deflection \( y_{BC} \) | \[ y_{BC} = \frac{-Px_1}{6EI} \left( 2aL + 3ax_1 - x_1^2 \right) \] |
| Slope \( \theta_{AB} \) | \[ \theta_{AB} = \frac{Pa}{6LEI} \left( L^2 - 3x^2 \right) \] |
| Slope \( \theta_{BC} \) | \[ \theta_{BC} = \frac{-P}{6EI} \left( 2aL + 6ax_1 - 3x_1^2 \right) \] |
| Moment \( M_{AB} \) | \[ M_{AB} = \frac{-Pax}{L} \] |
| Moment \( M_{BC} \) | \[ M_{BC} = -P \left( a - x_1 \right) \] |
| Shear \( V_{AB} \) | \[ V_{AB} = \frac{-Pa}{L} \] |
| Shear \( V_{BC} \) | \[ V_{BC} = P \] |
| Reactions \( R_A \), \( R_B \) | \[ R_A = \frac{-Pa}{L}, \quad R_B = \frac{P(L+a)}{L} \] |
| 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 |