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BackSimple beam - Two equal couple moments Mo at each end Calculator
Formula
| Quantity | Formula |
|---|---|
| Deflection \(y_{AB}\) | \(\frac{-M_{0}x}{2EI}(L-x)\) |
| Maximum Deflection \(y_{\text{MAX}}\) | \(\frac{-M_{0}L^{2}}{8EI} \, \text{at} \, x = \frac{L}{2}\) |
| Slope \(\theta_{AB}\) | \(\frac{-M_{0}}{2EI}(L-2x)\) |
| Slope \(\theta_{A}, \theta_{B}\) | \(\theta_{A} = -\theta_{B} = \frac{-M_{0}L}{2EI}\) |
| Moment \(M_{AB}\) | \(M_{0}\) |
| Shear \(V_{AB}\) | 0 |
| Reactions \(R_{A}, R_{B}\) | \(R_{A} = R_{B} = 0\) |
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 |