## Vibration Performance of Composite Flooring

Mark Davies, Technical Manager, ComFlor® (BEng Hons MRes), discusses vibration performance of composite flooring.

The trend towards longer span, lightweight composite floor systems, with their tendency to lower natural frequencies and reduce natural damping, has created a greater awareness of the dynamic performance of floors when subjected to pedestrian traffic. The most usual and important internal source of dynamic excitation is pedestrian traffic. A person walking at a regular pace applies a periodically repeated force to the floor, which may cause a build up of response.

In general, where such activities are envisaged, the structure should not only be sufficiently strong but also comply with comfort and serviceability criteria. Dynamic excitation can range from a given walking pace along a floor, a quicker pace down a staircase, to synchronised crowd activities in places such as sporting stadiums, dance floors etc. Human perception, discomfort and acceptability to vibration response vary between humans. No exact limit can be imposed that will guarantee that the floor response will not give rise to adverse comments from occupants throughout its lifetime of use. Instead of absolute solutions, current standards seek to guide designers toward solutions, which will attract a ‘low probability’ of adverse comment. Current standards describe human discomfort in terms of the perceived ‘acceleration’ of the floor as opposed to the ‘amplitude’ of vibration. Suitability in relation to vibration serviceability is assessed, by comparing predicted acceleration with a set of defined acceptance criteria. Personal discomfort is realised to a different degree for a person sitting at an office desk, for someone operating a machine or for a spectator watching sport, and this is recognised in the Standards by applying multiplying factors to the acceptance criteria for different situations.

‘Design Guidance on the Vibration of Floors’ publication P076 was first published by the Steel Construction Institute (SCI) in 1989, and related only to normal office building environments. Since then, measurements taken on hospitals, office and residential floors indicated that the first edition was too conservative in certain circumstances. Also, the floor types considered in the development of the original guide were not representative of that encountered in modern construction, for example, the Tata Slimdek system, and that information on some special floors such as dance floors were out-of-step with current recommendations. As P076 was conservative in its advice, a common misconception had arisen that, composite floors within hospital buildings could not be designed to meet the more strict limits specified within the NHS performance standard for hospitals, Health Technical Memorandum HTM 2045. As a result, SCI P331 published in 2004, entitled ‘Design Guide on the Vibration of Floors in Hospitals’, enabled designers to calculate the vibration response of such sensitive floors more accurately, and to enable the response to be compared with the HTM 2045 limits. The guidance was valid for composite floors using hot rolled steel sections, including the Slimdek® System from Tata Steel

The latest guidance document SCI P354 published 2007, entitled ‘Design of Floors for Vibration: A New Approach’, has been written to enable designers to determine the vibration response of sensitive floors with improved accuracy. It will enable the response to be compared with BS 6472 and ISO 10137 for general structures, and with the previously mentioned specific NHS performance standard for hospitals, Health Technical Memorandum 2045.

This article highlights the latest vibration design guidance given in SCI P354, entitled ‘Design of Floors for Vibration: A new approach’, and also summarises to the designer the current code requirement clauses in relation to vibration.

**General Assessment for establishing Vibration Response**

The use of Finite Element (FE) modelling along with suitable design methods may be used to assess the floor response. It is particularly useful for structures, which are complex or have very stringent requirements with regard to vibration. Also it will give a better prediction than that given by hand calculation methods. However for regular rectilinear grids, a simplified assessment for steel floors can suffice.

**Simplified Assessment for Steel Floors**

The simplified design procedure for assessing the dynamic performance of floors comprise of:

§ Definition of natural frequency

§ Definition of modal mass for the floor

§ Evaluation of the response

§ Checking of the response against acceptance criteria

Section 7 of P354 provides a detail of this process, which can be summarised as follows:

Vibration in composite floors is generally concerned with the movement of mass, and is classed into 2 categories, continuous and discrete systems. The floor can be modelled as a simple ‘spring-mass-damper’ system. The static deflection under loading, calculated from the beam and slab inertias are used to determine the lowest natural frequency of the floor, known as the fundamental frequency, which will correspond to the simplest mode shape. Increasing the excitation frequency can change the object mode shape. To ensure that the walking frequency activities will be outside the range which could cause resonant or close-to resonant excitation of the fundamental mode of vibration of the floor, no floor structure should have a fundamental frequency less than 3 Hz. Similarly, no single element within the floor structure should have a fundamental frequency less than 3 Hz.

When the initial fundamental frequency of the floor system is calculated from the determined boundary conditions (for a conventional floor slab, there are 2 modes, Mode A and Mode B, which depend on whether or not the primary beam form nodal lines), the lower of the 2 frequencies is used in the modal mass calculation.

The mass of the floor plays an important criteria known as ‘modal mass’ which is a measure of how much mass is involved in the mode shape, and hence how much kinetic energy there is in the system. The modal mass is a function of the floor mass (plus dead and a percentage of imposed load), effective floor length and effective floor width. The model mass equation differs slightly between shallow and deep deck systems.

