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BackFixed-pinned beam - Two equal concentrated loads symmetrically placed Calculator
Formula
| Property | Formula |
|---|---|
| Deflection (\(y_{AC}\)) | \(y_{AC} = \frac{Px^2}{12EI L^2} [(3a^2 - 3aL - 2L^2)(L-x) + 2L(3a^2 - 3aL + L^2)]\) |
| Deflection (\(y_{CD}\)) | \(y_{CD} = \frac{-Pa(3(L-a)(L-x)^3 - 6L^2(L-x)^2)}{12EI L^2 a^2} + \frac{-Pa[3L^2(L+a)(L-x) - 2L^2 a]}{12EI L^2}\) |
| Deflection (\(y_{DB}\)) | \(y_{DB} = \frac{-P(L-x)}{12EI L^2} [(3aL - 3a^2 - 2L^2)(L-x)^2 + 3aL^2(L-a)]\) |
| Slope (\(\theta_{AC}\)) | \(\theta_{AC} = \frac{Px}{12EI L^2} [(3a^2 - 3aL - 2L^2)(2L - 3x) + 4L(3a^2 - 3aL + L^2)]\) |
| Slope (\(\theta_{CD}\)) | \(\theta_{CD} = \frac{-Pa}{4EI L^2} [-3(L-a)(L-x)^2 + 4L^2(L-x) - L^2(L+a)]\) |
| Slope (\(\theta_{DB}\)) | \(\theta_{DB} = \frac{P}{4EI L^2} [(3aL - 3a^2 - 2L^2)(L-x)^2 + aL^2(L-a)]\) |
| Moment (\(M_{AC}\)) | \(M_{AC} = \frac{P}{2L^2} [3a^2 L - 3aL^2 + x(2L^2 + 3aL - 3a^2)]\) |
| Moment (\(M_{CD}\)) | \(M_{CD} = \frac{-Pa}{2L^2} [3(L-a)(L-x) - 2L^2]\) |
| Moment (\(M_{DB}\)) | \(M_{DB} = \frac{-P(L-x)}{2L^2} [3aL - 3a^2 - 2L^2]\) |
| Shear (\(V_{AC}\)) | \(V_{AC} = \frac{P}{2L^2} (2L^2 + 3aL - 3a^2)\) |
| Shear (\(V_{CD}\)) | \(V_{CD} = \frac{3Pa(L-a)}{2L^2}\) |
| Shear (\(V_{DB}\)) | \(V_{DB} = \frac{P}{2L^2} (3aL - 3a^2 - 2L^2)\) |
| Reaction (\(R_A\)) | \(R_A = \frac{P}{2L^2} (2L^2 + 3aL - 3a^2)\) |
| Reaction (\(R_B\)) | \(R_B = \frac{P}{2L^2} (3a^2 + 2L^2 - 3aL)\) |
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 |