Aircraft fuselage stresses — margins around cutouts under cabin differential pressure.

Stress concentration factor margin study for holes, fillets, and notches.

Consolidated margin-of-safety summary report across multiple load cases.

Mohr's circle, principal stresses and von Mises, Tresca and maximum-principal margins with the plane-stress yield locus.

Stress-strength interference reliability of a series system of items with redundancy, mission failure probability and failure rate.

Hertz contact for ball and line contacts, including a cylinder in a groove: contact patch, peak pressure, subsurface shear and yield margin.

Miles equation and spectrum integration for a single-degree-of-freedom item: RMS and 3-sigma acceleration, displacement, equivalent static load and stress margin.

Helical compression spring rate, stress and solid height, and Belleville washer stack load-deflection with series and parallel stacking.

Fatigue life scatter factor from test data at a chosen reliability and confidence, and the Gumbel estimate of a rare maximum load.

Block fatigue damage with a two-point S-N curve, Goodman mean-stress correction, notch factor and Miner summation, with life and margin.

Cycles to grow a crack from its initial to its critical length using the Paris law, with scatter factor and margin.

One table of margins of safety from many checks: lowest margin, its line, count of negative margins and a bar plot.

Local notch-root stress and strain past yield from Kt, the nominal stress and a Ramberg-Osgood curve using Neuber's rule.

Convert a point or vector between two 3D coordinate systems with an origin shift and three rotations; gives the rotation matrix.

Combined-load margin of safety from a general interaction equation with two or three ratios and their exponents.

Median-rank Weibull fit of failure lives: shape, characteristic life, B10, mean life and reliability at a chosen life.

Peak force, deflection, impact factor and deceleration for a weight dropped onto a linear spring-like structure.

Principal stresses, maximum shear, von Mises and Tresca stress and yield margins from the six components of a 3D stress state.

Reliability of series, parallel or k-of-n arrangements, with the weakest component and the part reliability needed for a target.

Contact pressure, PV value, Archard wear volume and depth, and time to reach an allowable wear depth for a sliding contact.

Hoop and radial centrifugal stress in a solid disc or a disc with a hole, and the speed at first yield.

Combined stiffness, deflection, load sharing and stored energy for springs or load paths in series or in parallel.

Lewis bending stress, tooth force and margin for a spur gear tooth.

Natural frequency, magnification and transmissibility of a damped mass on a spring.

Von Mises stress and margins in a round tube under axial load, bending, torque and shear.

Rated life in revolutions and hours for a rolling bearing, with reliability factor and required load rating.

Convert stress and pressure, force, length and moment between common engineering units.

Goodman and Gerber fatigue safety factors and a yield check for a cyclic stress with mean value.

First lateral critical speed of a shaft on two supports with a disc at mid-span, and separation from running speed.

Stress intensity, fracture stress, critical crack length and net-section yield for a center-cracked plate.

Principal strains and stresses, maximum shear and von Mises stress from a rectangular strain gauge rosette.

Tension, support angle, length and margin of a uniformly loaded cable from span and sag.

Total weight, center of gravity and moments of inertia from a list of weights and positions.

Mean, standard deviation and normal-distribution A-basis and B-basis values from a list of test results.

Linear or log-log interpolation of a pasted x and y table, with the slope and a plot.

Worst-case and statistical tolerance stack-up with the gap range and margin against a required gap.

Strut stroke and gear load needed to absorb a sink speed, with the margin on the available stroke.

Stored energy, rim speed, hoop stress and speed limit of a thin ring flywheel.

Tension ratio and holding force for a rope wrapped round a drum.

Overall ratio, output speed, torque and power of a two-stage spur gear train.

Push and pull force, speed, power and rod stress of a double-acting hydraulic cylinder.

Concentration factor, net and peak stress of a plate with a central hole in tension.

Peak acceleration, amplification and displacement of an item hit by a half-sine shock pulse.

Natural frequency, transmissibility and isolation efficiency of a spring mount.

Tension in each leg of a multi-leg lifting sling from load and angle, with margin.

Bending stress, rate and deflection of a round-wire helical torsion spring with yield margin.

Combined axial and bending sweep with the interaction boundary, load envelope and worst-ratio margin.

Surface, size, load, temperature and reliability corrections to the endurance limit and a Goodman check.

Notch sensitivity and fatigue notch factor from the stress concentration, radius and strength.

Force against stroke and energy absorbed for a gas spring.

Stroke, force and deceleration for a crushable energy absorber stopping a mass.

Centrifugal force, g-load and fastener load of a mass on a rotating arm.

First three transverse natural frequencies and wave speed of a taut cable.

First three natural frequencies of a simply supported rectangular plate.

Torsional natural frequency of two discs on a shaft, with separation from operating speed.

Damping ratio, Q and decay times from a free vibration decay.

In-plane bending natural frequencies of a thin circular ring.

Stress intensity factor and fracture margin for central, edge and surface cracks.

Natural frequencies and mode shapes of two masses in a spring chain.

First two sloshing frequencies of liquid in an upright round tank.

Ratio, chain length, speed, pull and wrap of a two-sprocket chain drive.

Centrifugal pull and root stress of a rotating blade.

Flywheel inertia, stored energy, equivalent ring weight and rim stress.

Peak acceleration, velocity and displacement of sinusoidal vibration at one frequency.

Surge frequency of a helical compression spring against its operating frequency.

Mean, alternating, range and ratios from the maximum and minimum stress.

Permissible residual unbalance of a rotor from its balance grade, weight and speed.

Force to punch a round hole in sheet and the margin against the press.

Press force to bend sheet in a V die.

Safety factor and sheave ratio of a wire rope under a working load.

Load against deflection of a single coned disc spring.

Torque capacity of a multi-surface friction clutch for a clamp force.

Motor power to lift a load at a speed with acceleration and efficiency.

Friction torque, power loss and pressure of a lightly loaded journal bearing.

Torque, rate, arm force and shear stress of a round torsion bar.

DN value of a rolling bearing against a typical speed limit.

Outer-fiber stress and smallest elastic radius for bending a strip or wire.

Holding force and safety factor of suction cups for a lift or side pull.

Dynamic pressure, wind force and overturning moment on a flat surface.

Peak g and pad area for a cushioned drop.

Stroke, speed, acceleration and inertia force of a slider-crank mechanism.

Force and power for a wheeled vehicle on a grade.

Drive torque and speed for a ball screw.

Rack force and speed from pinion torque.

Reflected inertia and motor torque through a gear ratio.

Pull and motor power for a belt conveyor.

Displacement, compression ratio and piston speed.

Power from water flow and head.

Axle loads and lift-off limit when braking.

Time and peak speed of a trapezoidal move.

Rope capacity and line pull of a winch drum.

Damping ratio and overshoot of a spring-mass-damper.

Natural frequency and isolation from static sag.

A linear actuator moves a load with ramps up and down in speed.

Springs combine in series and in parallel.