Simple beam - Couple moment Mo at left end I Calculator
Formula
| Deflection (AB) |
\( y_{\mathrm{AB}} = \frac{M_0 x}{6 L E I}\left(2 L^2-3 L x+x^2\right) \) |
| Maximum Deflection |
\( y_{\mathrm{MAX}} = \frac{M_0 L^2}{9 \sqrt{3} E I} \quad \text{at} \quad x = \left(\frac{3-\sqrt{3}}{3}\right) L \) |
| Slope (AB) |
\( \theta_{\mathrm{AB}} = \frac{M_0}{6 L E I}\left(2 L^2-6 L x+3 x^2\right) \) |
| Slope at A |
\( \theta_{\mathrm{A}} = \frac{M_0 L}{3 E I} \) |
| Slope at B |
\( \theta_{\mathrm{B}} = \frac{-M_0 L}{6 E I} \) |
| Moment (AB) |
\( M_{\mathrm{AB}} = \frac{-M_0}{L}(L-x) \) |
| Shear (AB) |
\( V_{\mathrm{AB}} = \frac{M_0}{L} \) |
| Reactions |
\( R_{\mathrm{A}} = \frac{M_0}{L} \quad R_{\mathrm{B}} = \frac{-M_0}{L} \) |
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 |
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