Experimental Study on Vibration Characteristics of Steel Two Girder Bridges

Transcription

1 Experimental Study on Vibration Characteristics of Steel Two Girder Bridges Koichiro Fumoto 1, Jun Murakoshi 2, Masao Miyazaki 3 ABSTRACT Simplified road bridges with two main girders (steel two-girder bridges) are used as economical bridges in Japan, with span length of more than 50m. As they have lower structural damping and less torsional stiffness than conventional girder bridges, they can be vulnerable to the wind-induced vibrations when their spans become longer. In evaluating the aerodynamic stability of the bridges, the vibration characteristics such as natural frequencies and structural damping are very important parameters, which have hardly been measured accurately by using exciters on two-girder bridges. In this study, those parameters were investigated by vibration tests using the exciter on the bridges with span lengths of 60m and 70m. Also, simple prediction formulae of the natural frequency and structural damping of the bridges were proposed based on the results. KEYWORDS: twin- girder, aerodynamic stability, vibration characteristics, vibration experiment 1. INTRODUCTION In recent years, an increasing number of the rationalized form bridge have been constructed, which applies highly durable PC deck slabs to increase the deck slab support interval, reducing the number of main girders and at the same time, by either simplifying or eliminating the crossbeams, lateral bracing, and other lateral connecting members (below called, steel two-girder bridges ). Originally this form was used for bridges with span length up to about 50m, but recently, it has been reported that the applicable span length has been greatly increased in order to further lower costs 1). Regarding the wind resistance performance of this bridge form, the simplification or elimination of lateral connecting members has reduced its torsional stiffness below that of conventional steel bridges with many main girders, and the use of rubber bearings since the revision to the Road Bridge Guideline of 1996 has lowered structural damping. These changes have altered vibration characteristics, causing concern with wind resistance of long spans Example 2) - 4). Until now, wind tunnel testing of two dimensional models has been done during design, and it has been reported that this has confirmed wind resistance and contributed to the improvement of bridge sections Example 5) - 7). But because wind tunnel testing is expensive and time-consuming, proposing a method that can provide an approximate verification of dynamic wind resistance without wind tunnel testing is extremely significant. The goal of this study is to develop a method of estimating structural characteristics necessary to verify wind resistance in order to simply and efficiently predict the characteristics of vibration caused by wind at the wind resistance design stage of medium and long bridges based on the results of multiple tests. Specifically, a study of natural frequency and structural damping predication formulae was done by conducting actual bridge vibration testing of steel two-girder bridges 2) - 4) and performing a comparative analysis with the results of past research. Then, a study of the precision of the analysis of frequencies that impact on the wind resistance of steel two-girder bridges was done. 2. VIBRATION TESTING OF THE ACTUAL BRIDGE 8), 9), 10), 11), 12) 1 Senior Researcher, the Structures Research Group, Public Works Research Institute (1-6 Minamihara, Tsukuba City, ) 2 Team Leader, the Structures Research Group, Public Works Research Institute (1-6 Minamihara, Tsukuba City, ) 3 Japan Bridge Association, Vibration Subcommittee ( Ginza, Chuo-ku, Tokyo, )

