Simple Beam - Concentrated Load at Center
Structural Related Articles
- See beam design formulas
- See frame design formulas
- See plate design formulas
- See geometric properties of structural shapes
- See welding stress and strain connections
- See welding symbols
Simple Beam - Concentrated Load at Center formulas
| \(\large{ R = V = \frac{P}{2} }\) | |
| \(\large{ M_{max} }\) (at point of load) \(\large{ = \frac{P\;L}{4} }\) | |
| \(\large{ M_x \; }\) when \(\large{ \left( x < \frac{L}{2} \right) = \frac{ P\;x}{2} }\) | |
| \(\large{ \Delta_{max} }\) (at point of load) \(\large{ = \frac{ P\;L^3}{48\; \lambda\; I} }\) | |
| \(\large{ \Delta_x \; }\) when \(\large{ \left( x < \frac{L}{2} \right) = \frac{P\;x}{48 \;\lambda\; I} \; \left( 3\;L^2 - 4\;x^2 \right) }\) |
Where:
\(\large{ \Delta }\) = deflection or deformation
\(\large{ x }\) = horizontal distance from reaction to point on beam
\(\large{ M }\) = maximum bending moment
\(\large{ V }\) = maximum shear force
\(\large{ \lambda }\) (Greek symbol lambda) = modulus of elasticity
\(\large{ I }\) = moment of inertia
\(\large{ R }\) = reaction load at bearing point
\(\large{ L }\) = span length of the bending member
\(\large{ P }\) = total concentrated load