Overhanging Beam - Point Load Between Supports at Any Point
- See Article Link - Beam Design Formulas
- 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.
Overhanging Beam - Point Load Between Supports at Any Point formulas |
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\( R_1 \;=\; V_1 \; ( max.\; when\; a < b) \;=\; P\;b \;/\; L \) \( R_2 \;=\; V_2 \; (max. \;when\; a > b ) \;=\; P\;a\;/\;L \) \( M_{max} \; \left(at \;point \;of \;load \right) \;=\; P\;a\;b\;/\;L \) \( M_x \; \left( x < a \right) \;=\; P\;b\;x\;/\;L \) \( \Delta_{x_1} \;=\; ( P\;a\;b\;x_1 \;/\;6\; \lambda\; I\;L ) \; ( L + a ) \) \( \Delta_a \; (at\; point \;of \;load ) \;=\; P\;a^2\; b^2 \;/\;3\; \lambda\; I\;L \) \( \Delta_x \; (when\; x < a ) \;=\; ( P\;b\;x \;/\;6\; \lambda\; I\;L) \; ( L^2 - b^2 - x^2 ) \) \( \Delta_x \; ( when\; x > a ) \;=\; [\; P\;a \; ( L - x ) \;/\; 6\; \lambda\; I\;L\;] \; ( 2\;L\;x - x^2 - a^2 ) \) \( \Delta_{max} \; (at\; x = \sqrt{ \frac{ a \; (a + 2\;b ) }{3} } \; when\; a > b) \;=\; P\;a\;b \; ( a + 2\;b ) \; \sqrt{ 3\;a \; ( a + 2\;b) } \;/\; 27\; \lambda \;I\;L \) |
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| Symbol | English | Metric |
| \( \Delta \) = deflection or deformation | \(in\) | \(m\) |
| \( x \) = horizontal distance from reaction to point on beam | \(in\) | \(m\) |
| \( M \) = 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) | \(in^4\) | \(m^4\) |
| \( L \) = span length of the bending member | \(in\) | \(m\) |
| \( P \) = total concentrated load | \(lbf\) | \(N\) |
Tags: Beam Support