Checking a dynamic analysis

Before reading any result

Three arithmetic checks that need no engineering judgement and take a few minutes between them. They catch the largest errors, which are the ones least likely to announce themselves.

1. Count the modes against the degrees of freedom.

   Why: A model with n degrees of freedom has exactly n modes. A rigid-diaphragm building with N levels has exactly 3N.

   Catches: Nodes left outside a diaphragm constraint, unconnected elements and unintended releases — all of which add degrees of freedom you did not know were there.

2. Compare the first period against a rule of thumb.

   Why: T ≈ 0.1N seconds for an N-storey building is crude and gets the order right.

   Catches: Accidental mechanisms, missing restraints and gross stiffness errors. A period three times the estimate needs explaining before anything else is read.

3. Check the total seismic mass against floor area × mass per square metre.

   Why: A concrete frame is roughly 1 000–1 400 kg/m² of floor area including a realistic imposed-load fraction.

   Catches: A mass source set to self-weight only — the single most common gross error in seismic modelling, and one that a 90% effective-mass check does NOT catch, because effective mass is a percentage of the mass in the model.

Modal results

The modal table carries more diagnostic information than any other output, and most of it is in columns people do not read.

1. Look at the first three modes and their effective masses in every direction at once.

   Why: A regular building gives two translational modes and then a torsional one.

   Catches: Torsional softness. If the torsional period exceeds either translational period, the lateral system is too close to the plan centre and the configuration needs reconsidering, not just analysing.

2. Confirm the effective masses sum to the total mass.

   Why: They must. Every kilogram belongs to some mode.

   Catches: Constraint errors and mass that has been assigned to restrained degrees of freedom.

3. Look for modes with very long periods and near-zero effective mass.

   Why: A mode with almost no mass moving very slowly is a mechanism, not a structural mode.

   Catches: Unconnected nodes, members released at both ends, and elements with no stiffness assigned. The mode SHAPE identifies which node it is.

4. Check that the mode shapes are plausible for the structure.

   Why: A shear building's nth mode has n − 1 sign changes. A cantilever's modes have a characteristic curvature.

   Catches: Local modes masquerading as global ones, and models whose stiffness distribution is not what was intended.

5. Confirm the rotational inertia of every diaphragm is non-zero.

   Why: A rigid floor has three degrees of freedom, and the third needs I₀ = m(a² + b²)/12 about the centre of mass.

   Catches: A missing torsional mode. Left at zero, the mode does not appear as wrong — it disappears, and nothing in the output says so.

Damping

Damping is the least reliable input in the model and the one most often left at a default.

1. Read the damping ratio the model actually DELIVERS in each mode, not the one you asked for.

   Why: Rayleigh damping is exact at two frequencies and wrong everywhere else.

   Catches: Modes receiving several times the intended damping, and long-period modes receiving absurd amounts because the mass-proportional term goes as 1/ω.

2. Check where the Rayleigh anchors were placed.

   Why: They should bracket the modes carrying meaningful mass.

   Catches: Anchors placed on the first and last mode, which over-damps everything in between; and anchors placed on a base-isolated structure's isolated mode, which is a special trap.

3. Ask whether the damping model can be classical at all.

   Why: Modal superposition requires ΦᵀCΦ to be diagonal.

   Catches: Base-isolated structures and structures with dampers in some bays only — both non-classical, and neither valid for modal superposition however plausible the output looks.

Response-spectrum analysis

Two failure modes dominate: units, and combination rules applied to the wrong situation.

1. Divide the base shear by the seismic weight before reading anything else.

   Why: For an ordinary building on an ordinary site that coefficient lands roughly between 0.05 and 0.4.

   Catches: A spectrum entered in m/s² where g was expected, or the reverse. The error factor is 9.81 and both numbers are dimensionally valid accelerations, so nothing warns you.

2. Check the very short period end of the entered spectrum equals the site PGA.

   Why: As T → 0 the structure is rigid and rides with the ground.

   Catches: Units errors, and spectra entered with the wrong anchor.

3. Use CQC rather than SRSS where any two modal periods are within about 10%.

   Why: SRSS assumes well-separated modes and UNDER-predicts when they are not.

   Catches: Torsionally coupled buildings and symmetric plans, where two lateral modes nearly coincide.

4. Confirm cumulative effective mass reaches the required fraction, usually 90%.

   Why: Missing modes mean missing base shear.

   Catches: Too few modes extracted — but note this check cannot see a wrong mass SOURCE, which is a different and more serious error.

Time-history analysis

The one class of analysis where the answer can be plausible, stable and wrong, and where a single extra run settles it.

1. Run it twice, at Δt and Δt/2, and compare the quantity you will actually use.

   Why: A step is adequate when halving it stops changing the answer. Nothing else establishes that.

   Catches: Everything below, and it is the only check that does.

2. Choose Δt against the HIGHEST period carrying meaningful mass, not the first.

   Why: Δt = T₁/50 sounds generous and may be T₈/4.

   Catches: Under-resolved higher modes. Displacement will look converged while acceleration is 40% out, because higher modes contribute little displacement and a great deal of acceleration.

3. Check convergence on acceleration separately from displacement.

   Why: Acceleration is the second derivative and converges last.

   Catches: A model adequate for drift and useless for floor-mounted equipment.

4. Verify the energy balance closes.

   Why: Input work must equal kinetic plus strain plus dissipated energy.

   Catches: Integration error, at a level nothing in the displacement plot would reveal. A well-converged linear run closes to better than a thousandth.

5. Confirm which output is relative and which is absolute.

   Why: Relative displacement deforms the structure; absolute acceleration is what the floor and its contents feel.

   Catches: The two being interchanged — a mistake which produces a number of the right order and the wrong meaning.

Nonlinear analysis

Everything above still applies, plus the checks that only exist once the model can yield.

1. Confirm every step converged.

   Why: An unconverged step is an equilibrium violation carried forward into every step after it.

   Catches: Silent non-convergence, which many packages report only in a log file nobody opens.

2. Look at the residual displacement and the ductility demand, not only the peak.

   Why: Peak displacement can be acceptable while the structure ends the event permanently displaced.

   Catches: Models with no post-yield stiffness, where drift accumulates in one direction.

3. Check that a nonlinear model with a very high yield strength reproduces the linear result exactly.

   Why: If nothing yields, the two analyses are the same problem.

   Catches: Errors in the iteration scheme itself, before any real nonlinear result is trusted.

4. Do not read a response spectrum, or superpose modes, on a model that yields.

   Why: Both rest on superposition, which yielding removes.

   Catches: A category error that produces a perfectly formatted and meaningless answer.

Audit exercises

Six analyses that ran to completion without a single warning. Each one has something wrong with it.

Rapid audit questions

44 short scenarios, one fault each — and a few with nothing wrong at all, because an engineer who finds a fault every time is pattern-matching rather than auditing. These build the reflex; the six exercises above build the method.