# 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 $$in$$ $$mm$$

Tags: Beam Support