nassif, liu, su, and gindy 1 - transportation research boarddocs.trb.org/prp/11-3446.pdf · nassif,...

Nassif, Liu, Su, and Gindy

1

VIBRATION VERSUS DEFLECTION CONTROL FOR HIGH-PERFORMANCE 1 STEEL (HPS) GIRDER BRIDGES 2

3 Hani Nassif, Ph.D., P.E., Associate Director 4

Center for Advanced Information Processing (CAIP) 5 Rutgers Infrastructure Monitoring and Evaluation (RIME) Group 6

Rutgers, The State University of New Jersey 7 96 Frelinghuysen Road, Piscataway, NJ 08854 8 Phone: (732) 445-4414, Fax: (732) 445-4775 9

[email protected] 10 11

Ming Liu, Ph.D., P.E. 12 Civil Engineer (Structural) 13

Technical Service Center - Bureau of Reclamation 14 U.S. Department of the Interior 15

Denver Federal Center 16 Bldg. 67 (86-68110) 17

P.O. Box 25007, Denver, CO 80225-007 18 [email protected] 19

20 Dan Su*, Ph.D. Candidate, Research Assistant 21

Center for Advanced Information Processing (CAIP) 22 Rutgers Infrastructure Monitoring and Evaluation (RIME) Group 23

Rutgers, The State University of New Jersey 24 96 Frelinghuysen Road, Piscataway, NJ 08854 25

[email protected] 26 27

Mayrai Gindy, Ph.D., Associate Professor 28 Dept. of Civil & Environmental Engineering 29

University of Rhode Island 30 1 Lippitt Road, 201 Bliss Hall 31

Kingston, RI 02881 32 [email protected] 33

34

* Corresponding Author 35

Word count: 4093 36 Abstract: 249< 250 37

Figures & Tables: 13x250 = 3250 38 Total: 7343 39

Submission Date: 11/15/2010 40 41

TRB 2011 Annual Meeting Paper revised from original submittal.


2

ABSTRACT 1 Utilization of High Performance Steel (HPS) in highway bridges has proven to be successful in 2 terms of structural performance and in the cost efficiency of the constructed bridges. However, 3 the use of optional deflection criteria as specified in the American Association of State Highway 4 Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Bridge Design 5 Specifications, Article 2.5.2.6, may impede the use of HPS in highway bridges. Besides the 6 deflection criteria, the current AASHTO LRFD Bridge Design Specifications also provide a 7 depth-to-span limitation table 2.5.2.6.3-1 for steel superstructure designs. The values in table 8 2.5.2.6.3-1 are primarily based on the use of Grade 36 steel and were initially a carryover from 9 railroad bridge construction. Therefore, both the deflection criteria and depth-to-span limitation 10 need to be evaluated for bridges constructed with HPS. This paper presents an investigation of 11 the vibration control (e.g. acceleration and velocity) of HPS bridges using a 3-D dynamic 12 computer model. The 3-D dynamic model was validated using field test data on various bridges 13 including a 3-span continuous steel girder bridge. A suite of typical bridges designed with 14 various slab thicknesses and span-to-depth ratios were selected for this study. In particular, the 15 effects of the steel girder depth and concrete slab thickness on bridge vibration were identified. 16 The analysis results indicated that bridge vibrations is better controlled by choosing optimal 17 concrete slab thicknesses (i.e. adding to the mass and moment of inertia of composite girder) 18 rather than specifying the span-to-depth ratio limits, deflection limits, or first natural frequency. 19

20

Key Words: 21

Vibration 22

Bridges 23

Deflection 24

Slab thickness 25

Span-to-depth ratio 26

27



3

INTRODUCTION 1 High Performance Steel (HPS) was developed in the early 1990’s to provide an enhanced 2

Grade 70 yield strength structural steel material, improved welding capabilities and weathering 3 durability. The use of HPS-485W (70W) steel in highway bridges has proven to be successful in 4 terms of structural performance and in the cost efficiency of the constructed bridges. However, 5 it has been realized that the use of the optional design criteria for deformation (or deflection) 6 control, as specified in American Association State Highway Transportation Officials 7 (AASHTO) Load and Resistance Factors Design (LRFD) Bridge Design Specifications [1], 8 Subsection 2.5.2.6, and Table 2.5.2.6.3-1 “Traditional Minimum Depths for Constant Depth 9 Superstructures” may impede the use of HPS in bridge construction. If the deflection 10 requirements become the controlling design issue, the most economical bridge designs, based on 11 ultimate strength criteria, cannot be achieved. As a result, the rationality of using deflection 12 requirements must be carefully studied for current bridge design practices. One of the important 13 questions that needs to be addressed is whether the vibration can be effectively controlled by 14 applying the deflection limit specifications to the design? The use of a deflection design 15 parameter is an option that many states (e.g. New Jersey) impose in order to indirectly control 16 vibration. Vibration control of a constructed bridge is desired because the service life of a bridge 17 that is too flexible becomes questionable. Also, a motorist’s perception of using a safe bridge is 18 important to the State Highway Agencies. 19