2 2.1 Experiment Purpose To evaluate wind resistance of a bridge, it is extremely important to clarify its natural frequency, structural damping, and other structural characteristics, but until now, few experimental studies of the vibration characteristics of a steel two-girder bridge have been performed using an exciter. Comparisons of actual bridges have been done by performing level difference excitation or crane excitation using large vehicles, but it is difficult to produce a certain degree of amplitude by these methods and so it is necessary to perform vibration testing using exciters in order to obtain data with highly reliable precision. So as part of joint research with the Japan Bridge Association (below, JBA ), exciter vibration testing was done using two steel two-girder bridges (Bridge A (maximum span length 60m: skew bridge) 10), Bridge B (maximum span length 70m) 11) and one steel narrow box-girder bridge (Bridge C, maximum span 110m) 12) to study their vibration characteristics. The steel narrow box-girder bridge was made by narrowing the width of the box section from the width of a conventional box-girder bridge and simplifying the internal structure of the box-girder, and because it is assumed that this lowers its torsional stiffness, it was tested in the same way as the steel two-girder bridge. 2.2 Experiment The experiment was done by the procedure: microtremor measurement without excitation and preliminary excitation test to determine the frequency produced by the exciter, then causing resonance using the exciter followed by shutting off all the exciters at once and performing a excitation test to measure the vibration characteristics of the bridge. The exciter that was used (0.1 to 2.0Hz) is owned by the Public Works Research Institute (Photo 1). After reaching steady excitation state up to 100 gal that is the standard for usability in the Wind Resistance Design Manual 13), the exciter was abruptly shut off to measure the structural damping of the free vibration state. 2.3 Summary of the Results Of the test results, the series of vibration test results were organized according to the concept of the prediction formulae in the Wind Resistance Manual Natural Frequency Figure 1 plots the results of measurements of vibration of the other steel two-girder bridges that were vibration tested by crane excitation or level difference excitation etc. 8), but the prediction formulae in the Wind Resistance Design Manual provide values on the bottom limit side regardless of the bridge form. Using the data in Figure 1, it is impossible to clarify clear tendencies by bridge form and by girder section, but in order to approximately estimate the vertical deflection primary frequency, it is assumed to be a practical yardstick, even when the prediction formula is provided as a function only of the maximum span length as in the past. Figure 2 organizes the frequency ratios used to obtain the torsional primary frequency. The frequency ratios of the two-girder bridges that were vibration tested including bridge A and bridge B range from 1.1 to 1.3, the prediction formula f f h =2.0for the open section spandrel beam shows differing tendencies, and it appears to be necessary to newly set approximately f f h =1.1 on the lower limit value side. But on bridge C, it is f f h =1.9, that is greater than that of the steel two-girder bridges, and is a value closer to the prediction formula for the open section spandrel beam in the Wind Resistance Design Manual. This presumably occurs because on this bridge, the box-girder section is much wider than the conventional steel narrow box girder, and rather, it is a value closer to this, because it approximates that of the open section spandrel beam in the Wind Resistance Design Manual Logarithmic Damping Ratio

3 The logarithmic damping ratio has long been said to have amplitude dependency. Therefore, a vibration test was done, varying the amplitude of the excitation. Figure 3 shows the result for bridge B. This result shows that it has amplitude dependency. It also reveals that as the amplitude rises, the structural damping also increases, and in bridge B, a comparison of structural damping at amplitude of 10gal (logarithmic damping ratio, approx ) and structural damping at amplitude of 120gal (logarithmic damping ratio, 0.040) shows an increase of approximately 60%. And it was confirmed that in all bridges, the values of the frequency and structural damping are generally stable during steady excitation test from an amplitude of 50 to 100gal. Regarding the amplitude dependency of the structural damping, first it is assumed that the vibration does not move the entire bridge, leaving places where it is locally ineffective, and although this is a peculiarity of rubber, it may be impacted by the non-linear property of the equivalent stiffness and equivalent damping constant (in all cases, three constituents: horizontal, vertical, and rotational) in the minute vibration range of rubber bearings that distribute horizontal force during an earthquake. These results have confirmed that the structural damping with amplitude of 100gal (logarithmic damping ratio) has a value of 0.04 or more at the vertical deflection primary mode, and 0.05 or more at torsional primary mode. Regarding the structural damping with amplitude of 100gal of bridge A and bridge C (logarithmic damping ratio), value of 0.04 gal or more and value of 0.05gal or more were confirmed under the vertical deflection primary mode and torsional primary mode of bridge A respectively, and value of 0.05 or more were confirmed under vertical deflection primary mode and torsional primary mode at bridge C. The results of measurements of structural damping were organized by form of bridge and by type of bearing 9), but scattering is large, and it is difficult to state that it is possible to specify a certain value as stipulated in the Wind Resistance Design Manual. But as an overall tendency, structural damping tends to be smaller with rubber bearings than with steel bearings, and it is also impacted by the friction resistance of bearings. Therefore, with reference to the prediction formula =0.75/L for structural damping of a bridge using steel bearings in the Wind Resistance Design Manual (logarithmic damping ratio), if it is assumed that it will be on the safe side if the same form is used for a bridge with rubber bearings, the yardstick is approximately the prediction formula =0.35/L. Figure 4 shows that this prediction formula approximately predicts the lower limit side of the structural damping of steel two-girder bridges and steel box-girder bridges that include bridges A, B, and C Amplitude Dependency of the Natural Frequency This free damping test revealed amplitude dependency of the natural frequency and of structural damping. The method was to divide the size of the amplitude into a number of tens of levels based on damping wave form data obtained by the free damping test to obtain the frequency for each amplitude. Here, Figure 5 shows the frequency amplitude relationship based on bridge B. According to this, if amplitude dependency is confirmed using the vertical deflection primary mode as an example, a comparison of the frequency with amplitude of 10 gal (approx. 1.33Hz) with the frequency with amplitude of 120gal (approximately 1.31Hz) reveals a fall of about 2%. If the amplitude dependency is confirmed taking the primary mode as the example, frequency of amplitude 10gal (approx. 1.33Hz) and frequency of amplitude 120gal (approx. 1.31Hz) are compared, revealing a decline of about 2%. Amplitude dependency of structural damping (friction damping in particular) has been pointed out in the past, but this study has confirmed that although only small, the natural frequency also has amplitude dependency. And this tendency was also seen in bridge A and bridge C, and a comparison of amplitude of 10gal with amplitude of 100gal reveals that while it is relatively not great, it falls from between 4% and 2%. 3. FREQUENCY ANALYSIS PRECISION

