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Formula
| Quantity | Formula |
|---|---|
| Deflection (AC) | \( y_{AC} = \frac{M_0 x^2}{8 L E I} (2x - L) \) |
| Deflection (CB) | \( y_{CB} = -\frac{M_0}{8 L E I} \left(5Lx^2 - 2x^3 - 4L^2x + L^3\right) \) |
| Slope (AC) | \( \theta_{AC} = \frac{M_0 x}{4 L E I} (3x - L) \) |
| Slope (CB) | \( \theta_{CB} = -\frac{M_0}{8 L E I} \left(10Lx - 6x^2 - 4L^2\right) \) |
| Moment (AC) | \( M_{AC} = \frac{M_0}{4 L} (6x - L) \) |
| Moment (CB) | \( M_{CB} = -\frac{M_0}{4 L} (5L - 6x) \) |
| Shear | \( V_{AB} = \frac{3 M_0}{2 L} \) |
| Reaction (RA) | \( R_A = \frac{3 M_0}{2 L} \) |
| Reaction (RB) | \( R_B = -\frac{3 M_0}{2 L} \) |
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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