Computational Engineering / Diagnosing computational models
Units, signs and magnitude
The most common serious error in structural modelling is a factor of a thousand — and the technique for finding which input it is in.
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Read the lesson register and outstanding review notesWhy this matters
Ask an experienced analyst what they see most often and the answer is not a subtle modelling misjudgement. It is a unit slip, a wrong sign, or an order-of-magnitude mistake in a dimension, a material property or a load.
What makes them dangerous is not that they are hard to make. It is that the model runs cleanly, produces well-formatted results, and gives no signal at all — and that the auto-fitting view means a model a thousand times too big looks exactly like one that is right.
By the end of this lesson you should be able to
- Localise a numerical error by comparing which outputs moved and which did not
- Explain why determinate moments are independent of stiffness and why that matters
- Compute the factor a given unit slip produces in each output
- Check the sign of a result against what the structure physically does
Compare quantities with different dependencies
For a first-order, statically determinate model under specified loads, reactions and member forces follow from equilibrium. Deflections also depend on stiffness. Agreement in moment with disagreement in deflection therefore suggests checking E, I, shear flexibility and boundary assumptions. It does not rule out compensating geometry or loading errors.
Unit factors depend on the quantities: mm to m gives 10³; mm² to m² gives 10⁶; mm³ to m³ gives 10⁹; and mm⁴ to m⁴ gives 10¹². Numerical values of density in kg/m³ and unit weight in kN/m³ differ by 1000/g, approximately 102. They are different physical quantities, not interchangeable units.
Mass and self-weight
If dynamic mass is entered independently of static loads, a mass error may leave static output unchanged. If density generates self-weight, it affects that loading too. Inspect the mass source, total mass and generated weight directly. With stiffness fixed and mass scaled uniformly, frequency changes inversely with the square root of the mass factor.
Signs
Check the software’s load, axis and member-force conventions. Display load arrows, inspect local axes and use a simple known case where needed. A reversed pressure can produce a plausible magnitude with the wrong tension/compression sense, so magnitude alone is insufficient.
Try it
Unit error laboratory
A consistent steel cantilever, then one named unit slip applied to it. Read what every output does.
Slip
A length typed in millimetres into a field expecting metres is a thousand times too big.
- Quantity affected
- length
- Factor applied
- 1000.0000
| Output | Correct | With the slip | Ratio |
|---|---|---|---|
| Flexural rigidity EI | 94500.0000 | 94500.0000 | unchanged |
| Tip deflectionloudest | 0.0190 | 1.90e+7 | × 1.00e+9 |
| Root moment | 150.0000 | 150000.0000 | × 1000.0000 |
| Self-weight per metre | 0.8779 | 0.8779 | unchanged |
| Base reaction | 30.2674 | 5292.3814 | × 174.8543 |
| Tip stiffness | 1312.5000 | 1.31e-6 | × 1.00e-9 |
| Modal mass | 0.1266 | 126.5644 | × 1000.0000 |
| First frequency | 16.2074 | 1.62e-5 | × 1.00e-6 |
The moment has moved, which means the error is in the geometry or the load rather than in the stiffness. In a determinate structure the moment comes from equilibrium alone.
The technique
- Compare a quantity that depends on stiffness with one that does not. In a determinate structure the moment does not.
- Moment right, deflection wrong: stiffness. Both wrong: geometry or load. Both right, frequency wrong: mass.
- The powers of length are what set the factors — 10³ for a dimension, 10⁶ for an area, 10¹² for a second moment of area.
What this shows: A slip is detectable if you look at the right number and invisible if you look at the wrong one — and a mass error is invisible to every static check there is.
Worked example
Localising an error in one comparison
Given
- A simply supported beam, 8 m span, 30 kN/m uniformly distributed
- The model reports a maximum moment of 240 kN·m
- It reports a maximum deflection of 47 mm
- The section is a 533 × 210 × 92 UB with I = 55 200 cm⁴, in S355 steel
Find
Whether there is an error, and if so where
Practice
A model's self-weight comes out 102 times too large. The density field was filled with a value taken from a materials table. What is the ratio between concrete's density in kg/m³ and its unit weight in kN/m³, to one decimal place?
Practice
A modal mass is entered a thousand times too large. Frequency goes as 1/√m. By what factor is the reported frequency wrong? Give the factor by which it is too low.
Check yourself
Why can a dynamic-mass entry error leave static results unchanged when self-weight and other static loads are defined independently?
Check yourself
A first-order determinate beam has correct member forces but a deflection 10⁸ times too small. Which unit error is worth checking first?
Summary
- Correct determinate forces with incorrect deflection suggest checking stiffness, without excluding compensating errors
- Unit conversion factors follow the powers of the base dimensions
- A separately entered dynamic mass can be wrong even when static checks pass
- Look at the load arrows; sign conventions differ and both are defensible
- A wrong-sign result with the right magnitude is the most dangerous kind