Langford Analytic · Knowledge Base
Reference Library
Engineering data, equations and relationships for everyday analysis and design. Formulae, constants, material properties, conversion factors and technical tables in a concise format designed for day-to-day engineering work.
Mechanics & Structures
Stress and Strain FormulaeDefinitions and relationships for normal stress, shear stress, normal strain and shear strain under uniaxial and multiaxial loading.Principal Stress and Mohr's CirclePrincipal stresses, maximum shear stress, and Mohr's circle relationships for 2D and 3D stress states.von Mises and Tresca Yield CriteriaEquivalent stress expressions for ductile metal yielding under multiaxial loading. von Mises (distortion energy) and Tresca (maximum shear).Section Properties for Common ShapesSecond moment of area, polar moment, radius of gyration and section modulus for rectangles, circles, tubes, I-sections and thin-walled sections.
Beams & Deflection
Buckling & Stability
Euler Buckling ReferenceEuler buckling load, critical stress, effective length factors and the Johnson-Euler transition for intermediate slenderness.Effective-Length ReferenceReference for effective length factors, rotational and translational restraint, and the relationship between end fixity and buckling load.Slenderness Ratio ReferenceReference for slenderness ratio, radius of gyration, transition slenderness and column behaviour regimes.Plate Buckling TerminologyGlossary of key terms for plate buckling — buckling coefficient, aspect ratio, effective width, post-buckling and tension field.Shell Buckling TerminologyGlossary of key terms for shell buckling — curvature, membrane stress, knock-down factor, imperfection sensitivity, classical critical load.Local vs Global Buckling — Quick ReferenceReference distinguishing local and global buckling modes, mode interaction, and the governing mode for common structural configurations.Eigenvalue vs Nonlinear Buckling — Quick ReferenceQuick reference comparing eigenvalue and nonlinear buckling analysis — assumptions, outputs, limitations and when to use each.Imperfection TerminologyGlossary of imperfection types and terms used in buckling analysis — geometric, eigenmode-based, measured, amplitude, sensitivity.
Fasteners & Joints
Bolt Tensile and Shear Stress AreaTensile stress area, shear area, and stiffness relationships for threaded fasteners under axial and shear loading.Bearing and Net-Section StressBearing stress, bearing allowable, net-section stress and edge-margin relationships for fastener holes and lugs.Weld Throat and Weld-Group PropertiesEffective throat thickness, weld stress formulae and weld-group section properties for fillet and butt welds.Fastener Strength TablesTabulated shear and tension allowables for common aerospace fasteners. Values are for single shear unless stated. Always verify against MMPDS.
Fatigue & Fracture
Fatigue and Mean Stress RelationshipsStress range, stress amplitude, stress ratio, Goodman, Gerber, Soderberg and Miner's rule equations with notation.Fatigue S-N Curve DataBasquin constants and endurance limits for common aerospace materials at R = −1. Apply modifying factors before use.Stress Concentration Factors (Kt)Elastic stress concentration factors for common geometries: holes, fillets, notches and keyways. Kf for fatigue.Fracture Mechanics Quick ReferenceStress intensity factor K, fracture toughness KIC, Paris law for crack growth, and critical crack size relationships.
Dynamics & Vibration
Materials
Engineering Material PropertiesMechanical properties for common aerospace and structural materials. All values are room temperature unless stated. Values are typical — verify against the material specification for design.Composite Ply Properties ReferenceEngineering constants and strength allowables for unidirectional composite plies. Values are mean at room temperature unless stated.Safety Factors by IndustryTypical design safety factors for aerospace, marine, motorsport and industrial applications with applicable standards.Common Aerospace Load FactorsManoeuvre, gust and inertia load factors for aerospace structural sizing. Indicative — derive from the applicable flight envelope.
