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BackSimple beam - Uniform load partially distributed at left end (I) Calculator
Formula
| Quantity | Formula |
|---|---|
| Deflection \(y_{AC}\) | \(-\frac{w_0 x}{384EI} \left(9L^3 - 24Lx^2 + 16x^3 \right)\) |
| Deflection \(y_{CB}\) | \(-\frac{w_0 L}{384EI} \left(8x^3 - 24Lx^2 + 17L^2x - L^3 \right)\) |
| Slope \(\theta_{AC}\) | \(-\frac{w_0}{384EI} \left(9L^3 - 72Lx^2 + 64x^3 \right)\) |
| Slope \(\theta_{CB}\) | \(-\frac{w_0 L}{384EI} \left(24x^2 - 48Lx + 17L^2 \right)\) |
| \(\theta_A\) | \(-\frac{3w_0 L^3}{128EI}\) |
| \(\theta_B\) | \(\frac{7w_0 L^3}{384EI}\) |
| Moment \(M_{AC}\) | \(\frac{w_0}{8} \left(3Lx - 4x^2 \right)\) |
| Moment \(M_{CB}\) | \(\frac{w_0}{8} \left(L^2 - Lx \right)\) |
| Shear \(V_{AC}\) | \(\frac{w_0}{8} \left(3L - 8x \right)\) |
| Shear \(V_{CB}\) | \(-\frac{w_0 L}{8}\) |
| \(V_A = R_A\) | \(\frac{3w_0 L}{8}\) |
| \(V_B = -R_B\) | \(-\frac{w_0 L}{8}\) |
| Reactions \(R_A\) | \(\frac{3w_0 L}{8}\) |
| Reactions \(R_B\) | \(\frac{w_0 L}{8}\) |
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 |