The effective floor length is a function of number of bays in the direction of the secondary beam spacing, dynamic flexural rigidity EI of the secondary beam, floor beam spacing, the fundamental frequency of the floor, and floor mass (plus dead and a percentage of imposed load).

The effective floor width is a function of number of bays in the direction of the primary beam spacing, dynamic flexural rigidity EI of the floor, floor beam spacing, the fundamental frequency of the floor, floor mass (plus dead and a percentage of imposed load), and influence of the floor frequency on the slab response.

The modal mass can then be used to determine the required response acceleration a_{w,rms}.

The response within the floor is the measure of the accelerations generated by the excitation. If the fundamental frequency is between 3 and 10Hz, this is classified as a ‘low’ frequency floor, whereas a frequency above 10 Hz is classified as a ‘High’ frequency floor. This will govern which response factor equation is used, which is a function of modal mass, the mode shape factor, critical damping ratio, weight of a statistical average human being, the resonance build-up factor, and the appropriate code-defined weighting factor.

Once the response acceleration aw,rms has been determined, the response factor R, may be calculated where R = a_{w,rms} /0.005. The value of response factor should not exceed the value of the appropriate multiplying factor as specified in the relevant code of practice such as BS 6472, for multiplying factors specified for ‘low probability of adverse comment’.

If the response factor is greater than the appropriate multiplying factor, a procedure known as Vibration Dose Values (VDV) can be used. This calculates the number of walking crossings per hour for various response factors and corridor lengths for various x, y, or z axis vibrations in office, residential, general laboratory or hospital ward environments for a given working hours/day and hours/night period. If the VDV is high, for example, a calculated 3696 crossings across the floor in a 16 hr day (i.e. 231 times per hour) for a ‘low probability of adverse comment’, then this level of activity is unlikely to occur in a quite office for example, therefore the floor can be classed as acceptable.

A working example of this procedure is given in Appendix D.1 of P354, which is summarised as follows:

1. Determine the floor plan layout and loading criteria – D.1

2. Determine the composite floor slab second moment of inertia – D.1.1

3. Determine the primary and secondary beam second moment of inertias – D.1.2

4. Determine the mode shapes and beam boundary conditions – D.1.3

5. Determine the fundamental natural frequency of Modes A and B. Lowest frequency governs – D.1.4

6. Determine the modal mass for either the shallow or deep deck system – D.1.5

7. Determine the floor response based on either a ‘Low’ or ‘High’ frequency floor – D.1.6

8. Does the response factor exceed the appropriate multiplying factor? – D.1.6

9. If so then use the vibration dose value (VDV) method. Is this acceptable? – D.1.6

If the vibration dose value (VDV) is not acceptable, then can any improvement be obtained from altering walking paths or layout? If ‘yes’, then apply layout changes and repeat the above process. If not, then can a finite element model be created for a better prediction? If not, then adjust floor plan structure and repeat the above process.

An in-house spreadsheet has been developed within the Technical Department at Tata Panels and Profiles to determine the response factor of a composite floor, based on the example given in Appendix D.1. Therefore, if you wish to calculate the response factor for a composite floor system based on simplified regular rectilinear grids, then please contact us on the details given overleaf.

Also to assist the designer, the following information summarises at a glance the relevant current code requirement clauses in relation to vibration.

**Current Code Requirements Summary**

The relevant Eurocode requirements regarding vibration are given in:

1. EN 1990: 2002, Clause 3.4 –* ‘The verification of serviceability limit state should be based on criteria concerning vibrations that cause discomfort to people, or that limit the functional effectiveness of the structure’.*

2. EN 1990: 2002, A1.4.2 – *‘Stiffness criteria may be expressed in terms for vertical deflections and for vibrations’*

3. EN 1990: 2002, A1.4.4 –* ‘the natural frequency of vibrations of the structure or structural member should be kept above appropriate values’.*

4. EN 1993: 2005, 7.2.3 (1)B – *‘With reference to EN 1990 Annex A1.4.4, the vibrations of structures on which the public can walk should be limited to avoid significant discomfort to users, and limits should be specified for each project and agreed with the client’.*

**The relevant British Standard requirements regarding vibration are given in:**

1. BS6399-1 Clause 5 –* ‘static load design is not sufficient where dynamic loading occurs in buildings and structures that are susceptible to dynamic excitation. In such cases, the design should take into account of the load-structure interaction and natural frequency, mass, damping and mode shape of the structure. Furthermore, the structural design with oscillation or vibration as a serviceability criterion, separate considerations are necessary, e.g. the operation of equipment and comfort of users and occupiers of a building’.*

2. BS5950-1: 2000 Clause 2.5.3 –* ‘Vibrations and oscillation of building structures should be limited to avoid discomfort to users and damage to contents. Reference to specialist literature should me made as appropriate’.*

*3. BS8110-1 1997 Clause 2.2.3.5 ‘Discomfort or alarm to occupants, structural damage, and interface with proper function should be avoided. Acceptable vibration limits are described in specialist literature’.*

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