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BackCantilever beam - Concentrated load P at free end Calculator
Formula
| Deflection \(y\) | \(y_{AB} = \frac{6EI}{-P} (3Lx^2 - x^3)\) | \(y_{MAx} = y_B = -\frac{PL^3}{3EI}\) |
| Slope \(\theta\) | \(\theta_{AB} = -\frac{P}{2EI} (2Lx - x^2)\) | \(\theta_{MAx} = \theta_B = -\frac{PL^2}{2EI}\) |
| Moment \(M\) | \(M_{AB} = -P(L - x)\) | \(M_{MAx} = M_A = -PL\) |
| Shear \(V\) | \(V_{AB} = V_A = V_B = P\) | |
| Reactions \(R\) | \(R_A = P\) | |
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 |