Identification of critical mode shape for analysis of a G+15 storied building
Abstract
While analysing a G+15 storied apartment building, each of its individual modes is compared with the actual vibration of the building, which results from combining all the modes.
The structure is modelled with a semi-rigid diaphragm. That choice suits this building because of its horizontal irregularities: re-entrant corners, slab openings and secondary beams.
Modelling and analysis are done in CSI ETABS, finite element software for the analysis and design of multistoried buildings.
Introduction
The mode shapes of a building are its natural patterns of vibration when an external force such as an earthquake or wind acts on it. These vibrations make the building sway or oscillate, and each mode shape is one way that movement can happen.
ETABS gives 12 mode shapes by default, but the number should be raised until mass participation passes 90%. For accuracy, this structure is analysed with 33 mode shapes.
Study of Analysis Result
- The time period falls from the first mode to the last. The largest displacement and drift therefore occur in mode 1 and shrink as the time period drops.
Under various building codes, about 65% of the mass should participate in modes 1, 2 and 3, for translation in X, translation in Y and rotation respectively.
The lower participation in mode 3 and the other modes may come from the horizontal irregularities of the structure, shown below.
The plan has 8 re-entrant corners, openings for the lift wall and staircase, and secondary beams resting on main beams. These create additional torsion, which the mass participation ratios confirm. Such torsion is hard to account for by hand, so this structure needs a dynamic analysis.
Comparing Mode Shapes for Translation in X
The structure is analysed dynamically with the response spectrum from NBC 105:2020. The two dominant modes for translation in X are mode 1 and mode 6, with 68.16% and 13.55% mass participation in X.
RSX (response spectrum in the X-direction) is the combined result of every mode's participation in X. Modes 1 and 6 are each compared with that combined result.
Result of the Comparison
Conclusion
Comparing the dominant individual modes for X translation with the combined response spectrum result leads to these conclusions:
- The critical mode shape is always the first mode in a given direction, as long as little torsion develops in the structure. Modes 1 and 2 are the critical modes for translation in X and Y.
- Analysing the structure for its individual critical modes gives results close to the full response.
- Storey shear and storey displacement vary non-linearly from one mode shape to the next.