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BackSimple beam - Uniform load partially distributed at left end (II) Calculator
Formula
| Quantity | Formula |
|---|---|
| Deflection \(y_{AC}\) | \(-\frac{w_0 x}{24LEI} \left(a^4 - 4a^3L + 4a^2L^2 + 2a^2x^2 - 4aLx^2 + Lx^3 \right)\) |
| Deflection \(y_{CB}\) | \(-\frac{w_0 a^2}{24LEI} \left(-a^2L + 4L^2x + a^2x - 6Lx^2 + 2x^3 \right)\) |
| Slope \(\theta_{AC}\) | \(-\frac{w_0}{24LEI} \left(a^4 - 4a^3L + 4a^2L^2 + 6a^2x^2 - 12aLx^2 + 4Lx^3 \right)\) |
| Slope \(\theta_{CB}\) | \(-\frac{w_0 a^2}{24LEI} \left(4L^2 - 12Lx + 6x^2 \right)\) |
| Moment \(M_{AC}\) | \(-\frac{w_0}{2L} \left(a^2x - 2aLx + Lx^2 \right)\) |
| Moment \(M_{CB}\) | \(\frac{w_0 a^2}{2L} \left(L - x \right)\) |
| Shear \(V_{AC}\) | \(-\frac{w_0}{2L} \left(a^2 - 2aL + 2Lx \right)\) |
| Shear \(V_{CB} = V_C = V_B\) | \(-\frac{w_0 a^2}{2L}\) |
| Reactions \(R_A\) | \(\frac{w_0 a}{2L} \left(2L - a \right)\) |
| Reactions \(R_B\) | \(\frac{w_0 a^2}{2L}\) |
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 |