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Structures

91 tools in 14 sections. Each tool page shows the method with the numbers substituted, its references and the published examples it reproduces.

Materials 7

MIL-HDBK-5J Allowables This tool provides access to the MIL-HDBK-5J material properties database. Select a material using the cascading dropdowns to view its complete property data including…
Material Finder Reverse lookup of the MIL-HDBK-5J database: enter the strength, stiffness and density you need, the basis, grain direction and operating temperature, and the tool ranks…
Material Comparator Side-by-side comparison of up to six MIL-HDBK-5J materials: type each one the way an engineer says it (2024-T3 sheet 0.1, 7075-T651 plate 1.5, Ti-6Al-4V annealed sheet,…
Reference Stress The following analysis calculates the compressive reference stresses at secant Moduli .7 Ec and .7 G.
Plastic Bending Allowables The following analysis calculates the Cozzone stresses and plastic bending allowables given material modulus, ultimate strength, yield, ultimate strain, and section…
Triaxiality Cutoff The following analysis produces a strain allowable for a particular stress state. This allowable is a modification to a handbook strain allowable which was measured…
FEA Stress-Strain Input Turns handbook material properties (E, Ec, ν, Ftu, Fty, Fcy, the Ramberg-Osgood exponents nt and nc and the elongation) into the nonlinear material input of the…

Composites 4

MIL-HDBK-17 Lamina Statistically based lamina and laminate property data of the polymer-matrix composite systems in MIL-HDBK-17-2F (2002), the last open release of the Composite Materials…
MIL-HDBK-23 Core Sandwich core and adhesive properties from MIL-HDBK-23A, Structural Sandwich Composites (1968, notices to 1974), the handbook that preceded CMH-17 Volume 6.
Classical Laminate Theory Classical laminate theory for a laminate built from up to four lamina (handbook data from My Lamina or typed values) in any stacking sequence, entered ply by ply or as a…
Sandwich Panel Strength, stiffness and stability of a flat honeycomb or foam core sandwich panel with thin facings, by the classical sandwich theory of MIL-HDBK-23A and Allen with…

Frames and Trusses 1

Truss and Frame Analysis Plane trusses and rigid frames by the direct stiffness method. The structure is typed as text: nodes with coordinates, members with their end nodes and E, A, I (defaults…

Beams 7

Section Properties Cross-section properties of a beam from a section drawn on the screen: click points on the grid to lay out the outer boundary, drag or type the coordinates to adjust…
Beam Stress Fiber stresses and strains of a straight beam from the section resultants (axial force, two shears, torque and two bending moments) on a section drawn on the screen or…
Beam Deflection Reactions, shear and moment diagrams, slopes and deflections of a single-span beam by the classical closed forms: simply supported, cantilever, fixed at both ends,…
Continuous Beam and Moment Distribution Continuous beams of up to eight spans on pinned, fixed, free (cantilever) or spring supports, with support settlements, under uniform, partial, triangular, point and…
Curved Beam Stresses in a beam curved in the plane of bending, for a section drawn on the screen: the section constants of the Winkler (curved-beam) theory are computed exactly for…
Curved Beam Thin-Walled Stresses in a curved beam of I, T or channel section built from plate dimensions, with Bleich's correction for the flanges: in a curved beam the radial component of the…
Lateral-Torsional Buckling Lateral-torsional buckling strength of a doubly symmetric I-beam or a channel bent about its strong axis: the elastic critical moment of Timoshenko (warping and…

