4. Analysis

The analysis pipeline is: semantic model → generated mesh → assembled finite
element model → solve → results. Everything in this chapter happens on the
Go server; the browser sends the model and receives results.

4.1 The three analysis methods

The Run analysis modal offers one method at a time, each a superset of the
previous:

Each method can run several load cases/combinations in one pass; every solved
item becomes a result set, and envelopes are built automatically.

Orthogonal to the method, no-tension soil (a soil zone with Compression
only ticked) wraps any run in a contact loop: solve, lift off every
compression-only spring whose node rose, repeat until the contact state
settles (max 20 passes, usually 2–4). Combinations with no-tension soil solve
directly rather than by superposition. See
§7.1.

4.2 Mesh generation (MESH)

Before running, the model must be meshed. MESH opens Mesh Generation:

Generate Mesh writes the mesh type and each slab's mesh size, then meshes.
Clear Mesh discards it. The meshing rules and element formulations are in
§2.18.

Normally you do not need this dialog: Run Analysis regenerates the mesh
automatically, and the slab tool's own Mesh size field controls refinement.

4.3 Validate (CHK)

CHK runs ValidateAll = semantic validation + mesh build + mesh checks
(duplicate nodes/elements, degenerate elements, disconnected components,
stray restraints). See §2.17 for the
full message list. Validation is the cheapest way to catch model problems;
the run refuses models with errors.

4.4 The Run analysis modal

Toolbar: ▶ Run Analysis. The modal has a live This run summary and
status banner; Close dismisses it, Run Analysis starts the run
(button changes to Running… and disables). The modal cannot be closed
during a run, and there is no abort button - navigating away cancels the
request (the server logs it as client closed the request).

Step 1 - Method

Tabs: Elastic, Cracked, Long-term.

Elastic

No options. The default and fastest method. One linear solve per selected load
item; combination superposition is used where possible.

Cracked - fields

Fixed-ratio mode is a simple secant method: elements whose tensile demand
exceeds the concrete tensile strength progressively relax toward E/Ec = 0.4
(default), uncracked elements return to 1.0, with under-relaxation 0.6 and a
0.01 relative convergence tolerance. It answers "how much softer is this slab
once it cracks" without needing reinforcement data.

ρ-dependent mode computes a real cracked section per element:

n   = Es / Ec
Icr from the transformed cracked section (As, d, b = 1000 mm)
Mcr = fct × t²/6 × 1000              [kN·m/m]
Ief = Icr / [1 − (1 − Icr/Ig)(Mcr/Ms)²]     (AS 3600 Cl 8.5.3.2 / ACI Eq. 24.2.3.5b)
Ief ≤ 0.6·Ig when pt = As/d < 0.005          (AS 3600 cap)
ratio = Ief / Ig

When strip reinforcement is available the per-element steel is taken from the
strip; otherwise the entered Ast/Asc values apply. Concrete tensile strength:
0.6√f′c (AS 3600/CSA), 0.62√f′c (ACI), 0.30·f′c^(2/3) (EC2/default).

Cracked runs report iterations, converged flag, cracked element count and the
residual history (plotted in Charts → Convergence). If iteration stalls:
reduce the ratio, raise Max iterations, or use the fixed-ratio mode.

Long-term - fields

Read-outs show the computed φcc = …, kcs = …, and for ACI
ρ′ = … → λΔ = …. Σ Calculate φcc opens the Creep Factor Calculator
(f′c 32, τ 28 d, time 10 950 d default, t_h 200 mm, k4 0.65, k5 1.0) with a
Use this value button that writes φcc into the override.

AS 3600 model (Cl 3.1.8.3 / 8.5.3.2):

growth(t) = 1 + φcc(t) + kcs × k2(t)

k2  = t^0.8 / (t^0.8 + 0.15·t_h)          (≤ 1; t in days, t_h in mm)
k3  = 1.28 τ^(−0.118)
φcc.b from Table 3.1.8.2:
      f'c  20    25    32    40    50    65    80    100
      φcc.b 5.2   4.2   3.4   2.8   2.4   2.0   1.7   1.5
φcc = k2 · k3 · k4 · k5 · φcc.b
kcs = max(0.8, 2 − 1.2·Asc/Ast)  (≤ 2);   Ast = 0 → 0.8

The solver applies the growth to the sustained load effects only; transient
cases contribute their instantaneous deflection. The result set gains a
time-history curve you can scrub with the Time slider, and the Deflection
selector offers Short-term (instantaneous), Sustained (creep, no
shrinkage) and Long-term (creep + shrinkage).

