12 - Floor Vibration

› Note 11  Level 1

32

Introduction

This Technical Guidance Note is an introduction to the assessment of floor vibrations. Since the advent of lighter structures that have longer spanning elements within them, the built in dampening effect buildings have had historically has become less pronounced. Despite this, floor vibration can be an overlooked criterion during the design process. This can lead to expensive remedial works being carried out on structures after they have been built, as occupants complain of discomfort due to excessive movements and vibrations. It should also be noted that floor vibrations can in some cases have a detrimental effect on the integrity of the structure. This usually occurs when there is a continuous long term vibration inducing load, such as a piece of machinery that is causing a dynamic response within the structure. This can then lead to a fatigue based failure of the supporting structure. This scenario however is rare as vibrations from such machinery would have to match the harmonic of the supporting structure, which is unlikely. Also, it is usually the building’s occupants that generate vibrations and as their sense of comfort deteriorates, the cyclical movements within the structure drop to the point where fatigue induced failure cannot occur. The assessment of floor vibration concerns how the mass of its supporting structure moves when subjected to an imposed load. This is determined by ascertaining the natural frequency of the supporting structure to the floor, which is stated in Hz (cycles per second). Once that is calculated it is then possible to assess how the structure will move when subjected to various types of imposed loading.

TSE7_32-34.indd 32

Technical Technical Guidance Note

TheStructuralEngineer July 2012

Floor vibration Icon Legend

• Design principles

• Applied practice

• Worked example

• Further reading

• Web resources

Design principles In the first instance there are no fixed criteria stated in EN 1990:2002 (Eurocode 0) with regard to floor vibration. Instead it recommends each project is reviewed on a case by case basis and that any criteria are agreed with the client. This open approach stems from the varied methods that can be adopted to assess vibration. Each has their own strengths and weaknesses and it is for this reason that floor vibration criteria is established early in the life of a project. These criteria will often have a significant impact in the design of the structure and as such, thier imporance cannot be over emphasised. The UK National Annex to Eurocode does offer some limits which designers can discuss with clients. It should be noted that this is a very complex issue that cannot be readily explored comprehensively in a Level 1 technical guidance note. As such, this note serves only as an introduction to floor vibration and the reader is encouraged to seek out the texts referred to in the Further Reading section for more detailed and comprehensive guidance on the subject. Of special note is the Design of Floors for Vibration: New Approach by the Steel Construction Institute, from which this guide has drawn much of the theory behind the assessment of floor vibrations.

Floor vibration due to excitation This guide only concerns vibration of floors due to excitation that is internally sourced, which can originate from human activity and/or machinery. It does not cover the vibration of structures due to external elements such as rail tracks and roads or lateral vibrations of structures due to wind. Floor structures are designed to a minimum limit of natural frequency. This is assessed against the stiffness of the structure vs. the whole of the self-weight and super-imposed dead load elements, as well as 10% of the predicted imposed load. This percentage allows for semi-permanent and inactive installations such as furniture. For office buildings it is recommended that this limit is set at 4 Hz as minimum and for stages and dance floors this minimum is raised to 8.4 Hz due to the vigorous activity the floor would be subjected to. Floor structures that have a fundamental natural frequency of between 3 and 10 Hz are classified as low frequency floors, while those above that range are high frequency. It is advised that low frequency floors are designed for dynamic loads due to the increase in imposed loading from the relatively lively floor structure. This limit on natural frequency only addresses the likelihood of the base movement or harmonic of the structure matching that of a footfall of an adult, which lies between 1.5 to 2.5 Hz. For staircases however, the base harmonic is much higher. It ranges between 3-4 Hz due to the way in which people climb stairs. They exert a greater force at a higher frequency as people traverse them, hence the increase in the harmonic. If the lowest natural frequency of the structure is more than twice the footfall frequency, then the structure should not exhibit significant vibrations when exposed to imposed loading due to human occupancy. There is still the risk however that despite meeting this natural frequency criteria, significant floor vibrations

25/06/2012 18:18

www.thestructuralengineer.org

33

will occur. This is because the level of floor response could still be unacceptable. It is for this reason that excitation based response criteria must be met in order for a floor structure do be deemed satisfactory.

Damping Damping is a term to describe a facet of the structure that affects the energy within it that leads to a reduction in vibrations. All structures have inherent damping properties via their stiffness, the friction within connections, furniture, and other fixtures. Partitions can also be considered as components of damping as can high concentrations of human occupation.

Natural Frequency Assessment of simple structures The favoured method of determining the natural frequency of structures is via finite element analysis models, as they produce more accurate results. Nevertheless it is possible to calculate the natural frequency of simple structures such as a simply supported beam or a grillage of primary and secondary beams that support a floor.

