Proceedings of the Institution ofCivil EngineersStructures & Buildings 156November 2003 Issue SB4Pages 367–371

Paper 13029

Received 23/08/2002Accepted 17/12/2002

Keywords:buildings, structure & design/dynamics/field testing & monitoring

A. BlakeboroughLecturer, Department ofEngineering Science,University of Oxford

M. S. WilliamsLecturer, Department ofEngineering Science,University of Oxford

Measurement of floor vibrations using a heel drop test

A. Blakeborough and M. S. Williams

As floor vibration problems increase, there is a need for

simple and reliable methods of determining a floor’s

dynamic properties. This paper presents a technique

called the instrumented heel drop test, in which the

floor is excited by a series of heel drops performed on

top of a slim load cell placed on the floor. The test is

shown to give excellent resolution of natural frequencies

in the range 2 – 15 Hz, which corresponds well with the

frequency range of interest in floor vibration problems.

The method appears to offer some advantages over the

well-established technique of instrumented hammer

testing, in terms of the quality of frequency resolution

and the speed of the test.

1. INTRODUCTION

There is an increasing incidence of problematic floor vibrations

in structures such as office buildings, hospitals and domestic

housing.1–3

The problems are caused by a variety of factors

including recent trends towards long-span, lightweight

construction, the increasing need for very low-vibration

environments (as in hospital operating theatres, for example)

and changes of use of existing structures (such as conversion

of an office floor to a gymnasium). As a result there is a

growing need for measurement of floor dynamic parameters

such as natural frequencies, modal damping ratios and modal

masses.

In a dynamic test, the floor is excited (that is, set in motion) by

some means and its response is measured using an

accelerometer. Several different excitation methods are

available. A very simple method that has been used for many

years is the heel drop test,4in which a person stands in the

middle of the floor, rises onto their toes and then drops down

so that their heels strike the floor. This test has been widely

used over the past 30 years and has formed a part of many

proposed design procedures.5,6

These procedures idealise the

heel drop force time history as the triangular pulse shown in

Fig. 1, which corresponds to an impulse (that is, the integral of

force over the duration of the pulse) of 67 N s. Some design

guides that use the heel drop (such as the Canadian steelwork

code7and the Steel Construction Institute’s design guide

1) treat

it as an impulse of 70 N s.

The obvious advantages of the heel drop test are that it is easy

to perform and requires no expensive equipment. Its

widespread and long-standing use also means that it is a

well-calibrated and understood test. However, it has been

criticised8because it is an output-only test, in which only the

response of the floor is measured. The exciting force is

unknown and may vary significantly between tests. Output-

only tests are inherently less robust than true modal tests, in

which both the exciting force and the floor response are

measured, with the dynamic properties deduced from the

frequency response function between the two. For this reason,

other excitation methods such as instrumented impact

hammers or electrodynamic shakers are often preferred.

In this paper a testing method referred to as the instrumented

heel drop test is proposed. This is based on the premise that the

only real problem with the standard heel drop test is the failure

to measure the input force. This has been rectified by

performing the heel drop on a purpose-built load cell that sits

on the test floor. The remainder of the paper describes the load

cell, measurements of the heel drop forcing function, and

comparisons of floor dynamic properties calculated using an

instrumented heel drop test and an instrumented hammer test.

2. LOAD CELL DESIGN

The load cell comprises four steel load-sensing elements

sandwiched between 20 mm thick aluminium alloy top and

Force: N

2670

0.05

Time: s

Fig. 1. Idealised heel drop time history (after Murray6)

Structures & Buildings 156 Issue SB4 Blakeborough • Williams 367Measurement of floor vibrations

bottom plates (Fig. 2). The overall depth is 85 mm and the top

plate has plan dimensions 400 mm 3 400 mm, sufficient for a

person to stand on and perform a heel drop test without

difficulty (Fig. 3). It weighs 17 kg, making it easily portable.

When supporting a mass of 75 kg (the mass of a typical person)

the bending deflection of the top plate is about 0·01 mm and

its fundamental frequency is around 150 Hz. The load can thus

be transferred to the sensing elements without excessive

deformation or vibration within the load cell.

3. MEASUREMENTS OF HEEL DROP FORCE

The load cell was placed on a very stiff floor and was used to

measure a series of heel drops. The load was sampled at a

frequency of 256 Hz. Fig. 4 shows a typical heel drop time

history for a man of mass 75 kg. The static weight has been

subtracted from the force measurement so that the graph shows

only the dynamic variations in force. In the first part of the

signal the man rises from a normal standing position onto his

toes. This causes small fluctuations in force as he accelerates

upwards and then comes to rest. The man then balances on his

toes for about half a second before bringing his heels down,

causing an initial reduction in vertical force as his centre of

gravity accelerates downwards, followed by a very sharp

increase in force at the moment of heel impact. Following the

main impact there is a short period of heavily damped

oscillation at a frequency of around 5 Hz: this is due to vertical

vibration of the human body. Clearly, the total force input to

the floor is considerably more complex than the idealised

impulse in Fig. 1.

Figure 5 shows the time history of the main impact and

subsequent body vibrations for nine heel drops performed by

the same person. It can be seen that a single person is able to

achieve quite a high degree of repeatability, both for the

approximately triangular force pulse at heel impact and for the

subsequent body vibrations. The downward impulse due to heel

impact (that is, the area under the main positive force pulse) in

these nine tests ranged from 59·7 to 73·1 N s, with a mean of

65·6 N s. This agrees well with previous published work, which

suggests that a heel drop can be treated as an impulse of

67–70 N s.1,5–7

However, measurement of heel drop tests

performed by several different people showed quite a high

degree of scatter, which was only weakly correlated with the

variation in mass of the person.

This variability in the input force may be problematic in cases

where the force is not measured and is assumed to take some

arbitrary value. However, it is of far less concern in the

instrumented heel drop test, where the actual force is measured

on each occasion. A more important parameter is the frequency

content of the signal, as this governs the range of structural

frequencies likely to be excited by a heel drop. Fig. 6 shows the

power spectral densities computed from a series of heel drops

by four different people, in each case normalised to a peak

value of unity. Although there are some differences between

the curves, they all show quite similar overall trends. In each

case the peak power is achieved at a frequency in the range

2·5–5 Hz, and there is significant power at frequencies between

1 and 15 Hz. The heel drop would therefore be expected to be

effective at exciting floors with frequencies in this range.

Problem floors are likely to have frequencies well below 15 Hz,

so this frequency range is more than adequate.

4. COMPARISON OF INSTRUMENTED HEEL DROP

AND HAMMER TESTS

The instrumented heel drop test has been used to determine the

dynamic properties of a simple composite floor. The results

were compared with those from an instrumented hammer test

in order to evaluate the method. The tested floor comprised a

130 mm thick concrete slab supported on a regular grid of steel

universal beams. Primary beams were spaced at 3·6 m centres

and spanned 7·0 m between columns, as shown in Fig. 7. This

is a relatively stiff structure, which was not expected to be

prone to vibration problems.

In the tests reported here the excitation (either instrumented

hammer or heel drop) was applied at point A in Fig. 7, at the

midspan of a secondary beam, with the floor response

measured by an accelerometer positioned at B. Initial data

processing was performed using an Advantest R9211C

spectrum analyser, with further processing performed later on a

PC.Fig. 3. Performing a heel drop test on the load cell

Fig. 2. View of load cell showing one of the four load-sensingelements

Structures & Buildings 156 Issue SB4 Blakeborough • Williams368 Measurement of floor vibrations

For the instrumented heel

drop test, heel drops were

performed by a person of

mass 75 kg. Frequency

response functions (FRFs)

were computed from 40 s

samples of data, during

which time approximately

ten heel drops were

performed. It is normal to

average several samples to

minimise the effects of

measurement noise. In this

case, based on past

experience, six tests were

averaged to produce the final

FRFs. The test therefore took

a total of 4 min.

For comparison, a test was

performed using identical

equipment and processing

methods, except that the heel

drop was replaced by a

Dytran impact hammer, fitted

with its own load cell. For the

hammer test, ten averages

were taken, with

approximately ten hammer

blows in each 40 s sample.

The results are shown in Fig.

8. The top two plots show

the frequency response

function; as this is a

complex quantity it is

plotted as an amplitude (in

units of flexibility) and a

phase angle. Natural

frequencies are identified by

peaks in the FRF amplitude

and sudden shifts in phase

angle. The width of the FRF

peaks can be used to

estimate the damping

present, with a higher

damping level giving a

broader peak. The third plot

is the coherence, a measure

of the extent to which the

measured floor acceleration

is caused by the measured

input force rather than by

some other unmeasured

input. A coherence value of

zero means there is no

relationship between the

signals, while a value of 1·0

implies complete dependence.

A high coherence is a good

indicator of the quality of

the test data, and enables

Risingontotoes Balancing

Heel impact

Body vibration

Heels descending

0 0.5 1 1.5 2 2.5

Time: s

2000

1500

1000

500

0

�500

�1000

Forc

e: N

Fig. 4. Typical heel drop time history

2500

2000

1500

1000

500

0

�500

�1000

For

ce: N

1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6

Time: s

Fig. 5. Comparison of nine heel drops performed by a single person

1

0.8

0.6

0.4

0.2

0

Nor

mal

ised

PS

D

0 2 4 6 8 10 12 14 16 18 20

Frequency: Hz

Fig. 6. Power spectral density of heel drops performed by different people

Structures & Buildings 156 Issue SB4 Blakeborough • Williams 369Measurement of floor vibrations

more accurate estimates of the modal properties to be

extracted from the data.

