Dynamic Load Spectra for Girder Bridges

Transcription

1 TRANSPORTATION RESEARCH RECORD Dynamic Load Spectra for Girder Bridges HANI H. NASSIF AND ANDRZEJ S. NOWAK The dynamic load is an important component of bridge loads. The determination of the dynamic load factor (DLF), defined as the ratio of dynamic and static responses, is essential for the development of a new generation of reliability-based bridge design codes. Field measrements are performed to determine the actal variation of the DLF with varios trck as well as bridge parameters and to verify the available analytical models. The effects of varios parameters, sch as trck gross weight, trck speed, trck type, girder static stress, and girder position, on the DLF are presented. The field tests are carried ot on for steel girder bridges. Measrements are taken sing a weigh-in-motion system with strain transdcers. For each trck passage, the trck weight, speed, axle configration, and lane occpancy are determined and recorded.. A nmerical procedre is devel_oped to filter and process collected data. The DLF is determined nder normal trck traffic of varios load ranges and axle configrations. The field measrements confirm the reslts of the analytical stdy. In absolte terms, the response cased by dynamic load is practically constant and does not depend on_ trck weight. However, for exterior girders the static stress is small. Therefore, the DLF shold be considered on the basis of girders of maximm stress vales. The major load components inclde dead load, live load, and dynamic load. This paper deals with trck-indced dynamic loads in girder bridges. The dynamic load is time variant and random in natre and it depends on the vehicle type vehicle weight, axle configration, bridge span length, road roghness, and transverse position of a trck on the bridge. An example of the actal bridge response cased by an actal vehicle, a five-axle trck traveling at a highway speed, is shown in Figre 1. For comparison, also shown is an eqivalent static response, which represents the same vehicle traveling at crawling speed. The dynamic load is sally considered as an eqivalent static live load and is expressed in terms of a dynamic load factor (DLF). There are different definitions for DLF, as smmarized elsewhere (1) in a state-of-the-art report on dynamic testing of bridges. In this s.tdy, DLF is taken as the ratio of dynamic and static responses (2): DLF= Ddyn Dstat where Ddyn is the absolte maximm dynamic response at any point (e.g., stress, strain, or deflection) measred from the test data and Dsiai is the maximm static response obtained from the filtered dynamic response. The measrement of static load spectra is described by Nowak et al. (3). An accrate dynamic load model is reqired for the development of rational criteria for the design and evalation of bridges. Yet, the available data are insfficient and nclear. Analytical simlation procedres provided a basis for calclation of design. H. H. Nassif, Civil Engineering and Constrction Department, Bradley University, Peoria, Ill A. S. Nowak, Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, Mich (1) provisions (4). However, there is a need for field verification of the reslts. Therefore, the objective of this stdy is to determine the dynamic load factor based on the field measrement data. The work is carried ot on selected steel girder bridges. The obtained reslts are compared with DLFs calclated on the basis of the analytically simlated model ( 4). CODE PROVISIONS Most bridge codes specify the dynamic load as an additional static live load. The actal vales vary from one docment to another. In the crrent AASHTO (5), DLF or (1 + /), is specified as a fnction of span length only: 5 /= L where L is the span length in feet (1 ft = 5 m). However, the maximm vale of DLF is. This empirical eqation has been in effect since In the new load and resistance factor design (LRFD) AASHTO Code (6), live load is specified as a combination of HS2 trck (5) and niformly distribted load of 64 lb/ft (9 kn/m). DLF is eqal to 3 of the trck effect, with no dynamic load applied to the niform loading. PREVIOUS STUDIES The available data on dynamic load in bridges is limited (7). Some measrements were taken by the Ontario Ministry of Transportation (2). A total of 27 bridges were tested. The strctral types inclded prestressed concrete (girders and slabs), steel girders (rolled sections, plate girders, and box girders), steel trsses, and rigid frames. Data were recorded for test vehicles and actal traffic. The mean vales are abot.5 to.1 for prestressed concrete AASHTOtype girders and.8 to.2 for steel girders. The maximm observed vales exceed.5, and some of the coefficients of variation are over 1.. However, the correlation between DLF and trck weight is not available. On the other hand, it is expected that the largst DLFs correspond to lighter trcks. Considerable differences in DLF e observed for otherwise similar strctres, which indicates the importance of factors sch as srface condition. Cantieni (8) tested 226 bridges in Switzerland, mostly prestressed concrete. With the exception of 11 bridges, all were loaded with the same vehicle, nder the same load, and with the same tire pressre, ths minimizing the variability cased by trck dynamics. The effect of local nevenness in the pavement on the dynamic load was also investigated. The stdy showed that the dynamic fraction of the loadwas as high as. 7 for bridges with fndamental natral freqency (2)

2 7 TRANSPORTATION RESEARCH RECORD Axle Trck Weight: 19. Mg Speed : 14 km/hr simlations were carried ot for single trcks and two trcks sideby-side. For two trcks, the DLF was smaller by abot 5 percent compared with DLF for single trcks. al 2,Ji en... f rn Time. sec --Dynamic -----Static FIGURE 1. Dynamic and static response for Girder 3, Bridge 1, nder a five-axle trck (1 MPa = 6.89 ksi; 1 km =.6 mi, 1Mg=1,814 lb). between 2 and 4 Hz. However, as in the Ontario data (2), the static and dynamic loads were recorded separately, so that it is not possible now to determine the degree of correlation. It is also expected that the high vales of DLF are associated with lighter vehicles. O'Connor and Pritchard (9) fond that the dynamic load is vehicle dependent and varies with the sspension geometry. They carried their tests on a short-span composite steel and concrete bridge in Astralia. The reslts indicate that as the weight of the vehicle increases, the dynamic load decreases. Also, O'Connor and Chan (1) collected strain data and, sing those records, determined DLFs ranging from -.8 to As in the previos stdies, the extreme vales are associated with light trcks. Most of the theoretical stdies on vibration of beams nder moving loads concentrated on modeling only one of the parameterseither the vehicle, bridge, or srface roghness. The vehicle was modeled as a constant force (11), one degree-of-freedom system (12), two degrees-of-freedom system, or more realistic complex systems (13). The bridge was modeled as either a continos or discrete system (14). Discrete models can be in the form of simple beams,.simple beams with torsional degree of freedom, and orthotropic plates. The srface roghness was modeled sing the so-called artificial bmp on the approach method (13), and Honda and Kobori (14) sed a random process to represent the random road profile as a Forier series with random coefficients. The development of a new LRFD code reqired a verification of the load model. In particlar, there was a need for confirmation of the observation that the dynamic load factor decreases for heavier trcks and for mltiple trck occrrence. Therefore, a compter procedre was developed previosly (4) for simlation of the dynamic bridge behavior. The dynamic load was determined as a fnction of three major parameters: road srface roghness, bridge dynamics (freqency of vibration), and vehicle dynamics (sspension system). The bridge was modeled as a prismatic beam. Dynamic parameters of trcks were based on the available data. Road roghness was generated sing the actal measrement records. The DLF was calclated in terms of deflections. It was fond that the dynamic deflection is almost a constant, whereas static deflection is proportional to trck weight. Therefore, DLF decreases for heavier trcks. The EXPERIMENTAL PROGRAM The prpose of the experimental program is to measre the dynamic load amplification in simple-span steel girder bridges. Corresponding trck weights, in particlar axle loads and axle spacings, are also recorded. The measrements are taken simltaneosly by two systems: the weigh-in-motion (WIM) system (trck information and girder strains) and the dynamic system (accelerations) (15). The WIM system was developed by the bridge weigh systems. Its prpose is to measre and record all relevant trck information in addition to the strain response in each girder. The strain gages are placed on lower flanges close to the position of the maximm moment. The dynamic system, developed by Krenz Electronics, is set p to measre accelerations simltaneosly, and at the same location as, the strain gages. Both systems are triggered by special tape switches, pasted to the pavement. The same tape switches are sed to determine the trck speed, the nmber of axles, and axle spacings. For bridges are selected for the field tests. All of them are located in sotheastern Michigan. The span lengths vary from 9 to 24 m (3 to 8 ft). The same procedre is sed for all bridges, however, with a different eqipment setp. All selected strctres are mlti-simple-span bridges with steel girders and concrete slabs. The basic design parameters inclde span length, girder spacing, slab thickness, and skewness. The basic parameters of the selected bridges are given in Table 1. Girders are labeled starting from the exterior girder in the right lane (Girder 1) to the exterior girder in the left lane (Girder 8). The strain gages are attached to bottom flanges of girders. The location of the strain gage was 2 to 3 ft from midspan, depending on span length and access to the point of installation. The eqipment is calibrated sing trcks with known axle weights and spacings. The accracy of calclation for axle ioads is within 2 percent and for gross vehicle weight (GVW) within 1 percent (within 5 percent for three and five axle trcks). The measrements are carried ot for several days at each location. A compter program is developed for the atomated data processing. Each data file contained data from six or eight channels. Each record represents the passage of a trck over the bridge in either right or left lane. The data captring starts when the trck crosses over the first tape switch, which is abot 6 m (2 ft) from the bridge spport in either lane. The tape switch signal is sed to trigger the system and start collecting data from the accelerometers and strain transdcers. The data collection is atomatically stopped after the departre of the last trck axle from the bridge. However, this synchronization works for bridges with traffic intensity not higher than normal. On bridges with trcks of certain characteristics (e.g., heavy, 11 axles), the mnal trigger permits a better control of the data acqisition system. The strain records are smoothed and filtered sing the widely sed fast forier transform (FFT) techniqe (16). The FFT procedre is tilized assming that the measred strain-time (or acceleration-time data) can be represented as the sm of all contribtions from all mode shapes. FFT is also sed to determine the dominant freqencies as well as the ctoff freqency in the freqency domain. The ctoff freqency is best estimated, for each individal bridge,

3 Nassif and Nowak 71 TABLE 1. Parameters of the Tested Bridges Brtdge I Location Span No. of No. Girders (m) Girder Slab Brtdge Skew Spacing Thickness Width (m) (mm) (m) US-23/ Hron River M-14/ N.Y.C. Rail Road / Jackson Road l / 1 Pierce Road by minimizing the error in estimating the total energy nder the power spectrm plot in the freqency domain. After eliminating the contribtion of all modes (or freqencies) above the ctoff freqency in the freqency domain, inverse FFf is then performed to obtain the time-domain eqivalent static response (referred to as static response). This process is performed on varios trck strain records sing a compter program that was developed on the basis of available nmerical rotines (15). The dynamic and static response are then plotted and compared to determine the DLF. The WIM measrements provided data on trck weights., axle loads, axle configrations, and vehicle speeds. Most of the trcks traveled at abot 9 km/hr (6 mph). The trck traffic was a mixtre of mostly 5-axle vehicles with few very heavy 11-axle trcks. The GVW ranges were above the legal limits. tic stress) is practically independent of trck weight (or static stress), as shown in Figre 6. Therefore, the dynamic load factor, DLF, decreases with increasing static stress or trck weight. The variation of DLF with trck parameters is shown in Figres 7 throgh 9. Reslts for each bridge are shown corresponding to the most loaded interior girder. Observations indicate that the DLF decreases as the GVW increases for all bridges (Figre 7). Observations also indicate that among all types of vehicles (exclding light-weight two-axle vehicles), for- and five-axle trcks case the largest DLF vales (Figre 8). Additionally, the DLF decreases with an increase in trck speed (Figre 9). Moreover, to represent the variation of DLF with girder position, the mean vale of DLF, for right lane girders in each bridge, is plotted verss the girder position as shown in Figre 1. On average, the most loaded girders (Girders 3 and 4) will have vales of DLF below 1.2. MEASURED DYNAMIC LOAD The measrements are carried ot on for bridges listed in Table 1. Static and dynamic stress is determined for each girder. The reslting dynamic load factors (DLF) are plotted verss the static stress in each girder in Figres 2 throgh 5. The reslts are shown for a maximm of eight girders limited by the nmber of available data acqisition channels. In general, DLF decreases as the static stress in each girder increases. However, the DLF is the ratio of dynamic and static stress, and static response varies from girder to girder, depending on the positions of the girder and trck. The variation in DLF with respect to static stress in each girder is shown in Figres 2 throgh 5. It is shown that the exterior girders exhibit small static stress (almost negligible), whereas the interior girders have mch larger static stresses. In general, the static stress is proportional to trck weight. However, the dynamic stress (maximm dynamic stress-maximm sta- CONCLUSIONS The dynamic loads nder a normal highway traffic are measred for selected steel girder bridges. For each trck, the measred parameters inclde: axle loads, axle spacings, speed, strain record, and acceleration record. A nmerical procedre is developed for data processing, filtering, and smoothing. The DLF is calclated sing strain records. Observations indicate that the dynamic component of stress (i.e., dynamic increment) is practically independent of static component. Therefore, DLF decreases with increased static stress. For very heavy trcks, DLF does not exceed the theoretical reslts (4). Larger vales of DLF are observed in exterior girders; however, this is becase of a relatively smaller static load effect. Vales of DLF shold be based on those obtained from the most loaded interior girders.

4 2. a H H l J r : - r -r -- -r - t ) ;.-----; Max. Static Stress {MPa) ,..:a.. k : 1 1 & mmhhmh!mm JHm irde 2 L 1. o-...,.,....., Max. Static Stress {MPa) 2. =..;- s.., i as e. = 1. m m m, HmJ Girder 3 I Max. Static Stress {MPa) 2...:a m mm ml HH HL H Girde J j :8 : :...,.., HU..., i! o oi L o-._r-----r--.::::...r Max. Static Stress {MPa) 2. = mom HH'H.m.. (Hrder 5 L 2. m.mjh J Girder 6 L O [ f f o i.. L -...! I I i.o:..-., ;;.,, --i i ].. :..,.. t 1... L &... L ! : : : o! '----. :. : : -.I FIGURE 2. DLF erss static stress for Girders 1throgh6, Bridge 1 (1 MPa = 6.89 ksi).

5 . o Girder 11 lo : :!o!! I ,.., :; -.; c al.s al & 1.,.. J. o irder.. 2 J. a - t t l l I! i! ; : ! i i o 1 I I o 1 : :; 1. mmm + m L.. Girder L... - : r r j! i... i<u + -! o oi lo i : i 2....:;.; c r:.s al & : [ 'm.: :i:e.r:j!!! : : j j. Cbl l l -- a- - -t t l Ol o i o l.o-r--1.;;1::;, ;.-4-" FIGURE 3. DLF verss static stress for Girders 1throgh8, Bridge 2 (1 MPa = 6.89 ksi).

6 Max. StaUc Stress i I Girder s j omuuu! m m 'mm mm WU:UU : : i.o--., FIGURE 3. (continetf)

7 Nassif and Nowak 75 i I o Girder i j mmmhhmm! HH mmr.. U'mm H.. i. ' '.! j o Girder 2 j ::Hr H :1mmm: :m :: j o! i i : : : oj o I pi. I i.,.l i! j -4w!1f<ai@ : : o I o 1. O-+---= r-----r a o Girde L... : j o Girder 41 o r! --! 1. o,_;:..::---1'-'-_;:;_-..,_--=---r '! i i..s---- t t - t ---- (fll)t;:;' : : : io i i : :.... P r-- -r-- : al.. CH7'.&J._, : 1. : : ' FIGURE 4. DLF verss static stress for Girders 2 throgh 9, Bridge 3 (1 MPa = 6.89 ksi).

8 2,..---.,...--,,_..----:-----i a Hlrder L 1.-Fi-,,., a.: s i ":" ] 1 1. o..., --; ,._ o Girder I I Girder s} Hmm!HH,... i.. HUH: : ! r l \ I 1. -+""'-,, ----; "!" : T----P---'""'" FIGURE 4. (contined)

9 2.... r: 'ts D i nnmnmlmnnjmn ,--- erln ].!! - i i j ogf,. i io : : ' ' j FIGURE Max. Static Stress -(MPa) c.> r: 'ts m 1. DLF verss static stress for Girders 2 throgh 1, Bridge 4 (1 MPa = 6.89 ksi). i.r.-lm lo : : o T L, Oj

10 2. t.j.: «I f;i;. as! i 2, nmmjmjmm ngirdel T - t - o' ) :e : : l j :..:...:.. : : cp oo:,c) : [... f. o : cro : :o l. : --I i.o-+l-----i i : _ FIGURE 5. (continetf)

11 Nassif and Nowak 79 US23, Right Lane Ml4, Right Lane ,---. ' t j ri? (j))o I I :J Jllfi M.) o lo i o!:. UJ a Cd P i l i o: ri ii i i --g b. i r i. -3 I I I Max. Static Stress, MPa Max. Static Stress, MPa 3 194W, Right Lane 3 194E, Right Lane l! 15 :e ri en e o.o., UJ -15 al :s 15 ri fl) I)!:. UJ 1-15 = : r r o :;:. o ;g I Ma o ' 11 : Max. Static Stress, MPa Max. Static Stress, MPa FIGURE 6. Dynamic stress verss maximm static stress (1 MPa = 6.89 ksi).

12 2..; "d as 1 e. US23, Right Lane o Girder _ J 2...:a.; "d Ml4, Right Lane.. nm H.. mj Girder 4J..m Trck Weight, (Mg) as m & r r r () :. :.6(; o'. L. : l 'lo.mnml": : : ; : : Trck Weight, (Mg) 194W, Right Lane 194E, Right Lane 25 5{) Trck Weight, (Mg) Trck Weight, (Mg) FIGURE 7. DLF verss trck weight (1 mg = 1,814 lb).

