# Beam Design Formulas

Written by Jerry Ratzlaff on . Posted in Structural Engineering

## Nomenclature, Symbols, and Units for Beam Supports

 Symbol Greek Symbol Definition English Metric SI Value $$\Delta$$ Delta deflection or deformation $$in$$ $$mm$$ $$mm$$ - $$a, b$$ - distance to point load $$in$$ $$mm$$ $$mm$$ - $$w$$ - highest load per unit length $$\large{\frac{lbf}{in}}$$ $$\large{\frac{N}{m}}$$ $$N-m^{-1}$$ $$x$$ - horizontal distance from reaction to point on beam $$in$$ $$mm$$ $$mm$$ - $$w$$ - load per unit length $$\large{\frac{lbf}{in}}$$ $$\large{\frac{N}{m}}$$ $$N-m^{-1}$$ - $$M$$ - maximum bending moment $$lbf-in$$ $$N-mm$$ $$N-mm$$ - $$V$$ - maximum shear force $$lbf$$ $$N$$ $$kg-m-s^{-2}$$ $$\lambda$$ lambda modulus of elasticity $$\large{\frac{lbf}{in^2}}$$ $$MPA$$ $$N-mm^{-2}$$ - $$R$$ - reaction load at bearing point $$lbf$$ $$N$$ $$kg-m-s^{-2}$$ - $$I$$ - second moment of area (moment of inertia) $$in^4$$ $$mm^4$$ $$mm^4$$ - $$L$$ - span length of the bending member $$in$$ $$mm$$ $$mm$$ - $$P$$ - total concentrated load $$lbf$$ $$N$$ $$kg-m-s^{-2}$$ - $$W$$ - total load $$\left( \frac{w\;L}{2} \right)$$ $$lbf$$ $$N$$ $$kg-m-s^{-2}$$ -

## diagrams

• 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. 