dynamicbehaviorandserviceabilityanalysisofanewtypeof u … · 2020. 6. 30. · duced loads, which...

Research ArticleDynamic Behavior and Serviceability Analysis of a New Type ofU-Shaped Steel-Concrete Composite Floor Slab

Yaqin Lu 1 Hongkun Shang2 Zhengnong Li 3 Kejian Ma1 and Lan Jiang3

1Space Structures Research Center Guizhou University Guiyang China2College of Civil Engineering Qingdao University of Technology Qingdao China3Civil Engineering College Hunan University Changsha China

Correspondence should be addressed to Yaqin Lu luya_2000163com

Received 29 November 2019 Accepted 24 February 2020 Published 30 June 2020

Academic Editor Rosario Montuori

Copyright copy 2020 Yaqin Lu et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A new type of U-shaped steel-concrete composite floor is analyzed in detail +e experimental test and finite element analysis ofthe floor are conducted to study the natural frequency and serviceability characteristics of the new composite floor structure +enatural frequency of the floor is measured under the environmental random vibration stimulating method and the peak ac-celeration of the floor is measured under pedestrian-induced load +e experimental test results show that the U-shaped steel-concrete composite floor has better antiseismic behaviors and meet the specified serviceability requirements +e finite elementanalysis results indicate the constraints have a great impact on the calculation results +e experimental tests and FEM results ofthe floor are compared based on the modal assurance criterion and the results are in good agreement +e experimental testacceleration curves demonstrate that the peak values meet the requirements of Chinese specification

1 Introduction

+e floor structure system has a great influence on thebuildings +e conventional floor structure can meet theinterior space requirement of general buildings eg con-crete floor structure [1 2] prestressed concrete floorstructure [3] steel-concrete composite floor structure [4ndash6]and space grid-concrete slab composite structure [7] +econventional floor structure can be used for long-spanstructure through reasonable design and constructionHowever long-span buildings require a larger interior space+e section height of beam increases with the increase of thespan of the building thus increasing the total height ofconventional floor structures [8ndash10] +erefore it is nec-essary to invent an innovative floor structure which meetsthe larger interior space requirement and suits for long-spanindustrial and public buildings

To meet the requirement the U-shaped steel-concretecomposite floor system has been invented recently in Chinato provide a floor system with a desirable long-span capacityand minimum constructional height [11 12] +e floor

structure system is composed of top ribs bottom ribs shearkeys a thin plate of the surface layer and a U-shaped steelplate around the bottom ribs (Figure 1) Electrical andplumbing conduits can pass through the empty space be-tween the top and bottom ribs increasing the interior netheight or reducing the floor height +e cracking and tensileproblems of concrete beam bending large moment can besolved by adding U-shape steel around the bottom ribswhich enhances the span capacity of the U-shaped steel-concrete composite floor structure +e U-shaped steel-concrete composite floor system is suitable for long-spanindustrial and public buildings and has been applied inmanyprojects [11 12] (Figure 2) For example the effective span ofthe Heilongjiang University of Chinese Medicine Amuse-ment and Sports Center is 39m +e application of theaforementioned floor has the following advantages com-pared with the conventional floor lower construction costless material consumption lower floor height rapid con-struction speed and many others [13 14] +erefore it canmeet the large interior space requirement of industrial andpublic buildings

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 8321836 12 pageshttpsdoiorg10115520208321836

Long-span floor structure has the characteristics of largespan small mass large stiffness large damping ratio andsmall natural frequency Human activities have a greatimpact on the long-span buildings [15] Human discomfortmay be caused by excessive vibrations under human-in-duced loads which limits the application of the U-shapedsteel-concrete floor system+erefore it is very important tocarry out the dynamic behavior and serviceability of theaforementioned floor research program

A great deal of research on human-induced vibration hasbeen conducted in [16ndash23] and many countries havepublished the codes and guidelines for the human-inducedvibration of structures However they are suitable for theconventional floor structures As the U-shaped steel-concrete composite floor structure is an innovative floor

structure in China its mass stiffness damping andboundary conditions are different from those of the con-ventional floor structures As a new form of spatial structurethere are few research results available for the vibrationmechanism of the U-shaped steel-concrete composite floor

+e purpose of this paper is to analyze the dynamicbehavior and serviceability of the U-shape steel-concretecomposite floor

To achieve this goal the following work has been done

(1) +e experimental test of the vertical vibration modelof U-shaped steel-concrete composite floor slab wasperformed by environmental excitation +e pe-destrian-induced acceleration test of the floor wascarried out under eight kinds of test conditions

Concrete slab

Bottom ribs

Top ribs

Electrical and plumbing conduitShear key

U-shaped steel plate

Figure 1 Components of the composite floor

Figure 2 Engineering examples

2 Advances in Civil Engineering

(2) +e finite element analysis of the floor was estab-lished to study its vibration behavior andserviceability

(3) +e experimental test results and FEMmodal resultsof the structure were compared based on the modalassurance criterion including the natural frequencyand the peak acceleration under pedestrian-inducedloads

2 Materials and Methods

21 Criteria of Floor Serviceability +e vertical naturalfrequency of residences and apartments office buildings andhotels and long-span public buildings should respectivelynot be less than 5Hz 4Hz and 3Hz according to theConcrete Structures Design Specification [24]

