PREDICTION OF FLOOR VIBRATION INDUCED BY WALKING LOADS
AND VERIFICATION USING AVAILABLE MEASUREMENTS

This project is granted by the EPSRC for the period between August 2004 and July 2006

1. Background
    1.1 Causes and problems of floor vibration induced by walking loads
    1.2 Previous work
       1.2.1 Definition of walking loading
       1.2.2 Modelling of composite floor
       1.2.3 Prediction of floor response to walking loads
    1.3 Summary

2 Objectives

3. References

4. Final Report

1. BACKGROUND TO THE PROJECT

1.1 Causes and Problems of Floor Vibrations Induced by Walking Loads

Vibration of floors induced by human walking has not been a significant problem in the past. However, there have been a number of cases where
serviceability problems have occurred. This is because

*   The spans of floors are longer today than in the past.

*   Floors are lighter today than in the past, for instance due to the use of fibre-reinforced polymer (FRP) composite, concrete stress-ribbon and
prestress techniques.

Thus many long-span floors have low bending rigidity, mass, natural frequency and damping, and are sensitive to dynamic loads induced by pedestrians. Such floors can be seen in airport terminals, shopping centres and, in particular, modern offices. People in stationary positions, such as sitting or standing, easily perceive structural vibrations induced by other people walking where human-structure interaction [1.4] needs to be considered. They feel uncomfortable and are distracted, and this will affect the design of long-span floors.

Vibration problems of long-span floors were often noted after construction, but they were not reported as safety problems are not concerned. Why were engineers not able to identify such vibrations at the design stage? This is because walking loads have not been fully understood and properly defined, models of floors are inadequate and the methods for predicting floor response are oversimplified in related codes. It is only to be expected that the output (prediction of the responses) cannot be any better than the input (definition of the loads, models of floors and the quality of analysis methods). The unexpected vibrations of the Millennium Bridge, when thousands of people walked through, emphasised the significance of an understanding of walking loads and the structural response due to the loads, and the necessity to avoid such problems.

The problems discussed concern many new and existing long-span floors.  It is expected that in the future the spans of floors will be even longer, they will be even lighter and human expectation to the quality of living and working environment is even higher. Therefore, the vibration problems of floors addressed here are likely to be even more significant in the future and the design of problem-free long-span floors becomes an increasingly important issue in structural engineering.

1.2 Previous Work

Researchers in Canada [Allen 1993, Rainer 1998, Supplement 1995], USA [Ad Hoc Committee 1986], Singapore [Pan 1992, Tanaboriboon 1986], Switzerland [Bachmann 1997], UK [Ellis 2000, 2001, 2003, Ji, 1992, SCI 1989] and some other countries have carried out investigations on the vibration of floors induced by walking loads. Recently a comprehensive literature review on vibration serviceability of long-span concrete floor was published [Pavic 2002a, 2002b], which provided background information and current understanding of the topic.

1.2.1 Definition of walking loading

Walking is a periodical movement on a flat surface in which two feet move alternately from one position to another and do not leave the surface simultaneously. Similar to jumping loads, walking loads can be completely defined by seven parameters:

Static characteristics:         load intensity and location

Dynamic characteristics:   load amplitude, frequency range, phase lag, crowd effect and moving velocity

Here the load amplitude, phase lag, frequency and crowd effect are the keys for defining the loads. Walking loads are similar to the dance-type loads in that they have their own frequencies, but they result in different problems (see Table 1). There has been some information obtained from the measurement of walking loads [Bachmann 1997, Mouring 1994, Wheeler 1982]. These measurements obtained from small force platforms provided information of the loading induced by a single foot, but did not constitute a complete picture of the forces induced by continuous walking. The model of individual walking loads, similar to jumping loads, can normally be expressed by Fourier series:

                                                                        (1)   

                                                                     Load intensity G          Load factor   (Fourier coefficient)

                                                                     Load position x            Phase lag   and load frequency 

Different from jumping loads, G(x) indicates that the body weight moves from one position to another. When a constant walking velocity v is considered, . The difficulty using the load model lies in the determination of the Fourier coefficients (load factors) and phase lags to each harmonic term in the model. Some coefficients and phase lags were provided. The figure on the right shows the load models suggested by [Backmann 1997, Allen 1993]. It can be noted that there are about 20% differences between the peak values and the load patterns of the two curves are not the same. This is because the phase lag for each harmonic term cannot be determined experimentally. It is obvious that there is a lack of understanding and information on the models for walking loads, which is required for analysing and designing floors subject to the loads. 

1.2.2 Modelling of composite floors

The dynamic behaviour of long-span floors has been investigated experimentally and/or numerically [1.14, Pavic 2002b]. However, much of the theoretical investigations focused on flat concrete floors rather than composite floors. Composite floors denote the composite actions of steel beams and concrete or composite slabs that form a structural floor. Composite slabs comprise steel downstand beams, profiled steel decking (or sheeting) as the permanent formwork, lightweight or normal weight concrete slabs and anti-crack steel mesh. Composite floors have been widely used in construction as there are a number of advantages using such floor systems. Static and dynamic tests had been conducted on the composite floors of the Cardington steel framed building, but the modelling of the dynamic behaviour of the composite floors has not been performed. A reasonable model of composite floors in design is not a simple task due to the profile of the section and the composite actions [da Silva 2001].  It is also not clear how the beam-column connections affect the dynamic behaviour of composite floors.

It has been identified in our study of long-span flat concrete floors that columns connecting to the floor from the upper and lower storeys should be included in the model [1.14]. The inclusion of these columns will significantly affect the predicted natural frequencies but not the mode shapes. This finding is applicable to the investigation of dynamic behaviour of composite floors.

1.2.3 Prediction of floor response to walking loads

The vibration of floors subject to walking load can be predicted when the load model is defined and the dynamic behaviour of floors are understood. Current methods for analysis and design of floors [Pavic, 2002b] may be oversimplified or not be assessed, in particular, for composite floors. Some response measurements from building floors would provide useful information for understanding of the loading and the structures. Several experimental investigations conducted by the collaborator showed that the floor responses due to an individual walking and a crowd walking do not have significant differences and the floor response is dominated by its resonant mode and a particular load component that induces resonance [Ellis 2000, 2003]. When these observations can be explained theoretically, it will provide useful information to designers and building codes. These measurements will provide valuable validation for any prediction methods that are developed.

1.3 Summary

Whilst some experiments have been conducted for identifying walking loads and many floors have been built already, it is still necessary to establish the load models and sound methods for predicting the vibration of long-span floors induced by walking loads. There are several publications on measurements of walking loads [Bachmann 1997, Mouring 1994, Wheeler 1982] and floor response to walking loads [Ellis 2000, 2003]. These measurements provided valuable information for defining the walking load model and checking structural models and prediction methods. The applicant has noted the problems, difficulties and opportunities in this area and extended his work to walking loads and composite floors, and supervised several students working on the models of walking loads and floor structures [1.13, 1.14, El-Dardiry 2003].

 

2. Objectives

The project aims to provide models and methods for predicting floor vibrations induced by walking loads, which will allow vibration problems to be eliminated or minimised by a prediction at the design stage. It also aims to produce practical methods for structural engineers and a technical basis for related building codes. The specific objectives are:

a)    to define the walking loads using Fourier series based on the available measurements of walking loads obtained from small force platforms induced by a single foot.

b)    to investigate the models and dynamic behaviour of composite floors based on the Cardington steel framed building and available frequency measurements.

c)    to predict floor response to walking loads induced by an individual and a group of people using the FE method, based on the two Cardington test buildings and available response measurements.

d)    to provide an analytical method for evaluating floor vibrations due to walking loads, and to identify the critical situations which must be considered in design, and to verify the proposed load model and the analysis method using the response measurements on the Cardington building floors and a concrete beam at UMIST.

e)    to evaluate the proposed design method and the existing methods based on the Cardington building floors, and to summarise the results for peer review.

 

 

3. References

 

1.1        1.1  Ji, T. and Ellis, B. R, (1994), Floor vibration induced by dance type loads: theory, The Structural Engineer, Vol.72, No.3,   pp.37-44.

1.2        1.2 BSI, BS 6399, Part 1: Loading for Buildings (1996).

1.3        1.3 http://www.umist.ac.uk/civil/staff/tji/research/epsrc1/design.htm

1.4        1.4 Ellis, B. R. and Ji, T., (1997), Human-structure interaction in vertical vibrations, Structures of Buildings, the Proceedings of Civil   Engineers, Vol. 122, No.1, pp.1-9.

1.5         1.5 Ji, T. and Ellis, B. R, (1993), Evaluation of dynamic crowd effect for dance loads, IABSE Symposium: Structural Serviceability of Buildings, Goteburg.

1.6         1.6 Ellis, B. R and Ji, T., (1994), Floor vibration induced by dance type loads: verification, The Structural Engineer, Vol.72, No.3, pp.45-50.

1.7         1.7 Ji, T. and Ellis, B. R. (1997), Effective bracing systems for temporary grandstands, The Structural Engineer, Vol.75, No.6, pp. 95-100.

1.8         1.8 Ji, T. and Ellis (1998), B. R. The experimental determination of dynamic crowd effects The SECED Newsletter, October 1998.

