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BackFixed-pinned beam - Uniformly distributed load Calculator
Formula
| Category | Formula |
|---|---|
| Deflection \( y_{AB} \) | \[ y_{AB} = \frac{-w_0x^2}{48EI} \left( 3L^2 - 5Lx + 2x^2 \right) \] |
| Slope \( \theta_{AB} \) | \[ \theta_{AB} = \frac{-w_0x}{48EI} \left( 6L^2 - 15Lx + 8x^2 \right) \] |
| Moment \( M_{AB} \) | \[ M_{AB} = \frac{-w_0}{8} \left( L^2 - 5Lx + 4x^2 \right) \] |
| Shear \( V_{AB} \) | \[ V_{AB} = \frac{w_0}{8} \left( 5L - 8x \right) \] |
| Reactions \( R_A \), \( R_B \) | \[ R_A = \frac{5w_0L}{8}, \quad R_B = \frac{3w_0L}{8} \] |
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 |