Structural Analysis Formulas Pdf Link

[ \sigma = \fracPA ]

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

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:

Slenderness ratio:

[ \fracKLr, \quad r = \sqrt\fracIA ] For a pin-jointed truss in equilibrium at each joint:

Integral forms:

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) ] structural analysis formulas pdf

Effective length factors (K):

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

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

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

| End condition | (K) | |---------------|-------| | Pinned-pinned | 1.0 | | Fixed-free | 2.0 | | Fixed-pinned | 0.7 | | Fixed-fixed | 0.5 |

[ \fracdVdx = -w(x) \quad \textand \quad \fracdMdx = V(x) ] [ \sigma = \fracPA ] Where: ( M

[ \sigma_x = -\fracM yI ]

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