In this paper, a correlation between live load-induced vibration and various HPS bridge 20 parameters is established. An analysis model, based on the dynamic interaction between the 21 bridge, vehicle, and road roughness system, is validated using experimental data from various 22 types of bridges. A suite of HPS bridges are designed and then analyzed to identify the most 23 sensitive parameters that would affect bridge vibration and deflection response. Various types of 24 truck loading patterns (e.g. single, side by side) are considered. Typical road roughness profiles 25 are considered. The resulting bridge responses (i.e. acceleration and deflection) are compared 26 with human perception of vibration. The deflection criteria and depth-to-span ratio specified in 27 AASHTO LRFD Bridge Design Specifications, as well as Canadian and Australian Code 28 Specifications, are also evaluated. The effects of the steel girder depth and concrete slab 29 thickness on bridge vibration are identified. Results show that bridge vibration can be 30 effectively controlled by increasing the thickness of the concrete deck slab (i.e., adding mass and 31 moment of inertia) while maintaining shallow depths for the HPS girders. Moreover, increasing 32 the slab thickness would improve the durability of the bridge deck. 33

34

BACKGROUND 35 Use of deflection limits in the design of highway bridges, particularly when HPS is desired, is an 36 important consideration in the design process. The AASHTO LRFD Bridge Specifications 37 (2008) [1] establishes the use of a deflection design as an optional criteria. A number of State 38 Highway Agencies specify their own deflection limits as a mandatory requirement. New Jersey 39 [2] defaults to AASHTO’s deflection criteria of L/800 for vehicular bridges and L/1000 for 40 pedestrian bridges. It is perceived that these deflection limits are usually based on a rather 41 arbitrary and sometimes conservative approach in designing bridges [3]. This raises questions 42 with regard to the rationality of these deflections limits in that pursuing a conservative design 43 approach does not take advantage of today’s bridge construction technologies. In principle, 44



4

deflection limits were established to eliminate damage to any structural and non-structural 1 components due to excessive deformations as well as to avoid loss of aesthetic appearance and 2 interruption of its functionality. For highway bridges, vehicle rideability and human responses to 3 bridge vibration under normal traffic conditions play an important role in determining the 4 deflection limits. Moreover, if deflection limits should be specified as a design parameter, there 5 is a need for a rational approach to establish a limit state design philosophy that all designers can 6 justifiably use [5]. 7

Gindy (2004) [5] performed a detailed literature search that indicated that the origin of the 8 deformation requirements in bridge designs might be traced back to 1871 with a set of 9 specifications established by the Phoenix Bridge Company (PBC). The American Society of 10 Civil Engineering (ASCE) report on deflection limits of bridges (ASCE, 1958) [15] has been 11 widely cited for the evolution of these requirements. The following conclusions may be drawn 12 from the ASCE report: 13

(1) The deflection limits were established before the span-to-depth ratio limits; that is, the 14 span-to-depth ratio limits were used as indirect measures of the deflection limits; 15

(2) Both deflection and span-to-depth ratio limits were empirically derived, mainly for the 16 early bridge structures, such as wood plank decks, pony trusses, simple rolled beams, 17 and pin-connected through-trusses (Wu, 2003) [16]; 18

(3) The specified span-to-depth ratio limits for highway bridges (by AASHO) followed 19 what was established for railroad bridges (by American Railway Engineering 20 Association (AREA)); 21

(4) The deflection limit of L/800 was established in the 1930’s, primarily for the vibration 22 control of steel highway bridges; and 23

(5) No major changes have been made for steel highway bridges since 1936. 24

It is generally agreed that deformation requirements are intended to play an important role in 25 bridge vibration controls. Therefore, Wright and Walker (1971) [12] proposed a vibration-related 26 static deflection limit. The limit is a computed transient peak acceleration of a bridge, α, which 27 should not exceed 100 in./sec^2 (2.54 m/sec^2), where the static deflection,δs , is linked to α as 28 follows: 29

δ s = 0.05 × L ×α

(speed + 0.3 × fs × L) × fs (1) 30

where L = span length; speed = vehicle speed; and fs = natural frequency of a simple span 31 bridge, which may be estimated as 32

fs =π

2L2

EbIb

m (2) 33

Where EbIb = flexural rigidity of a girder section; m = unit mass of a girder section. It 34 should be noted that δs needs to be calculated for a live load with a girder distribution factor of 35 0.7. Nowak and Grouni (1988) [17] also stated that the deflection and vibration criteria should 36 be derived by considering human reactions rather than structural performance. In addition, 37 similar efforts that relate static deflection limits to the natural frequency of a bridge are shown in 38



