Verification

This manual checks MechCalc calculators point by point against published worked examples. Each example gives the inputs and example values from the source, runs the calculator on the same inputs, and lists both sets of numbers side by side.

How to read the results: Error (%) = (MechCalc − example value) / |example value| × 100, rounded to 2 decimal places; when the example value is 0, the absolute difference “Δ = …” is given instead. Numbers in the tables have 6 significant digits, and example values are copied with the digits printed in the source. Yes/no results have no error value; they show only “Match” or “No match”.

Result classes:

• Agrees: the MechCalc value matches the example value within the tolerance of that example; the tolerance is set from the precision of the example values of each example.
• Method difference: the two sides use different methods or conventions, the reason is known, and it is given in a note after the results table, together with which side is more accurate or whether both are approximations. A confirmed error in the example, where a printed number does not agree with the source’s own formula, is also listed as a method difference with the printed number as the example value; the note says what is wrong, what the value should be and whether the pass/fail verdict changes.
• Differences whose reason is not known, and results that come only from software reports, are never published.

Where the example values come from: textbook worked examples, problem collections, worked examples in standards or handbooks, journal papers, open-access and public-domain documents, and examples written for this manual and calculated by hand from the equations of the standard. The source line at the top of each entry gives the full reference. Example values are numbers printed in the source, or are derived directly from printed numbers by the source’s own definition (stated in a note in the Results Comparison or in the note above the summary table); they are never taken from calculator results.

Method consistency: same-method means the example value was calculated independently with the same equations and the same inputs as the calculator, so the comparison checks the implementation; cross-method means the two sides use different methods (for example, different editions of a standard), so the comparison shows how large the difference between the methods is and why. The “Method consistency” column of the index below shows which kinds each example has.

Numbering and structure: entry numbers look like VM-VDI2230-BOLT-004: the middle part is the calculator code and the end is a three-digit number; within one calculator, worked examples from the standard or handbook itself come first, and other examples are numbered in the order they are published. A number identifies one example: the entry is rerun and rewritten when the calculator is updated, but the number never moves to another example and is never reused. A number marked “Under verification” belongs to an example that is still being checked and has no entry yet. Each entry starts with the source and a calculator link that loads all inputs of the example, followed by four sections:

• Problem: a short description of the background, geometry, materials and loads.
• Inputs: all inputs; inputs not given in the source and estimated for this example are marked †, with the value and its basis given after the table.
• Calculation Steps: the whitebox steps from a real calculator run with the example’s inputs, keeping only the steps that are compared with example values; each step shows the equation, the numbers put in and the clause of the standard.
• Results Comparison: example value, MechCalc value and error for each checked quantity, with the reasons for method differences in notes after the table.

VDI 2230-1 Single-bolt Joint Calculation