Beam Fixed at Both Ends - Uniformly Distributed Load
- See Article Link - Beam Design Formulas
- Tags: Beam Support
diagram Symbols
- 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.
beam fixed at both ends - Uniformly Distributed Load formulas |
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\( R \;=\; V \;=\; w\; L\;/\;2 \) \( V_x \;=\; w \; [\; (L\;/\;2) - x \;] \) \( M_{max} \; (at \;ends ) \;=\; w\; L^2\;/\;12 \) \( M_1 \; (at\; center ) \;=\; w\; L^2\;/\;24 \) \( M_x \;=\; (w\;/\;12) \; ( 6\;L\;x - L^2 - 6\;x^2 ) \) \( M_{max} \; (at \;center ) \;=\; w\; L^4\;/\;384\; \lambda\; I \) \( \Delta_x \;=\; (w\; x^2\;/\;24\; \lambda\; I) \; ( L - x ) ^2 \) \( x \; (points \;of \;contraflexure ) \;=\; (\sqrt{3} - 3 )\; L \) |
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B F at B E - Uniformly Distributed Load - Solve for R\(\large{ R = \frac{w\; L}{2} }\)
B F at B E - Uniformly Distributed Load - Solve for Vx\(\large{ V_x = w \; \left( \frac{L}{2} - x \right) }\)
B F at B E - Uniformly Distributed Load - Solve for MmaxE\(\large{ M_{max} = \frac{w\; L^2}{12} }\)
B F at B E - Uniformly Distributed Load - Solve for M1\(\large{ M_1 = \frac{w\; L^2}{24} }\)
B F at B E - Uniformly Distributed Load - Solve for Mx\(\large{ M_x = \frac{w}{12} \; \left( 6\;L\;x - L^2 - 6\;x^2 \right) }\)
B F at B E - Uniformly Distributed Load - Solve for MmaxC\(\large{ M_{max} = \frac{w\; L^4}{384\; \lambda\; I} }\)
B F at B E - Uniformly Distributed Load - Solve for Δx\(\large{ \Delta_x = \frac{w\; x^2}{24\; \lambda\; I} \; \left( L - x \right) ^2 }\)
B F at B E - Uniformly Distributed Load - Solve for x\(\large{ x = \left(\sqrt{3} - 3 \right) L }\)
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Symbol | English | Metric |
\( R \) = reaction load at bearing point | \(lbf\) | \(N\) |
\( V \) = maximum shear force | \(lbf\) | \(N\) |
\( M \) = maximum bending moment | \(lbf-in\) | \(N-mm\) |
\( \Delta \) = deflection or deformation | \(in\) | \(mm\) |
\( w \) = load per unit length | \(lbf\;/\;in\) | \(N\;/\;m\) |
\( L \) = span length of the bending member | \(in\) | \(mm\) |
\( x \) = horizontal distance from reaction to point on beam | \(in\) | \(mm\) |
\( \lambda \) (Greek symbol lambda) = modulus of elasticity | \(lbf\;/\;in^2\) | \(Pa\) |
\( I \) = second moment of area (moment of inertia) | \(in^4\) | \(mm^4\) |
Tags: Beam Support