13 2...; g at I&. 't:s at & 1. 1 US23, Right Lane Nmber of Axles Ml4, Right Lane Nmber of Axles (';I:. 2...; g at f;r. 't:s at i & 194W, Right Lane 1. _.... w...-..i.,, Nmber of Axles f.o [ l ' i If 194E, Right Lane o! Girder4j! 1. 5 ::::[LI:::r::1::::1.::::1.:::.._::.1...:::1:.J::: : :!!! :. : i i : cb i i : : i i i i : : : ], 9 f l.! - f o r & : : : :!! l i 6 : i i i I. o_. """'--411it-_..._,.._---+"+, Nmber of Axles FIGURE 8. DLF verss trck type (nmber of axles).

14 US23, Right Lane Ml4, Right Lane t.j \ 85 : : 1...L L-:L I Speed (km/hr) 2. t.j.: 'ts as I94W, Right Lane n m nl nmjnnmnm n mi'l : ' '! ' ; 1 o ; T - i! \ 8 :8 \ \ ;oj.!?p ; :8 o : : : l : ' '. 1 o.: cd i. : l.o_, --'-- i,..; a.---'----' Speed (km/hr) 194E, Right Lane Speed (km/hr) FIGURE 9. DLF verss trck speed (1 km=.6 mi).

15 Nassif and Nowak 83 r.c..., r: E "Cl as "! 1.4 t) = 1.2 :s Right Lane --o--us23 _._Ml4 t, I 194\V > I l.ch G2 G3 G4 G5 Girder Position FIGURE 1. Mean DLF verss girder position. ACKNOWLEDGMENTS The presented research was sponsored by the Michigan Department of Transportation and Great Lakes Center for Trck Transportation research, which are grateflly acknowledged. REFERENCES I. Bakht, B., and S. G. Pinjarkar. Dynamic Testing of Highway Bridges A Review. In Transportation Research Record 1223, TRB, National Research Concil, Washington, D.C., 1989, pp Billing, J. R. Dynamic Loading and Testing of Bridges in Ontario. Canadian Jornal of Civil Engineering, Vol. 11, No. 4, 1984, pp Nowak, A. S., H. H. Nassif, and L. DeFrain. Effect of Trck Loads on Bridges. Jornal of Transportation Engineering, ASCE, Vol. 119, No. 6, 1993,pp Hwang, E.-S., and A. S. Nowak. Simlation of Dynamic Load for Bridges. Jornal of Strctral Engineering, ASCE, Vol. 117, No. 5, 1991, pp Standard Specification for Highway Bridges. AASHTO, Washington D.C., Nowak, A. S. Calibration of LRFD Bridge Design Code. Report UMCE Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, Paltre, P.,. Chaallal, and J. Prolx. Bridge Dynamics and Dynamic Amplification Factors-a Review of Analytical and Experimental Findings. Canadian Jornal of Civil Engineering, Vol. 19, 1992, pp Cantieni, R. Dynamic Load Tests on Highway Bridges in Switzerland. Report 211. Swiss Federal Laboratories of Material Testing and Research (EMPA), Dbendorf, Switzerland, O'Connor, C., and R. W. Pritchard. Impact Stdies on Small Composite Girder Bridge. Jornal of Strctral Engineering, ASCE, Vol. 111, No, 1985,pp O'Connor, C., and T. H. T. Chan. Dynamic Wheel Loads from Bridge Strains. Jornal of Strctral Engineering, ASCE, Vol. 114, No. 8, 1988,pp W, J. S., and C. W. Dai. Dynamic Responses of Mltispan Nonniform Beam de to Moving Loads. Jornal of Strctral Engineering, ASCE, Vol. 113, No. 3, March 1987, pp Blejwas, T. E., C. C. Feng, and R. S. Ayre. Dynamic Interaction of Moving Vehicles and Strctres. Jornal of Sond and Vibration, Vol. 67, No. 4, Dec. 1979, pp Gpta, R. K. Dynamic Loading of Highway Bridges. Jornal of the Engineering Mechanics Division, ASCE, Vol. 16, No. EM2, April 198,pp Honda, H., and T. Kobori. Vibration Control of Loshe Girder Bridge sing Design of Experiments. Proc., Japan Society of Civil Engineers, No. 31, Sept. 198, pp Nassif, H. H. Live Load Spectra for Girder Bridges. Ph.D. dissertation. University of Michigan, Ann Arbor, Paz, M. Strctral Dynamics-Theory and Comptation, 3rd ed. Van Nostrand Reinhold, New York, Pblication of this paper sponsored by Committee on Dynamics and Field Testing of Bridges.