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Formula
| Quantity | Formula |
|---|---|
| Moment \(M_{AC}\) | \(R_{A} x - \frac{w_{1}x^{2}}{2}\) |
| Moment \(M_{CD}\) | \(R_{A} x - \frac{w_{1}a}{2}(2x-a)\) |
| Moment \(M_{DB}\) | \(R_{B}(L-x) - \frac{w_{2}(L-x)^{2}}{2}\) |
| Shear \(V_{AC}\) | \(R_{A} - w_{1} x\) |
| Shear \(V_{CD}\) | \(R_{A} - w_{1} a\) |
| Shear \(V_{DB}\) | \(-R_{B} + w_{2}(L-x)\) |
| Reaction \(R_{A}\) | \(\frac{w_{1}a(2L-a) + w_{2}c^{2}}{2L}\) |
| Reaction \(R_{B}\) | \(\frac{w_{2}c(2L-c) + w_{1}a^{2}}{2L}\) |
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 |