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BackSimple beam - Load increasing uniformly to center Calculator
Formula
| Deflection (AC) | \[ y_{\mathrm{AC}} = \frac{-w_0 x}{960 L E I}\left(5 L^2 - 4 x^2\right)^2 \] |
| Deflection (CB) | \[ y_{\mathrm{CB}} = \frac{-w_0(L-x)}{960 L E I}\left(5 L^2 - 4 (L-x)^2\right)^2 \] |
| Maximum Deflection | \[ y_{\mathrm{MAX}} = \frac{-w_0 L^4}{120 E I} \quad \text{at} \quad x = \frac{L}{2} \] |
| Slope | No slope formula provided in the text |
| Moment (AC) | \[ M_{\mathrm{AC}} = \frac{w_0}{12 L}\left(3 L^2 x - 4 x^3\right) \] |
| Moment (CB) | \[ M_{\mathrm{CB}} = \frac{w_0(L-x)}{12 L}\left(3 L^2 - 4 (L-x)^2\right) \] |
| Shear (AC) | \[ V_{\mathrm{AC}} = \frac{w_0}{4 L}\left(L^2 - 4 x^2\right) \] |
| Shear (CB) | \[ V_{\mathrm{CB}} = \frac{-w_0}{4 L}\left(L^2 - 4 (L-x)^2\right) \] |
| Reactions | \( R_{\mathrm{A}} = R_{\mathrm{B}} = \frac{w_0 L}{4} \) |
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 |