- 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.
Three Span Continuous Beam - Equal Spans, Uniform Load on Two Spans to One Side formulas |
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\( R_1 \;=\; V_1 \;=\; 0.383\cdot w\cdot L \) \( R_2 \;=\; 1.200\cdot w\cdot L \) \( R_3 \;=\; 0.450\cdot w\cdot L \) \( R_4 \;=\; -\; (0.033\cdot w\cdot L ) \) \( V_{2_1} \;=\; 0.583 \cdot w\cdot L \) \( V_{2_2} \;=\; 0.617\cdot w\cdot L \) \( V_{3_1} \;=\; V_4 \;=\; 0.033\cdot w\cdot L \) \( V_{3_2} \;=\; 0.417\cdot w\cdot L \) \( M_1 \; ( at\; x = 0.383\;L \; from\; R_1 ) \;=\; 0.0735\cdot w\cdot L^2 \) \( M_2 \; ( at\; x = 0.538\;L \; from \; R_2 ) \;=\; 0.0534\cdot w\cdot L^2 \) \( M_3 \; (at\; R_3 ) \;=\; - \;(0.0333\cdot w\cdot L^2) \) \( \Delta_{max} \; (at\; 0.430\;L \; from \; R_1 ) \;=\; \dfrac{ 0.0059\cdot w\cdot L^4 }{ \lambda\cdot I } \) |
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| Symbol | English | Metric |
| \( FB \) = free body | \(lbf\) | \(N\) |
| \( SF \) = shear force | \(lbf\;/\;in^2\) | \(Pa\) |
| \( BM \) = bending moment | \(lbf\;/\;sec\) | \(kg-m\;/\;s\) |
| \( UDL \) = uniformly distributed load | \(lbf\) | \(N\) |
| \( \Delta \) = deflection or deformation | \(in\) | \(mm\) |
| \( w \) = load per unit length | \(lbf\;/\;in\) | \(N\;/\;m\) |
| \( M \) = maximum bending moment | \(lbf-ft\) | \(N-m\) |
| \( V \) = maximum shear force | \(lbf\) | \(N\) |
| \( \lambda \) (Greek symbol lambda) = modulus of elasticity | \(lbf\;/\;in^2\) | \(Pa\) |
| \( I \) = second moment of area (moment of inertia) | \(in^4\) | \(mm^4\) |
| \( R \) = reaction load at bearing point | \(lbf\) | \(N\) |
| \( L \) = span length under consideration | \(in\) | \(mm\) |
