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BackFixed-fixed beam - Concentrated load at center Calculator
Formula
| Parameter | Formula |
|---|---|
| Deflection (AC) | \( y_{AC} = \frac{-P x^2 (3L - 4x)}{48EI} \) |
| Deflection (CB) | \( y_{CB} = \frac{-P (L - x)^2 (4x - L)}{48EI} \) |
| Slope (AC) | \( \theta_{AC} = \frac{-P x (L - 2x)}{8EI} \) |
| Slope (CB) | \( \theta_{CB} = \frac{-P (L^2 - 3Lx + 2x^2)}{8EI} \) |
| Moment (AC) | \( M_{AC} = \frac{-P (L - 4x)}{8} \) |
| Moment (CB) | \( M_{CB} = \frac{P (3L - 4x)}{8} \) |
| Shear (AC) | \( V_{AC} = \frac{P}{2} \) |
| Shear (CB) | \( V_{CB} = \frac{-P}{2} \) |
| Reactions | \( R_A = R_B = \frac{P}{2} \) |
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 |