Module 15
Linear time-history analysis
The full answer, instant by instant — and the four choices an analyst makes that decide whether it is worth having.
What this module covers
- Compare direct integration with modal superposition on the same model
- Choose a time step from the modes that matter, and demonstrate convergence
- Extract drift, floor acceleration, base shear and member actions correctly
- Explain why several records are required rather than one
- Recognise the numerical artefacts a time-history analysis can produce
- Say when a time-history analysis is worth its cost over a spectrum analysis
Lessons
Two methods that must agree, four decisions that make them differ, and the outputs that converge at quite different rates.
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Module checkpoint
Check what you have taken in
5 questions
Question 1
A structure has T₁ = 2.0 s and its highest retained mode has T₁₀ = 0.11 s. Using Δt ≤ T/20 on the governing mode, what step should be used, in seconds?
Question 2
A building of 11 000 tonnes has a peak base shear of 19.4 MN. What is V/W?
Question 3
Two analyses of the same linear building give peak drifts differing by 0.4% and peak floor accelerations differing by 38%. What should be concluded?
Question 4
A 25 s record sampled at 0.01 s must be analysed at Δt = 0.002 s. By what integer factor must it be sub-sampled?
Question 5
Why do design standards require several ground-motion records rather than one?