- See Article - Beam Design Formulas
Simple Beam - Two Unequal Point Loads Unequally Spaced Formulas |
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\( R_1 \;=\; V_1 \;=\; (\; P_1 \cdot ( L - a ) \;) + \dfrac{ P_2\cdot b }{ L} \) \( R_2 \;=\; V_2 \;=\; \dfrac{ P_1 \cdot a + (\; P_2 \cdot ( L - b ) \;) }{ L }\) \( V_x \; [\; a < x < ( L - b ) \;] \;=\; R_1 - P_1 \) \( M_1 \; (max.\; when\; R_1 < P_1 ) \;=\; R_1 \cdot a \) \( M_2 \; (max.\; when\; R_2 < P_2 ) \;=\; R_2 \cdot b \) \( M_x \; (max.\; when\; x < a ) \;=\; R_1 \cdot x \) \( M_x \; [\; max.\; when\; a < x < \;( L - b ) \;] \;=\; R_1 \cdot x - (\;P_1\cdot ( x - a ) \;) \) |
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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 | \(lbf - in\) | \(N - mm\) |
| \( P \) = total concentrated load | \(lbf\) | \(N\) |
| \( L \) = span length of the bending member | \(in\) | \(mm\) |
| \( a, b \) = length to point load | \(in\) | \(mm\) |
| \( x \) = horizontal distance from reaction to point on beam | \(in\) | \(mm\) |
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.
