Simple Beam - Load Increasing Uniformly to 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 - Load Increasing Uniformly to Center formulas
\( R = V_{max} \;=\; W\;/\;2 \) \( V_x  \;  [ \; x < (L\;/\;2) \;]  \;=\; (W\;/\;2\;L^2)  \; ( L^2 - 4\;x^2 ) \) \( M_{max}  \; (at \;center) \;=\; W \;L\;/\;6  \) \( M_x \; [\;  x < (L\;/\;2) \;]   \;=\; W\;x  \; [\; (1/2) - (2\;x^2\;/\;3\;L^2) \;]  \) \( \Delta_{max} \; (at \;center) \;=\; W \;L^3 \;/\; 60 \; \lambda \;I \) \( \Delta_x \; [\;  x < (L\;/\;2) \;]  \;=\; (W\; x \;/\;480\; \lambda \;I \;L^2)  \; (  5\;L^2 - 4\;x^2 )^2   \)
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	\(in\)	\(mm\)
\( W \) = total load or \( w\;L\;/\;2 \)	\(lbf\)	\(N\)
\( w \) = highest load per unit length of UIL	\(lbf\;/\;in\)	\(N\;/\;m\)
\( L \) = 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)	\(in^4\)	\(mm^4\)