5

Canadian and Australian bridge design specifications (Ministry, 1991; CSA International, 2000; 1 AUSTROADS, 1992, AUSTRALIAN, 1996) [18], [19], [20], [21]. The red lines in Figure 1 2 shows the relationship between the first flexural frequency (in Hz) and static deflections limits 3 (in mm) at the sidewalk or edge of a bridge for various structure types from the Ontario Highway 4 Bridge Design Code (OHBDC). This was developed from extensive field data and analytical 5 models (Wright and Green, 1964) [11]. The green solid line in Figure 1 presents a similar 6 relationship that is adopted in the Australian Bridge Design Code. It is also noted that the static 7 deflection limits are usually absent in European bridge design specifications while the New 8 Zealand Bridge Manual in 1994 limits the maximum vertical velocity to 2.2 in./sec. (0.056 9 m/sec.) instead of using the maximum acceleration. 10

Debates on the necessity of deformation requirements in current bridge design specifications 11 focus on two aspects: (1) whether excessive deflections cause structural damage; and (2) whether 12 deflection limits provide effective control of bridge vibrations under normal truck traffic. Based 13 on the limited survey in the ASCE report (1958) [15], no evidence of serious structural damage 14 due to excessive vertical deflections was revealed. However, unfavorable psychological 15 reactions to bridge vibrations caused more concerns on bridge safety. Burke (2001) [23] argued 16 that, if deflection limits were not mandated, the effective service life of reinforced concrete deck 17 slabs could become considerably less than their normal replacement interval of 30 years. 18 Moreover, the report on National Cooperative Highway Research Program (NCHRP) project 20-19 7 (Roeder et al., 2002) [24] found that bridges clearly suffered severe structural damage due to 20 excessive deformation but provided little support for the idea that deflection limits should be 21 used as a method of controlling these structural damages. In addition, deflection limits were not 22 considered as the “good” method of controlling bridge vibrations (Azizinamini et al., 2004) [25]. 23

Factors regarding human perceptions to vibrations are based on research work by Reiher and 24 Meister (1931) [6], Goldman (1948) [7], Janeway (1950) [8], (Oehler, 1957, 1970) [9], [10], 25 Wright and Green (1964) [11], Oriard (1972) [22], and Ontario Ministry of Transportation (1995) 26 [13]. A comprehensive research on human responses to bridge vibrations was conducted by 27 Wright and Walker (1971) [12]. They concluded that peak accelerations were preferable to peak 28 velocities when evaluating human perceptions to bridge vibrations that typically ranged from 1 29 to 10 Hz. Thus, peak acceleration and frequency of bridge vertical vibrations will be considered 30 to be the most important parameters in this research. 31

It should be emphasized that the dynamic characterization of a heavy truck, such as its mass, 32 speed, traveling lane, suspension properties, and tire stiffness, significantly affects the dynamic 33 response of a bridge. In other words, the predicted dynamic behavior of a bridge under normal 34 moving loads (i.e. without consideration of the dynamic characterization of a heavy truck) may 35 not be sufficient to represent anticipated bridge vibrations. This is why some bridges that were 36 designed to satisfy a deflection limit may still have objectionable vibrations or unacceptable 37 structural performances while other bridges that fail to meet the existing deflection limits 38 perform satisfactorily. 39

40

EXPERIMENTAL PROGRAM 41 The Doremus Avenue Bridge, located near the port area of Newark, New Jersey, was selected for 42 the field study. The data collected from this bridge was used to validate a dynamic model 43 developed by Nassif et al. (2003) [26]. The dynamic model was used thereafter to analyze 44



6

various bridges designed with HPS. The field data collection was performed as part of an 1 extensive long-term monitoring program [Nassif et. al (2010)] [14]. The three equal spans (45 m, 2 148 ft) of this bridge were selected for the experimental study because Span 3 provides clear 3 access to the underside of the bridge. Details of the bridge cross section are presented in Figure 2. 4

The bridge was instrumented with several types of sensors including a Weigh-In-Motion 5 (WIM) system, accelerometers, strain gauges, and two types of displacement-measuring systems, 6 a permanent Linear Variable Differential Transformer (LVDT)-cable system and a portable laser 7 Doppler Vibrometer (LDV) system. Strain transducers are installed across all 10 girders for all 3 8 spans at maximum positive moment locations while the LVDT and LDV systems measure the 9 response of Girder 8 of Span 3 at the same location. The WIM system, installed at bridge 10 entrance, continuously records truck traffic information such as axle weights and spacing, 11 vehicle speed, vehicle class and lane position. The LVDT system measured the deflection of the 12 girder at the maximum positive moment location. The non-contact LDV provides readings for 13 the velocity and displacement of the girder. 14

During the data collection, when the weight of a truck is larger than the weight of an HS-20 15 truck (i.e., 72 kips), this truck is identified as a “heavy” truck, and then the data collection system 16 is triggered to record the bridge response for that loading event. The output files are all linked 17 by a timestamp and truck ID number. Periodically, the network is accessed remotely and the 18 files are downloaded and analyzed. 19