1.9         1.9 Ginty, D., Derwent, J. M. and Ji, T., (2001), The frequency ranges of dance-type loads, the Journal of Structural Engineer, Vol.79, No.6, pp.27-31.

1.10      1.10 Ji, T. and Ellis, B. R., (1999), The evaluation of sports stadia grandstands for dynamic crowd loads at pop concerts in the UK, The Fourth European Conference on Structural Dynamics, Prague, 6-10 June 1999.

1.11      1.11 Ellis, B. R., Ji, T. and Littler, J., (2000), The response of grandstands to dynamic crowd loads, Structures and Buildings, Vol.140, No.4, pp.355-365, The Proceedings of the Institution of Civil Engineers.

1.12      1.12 Ji, T and Wang, D., A supplementary condition for calculating periodical vibrations, the Journal of Sound and Vibration, Vol.241, No.5, pp.920-924.

1.13      1.13 Aikaterini, P and Ji, T, Frequency ranges of walking loads, submitted to the Journal of Structural Engineers.

1.14      1.14 El El-Dadiry, E., Wahyuni, E., Ji, T. and Ellis, B. R., (2002), Improving FE models of a long-span flat concrete floor using frequency measurements, Computers and Structures, Vol.80, pp.2145-2156.

 

2.1         Ad Hoc Committee on Serviceability Research, ASCE Journal of Structural Engineering, Vol.112, No.12, pp. 2646-2664.

2.2         Allen, D. E. and Murray, T. M. (1993), Design criterion for vibrations due to walking, AISC Engineering Journal, Vol.30, No.4, pp.117-129.

2.3         Aristidis, A, (1997), Modelling of Walking Loads, MSc dissertation, UMIST.

2.4         Bachmann, H., et al, (1997), Vibration Problems in Structures: Practical Guidelines,

2.5         British Standard Institution, BS5400, (1978), Steel, Concrete and Composite Bridges, Part 2: Specification for Loads, London.

2.6         Ellis, B. R., (2000), On the response of long-span floors to walking loads generated by individuals and crowds, The Structural Engineer, Vol.78, No.10, pp.17-25.

2.7         Ellis, B R, (2001), Serviceability evaluation of floor vibration induced by walking loads, The Structural Engineer, Vol.79, No.21, pp.30-36.

2.8         Ellis, B R, (2003), The influence of crowd size on floor vibrations induced by walking, The Structural Engineer, Vol.81 No.6, pp.20-27.

2.9         El-Dardiry, E, (2003), Floor vibration induced by walking loads, PhD Thesis, UMIST.

2.10      Ji, T. and Ellis, B. R.,(1992), Review of dynamic loads induced by human movements, BRE Note, N98/92.

2.11      Ji, T and El-Dardiry, E, (2002), Vibration assessment of a floor at Synagogue-Cazenove Road, London, Client Report, UMIST.

2.12      Mouring, S E and Ellingwood, B R, (1994), Guidelines to minimise floor vibrations from building occupants, Journal of Structural Engineering, ASCE, Vol.120, No.2, pp.507-526.

2.13      Pan T C, (1992) Vibration of pedestrian overpass, Journal of Performance of Constructed Facilities, Vol.6, No.1, pp.34-45.

2.14      Pavic, A and Reynolds, P, (2002), Vibration serviceability of long-span concrete building floors, part 1; review of background information, The Shock and Vibration Digest, Vol. 34, No. 3, pp.191-211,

2.15      Pavic, A and Reynolds, P, (2002), Vibration serviceability of long-span concrete building floors, part 2; review of mathematical modelling, The Shock and Vibration Digest, Vol. 34, No. 4, pp.279-297.

2.16      Rainer J H, Pernica, G and Allen D E, Dynamic loading and response of footbridges, (1988), Canadian Journal of Civil Engineering, Vol.15, No.1, pp. 66-71.

2.17      Steel Construction Institute, (1989), Design Guide on the Vibration Floors.

2.18      Supplement to the National Building Code of Canada: Commentary A: serviceability criteria for deflections and vibrations, Ottawa, National research Council of Canada, 1995.

2.19      Tanaboriboon, Y, Hwa, S S and Chor C H, (1986), Pedestrian characteristics study in Singapore, Journal of Transportation Engineering, Vol.112, No.3, pp 229-235.

2.20      Wheeler, J E, (1982), prediction and control pedestrian-induced vibration in footbridges, Journal of Structural Engineering, ASCE, Vol.108, No.9, pp.2045-2065.

2.21      Da Silva, J G S, et al, (2001), Dynamic analysis of composite steel decking floors subject to rhythmic load actions, Proceedings of the 8th International Conference on Civil and Structural Engineering Computing, Civil-Comp Press, UK.