Structural dynamics / tutorial
Setting up a time-history run
Pick the step from the right mode, count the cost, and demonstrate convergence.
Teaching basis and review status
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 notesThe three-storey building is to be run as a linear time history against a 30-second record. Two settings have to be chosen — the time step and the number of modes — and both are routinely chosen badly, in the same way: from the first mode.
Decide the settings, establish what they cost in run time, and then decide what evidence would actually show they are adequate. The last part is the one that separates a demonstrated result from an asserted one.
- T₁ = 0.3157 s, T₂ = 0.1127 s, T₃ = 0.0780 s
- All three modes retained
- Record duration 30 s, sampled at 0.01 s
Practice
Using Δt ≤ T/20 on the mode that governs, what time step should be used, in seconds?
Practice
How many steps does the 30-second record then take?
Practice
What is the ratio T₁/Δt — that is, how many time steps fall within one cycle of the first mode?
Practice
Halving the step gives a peak drift 0.3% different and a peak floor acceleration 4.1% different. Which figure decides whether the analysis has converged, if the output required is floor acceleration? Answer 4.1 for acceleration or 0.3 for drift.
Two settings, two demonstrations. The time step is justified by halving it and reporting the change in the governing quantity; the mode count is justified by adding modes and doing the same. Neither is established by asserting that the analysis converged.