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BackFixed-pinned beam - Concentrated load at any point Calculator
Formula
| Quantity | Formula |
|---|---|
| Deflection \(y_{AC}\) | \[ y_{AC} = \frac{-Pbx^2}{12EI L^3} \left( 3L^3 - 3b^2L - 3L^2x + b^2x \right) \] |
| Deflection \(y_{CB}\) | \[ y_{CB} = \frac{-Pa^2(L-x)}{12EI L^3} \left( 3bL^2 - (2L + b)(L-x)^2 \right) \] |
| Slope \(\theta_{AC}\) | \[ \theta_{AC} = \frac{-Pbx}{4EI L^3} \left( 2L^3 - 2b^2L - 3L^2x + b^2x \right) \] |
| Slope \(\theta_{CB}\) | \[ \theta_{CB} = \frac{-Pa^2}{4EI L^3} \left( 2L^3 - 4L^2x - 2bLx + 2Lx^2 + bx^2 \right) \] |
| Moment \(M_{AC}\) | \[ M_{AC} = \frac{-Pb}{2L^3} \left( L^3 - b^2L - 3L^2x + b^2x \right) \] |
| Moment \(M_{CB}\) | \[ M_{CB} = \frac{Pa^2}{2L^3} (L-x)(2L+b) \] |
| Shear \(V_{AC}\) | \[ V_{AC} = \frac{Pb}{2L^3} (3L^2 - b^2) \] |
| Shear \(V_{CB}\) | \[ V_{CB} = \frac{-Pa^2}{2L^3} (2L + b) \] |
| Reaction \(R_A\) | \[ R_A = \frac{Pb}{2L^3} (3L^2 - b^2) \] |
| Reaction \(R_B\) | \[ R_B = \frac{Pa^2}{2L^3} (2L + b) \] |
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 |