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BackSimple beam - Uniform load partially distributed Calculator
Formula
| Quantity | Formula |
|---|---|
| Deflection \(y_{AC}\) | \(\frac{R_{A}x^{3}}{6EI} + \alpha x\) |
| Deflection \(y_{CD}\) | \(\frac{R_{A}x^{3}}{6EI} - \frac{w_{0}}{24EI}(x-a)^{4} + \alpha x\) |
| Deflection \(y_{DB}\) | \(\frac{R_{B}(L-x)^{3}}{6EI} + \frac{\beta (L-x)}{L}\) |
| Slope \(\theta_{AC}\) | \(\frac{R_{A}x^{2}}{2EI} + \alpha\) |
| Slope \(\theta_{CD}\) | \(\frac{R_{A}x^{2}}{2EI} - \frac{w_{0}}{6EI}(x-a)^{3} + \alpha\) |
| Slope \(\theta_{DB}\) | \(\frac{-R_{B}(L-x)^{2}}{2EI} - \frac{\beta}{L}\) |
| Moment \(M_{AC}\) | \(R_{A} x\) |
| Moment \(M_{CD}\) | \(R_{A} x - \frac{w_{0}}{2}(x-a)^{2}\) |
| Moment \(M_{DB}\) | \(R_{B}(L-x)\) |
| Shear \(V_{AC}, V_{A}, V_{C}\) | \(R_{A}\) |
| Shear \(V_{CD}\) | \(R_{A} - w_{0}(x-a)\) |
| Shear \(V_{DB}, V_{D}, V_{B}\) | \(-R_{B}\) |
| Reaction \(R_{A}\) | \(\frac{w_{0}b}{2L}(2c+b)\) |
| Reaction \(R_{B}\) | \(\frac{w_{0}b}{2L}(2a+b)\) |
| \(\alpha\) | \(\frac{w_{0}b^{3}L - 6EI\beta - 3R_{B}c^{2}L - 3R_{A}L(a+b)^{2}}{6LEI}\) |
| \(\beta\) | \(\frac{4w_{0}ab^{3} + 3w_{0}b^{4} - 8R_{A}(a+b)^{3} - 12R_{B}c^{2}L + 8R_{B}c^{3}}{24EI}\) |
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 |