Horizontal natural frequency in a 10 story building : A comparison between CLT and concrete using estimate calculations

Sammanfattning: Tall slender buildings are easily set in motion by wind and earthquakes but by estimating the buildings horizontal natural frequencies in the design phase, these motions can be kept within acceptable boundaries. There are many parameters that decides the natural frequency of a building and it can therefore be difficult to calculate it. There are a few ways though to estimate horizontal natural frequencies of tall buildings and two methods have been tested in this report. Both methods give the frequency of a clamped-free cantilever but one of them requires a single degree of freedom system whilst the other handles a multi degree of freedom system. The methods are called SDOF method and MDOF method in this report. A fictional building was created for this project to be the reference object in the comparison between the two methods SDOF and MDOF. The walls and floors of the building was designed with the support of both an acoustic engineer and a structural engineer to create a realistic building. A building’s natural frequency is dependent of the self-weight, stiffness and height of the building and it was therefore important to design these components with care. The fictional building is called House 1 and is a 10 story, almost square building about 20 m wide and broad and 30 m high. This report does not only compare the natural frequencies obtained from the two different calculation methods, but it also shows the difference in frequency in timber and concrete structures. Shear walls constitutes the horizontal stabilization system of the fictional building and both a CLT core and a concrete core is designed and compared. It is only the walls that comes in two different versions, the floorings consist of CLT boards for both structures tested. The horizontal natural frequencies of House 1 were about 2 Hz and 3 Hz for the CLT version and concrete version respectively. It was expected to get frequencies within that range considering the height of House 1. The CLT core having a lower frequency than the concrete core was also expected since concrete is a stiffer material than wood. To be able to make a fair comparison between the SDOF method and the MDOF method, House 1 was designed with the same dimensions and stiffness on all floors because the SDOF method requires that. The results from the two methods are almost identical with only 0.3 Hz and 0.4 Hz difference for the concrete and CLT respectively. For a shear wall structure with a consistent stiffness, weight and dimension, any of the two methods can be used to estimate the horizontal natural frequency. However, it is not realistic for a building of 30 m or higher, to have the same dimensions on the load bearing structure on all floors which makes the MDOF method more accurate in more cases than the SDOF method.