Overhanging Beam - Uniformly Distributed Load on Overhang
- See Article Link - Beam Design Formulas
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 on Overhang formulas |
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\( R_1 \;=\; V_2 \;=\; w\; a^2 \;/\;2\;L \) \( R_2 \;=\; V_1 + V_2 \;=\; (w\; a \;/\;2\;L) \; ( 2\;L + a) \) \( V_2 \;=\; w \;a \) \( V_{x _1} \;=\; w \; ( a - x_1 ) \) \( M_{max} \; ( at\; R_2 ) \;=\; w \;a^2 \;/\;2 \) \( M_x \; (between\; supports ) \;=\; w \;a^2 \;x \;/\;2\;L \) \( M_{x_1} \; (for \;overhang ) \;=\; ( w \;/\;2) \; ( a - x_1)^2 \) \( \Delta_x \; (between\; supports ) \;=\; ( - \;w \;a^2\; x \;/\;12\; \lambda\; I \;L) \; ( L^2 - x^2 ) \) \( \Delta_{max} \; (between\; supports \;at\; x = \frac{L}{\sqrt{3}} ) \;=\; \frac{ - \;w\; a^2 \;L^2 }{18 \; \sqrt{3} \; \lambda\; I } \;=\; 0.03208 \; ( w \;a^2 \; L^2 \;/\; \lambda\; I) \) \( \Delta_{max} \; (for \;overhang \;at\; x_1 = a ) \;=\; ( w\; x^3 \;/\;24\; \lambda\; I ) \; ( 4\;L + 3\;a ) \) \( \Delta_{x1} \; (for \;overhang ) \;=\; ( w\; x_1 \;/\;24\; \lambda\; I ) \; ( 4\;a^2 \;L + 6\;a^2\; x_1 - 4\;a \;x_{1}{^2} + x_{1}{^3} ) \) |
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| Symbol | English | Metric |
| \( \Delta \) = deflection or deformation | \(in\) | \(mm\) |
| \( x \) = 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 | \(in\) | \(mm\) |
Tags: Beam Support