ACI 318 model (Table 24.2.4.1.3):

λΔ = ξ(t) / (1 + 50 ρ′),     ρ′ = Asc / (1000·d)   [d in mm]
ξ(t):  < 3 mo   m/3
       3–6 mo   1 + 0.2(m−3)/3
       6–12 mo  1.2 + 0.2(m−6)/6
       1–5 yr   1.4 + 0.6(m−12)/48
       ≥ 5 yr   2.0
shrinkage is folded into λΔ

Stage ages are measured from the previous stage; the horizon defaults to
2 000 days if the entered duration is not positive, clamped 1–100 000, and the
deflection-time curve is sampled at 32 points with factor(0) = 1.

4.5 Staged construction

Tick Staged construction to reveal the Stages editor. Default stages
when first opened:

Each stage card has: name, age (days after the previous stage), checkboxes
for cases (SW marked amber) and combinations, and a remove ×. + Add stage
adds a stage at age 30 with all cases selected. Stages with no load items are
dropped before the run; a stage with no explicit ids acts as a catch-all.

Semantics:

• A staged run evaluates the structure stage by stage, accumulating deflection
  history over time with the creep model applied from each load's application
  age.
• Per-stage factors come from the selected combos; self weight is included when
  any contributing case carries the SW flag.
• The run produces one result set labelled Staged construction, and
  the time-dependent curve is labelled Load History; the time slider then
  walks the construction history.
• If the model needs cracking as well, the cracked iteration runs inside each
  stage; failure to converge there aborts with
  stage N: cracked iteration did not converge.

Staged construction is the right tool for staged pours, backpropping questions
and "when do I strike the props" studies - not for ordinary single-stage
floors.

4.6 Step 2 - Loads

Described in §3.7. Points to
remember:

• every case and combination is selected by default;
• the Sustained / Short-term selector per row feeds the long-term run;
• Envelope: max and Envelope: min appear once two or more items are
  solved;
• a run with many combinations means many solves and a longer wait.

4.7 Running and reading the summary

After Run Analysis the status banner shows progress
(Solving <label> (i/n)…), then Analysis complete. The summary rows:

Reliability behaviour on the server:

The client retries 429s up to 6 times (2–10 s waits) and concurrent-solve
collisions up to 10 times (5–15 s waits). You can close the modal only by
finishing the run.

4.8 Solver internals you may need

Element formulations

Solution

• Dense direct solver up to ~2,896 free DOF (64 MiB), accepted only if the
  true relative residual ≤ 1e-6; otherwise the model is reported singular with
  the actual residual.
• Larger models use Jacobi/Block-Schwarz or incomplete-Cholesky preconditioned
  CG, falling back to BiCGSTAB, with a dense retry up to ~8,191 DOF.
• Targets: relative residual 1e-10; practical acceptance 1e-8 relative /
  1e-6 absolute after 200 iterations; a verified true residual ≤ 1e-6 accepts
  the result. The iteration cap is 8n clamped to [200, 20 000].
• Cracked iterations use a loose intermediate tolerance (1e-4); the reported
  result always comes from a full-accuracy solve.

Restraints and stability

• In 3D, suspended models without enough column restraint fix the in-plane
  translations (and drilling rotations where plates exist). Slab-on-ground and
  pile models instead get only the minimum planar pins, so the slab can deform
  in-plane and edge walls lean outward with the slab; pile groups with lateral
  stiffness restrain in-plane motion themselves, and only a single
  laterally-stiff pile gets the pins (one point cannot restrain in-plane
  rotation).
• Support types: fixed (all 6 DOF), pinned, rollers and per-axis pins; each DOF
  can carry a prescribed displacement.
• Springs contribute directly to the diagonal: Kx, Ky, Kz, Krx, Kry, Krz.
  A pile head's rotational spring falls back to the plain Kr value.

Equilibrium report

For every solve the server computes the applied and reaction resultants about
the origin, the imbalance and the maximum free-DOF residual. The ground-total
shown in the reactions table combines restrained-node reactions with mesh
spring forces (Σ(−kz·uz)). This is the number to compare against hand
calculations: applied ΣFz should equal ground reaction with opposite sign.

4.9 Analysis quality checklist

Before trusting a run:

1. Validation clean - CHK reports no errors (warnings checked).
2. Equilibrium closes - applied ΣFz ≈ ΣRz (within ~0.1 % for normal
   models).
3. Envelope sanity - ULS moments ≥ SLS moments; min-deflection envelope
   is not absurdly larger than a single case.
4. Mesh sensitivity - halve the mesh size once; peak moments should change
   by a few per cent, punching shear by a little more. If not, refine further.
5. Cracking - cracked deflection should exceed elastic; the cracked
   element count should be plausible (tension zones, not the whole slab).
6. Long-term factor - the growth factor is realistic for the age and
   environment (e.g. AS 3600 interior 10-year φcc ≈ 2–3, kcs ≈ 0.8–1.2).

4.10 Troubleshooting

→ Next: Chapter 5 - Results