Beam Fixed at Both Ends - Uniformly Distributed Load
beam fixed at both ends - Uniformly Distributed Load formulas |
||
|
\(\large{ R = V \;\;=\;\; \frac {w\; L} {2} }\) \(\large{ V_x \;\;=\;\; w \; \left( \frac {L} {2} - x \right) }\) \(\large{ M_{max} \; \left(at \;ends \right) \;\;=\;\; \frac {w\; L^2} {12} }\) \(\large{ M_1 \; \left(at\; center \right) \;\;=\;\; \frac {w\; L^2} {24} }\) \(\large{ M_x \;\;=\;\; \frac {w}{12} \; \left( 6\;L\;x - L^2 - 6\;x^2 \right) }\) \(\large{ M_{max} \; \left(at \;center \right) \;\;=\;\; \frac {w\; L^4} {384\; \lambda\; I} }\) \(\large{ \Delta_x \;\;=\;\; \frac {w\; x^2} {24\; \lambda\; I} \; \left( L - x \right) ^2 }\) \(\large{ x \; \left(points \;of \;contraflexure \right) \;\;=\;\; \left(\sqrt{3} - 3 \right) L }\) |
||
| Symbol | English | Metric |
| \(\large{ \Delta }\) = deflection or deformation | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ x }\) = horizontal distance from reaction to point on beam | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ w }\) = load per unit length | \(\large{\frac{lbf}{in}}\) | \(\large{\frac{N}{m}}\) |
| \(\large{ M }\) = maximum bending moment | \(\large{lbf-in}\) | \(\large{N-mm}\) |
| \(\large{ V }\) = maximum shear force | \(\large{lbf}\) | \(\large{N}\) |
| \(\large{ \lambda }\) (Greek symbol lambda) = modulus of elasticity | \(\large{\frac{lbf}{in^2}}\) | \(\large{Pa}\) |
| \(\large{ R }\) = reaction load at bearing point | \(\large{lbf}\) | \(\large{N}\) |
| \(\large{ I }\) = second moment of area (moment of inertia) | \(\large{in^4}\) | \(\large{mm^4}\) |
| \(\large{ L }\) = span length of the bending member | \(\large{in}\) | \(\large{mm}\) |
diagrams
- Bending moment diagram (BMD) - Used to determine the bending moment at a given point of a structural element. The diagram can help determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.
- Free body diagram (FBD) - Used to visualize the applied forces, moments, and resulting reactions on a structure in a given condition.
- Shear force diagram (SFD) - Used to determine the shear force at a given point of a structural element. The diagram can help determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.
- Uniformly distributed load (UDL) - A load that is distributed evenly across the entire length of the support area.
Article Links |
Tags: Beam Support Equations