Dynamic Fe Modelling of a Multi-storey Car Park

8/4/2019 Dynamic Fe Modelling of a Multi-storey Car Park

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Reprinted from the IMAC-XVII Proceedings, 1999, with permission of the Society for Experimental Mechanics, Inc., 7 School Street, Bethel,

CT 06801, 203-790-6373, Fax 203-790-4472, email [email protected], http://www.sem.org.

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DYNAMIC FE MODELLING OF A MULTI-STOREY CAR PARK

VERIFIED BY MODAL TESTING

P. Reynolds, A. Pavic and P. Waldron

University of Sheffield

Centre for Cement and Concrete

Sir Frederick Mappin Building

Mappin Street, Sheffield, S1 3JD

United Kingdom

ABSTRACT. This paper describes the application of

the FE modelling, modal testing and FE model

correlation and updating techniques to a 1500-tonne

car park floor structure. Firstly, a pre-test FE model,

constructed according to common civil engineering

practice, is presented. Next, the modal testing

performed on the structure is described and the results

from this testing are shown. Finally, the manual FE

model updating procedure as applied to this structure

is described and the correlation between the updated

FE model and the test results is presented. By usingthis procedure, inadequacies in the pre-test FE model

are highlighted and suggestions are made for better

modelling practice for similar future structures.

1. INTRODUCTION

Consideration of the vibration performance of civil

engineering structures is becoming increasingly

important with the current trend for more efficient and

slender structural forms. In particular, long-span

concrete floors, which traditionally have suffered fewvibration problems, are becoming more lively due to

improvements in their construction technology.

A programme of research is currently underway at the

University of Sheffield which is transferring advanced

modal testing and analysis technologies from the

mechanical and aeronautical disciplines to the civil

engineering sector. The aim of this technology transfer

is to provide more reliable analytical models suitable

for checking the vibration serviceability of long-span

and slender concrete floors. Obvious problems with

civil engineering structures, such as their size and the

fact that they must be tested in noisy open space

environments, mean that this transfer of technology is

by no means a simple process.

This paper describes the application of the modal

testing and analysis technologies to a full-scale

reinforced concrete floor structure in a multi-storey

car park. The pre-test analysis [1] comprising theconstruction of an FE model according to common

civil engineering practice is presented, followed by a

description of the modal testing and its results.

Finally, limited manual FE model updating is

performed to demonstrate the deficiencies in the initial

modal, which are then used to suggested guidelines for

the modelling of future similar structures.

2. THE TEST STRUCTURE

The test structure was a single floor in a multi-storeycar park. It weighed approximately 1500 tonnes and is

illustrated in Figure 1. The floor was constructed from

conventionally reinforced concrete and consisted of a

number of precast concrete beams of a proprietary

design connected together with cast in-situ reinforced

concrete. This system formed a ribbed slab with a slab

depth of 75 mm and an overall depth (including ribs)

of 500 mm. The slab was supported by three rows of

columns which were assumed to be rigidly connected





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to it, as well as a small number of shear walls. In-situ

cast edge beams were also present between the

peripheral columns. Finally, a system of four rampsconnected this slab to the adjacent car park levels.

Since the car park was constructed using a new system

of long-span concrete beams, the developers wanted to

check its vibration performance. It was recommended

that the combined FE analysis and modal testing

procedure would be the best method of accomplishing

this objective.

3. PRE-TEST FE MODELLING

A pre-test model was constructed according to

common civil engineering practice using the Ansys 5.2

FE code. The main floor area, being a ribbed slab, was

modelled using orthotropic shell elements (Shell63) in

which the stiffer direction represented the direction of

the ribs. The density of the concrete was adjusted to

take account of the fact that the slab was not of

uniform thickness. The edge beams were modelled

using beam elements having offset capability

(Beam44) and the columns and shear wall supports

were modelled using pins, which is a commonassumption in civil engineering dynamic modelling.

The ramps to the adjacent floors were assumed to be

horizontal for this model to simplify the geometry.

The dynamic modulus of elasticity for the concrete

was initially assumed to be 35 kN/mm2.

This configuration is illustrated in Figure 2 and the

first six natural frequencies and mode shapes

calculated from this model are presented in Table 1.

Figure 2: Configuration of Pre-Test FE Model

Figure 1: Layout of the Test Structure.





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4. MODAL TESTING

4.1 Selection of Test Grid

From the pre-test modelling, it was clear that the

modal testing should performed on the whole floorarea, rather than on a small portion of the floor as

originally requested by the designers of the floor

structure. This is important to note since there are

many guidelines for the vibration serviceability

assessment of floors which consider only a beam-like

strip of the floor having a limited width. Such

simplified models cannot take account of the large

floor mass which is actually engaged in vibration and

hence they tend to be overconservative.

For the tests described in this paper, which were

performed during construction, there were severe time

constraints imposed. The entire modal testing had to

be completed on two consecutive overnight sessions.

For this reason, a very coarse test grid containing 48

test points was selected as indicated in Figure 1.

However, to check whether or not this test grid wassufficient to describe all modes of interest without the

occurrence of spatial aliasing, an auto-MAC analysis

was performed for the first 10 modes. The auto-MAC

matrix is shown in Figure 3, indicating that the

selected test grid was adequate.

4.2 Condition of the Structure

Since the car park was still under construction at the

time of the tests, the contractor was asked to remove

any large items of equipment or materials from the

floor being tested. However, whilst most items had

been removed, there were several small piles of

materials left on the floor in addition to a fork-lift

truck. These could not be moved by the test personnel

and had to be left in place for the duration of the

testing. These sorts of practical problems are very

common when testing civil engineering structures,especially during construction.

There were also two temporary supports (props) which

provided vertical restraint to a small portion of the

floor when tested. The location of these props is

indicated in Figure 1. Since the existence of the these

props was not included in the pre-test FE model of the

structure, it was expected that the modal test results

would not be consistent with it. The location of these

Figure 3: Auto-MAC Plot for the Selected Test Grid

Mode Nat. Freq.

(Hz)

Mode Shape

1 5.70

2 6.14

3 6.73

4 7.25

5 7.97

6 8.22

Table 1: Results from Pre-Test FE Analysis.





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props was carefully measured for inclusion in the

updated FE models of the structure.

4.3 Modal Testing Procedures

Quality assurance procedures based on those

recommended by the UK Dynamic Testing Agency(DTA) [2,3] were followed throughout the test to

ensure that good quality data were obtained. These

procedures are described in detail by Pavic et al. [4]

and are not repeated in great detail here.

The structure was tested using excitation provided by

an APS Dynamics 113 electrodynamic shaker, capable

of applying a peak sinusoidal force of 130 N. It was

operated in 'free-armature mode', meaning that it was

placed onto the top surface of the floor and the force

was generated by accelerating reaction masses

attached to the shaker armature. The force was gauged

indirectly by measuring the acceleration of the moving

masses. The excitation signal utilised was 'triggered

random' as described by Taber et al. [5]. The response

of the structure was measured using low noise, high

sensitivity (1000 mV/g) Endevco 7754-1000

piezoelectric accelerometers. In these tests, the shaker

was used as a roving exciter and two fixed response

measurement locations were used as indicated in

Figure 1. The use of the roving shaker is unusual, but

is very practical when testing large-scale floors [4].

Both the excitation and response signals were digitallysampled on site using a Diagnostic Instruments DI-

2200 dual-channel portable spectrum analyser which

provided immediate calculation and storage of

frequency response functions (FRFs). In addition, the

excitation and response signals were recorded using a

Racal StorePlus VL analogue tape recorder for later

re-sampling, if required.

As a part of the QA system adopted, some limited

modal parameter estimation was performed on site,

using a portable notebook PC with the ICATS suite of software. This was done to ensure that the acquired

data were of reasonable quality. Any FRF

measurements which appeared to have been spoiled

were repeated.

4.4 Results from Modal Testing

The measured natural frequencies, modal damping

ratios and mode shapes corresponding to the first six

modes of vibration are presented in Table 2. They

have been expanded [6] to a more detailed finiteelement mesh for ease of visualisation.

It is clear from a visual comparison of the measured

and predicted modal properties (Tables 1 and 2) that

there are significant differences. In particular, the most

notable are:

• the natural frequencies predicted by the pre-test

FE model are lower than those measured in the

modal testing,

• the effect of the temporary props can be seen

clearly, and

• the visual comparison between the measured and

calculated pairs of the fourth and higher modes is

visibly worse than for the first three modes.