Loads and Dynamics 10

V-n Diagram and Load Factors Maneuver and gust envelope of an airplane from the airworthiness rules: the limit maneuvering load factors of 14 CFR 23.337 (normal, utility, acrobatic and commuter…
Random Vibration Response Response of a single-degree-of-freedom component to a base random vibration given as an acceleration power spectral density: the input PSD from breakpoints (frequency…
Shock Response Spectrum Shock response spectrum (SRS) of a transient base acceleration: a classical pulse (half-sine, haversine, terminal-peak or initial-peak sawtooth, trapezoidal,…
Wing Span Loads Spanwise lift distribution of a wing by Schrenk's approximation (NACA TM 948, 1940) and the shear, bending moment and torque it produces along the span with inertia…
Inertia and Gyroscopic Loads Inertia loads of the mass items of an airplane under a load-factor and angular-rate condition, and the gyroscopic couples of its engines.
Landing Gear Loads Landing-impact loads of an airplane landing gear from the drop-test energy balance of 14 CFR Part 23 (2016 edition, Amendment 23-62) or Part 25: the limit descent…
Pressurization Loads Cabin pressurization loads on a fuselage. The differential pressure follows from the cabin and flight altitudes by the 1976 U.S.
Modal Estimates Natural frequencies and mode shapes of simple structures for a first dynamic check: uniform Bernoulli-Euler beams with the six classical end-condition pairs from the…
Stick Model Lumping Lumped-mass and stiffness stick model of a wing or fuselage from distributed data, with a Myklestad bending pass and a Holzer torsion pass for the uncoupled natural…
Fatigue Spectrum Generation A flight-by-flight fatigue load sequence from a mission profile and exceedance data, ready to paste into the Spectrum Fatigue Life and Crack Growth tools: mission…

Joints 7

Fastened Joint Stiffness Calculates effective shear and tension fastener stiffness for a single or double lap joint.
Fastened Joint Strength The following analysis calculates the ultimate and yield strength of a single-fastener shear joint. If input loads are given, a margin of safety for each is calculated.
Non-Structural Shim This tool provides guidance when using non-structural shims in single-shear joints. Assumes all the fastener eccentric load is balanced by prying on the head and tail.
Lug Strength Strength of pin-loaded lugs by the method of Cozzone, Melcon and Hoblit (Product Engineering, May 1950 and June 1953) as codified in Section 9 of the Air Force Stress…
Bolt Group Loads Load on each fastener of a bolted or riveted pattern under a general load set: in-plane forces and the moment about the pattern's normal are shared by the rigid-plate…
Weld Group Stress Stresses in a fillet-weld group treated as lines (Blodgett's method as presented in Shigley's Mechanical Engineering Design, Chapter 9): the throat area, centroid, unit…
Beam-in-Socket This beam-in-socket analysis produces maximum pin bearing stress, maximum pin shear and bending loads. Also referred to as a pin-in-socket analysis.

Stress and Strain 6

Mohr's Circle Mohr's circle for plane stress, plane strain and a general three-dimensional stress state: the centre and radius, the principal stresses or strains with both principal…
Strain Transformation 2D Calculates the engineering and principal strain values and directions given the strain components and rotation angle. Also outputs stresses if moduli are known.
Strain Gage to Strain State Calculates the engineering and principal strain values and directions given the strain values of a rossete strain gage. Also outputs stresses if moduli are known.
Stress to Strain 3D Calculates the engineering and principal strain values and directions given the three-dimensional stress components.
Strain to Stress 3D Calculates the stress components and principal stress values given the three-dimensional strain components measured in microstrain.
Linear to True Stress The following analysis produces an estimated local stress and strain from an elastic point stress using the Neuber and Glinka methods and a weighted Unified Estimate…

Stability 4

Column Stability Compression strengths of columns can be predicted using theoretical elastic solutions for slender, symmetrical and centroidally-loaded columns.
Column Buckling Tables Critical stress and load of a centrally loaded column about both axes for the six classical end conditions, with the theoretical effective-length factor K of Timoshenko…
Beam Column Strength Analyzes beam-columns subjected to combined axial compression and lateral loading using the Gittleman Method.
Plate Buckling Analyses a web buckling capability of an orthotropic or isotropic plate given a general loading N_xx, N_yy, N_xy.

