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BackCantilever beam - Load increasing uniformly to fixed end Calculator
Formula
| Parameter | Formula |
|---|---|
| Deflection (\(y_{AB}\)) | \(-\frac{w_0 x^2}{120LEI} (10L^3 - 10L^2x + 5Lx^2 - x^3)\) |
| Maximum Deflection (\(y_{MAX}\)) | \(\frac{w_0 L^4}{30EI}\) at \(x = L\) |
| Slope (\(\theta_{AB}\)) | \(-\frac{w_0 x}{24LEI} (4L^3 - 6L^2x + 4Lx^2 - x^3)\) |
| Slope at B (\(\theta_B\)) | \(-\frac{w_0 L^3}{24EI}\) |
| Moment (\(M_{AB}\)) | \(-\frac{w_0}{6L} (L - x)^3\) |
| Shear (\(V_{AB}\)) | \(\frac{w_0}{2L} (L - x)^2\) |
| 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 |