# Frame Design Formulas

Written by Jerry Ratzlaff on . Posted in Structural Engineering

## Nomenclature, Symbols, and Units for Frame Supports

SymbolGreek SymbolDefinitionEnglishMetricSIValue
$$\Delta$$ Delta deflection or deformation $$in$$ $$mm$$ $$mm$$ -
$$h$$ - height of frame $$in$$ $$mm$$ $$mm$$ -
$$x$$ - horizontal distance from reaction point $$in$$ $$mm$$ $$mm$$ -
$$H$$ - horizontal reaction load at bearing point $$lbf$$ $$N$$ $$kg-m-s^{-2}$$ -
$$I_h$$ - horizontal member second moment of area (moment of inertia) $$in^4$$ $$mm^4$$ $$mm^4$$ -
$$w$$ - load per unit length $$\large{\frac{lbf}{in}}$$ $$\large{\frac{N}{m}}$$ $$N-m^{-1}$$  -
$$M$$ - maximum bending moment $$lbf-in$$ $$N-mm$$ $$N-mm$$  -
$$\lambda$$ lambda modulus of elasticity $$\large{\frac{lbf}{in^2}}$$ $$MPA$$ $$N-mm^{-2}$$  -
$$A, B, C, D, E$$ - point of intrest on frame - - -  -
$$L$$ - span length under consideration $$in$$ $$mm$$ $$mm$$  -
$$P$$ - total concentrated load $$lbf$$ $$N$$ $$kg-m-s^{-2}$$ -
$$I_v$$ - vertical member second moment of area (moment of inertia) $$in^4$$ $$mm^4$$ $$mm^4$$  -
$$R$$ - vertical reaction load at bearing point $$lbf$$ $$N$$ $$kg-m-s^{-2}$$ -

## 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. 