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FEARev. Q3 2026

Hand calc check

Produce a documented first-principles hand calculation for common mechanical problems: beam bending and deflection, shaft sizing under combined loading, column buckling, thin and thick pressure vessels, thermal expansion and stress, press fits, spring rates, and bearing life. Use whenever the user asks to size or check a component, wants a quick calc, needs a stress or deflection estimate, or asks for the engineering justification behind a dimension.

Daniel Weber portraitDaniel WeberApplication EngineerMathWorks logoMathWorks

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Hand Calc Check

Produces the calc sheet a checker can follow: assumptions, free body, equations by name, numbers with units, and a margin against a stated criterion. One page of clear math beats ten pages of the wrong FEA.

Required inputs

  1. Geometry with dimensions and units.
  2. Loads: magnitude, direction, application points, static or cyclic. If the user gives a scenario instead of loads ("a person steps on it"), derive the load and state the assumption (e.g., 100 kg person, dynamic factor 2).
  3. Material with grade, so yield/ultimate/modulus can be stated with a source caveat.
  4. The criterion: yield with what safety factor, deflection limit, life target. If none given, propose one appropriate to the application and say it is proposed.

Method

  1. Idealize and declare. State the model in one line: "treated as a cantilever with end load," "thin-walled pressure vessel, r/t = 18 so thin-wall valid." Every idealization that could be unconservative gets flagged.
  2. Free body. Describe (or sketch in text/ASCII) the FBD: supports, loads, reactions. Solve reactions first.
  3. Solve with named equations. Use standard forms and name them (Euler buckling, Roark case reference, Lame equations, Goodman line, L10 bearing life). Show substitution with units carried through, then the result. No skipped steps between formula and answer.
  4. Stress concentration. Apply Kt at holes, fillets, and steps for fatigue and brittle materials; state the Kt source (Peterson chart approximation) and value. For ductile static cases, note when Kt may be neglected and why.
  5. Combined loading. Shafts: combine bending and torsion (distortion energy or ASME shaft equation, state which). Report the governing location, not just the maximum values separately.
  6. Margin. MS = capacity/demand minus 1, or SF = capacity/demand, against the stated criterion. Report at the governing location and load case.
  7. Sensitivity. Identify the input the answer is most sensitive to and show the margin at a plausible worst value of that input (e.g., load plus 25 percent, wall at minimum tolerance).

Covered problem types

Beams (deflection, stress, standard cases and superposition), shafts (static and fatigue with Goodman/Soderberg, keyway Kt), columns and struts (Euler with end conditions, Johnson for intermediate slenderness), pressure (thin wall hoop/axial, thick wall Lame, end cap loads), thermal (free expansion, constrained stress alpha x E x dT, interface fits over temperature), press and shrink fits (interference pressure, holding torque, assembly force), springs (rate, stress, solid height, Wahl factor), bearings (L10 life from dynamic capacity, equivalent load), simple weld and lug checks (throat shear, bearing/tear-out/net section).

Output format

A calc sheet in this order: Problem statement, Assumptions (numbered), Inputs table with units, FBD description, Calculation with named equations, Result and margin, Sensitivity note, Limitations. Keep it dense; it should paste into a design record as-is.

Guardrails

  • Units discipline is absolute: carry units in the substitution line and sanity-check the result's magnitude against experience (a 2 meter steel beam deflecting 4 km means a units error, say so and fix it).
  • Material properties are typical unless the user provides spec minimums; flag this in every calc used for a margin.
  • State when the problem has outgrown a hand calc: significant plasticity, contact-dominated behavior, dynamic response near resonance, or geometry far from standard cases. Recommend the next tool rather than stretching the formula.
  • Never silently change the user's numbers. If an input looks wrong, ask or flag it, then proceed with it labeled "as given."

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