4 A discrepancy of more than 10% was found between natural frequency measured in a steel two-girder bridge and a value obtained by analysis based on a three-dimensional skeleton model (the rotational stiffness of rubber bearings and the stiffness of the concrete barrier curb are not considered) (Table 1). The natural frequency is an important parameter that determines the manifest wind speed of the flutter, the galloping and the vortex excitation, so it is important to more precisely analyze the natural frequency in order to more rationally verify wind resistance. This section of this report explains how a 3-dimensional FEM model and a three-dimensional skeleton model were prepared for the steel two-girder bridge described in the previous section and the analytical values of the natural frequency of the two models were compared at the same time as, focusing on the contribution of rotation stiffness of the rubber bearings and the stiffness of the concrete barrier curb as factors causing discrepancies with measured values, their impact on the natural frequency was studied. 3.1 Analysis Models Three-dimensional Skeleton Analysis Model The three-dimensional skeleton model forms a skeleton with the main girders, crossbeams, and substructure as elastic beam elements and models the rubber bearings as translation/rotation linear spring elements. A mesh of main girders and crossbeam elements was modeled at the bottom surface of the deck slabs, and the stiffness of the deck slabs was added to the stiffness of the main girder beam elements. The mass of the superstructure was arranged divided into two parts on nodes of the main girder beam elements, and the mass of the substructure was similarly arranged on nodes of beam elements. This analysis focuses on the vibration mode of the superstructure, so with the boundary condition of the foundation assumed to be constraint in all directions, deformation at the foundation position was ignored. As the boundary condition of the rubber bearings, the translation motion in the bridge axis direction and the vertical direction are treated as elastic support based on the horizontal spring constant K S and vertical spring constant K V of the horizontal force distribution type rubber bearings during an earthquake shown in the Road Bridge Bearing Manual 14). The translation motion at right angles to the bridge axis was treated as constraint, because it is equipped with side blocks. Rotation deformation was considered to be unrestricted in all directions by ignoring the rotational stiffness of the rubber bearings (see Fig. 6) Three-dimensional FEM Model The three-dimensional FEM model consisted of the main girders and crossbeams as shell elements (only the crossbeam flanges are beam elements) and the deck slabs as solid elements divided into a single layer. It has been pointed out that in the case of a high order vibration mode, the number of divisions has an impact on the precision of the calculation of the static displacement and the natural frequency of the overall system, but the object here is the primary mode so it has only a small impact. Among secondary members, only stiffening members above bearing points were modeled by shell elements. The modeling of the substructure, boundary conditions of the foundation, and boundary conditions of the bearings were handled in the same way as by the skeleton model. The mass of the superstructure was considered based on the material density of each element (unit mass), but with this method, the masses of stiffening members, gussets, connecting bolts, etc. are not considered, so the material density of steel material was adjusted so that it conforms with the steel weight shown in the design calculation documents. And the masses of the inspection road and temporary paving etc. were added as supplementary mass. As confirmation of the distribution of these masses, it was confirmed that the bearing point reaction force when gravity acceleration was added to perform static analysis conformed with the bearing point reaction force in the design calculation documents and the skeleton model within an error of 1% or less. (see Figure 7) 3.2 Impact Of The Concrete Barrier Curb (Sensitivity Analysis) The impact of the concrete barrier curb and the rotation of the rubber bearings were considered based

5 on this model. Table 2 shows the results. The rotating spring constant K r is not stipulated by the Road Bridge Bearing Manual 14), so the formula proposed by Reicha 15) was used. This formula is an equation induced from relatively large amplitude testing, and it is highly likely that it is unsuited for a case were deformation of a bearing such as vortex excitation occurs in the micro amplitude range, but it is used here as one index. Considering the stiffness of the concrete barrier curb in the basic model in a comparison of measured and analytical values increases the precision of the estimation about 5% in the cases of both bridges. The sensitivity to the stiffness of this concrete barrier curb was the highest in this sensitivity analysis, and it can be stated that the stiffness of a concrete barrier curb cannot be ignored if it is newly constructed in order to perform eigenvalue analysis. Incidentally, on bridge A, the difference between the skeleton and FEM models is large. This is presumably caused by the fact that bridge A is a skew bridge, and other factors that make it difficult to model it with a skeleton model. 4. CONCLUSIONS The purpose of this research was to study the vibration characteristics and other factors that play an important role in hypothesizing vibration phenomena caused by wind in steel two-girder bridges based on the results of a series of vibration tests of actual bridges performed as cooperative research with the JBA. Analysis models were studied to improve the precision of the estimation of the natural frequency that is an important parameter in the verification of wind resistance. The following are the major results obtained from this research. 1) Vibration testing of two steel two-girder brides (maximum span lengths of 60m and 70m) confirmed that the natural frequency ratio of vertical and torsional 1 st mode is about 1.1, and that although structural damping is a value lower than that of conventional steel bearings, if paving is laid, the predicted structural damping (logarithmic damping ratio) is 0.04 or more in the 1 st vertical deflection mode, and is 0.05 or more in the 1 st torsional mode. 2) The results of the vibration testing of steel two-girder bridges etc. have confirmed that structural damping etc. is amplitude dependent. 3) It was also confirmed that to estimate structural characteristics, the frequency of deflection does not cause problems using the prediction formulae in the present Road Bridge Wind Resistance Design Manual, but it would be better to revise the frequency ratio or structural damping prediction formulae when calculating the frequency of torsion. 4) Natural frequency analysis performed using a three-dimensional FEM model has confirmed that differences between modeling impacts the natural frequency. The results confirmed that modeling a concrete barrier curb to consider the section stiffness reduces discrepancies between analytic values and measured values. ACKNOWLEDGMENTS We obtained valuable test data to conduct this research by measuring three bridges with the assistance of the Japan Highway Public Corporation (organization name at the time of the test). The authors wish to conclude by expressing their deep gratitude to everyone who participated in providing this assistance. REFERENCES 1) Japan Bridge Association: Birth of new bridges II, May ) Yamada, Daihara, Kamishima, Sawada, Edamoto, Shinohara: Wind resistance of two-girder bridges, Kyoryo to kiso (Bridges and Foundations), Vol. 36, No. 2, February ) Watanabe, Harikane, Kuroda, Narita: Wind-resistance characteristics of long-span steel two-girder

6 bridges, Proceedings of the 57 th Annual Conference of the Japan Society of Civil Engineers, I-478, September ) Shimizu, Yamada, Katsuchi, Kamishima, Research on long span two-girder bridges from the perspective of wind resistance stability, Proceedings of the 56 th Annual Conference of the Japan Society of Civil Engineers, I-B357, September ) Hagino, Sakuma, Muramatsu, Nanjo, Hatanaka: Study of the wind resistance of a steel two-girder bridge (Ananaigawa Bridge), Proceedings of the 58 th Annual Conference of the Japan Society of Civil Engineers, I-093, September ) Aoki, Sasaki, Kaneshige, Maehara: Study of wind resistance stability of a steel two-girder compound rigid-frame bridge (Imabeppugawa Bridge), Proceedings of the 56 th Annual Conference of the Japan Society of Civil Engineers, I-B349, September ) Yasuda, Honke, Shimizu, Abe, Okuda, Osugi: Bridge use vibration control devices (keel dampers), Kyoryo to kiso (Bridges and Foundations), April ) Murakoshi, Fumoto, Ashizuka, Kiyota, Miyazaki: Empirical study of wind resistance stability and vibration characteristics of steel two-girder bridges, Proceedings of the Vibration Colloquium, p. 357 p. 362, September ) Fumoto, Murakoshi, Suzuki, Idei, Goshima, Miyazaki, Kiyota: Field vibration testing of bridges using exciters, Proceedings of the 59 th Annual Conference of the Japan Society of Civil Engineers, I-673, September ) Fumoto, Murakoshi, Arai, Ashizuka. Miyazaki, Kiyota: Steel two-girder bridge vibration tests, Proceedings of the 58 th Annual Conference of the Japan Society of Civil Engineers, I-766, September )Fumoto, Kutsuna, Kiyota, Miyazaki, Arai: Field vibration testing of a long-span two-girder bridge, Proceedings of the 60 th Annual Conference of the Japan Society of Civil Engineers, I-534, September ) Fumoto, Kutsuna, Arai, Kiyota, Miyazaki: Field vibration testing of a long-span two-girder bridge (narrow box girder), Proceedings of the 60 th Annual Conference of the Japan Society of Civil Engineers, I-534, September ) Japan Road Association: Road Bridge Wind Resistance Design Manual, July ) Japan Road Association: Road Bridge Bearing Manual, April ) Reicha, C.Design of Elastomer Bearings, PCI Journal, pp.62-78, October, 1964.

