Structural Analysis Formulas Pdf ✦ Fast & Recent

Author: Engineering Reference Compilation Date: April 17, 2026 Subject: Summary of fundamental equations for beam deflection, moment, shear, axial load, and stability. Abstract This paper presents a curated collection of fundamental formulas used in linear-elastic structural analysis. It covers equilibrium equations, beam shear and moment relationships, common deflection cases, column buckling, and truss analysis. The document is intended as a quick reference for students and practicing engineers. 1. Fundamental Equilibrium Equations For a structure in static equilibrium in 2D:

[ \sum F_x = \sum F_y = \sum F_z = 0 ] [ \sum M_x = \sum M_y = \sum M_z = 0 ] Normal stress:

[ \sigma_x = -\fracM yI ]

(radius (r)): [ I = \frac\pi r^44, \quad A = \pi r^2 ] structural analysis formulas pdf

[ \tau_\textmax = \frac3V2A ] Critical load for a slender, pin-ended column:

[ \sum F_x = 0 \quad \sum F_y = 0 \quad \sum M_z = 0 ]

[ \fracdVdx = -w(x) \quad \textand \quad \fracdMdx = V(x) ] The document is intended as a quick reference

(( b \times h )) maximum shear (at neutral axis):

Where: ( V ) = shear force, ( Q ) = first moment of area about neutral axis, ( I ) = moment of inertia, ( b ) = width at the point of interest.

[ \delta = \fracPLAE ]

In 3D:

Where: ( M ) = internal bending moment, ( y ) = distance from neutral axis, ( I ) = moment of inertia of cross-section. The differential equation:

[ \tau_\textavg = \fracVQI b ]

Distribution factor at joint: [ DF = \frack_i\sum k ] Rectangle (width (b), height (h)): [ I = \fracb h^312, \quad A = bh ]

Where: ( P ) = axial load, ( A ) = cross-sectional area, ( L ) = original length, ( E ) = modulus of elasticity. For a beam with distributed load ( w(x) ) (upward positive):