Structural Analysis Formulas Pdf Apr 2026

Integral forms:

| Case | Max Deflection (( \delta_\textmax )) | Location | |------|-------------------------------------------|----------| | Cantilever, end load (P) | (\fracPL^33EI) | free end | | Cantilever, uniform load (w) | (\fracwL^48EI) | free end | | Simply supported, center load (P) | (\fracPL^348EI) | center | | Simply supported, uniform load (w) | (\frac5wL^4384EI) | center | | Fixed-fixed, center load (P) | (\fracPL^3192EI) | center | | Fixed-fixed, uniform load (w) | (\fracwL^4384EI) | center | For a prismatic beam (rectangular cross-section approximation):

[ \fracd^2 vdx^2 = \fracM(x)EI ]

In 3D:

Slenderness ratio:

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

(( b \times h )) maximum shear (at neutral axis): structural analysis formulas pdf

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:

[ P_cr = \frac\pi^2 EI(KL)^2 ]

[ \fracdVdx = -w(x) \quad \textand \quad \fracdMdx = V(x) ] Integral forms: | Case | Max Deflection ((

Effective length factors (K):

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

Where: ( M ) = internal bending moment, ( y ) = distance from neutral axis, ( I ) = moment of inertia of cross-section. The differential equation: The document is intended as a quick reference

[ \tau_\textavg = \fracVQI b ]