Simple Beam - Concentrated Load at Center

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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 - Concentrated Load at Center formulas
\( R \;=\; V \;=\; P\;/\;2  \) \( M_{max} \; (at\; point \;of\; load ) \;=\; P\;L\;/\;4  \) \( M_x   \; [\; x < (L\;/\;2) \;] \;=\; P\;x\;/\;2  \) \( \Delta_{max} \; (at \;point\; of\; load ) \;=\; P\;L^3\;/\;48\; \lambda\; I  \) \( \Delta_x  \; (  x < \frac{L}{2} )  \;=\; ( P\;x\;/\;48 \;\lambda\; I ) \; (  3\;L^2 - 4\;x^2 )  \)
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	\(in\)	\(mm\)
\( P \) = total concentrated load	\(lbf\)	\(N\)
\( L \) = 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)	\(in^4\)	\(mm^4\)