Where: δ is the maximum deflection due to the applied load and self-weight in mm g is acceleration due the gravity, which equals 9.81 m/s2 From this it is possible to derive the natural frequency (f1) of a simply supported beam from this basic equation:

18 f1 = d Where: δ is the maximum deflection due to the applied load and self-weight in mm

Mode Shapes The natural frequency of a structure has a mode shape attributed to it. All structures have almost countless mode shapes, but it is the first few that are of interest as they define the lowest natural frequency of the structure. Figure 1 shows the first three mode shapes of a simply supported beam:

EI mL4

Where: fn is the dynamic natural frequency of the beam EI is the flexural rigidity of the member in Nm2 m is the unfactored effective mass of the structure and elements it is supporting in kg/m L is the span of the member in m κn is a constant that represents the support conditions of the beam for the nth node of vibration It is possible to simplify this equation if it is assumed that only a uniformly distributed load is applied to the beam, that it is simply supported and the value of κn is taken to be π2. Following these assumptions, the resulting equation is the same as that used to determine the mid span deflection of a simply supported beam, thus:

5mgL4 d = 384EI

TSE7_32-34.indd 33

Vibration Dose Value (VDV) BS 6472 Part 1 is the guide to evaluation of human exposure to vibration in buildings and addresses the excitation issue raised previously. It does this by defining acceptable limits of what it terms the vibration dose value or VDV. This is based on how a human adult perceives vibrations in a floor structure and is defined in Clause 3.5 as:

VDVb/d,day/night = a # a 4 (t) dt k T

0.25

0

Where:

VDVb/d,day/night is the vibration dose value in

m•s-1.75

α(t) is the frequency weighted acceleration in m•s-2 T is the total period of the day or night (in seconds) during which any vibration can occur

The base equation to determine a natural frequency for a beam is thus:

l fn = 2rn

typically this is at its mid-span • All loads modelled can only be permanent in nature. This includes 10% of imposed loads that are based on fixtures • Analysis of at least 10 mode shapes is advisable in order to achieve accurate results • The material properties of any concrete in the structure should allow for long term effects

Figure 1 Mode shapes for a simply supported beam

The first mode shape is often cited as being aligned to the fundamental frequency of the structure. Mode shapes are expressed in nondimensioned diagrams that are based on the maximum deflection of the structure within a defined shape.

Modelling of structures to determine natural frequency For more complex structures computer analysis tools are used to determine the natural frequencies of a structure. The methodology used to create FE models for natural frequency analysis is somewhat different to those for stress and serviceability and can be summarised as follows: • All elements within the structure are broken up into many elements. The more elements there are, the more accurate the result of the analysis • All connections between elements are modelled as continuous/fixed • Vertical elements should be split at the point of contraflexture with a pinned connection;

Table 1 of BS 6472 defines the acceptable limits of VDV for residential buildings. From this table it can be extrapolated that in a 16 hour day the VDV can range between 0.2 and 0.4 m•s-1.75 and during an 8 hour night can range from 0.1 to 0.2 m•s-1.75. If these criteria are met, then there is a low probability of any adverse comment being generated by the occupants of a building due to floor vibrations. A note to Table 1 of BS 6472 states that for offices these ranges are multiplied by 2 and 4 respectively. More information on how the value of VDV is determined for structures, can be found in BS 6472 Part 1.

Response Factor (R) As stated previously, EN 1990:2002 (Eurocode 0) does not offer any advice with regard to the acceptable limits on floor vibration. It places that responsibility onto both the client and the structural engineer. In some instances clients stipulate design criteria with regard to floor vibrations in terms of a response factor (R). Its derivation is based on the acceleration of the structure as it moves during vibrations. It is recommended that the values given in Table 1 are not exceeded by the response factor in order for the floor structure to be acceptable.

26/06/2012 12:56

› Note 11

34

Room Type

Workshop

Office

Residential

Hospital operating theatres

TheStructuralEngineer July 2012

Time of day

Limiting response factor value (R)

Day

8

Night

4

Day

4

Night

4

Day

2-4

Night

1.4

Day

1

Night

1

Table 1 Limiting values of response factor (R) vs. room type

Level 1

Technical Technical Guidance Note

Remedial works to address floor vibration When a building suffers a change of use to the point where a rhythmic activity is very likely, an assessment of the structure is required. This typically consists of a combination of testing and modelling of the structure to determine what alterations are needed in order for the structure to perform adequately. These alterations focus on making the structure stiffer without significantly adding to its mass. They can include reducing the span of primary beams by adding additional supports to the structure, stiffening beams by altering its section profile and stiffening the support connections.

Worked example A simply supported steel beam spanning 8m is supporting a 3m high, 140mm thick blockwork wall and a timber floor that is to have office furnishings placed upon it. The imposed load has been set at 4 kN/m². The beam is to have a natural frequency that is greater than 4 Hz. Check to see if a 457x152x67 UB can meet this criteria, ignoring design stress considerations.

Eurocode 0.

Applied practice

The applicable codes of practice for floor vibration are as follows: BS EN 1990: Eurocode Basis of Structural Design BS EN 1990: UK National Annex to Eurocode: Basis of Structural Design ISO 10137: Bases for the design of structures – Serviceability of buildings and walkways against vibration BS 6472 Part 1: Guide to evaluation of human exposure to vibration in buildings - Vibration sources other than blasting

Glossary and further reading Damping – Dissipation of energy in a vibrating system. Mode Shape – Deflected shape at a particular natural frequency of a system undergoing free vibration.

Natural Frequency – Frequency at which a mode of vibration will oscillate under free vibrations.

Vibration Dose Value (VDV) – a number attributed to structures against which the level of comfort can be approximately measured. Further Reading SCI (2009) P354 Design of Floors for Vibration: New Approach Ascot, Berkshire: Steel Construction Institute Breeze, G. (2011) Dynamic Comfort Criteria for Structures Watford: BRE Press

Web resources For more information on this subject, visit: Steel Construction Institute: www.steel-sci.org/ Building Research Establishment: www.bre.co.uk/ The Institution of Structural Engineers library: www.istructe.org/resources-centre/library

TSE7_32-34.indd 34

25/06/2012 18:18