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BackSimple beam - Uniformly distributed load Calculator
Formula
| Quantity | Formula | Notes |
|---|---|---|
| Deflection \(y_{AB}\) | \(-\frac{w_0 x}{24EI} \left(L^3 - 2Lx^2 + x^3 \right)\) | |
| Maximum Deflection \(y_{\text{MAX}}\) | \(-\frac{5w_0 L^4}{384EI}\) | At \(x = \frac{L}{2}\) |
| Slope \(\theta_{AB}\) | \(-\frac{w_0}{24EI} \left(L^3 - 6Lx^2 + 4x^3 \right)\) | |
| Maximum Slope \(\theta_A = -\theta_B\) | \(-\frac{w_0 L^3}{24EI}\) | |
| Moment \(M_{AB}\) | \(\frac{w_0 x}{2} \left(L - x \right)\) | |
| Maximum Moment \(M_{\text{MAX}}\) | \(\frac{w_0 L^2}{8}\) | At \(x = \frac{L}{2}\) |
| Shear \(V_{AB}\) | \(\frac{w_0}{2} \left(L - 2x \right)\) | |
| Reactions \(R_A = R_B\) | \(\frac{w_0 L}{2}\) |
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 |