Composites
Thermal
Pressure & Fluid
Units & Conversions
Engineering Constants
Seismic
Seismic Frequency to Period ConversionThe relationship between natural frequency and natural period, with conversion formulas and worked values for common seismic frequencies.g to SI Acceleration ConversionConverting acceleration expressed in multiples of g to SI units (m/s^2) and to imperial units (in/s^2), with the standard gravitational acceleration values.Modal Participation Factor ReferenceDefinition, formula and interpretation of the modal participation factor, which quantifies how much each mode contributes to the response in a given direction.Effective Modal Mass ReferenceDefinition, formula and use of the effective modal mass, which quantifies the fraction of total mass that participates in each mode for a given direction.Cumulative Modal Mass ReferenceHow cumulative modal mass participation is computed and used to verify that sufficient modes have been extracted for seismic analysis.SRSS Combination EquationThe square root of sum of squares modal combination method, its formula, applicability conditions and limitations.CQC Combination FormulationThe complete quadratic combination method, its formula, the role of the correlation coefficient and when it is preferred over SRSS.Response Spectrum TerminologyKey terms used in response spectrum analysis: spectral acceleration, spectral velocity, spectral displacement, ZPA, amplified region, rigid region and spectrum ordinates.Damping Ratio ReferenceTypical damping ratios used in seismic analysis for different construction types and equipment classes, with notes on justification and spectrum scaling.Critical Damping ReferenceThe concept of critical damping, its relation to the damping ratio, and how it appears in seismic analysis formulas.Base Excitation TerminologyKey terms for base excitation in seismic analysis: support motion, influence vector, effective earthquake force and rigid body modes.Directional Combination TerminologyTerms and methods for combining seismic responses from multiple directions: SRSS directional, 100-40-40, and the distinction between modal and directional combination.Spectral Acceleration ReferenceDefinition, units and interpretation of spectral acceleration, the primary quantity extracted from a response spectrum for seismic design.Spectral Velocity ReferenceDefinition and use of spectral (pseudo-velocity) in seismic analysis, its relationship to spectral acceleration and displacement.Spectral Displacement ReferenceDefinition and use of spectral displacement in seismic analysis, its relationship to spectral acceleration and its role in drift and clearance assessment.Rigid Response ConceptsThe concept of rigid response in seismic analysis: the rigid-flexible boundary, the rigid component of response and how rigid and periodic responses are combined.Seismic Load NotationCommon notation used in seismic load definitions: E, Eh, Ev, QE, load combinations and direction subscripts.
Turbomachinery
Turbomachinery Structural TerminologyGlossary of key terms used in turbomachinery structural analysis — from aerofoil and blisk through fir-tree, nodal diameter and ZZENF.Centrifugal Load ReferenceKey equations and relationships for centrifugal loading in rotating turbomachinery components.Rotating Disc Stress TerminologyGlossary of terms for rotating disc stress analysis — radial, hoop, bore, rim, web and blade pull.Blade Root TerminologyGlossary of terms for blade root attachments — fir-tree, dovetail, tangs, contact faces, fretting.Engine Order ReferenceKey relationships for engine order excitation in turbomachinery — frequency, resonance speed and excitation sources.Campbell Diagram TerminologyGlossary of terms for Campbell diagrams — crossings, engine order lines, frequency curves and resonance speed.Cyclic Symmetry ReferenceKey terms and relationships for cyclic symmetry analysis in turbomachinery FEA.Overspeed TerminologyGlossary of terms for overspeed analysis — burst margin, yield margin, plastic deformation and containment.Blade-Off TerminologyGlossary of terms for blade-off analysis — imbalance, containment, fragment energy and blade release.
