Cumulative tutorial 08
Three storeys: modes and mass
Read a modal output and decide how many modes the analysis actually needs.
A 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.
What you are given
- Three floors, 400 tonnes each
- Three storeys, 800 MN/m each
- Total mass 1 200 tonnes
Tutorial 08
Work the problem
4 questions
Question 1
The eigensolver reports T₁ = 0.3157 s. What is the first natural frequency, in Hz?
Question 2
The first mode carries 91.41% of the mass. How much mass does it mobilise, in tonnes?
Question 3
The second mode carries 7.488%. What is the cumulative effective mass over the first two modes, as a percentage?
Question 4
Floor accelerations are also required, for equipment. How many modes should be retained?
What this establishes
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.