Overhanging Beam - Uniformly Distributed Load Overhanging Both Supports

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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.

 

 

 

 

Overhanging Beam - Uniformly Distributed Load Overhang Both Supports formulas
\( R_1 \;=\;  [\;w\; L \; ( L\; -\; 2\;c ) \;] \;/\;2\;b      \)  \( R_2 \;=\; [\; w\; L \; ( L \;-\; 2\;a ) \;]   \;/\;2\;b    \)  \( V_1  \;=\;   w\;a   \)  \( V_2  \;=\;   R_1 - V_1   \) \( V_3  \;=\;   R_2 - V_4   \) \( V_4  \;=\;   w\;c   \) \( V_{x_1}  \;=\;   V_1 -  [\; w \; ( a - x_1 ) \;]  \) \( V_x \; ( x < b )   \;=\;   R_1 - [\; w \; ( a + x ) \;]   \) \( M_1 \;=\; - \; (w\; a^2\;/\;2)    \) \( M_2 \;=\; - \; (w \;c^2\;/\;2)    \) \( M_3 \;\;=\;\;  R_1 \; [\; (R_1\;/\;2\;w) - a  \;]   \) \( M_x \;=\; R_1 \; x \; - [\; w \; ( a + x )^2\;/\;2 \;]     \)
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	\(lbf\)	\(N\)
\( \lambda  \)   (Greek symbol lambda) = modulus of elasticity	\(lbf\;/\;in^2\)	\(Pa\)
\( R \) = reaction load at bearing point	\(lbf\)	\(N\)
\( I \) = second moment of area (moment of inertia)	\(in^4\)	\(mm^4\)
\( L \) = span length of the bending member	\(in\)	\(mm\)
\( a, b, c \) = span length under consideration	\(in\)	\(mm\)