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BackSimple beam - Couple moments M1 and M2 at each end I Calculator
Formula
| Deflection (AB) | \( y_{\mathrm{AB}} = \frac{-x(L-x)}{6 L E I}\left[\left(M_1-M_2\right) x-\left(2 M_1+M_2\right) L\right] \) |
| Slope (AB) | \[ \theta_{\mathrm{AB}} = \frac{1}{6 L E I}\left[\left(M_1-M_2\right)\left(3 x^2-2 L x\right)-\left(2 M_1+M_2\right)\left(2 L x-L^2\right)\right] \] |
| Moment (AB) | \( M_{\mathrm{AB}} = \frac{1}{L}\left[\left(M_1-M_2\right) x-L M_1\right] \) |
| Shear (AB) | \( V_{\mathrm{AB}} = \frac{M_1-M_2}{L} \) |
| Reactions | \( R_{\mathrm{A}} = \frac{M_1-M_2}{L} \quad R_{\mathrm{B}} = \frac{M_2-M_1}{L} \) |
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 |