Simple Beam - Uniform Load Partially Distributed at Any Point

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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 - Uniform Load Partially Distributed at Any Point formulas
\( R_1 \;=\; V_1 \; ( max. \;when\; a < c )  \;=\; (w \;b\;/\;2\;L) \; ( 2\;c + b )  \) \( R_2 \;=\; V_2 \; ( max. \;when\; a > c ) \;=\; ( w \;b \;/\;2\;L) \; ( 2\;a + b )  \) \( V_x  \; [ \; a < x  < ( a + b ) \;]  \;=\; R_1 -  [\;w \; ( x - a )\;]  \) \( M_{max} \; [\; at \;  x = a + (R_1\;/\;w) \;]  \;=\; R_1 \; [\;  a + ( R_1 \;/\; 2\;w )  \;]  \) \( M_x \; ( x < a )  \;=\; R_1  \;x  \) \( M_x \; [ \; a < x < \; ( a + b ) \;]  \;=\; (R_1 \;x)  - [\; (w\;/\;2) \; ( x - a )^2 \;]  \) \( M_x \; [ \; x > ( a + b ) \;]  \;=\; R_2 \; ( L - x )  \)
Symbol	English	Metric
\( x \) = horizontal distance from reaction to point on beam	\(in\)	\(mm\)
\( w \) = load per unit length	\(lbf\;/\;in\)	\(N\;/\;m\)
\( M \) = maximum bending moment	\(lbf-in\)	\(N-mm\)
\( V \) = maximum shear force	\(lbf\)	\(N\)
\( R \) = reaction load at bearing point	\(lbf\)	\(N\)
\( L \) = span length of the bending member	\(in\)	\(mm\)
\( a, b, c \) = width and seperation of UDL	\(in\)	\(mm\)