Pressure & Containment
Pressure Analysis Terminology ReferenceConcise definitions of pressure, containment, membrane stress, hoop stress, longitudinal stress, radial stress, end thrust, nozzle, head, discontinuity, stress classification and related terms.Absolute vs Gauge Pressure ReferenceReference table of absolute, gauge and differential pressure relationships, atmospheric pressure values and conversion factors.Thin-Wall Pressure Relationships ReferenceConcise reference of thin-wall pressure vessel formulae — hoop stress, longitudinal stress, spherical stress, end thrust and displacement.Thick-Wall Cylinder ReferenceLame equation reference for thick-walled cylinders — radial and circumferential stress, axial stress, inner and outer surface values.Pressure End-Thrust ReferenceConcise reference for pressure end thrust at closures, bends, reducers and expansion joints.Pressure Vessel Nozzle Terminology ReferenceConcise reference of nozzle terminology — radial nozzle, non-radial nozzle, reinforcing pad, forged insert, nozzle neck, flange face, flexibility factor.External Pressure Buckling ReferenceConcise reference for external pressure buckling — key parameters, eigenvalue vs nonlinear analysis and imperfection sensitivity.Stress Linearisation Terminology ReferenceConcise reference for stress linearisation terms — SCL, membrane, bending, peak, primary, secondary, stress classification.Pressure Piping Load ReferenceConcise reference for pressure piping loads — sustained, thermal, occasional, pressure thrust, nozzle loads and support reactions.Pressure & Containment Verification ReferenceConcise reference for pressure and containment analysis verification checks — pressure resultant, equilibrium, analytical comparison, mesh convergence and displacement.
Probabilistic & Reliability
Probability & Reliability TerminologyConcise reference for probability and reliability terms used in engineering analysis — aleatory, epistemic, CDF, PDF, quantile, reliability index, FORM, SORM, POD, posterior and more.PDF / CDF ReferenceQuick reference for the relationship between PDF, CDF, exceedance probability and quantiles, with the key formulas for engineering use.Common Engineering Probability DistributionsA concise reference for the normal, lognormal, Weibull, extreme-value, uniform and triangular distributions — parameters, range and typical engineering applications.Reliability Index ReferenceQuick reference for the reliability index beta, its relationship to failure probability and illustrative beta-to-Pf conversion values.Limit-State Function ReferenceQuick reference for common limit-state functions in structural reliability — stress, displacement, fatigue, buckling, fracture and combined stress.FORM / SORM TerminologyConcise reference for FORM and SORM terms — design point, most probable failure point, standard-normal space, reliability index, sensitivity factors, curvature correction.Monte Carlo TerminologyConcise reference for Monte Carlo terms — sampling, convergence, variance, estimator, confidence interval, importance sampling, subset simulation.Bayesian Updating TerminologyConcise reference for Bayesian terms — prior, likelihood, posterior, evidence, conjugate, MCMC, credible interval, posterior predictive.Sensitivity Analysis TerminologyConcise reference for sensitivity analysis terms — local vs global, variance contribution, Sobol indices, screening, elementary effects, interaction.
Ballistics & Penetration
High-Velocity Impact TerminologyConcise reference for high-velocity impact terms — ballistic limit, perforation, penetration, plugging, petalling, spall, adiabatic shear, and more.Penetration vs Perforation ReferenceQuick reference for the distinction between indentation, penetration, partial penetration, complete perforation and the residual structural response.Stress-Wave TerminologyConcise reference for stress-wave terms — compression wave, tensile wave, wave speed, impedance, reflection, transmission, free surface, interface.High-Strain-Rate TerminologyConcise reference for high-strain-rate material terms — strain rate, flow stress, rate sensitivity, DIF, adiabatic, Taylor-Quinney, shear band.Impact Energy & Momentum ReferenceQuick reference for kinetic energy, momentum, impulse and their relationships in impact analysis.Plugging / Petalling / Spall TerminologyConcise reference for the three principal penetration failure mechanisms — plugging, petalling and spall — and their characteristics.Explicit Impact Energy TermsConcise reference for the energy components in explicit impact FEA — internal, kinetic, contact, hourglass, deleted and total energy.Residual Structural Strength TerminologyConcise reference for residual strength terms — remaining section, residual stress, CAI, hidden damage, inspection-informed reassessment.
