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BackOverhanging beam - Concentrated load at any point between supports Calculator
Formula
| Category | Formula |
|---|---|
| Deflection \( y_{AC} \) | \[ y_{AC} = \frac{-Pbx}{6LEI} \left( L^2 - b^2 - x^2 \right) \] |
| Deflection \( y_{CB} \) | \[ y_{CB} = \frac{-Pa(L-x)}{6LEI} \left( 2Lx - a^2 - x^2 \right) \] |
| Deflection \( y_{BD} \) | \[ y_{BD} = \frac{Pabx_1}{6LEI} \left( L + a \right) \] |
| Slope \( \theta_{AC} \) | \[ \theta_{AC} = \frac{-Pb}{6LEI} \left( L^2 - b^2 - 3x^2 \right) \] |
| Slope \( \theta_{CB} \) | \[ \theta_{CB} = \frac{-Pa}{6LEI} \left( 2L^2 - 6Lx + a^2 + 3x^2 \right) \] |
| Slope \( \theta_{BD} \) | \[ \theta_{BD} = \frac{Pab(L+a)}{6LEI} \] |
| Moment \( M_{AC} \) | \[ M_{AC} = \frac{Pbx}{L} \] |
| Moment \( M_{CB} \) | \[ M_{CB} = \frac{Pa}{L} (L - x) \] |
| Moment \( M_{BD} \) | \[ M_{BD} = 0 \] |
| Shear \( V_{AC} \) | \[ V_{AC} = \frac{Pb}{L} \] |
| Shear \( V_{CB} \) | \[ V_{CB} = \frac{-Pa}{L} \] |
| Shear \( V_{BD} \) | \[ V_{BD} = 0 \] |
| Reactions \( R_A \), \( R_B \) | \[ R_A = \frac{Pb}{L}, \quad R_B = \frac{Pa}{L} \] |
| 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 |