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BackCantilever beam - Uniform load partially distributed at free end Calculator
Formula
| Category | Formula |
|---|---|
| Deflection (\( y_{AC} \)) | \[ y_{AC} = \frac{-w_0 b x^2}{12EI}(3L + 3a - 2x) \] |
| Deflection (\( y_{CB} \)) | \[ y_{CB} = \frac{-w_0}{24EI}(x^4 - 4Lx^3 + 6L^2x^2 - 4a^3x + a^4) \] |
| Slope (\( \theta_{AC} \)) | \[ \theta_{AC} = \frac{-w_0 b x}{2EI}(L + a - x) \] |
| Slope (\( \theta_{CB} \)) | \[ \theta_{CB} = \frac{-w_0}{6EI}(x^3 - 3Lx^2 + 3L^2x - a^3) \] |
| Slope at B (\( \theta_B \)) | \[ \theta_B = \frac{-w_0}{6EI}(L^3 - a^3) \] |
| Moment (\( M_{AC} \)) | \[ M_{AC} = \frac{-w_0 b}{2}(L + a - 2x) \] |
| Moment (\( M_{CB} \)) | \[ M_{CB} = \frac{-w_0}{2}(L - x)^2 \] |
| Shear (\( V_{AC} \), \( V_A \), \( V_C \)) | \[ V_{AC} = V_A = V_C = w_0 b \] |
| Shear (\( V_{CB} \)) | \[ V_{CB} = w_0(L - x) \] |
| Reactions (\( R_A \)) | \[ R_A = w_0 b \] |
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 |