Simple Beam - Two Unequal Point Loads Unequally 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 Unequal Point Loads Unequally Spaced Formulas
\( R_1 \;=\; V_1 \;=\; [\; P_1 \; (  L \;- \;a ) \;] + (P_2\; b \;/\; L) \)  \( R_2 \;=\; V_2  \;=\; P_1 \;a +[\; P_2 \; ( L - b ) \;] \;/\; L \)  \( V_x  \; [\; a < x  < ( L - b ) \;] \;=\; R_1 - P_1  \)  \( M_1 \; (max.\; when\;  R_1 < P_1 )  \;=\; R_1\; a  \) \( M_2 \; (max.\; when\;  R_2 < P_2 ) \;=\; R_2\; b \) \( M_x \; (max.\; when\;  x < a )  \;=\; R_1\; x  \) \( M_x \; [\; max.\; when\; a < x < \;(  L - b ) \;]  \;=\; R_1\; x  - [\;P_1\; ( x - a ) \;]  \)
Symbol	English	Metric
\( R \) = reaction load at bearing point	\(lbf\)	\(N\)
\( V \) = maximum shear force	\(lbf\)	\(N\)
\( M \) = maximum bending moment	\(lbf - in\)	\(N - mm\)
\( P \) = total concentrated load	\(lbf\)	\(N\)
\( L \) = span length of the bending member	\(in\)	\(mm\)
\( a, b \) = length to point load	\(in\)	\(mm\)
\( x \) = horizontal distance from reaction to point on beam	\(in\)	\(mm\)