- 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.
Two Span Continuous Beam - Equal Spans, Two Equal Concentrated Loads Symmetrically Placed formulas |
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\( R_1 \;=\; V_1 \;=\; \dfrac{ P\cdot b }{ 4\cdot L^3 } \cdot (\; 4\cdot L^2 - a \cdot ( L + a ) \;) \) \( R_2 \;=\; \dfrac{ P\cdot a }{ 2\cdot L^3 } \cdot (\; 2\cdot L^2 + b \cdot ( L + a ) \;) \) \( R_3 \;=\; V_3 \;=\; -\; \dfrac{ P\cdot a\cdot b }{ 4\cdot L^3 } \cdot ( L + a ) \) \( V_2 \;=\; \dfrac{ P\cdot a }{ 4\cdot L^3 } \cdot (\; 4\cdot L^2 + b \cdot ( L + a ) \;) \) \( M_1 \; \left(at\; support\; R_2 \right) \;=\; \dfrac{ P\cdot a\cdot b }{ 4\cdot L^2 } \cdot ( L + a ) \) \( M_{max} \;=\; \dfrac{ P\cdot a\cdot b }{ 4\cdot L^3 } \cdot (\; 4\cdot L^2 - a \cdot ( L + a ) \;) \) |
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| Symbol | English | Metric |
| \( a, b \) = horizontal distance to point load | \(in\) | \(mm\) |
| \( M \) = maximum bending moment | \(lbf-in\) | \(N-mm\) |
| \( V \) = maximum shear force | \(lbf\) | \(N\) |
| \( R \) = reaction load at bearing point | \(lbf\) | \(N\) |
| \( L \) = span length under consideration | \(in\) | \(mm\) |
| \( P \) = total consideration load | \(lbf\) | \(N\) |
