Structural Analysis Formulas Pdf Page

Member force (axial): [ F = \sigma A = \frac\delta AEL ] Carry-over factor (for prismatic member): 1/2 Member stiffness: [ k = \frac4EIL \quad (\textfixed far end) \quad \textor \quad k = \frac3EIL \quad (\textpinned far end) ]

[ \sigma = \fracPA ]

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

Integral forms:

Where ( v(x) ) = vertical deflection. Common solutions: Member force (axial): [ F = \sigma A

[ \tau_\textavg = \fracVQI b ]

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: Abstract This paper presents a curated collection of

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