+e vertical natural frequency of the floor structureshould not be less than 3Hz according to the TechnicalRegulations on Concrete Structures in High-Rise Buildings[25] the peak value of the vibration acceleration is shown inTable 1 +e limit of peak acceleration can be chosen bylinear interpolation when the vertical natural frequency isbetween 2 and 4Hz

+e natural frequency of the floor structure should bebetween 4Hz and 8Hz according to Code of Design andConstruction of Composite Building [26] the vertical peakacceleration of residences and office buildings shoppingmall and interior gallery should respectively not be morethan 0005g and 0015g where g is the acceleration ofgravity

ATC40 shows the serviceability of the floor based ondamping ratio and peak acceleration listed in Table 2 β isdamping ratio α0 is maximum peak acceleration and g isthe acceleration of gravity

22 Project Description As shown in Figure 3 the floorconnects with the other rooms +e yield strength of theU-shaped steel is 310Nmm2 and the compressive strengthof concrete is 191Nmm2 +e plane span of the floor is252m and the total height of the floor is 12m Figure 4schematically shows the U-shaped steel-concrete compositefloor

23 Field Measurements of the Floor Slab +e experimentaltest on the vertical vibration and peak acceleration of theU-shaped steel-concrete composite floor were performed+e natural frequency damping ratio modal shape andvertical peak acceleration were obtained All of the test datawere collected by the DHC DH5910 data collector systemwhich had eight channels and seven TAISETE TST126Vaccelerometer sensors and a laptop

231 Modal Test +e test methods include the peak pickupmethod and the power spectrum principle +e maximumvalue of the frequency-response function (FRF) is near thenatural frequency [27] In this method the FRF is replacedby the power spectrum of the response If a mode

corresponds to a peak value of the power spectrum thisvalue can be used to obtain the natural frequency

+e degree of freedom of the structure is N where N isthree times of the number of floors the external load is excitedon point p and the FRF of point l can be expressed as [27]

Hlp(ϖ) 1113944N

r1

1Ker

1 minus ϖ2r1 minus ϖ2r( 1113857

2+ g2

r

+ jminus gr

1 minus ϖ2r( 11138572

+ g2r

⎡⎣ ⎤⎦

(1)

where ϖr ωωr is the frequency ratio ωr is the naturalfrequency of the structure Ker Krϕlrϕpr is the equivalentstiffness of the rth order Kr is the modal stiffness of the rthorder and ϕlr and ϕpr are the modal vectors of the rth orderat points l and p respectively

+e self-power spectrum and cross-power spectrum canbe obtained from the test data as follows

Gxx(ω) minus |H(ω)|2Gyy(ω) 0 (2)

where Gxx and Gyy are unilateral self-power spectral densityfunctions respectively +e extreme point of the self-powerspectrum can be obtained by deriving ω

In a system that can be input output and tested thenatural frequency appears in the position of the frequencyresponse function and the corresponding peak value alsoappears in the amplitude-frequency diagram +e envi-ronmental random vibration stimulating method is adoptedin this test which can only test the response signal of thesystem and calculate the frequency of the floor according tothe above formula

In the experimental test seven acceleration sensors areemployed to measure the vibration responses of the long-span floor According to the vibration characteristics of thefloor obtained by FEM and the field situation the inter-section points of the top ribs and bottom ribs are selected asthe measuring points +ere are a total of 38 measuringpoints and the distribution is shown in Figure 5 Measuringpoint 8 is the modal reference point which is a fixed pointduring the whole testing process

+e test had been done under environmental randomvibration stimulating method and any activity in the U-shapesteel-concrete composite floor was forbidden +e naturalfrequency modal shape and damping ratio can be obtainedfrom the measured responses of the structure +e mainstructure of the MNG project had been completed beforetesting Firstly the data collecting system collected and ana-lyzed the vibration responses of the floor +en the frequencyresponse function data are analyzed using the DHC modalanalysis system Finally the modal parameters were obtainedby the modal parameter identification method

+e precise locations for all measuring points were ac-quired with the measuring instrument Measuring points weremarked polished and numbered+e sampling frequency was100Hz and the analyzing frequency was 3906Hz

+e test equipment was calibrated to meet the accuracyrequirements the position of the reference point was fixed+e test data for all measuring points are acquiredsequentially

Advances in Civil Engineering 3

232 Pedestrian-Induced Acceleration A time-historyanalysis method was applied to analyze the vertical vibrationaccelerations of the floor +e peak acceleration excited bypedestrian-induced vibration can be expressed as

αp Fp

βωg (3)

Fp p0eminus 035fn (4)

where αp is the vibration acceleration of the floor (ms2) Fp

is the pedestrian-induced force with the frequency near thenatural frequency (kN) β is the damping ratio of the floor isthe impedance of the floor g is acceleration of gravity p0 isthe force by pedestrian-induced vibration and fn is thevertical natural frequency of the floor

While measuring the peak acceleration of the floor eighttest conditions were considered solo experimenter steppingsolo experimenter jumping solo experimenter walkingalong a designated route 10 experimenters in a line walkingalong a designated route 10 experimenters in a row walkingalong a designated route 12 experimenters stepping 12experimenters jumping and 12 experimenters walking in adesignated area +e weight of an experimenter is 70 kg

