Structural dynamics / tutorial
From modes to base shear
Turn a modal output and a spectrum into a force, then check it is credible.
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 assessed against a synthetic firm-ground record. The modal analysis is done; the spectrum has been generated. Convert them into a base shear, then apply the check that catches most errors in this chain.
The record is generated for teaching and is not a real strong-motion record.
- Total seismic mass 1 200 tonnes
- Mode 1: T = 0.3157 s, effective mass 91.41%, spectral acceleration 5.104 m/s²
- Mode 2: T = 0.1127 s, effective mass 7.488%, spectral acceleration 4.778 m/s²
- Mode 3: T = 0.0780 s, effective mass 1.104%, spectral acceleration 4.465 m/s²
Practice
What base shear does mode 1 contribute, in MN?
Practice
What base shear does mode 2 contribute, in MN?
Practice
Combining all three modes by SRSS, what is the total base shear, in MN?
Practice
The seismic weight is 11.77 MN. What is the base shear coefficient V/W?
The coefficient is the single most informative check in the chain, because it tests the mass, the spectrum, the units and the combination all at once. Compute it before looking at a single member force.