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BackCantilever beam - Uniform load partially distributed Calculator
Formula
| Parameter | Formula |
|---|---|
| Deflection (\(y_{AC}\)) | \(-\frac{w_0 b x^2}{12EI} (6a + 3b - 2x)\) |
| Deflection (\(y_{CD}\)) | \(-\frac{w_0}{24EI} (x^4 - 4(a+b)x^3 + 6(a+b)^2x^2 - 4a^3x + a^4)\) |
| Deflection (\(y_{DB}\)) | \(-\frac{w_0}{24EI} \left[4x((a+b)^3 - a^3) - (a+b)^4 + a^4\right]\) |
| Slope (\(\theta_{AC}\)) | \(-\frac{w_0 b x}{2EI} (2a + b - x)\) |
| Slope (\(\theta_{CD}\)) | \(-\frac{w_0}{6EI} (x^3 - 3(a+b)x^2 + 3(a+b)^2x - a^3)\) |
| Slope (\(\theta_{DB}\)) | \(-\frac{w_0}{6EI} ((a+b)^3 - a^3)\) |
| Moment (\(M_{AC}\)) | \(-\frac{w_0 b}{2} (2a + b - 2x)\) |
| Moment (\(M_{CD}\)) | \(-\frac{w_0}{2} (a+b-x)^2\) |
| Moment (\(M_{DB}\)) | \(M_{DB} = M_D = M_B = 0\) |
| Shear (\(V_{AC}\)) | \(V_{AC} = V_A = V_C = w_0 b\) |
| Shear (\(V_{CD}\)) | \(V_{CD} = w_0(a+b-x)\) |
| Shear (\(V_{DB}\)) | \(V_{DB} = V_D = V_B = 0\) |
| 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 |