Simple Beam - Uniformly Distributed Load

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• 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.

 

Simple Beam - Uniformly Distributed Load formulas
\( R \;=\; V_{max} \;=\; w \; L\;/\;2 \) \( V_x  \;=\; w  \; [\; (L\;/\;2)  - x \;]  \) \( M_{max} \; \left(at \;center \right)  \;=\; w \; L^2\;/\;8  \) \( M_x  \;=\; (w \; x\;/\;2) \;  ( L  - x )   \) \( \Delta_{max} \; \left(at \;center \right)  \;=\; 5 \;w \;L^4\;/\;384\; \lambda \;I \) \( \Delta_x  \;=\; (w\; x\;/\;24\; \lambda \;I )  \; ( L^3 - 2\;L\;x^2 + x^3 )  \)
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)	\(in^4\)	\(mm^4\)