Overhanging Beam - Uniformly Distributed Load Over Supported Span

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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.

 

Overhanging Beam - Uniformly Distributed Load Over Supported Span formulas
\( R \;=\; V \;=\; w\; L \;/\;2 \)  \( V_x \;=\;   w \; [\; (L\;/\;2) - x \;]  \)  \( M_{max} \; (at \;center )  \;=\; w\; L^2 \;/\;8 \)  \( M_x \;=\;  (w\; x \;/\;2) \; ( L - x )  \) \( \Delta_{max} \; \left(at \;center \right)  \;=\; 5\;w\; L^4 \;/\;384\; \lambda \; I \) \( \Delta_x   \;=\;   (w\; x \;/\;24\; \lambda\; I)  \; ( L^3 - 2\;L\;x^2 + x^3 )  \) \( \Delta_{x_1}   \;=\;   -\; w \; L^3 \;x_1 \;/\;24\; \lambda\; I   \)
Symbol	English	Metric
\( \Delta \) = deflection or deformation	\(in\)	\(mm\)
\( x \) = horizontal distance from reaction to point on beam	\(in\)	\(mm\)
\( w \) = load per unit length	\(lbf\;/\;in\)	\(N\;/\;mm\)
\( M \) = maximum bending moment	\(lbf-in\)	\(N-mm\)
\( V \) = maximum shear force	\(lbf\)	\(N\)
\( \lambda  \)   (Greek symbol lambda) = modulus of elasticity	\(lbf\;/\;in^2\)	\(Pa\)
\( R \) = reaction load at bearing point	\(lbf\)	\(N\)
\( I \) = second moment of area (moment of inertia)	\(in^4\)	\(mm^4\)
\( L \) = span length of the bending member	\(in\)	\(mm\)