Structural dynamics / tutorial
Three storeys: modes and mass
Read a modal output and decide how many modes the analysis actually needs.
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 notesA uniform three-storey shear building is analysed. The eigensolver returns three modes. Before any loading is applied, establish what the modal output says about the building — and how many modes will be needed.
- Three floors, 400 tonnes each
- Three storeys, 800 MN/m each
- Total mass 1 200 tonnes
Practice
The eigensolver reports T₁ = 0.3157 s. What is the first natural frequency, in Hz?
Practice
The first mode carries 91.41% of the mass. How much mass does it mobilise, in tonnes?
Practice
The second mode carries 7.488%. What is the cumulative effective mass over the first two modes, as a percentage?
Practice
Floor accelerations are also required, for equipment. How many modes should be retained?
Two modes and three modes give the same base shear to within a per cent and can give floor accelerations differing by tens of per cent. The mass criterion answers one question. Always ask what quantity the analysis exists to produce before deciding it has enough modes.