Module 8 · Lesson 8.3
The validation calculation
One hand check per system — the only kind that actually gets done.
Why this matters
Everything in this stage has been about how a model can be wrong. This lesson is the practical answer: for each system, the one calculation that takes minutes, needs no software, and would catch the failure that system is prone to.
The constraint is real. A check that takes half a day does not get done under programme pressure, so it does not matter how good it is. A check that takes five minutes gets done, and therefore catches things.
By the end of this lesson you should be able to
- Name the usual model, the usual failure and the hand check for nine systems
- Use the free bending moment as a universal check
- Estimate a floor's frequency from its deflection
- Recognise a linear model reporting behaviour the material cannot deliver
The table
| System | Usual model | Watch for | Hand check |
|---|---|---|---|
| Truss | Pin-jointed bars | Chord continuity puts bending into members sized for axial force; panel loads are not a UDL | Chord force ≈ M/d, with M from the actual point loads |
| Steel frame | Line elements, rigid or pinned | Real connections are neither | Portal method or a sub-frame by moment distribution |
| Composite floor | Beams with a transformed section | The effective width assumed, and composite stiffness used at the construction stage | wL²/8 on the bare steel, then again on the composite section |
| Flat slab | Shell mesh on point supports | The peak over a support is a singularity | Total static moment across the panel = wL²/8 |
| Core and walls | One stick with gross I | Shear deformation omitted; openings not modelled | wH⁴/8EI plus wH²/2GA — compare the two terms |
| Foundations | Springs, or full fixity | Full fixity is almost never right; a default spring is a number nobody derived | Compare base moment for fixed and pinned |
| Timber | Frame elements with timber's modulus | Connection slip dominates deflection and no element has it | Sum the connection slips along the load path |
| Masonry | Shells, or struts and ties | Tension the material cannot carry | Check the resultant stays in the middle third |
| Floor vibration | The static model, reused | The static mesh and stiffness assumptions are both wrong for dynamics | f₁ ≈ 18/√δ, δ in mm |
Three checks worth learning by heart
wL²/8. The free bending moment. Whatever the end conditions, whatever the connection stiffness, the sagging moment at midspan plus the average of the end moments equals wL²/8. It applies to a simply supported beam, a fixed one, a portal, a continuous beam and a slab strip. If a model's moments do not add up to it, stop.
Total static moment. The slab version of the same idea, and the answer to the singularity problem. Integrate the model's moments across a panel and the total must be wL²/8 per unit width. It is independent of mesh, of element type and of how the peak behaves.
f₁ ≈ 18/√δ. The fundamental frequency of a floor in hertz, with δ the static deflection in millimetres under the vibrating mass. A 10 mm deflection gives 5.7 Hz. It takes seconds and it is close enough to tell you whether a floor is anywhere near a problem — which is what you need before deciding whether a dynamic model is worth building.
Two failures that no arithmetic catches
Some errors are not arithmetic errors and no check of the numbers will find them.
A linear model reporting tension in masonry. The analysis is correct; the material cannot deliver what the analysis assumes. The check is not numerical — it is looking at the sign of the stress and asking whether the material can do that.
A timber structure modelled without connection slip. No element in a standard library contains it, so the model's deflection can be right to four figures and half the real value. The check is to add the slips along the load path by hand and see whether they are comparable with the computed deflection. If they are, the model is missing most of the answer.
Both of these are Module 6's point arriving in practice: the model discarded a behaviour, and no amount of checking the retained behaviours will reveal it.
Try it
System validation workshop
Pick a system. Decide what its usual model gets wrong before revealing it, then read the hand check that would catch it.
System
For the frequency check in the last row of the guide.
- Usual model
- Pin-jointed bar model.
What does this model get wrong often enough to check every time?
The frequency check, live
- Static deflection
- 10 mm
- Estimated f₁ = 18/√δ
- 5.69 Hz
Above the range where walking excitation is worst, so a dynamic model is a choice rather than a default. That judgement took seconds.
What this shows: A check that takes half a day does not get done. Every one of these takes minutes.
Practice
A floor deflects 8 mm under the vibrating mass. Estimate its fundamental frequency.
Practice
A 9 m slab strip carries 12 kN/m². What total static moment must the model's moments integrate to, per metre width?
Check yourself
A linear elastic model of a masonry wall reports tension across a bed joint. What is the correct conclusion?
Check yourself
Why does the course insist that a validation check takes minutes rather than hours?
Summary
- Nine systems, each with a usual model, a usual failure and a five-minute check
- A check that takes half a day does not get done, so it does not matter how good it is
- wL²/8 checks any beam, portal or slab strip regardless of end conditions
- Integrating to the total static moment survives a singularity
- f₁ ≈ 18/√δ decides whether a dynamic model is worth building
- A discarded behaviour cannot be found by checking the retained ones
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