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BackFixed-fixed beam - Uniform load partially distributed at left end II Calculator
Formula
| Quantity | Formula |
|---|---|
| Deflection \(y_{AC}\) | \[ y_{AC} = \frac{-x^2}{24EI} \left(w_0 x^2 - 4R_A x - 12M_A \right) \] |
| Deflection \(y_{CB}\) | \[ y_{CB} = \frac{3(M_B + L R_B)x^2 - R_B x^3}{6EI} + \frac{L^2 (3M_B + LR_B) - 3(2M_B + LR_B)Lx}{6EI} \] |
| Slope \(\theta_{AC}\) | \[ \theta_{AC} = \frac{-x}{6EI} \left(w_0 x^2 - 3R_A x - 6M_A \right) \] |
| Slope \(\theta_{CB}\) | \[ \theta_{CB} = \frac{-1}{2EI} \left[ R_B x^2 - 2(M_B + L R_B)x + L(2M_B + L R_B) \right] \] |
| Moment \(M_{AC}\) | \[ M_{AC} = R_A x + M_A - \frac{w_0 x^2}{2} \] |
| Moment \(M_{CB}\) | \[ M_{CB} = R_B (L - x) + M_B \] |
| Shear \(V_{AC}\) | \[ V_{AC} = R_A - w_0 x \] |
| Shear \(V_{CB}\) | \[ V_{CB} = -R_B \] |
| Reaction \(R_A\) | \[ R_A = \frac{w_0 (L + b) a^2}{2L} - \frac{M_A + M_B}{L} \] |
| Reaction \(R_B\) | \[ R_B = \frac{w_0 a^2}{2L} + \frac{M_A - M_B}{L} \] |
| Where \(M_A\) | \[ M_A = \frac{-w_0 a^2}{12L^2} \left(6L^2 - 8La + 3a^2 \right) \] |
| Where \(M_B\) | \[ M_B = \frac{-w_0 a^3}{12L^2} \left(4L - 3a \right) \] |
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 |