Home
BackCantilever beam - Load increasing uniformly to free end Calculator
Formula
| Parameter | Formula |
|---|---|
| Deflection (\(y_{AB}\)) | \(-\frac{w_0 x^2}{120LEI} (20L^3 - 10L^2x + x^3)\) |
| Maximum Deflection (\(y_{MAX}\)) | \(-\frac{11w_0 L^4}{120EI}\) at \(x = L\) |
| Slope (\(\theta_{AB}\)) | \(-\frac{w_0 x}{24LEI} (8L^3 - 6L^2x + x^3)\) |
| Slope at B (\(\theta_B\)) | \(-\frac{w_0 L^3}{8EI}\) |
| Moment (\(M_{AB}\)) | \(-\frac{w_0}{6L} (2L^3 - 3L^2x + x^3)\) |
| Shear (\(V_{AB}\)) | \(\frac{w_0}{2L} (L^2 - x^2)\) |
| Reactions (\(R_A\)) | \(\frac{w_0 L}{2}\) |
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 |