Home
BackCantilever beam - Couple moment Mo at free end Calculator
Formula
| Parameter | Formula |
|---|---|
| Deflection \(y_{AB}\) | \(y_{AB} = \frac{M_0 x^2}{2EI}\) |
| Deflection at \(x = L\) (\(y_{MAx}\) for segment AB) | \(y_{MAx} = -\frac{M_0 L^2}{2EI}\) |
| Slope \(\theta_{AB}\) | \(\theta_{AB} = -\frac{M_0 x}{EI}\) |
| Moment \(M_{AB}\) (\(M_A = M_B\)) | \(M_{AB} = M_A = M_B = -M_0\) |
| Shear \(V_{AB}\) (\(V_A = V_B\)) | \(V_{AB} = V_A = V_B = 0\) |
| 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 |