Module 20 · Lesson 20.1
How to find an error
Not by reading the calculation again. This lesson is about the three things that find most of what is findable, and about why checking has levels rather than a single state called 'checked'.
Why this matters
Nineteen modules have produced answers, and each one quietly assumed that the answer was right.
In practice you cannot assume that, and the interesting question is not whether to check but how. Because the instinctive method — read the calculation through again — is close to the least effective one available. It finds transcription slips and misses everything that follows from a belief you hold, which is where the serious errors live.
This lesson is about methods that find errors the calculation itself cannot show you.
By the end of this lesson you should be able to
- Check by order of magnitude before checking by arithmetic
- Say what each level of independence can and cannot find
- Rank findings by consequence, not by the size of the error
- Ask the questions that find the most per minute
What you should already know
- What governs each member type (Module 19)
- Erection stages as structures (Module 18)
- Frame stability and αcr (Modules 4 and 16)
Check the exponent before the digits
Almost nothing that goes seriously wrong is wrong in the third significant figure.
The errors that hurt are factors: a moment computed in N·mm and reported as kNm, a load applied per metre where it should be per square metre, a missing conversion from kilograms to tonnes. Every one of those is out by a factor of a thousand or more — and every one of them is invisible if you re-read the arithmetic, because the arithmetic is correct. It is the quantity that is wrong.
So the first check is not a calculation at all. It is: is this the right size?
For that you need a handful of bands in your head — the ranges inside which an answer is unremarkable. A steel-framed office at 45 to 90 kg/m². A floor beam at span/15 to span/25. A braced frame with αcr between 10 and 40.
Those are deliberately wide. A value outside one is not wrong; it is a value that needs a reason. A value a hundred times outside one is almost never a design that is merely unusual.
Try it
Is it the right order of magnitude
The axis is logarithmic, because the errors that matter are factors rather than percentages. Move the exponent and watch how far a missing thousand puts you outside the band — and how invisible it would be on a calculator.
Quantity
- Value
- 62.00 kg/m²
- Usual range
- 45 to 90 kg/m²
- Inside the band
- yes
- Factor outside
- 1.0
- Why this band
- Rises with span and with the number of storeys the columns must carry.
62 kg/m² sits inside the usual range of 45 to 90. Unremarkable — which is all this check can tell you. Rises with span and with the number of storeys the columns must carry.
Things worth trying
- Start at the defaults — 62 kg/m² for a multi-storey office. It sits inside the band, and the verdict says the only thing this check can say: unremarkable.
- Now set the power of ten to 3. That is the same building with a missing kilogram-to-tonne conversion: 62 000 kg/m². The value is over a hundred times outside the band, and the verdict names the likely cause rather than just flagging it.
- Note the point of the logarithmic axis: a factor of 1000 is three divisions. On a linear scale it would be off the page, and on a calculator readout it is three keystrokes.
- Set the power of ten back to 0 and take the value to 108. Now it is 1.2 times outside — flagged, but the verdict says 'needs a reason' rather than 'units error'. Being unusual is not being wrong.
- Try 9 kg/m². Too LOW is caught the same way, and it should be: forgetting to include the columns or the connections lands here.
- Switch the quantity to the braced-frame alpha-cr. The band starts at 10, which is the sway criterion used all course. Put in 3.75 — Module 18's erection stage — and it fails, exactly as it should.
- Switch to 'Beam utilisation at final design' and try 0.4. It is flagged, and the reason matters: a beam at 40% is not wrong, but there should be a written reason, and 'a serviceability limit governs' is one.
- The habit worth taking from this: check the exponent before checking the digits. Almost nothing that goes seriously wrong is wrong in the third significant figure.
"It was checked" is not an answer
Checking is not a state a design is in. It has levels, and the levels are not interchangeable, because each one has a structural blind spot — a class of error it cannot find however careful the checker is or however long they spend.
Self-check. You re-read your own work. This finds transcription slips and obvious arithmetic. It cannot find any error that follows from a belief you hold, because on re-reading you will hold the belief again and make the same inference from it.
Arithmetic check. A colleague re-runs the same calculation in the same model. This finds arithmetic and units. It cannot find a wrong model, because the checker is working inside it.
Independent calculation. A colleague repeats the calculation by their own method. This finds errors of method, and some wrong assumptions — the ones the other method needs to make differently. It cannot find a shared misreading of the brief, because both engineers read the same brief.
Independent design. A separate party starts from the brief and forms their own design. This finds misread briefs and missing load cases, because nothing was shared. It still cannot find an error in the brief itself, or in the standard both parties relied on.
The useful question is never "was it checked?" It is "checked how independently?" — and the answer determines which classes of error are still live.
Worked example
Two findings, and which one to act on first
Given
- Finding A: the moment on a floor beam was under-estimated by 5%. The beam was at 98%
- Finding B: the axial load on a brace was under-estimated by 50%. The brace was at 20%
- Neither member's failure would spread beyond itself
Find
Which finding is more serious, and why
Try it
How independent, and how serious
Two questions a review has to answer. The first decides what can be found at all; the second decides where to spend attention once something has been.
Level of checking
Failure would spread beyond the member
- Level
- arithmetic check
- Adequate for
- Low-consequence work, and only where the method itself is well established and unchanged.
- Finds
- Arithmetic errors
- —
- Transcription between documents
- —
- Units within the calculation
- Structurally blind to
- A wrong model, because the checker is working inside it
- —
- A missing load case
- —
- An inappropriate method
- —
- An error in the assumption the spreadsheet was built on
- Utilisation before
- 98 %
- Utilisation after correction
- 103 %
- Crosses the resistance
- YES
- Severity
- significant
Correcting this takes the check from 98% to 103% — past its resistance. The size of the error is not what makes this serious; crossing unity is.
Things worth trying
- Start at the defaults — an arithmetic check, a 5% error on a member at 98%. Correcting it takes the check to 103%: it crosses the resistance, and it is significant.
- Now set the utilisation to 20 and the error to 50. A TEN TIMES larger error, and it is only a minor finding — the member had the margin to absorb it. Severity follows consequence, not the size of the number.
- That comparison is the whole point. A review that ranks findings by how wrong the number is will spend its attention in the wrong place.
- Go back to 98% with 5% and switch the failure mode to progressive. The numbers do not move and the severity goes from significant to critical, because the consequence did.
- Now read the checking levels. On 'arithmetic check', look at what it is blind to: a wrong model, because the checker is working inside it. That is not a matter of effort or care.
- Move up to 'independent calculation'. The blind spot shrinks, but a shared misreading of the brief survives — both engineers read the same brief the same way.
- Move to 'independent design'. Now a misread brief IS found, because the checker read it themselves. But even this level cannot find an error in the brief itself.
- Note that every level has a blind spot, including the highest. 'It was checked' is not an answer to 'how do you know it is right'. The useful question is: checked how independently?
Practice
A column check was at 96% of resistance. A review finds that the axial load was under-estimated by 7%. What is the utilisation once the error is corrected, as a percentage?
Check yourself
A design is checked by a colleague who re-runs the same spreadsheet and confirms every number. What class of error is still live?
Summary
- Check the exponent before the digits — serious errors are factors, not percentages
- 62 000 kg/m² is over a hundred times outside its band; 108 is 1.2 times and merely unusual
- Checking has levels, and each has a blind spot that effort cannot close
- A check inside the same model cannot question the model
- Even independent design cannot find an error in the brief itself
- A 5% error at 98% crosses the resistance; a 50% error at 20% does not
- Severity follows consequence, so a finding register sorted by error size is sorted wrongly
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint