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NOTES

Dynam ic testing of a n open web steel joist floorM . Y . T . C H A N N D M . S . C H E U N G

PllOlic Works Canndcr, Ormrvn, OI I ~ . , nrznda K I A OM2Received June 27, 1980

Revised manuscript accepted February 1 1 , 198 1A non-composite open web steel joist warehouse floor was tested to determine its dyn amic characteristics and maximustrain levels under actual operation al conditions. Altogethe r 28 tests were carried out. The strain and acceleration informatifor each test was recorded on strip chart and magnetic tape recorders. The recorded data were examined and analyzed througa dual channel spectrum analyzer and the results were compared with calculated values. Good agreements are noted.On a soumis un plancher d'entrep6 t, port6 sans goujonnage par des poutrelles d'acier en treillis, a des essais destin es a faiconnaitre ses param ttres dynamiques et ses deformations maximales en service normal. Au total, on a effectue 28 essais. Ldeformations et les accClCrations ont fait I'objet d ' u n enregistrement dou ble, par voie graph ique et sur ruban magndtique,cours de chaque ess ai. Ces enreg istrements ont etC i tudie s au moyen d'un analyseur spectral i deux canau x. On a note ubonne concordance entre les relev6s expkrimentaux et les risultats dcs calculs. [Traduit par la revu

Can. I. Ci v . Eng . . 8 . 257-262 (1981)Introduction points. Th e concrete deck has a thickness of 76 mm n

B~~~~~~~ (heir higher f lexibil i tyan d l o w e r da lnp ing is reinforced with a wire mesh. Because the originv a l u e s , l o n g span floorsof l igh ter cons t rL lc t ion an shop drawings were not available, the exact size ani n problems of objectionable f loor make of the joists canno t be accurately ascertained. S ivibra t ion ( L ~ ~ ~ ~ ~966: 1974; an d ~~i~~~ n l e a s ~ ~ r e n ~ e n tf the joists gave an approximate mome1976) . ~ ~ i ~ ~ lf this type o f c o n s t r L l c t i o n ar e open we b of inertia of 9 . I6 x lo7 111111~~n d cro ss sectional ars t e e l joist f l o o r s , of ourse , objectionable floor i b r a of 1610 mm'. The floor was designed for a live load

( i o n s can r e s u l t of hulna n ac t iv i t ie s fo r 7.18 kPa and a dead load of 2.49 kPa. Th e floor haswhich the *lOorser e not r e a l l y designed, (his case , bare concrete finish with ceiling panels attached to ithe dynanlic na tu re of the applied loads may a lso over- underside. Cracks in the con crete floor w ere quite sistress (he joists a nd tilreaten th e sa fe ty of th e f loor , nificant and visible. I t is understood that thc crac

hi^ note describes the llleasurelllent for were caused by a heavy forklift (net vehicle weigdete l-l l l ining yna mi ccharacter is t icsan d s t ra in leve ls of about 17.8 kN) ;I fe w y ea rs a go . Be c a ~ ~ s ef the seveopen web steel joist f l o o r s , ~ ~ ~ ~ h ~ ~t i n v e s t i g a t e s cracks, and to a cer ta in extent , the ~~ndesirablelothe po ssibility and reliability of e x t r a c t i n g infor. vibrations, the use of the heavy forklift has since beenlation from acceleration signals. This techniq~~es very p r o h i b i t e d .useful, as the installation of strain gages (us ed primarilyfor s tress measurements) is gene~xlly ery t ime con- Description of the testsum ing and the steel joists can at times be inaccessible. A bay of the warehouse was cleared for the testinThis note is a brief summ ary of the test, the data program. A light forklift (net vehicle weight abocollection and analysis metho ds, and some compa risons 5.3 kN) and a heavy forklift (net vehicle weight abobetween calculated and obse rved results. 17.8 kN ) were used to excite the floo rs. The heavforklift was not loaded while the light forklift carriedDescription of the floor load of about 3.1 k N. T he tests involved a single forThe floor chosen for this study is a non-composite lift trave lling the floor eith er in circles o r in a set direopen web steel joist warehouse floor. A typical bay of tion (parallel or perpendicular to the joists ). Som eof ththe floor measures 9.15 x 9 .15 rn. The 610 mni deep tests required the operator to make abrupt stops durinjoists spanning the 9.15 m bays are spaced at 610 nlm the run. Impact tests were performed by dropping thcentre to centre. The joists are supported on W W F 3.1 kN load off the light forklift at a height of approx686 x 147 girders and tie joists are located between the mately 76 m m . A summary of the various test casbays . Bridgings are provided at the quarter and nlid considered is shown in Tab le 1.

03 15- 146818 11020257-06$01.00100 98 1 National Research Council of CanadaIConseil national de recherches du Canada

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CAN. J . C I V . ENG. VOL. 8. 1981TABLE . Warehouse floor vibration tests ture compensating gage . Each gage was equipped witan individual amplifier placed in the immediate vicinitType of test Test number" of the gage. The gages were installed in the usua

Impact parallel to joists 1, 2, 3Impact perpendicular to joists 4, 5Roving parallel to joists 6, 7, 22Roving perpendicular to joists 10, 11, 18, 19Roving in circles 14, 15, 25, 26Roving parallel to joists and braking 8, 9, 23, 24Roving perpendicular to joistsand braking 12, 13, 20, 21Roving in circles and braking 16, 17, 27Static measurement of strains dueto storage materials 28

*Light forklift used for tests nos. 1-17; heavy forklift used fortests nos. 18-27.

610 mm S.S. OWSJ\

U UW W F 68 6 mmX147 kg

A Accelerometers 0 train GagesFIG . I . Instrumentation layout for floor vibration te st.Strain gages are attached to bottom cord of the simply sup-ported open web steel joist (S.S. OWSJ).

InstrumentationThe accelerations of the floor were measured withaccelerometers, while strain gages w ere used to monitorthe strains in the joists. Th e 4 accelerom eters and 3strain gages used in the testing program were laid out asshown in Fig. 1 . The strain gages employed wereMicro-Measurements CEA-06-250UW-350 foil gages.They have a 350 5 1 resistance and a rated gage facto r of2.125 * 5%. The gages were connected in a standard114 bridge configuration, without an external tempera-

manner, the surface being prepared by grinding anbuffing, followed by degreasing prior to gage bondingTh e accelerometers used were Columbia Instrumentservo SA 107 FDC accelerometers. These accelerometers hav e a sensitivity of 5 V/g and a rated noise flooof 0.1 mV rms in the frequency range of dc- 100 HzThe accelerometer output was connected to a transdution filter - amplifier unit; this provides high and lowpass filters with settings of 0.5 , 1 , and 10 Hz and 1, 120, and 50 Hz respectively, as well as gains of 1, 1and 100. Floor mounts in the form of steel angles, eacweighing about 13.3 N were used to secure the acceerometers to the floor.A Racal Thermion ic Store 7D FM ta pe recorder ana Honeywell visicorder were employed in the datacquisition. The strain data were simultaneouslrecorded on the visicorder and the tape recorder. Thacceleration signals were recorded on the tape recordand also displayed as dynamic displacements on thvisicorder. This was achieved by connecting the acceerom eter output simultaneous ly to a multichanndouble integrator.

Data analysisTh e data recorded o n the magnetic tape were playeback through a Nicolet Scientific Inc. mod el 660A duchannel spectrum analyzer of the FFT type. For resulthat required plotting , the data were transferred to a darecorder adaptor which has dual mini floppy dis

drives, and is connected to a HP digital pen plotter.(t r) St/-trill dtrtnBoth the strains and the dynamic displacements cabe read off the visicorder traces by using the appropriascale factor. W ith the exception of the test cases involing impact loadings and sudden stopping of the forklifts, the majority of the strain data were essentiallstatic. So me of the critical cases for strain gage no. were digiti zed through the an alyzer and th e results werplotted for presentation in this note.The results of test no. 4 are shown in Fig. 2, wherthe maxim um static or crawl strain is seen to be 160 p cThe impact strain history is shown in F ig. 3 , where aexpanded time scale has been used. The maximumdynamic strain as measured from Fig. 3 has a peak peak value of 928 WE , thus the maximum strain exprienced during this test was 544 p c or 108.8 MP(assuming E , = 200 GPa) .The results of test no. 21 are shown in Fig. 4. T hmaximu m crawl strain in this case is abou t 135 p c . T hstrain history of the second braking action is shown iFig. 5 using a larger time scale. The maxim um dynam

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NOTES 25

FIG.2. Strain history, test no. 4, gage no. 2 . FIG.5. Strain history, test no. 21 , gage no. 2.

40032 024 016080+

b 0 - -2 -80

-160-240 -'-320 ---400

0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00Time ( s l

------

--

-r , - ---

-0.60 I0.25 0.50 0 .75 1.00 1.25 1.50 1.75 2.0

Time ( s )

2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0T ~ m e s ) T ime ( s )

FIG.3. Strain history, test no. 4, gage no. 2. FIG. 6. Acceleration history, test no. 4, accelerometno. 1 .

-320 I-400 t

5.0 10.0 15.0 20.0 25.0 30.0 35. 0 40.0Time ( s )

FIG.4. Strain history, test no. 21, gage no. 2.strain measures 260 pc peak to peak, thus the maxi-mum strain experienced was 265 pc or 53 MPa.Static strains due to the normal floor load were alsorecorded at the end of the dynamic tests. These valueswere 131 , 160, and 15 0 pc, respectively, for straingages nos. 1, 2, and 3.

The impact or dynamic amplification factor (expressed as a ratio of the total strain vs. the crawl strainin the 2 cases shown are exceptionally high (200 and340%). The solnewhat lower crawl strain observed itest no. 21 is due to the heavy forklift's larger axle anwheel spacin gs, and als o to its position relative to straigage no . 2 at the mom ent of braking. From the resultshown, it is obvious that impact loading and suddebraking of the forklift can produce strains that are morthan 3 times those due to identical loads but appliestatically.(O) Accelerrrtion clrttrrTh e acceleration data recorded on the magnetic tapwere digitized and examined through the NSI 600analyzer. The results were found to have essentially thsame trend as the strain data, i. e. , significant levels oacceleration were observed only when im pact or suddestopping of the forklift occurred. Plots of the accelertion histories of 2 such test cases are shown in Figs.an d 7 . Figure 6 show s that the peak acceleration of teno. 4 as measured by accelerometer no. 1 was 0.5 6s

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CAN. J. CIV. ENG

FIG. 7 . Acceleration history, test no. 2 7 , accelerometer

Acc.1.rOmel.r No . 1

t f i A c c e l e r o m l f e r No . 2 +20 40 60 80 100 120 140 160 180 200

Frequency (Hz)FIG. 8 . Fourier spectra of impact vibration, test no. 4,accelerometers nos. 1 and 2 .

From Fig. 7, i t can be seen that the peak accelerationexperienced by acceleronieter no. 2 during test no. 27was 0 .16g.( c ) F r e q ~ i e t z c i e sThe recorded acceleration signals were examin ed fortheir frequency contents by using the FFT function ofthe analyzer. The FFT procedure yields a conlplexfunction in the frequency domain, from which thenatural frequencies of the structure can generally beidentified by the various peaks of the Fourier ampli-t ud es . F i g ~ ~ r eshows the Fo urier spectra for test no. 4obtained from accelerometers no. 1 and 2. Because thetime domain signal was an i mp ~l lse f a very shortduration, the spectra are broad band and have very fewdistinct peaks. T o identify the natural frequencies fromFig. 8, it was necessary to digitize each spectrum andfeed the results into a minicomputer. The averageamplitude of the spectrum was comp uted and used as athreshold. Th e 5 largest am plitudes in the spectrum thatexceeded the threshold were selected. Using thisapproach, the natural frequencies corresponding to the

I. VOL. 8, 19810 320 1 I

0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.0Time ( 5 )

FIG.9. 6 Hz decay curve, test no. 4 , accelerometer no. 1.

-0.32-0.40 1

0.25 0.50 0.75 1.00 125 1.50 1.75 2.0Time ( 5 )

FIG. 10. 11 Hz decay curve, test no. 4, accelerometno. 1.first and second mode of floor vibration were found tbe 5.6 and 10.8 Hz, respectively. The high frequencieshown in the plot are generally of no interest as far astructural vibration is concerned, because they arusually very highly damped. To obtain additional anmore accurate frequency information, other means oexcitation (such as frequency sweeps with a shakeshould be employed.(11) D ~ ~ r t l p i t l g. C I ~ ~ O SThe modal damping ratios are generally determineusing the half power (o r bandwidth) method (Clougand Penzien 1975). But because the frequencies arclosely spaced and the pea ks are not distinct, the damping ratios were determined by examining the decacurves. This involved displaying the acceleratiosignals after filtering them through a narrow bandpasfilter set at the desired frequencies. The bandpasfrequencies were set at approximately 6 an d 1 1 Hz fothe first and second mode, respectively. The results oaccelerometer no. 1 are shown in Figs. 9 and 10 for teno . 4. The damping ratios can be determined from th

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STATIC CALCULATION

I - 8.157 X 10'mrn4Moment - 4. 2 X 2.87 - 11.2 kN.rnStress - M y A - 11.2 X 0 . 3 0 4 8 / 19.157 X l o - ' ) - 3 7 . 3 3 M P U

NOTES 26

FREQUENCY CALCULATION0.6

11 mode nuturd frequency for S.S. bean 18 0 -&[ElWhere O s the natural frequency In Hz 2~ mL - span - 9.15 rnU - flexural rigidity - 2 .0 X 10 X 8.157 X 16' - 1 8 3 0 0 k ~ . r n 'rn - rnws/unit length - 2.49 X 0.81/ 9.808 - 0.155 kN.seoL/ mEThe frequency calculated with the d o v e values is 8.45 Hz.

FIG. 1 1. Beam theory calculations.

StaticDeflectionDynmicDeflection

Static deflection a mid-span b eaed on simple beam calculatio n b 4.597 rnmDynamic deflection a mid-.pan from integra tor is 22.86 rnm pk. to pk.Total displwernsnt a mid-spm is 4.597 + 11.43 - 16.027 rnmAssume di~place ment curve is Y - 16.027 sin X/9.15)Moment - -El$ - 18314 X X 0.016 - 34.6 kN.m

dX 9.15Stress - My/l - 34.60 X 0.3048/ (9.157 X 10'1 - 115 MPaFIG. 12. Calculation of stress from acceleration data.

decay curves by calculating the log decrement. Usingthis approach, the first and second mode dam ping ratioswere estimated to be 6 and 12%, respectively.The following factors probably contributed to therather high dampi ng ratios of the floor: (1) the cracks inthe concrete floor: (2 ) he noncomposite construction o fthe floor; (3) the mass of the ceiling panels; and (4 ) themass of the storage materials in the adjacent bays.Theoretical calculations

A static analysis of test no. 4 and a free vibrationanalysis were carried out using the STARD YNE (Co n-trol Data Corporation 1979) finite element packag e. Inthe analyses the f lo or was treated as a stiffened plateresting on 4 edge beams and supported at the comers.The concrete tloor was idealized by 76 mm thickquadrilateral plate elements while noncomposite beamelements were used for the joists and the girders. Th e

f in it e e le m en t mesh ~ ~ s e das a 15 X 15 grid. Becausof the severe cracks in the concrete floor, the stiffnesof the plate elements was reduced by using a moduluof elasticity equal to a half of the estimated value o19.8 G Pa. Th e moment of inertia and You ng's moduluof the joists and supporting girders were not reducedThe static moment and deflection calculated at midspaof the mid dle joist for test no. 4 were 8.3 kN.m an4.29 mm, respectively. The first and second modnatural frequencies were found to be 5 .1 and 10.9 Hzrespectively. The first mode shape has 1 half sine wavin directions parallel and perpendicular to the joistsThe second m ode shape has I half wave in the directioof the joists and 2 half waves in the direction perpendicular to the joists. Th ese results are in reasonablgood agreement with the experimental values.Due to its severe cracks, the concrete floocontributes very little to the flexural stiffness and virtually ineffective in the lateral distribution of loadConsequently, even sim ple beam calculations, such athose shown i n Fig. 11 , will yield reasonably accuraresults.To determ ine the maximum stress from the integrateacceleration si gnals , it is necessary to know the crawl ostatic displacements beforehand, because double integration of the acceleration will yield only the displacement amplitudes as measured from the static equilbrium position. The calculation of the maximum stresfor test no. 4 is shown in F ig. 12. Th e good agreemenobtained is a result of the easily predictable statideflections of the floor.Conclusions

From the results presented, the following conclusions may be drawn.( 1 ) While the combination of high acceleratiolevels (0.56s) and the 5-6 Hz fundamental frequencwill have exceeded the annoyance threshold of floovibrations, serious objectionable vibrations are nolikely to be a pro ble n~ , ince the floor is used priinarilfor storage. Furthermore, because of the high dampinvalue of the tloor, the duration of peak level vibratiowill be very short. In the floor vibrations should annocertain people, it will not likely be for reasons odecreased efficiency or discomfort, but due to doubtabout the structure's safety, which in this case seemjustified.(2 ) Any sudden application of load is dynamic inature and hence could result in stresses that are mantimes those due to the same load but applied staticallor gradually.(3 ) Dynamic d isplacen~entscan be obtained bintegrating the accelerations. However, if the frequencies of vibration are low er than a certain cut-off point othe integrator (0.8 Hz f or the one used in this test

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262 CAN. J. CIV. ENG. VOL. 8, 1981there will be phase distortion problems and the resultswill be worthless.

(4) Satisfactory stress information could beextracted from acceleration measurements, providedthe staitc displacements can be determined with areasonable degree of accuracy. This implies a simplestructural geometry and boundary conditions (such asthose of this test floor), and a good knowledge of themechanical properties of the structural members (i.e.,moment of inertia, Young's modulus, Poisson's ratio,etc). Generally speaking, displacement transducers(such as LVDTs) will yield more reliable results sincethey remove at least one level of approximation.

ALLEN,D. L. 1974. Vibrational behavior of long spafloor slabs. Canadian Journal of Civil Engineering1 , pp. 108- 115.ALLEN, . E ., and RAINER,. H. 1976. Vibration criteria folong-span floors. Canadian Journal of Civil Engineering3, pp. 165-173.CLOUGH, . W., and PENZIEN.. 1975. Dynamic of Structures. McGraw-Hill Book Company, New York, NYp. 634.CONTROL ATACORPORATION.979. Stardyne user's guideMinneapolis. MN.LENZEN, . H . 1966. Vibration of steel joists. AmericaInstitute of Steel Construction Engineering Journal, 3(3)p. 133.

Increase of stress in unbonded tendons in prestressed concrete beams and slabsPERUMALSAMY. BALAGURUDepartm ent of Civil and Etlvironmental Etzgineering, Rutgers , The State Utziversity of Ne w Jersey , Piscatarvay, NJ , U .S.A

Received December 9, 1980Manuscript accepted January 5 , 198 1

In the case of prestressed concrete beams with unbonded tendons, in order to design for strength and serviceability, one hato evaluate the effective prestressing force in the tendon, which is beam dependent rather than section dependent, both aultimate and working loads. The formulae available in the published literature deal only with ultimate loadcondi tions. A simpequation to predict the tendon stress changes for the complete loading range is presented in this paper. The formula wadeveloped using the basic theory of flexure to obtain the equation for the elastic curve, and numerical integration to obtain thcurve lengths. Using the computer generated results of the increase in tendon strain for various span lengths, eccentricitiesand maximum deflections, a regression equation was developed. This regression equation predicts the increase in tendon strainas a function of the span-eccentricity and eccentricity - maximum deflection ratios. The recently published stress-strainrelation which seems to be very accurate is then used to predict the tendon stress. The results are compared with a set oexperimental results. The suggested formula is also consistent with some of the available equations for the prediction of thetendon stress at ultimate load.

Pour une poutre en bkton prkcontrainte en moyen de clbles non adhkrents, le calcul aux Ctats limites de service et drksistance impose le calcul de l'effort rkel dans le clble, qui dkpend du comportement d'ensemble de la poutre plut6t que dla section, tant B I'ktat ultime qu'en rkgime klastique. Les formules prksentement disponibles dans la littkrature technique nvisent que l'etat limite de rksistance (rupture). Cet article prksente une expression simple applicable au calcul des changementde tension pour tout ktat de chargement. En se basant sur la thkorie usuelle de la flexion,,on dkrive I'kquation de la dkformkqu'on intkgre numkriquement pour obtenir la longueur des troqo ns courbes. A partir des augmentations de dilatation calculkepour diffkrentes portkes, excentricitks et flbches, l'auteur a ktabli une kquation de regression qui permet le calcul de la variatiode la dilatation dans le c2ble en fonction des rapports flkche-excentricitk et excentricitk-portke. On peut alors calculer ltension dans le clble par retour i la relation contrainte-dilatation d'une grande exactitude publike rkcemment. Ces rksultasont comparks B des observations expkrimentales. La formule proposke semble en accord avec quelques expressions permettanle calcul de la tension sous la charge limite. [Traduit par la revueCan . J. Civ. Eng , . 262-268 (1981)

Introduction span-depth ratio; (iv) the deflected shape of the beamIn the case of beams with unbonded tendons, since (v) the maximum deflection; and (vi) the amount othe steel can slip with respect to the surrounding con- initial prestress.Crete, the stress chang e in the tendon is member depen- The American Concr ete Institute (19 77) code provident rather than section dependent. The stress in the sions recommend a s imp le formula to predic t the strestendon would depend on , amon g other things: (i) the in the post tensioned tend ons at the time of flexurinitial cable profile; (ii) beam end conditions; (iii) the failure. However, data fro m recent tests of a number o

03 15- 146818 11020262-07$0 ,001001981 National Research Council of CanadaIConseil national de recherches du Canada