Plates and Shells 10

Plate Bending Small-deflection bending of flat plates: rectangular plates under uniform, linearly varying and patch or point loads with simply supported, clamped and free edges by the…
Cylindrical Shell Buckling Buckling of a thin isotropic circular cylindrical shell by NASA SP-8007 (1968): the classical axial buckling stress E t / (r √(3(1 − ν²))) with the lower-bound…
Curved Panel Buckling Compression and shear buckling of a curved sheet panel between stringers and frames (a fuselage or wing skin bay) by NACA TN 3783, Handbook of Structural Stability Part…
Sphere and Cone Buckling Buckling of thin spherical shells under external pressure and of truncated conical shells under axial compression, bending, external or internal pressure and torsion, by…
Membrane Shell Stresses Membrane (thin-shell) stresses of pressure-vessel shapes and the discontinuity stresses at their junctions.
Large-Deflection Plates Plates whose deflection is of the order of the thickness, where mid-plane stretching carries part of the pressure: the von Kármán equations for a rectangular plate under…
Plate Vibration Natural frequencies and mode shapes of thin rectangular and circular plates after Leissa's Vibration of Plates (NASA SP-160): the exact solution for all edges simply…
Circular and Annular Plates Small-deflection bending of solid circular and annular plates by the exact axisymmetric solution of the plate equation (Timoshenko and Woinowsky-Krieger, Chapter 3): a…
Orthotropic Plate Bending Small-deflection bending of orthotropic and stiffened rectangular plates by Huber's equation D_x w,xxxx + 2H w,xxyy + D_y w,yyyy = q (Timoshenko and Woinowsky-Krieger,…
Thermal Bending of Plates Thermal stresses and deformations of a flat rectangular plate: a temperature gradient through the thickness (linear or parabolic) on a plate whose edges are free, simply…

Thin-Walled Structures 10

Crippling Strength Crippling (local post-buckling failure) stress and load of formed and extruded thin-walled compression members: angle, channel, zee, tee, I, cruciform, hat, lipped…
Effective Sheet Width Width of buckled sheet that keeps acting with a stringer in a compression panel: the sheet buckling stress for the stringer pitch and edge condition, then the effective…
Stiffened Panel Compression Compressive strength of a riveted sheet-stringer panel between frames: the stringer crippling stress by Gerard's generalized formulas (NACA TN 3784 and TN 3785), the von…
Diagonal Tension Web Strength analysis of a plane stiffened shear web working in incomplete diagonal tension by the engineering theory of Kuhn, Peterson and Levin (NACA TN 2661, 1952,…
Box Beam Shear Flow Shear flow and rate of twist of single- and multi-cell thin-walled closed boxes under shear loads and torque, the Bredt–Batho theory of Megson's Aircraft Structures and…
Open Section Shear Flow Shear flow distribution and shear centre of a thin-walled open section under transverse shear loads, by the thin-wall bending-shear equation of Megson and Bruhn: the…
Local Buckling Coefficients Elastic and plastic local buckling of the flat plate elements of a thin-walled section by NACA TN 3781 (Gerard and Becker 1957, Handbook of Structural Stability Part I):…
Shear-Resistant Web Design check of a stiffened plane shear web that must stay unbuckled at limit load (the shear-resistant beam of NACA TN 2661 Section 1 and Bruhn Chapter C10), the…
Shear Lag in Box Beams Shear lag in the stringer-sheet cover of a box beam under bending by Kuhn's substitute single-stringer method (NACA Report 739, Kuhn and Chiarito 1942): the cover's…
Beam-Column with Crippling A thin-walled stringer or stiffener, with or without its effective sheet, carrying axial compression together with a lateral load or end moments: the exact pin-ended…

Contact 1

Contact Stress Hertz contact stresses for the contacts engineers meet in practice: sphere on sphere or flat, ball in a seat, cylinder on cylinder or flat, pin in a groove or bore,…

