Cumulative tutorial 06
A two-storey frame from first principles
Two masses, two stiffnesses, two frequencies — and a check that they are right.
A 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.
What you are given
- Both floor masses 300 tonnes
- Both storey stiffnesses 250 MN/m
- Shear-building idealisation: rigid floors, all deformation in the columns
Tutorial 06
Work the problem
4 questions
Question 1
What is the first natural circular frequency, in rad/s?
Question 2
What is the first natural period, in seconds?
Question 3
What is the second natural circular frequency, in rad/s?
Question 4
What is the frequency separation ω₂/ω₁?
What this establishes
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.