Home
BackFixed-fixed beam - Two equal concentrated loads symmetrically placed Calculator
Formula
| Quantity | Formula |
|---|---|
| Deflection \(y_{AC}\) | \[ y_{AC} = \frac{-Px^2}{6EIL} \left(3aL - 3a^2 - Lx\right) \] |
| Deflection \(y_{CD}\) | \[ y_{CD} = \frac{-Pa^2}{6EIL} \left(3Lx - 3x^2 - aL\right) \] |
| Deflection \(y_{DB}\) | \[ y_{DB} = \frac{-P(L-x)^2}{6EIL} \left(3aL - 3a^2 - L(L-x)\right) \] |
| Slope \(\theta_{AC}\) | \[ \theta_{AC} = \frac{-Px}{2EIL} \left(2aL - 2a^2 - Lx\right) \] |
| Slope \(\theta_{CD}\) | \[ \theta_{CD} = \frac{-Pa^2}{2EIL} \left(L - 2x\right) \] |
| Slope \(\theta_{DB}\) | \[ \theta_{DB} = \frac{P(L-x)}{2EIL} \left[2aL - 2a^2 - L(L-x)\right] \] |
| Moment \(M_{AC}\) | \[ M_{AC} = \frac{P}{L} \left(Lx - aL + a^2\right) \] |
| Moment \(M_{CD}\) | \[ M_{CD} = \frac{Pa^2}{L} \] |
| Moment \(M_{DB}\) | \[ M_{DB} = \frac{P}{L} \left(L^2 - Lx - La + a^2\right) \] |
| Shear \(V_{AC}\) | \[ V_{AC} = P \] |
| Shear \(V_{CD}\) | \[ V_{CD} = 0 \] |
| Shear \(V_{DB}\) | \[ V_{DB} = -P \] |
| Reactions \(R_A = R_B\) | \[ R_A = R_B = P \] |
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 |