- See Article - Beam Design Formulas
Simple Beam - Concentrated Load at Center formulas |
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R \;=\; V \;=\; \dfrac{ P }{ 2 } M_{max} \; (at\; point \;of\; load ) \;=\; \dfrac{ P \cdot L }{ 4 } M_x \; [\; x < (L\;/\;2) \;] \;=\; \dfrac{ P \cdot x }{ 2 } \Delta_{max} \; (at \;point\; of\; load ) \;=\; \dfrac{ P \cdot L^3 }{ 48 \cdot \lambda\cdot I } \Delta_x \; ( x < \frac{L}{2} ) \;=\; \dfrac{ P \cdot x }{ 48 \cdot \lambda \cdot I } \cdot ( 3 \cdot L^2 - 4 \cdot x^2 ) |
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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 |
| \Delta = deflection or deformation | in | mm |
| P = total concentrated load | lbf | N |
| L = span length of the bending member | in | mm |
| x = horizontal distance from reaction to point on beam | in | mm |
| \lambda (Greek symbol lambda) = modulus of elasticity | lbf\;/\;in^2 | Pa |
| I = second moment of area (moment of inertia) | in^4 | mm^4 |
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.
