Modeling floor diaphragms

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Modelling floor diaphragms

The slab with a hole is modelled either accurately as a diaphragm using finite elements, either approximately using the appropriate assumptions, e.g. ignoring the diaphragmatic behaviour.

The analysis methods, presented in previous paragraphs, form the principle rules in static and dynamic analysis of earthquake resistant structures. They are based on general assumptions allowing separate analysis of slabs and frames. Slabs can be analysed separately, provided that particular geometrical rules and secondary reinforcement placement rules are followed, thus balancing the inevitable effect of frames on slabs. Frames (beams-columns) can be modelled with members, taking into consideration the slabs effect, firstly by using the effective flange width and secondly by assuming diaphragmatic restraints on all slab nodes. Referring to columns and especially to walls, the actual geometry of column and beam members is considered by using rigid bodies. The design of most significant construction works has been performed using the above modelling scheme, whereas it stands as the principle rule for structural design according to EC2, EC8 and any other international regulations.

Two-dimensional finite elements

The diaphragmatic behaviour is ensured and not affected by this hole despite its size

Nowadays, two-dimensional finite elements are widely used since, in general, they provide more accurate results. Due to certain limitations imposed by the modal response spectrum analysis, in countries with zero or low seismic actions, two-dimensional finite elements have been established even for common buildings, whereas in highly seismic regions, members are mainly used. In modal response spectrum analysis, members provide sufficient accuracy for the calculation of design seismic accelerations. The combination of the two methods, called the dual model, is considered to be successful and is based on forming two consecutive models of the same structure: (a) The first one takes into account members for beams, columns and walls using rigid bodies technique, while the seismic behaviour of slabs is accounted through diaphragmatic restraining. The seismic design accelerations derive from the modal response spectrum analysis of the structure (as indicated in §3.3.2). (b) The second one models beams and columns with members, while slabs and walls are modelled with two-dimensional finite elements. The design seismic accelerations are applied on each mass m, resulting to seismic forces F=m×a used for the calculation of the structure's stress resultants. The dual seismic model is used in special cases, mainly in structures of slabs and walls containing large holes behaving as sensitive ‘necks’ for carrying horizontal seismic forces, as shown in the following figures.
In reinforced concrete buildings, the human factor (despite good intentions and despite the level of knowledge, conception and attention) affects chaotically the structural quality in different aspects. This phenomenon is particularly intense when seismic requirements arise, materials are non-homogeneous and construction is non-industrialized.
This book contributes to the smooth transition from the traditional calculation methods to the more accurate future methods while dealing with both of them.