Simple Beam - Two Point Loads Equally Spaced

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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.

 

Simple Beam - Two Point Loads Equally Spaced formulas
\( R \;=\; V  \;=\; P  \)  \( M_{max} \; ( between\; loads ) \;=\; P\;a  \)  \( M_x \; (  x < a )  \;=\; P\;x  \)  \( \Delta_{max} \; ( at \;center ) \;=\; ( P\;x \;/\;24\; \lambda\; I ) \;l \; ( 3\;L^2  - 4\;a^2 )   \) \( \Delta_x \; (  x < a )  \;=\; ( P\;x \;/\;6\; \lambda \;I) \; ( 3\;L\;a  - 3\;a^2 - x^2 )   \) \( \Delta_x  \; [\; a <  x  < (  L - a ) \;]  \;=\; ( P\;a  \;/\;6\; \lambda\; I)  \; ( 3\;L\;x  - 3\;x^2 - a^2 )   \)
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	\(lbf\)	\(N\)
\( a \) = length to point load	\(in\)	\(mm\)
\( x \) = 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)	\(in^4\)	\(mm^4\)
\( L \) = span length of the bending member	\(in\)	\(mm\)