Structural dynamics / tutorial
A two-storey frame from first principles
Two masses, two stiffnesses, two frequencies — and a check that they are right.
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 two-storey shear frame is to be analysed by hand before anyone opens a package. The floors are equal and the storeys are equally stiff, which makes the closed form available and gives a check on whatever the software later reports.
- Both floor masses 300 tonnes
- Both storey stiffnesses 250 MN/m
- Shear-building idealisation: rigid floors, all deformation in the columns
Practice
What is the first natural circular frequency, in rad/s?
Practice
What is the first natural period, in seconds?
Practice
What is the second natural circular frequency, in rad/s?
Practice
What is the frequency separation ω₂/ω₁?
This closed form exists only for the uniform two-storey case, and that is exactly what makes it valuable: it is a check on the eigensolver. Any package should reproduce 17.84 and 46.71 rad/s to several figures, and if it does not, the model is wrong before anything interesting has been asked of it.