- See Article - 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.
Simple Beam - Uniform Load Partially Distributed at Any Point formulas |
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\( R_1 \;=\; V_1 \; ( max. \;when\; a < c ) \;=\; \dfrac{ w \cdot b }{ 2 \cdot L } \cdot ( 2 \cdot c + b ) \) \( R_2 \;=\; V_2 \; ( max. \;when\; a > c ) \;=\; \dfrac{ w \cdot b }{ 2 \cdot L } \cdot ( 2 \cdot a + b ) \) \( V_x \; [ \; a < x < ( a + b ) \;] \;=\; R_1 - (\;w \cdot ( x - a )\;) \) \( M_{max} \; [\; at \; x = a + (R_1\;/\;w) \;] \;=\; R_1 \cdot \left( a + \dfrac{ R_1 }{ 2 \cdot w } \right) \) \( M_x \; ( x < a ) \;=\; R_1 \cdot x \) \( M_x \; [ \; a < x < \; ( a + b ) \;] \;=\; (R_1 \cdot x) - \left( \dfrac{ w }{ 2 } \cdot ( x - a )^2 \right) \) \( M_x \; [ \; x > ( a + b ) \;] \;=\; R_2 \cdot ( L - x ) \) |
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| Symbol | English | Metric |
| \( R \) = reaction load at bearing point | \(lbf\) | \(N\) |
| \( V \) = maximum shear force | \(lbf\) | \(N\) |
| \( M \) = maximum bending moment | \(lbf - in\) | \(N - mm\) |
| \( w \) = load per unit length | \(lbf\;/\;in\) | \(N\;/\;m\) |
| \( L \) = span length of the bending member | \(in\) | \(mm\) |
| \( x \) = horizontal distance from reaction to point on beam | \(in\) | \(mm\) |
| \( a, b, c \) = width and seperation of UDL | \(in\) | \(mm\) |