Twelve experimenters were selected and measured onheight weight and normal step frequency For the jumpingtests the test conditions were divided into three frequencies17Hz 21Hz and 24Hz +e acceleration measuringpoints are located near the centroid of the first modal asshown in Figure 3 the experimenters stood precisely at the

1950

times 5

= 9

750

1950

times 8

= 1

5600

1800 times 65 = 11700

1800 times 45 = 8100

6

5

4

3

2

1

12

11

10

9

8

7

18

17

16

15

14

13

25

24

23

22

21

20

30

29

28

27

26

34

33

32

31

38

37

36

35

19

1800 times 5 = 9000 1800 times 5 = 9000 1800 times 5 = 9000

1950

times 6

= 1

1700

22053

Figure 5 Measuring point layout of the composite floor

Top ribs Concrete slab

Shear key

Bottom ribs


200 200 200 200

250

250

700

1200

1400

Figure 4 Profile of the composite floor

(a) (b)

Figure 3 Long-span composite floor (a) exterior view (b) interior view

Table 2 Vertical vibration acceleration limit of floor in ATC

Activity environment β α0 (g)Residence office 002sim005 0005Shopping mall 002 0015Interior gallery 001 0015

Table 1 Vertical vibration acceleration limit of the floor

Activity environmentPeak acceleration limit (ms2)

Vertical natural frequency not more than 2Hz Vertical natural frequency not less than 4HzResidence office 007 005Shopping mall interior gallery 022 015


center point of each grid +e experimenters jumpedaccording to the frequency of the sound When the jumpingfrequency agreed well with the sound frequency the datacollecting system began to work+e excitation time of everymeasurement lasted 40 s

24 Finite Element Analyses

241 Modal Test +e beam element is used to model thecolumns top ribs bottom ribs shear keys and U-shapedsteel +e shell element is used to model the thin plate framebeams and shear walls Under the action of dynamic loadthe elastic modulus of the concrete increased by 20Poissonrsquos ratio is 02 and the damping ratio is 002+e FEMmodel is shown in Figure 6 Based on the stiffness of the topbottom layer columns the height of the topbottom layercolumns is half the height of the story +e linear dis-placement constraint in three directions is at the end of thecolumns Petyt and Mirza [28] prove that flexural stiffnessplays an important role in the natural frequency of the floor+e boundary conditions have a significant impact on thenatural frequency and dynamic responses [29]+e test flooris part of the main structure and is connected with otherstructures +e constraints excited by other connectedstructures may affect the stiffness of the floor [30] +us theboundary conditions are assumed as follows (1) theboundary conditions between the floor slab and the framebeams are fixed support ie FEM I and (2) the boundaryconditions between the floor slab and the frame beams aresimple support ie FEM II

242 Pedestrian-Induced Acceleration +e mode is de-scribed in Section 241

+e dynamic responses of jumping excitation refer to thesummarized time-history curves proposed by Liu et al [31](Figure 7) a is the jump dynamic factor b is the duration offeet on the ground and T is the jumping period Based onthe measured data when the jumping frequency fge 24Hzthen a 40 and b 045 when the jumping frequencyfle 20Hz then a 30 and b 055 +e jumping excitationis placed in the center of the shaded grid in Figure 6 and theexcitation time lasts 40 s

3 Results and Discussion

31 Model Test Results +e environmental random vibra-tion stimulating method was used in the experimental testand the DHC modal analysis system was used to analyze theacquired data +e first four orders of natural frequenciesand the damping ratio were obtained and the results arepresented in Table 3 Figure 8 displays the first four orders ofthe modal shapes

32 Peak Value of Pedestrian-Induced Acceleration +eproject is an open public space where visitors can sometimesbe relatively concentrated +e last five test conditions arecloser to the actual conditions in the building In this sectionthe eight test conditions in Section 23 are presented

Figure 9 shows these experimental test scenes +e experi-menter stood at the point 8 during solo experimenterstepping and jumping +e designated route is along thespan direction at the midpoint of the long side of the floorduring solo experimenter walking 10 experimenters in a linewalking and 10 experimenters in a row walking 12 ex-perimenters stood at the center of each grid (+) in theshadow of Figure 5 during 12 experimenters stepping andjumping +e designed area is the shadow in Figure 5 during12 experimenters walking

Table 4 lists the peak accelerations of the measuredpoints under the eight test conditions peak acceleration ateach measured point during solo experimenter stepping(mms2) peak acceleration at each measured point duringsolo experimenter jumping (mms2) peak accelerationduring solo experimenter walking along a designated route(mms2) peak acceleration 10 experimenters in a linewalking along a designated route (mms2) peak acceleration10 experimenters in a row walking along a designated route(mms2) peak acceleration at eachmeasured point during 12experimenters stepping (mms2) peak acceleration at eachmeasured point during 12 experimenters jumping (mms2)peak acceleration 12 experimenters walking in a designatedarea (mms2)

+e following points can be observed from Table 4 (1)the peak accelerations increases with the increase of the

Figure 6 FEM of the composite floor

t1 = b times Ta

times P 0

P (k

N)

Time (sec)

T

Figure 7 Simplified time history curve of jump excitation

Table 3 Measured modal data of composite floor

Order 1 Order 2 Order 3 Order 4Natural frequency (Hz) 596 862 1222 1515Damping ratio () 424 209 447 068


active frequency at the same measured point under theeight test conditions (2) Under the eight test conditionsthe peak accelerations appears at the measured point 15which is almost located in the center of the floor (3) +epeak acceleration under solo experimenter jumping islarger than that under solo experimenter stepping at thesame active frequency because the impact force of thejumping on the floor increases larger (4) 10 experi-menters in a line are more disadvantageous than 10 ex-perimenters in a row walking along the span direction atthe midpoint of the long side of the floor (5) +e ex-perimental results of 12 experimenters stepping andjumping are similar to (3) the peak acceleration is not bigwhen 12 experimenters walking in the designated areaand the peak acceleration of the floor can meet thespecification when many people walk freely (6) +ebiggest peak acceleration of measured point 15 is 0028ms2 under 12 experimenters jumping +e measured resultsof the peak acceleration meet the requirement of less than005ms2 Also the measured points near the centroid ofthe floor possess the larger peak accelerations at the samejumping frequency

+e acceleration time-history curve of measured point15 under the test conditions of a jumping frequency of24Hz with 12 experimenters is shown in Figure 10

33 Modal Analyses Results of FEM +e dynamic structuralanalysis is based on the dynamic response and the massequation of the concentrated node It is important to definethe node quality in the FEM analysis +e test floor wasundecorated and the node quality was defined as one timesthe load As listed in Table 5 because of the influence of theboundary conditions the natural frequency of FEM I ishigher than that of FEM II

Figure 11 shows the first six mode shapes obtained by theFEM I analyses

331 Comparison of Results Experimental Test and FEMAnalyses +e comparison between the experimental testsand FEM analyses under the fixed support boundary con-dition reveals the following incomplete corresponding re-lations of the mode shapes +e first two mode shapes of theFEM analyses correspond to the first two mode shapes of theexperimental tests +e fourth mode shape of the FEManalyses corresponds to the third mode shape of the ex-perimental test +e sixth mode shape of the FEM analysescorresponds to the fourth mode shape of the experimentaltest +ese results reflect the complexity of the test envi-ronment and indicate some mode shapes cannot be excitedMoreover some signal strengths are too weak to be acquired

As shown in Table 6 the deviations between FEM I andthe experimental tests are less than 5 +e deviationsbetween FEM II and the experimental tests are larger themaximum error is minus 3314 and the minimum error isminus 181 +e results show that the boundary condition ofFEM I is in accordance with the actual condition +e testedfloor is connected with adjacent structures which constrainthe rotation of the floor so the boundary condition ap-proximates the fixed support +us the restraint effect ofadjacent structures excitation cannot be ignored in the FEManalysis

+rough the comparison between the experimental testmode shapes and FEM I it is found that the results of FEM Iare basically in agreement with the ideal situation and thecenter of the experimental mode is slightly shifted to the leftbecause of constraining forces from the connected structureswhich are the left crossed shear keys and the thickerU-shaped steel +e mode shape curves of the experimental

(a) (b)

(c) (d)

Figure 8 Measured mode shape of composite floor (a) order 1 (b) order 2 (c) order 3 (d) order 4


test are smooth and the mode shapes curves of FEM I haveedges +is difference is due to the boundary conditions +eboundary condition in the FEM I is fixed support which theactual condition cannot meet

+e natural frequency of the experimental test (596Hz)or the FEM I (618Hz) exceeds the specification requirementof 3Hz +e results show that the U-shaped steel-concrete

composite floor is suitable for long-span floors andmeets thespecification requirement of serviceability

332 Comparison of Results Similarity Metric Computation+e similarity between experimental test data and FEM datais estimated by using the modal assurance criterion [32]

(a) (b)

(c) (d)

(e) (f )

(g) (h)

Figure 9 Experimental test (a) solo experimenter stepping (b) solo experimenter jumping (c) solo experimenter walking along adesignated route (d) 10 experimenters in a line walking along a designated route (e) 10 experimenters in a row walking along a designatedroute (f ) 12 experimenters stepping (g) 12 experimenters jumping (h) 12 experimenters walking in a designated area


Table 4 +e peak accelerations of the measured points under the eight test conditions

Measuring point 8 9 14 15 16 22 27(a)17Hz 137 098 059 085 089 065 04221Hz 178 130 092 132 127 084 07324Hz 267 274 106 312 176 214 081(b)17Hz 144 102 078 112 115 081 05321Hz 239 157 196 144 142 091 07824Hz 341 282 121 373 196 225 126(c)17Hz 197 140 056 062 151 107 06021Hz 310 335 074 087 220 238 19124Hz 446 403 502 626 554 409 255(d)17Hz 277 231 199 275 239 162 18921Hz 839 818 504 735 864 747 60524Hz 1065 987 1068 1427 1233 699 395(e)17Hz 234 222 177 244 224 110 06321Hz 311 344 317 439 509 141 10224Hz 680 647 674 749 648 634 497(f )17Hz 1217 1306 1267 1222 1239 1187 113221Hz 1357 1363 1301 1409 1400 1272 114824Hz 1740 2046 1846 2242 2138 2076 1391(g)17Hz 1801 2084 2023 2156 2091 2100 126921Hz 2012 2183 2124 2302 2181 2208 148324Hz 2145 2589 2354 2823 2761 2742 1866(h)17Hz 161 123 082 145 124 106 07521Hz 267 276 272 335 344 328 23924Hz 695 602 706 964 778 764 519