Obviously, the pre-test FE model was unsuitable for

accurate calculation of the modal properties of this

floor structure. Therefore, an improved model was

developed which is presented in Section 5.

Mode Nat. Freq.

(Hz)

?

(%)

Mode Shape

1 6.41 0.78

2 6.82 2.88

3 7.32 2.38

4 7.58 1.82

5 7.99 1.10

6 8.50 1.03

Table 2: Results from Modal Testing.

effect of

temporary supports





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It also appeared, particularly for the first two modes,

that the magnitude of the mode shape ordinates was

lower than expected at points remote from the

response measurement location. It is possible that this

was an unfortunate effect of the very low signal-to-

noise ratio on the response channel caused by an

inability to excite this structure properly using theshaker. The authors believe, therefore, that for

structures significantly larger than this, a larger exciter

would be required.

5. FE MODEL CORRELATION AND MANUAL

UPDATING

Throughout the updating process, the degree of

correlation between the FE model and the test data

was determined primarily using the values of natural

frequencies and a visual inspection of the mode

shapes. However, for the more refined models which

had modal properties quite close to the test data, the

more formal correlation measures of Modal Assurance

Criterion (MAC) and Coordinate Modal Assurance

Criterion (COMAC) were used.

5.1 Manual Updating of the FE Model

The most significant improvements to the pre-test FE

model were achieved by:

• Explicit modelling of the columns. In civil

engineering practice, it has been common to

idealise column/slab connections as pin supports.

This inaccuracy in the boundary conditions has

been shown to reduce significantly the apparent

stiffness of the floor system [7]. For this reason,

the columns were included in the updated model.

They were assumed to be rigidly fixed at the

connection with the floors directly above and

below.

•

Explicit modelling of the temporary supports. Thetemporary supports which were encountered on

site were included in the updated FE model. Due

to their location, which, incidentally, was quite

close to an antinode of the first mode of vibration

corresponding to the unpropped structure, the

inclusion of these supports was found to be vital

to the accuracy of the updated model.

• Explicit modelling of the ribs. Rather than

approximating the ribbed slab structure as an

orthotropic slab, the relatively deep and narrow

ribs (Figure 1) were modelled explicitly using

offset beam elements (Beam44). However, this

greatly increased the complexity of the FE model

and produced only limited gains in accuracy. This

will be discussed further in Section 6.

• Modelling of the centre beam using shell elements.Since the centre beam was 1200 mm wide and

500 mm deep, the decision was taken to model it

using shell elements (Shell63). This enabled its

lateral stiffness to be reduced as described below.

• Other improvements. Other general improvements

and updates to the model included better

modelling of the structural geometry and

improvements in the idealisation of some of the

boundary conditions (such as at the ends of the

ramps which were modelled as fixed rather than

pinned).

In addition to these model refinements, material

properties which were deemed to be uncertain were

adjusted. The global dynamic modulus of elasticity

was varied since the inherent variability of concrete as

a material dictates that this parameter is always rather

uncertain. For this structure, the optimum value of

Young's modulus was determined to be 34 kN/mm2,

quite close to the originally assumed 35 kN/mm2.

There were also indications that there was some lack

of stiffness at the centre beam (indicated in Figure 1).

This was thought to be caused by a lack of continuityat this location due to the existence of the construction

joints between the precast concrete elements and the

in-situ cast concrete. To model this lack of continuity,

the dynamic modulus of the orthotropic shell

elements, representing the lateral stiffness of the

centre beam, was reduced to only 3.4 kN/mm2.

The configuration of the updated FE model is shown

in Figure 4, which has been plotted using realistic 3-D

element dimensions to aid visualisation.

Figure 4: Configuration of Updated FE Model





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5.2 Results from Updated FE Model

The results calculated from the updated FE model are

presented in Table 3. It can be seen that the modal

properties predicted by the updated FE model are

significantly closer to those measured from testing

than the pre-test model (Table 1 and Figure 5). The

MAC plot presented in Figure 5 indicates a reasonable

correlation between the first four modes. However, the

COMAC plot indicates portions of the structure for

which the correlation is low, even for these first four

modes. These locations were identified as those which

were far from the accelerometer reference position forwhich it was thought that there was a poor signal to

noise ratio which reduced the quality of the measured

modal data.

Nevertheless, this updated FE model was considered

to be sufficiently accurate for further studies of floor

vibration serviceability under low-level dynamic

loading.

6. CONCLUSIONS

It has been demonstrated that an FE model constructed

according to common civil engineering modelling

practice was unable to predict accurately the modal

properties of a structure at the design stage. However,

it is not economically viable to model such structures

in intricate detail in the normal civil engineering

design office. For this reason, some suggestions are

made here so that a better prediction of dynamic

behaviour may be made using a reasonably economic

FE model.

Firstly, the presence of columns should be included

explicitly in an FE model of a reinforced concrete

floor structure, rather than simple pin supports. This

tends to produce results which correlate more closely

with measured data. More importantly, this

assumption has the overall effect of increasing the

stiffness and natural frequencies of the floor system.

This is, in general, more beneficial as to the floor

vibration serviceability.

Mode Nat. Freq.

(Hz)

Mode Shape

1 6.39

2 6.63

3 7.40

4 7.87

5 8.23

6 8.45

Table 3: Results from Updated FE Analysis.

Figure 5: Correlation between the Updated FE Model

and the Modal Test Data.





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Due to the 'global' nature of the lowest modes of

vibration in floors, which are normally the most

important for vibration serviceability analysis, a

'smeared' distribution of mass and stiffness only is

required. Specifically, experience in modelling this

particular structure showed that the explicit modelling

of the ribs in this ribbed slab structure greatlyincreased the development and processing time for the

model. However, it only produced limited gains in

accuracy, as indicated by the results in Table 4 which

compares explicit versus smeared modelling of the

ribs with all other modelling details kept equal. The

authors suggest that such structures may be modelled

reasonably accurately in a design environment using

orthotropic shell elements, provided that the element

thickness and material properties are carefully

considered.

Mode Nat. freq. from

explicit modelling

of ribs (Hz)

Nat. freq. from

smeared modelling

of ribs (Hz)

1 6.39 6.48

2 6.63 6.71

3 7.40 7.49

4 7.87 7.94

5 8.23 8.31

6 8.45 8.57

Table 4: Explicit Versus Smeared Modelling of Ribs.

7. RECOMMENDATIONS FOR FURTHER

WORK

For civil engineering structures, the behaviour of the

as-built structure will always be more or less different

from that predicted by an FE model. For this reason, it

is recommended that the modal testing technology is

applied to a large number of civil engineering

structures so that the civil engineering community may

build up experience of the vibration behaviour these

structures. In this way, improvements may be made inthe modelling of similar structures in the future.

ACKNOWLEDGEMENTS

The authors would like to acknowledge Mihail

Petkovski and Michael Hartley for their assistance

during the field modal testing. The updating exercises

in this paper have been conducted as part of an

EPSRC funded project (GR/L68742) entitled

"Experimental FE model updating using fast modal

testing of prototype civil engineering structures".

REFERENCES

[1] Heylen, W., Lammens, S. and Sas, P. Modal

Analysis Theory and Testing. Leuven, Belgium: KU

Leuven, 1997.

[2] DTA, Modal Testing, DTA Handbook - Volume 3,

Dynamic Testing Agency, London, UK, 1993.

[3] DTA, Primer on Best Practice in Dynamic

Testing, Dynamic Testing Agency, London, UK, 1993.

[4] Pavic, A., Reynolds, P. and Waldron P., Modal

Testing of a Full-scale Concrete Floor: Test Specifics

and QA Procedures. Proceedings of the 3rd

International Conference on Modern Practice in Stress

and Vibration Analysis. Dublin, Ireland, pp233-240,

3-5 September 1997.

[5] Taber, R. C., Brown, D. L., Vold, H. and

Rocklin, G. T. Exponential Window for Burst

Random Excitation. Proceedings of the 3rd

International Modal Analysis Conference. Orlando,

Florida, USA: SEM, pp840-844, 28-31 January 1985.

[6] ICATS. MODENT, MODESH, MODACQ and

MESHGEN Reference Manual. London: ICATS,

1997.

[7] Reynolds, P., Pavic, A. and Waldron, P. Modal

Testing, FE Analysis and FE Model Correlation of a

600 tonne Post-Tensioned Concrete Floor , 23rd

International Seminar on Modal Analysis (ISMA 23),

Leuven, Belgium, pp1129-1136, September 1998.

Dynamic Fe Modelling of a Multi-storey Car Park

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