[ P_cr = \frac\pi^2 EI(KL)^2 ]
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: structural analysis formulas pdf
Where: ( V ) = shear force, ( Q ) = first moment of area about neutral axis, ( I ) = moment of inertia, ( b ) = width at the point of interest. [ P_cr = \frac\pi^2 EI(KL)^2 ] Author: Engineering
| End condition | (K) | |---------------|-------| | Pinned-pinned | 1.0 | | Fixed-free | 2.0 | | Fixed-pinned | 0.7 | | Fixed-fixed | 0.5 | The document is intended as a quick reference
[ V(x) = -\int w(x) , dx + C_1 ] [ M(x) = \int V(x) , dx + C_2 ] For pure bending of a linear-elastic, homogeneous beam:
In 3D: