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BackCantilever beam - Concentrated load P at any point Calculator
Formula
| Deflection \(y\) | \(y_{AC} = \frac{6EI}{-P} (3ax^2 - x^3)\) | \(y_{CB} = \frac{6EI}{-Pa^2} (a-x)^2(3x-a)\) |
| Deflection at \(x = L\) (\(y_{MAx} = y_B\)) | \(y_{MAx} = y_B = -\frac{Pa^2}{6EI}(3L-a)\) | |
| Slope \(\theta\) | \(\theta_{AC} = -\frac{P}{2EI}(2ax - x^2)\) | \(\theta_{CB} = \theta_C = \theta_B = -\frac{Pa^2}{2EI}\) |
| Moment \(M\) | \(M_{AC} = -P(a-x)\) | \(M_{CB} = M_C = M_B = 0\) |
| Moment at \(x = a\) (\(M_{MAx} = M_A\)) | \(M_{MAx} = M_A = -Pa\) | |
| Shear \(V\) | \(V_{AC} = V_A = V_C = P\) | \(V_{CB} = V_C = V_B = 0\) |
| 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 |