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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 are.
Two Span Continuous Beam - Equal Spans, Uniform Load on One Span formulas |
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\( R_1 \;=\; V_1 \;=\; \dfrac{ 7\cdot w\cdot L }{ 16 } \) \( R_2 \;=\; V_2 + V_3 \;=\; \dfrac{ 5\cdot w\cdot L }{ 8 } \) \( R_3 \;=\; V_3 \;=\; \dfrac{ w\cdot L }{ 16 } \) \( V_2 \;=\; \dfrac{ 9\cdot w\cdot L }{ 16 } \) \( M_{max} \; (at\; x = \frac{7\;L}{16} ) \;=\; \dfrac{ 49\cdot w\cdot L^2 }{ 512 } \) \( M_1 \; \left(at \;support\; R_2 \right) \;=\; \dfrac{ w\cdot L^2 }{ 16 } \) \( M_x \; \left( x < L \right) \;=\; \dfrac{ w\cdot x }{ 16 } \cdot ( 7\cdot L - 8\cdot x ) \) \( \Delta_{max} \; ( 0.472 \; L \; from\;R_1 ) \;=\; 0.0092 \cdot \dfrac{ w\cdot L^4 }{ \lambda\cdot I } \) |
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| Symbol | English | Metric |
| \( \Delta \) = deflection or deformation | \(in\) | \(mm\) |
| \( x \) = horizontal distance from reaction to point on beam | \(in\) | \(mm\) |
| \( w \) = 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 | \(lbf\;/\;in^2\) | \(Pa\) |
| \( I \) = second moment of area (moment of inertia) | \(in^4\) | \(mm^4\) |
| \( R \) = reaction load at bearing point | \(lbf\) | \(N\) |
| \( L \) = span length under consideration | \(in\) | \(mm\) |