20

BRIDGE DYNAMIC MODEL 21 Deformation requirements are intended to play a significant role in controlling bridge vibrations. 22 Therefore, it is important to understand the dynamic/vibration behavior of a bridge subjected to 23 normal truck traffic loading conditions. In this study, a three-dimensional dynamic computer 24 model (3-D Model) developed by Nassif et al. (2003) [26] was used to predict the responses of 25 girder bridges. The model consists of three sub-models: bridge model, vehicle model, and road 26 roughness model to represent the interaction between the truck, bridge, and road roughness. The 27 bridge model is based on the efficient grillage analysis approach. The five axle semi tractor-28 trailer vehicle model is a three dimensional representation of the most common truck on the 29 highways as observed by Nassif (1993) [4]. The bridge response is computed from the 3-D 30 computer model using the Newmark- β method. Nassif et al. (2003) [26] presented the 31 experimental validation of this 3-D model by comparing computed Dynamic Load Factor (DLF) 32 with the experimental results based on field tests done by Nassif and Nowak (1995) [27]. 33

As described previously, the experimental data collected from the Doremus Avenue Bridge 34 was used to validate the model. It is also noted that the 3-D dynamic model has also been 35 calibrated using data from dynamic tests performed on more than four bridges in the State of 36 Michigan. The Doremus Avenue Bridge grillage model was assembled using 480 longitudinal 37 and 441 transverse elements. The stiffness matrix of the bridge model is calibrated by matching 38 the measured static stresses with the calculated ones from 3-D Model, as shown in Figure 3. The 39 possible reasons causing the variation of the measurements includes the road roughness, 40 variation in truck dynamics (e.g., suspension and axle configuration), and variation of truck 41 loading location. Next, the mass matrix of the bridge model is calibrated by matching the first 42 natural frequency to the free vibration testing (i.e. 1.59 Hz as shown in Figure 4) with those 43 calculated from 3-D Model. 44



7

As a result, the calibrated dynamic models were applied to a suite of designed HPS bridges 1 with various depth-to-span ratio and slab thickness. A parametric study was performed to 2 identify the effects of the superstructure, truck traffic, and road roughness profiles on bridge 3 vibration levels, with particular emphasis on the effects of the steel girder depth and concrete 4 slab thickness. Two 5-axle trucks obtained from the field testing of Doremus Avenue Bridge 5 were used in this study with typical truck properties. The configurations of these two trucks are 6 shown in Figure 5. Both multiple truck configurations (i.e. two trucks side-by-side) and one 7 single truck configuration were also considered in this study. 8

9

ANALYSIS RESULTS 10 As stated earlier, the deflection limits and span-to-depth ratio specifications from AASHTO 11 LRFD Bridge Design Specification need to be evaluated. Figure 6 shows a plot of the maximum 12 static deflections versus the depth-to-span ratios for different concrete slab thicknesses. It is 13 noted that the depth-to-span limitation was used as D/L = 0.027 for these designed bridges. 14 From Figure 6, it can be observed that the deflection limits can still be met, even if the minimum 15 depth-to-span ratios are not satisfied. It is also observed that, for concrete slab thickness ranging 16 from 8.66” to 12” (0.220 m to 0.305 m), when there is a decrease in the steel girder depth there is 17 a slight increase in the maximum static deflections. On the other hand, Table 1 shows that the 18 maximum vertical accelerations depend on both bridge and truck properties. For example, Truck 19 A generally induces higher vibrations than Truck B for the same bridge. The multiple-presence 20 of trucks (i.e. side by side) often does not increase the bridge vibrations, although multiple 21 presences of trucks always generate more static deflection. Figure 7 shows that the bridge 22 vibration can be well controlled under the “perceptible” level by changing the concrete slab 23 thickness, even if the D/L limit is not satisfied. This indicates that a shallower HPS girder can be 24 used if the depth-to-span ratio limit is ignored. On the other hand, if the depth-to-span ratio limit 25 is considered, a larger girder depth needs to be used, which means that the cost of the section will 26 increase. Moreover, Figure 8 shows the acceleration records in the time domain for the concrete 27 slab thickness of 8.66 inches (0.220 m). It can be observed the peak acceleration decreases from 28 24.5 in./sec.2 (0.62 m/sec.2) to 20.49 in./sec.2 (0.52 m/sec.2), which is around 16 % of reduction, 29 even if the depth-to-span ratio changes from 0.016 to 0.032 (i.e. doubling the depth-to-span ratio). 30 This indicates that the change in the steel girder depth has little effect on the bridge vibrations for 31 the same concrete slab thickness. In contrast, Figure 9 shows the acceleration records in the time 32 domain. It can be observed that when the slab thickness increased from 8.66 in. (0.220 m) to 12 33 in. (0.305 m), the peak acceleration deceased by 54%, from 35.72 in./sec.2 (0.91 m/sec.2) to 34 16.56 in./sec.2 (0.42 m/sec.2). This suggests that the increase in slab thickness has a significant 35 effect on the vibration control of HPS bridges. 36

As mentioned previously, vehicle rideabilities and human responses to bridge vibration play 37 an important role in determining the deflection limits. Therefore, the Australian and Canadian 38 bridge design codes relate the static deflection limits to the first natural frequency of bridge as 39 was shown earlier in Figure 1. Figure 10 shows the calculated static deflections per the New 40 Jersey Bridge Design Specifications and those specified in the Australian and Canadian bridge 41 design codes. It is interesting to note that, while the deflection limits are met according to the 42 Australian bridge design codes for all of these 12 bridges, the two bridges that have a concrete 43 slab thickness of 8.66” (0.220 m) with depth-to-span ratio equal to 0.027 and 0.032, respectively, 44 do not meet the deflection limits in the Canadian bridge design code. Moreover, the two bridges 45



8

that do not meet the NJ bridge design specifications (i.e. L/1000) do have the concrete slab 1 thickness of 8.66” (0.220 m) with reduced depth-to-span ratio of 0.016 and 0.022, respectively. 2 Figure 11 (a), (b), and (c) show plots of the maximum vertical accelerations versus the first 3 natural frequency for different concrete slab thicknesses under various loading conditions. The 4 bridges with the concrete slab thickness of 8.66” (0.220 m) experience the most unpleasant 5 vibrations (see Figure 11 (a)). Moreover, Figure 11 provides strong evidence that the bridges 6 with the same first natural frequency may experience large variation in their maximum vertical 7 accelerations under different truck loads. In other words, the first natural frequency, as used by 8 the Canadian as well as Australian Codes, does not effectively control bridge vibrations. Figure 9 12 shows the variation of the maximum acceleration versus the girder moment of inertia. It is 10 observed that there is a strong correlation between maximum acceleration and girder moment of 11 inertia. Figure 12 illustrates the effect of the slab thickness in reducing the maximum vertical 12 acceleration, indicating that control of vibration can be achieved by increasing mass and stiffness 13 of the composite girder without the need to increase steel girder depth. The authors also noted 14 that the moment of inertia of composite girder increased by 10% (from 51.6 ft4 to 57.3 ft4) even 15 the D/L increased from 0.021 to 0.032, compared to an increase by 22% (from 51.6 ft4 to 66.5 16 ft4) when the slab thickness increased from 10 in. to 12 in. with D/L equals to 0.021. This 17 confirms that the increase of slab thickness can enhance the stiffness of the composite girder 18 effectively leading to further reduction to the vibration of the structure. 19

20

CONCLUSIONS 21 This paper presents results of a comprehensive evaluation of the deflection criteria from various 22 Codes using a 3-D dynamic model. A parametric study was conducted to identify the most 23 sensitive parameters to control the vibration of steel girder bridges. Based on the analysis results, 24 the following conclusions could be made: 25

• Neither depth-to-span limitations nor static deflection criteria could provide an effective 26 vibration control of steel girder bridge under normal truck traffic conditions. 27

• If the depth-to-span ratio limit is not considered, the more economic design can be 28 achieved by choosing shallower HPS girder sections while controlling the bridge 29 vibration well under the “perceptible” level by increasing the concrete slab thickness. 30

• Bridges with the same first natural frequency may experience large variation in their 31 maximum vertical accelerations under different truck loads. Therefore, the first natural 32 frequency of the bridge, as used by the Canadian as well as Australian Codes, may not 33 effectively control bridge vibrations. 34

• The vertical acceleration of HPS girder bridges can be effectively controlled by 35 increasing the mass and stiffness of the composite girder (i.e. increase concrete deck 36 thickness) without the need to increase HPS girder depth. 37

38

ACKNOWLEDGEMENTS 39

The research project related to instrumentation and monitoring of the Doremus Avenue Bridge is 40 sponsored by the New Jersey Department of Transportation (NJDOT) that is gratefully 41 acknowledged. The financial support and the technical assistance of NJDOT staff Harry Capers, 42



9

Jr. (retired), Nick Vittilo (retired), Jose Lopez (retired), W. Lad Szalaj (retired), and Dick Dunne 1 is gratefully acknowledged. The help of previous graduate students Nakin Suksawang, Joe Davis, 2 and Talat Abu-Amra, is also acknowledged. The analytical work by the second author was done 3 prior to his employment at the Bureau of Reclamation, the U.S. Department of Interior. The 4 findings expressed in this article are those of the authors and do not necessarily reflect the view 5 of NJDOT. 6

7

REFERENCES 8 1. AASHTO (2008). Load Resistance and Factor Design, Bridge Design Specifications. 9

America Association of State Highway and Transportation Official, Washington, D.C. 10

2. “New Jersey Bridge Design Specifications,” (2006), New Jersey Department of 11 Transportation, Trenton, NJ. 12

3. Demitz, J. R., Mertz, D. R., and Gillespie, J. W. (2003, March). Deflection Requirements 13 for Bridges Constructed with Advanced Composite Materials. Journal of Bridge 14 Engineering, 8(2), 73-83. 15

4. Nassif, H. H. (1993). Live Load Spectra for Girder Bridges. Ph.D. Dissertation, 16 Department of Civil Engineering, University of Michigan, Ann Arbor, Michigan, pp. 259. 17

5. Gindy, M. (2004). Development of a Reliability-Based Deflection Limit State for Steel 18 Girder Bridges. Ph.D. Dissertation, Department of Civil Engineering, Rutgers, The State 19 University of New Jersey, Piscataway, New Jersey, pp. 267. 20

