Simple beam - Concentrated load at center Calculator
Formula
| Deflection (AC) |
\( y_{\mathrm{AC}} = \frac{-Px}{48EI}(3L^{2}-4x^{2}) \) |
| Deflection (CB) |
\( y_{\mathrm{CB}} = \frac{-P(L-x)}{48EI}(3L^{2}-4(L-x)^{2}) \) |
| Maximum Deflection |
\( y_{\mathrm{MAX}} = y_{\mathrm{C}} = \frac{-PL^{3}}{48EI} \quad \mathrm{at} \quad x = \frac{L}{2} \) |
| Slope (AC) |
\( \theta_{\mathrm{AC}} = \frac{-P}{16EI}(L^{2}-4x^{2}) \) |
| Slope (CB) |
\( \theta_{\mathrm{CB}} = \frac{-P}{16EI}(4x^{2}-8Lx+3L^{2}) \) |
| Slope at A and B |
\( \theta_{\mathrm{A}} = -\theta_{\mathrm{B}} = \frac{PL^{2}}{16EI} \) |
| Moment (AC) |
\( M_{\mathrm{AC}} = \frac{Px}{2} \) |
| Moment (CB) |
\( M_{\mathrm{CB}} = \frac{P(L-x)}{2} \) |
| Shear (AC) |
\( V_{\mathrm{AC}} = V_{\mathrm{A}} = \frac{P}{2} \) |
| Shear (CB) |
\( V_{\mathrm{CB}} = V_{\mathrm{B}} = \frac{-P}{2} \) |
| Reactions |
\( R_{\mathrm{A}} = R_{\mathrm{B}} = \frac{P}{2} \) |
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 |
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