Beam Fixed at Both Ends - 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
Beam Fixed at Both Ends - Concentrated Load at Center formulas
| \(\large{ R = V = \frac {P} {2} }\) | |
| \(\large{ M_{max} }\) (at center and ends) = \(\large{ \frac {P \;L} {8} }\) | |
| \(\large{ M_x \; }\) when \(\large{ \left( x < \frac {L}{2} \right) = \frac {P} {8} \; \left( 4\;x - L \right) }\) | |
| \(\large{ \Delta_{max} }\) (at center) = \(\large{ = \frac {P\;L^3}{192\; \lambda\; I} }\) | |
| \(\large{ \Delta_{max} \; }\) when \(\large{ \left( x < \frac {L}{2} \right) = \frac {P\;x^2} {48\; \lambda\; I} \; \left( 3\;L - 4\;x \right) }\) |
Where:
\(\large{ I }\) = moment of inertia
\(\large{ L }\) = span length of the bending member
\(\large{ M }\) = maximum bending moment
\(\large{ P }\) = total concentrated load
\(\large{ R }\) = reaction load at bearing point
\(\large{ V }\) = shear force
\(\large{ w }\) = load per unit length
\(\large{ W }\) = total load from a uniform distribution
\(\large{ x }\) = horizontal distance from reaction to point on beam
\(\large{ \lambda }\) (Greek symbol lambda) = modulus of elasticity
\(\large{ \Delta }\) = deflection or deformation