Table 5 Calculated frequencies of two types of FEM

Order 1 Order 2 Order 3 Order 4 Order 5 Order 6FEM I 618 889 1168 1226 1445 1586FEM II 436 706 786 943 986 1013

ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)

Simulation curveExperimental curve

Figure 10 Time history of the acceleration response of point 15


(MAC) In this section MAC is used to verify the experi-mental test results

ϕa is the mode vector of the experimental test and ϕb isthe corresponding mode vector of FEM I or FEM II +esimilarity can be calculated as

MAC ϕa ϕb( 1113857 ϕT

aϕb1113872 11138732

ϕTaϕa1113872 1113873 ϕT

b ϕb1113872 1113873 (5)

If the two mode shapes are similar the MAC value is 1+ere are 38 measuring points in this experimental

test the first fourth order mode vectors of each measuredpoints are extracted In addition the first second fourthand sixth order mode vectors of FEM I or FEM II areselected After extraction the data are normalized +eMAC values of the experimental test and FEM I or FEM IIare calculated by (5) +e results are shown in Table 7 +e

similarity between the experimental test and FEM I isalmost all over 08 On the whole the experimental testresults are reliable +e similarity between FEM I and theexperimental test is better than that between FEM IIandthe experimental test

34 Comparison of Results between Experimental Test andFEM In this section the acceleration time-history curvesof three measured points (No 9 No 15 and No 27) arecompared with that of FEM during 12 experimentersjumping under a frequency 24 Hz +ese results are

(a) (b)

(c) (d)

(e) (f )

Figure 11 Mode shapes of FEM I (a) order 1 (b) order 2 (c) order 3 (d) order 4 (e) order 5 (f ) order 6

Table 6 Comparison of FEM and experimental test frequency

Mode shape Field test frequency (Hz)FEM I (fixed) FEM II (simple)

Frequency (Hz) Relative error () Frequency (Hz) Relative error ()Order 1 596 618 356 436 minus 2685Order 2 862 889 304 706 minus 1810Order 3 1168 786Order 4 1222 1226 008 943 minus 2283Order 5 1445 986Order 6 1515 1586 448 1013 minus 3314

Table 7 Mode shape similarity between FEM and field test

Order 1 Order 2 Order 3 Order 4FEM I and tests 0824 0793 0872 0841FEM II and tests 0751 0712 0773 0681


plotted in Figure 12 +e results indicate that the accel-eration time-history curves agree well with the experi-mental test curves

Figure 13 compares the peak accelerations between theexperimental test data and the FEM data +e results showthat the experimental results are higher than those of FEM+ismay be due to the fact that the FEMmodel only the floor

tested where the experimental test floor model is connectedto other rooms and partitions in some places

4 Conclusions

In this paper the dynamic responses of the U-shaped steel-concrete composite floor are studied by the method of

ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)


(a)

Acc

(mm

s2 )

Time (sec)

ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40


(b)

Acc

(mm

s2 )

ndash30

ndash20

ndash10

0

10

20

30

0 10 20 30 40Time (sec)


(c)

Figure 12 Time-histories of the acceleration response (a) point 9 (b) point 15 (c) point 27

15

20

25

30

5 10 15 20 25 30

Acc

(mm

s2 )

Monitoring point number


Figure 13 Peak acceleration at each measured point


experimental tests and FEM analyses in the MNG projectBased on the results obtained from this investigation thefollowing significant conclusions are drawn

(1) +e natural frequencies obtained by the experi-mental test and FEM Ianalyses are 596Hz and618Hz respectively +e results meet the specifi-cation requirement of 3Hz +us the U-shapedsteel-concrete composite floor can be used in long-span floors and the natural frequency can meet thespecification requirement

(2) In the FEM modal analyses the natural frequency ofthe FEM Ianalyses is similar to that of the experi-mental test when the boundary conditions of thefloor slabs and the frame beams are fixed supportsthe natural frequency deviation of the FEM II an-alyses and the experimental test is larger when theboundary conditions are simple supports +us therestraint effect of adjacent structures excitationcannot be ignored in FEM analyses

(3) +e MAC is applied to estimate the similarity be-tween the experimental test data and the FEM data+e vectors extracted are the first four ordersrsquo modevectors of the experimental test and the first- sec-ond- fourth- and sixth-order mode vectors of FEMI and FEMII +e MAC values of the experimentaltest and FEM I are almost all over 08 and the ex-perimental test results are reliable +e similaritybetween FEM I and the experimental test is betterthan that between FEMII and the experimental test

(4) +e peak accelerations are measured under eight testconditions +e peak accelerations increases with theincrease of the active frequency at the same mea-sured point because the impact force on the floorincreases largely and the peak accelerations is almostlocated in the center of the floor +e biggest peakacceleration is 0028ms2 under 12 experimentersjumping which can meet the specification require-ment of less than 005ms2

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is research was supported by the Natural Science Foun-dation of Guizhou Province (project no [2018]1038) theNatural Science Foundation of Department of Education ofGuizhou Province (project no [2015]430) and the Intro-duction of Talents Research Program of Guizhou University(project no [2016]16)

References

[1] H Y Huang W S Chang and K M Mosalam ldquoFeasibility ofshape memory alloy in a tuneable mass damper to reduceexcessive in-service vibrationrdquo Structural Control and HealthMonitoring vol 24 no 2 pp 18ndash58 2017

[2] B Ellingwood and A Tallin ldquoStructural serviceability floorvibrationsrdquo Journal of Structural Engineering vol 110 no 2pp 401ndash418 1984

[3] P Aleksandar R Paul W Peter et al ldquoDynamic modelling ofpost-tensioned concrete floors using finite element analysisrdquoFinite Elements in Analysis and Design vol 37 no 4pp 305ndash323 2001

[4] G S A Silva Jose A L De Andrade Sebastiao and D C LopesElvis ldquoParametric modelling of the dynamic behavior of asteelndashconcrete composite floorrdquo Engineering Structuresvol 75 pp 327ndash339 2014

[5] A V A Mello J G S Da Silva P C G D S VellascoS A L De Andrade and L R O De Lima ldquoDynamic analysisof composite systemsmade of concrete slabs and steel beamsrdquoJournal of Constructional Steel Research vol 64 no 10pp 1142ndash1151 2008

[6] Q H Han Y H Wang J Xu et al ldquoNonlinear numericalanalysis of elastic concrete-steel composite beamsrdquo Journal ofTianjin University vol 47 pp 91ndash95 2014

[7] W D Varela and R C Battista ldquoControl of vibrations in-duced by people walking on large span composite floordecksrdquo Engineering Structures vol 33 no 9 pp 2485ndash24942011

[8] S S De Silva and D P +ambiratnam ldquoDynamic charac-teristics of steel-deck composite floors under human-inducedloadsrdquo Computers and Structures vol 87 no 17 pp 1067ndash1076 2009

[9] J G S Da Silva P C G D S Vellasco S A L De AndradeF J D C P Soeiro and R N Werneck ldquoAn evaluation of thedynamical performance of composite slabsrdquo Computers ampStructures vol 81 no 18-19 pp 1905ndash1913 2003

[10] E El-Dardiry and T Ji ldquoModelling of the dynamic behavior ofprofiled composite floorsrdquo Engineering Structures vol 28no 4 pp 567ndash579 2005

[11] J J Liu K J Ma Y H Wei et al ldquoComfort degree analysisand field measurement of single-span multistoried large-spansteel grid cassette structural composite open web floorsrdquoBuilding Structure vol 46 no 16 pp 79ndash82 2016

[12] L Jiang K J Ma H G Zhang et al ldquo+e dynamic propertyand comfort degree study on the steel-concrete compositevierendeel sandwich platerdquo Earthquake Engineering andEngineering Dynamics vol 37 no 6 pp 122ndash131 2017

[13] R M Lawson J Lim S J Hicks and W I Simms ldquoDesign ofcomposite asymmetric cellular beams and beams with largeweb openingsrdquo Journal of Constructional Steel Researchvol 62 no 6 pp 614ndash629 2006

[14] S Hicks ldquoCurrent trend in modern floor constructionrdquoBritish Constructional Steelwork Association vol 11 no 1pp 32-33 2003

[15] S Ivanovic A Pavic and P Reynolds ldquoVibration comfort-ableness of footbridges under human-induced excitation aliterature reviewrdquo Journal of Sound and Vibration vol 279pp 1ndash74 2005

[16] V Racic A Pavic and J M W Brownjohn ldquoExperimentalidentification and analytical modelling of human walkingforces literature reviewrdquo Journal of Sound and Vibrationvol 326 no 1-2 pp 1ndash49 2009


[17] S Yao J R Wright A Pavic and P Reynolds ldquoExperimentalstudy of human-induced dynamic forces due to jumping on aperceptibly moving structurerdquo Journal of Sound and Vibra-tion vol 296 no 1-2 pp 150ndash165 2006

[18] S C Kerr and N W M Bishop ldquoHuman induced loading onflexible staircasesrdquo Engineering Structures vol 23 no 1pp 37ndash45 2001

[19] V Racic and A Pavic ldquoMathematical model to generate near-periodic human jumping force signalsrdquo Mechanical Systemsand Signal Processing vol 24 no 1 pp 138ndash152 2010

[20] V Racic J M W Brownjohn and A Pavic ldquoReproductionand application of human bouncing and jumping forces fromvisual marker datardquo Journal of Sound and Vibration vol 329no 16 pp 3397ndash3416 2010

[21] V Racic and A Pavic ldquoStochastic approach to modelling ofnear-periodic jumping loadsrdquoMechanical Systems and SignalProcessing vol 24 no 8 pp 3037ndash3059 2010

[22] V Racic and J M W Brownjohn ldquoStochastic model of near-periodic vertical loads due to humans walkingrdquo AdvancedEngineering Informatics vol 25 no 2 pp 259ndash275 2011

[23] S-I Nakamura T Kawasaki H Katsuura and K YokoyamaldquoExperimental studies on lateral forces induced by pedes-triansrdquo Journal of Constructional Steel Research vol 64 no 2pp 247ndash252 2008

[24] China Construction Industry Press Concrete Structure DesignSpecification GB 50010-2010 China Construction IndustryPress Beijing China 2010

[25] China Construction Industry Press Technical Regulations onConcrete Structure in High-Rise Buildings JGJ 3-2010 ChinaConstruction Industry Press Beijing China 2010

[26] China Planning Press Code of Design and Construction ofComposite Buildings CECS 273 China Planning Press Bei-jing China 2010

[27] G De Rocek ldquoBenchmark study on system identificationthrough ambient vibration measurementsrdquo in Proceedings ofthe 18th IMAC pp 1106ndash1112 San Antonio TX USAFebruary 2000

[28] M Petyt and W H Mirza ldquoVibration of column-supportedfloor slabsrdquo Journal of Sound and Vibration vol 21 no 3pp 355ndash364 1972

[29] P Aleksandar and R Paul ldquoVibration comfortableness oflong-span concrete building floorsrdquo e Shock and VibrationDigest vol 34 no 7 pp 191ndash211 2002

[30] X Zhou J Liu L Cao and J Li ldquoVibration serviceability ofpre-stressed concrete floor system under human activityrdquoStructure and Infrastructure Engineering vol 13 no 8pp 967ndash977 2017

[31] J Liu C Xiao C Pan et al ldquoInvestigation on response of floorvibration under jumping and walking excitationrdquo BuildingStructure vol 38 no 11 pp 108ndash110 2008

[32] R J Allemang and D L A Brown ldquoCorrelation coefficient formodal vector analysisrdquo in Proceedings of the 1st IMACpp 110ndash116 Orlando FL USA 1982


Long-span floor structure has the characteristics of largespan small mass large stiffness large damping ratio andsmall natural frequency Human activities have a greatimpact on the long-span buildings [15] Human discomfortmay be caused by excessive vibrations under human-in-duced loads which limits the application of the U-shapedsteel-concrete floor system+erefore it is very important tocarry out the dynamic behavior and serviceability of theaforementioned floor research program

A great deal of research on human-induced vibration hasbeen conducted in [16ndash23] and many countries havepublished the codes and guidelines for the human-inducedvibration of structures However they are suitable for theconventional floor structures As the U-shaped steel-concrete composite floor structure is an innovative floor

structure in China its mass stiffness damping andboundary conditions are different from those of the con-ventional floor structures As a new form of spatial structurethere are few research results available for the vibrationmechanism of the U-shaped steel-concrete composite floor

+e purpose of this paper is to analyze the dynamicbehavior and serviceability of the U-shape steel-concretecomposite floor

To achieve this goal the following work has been done

(1) +e experimental test of the vertical vibration modelof U-shaped steel-concrete composite floor slab wasperformed by environmental excitation +e pe-destrian-induced acceleration test of the floor wascarried out under eight kinds of test conditions

Concrete slab

Bottom ribs

Top ribs

Electrical and plumbing conduitShear key


Figure 1 Components of the composite floor

Figure 2 Engineering examples














Hlp(ϖ) 1113944N

r1

1Ker


2+ g2

r

+ jminus gr

1 minus ϖ2r( 11138572

+ g2r

⎡⎣ ⎤⎦

(1)












αp Fp

βωg (3)






1950

times 5

= 9

750

1950

times 8

= 1

5600

1800 times 65 = 11700

1800 times 45 = 8100

6

5

4

3

2

1

12

11

10

9

8

7

18

17

16

15

14

13

25

24

23

22

21

20

30

29

28

27

26

34

33

32

31

38

37

36

35

19


1950

times 6

= 1

1700

22053



Shear key

Bottom ribs


200 200 200 200

250

250

700

1200

1400


(a) (b)




















t1 = b times Ta

times P 0

P (k

N)

Time (sec)

T












(a) (b)

(c) (d)







(a) (b)

(c) (d)

(e) (f )

(g) (h)







ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)







aϕb1113872 11138732

ϕTaϕa1113872 1113873 ϕT

b ϕb1113872 1113873 (5)





(a) (b)

(c) (d)

(e) (f )











4 Conclusions


ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)


(a)

Acc

(mm

s2 )

Time (sec)

ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40


(b)

Acc

(mm

s2 )

ndash30

ndash20

ndash10

0

10

20

30

0 10 20 30 40Time (sec)


(c)


15

20

25

30

5 10 15 20 25 30

Acc

(mm

s2 )










Data Availability




Acknowledgments


References















































Hlp(ϖ) 1113944N

r1

1Ker


2+ g2

r

+ jminus gr

1 minus ϖ2r( 11138572

+ g2r

⎡⎣ ⎤⎦

(1)












αp Fp

βωg (3)






1950

times 5

= 9

750

1950

times 8

= 1

5600

1800 times 65 = 11700

1800 times 45 = 8100

6

5

4

3

2

1

12

11

10

9

8

7

18

17

16

15

14

13

25

24

23

22

21

20

30

29

28

27

26

34

33

32

31

38

37

36

35

19


1950

times 6

= 1

1700

22053



Shear key

Bottom ribs


200 200 200 200

250

250

700

1200

1400


(a) (b)




















t1 = b times Ta

times P 0

P (k

N)

Time (sec)

T












(a) (b)

(c) (d)







(a) (b)

(c) (d)

(e) (f )

(g) (h)







ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)







aϕb1113872 11138732

ϕTaϕa1113872 1113873 ϕT

b ϕb1113872 1113873 (5)





(a) (b)

(c) (d)

(e) (f )











4 Conclusions


ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)


(a)

Acc

(mm

s2 )

Time (sec)

ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40


(b)

Acc

(mm

s2 )

ndash30

ndash20

ndash10

0

10

20

30

0 10 20 30 40Time (sec)


(c)


15

20

25

30

5 10 15 20 25 30

Acc

(mm

s2 )










Data Availability




Acknowledgments


References




































αp Fp

βωg (3)






1950

times 5

= 9

750

1950

times 8

= 1

5600

1800 times 65 = 11700

1800 times 45 = 8100

6

5

4

3

2

1

12

11

10

9

8

7

18

17

16

15

14

13

25

24

23

22

21

20

30

29

28

27

26

34

33

32

31

38

37

36

35

19


1950

times 6

= 1

1700

22053



Shear key

Bottom ribs


200 200 200 200

250

250

700

1200

1400


(a) (b)




















t1 = b times Ta

times P 0

P (k

N)

Time (sec)

T












(a) (b)

(c) (d)







(a) (b)

(c) (d)

(e) (f )

(g) (h)







ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)







aϕb1113872 11138732

ϕTaϕa1113872 1113873 ϕT

b ϕb1113872 1113873 (5)





(a) (b)

(c) (d)

(e) (f )











4 Conclusions


ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)


(a)

Acc

(mm

s2 )

Time (sec)

ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40


(b)

Acc

(mm

s2 )

ndash30

ndash20

ndash10

0

10

20

30

0 10 20 30 40Time (sec)


(c)


15

20

25

30

5 10 15 20 25 30

Acc

(mm

s2 )










Data Availability




Acknowledgments


References















































t1 = b times Ta

times P 0

P (k

N)

Time (sec)

T












(a) (b)

(c) (d)







(a) (b)

(c) (d)

(e) (f )

(g) (h)







ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)







aϕb1113872 11138732

ϕTaϕa1113872 1113873 ϕT

b ϕb1113872 1113873 (5)





(a) (b)

(c) (d)

(e) (f )











4 Conclusions


ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)


(a)

Acc

(mm

s2 )

Time (sec)

ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40


(b)

Acc

(mm

s2 )

ndash30

ndash20

ndash10

0

10

20

30

0 10 20 30 40Time (sec)


(c)


15

20

25

30

5 10 15 20 25 30

Acc

(mm

s2 )










Data Availability




Acknowledgments


References










































(a) (b)

(c) (d)







(a) (b)

(c) (d)

(e) (f )

(g) (h)







ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)







aϕb1113872 11138732

ϕTaϕa1113872 1113873 ϕT

b ϕb1113872 1113873 (5)





(a) (b)

(c) (d)

(e) (f )











4 Conclusions


ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)


(a)

Acc

(mm

s2 )

Time (sec)

ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40


(b)

Acc

(mm

s2 )

ndash30

ndash20

ndash10

0

10

20

30

0 10 20 30 40Time (sec)


(c)


15

20

25

30

5 10 15 20 25 30

Acc

(mm

s2 )










Data Availability




Acknowledgments


References







































(a) (b)

(c) (d)

(e) (f )

(g) (h)







ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)







aϕb1113872 11138732

ϕTaϕa1113872 1113873 ϕT

b ϕb1113872 1113873 (5)





(a) (b)

(c) (d)

(e) (f )











4 Conclusions


ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)


(a)

Acc

(mm

s2 )

Time (sec)

ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40


(b)

Acc

(mm

s2 )

ndash30

ndash20

ndash10

0

10

20

30

0 10 20 30 40Time (sec)


(c)


15

20

25

30

5 10 15 20 25 30

Acc

(mm

s2 )










Data Availability




Acknowledgments


References







































ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)







aϕb1113872 11138732

ϕTaϕa1113872 1113873 ϕT

b ϕb1113872 1113873 (5)





(a) (b)

(c) (d)

(e) (f )











4 Conclusions


ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)


(a)

Acc

(mm

s2 )

Time (sec)

ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40


(b)

Acc

(mm

s2 )

ndash30

ndash20

ndash10

0

10

20

30

0 10 20 30 40Time (sec)


(c)


15

20

25

30

5 10 15 20 25 30

Acc

(mm

s2 )










Data Availability




Acknowledgments


References






































aϕb1113872 11138732

ϕTaϕa1113872 1113873 ϕT

b ϕb1113872 1113873 (5)





(a) (b)

(c) (d)

(e) (f )











4 Conclusions


ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)


(a)

Acc

(mm

s2 )

Time (sec)

ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40


(b)

Acc

(mm

s2 )

ndash30

ndash20

ndash10

0

10

20

30

0 10 20 30 40Time (sec)


(c)


15

20

25

30

5 10 15 20 25 30

Acc

(mm

s2 )










Data Availability




Acknowledgments


References






































4 Conclusions


ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40

Acc

(mm

s2 )

Time (sec)


(a)

Acc

(mm

s2 )

Time (sec)

ndash30

ndash20

ndash10

0

10

20

30

0 5 10 15 20 25 30 35 40


(b)

Acc

(mm

s2 )

ndash30

ndash20

ndash10

0

10

20

30

0 10 20 30 40Time (sec)


(c)


15

20

25

30

5 10 15 20 25 30

Acc

(mm

s2 )










Data Availability




Acknowledgments


References








































Data Availability




Acknowledgments


References



































dynamicbehaviorandserviceabilityanalysisofanewtypeof u … · 2020. 6. 30. · duced loads, which...

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