Creep & High-Temperature
Creep TerminologyConcise reference for creep and high-temperature analysis terms — primary, secondary, tertiary, creep rate, rupture, relaxation, homologous temperature and more.Primary / Secondary / Tertiary CreepQuick reference for the three stages of creep — their characteristics, significance and engineering use.Norton Creep Law — Quick ReferenceQuick reference for the Norton creep law — the power-law relationship for secondary creep rate.Larson–Miller Parameter — Quick ReferenceQuick reference for the Larson-Miller parameter — the time-temperature parameter for creep rupture extrapolation.Stress Relaxation TerminologyConcise reference for stress relaxation terms — imposed strain, declining stress, preload loss, relaxation curve, creep-relaxation coupling.Creep Rupture TerminologyConcise reference for creep rupture terms — rupture time, stress-rupture curve, damage fraction, remaining life, safety factor.Creep-Fatigue TerminologyConcise reference for creep-fatigue interaction terms — hold time, dwell, interaction diagram, damage fraction, TMF, in-phase, out-of-phase.Homologous TemperatureQuick reference for homologous temperature — the ratio of operating temperature to melting point that indicates the creep regime.
Random Vibration
Random Vibration TerminologyA reference glossary of key random vibration terms — PSD, RMS, Grms, Gaussian, stationarity, coherence, spectral moments and more.PSD Units ReferenceA quick reference for PSD units across different quantities — acceleration, velocity, displacement, force and stress — with conversion factors.ASD vs PSD ReferenceA quick reference for the relationship between amplitude spectral density and power spectral density, with common pitfalls.RMS & Variance ReferenceA quick reference for the relationships between PSD, variance, RMS and standard deviation for random vibration signals.PSD Slope ReferenceA quick reference for PSD slopes in dB/octave, their power-law equivalents and common engineering meanings.Cross-Spectral Density ReferenceA quick reference for cross-spectral density — definition, relationship to coherence and role in multi-input analysis.Coherence ReferenceA quick reference for the coherence function — definition, range, interpretation and use in multi-input analysis and measurement quality.Miles Equation ReferenceA quick reference for Miles equation — the formula, variables, validity conditions and typical use cases.Random Vibration Fatigue TerminologyA reference glossary of key terms in random vibration fatigue — spectral moments, irregularity factor, narrow-band, Dirlik, Rayleigh, damage rate.
Shock & Transient Dynamics
Mechanical Shock TerminologyConcise reference to mechanical shock terminology, response quantities and common qualification language.Shock Pulse DefinitionsConcise reference to idealised shock-pulse definitions, parameters and engineering interpretation.Impulse & Momentum ReferenceConcise reference to impulse, momentum, velocity change and their use in transient structural assessment.SRS TerminologyConcise reference to shock response spectrum terminology, damping conventions, response quantities and plotting conventions.Primary vs Residual SRSConcise reference to primary and residual shock response spectra and the engineering distinction between them.Pyroshock TerminologyConcise reference to pyroshock terminology, high-frequency response characteristics and qualification context.Sampling & Aliasing ReferenceConcise reference to sampling rate, filtering, aliasing and bandwidth control for measured and analysed shock signals.Shock Isolation TerminologyConcise reference to shock-isolation terminology, frequency ratio, transmissibility and transient-response concepts.
Advanced Damage & Failure
Composite Damage Terminology ReferenceA reference glossary of key composite damage terms — initiation, evolution, intralaminar, interlaminar, delamination, BVID, CAI, progressive failure.Composite Failure Criteria Comparison ReferenceA quick reference comparing maximum stress, maximum strain, Tsai-Hill, Tsai-Wu, Hashin, Puck and LaRC criteria — mode ID, interaction, data needs.Progressive Damage ReferenceA quick reference for progressive damage concepts — damage variables, degradation laws, energy-based evolution and mesh objectivity.Delamination Terminology ReferenceA quick reference for delamination terms — Mode I/II/III, fracture toughness, energy release rate, mixed mode, cohesive zone, VCCT.Cohesive-Zone Modelling ReferenceA quick reference for cohesive-zone modelling — traction-separation law, parameters, mesh requirements and verification tests.BVID ReferenceA quick reference for barely visible impact damage — definition, threshold, detection methods and structural significance.Compression-After-Impact ReferenceA quick reference for CAI — test procedure, failure mechanism, strength retention and design significance.Composite Failure Verification ReferenceA quick reference for composite damage model verification — single-element tests, coupon tests, mesh sensitivity, energy and failure mode.