Module 6 · Lesson 6.2
Choosing the level
Matching the question to the cheapest model that can answer it — and pricing the alternatives first.
Why this matters
The instinct that a more detailed model is a better model is wrong, and expensively so. A more detailed model answers a different set of questions, takes longer to build, takes longer to check, and gives more places for an error to hide.
The skill is choosing the cheapest level that answers the question honestly — and knowing what each level would have cost before building any of them.
By the end of this lesson you should be able to
- Match a question to the cheapest level that answers it
- Recognise that a model outside its range still returns a number
- Estimate model size at each level before committing
- Explain why a solid model is not an assumption-free model
Questions, and what can answer them
| Question | Cheapest honest level |
|---|---|
| What force does each member carry? | Hand calculation |
| How much does the structure move overall? | Hand calculation |
| At what load does it buckle? | 2D line model |
| What is the fundamental frequency? | 3D line model |
| How does the slab span in two directions? | Shell |
| What pressure reaches the ground? | Shell |
| What is the stress at a notch or a cope? | Solid |
| Does this connection work? | Solid |
Two things are worth drawing out of that table.
First, most structural questions are answered several rungs below where people reach for. Member forces and overall movement — the two things most analyses are actually for — need nothing more than a hand calculation to check, and a line model to produce.
Second, the table is about what can be answered honestly. A 2D line model asked for the stress at a cope will return a number: force divided by area, uniform over the section, entirely wrong for the question and reported with the same confidence as everything else. Nothing about the output distinguishes a question inside the model's range from one outside it.
Pricing the levels
For a six-storey building on a 4 × 3 bay grid, 32 m by 24 m, with a 0.5 m shell mesh:
| Level | Nodes | Degrees of freedom |
|---|---|---|
| Hand calculation | 0 | 0 |
| One 2D frame | 35 | 105 |
| Full 3D frame | 140 | 840 |
| Frame plus shell floors | 18 572 | 111 432 |
The step from a 3D frame to a shelled model is a factor of 133. That is not a reason to avoid it — it is a reason to know, before starting, that you are asking for a model two orders of magnitude larger, and to be able to say what question justifies it.
The arithmetic behind those counts is stated rather than hidden: one node per column line per level for the frame, and plan area divided by the square of the mesh size for the floors. A reader who disagrees with the meshing rule can disagree with the rule, rather than with a number that appeared from nowhere.
Solid models are not assumption-free
It is tempting to treat a solid model as the ground truth against which the others are approximations. It is not.
A solid model has assumed a constitutive law, a mesh fine enough to resolve whatever is being asked about, boundary conditions that are usually a bigger idealisation than anything in the interior, and a load application that is itself an abstraction of something real. What it removed was the beam assumption. Everything else is still there, and some of it is now harder to see.
Refining the model moves the assumptions; it does not remove them.
The 'what would change my mind' test
Before building at a level, ask what result would make you conclude the level was wrong. If nothing would — if any answer the model gives will be accepted — then the model is not being used to find anything out, and a cheaper one would do exactly as well.
Try it
Element and level selector
Choose a question. See which levels answer it honestly, what each discards, and what each would cost to build.
The question the model must answer
Cheapest level that answers this honestly: Hand calculation
| Level | Answers it? | Freedoms |
|---|---|---|
| Hand calculation | yes | 0 |
| Two-dimensional line model | yes | 105 |
| Three-dimensional line model | yes | 840 |
| Shell model | no — it would still return a number | 111,432 |
| Solid model | no — it would still return a number | 110,592 |
What hand calculation discards, permanently
- Continuity
- Load sharing
- Everything three-dimensional
How the freedom counts are arrived at
- No model. One span, one formula.
- One frame taken out of the building: 5 columns × 7 levels, three freedoms each.
- Every column line at every level: 5 × 4 × 7 nodes, six freedoms each.
- The frame plus a 0.5 m mesh over 6 floors of 768 m²: 3072 nodes per floor.
- The same mesh carried through 0.25 m of thickness in 2 layers, floors only.
What this shows: A model outside its range returns a number rather than a refusal — so the check has to happen before the question is asked.
Practice
A 3D frame model of the building above has 840 degrees of freedom and the shelled model has 111 432. By what factor does the model grow?
Practice
The shell mesh above is 0.5 m. If it is halved to 0.25 m, by what factor does the number of shell nodes increase?
Summary
- Most structural questions are answered several rungs below where people reach
- A model outside its range returns a number, not a refusal
- A shelled model of this building is 133 times the size of the frame model
- Mesh nodes go as the inverse square of the size in 2D, the inverse cube in 3D
- A solid model moved the assumptions; it did not remove them
- If no result would change your mind, a cheaper model would do as well
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