Stress Concentrations 18

Round Hole Uniaxial Stress Stresses around a round hole in an infinite plate under uni-axial stress, from the Kirsch (1898) elasticity solution: radial, tangential and shear stress at a point…
Round Hole General Load Stresses around a round hole in an infinite plate under any uniform in-plane far-field state given as stress resultants N_xx, N_yy, N_xy and the plate thickness t…
Round Hole Finite Strip Stresses around a central round hole in a long strip of finite width W under an axial load P, from Howland's (1930) series solution carried to convergence: the stress…
Pin-Loaded Hole Stresses around a round hole in an infinite plate loaded by a pin: the pin presses on the half of the hole facing the load with a frictionless cosine pressure p = p_0…
Pressurized Hole Stresses around a round hole in an infinite plate that carries a uniform internal pressure (fluid pressure, or the contact pressure of an interference-fit pin or…
Hole in Plate Bending Moments and surface stresses around a round hole in a thin plate under uniform remote bending and twisting moments M_xx, M_yy, M_xy per unit width (Kirchhoff plate…
Rotating Disk With Hole Stresses in a thin uniform disk with a central hole spinning at constant speed (Lamé-type closed form): radial and hoop stress at any radius, the peak hoop stress at the…
Elliptic Hole Uniaxial Stress Stresses around an elliptic hole in an infinite plate under uni-axial stress, from the Inglis (1913) / Kolosov-Muskhelishvili elasticity solution: the stress components,…
Elliptic Hole General Load Stresses around an elliptic hole, aligned with the plate axes or inclined, in an infinite plate under any uniform in-plane far-field state given as stress resultants…
Rounded Square Hole Stresses around a square hole with rounded corners in an infinite plate under any uniform in-plane far-field state given as stress resultants N_xx, N_yy, N_xy and the…
Two Holes Stresses around two interacting round holes of diameters D_1 and D_2, centers s apart on the x axis, in an infinite plate under any uniform in-plane far-field state…
Row of Holes Stresses around an infinite row of equal round holes in an infinite plate under any uniform in-plane far-field state given as stress resultants N_xx, N_yy, N_xy and the…
Drawn Cutout Stresses around one or more cutouts of any shape drawn on the screen, in an infinite plate under a uniform far-field state given as the resultants N_xx, N_yy, N_xy and…
Semicircular Edge Notch Stresses around a semicircular notch of radius ρ on the straight free edge of a semi-infinite plate under uniform tension σ = N_yy / t parallel to the edge (Maunsell…
Neuber Hyperbolic Notch Stress concentration factors for a flat bar with symmetric hyperbolic notches or a round bar with a hyperbolic circumferential groove, from Neuber's exact deep-notch…
Circular Inclusion Stresses in and around a circular elastic inclusion (a plug, bushing, fiber or second-phase particle) perfectly bonded in an infinite plate under any uniform in-plane…
Elliptic Inclusion Stresses in and around an elliptic elastic inclusion (a plug, fiber cross-section or second-phase particle), aligned with the plate axes or inclined, perfectly bonded in…
Spherical Cavity Stress concentration at a spherical cavity (a pore, void or casting defect) in an infinite elastic solid under remote uniaxial tension, from the closed-form solution of…

Fatigue 4

Notch Sensitivity Fatigue notch factor K_f = 1 + q (K_t − 1) of a notch, hole or fillet from its elastic stress concentration factor K_t, its root radius r and the notch sensitivity q of…
Low-Cycle Fatigue Estimates the fatigue life at a point from an elastic stress range using the Ramberg-Osgood cyclic curve, the Coffin-Manson strain-life relation and the…
Spectrum Fatigue Life Fatigue life of a part under a variable-amplitude stress history: the history is rainflow counted (ASTM E1049), every cycle's life comes from the MIL-HDBK-5J best-fit…
Random Vibration Fatigue Fatigue damage and life of a structure under a stationary Gaussian random vibration given as an acceleration power spectral density: the input PSD by breakpoints…

Damage Tolerance 2

Center Crack Elastic stress field of a through crack of length 2a in an infinite plate under any uniform in-plane far-field state given as N_xx, N_yy, N_xy and the thickness t…
Crack Growth Fatigue crack growth from an initial to a critical crack size by the Paris, Walker, Forman or NASGRO equation: stress intensity from the geometry factor of a centre…