- 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.
Four Span Continuous Beam - Equal Spans, Uniformly Distributed Load formulas |
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\( R_1 \;=\; V_1 \;=\; R_5 \;=\; V_5 \;=\; 0.393\cdot w\cdot L \) \( R_2 = R_4 \;=\; 1.143\cdot w\cdot L \) \( R_3 \;=\; 0.928\cdot w\cdot L \) \( V_{2_1} \;=\; V_{4_2} \;=\; 0.607\cdot w\cdot L \) \( V_{2_2} \;=\; V_{4_1} \;=\; 0.536\cdot w\cdot L \) \( V_{3_1} \;=\; V_{3_2} \;=\; 0.464\cdot w\cdot L \) \( M_1 \; (at\; 0.393\;L \; from \; R_1 ) = M_7 \; \left(at\; 0.393\;L \; from \; R_5 \right) \;=\; 0.0772\cdot w\cdot L^2 \) \( M_2 \; (at\; R_2 ) \;=\; -\; ( 0.1071\cdot w\cdot L^2 ) \) \( M_3 \; (at\; 0.536\;L \; from \; R_2 ) = M_5 \; \left(at\; 0.536\;L \; from \; R_4 \right) \;=\; 0.0364\cdot w\cdot L^2 \) \( M_4 \; (at\; R_3 ) \;=\; -\; ( 0.0714\cdot w\cdot L^2) \) \( \Delta_{max} \; (at\; 0.440\;L \; from \; R_1 \; and \; R_5 ) \;=\; \dfrac{ 0.0065\cdot w\cdot L^4 }{ \lambda\cdot I } \) |
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| Symbol | English | Metric |
| \( \Delta \) = deflection or deformation | \(in\) | \(mm\) |
| \( w \) = load per unit length | \(lbf\;/\;in\) | \(N\;/\;m\) |
| \( M \) = 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) | \(in^4\) | \(mm^4\) |
| \( L \) = span length under consideration | \(in\) | \(mm\) |