6. Reiher, H. and Meister, F. J. (1931). The Effect of Vibration on People. (in German(, 21 Forschung auf dem Gebeite des Ingenieurwesens, Vol. 2, No. II, P381. Translation: 22 Report No. F-TS-616-RE, Headquarters Air Material Command, Wright Field, Ohio, 23 1946. 24

7. Goldman, D. E. (1948). A Review of Subjective Responses to Vibratory Motion of the 25 Human Body in the Frequency Range 1 to 70 Cycles per Second. Naval medical research 26 institute, National naval medical center, Bethesda, MD. 27

8. Janeway, R. N. (1950). Vehicle Vibration Limits for Passenger Comfort. From Ride and 28 Vibration Data, Special Publications Department (SP-6), Society of Automotive Engineers, 29 Inc., p. 23. 30

9. Oehler, L. T. (1957). Vibration Susceptibilities of Various Highway Bridge Types. 31 Michigan State Highway Department (Project 55 F-40 No. 272). 32

10. Oehler, L. T. (1970, February). Bridge Vibration – Summary of Questionnaire to State 33 Highway Departments. Highway Research Circular. Highway Research Board (No. 107). 34

11. Wright, D. T. and Green, R. (1964, May). Highway Bridge Vibration. Part II: Report No. 35 5 Ontario Test Programme. Ontario Department of Highways and Queen’s University. 36 Kingston, Ontario. 37

12. Wright, R. N. and Walker, W. H. (1971, November). Criteria for the Deflection of Steel 38 Bridges. Bulletin for the America Iron and Steel Institute, No. 19. 39



10

13. Ontario Ministry of Transportation, Quality and Standards Division (1995) Ontario 1 Highway Bridge Design Code/Commentary and March 1995 update, Quality and 2 Standards Division, Toronto, Ontario, Canada. 3

14. Nassif, H., Suksawang, N., Davis, J., Gindy, M., Abu-Amra, T. (2010) “Instrumentation, 4 Field Testing, and Monitoring of the Doremus Avenue Bridge: Superstructure, “FHWA-5 NJ-2005-13, Final Report Submitted to NJDOT, 155 pp. 6

15. American Society of Civil Engineering. (1958, May). Deflection Limitation of a Bridge. 7 Journal of the Structural Division, 84, (Rep. No. ST3). 8

16. Wu, H. (2003) Influence of Live-Load Deflections on Superstructure Performance of Slab 9 on Steel Stringer Bridges. Ph.D. Dissertation, Department of Civil and Environmental 10 Engineering, West Virginia University 11

17. Nowak, A. S. and Grouni, H. N. (1988). Serviceability Considerations for Guideways and 12 Bridges. Canadian Journal of Civil Engineering, 15(4), 534-537. 13

18. Ministry of Transportation, Quality and Standards Division (1991) Ontario Highway 14 Bridge Design Code/Commentary, (3rd edition). Toronto, Ontario, Canada. 15

19. CSA International (2000, May). CAN/CSA– S6- 00 and Commentary. Canadian 16 Highway Bridge Design Code. Canadian Standards Association, Toronto, Ontario, 17 Canada. 18

20. ’92 AUSTROADS BRIDGE Design Code (1992). SECTION TWO-CODE Design Loads 19 and its COMMENTARY, AUSTROADS, HAYMARKET, NSW, AUSTRALIA. 20

21. ’96 AUSTRALIAN BRIDGE Design Code (1996). SECTION SIX-CODE Steel and 21 Composite Construction, AUSTROADS, HAYMARKET, NSW, AUSTRALIA. 22

22. Oriard, L. L. (1972). Blasting Operations in the Urban Environment. Bulletin of the 23 Association of Engineering Geologists, IX (1.), pp 27-46 24

23. Burke, M. P. (2001). “Superstructure Flexibility and Disinetegration of Reinforced 25 Concrete Deck Slabs: An LRFD Perspective,” Transportation Research Record No. 1770, 26 pp. 76-83, Paper No. 01-0132. 27

24. Roeder, C. W., Barth, K. B., and Bergman, A. (2002, May). Improved Live Load 28 Deflection Criteria for Steel Bridges. Final Report NCHRP 20-07/133, University of 29 Washington, Seattle, WA. 30

25. Azizinamini, A., Barth, K., Dexter, R., Rubeiz, C. (2004). High Performance Steel: 31 Research Front- Historical Account of Research Activities. Journal of bridge engineering, 32 Vol. 9, No.3, p212-217. 33

26. Nassif, H. H., Liu, M., and Ertekin, O. (2003, March). Model Validation for Bridge- 34 Road-Vehicle Dynamic Interaction System. ASCE Journal of bridge engineering, Vol. 8, 35 No. 2, p112-120. 36

27. Nassif, H. and Nowak, A. (1995) “Dynamic Load Spectra for Girder Bridges,” 37 Transportation Research Board 1476, TRB, National Research Council, Washington, D. 38 C., pp. 69-83. 39

40



11

LIST OF FIGURES 1 FIGURE 1 Cross-Section of Instrumented Span Of The Doremus Avenue Bridge 2

FIGURE 2 Static Deflection vs. First Flexural Frequency (Ministry, 1991; CSA International, 3 2000; AUSTROADS, 1992; AUSTRALIAN, 1996) [18, 19, 20, 21] (U=Unacceptable, 4 A=Acceptable) 5

FIGURE 3 Validation of 3-D Dynamic Model by Measured Stresses at Span 2, Girder 9 6

FIGURE 4 Measured Acceleration Records on Span 3, Girder 8 (Interior), Middle Span (Gindy 7 2004) [5] 8

FIGURE 5 Configurations of Truck A and B 9

FIGURE 6 Maximum Static Deflection vs. Depth-to-Span Ratio (D/L) 10

FIGURE 7 Maximum Vertical Acceleration vs. Depth-to-Span Ratio (D/L) 11

FIGURE 8 Acceleration Records with Identical Slab Thickness 12

FIGURE 9 Acceleration Records with Different Slab Thickness 13 FIGURE 10 Maximum Static Deflection vs. First Natural Frequency 14 FIGURE 11 Maximum Vertical Acceleration vs. First Natural Frequency 15 FIGURE 12 Variation of Maximum Vertical Acceleration vs. Girder Moment of Inertia. 16

17



12

0

20

40

60

80

100

120

140

160

180

200

220

0 2 4 6 8 10

Stat

ic D

efle

ctio

n (m

m)

First Flexural Frequency (Hz)

CSA-w/o sidewalk

CSA-with sidewalk, little pedestrian use

CSA-with sidewalk, significant pedestrian use

AUSTRALIAN

U

A

U

A

1 Figure 1. Static Deflection vs. First Flexural Frequency (Ministry, 1991; CSA International, 2

2000; AUSTROADS, 1992; AUSTRALIAN, 1996) [18, 19, 20, 21] (U=Unacceptable, 3 A=Acceptable) 4

5

6 7

Figure 2. Cross-Section of Instrumented Span of the Doremus Avenue Bridge 8



13

1 Figure 3. Validation of 3-D Bridge Dynamic Model using Measured Stresses at Span 2, Girder 9 2

3

4 Figure 4. Measured Acceleration Records on Span 3, Girder 8 (Interior), Middle Span (Gindy 5

2004) [5] 6

First natural frequency = 1.59 H



14

A B C D

1 2 3 4 514’-8” 4’-7” 23’-4” 4’-6”

10.76 kips 15.74kips

15.74kips

17.05kips

17.05kips

Truck A

13’-4” 4’-5” 23’-6” 4’-7”

10.34 kips 13.87kips

13.87kips

19.26kips

19.26kips

Truck B

1 Figure 5. Configurations of Truck A and B 2

3

0.010

0.015

0.020

0.025

0.030

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

0.01 0.02 0.03 0.04

Max

imum

Sta

tic D

efle

ctio

n (in

.)

Depth-to-Span Ratio (D/L)

t = 8.66"t = 10"t = 12"

> L / 1000

< L / 1000

D / L < 0.027

D / L > 0.027

Max

imum

Stat

ic D

efle

ctio

n (m

)

4 Figure 6. Maximum Static Deflection vs. Depth-to-Span Ratio (D/L) (t = Concrete Slab 5

Thickness) 6 7



15

0.5

0.7

0.9

1.1

1.3

1.5

1.7

20

30

40

50

60

70

0.01 0.02 0.03 0.04

Depth-to-Span Ratio (D/L)

t = 8.66"t = 10"t = 12"

Unpleasant

Perceptible

D / L < 0.027

D / L > 0.027

Max

imum

Ver

tical

Acc

eler

atio

n (m

/sec.2 )

Max

imum

Ver

tical

Acc

eler

atio

n (in

./sec

.2 )

1 Figure 7. Maximum Vertical Acceleration vs. Depth-to-Span Ratio (D/L) (t = Concrete Slab 2

Thickness) 3

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-30

-20

-10

0

10

20

30

0 1 2 3 4 5 6 7 8 9 10 11 12

Acc

eler

atio

n (in

. / se

c.2 )

Time (sec.)

t = 8.66", D/L=0.016

t = 8.66", D/L=0.032

Acc

eler

atio

n (m

/sec

.2 )

4 Figure 8. Acceleration Records with Identical Slab Thickness ((t = Concrete Slab 5

Thickness)) 6



16

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

-30

-20

-10

0

10

20

30

0 1 2 3 4 5 6 7 8 9 10 11 12

Acc

eler

atio

n (in

. / se

c.2 )

Time (sec.)

t = 8.66"

t = 12"

Acc

eler

atio

n (m

/sec

.2 )

1 Figure 9. Acceleration Records with Different Slab Thickness (t = Concrete Slab 2

Thickness) 3

0.010

0.015

0.020

0.025

0.030

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.2 1.3 1.4 1.5 1.6 1.7 1.8

Max

imum

Sta

tic D

efle

ctio

n (in

.)

