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BackCantilever beam - Uniformly distributed load Calculator
Formula
| Category | Formula |
|---|---|
| Deflection (\( y_{AB} \)) | \[ y_{AB} = \frac{-w_0}{24EI}(x^4 - 4Lx^3 + 6L^2x^2) \] |
| Maximum Deflection (\( y_{\text{MAX}} = y_B \)) | \[ y_{\text{MAX}} = y_B = \frac{-w_0 L^4}{8EI} \quad \text{at } x = L \] |
| Slope (\( \theta_{AB} \)) | \[ \theta_{AB} = \frac{-w_0}{6EI}(x^3 - 3Lx^2 + 3L^2x) \] |
| Slope at B (\( \theta_B \)) | \[ \theta_B = \frac{-w_0 L^3}{6EI} \] |
| Moment (\( M_{AB} \)) | \[ M_{AB} = \frac{-w_0}{2}(L - x)^2 \] |
| Maximum Moment (\( M_{\text{MAX}} = M_A \)) | \[ M_{\text{MAX}} = M_A = \frac{-w_0 L^2}{2} \] |
| Shear (\( V_{AB} \)) | \[ V_{AB} = w_0(L - x) \] |
| Reactions (\( R_A \)) | \[ R_A = w_0 L \] |
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 |