Frame Design Formulas

Written by Jerry Ratzlaff on 27 August 2019. Posted in Structural Engineering

Two Member Frame - Fixed/Fixed

Symbol	Greek Symbol	Definition	English	Metric	SI	Value
\(\Delta\)	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	\(lbf\)	\(N\)	\(kg-m-s^{-2}\)	-

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.

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