Structural dynamics / tutorial
What a spectrum analysis does not tell you
The same building, the same record, two methods, and the gap between them.
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 has been analysed twice against the same record: once by response spectrum, once by time history. The two do not agree exactly, and the gap between them is not an error in either — it is a consequence of what the spectrum method throws away.
Quantify what the spectrum gives, what it discards, and how large the discarding is on this building. Then decide whether the extra cost of the time history bought anything worth having.
- Modal base shears: 5.598, 0.429 and 0.059 MN
- SRSS total 5.615 MN; absolute sum 6.087 MN
- Seismic weight 11.77 MN
Practice
What fraction of the SRSS base shear comes from mode 1 alone?
Practice
By what factor would adding the modal peaks in absolute terms over-estimate the answer?
Practice
What is the base shear coefficient from the spectrum analysis?
Practice
A time history of the same record gives a peak base shear of 5.34 MN. By what percentage does the spectrum analysis exceed it?
What the spectrum discards is time. It cannot tell you when the peak occurred, in what order members reached their worst, how many large cycles there were, or what the structure was doing at the instant a particular column peaked. If none of those matter, the spectrum is the cheaper and better-founded choice.