Cumulative tutorial 13
Setting up a time-history run
Pick the step from the right mode, count the cost, and demonstrate convergence.
The 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.
What you are given
- 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
Tutorial 13
Work the problem
4 questions
Question 1
Using Δt ≤ T/20 on the mode that governs, what time step should be used, in seconds?
Question 2
How many steps does the 30-second record then take?
Question 3
What is the ratio T₁/Δt — that is, how many time steps fall within one cycle of the first mode?
Question 4
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.
What this establishes
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.