Computational Engineering / Modelling structural systems
Floors and cores
Four models of one floor panel against the exact answer — and when a core needs more than a stick.
Lesson review: expert verification remains open
This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.
Checks needed for project use
- A computational engineering reviewer must check algorithms, convergence claims, statistical assumptions and numerical examples beyond the cases explicitly recorded.
- A slab specialist must verify two-way reinforcement/design-region treatment and the plate explorer before design use.
- The coupled-core option is an illustrative stiffness interpolation, not a validated explicit openings/coupling-beam model.
- Check reference tables and numerical examples against actual local model geometry; no complete FE benchmark performed.
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesWhy this matters
Floor panels and cores can respond differently when two-way action, shear deformation or openings are represented. Compare models with stated assumptions and distinguish analytical reference solutions from numerical simulations. Agreement for an idealised case does not establish adequacy for the actual structure.
By the end of this lesson you should be able to
- Compare a one-way model against the exact plate solution
- Say how the error depends on the panel's aspect ratio
- Recognise a peak moment that is a singularity
- Decide when a core stick model needs shear deformation and openings
What you should already know
- Module 6's shear deformation — the core lesson is the same idea at building scale
- Module 12's mesh convergence, for the singularity
A simply supported panel
The example compares a 5 m × 5 m panel under 10 kN/m² using linear elastic plate assumptions and Poisson's ratio 0.2. The one-way strip moment is 31.25 kN·m/m; the converged Navier-series centre moment is approximately 11.05 kN·m/m. A simple orthogonal-strip approximation gives 15.63 kN·m/m.
For the corresponding 5 m × 15 m panel, the short-span centre moments are approximately 31.25, 30.87 and 29.58 kN·m/m. These comparisons concern the specified moment in idealised panels. They do not establish that a one-way reinforcement layout is adequate for every two-way slab.
The current explorer's row labelled as shell finite elements reproduces the analytical plate result; it is a reference target, not an independently executed shell analysis. A real shell model needs its own mesh-convergence and formulation checks.
Aspect ratio affects two-way action, but supports, continuity, loading, cracking and reinforcement also matter. Check both directions, twisting effects, shear and serviceability as applicable. A greater short-span moment alone is not a complete safety comparison.
Local support peaks
Idealised point supports in plate models can produce singular moment peaks. Refinement may increase the local peak without yielding a usable finite design value. Represent the support region appropriately and examine integrated section actions and equilibrium over suitable design regions.
The beam relation wL²/8 is not a universal integral of a two-way slab moment field. Account for signed end moments, reactions, transverse shear transfer and twisting according to the chosen free body and slab design method. Integrated results also need a convergence check.
Core models
The explorer compares bending-only and shear-flexible stick estimates. Its coupled-wall option interpolates an effective second moment using a coupling parameter; it does not explicitly analyse openings and coupling beams. The reported 1.07, 1.31 and 2.38 mm values illustrate these assumptions, not three independently verified representations of a real core.
For the illustrated cantilever and loading, adding shear deformation increases the estimate by about 22% relative to bending alone. Assess its importance for the question and geometry. Openings, cracking, coupling and interaction with other lateral systems need justified stiffness representations.
Under the same statically determinate first-order lateral loading, total base moment follows from equilibrium. The distribution between a core and frame, their deformation and dynamic properties depends on stiffness.
Try it
Slab model comparison
One panel, four models, compared against the exact series solution of the plate equation.
The short span is fixed at 5 m.
| Model | Moment | Error | Deflection |
|---|---|---|---|
| One-way strip | 31.25 | +182.8 % | 2.00 mm |
| Orthogonal grillage | 15.63 | +41.4 % | 1.00 mm |
| Plate theory (exact) | 11.05 | — | 0.62 mm |
| Shell reference target | 11.05 | — | 0.62 mm |
At 1.00:1 the panel spans substantially both ways, and a one-way model over-predicts the moment by 183 %. Conservative, and expensive on every panel of the floor.
What each model is blind to
- One-way strip: Two-way action, corner torsion, and the reaction that actually goes onto the long-side supports.
- Orthogonal grillage: Twisting moment, which is why it over-predicts the span moments.
- Plate theory (exact): Cracking, reinforcement, creep, and the supports actually being beams that deflect.
- Shell reference target: Nothing plate theory does not — but it will happily report a peak moment at a point support that is a singularity, not a result.
What this shows: The one-way moment never changes — what changes is the truth it is compared with.
Try it
Core model comparison
A stick, a stick with shear deformation, and coupled walls — the same core, three models.
1 is fully continuous walls; 0 is two independent walls.
| Model | Deflection | vs bending only |
|---|---|---|
| Stick model, bending only | 1.071 mm | × 1.000 |
| Stick model, with shear deformation | 1.311 mm | × 1.224 |
| Coupled walls | 2.383 mm | × 2.224 |
- Height / width
- 5.00
- Shear passes a fifth of the movement below
- H/D = 4.73
- Base moment
- 5400 kN·m
identical in all three — statics does not care how it is modelled
At this slenderness bending dominates and the stick model is a reasonable first estimate. The openings are still not in it.
What each model is
- Stick model, bending only: One vertical line element with the core's gross second moment of area. The cheapest possible model of a core.
- Stick model, with shear deformation: The same element, with the shear area included. For a squat core this is not a refinement.
- Coupled walls: Illustrative effective-stiffness interpolation using the coupling parameter; openings and coupling beams are not modelled explicitly.
What this shows: Shear deformation is not a refinement for a squat core, and openings more than double the movement.
Worked example
Is a one-way model good enough for this panel?
Given
- A 5 m × 10 m simply supported panel, 250 mm thick, 10 kN/m²
- The designer proposes to model it as a one-way strip spanning 5 m
Find
The error, and whether it is acceptable
Practice
A one-way strip model of a square panel gives 31.25 kN·m/m and the exact plate solution gives 11.05. By what percentage does the one-way model over-predict?
Practice
A core's top deflection is 1.07 mm from bending alone and 1.31 mm with shear included. What percentage of the total does the bending-only stick model omit?
Check yourself
A one-way model of a square panel over-predicts the moment by 183 %. Why is that still not simply 'safe'?
Check yourself
Why does over-estimating a core's stiffness put load in the wrong place?
Summary
- A one-way model of a square panel over-predicts by 183 %, of a 3:1 panel by 5.6 %
- The one-way moment never changes; the truth it is compared with does
- Aspect ratio informs the idealisation; support, load-transfer and design requirements still need consideration
- A peak over a point support is a singularity — integrate rather than refine
- Shear deformation adds 22 % to a squat core, and openings more than double it
- All core models give the same base moment; only the stiffness differs