The results show that both test methods give very similar

estimates of the natural frequencies, the lowest of which is at

10·9 Hz. However, there are some significant differences:

(a) The instrumented heel drop test gives near-perfect

coherence across the frequency range shown, whereas the

hammer test coherence is poor at low frequencies and also

shows some localised reductions at a few frequencies

between 10 and 16 Hz.

(b) At low frequencies (below 4 Hz) the hammer test gives very

poor data, with numerous spurious FRF peaks accompanied

by poor coherence, whereas the heel drop test gives a

smooth FRF and excellent coherence. The heel drop FRF

Hammer

Heel drop

90

0

�90

�180

Pha

se: d

egre

e

2 4 6 8 10 12 14 16 18 20

Frequency: Hz

Hammer

Heel drop

0.3

0.2

0.1

0

Fle

xibi

lity:

10�

6 m/N

2 4 6 8 10 12 14 16 18 20

Frequency: Hz

Hammer

Heel drop

1

0.5

0

Coh

eren

ce

2 4 6 8 10 12 14 16 18 20

Frequency: Hz

Fig. 8. Modal test results: comparison of FRF amplitude, phase and coherence determined by instrumented heel drop test andinstrumented hammer test

7000

3000

2333

180012

00

3600

B

A

Fig. 7. Floor layout showing test locations (dimensions in mm)

Structures & Buildings 156 Issue SB4 Blakeborough • Williams370 Measurement of floor vibrations

does begin to deteriorate at frequencies below 2 Hz (not

shown in the figure).

(c) At intermediate frequencies (from 4 to about 15 Hz, the key

frequency range for most floors) the instrumented heel

drop test gives a much smoother FRF and a vastly superior

coherence, making it easier to obtain accurate estimates of

modal damping and stiffness.

(d) It is only at the less interesting, higher frequencies (above

15 Hz) that the performance of the two techniques is

similar.

This contrast is in spite of the fact that the heel drop results

were obtained using fewer averages and therefore a shorter test

duration. The improvement is due to the fact that the heel drop

puts a large amount of energy into the frequency range of

interest, whereas the hammer spreads the energy over a much

wider range.

The instrumented heel drop test is therefore particularly

suitable for modal testing of structures with frequencies in the

range 2–15 Hz.

5. CONCLUSIONS

As floor vibration problems increase, there is a need for simple

and reliable methods of determining a floor’s dynamic

properties. This paper has shown that, by using a simple load

cell placed on the floor, the well-known heel drop test can be

adapted to be part of an effective modal testing technique. The

instrumented heel drop test has been shown to give excellent

resolution of frequency response functions in the range

2–15 Hz, making it ideally suited to determining the modal

properties of potentially problematic floors.

6. ACKNOWLEDGEMENTS

The authors gratefully acknowledge the support of the Steel

Construction Institute.

REFERENCES

1. WYATT T. A. Design Guide on the Vibration of Floors. Steel

Construction Institute, Ascot, 1989, SCI Publication 076.

2. WILLIAMS M. S. and WALDRON P. Evaluation of methods for

predicting occupant-induced vibrations in concrete floors.

The Structural Engineer, 1994, 72, No. 20, 334–340.

3. MURRAY M. M., ALLEN D. E. and UNGAR E. E. (1997) Floor

Vibrations due to Human Activity. American Institute of

Steel Construction, Chicago, AISC/CISC Steel Design Guide

Series 11.

4. LENZEN K. H. and MURRAY T. M. (1969) Vibration of steel

joist concrete slab floor systems. Department of Civil

Engineering, University of Kansas, Lawrence, Kansas, 1969,

Report No. 29.

5. ALLEN D. E. Vibrational behavior of long-span floor slabs.

Canadian Journal of Civil Engineering, 1974, 1, 108–115.

6. MURRAY T. M. Design to prevent floor vibrations.

Engineering Journal, American Institute of Steel

Construction, 1975, 12, No. 3, 82–87.

7. CANADIAN STANDARDS ASSOCIATION. Steel Structures for

Buildings: Limit States Design. Appendix G: Guide for Floor

Vibrations. Canadian Standards Association, Rexdale,

Ontario, 1989, Canadian Standard CAN3-S16·1-M89.

8. CAVERSON R. G., WALDRON P. and WILLIAMS M. S. (1994)

Review of vibration guidelines for suspended concrete slabs.

Canadian Journal of Civil Engineering, 21, 931–938.

Please email, fax or post your discussion contributions to the secretary by 1 May 2004: email: daniela.wong@ice.org.uk;

fax: þ44 (0)20 7799 1325; or post to Daniela Wong, Journals Department, Institution of Civil Engineers, 1–7 Great George Street,

London SW1P 3AA.

Structures & Buildings 156 Issue SB4 Blakeborough • Williams 371Measurement of floor vibrations