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BackFixed-fixed beam - Concentrated load at any point Calculator
Formula
| Category | Formula |
|---|---|
| Deflection (\( y_{AC} \)) | \[ y_{AC} = \frac{-Pb^2x^2}{6EI L^3}(3aL - 3ax - bx) \] |
| Deflection (\( y_{CB} \)) | \[ y_{CB} = \frac{-Pa^2(L - x)^2}{6EI L^3}(3bx - aL + ax) \] |
| Slope (\( \theta_{AC} \)) | \[ \theta_{AC} = \frac{-Pb^2x}{2EI L^3}(2aL - 3ax - bx) \] |
| Slope (\( \theta_{CB} \)) | \[ \theta_{CB} = \frac{Pa^2(L - x)}{2EI L^3} \left[x(3b + a) - L^2 \right] \] |
| Moment (\( M_{AC} \)) | \[ M_{AC} = \frac{-Pb^2x}{L^3}(aL - 3ax - bx) \] |
| Moment (\( M_{CB} \)) | \[ M_{CB} = \frac{Pa^2}{L^3}(L^2 + bL - Lx - 2bx) \] |
| Shear (\( V_{AC} \)) | \[ V_{AC} = \frac{Pb^2}{L^3}(L + 2a) \] |
| Shear (\( V_{CB} \)) | \[ V_{CB} = \frac{-Pa^2}{L^3}(L + 2b) \] |
| Reactions (\( R_A \)) | \[ R_A = \frac{Pb^2}{L^3}(L + 2a) \] |
| Reactions (\( R_B \)) | \[ R_B = \frac{Pa^2}{L^3}(L + 2b) \] |
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 |