- See Article - Beam Design Formulas
Overhanging Beam - Uniformly Distributed Load Over Supported Span formulas |
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R=V=w⋅L2 Vx=w⋅(L2−x) Mmax(atcenter)=w⋅L28 Mx=w⋅x2⋅(L−x) Δmax(atcenter)=5⋅w⋅L4384⋅λ⋅I Δx=w⋅x24⋅λ⋅I⋅(L3−2⋅L⋅x2+x3) Δx1=−w⋅L3⋅x124⋅λ⋅I |
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| Symbol | English | Metric |
| Δ = deflection or deformation | in | mm |
| x = horizontal distance from reaction to point on beam | in | mm |
| w = load per unit length | lbf/in | N/mm |
| M = maximum bending moment | lbf−in | N−mm |
| V = maximum shear force | lbf | N |
| λ (Greek symbol lambda) = modulus of elasticity | lbf/in2 | Pa |
| R = reaction load at bearing point | lbf | N |
| I = second moment of area (moment of inertia) | in4 | mm4 |
| L = span length of the bending member | in | mm |
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.
