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BackCantilever beam - Couple moment Mo at any point Calculator
Formula
| Parameter | Formula |
|---|---|
| Deflection \(y_{AC}\) | \(y_{AC} = \frac{M_0 x^2}{2EI}\) |
| Deflection \(y_{CB}\) | \(y_{CB} = \frac{M_0 a}{2EI} (2x - a)\) |
| Deflection at \(x = L\) (\(y_{MAx}\) for segment AC) | \(y_{MAx} = \frac{M_0 a}{2EI} (2L - a)\) |
| Slope \(\theta_{AC}\) | \(\theta_{AC} = \frac{M_0 x}{EI}\) |
| Slope \(\theta_{CB}\) (\(\theta_C = \theta_B\)) | \(\theta_{CB} = \theta_C = \theta_B = \frac{M_0 a}{EI}\) |
| Moment \(M_{AC}\) (\(M_A\)) | \(M_{AC} = M_A = -M_0\) |
| Moment \(M_{CB}\) (\(M_B\)) | \(M_{CB} = M_B = 0\) |
| Shear \(V_{AC}\) (\(V_A = V_C\)) | \(V_{AC} = V_A = V_C = 0\) |
| Shear \(V_{CB}\) (\(V_C = V_B\)) | \(V_{CB} = V_C = V_B = 0\) |
| Reactions \(R_A\) | \(R_A = 0\) |
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 |