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BackFixed-pinned beam - Couple moment Mo at supported end Calculator
Formula
| Property | Formula |
|---|---|
| Deflection (\(y_{AB}\)) | \(y_{AB} = \frac{M_0 x^2 (L-x)}{4EI L}\) |
| Slope (\(\theta_{AB}\)) | \(\theta_{AB} = \frac{M_0 x (2L-3x)}{4EI L}\) |
| Moment (\(M_{AB}\)) | \(M_{AB} = \frac{M_0 (L-3x)}{2L}\) |
| Shear (\(V_{AB}\)) | \(V_{AB} = \frac{-3M_0}{2L}\) |
| Reaction (\(R_A\)) | \(R_A = \frac{-3M_0}{2L}\) |
| Reaction (\(R_B\)) | \(R_B = \frac{3M_0}{2L}\) |
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 |