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BackSimple beam - Load increasing uniformly to right end Calculator
Formula
| Deflection (AB) | \[ y_{\mathrm{AB}} = \frac{-w_{0} x}{360 L E I}\left(7 L^{4}-10 L^{2} x^{2}+3 x^{4}\right) \] |
| Maximum Deflection | \[ y_{\mathrm{MAX}} = -0.00652 \frac{w_{0} L^{4}}{E I} \quad \text{at} \quad x = 0.5193 L \] |
| Slope (AB) | \[ \theta_{\mathrm{AB}} = \frac{-w_{0}}{360 L E I}\left(7 L^{4}-30 L^{2} x^{2}+15 x^{4}\right) \] |
| Slope (A and B) | \[ \theta_{\mathrm{A}} = \frac{-7 w_{0} L^{3}}{360 E I} \quad \theta_{\mathrm{B}} = \frac{w_{0} L^{3}}{45 E I} \] |
| Moment (AB) | \( M_{\mathrm{AB}} = \frac{w_{0}}{6 L}\left(L^{2} x - x^{3}\right) \) |
| Shear (AB) | \[ V_{\mathrm{AB}} = \frac{w_{0}}{6 L}\left(L^{2}-3 x^{2}\right) \] |
| Reactions | \( R_{\mathrm{A}} = \frac{w_{0} L}{6} \quad R_{\mathrm{B}} = \frac{2 w_{0} L}{6} \) |
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 |