First Natural Frenquency (Hz)

t = 8.66"t = 10"t = 12"

Canadian bridge design code

Australian bridge design code

> L /1000

< L / 1000

New Jersey bridge design specifications

Max

imum

Stat

ic D

efle

ctio

n (m

)

4 Figure 10. Maximum Static Deflection vs. First Natural Frequency (t = Concrete Slab 5

Thickness) 6 7



17

0.5

0.7

0.9

1.1

1.3

1.5

1.7

20

30

40

50

60

70

1.2 1.3 1.4 1.5 1.6 1.7 1.8

First Natural Frenquency (Hz)

Truck A

Truck B

Trucks A & B (Side by Side)

Unpleasant

Perceptible*

Max

imum

Ver

tical

Acc

eler

atio

n (m

/sec.

2 )

Max

imum

Ver

tical

Acc

eler

atio

n (in

/sec.

2 )

1 (a) Concrete Slab Thickness: 8.66” 2

0.5

0.7

0.9

1.1

1.3

1.5

1.7

20

30

40

50

60

70

1.2 1.3 1.4 1.5 1.6 1.7 1.8First Natural Frenquency (Hz)

Truck A

Truck B


Unpleasant

Perceptible*

Max

imum

Ver

tical

Acc

eler

atio

n (in

/sec.

2 )

Max

imum

Ver

tical

Acc

eler

atio

n (m

/sec.

2 )

3 (b) Concrete Slab Thickness: 10” 4



18

0.5

0.7

0.9

1.1

1.3

1.5

1.7

20

30

40

50

60

70

1.2 1.3 1.4 1.5 1.6 1.7 1.8First Natural Frenquency (Hz)

Truck A

Truck B


Unpleasant

Perceptible*

Max

imum

Ver

tical

Acc

eler

atio

n (in

/sec.

2 )

Max

imum

Ver

tical

Acc

eler

atio

n (m

/sec.2 )

1 (c) Concrete Slab Thickness: 12” 2

* Based on 0.5 × (Frequency) ½ 3

Figure 11. Maximum Vertical Acceleration vs. First Natural Frequency 4



19

0.5

0.7

0.9

1.1

1.3

1.5

1.7

0.17 0.27 0.37 0.47 0.57 0.67

20

30

40

50

60

70

20 40 60 80

Moment of Inertia (m4)

Moment of Inertia (ft4)

t = 8.66"

t = 10"

t = 12"

Unpleasant

Perceptible

Max

imum

Ver

tical

Acc

eler

atio

n (m

/sec

.2 )

Max

imum

Ver

tical

Acc

eler

atio

n (in

./sec

.2 )

1 Figure 12. Variation of Maximum Vertical Acceleration vs. Composite Girder Moment of 2

Inertia (t = Concrete Slab Thickness) 3

4

5



20

LIST OF TABLES 1 TABLE 1 Maximum Vertical Acceleration for Different Depth-To-Span Ratios And Slab 2 Thickness Under Various Truck Loading Conditions 3

4



21

Table 1. Maximum vertical acceleration for different depth-to-span ratios and slab thickness 1 under various truck loading conditions 2

Steel Girder Depth, m (in.) 1.44 (56.69) 1.20 (47.24) 0.96 (37.79) 0.72 (28.34) D / L = 0.032 0.027 0.021 0.016

Satisfy minimum D / L = 0.027? Yes Yes No No

Concrete Slab Thickness

8.66 in (0.220 m) Maximum Acceleration, m / sec.^2 (in./sec.^2)

Truck A 1.39 (54.79) 1.49 (58.64) 1.37 (53.82) 1.42 (55.75) Truck B 0.91 (35.79) 1.05 (41.23) 0.94 (37.02) 1.46 (57.42)

Trucks A & B (Side by Side) 1.51 (59.60) 1.52 (59.91) 1.40 (55.21) 1.41 (55.53)

Concrete Slab Thickness 10 in (0.254 m) Maximum Acceleration, m / sec.^2 (in./sec.^2)

Truck A 1.00 (39.30) 1.01 (39.91) 1.02 (40.29) 1.16 (45.80) Truck B 0.77 (30.13) 1.05 (41.46) 0.89 (34.99) 0.84 (33.26)

Trucks A & B (Side by Side) 1.14 (45.05) 1.15 (45.08) 1.18 (46.47) 1.18 (46.36)

Concrete Slab Thickness 12 in (0.305 m) Maximum Acceleration, m / sec.^2 (in./sec.^2)

Truck A 0.71 (28.09) 0.73 (28.84) 0.80 (31.47) 0.86 (33.74) Truck B 0.73 (28.86) 0.69 (27.23) 0.76 (29.89) 0.63 (24.80)

Trucks A & B (Side by Side) 0.71 (28.14) 0.73 (28.55) 0.73 (28.89) 0.77 (30.24) 3 4 5


nassif, liu, su, and gindy 1 - transportation research boarddocs.trb.org/prp/11-3446.pdf · nassif,...

Documents