7 Photo 1. View of the Installed Excitation f h Vertical deflection natural frequency Bridge A Bridge B L Maximum span length L (m) Figure 1. Deflection Frequency and Span Length Steel two-girder bridge f/f h Frequency ratio Bridge A Prediction formula based on the Wind Resistance Manual (Case of truss girders, open section spandrel beam) f f /f h =2.0 /f h =2.0 Bridge B Steel f two-girder /f h =1.1 bridge f /f h =1.1 L (m) Maximum span length L (m) Figure 2. Frequency Ratio and Span Length

8 Damping ratio Bending primary mode: amplitude Vs damping ratio Damping ratio at each amplitude analyzed based on free damping wave form (early morning 25 C) Damping ratio at each amplitude analyzed based on free damping wave form (mid day 30 C or higher) Regression curve based on the method of least squares (early morning 25 C) Regression curve based on the spline method (early morning 25 C) Amplitude (gal) (a) Vertical deflection primary mode Damping ratio Torsion primary mode: amplitude Vs damping ratio Damping ratio at each amplitude analyzed based on free damping wave form (early morning 25 C) Damping ratio at each amplitude analyzed based on free damping wave form (mid day 30 C or higher) Regression curve based on the method of least squares (early morning 25 C) Regression curve based on the spline method (early morning 25 C) (b) Torsional primary mode Amplitude (gal) Figure 3. Amplitude Dependency of Structural Structural damping (logarithmic damping ratio) Bridge A B C Maximum span length L (m) Figure 4. Structural Damping of Girder Bridges Conventional concrete bridge Steel bearings Conventional steel bridge Steel box-girder bridge (deflection) Steel box-girder bridge (torsion) PC slab steel girder (deflection) Rubber bearings PC slab steel girder (torsion) Prediction formula (steel bearings) =0.75/ L Prediction formula (rubber bearings) =0.35/ L

9 Frequency (Hz) Bending primary mode: amplitude Vs frequency Frequency based at amplitude analyzed based on free damping wave form (early morning 25 C) Microtremors Frequency at each amplitude analyzed based on free damping wave form (mid day 30 C or higher) Various tests Regression curve based on the method of least squares (early morning 25 C) Sweep test Damping test (a) Vertical deflection primary Amplitude (gal) Frequency (Hz) Torsional primary mode: amplitude Vs frequency Microtremors Sweep test Damping test Frequency based at amplitude analyzed based on free damping wave form (early morning 25 C) Frequency at each amplitude analyzed based on free damping wave form (mid day 30 C or higher) Various tests Regression curve based on the method of least squares (early morning 25 C) (b) Torsional primary mode Amplitude (gal) Figure 5. Amplitude Dependency of Natural Frequency Table 1. Comparison of Measured Natural Frequencies with Analytical Values Based on a Skeleton Model Mode Vertical deflection primary Torsional primary Frequency ratio Bridge A (paved) Bridge B (paved) Measured Analytical Ratio Measured Analytical Ratio values values Analytical/measured values values Analytical/measured % % % % % %

10 Boundary conditions of the foundation is constraint in all directions Crossbeam beam element Superstructure mass point Rigid beam element Bearing spring Bridge pier beam element Figure 6. Three-dimensional Stereoscopic Superstructure (main girder and deck slab) model shape Temporary paving range (between main girders) Superstructure inspection road (micro-rigidity beam element) * Position 1,650mm towards the inside from G2 Steel plates: shell element Concrete: solid element Deck slab: 40N/mm 2 Half concrete barrier curb: 30N/mm 2 * In the temporary paving range on the top surface of the deck s the temporary paving is model by a micro-rigid shell element (f considering mass) lab, ed or Intermediate crossbeam (Web: shell element, Flange: beam element) Figure 7. FEM Analysis Model Table 2. Frequency When Considering Impacts Frequency Deflection primary Torsional primary Frequency ratio Analytical value Skeleton % FEM % Skeleton % FEM % Skeleton % FEM Bridge A (with temporary paving) Basic model Concrete barrier curb stiffness considered % % % % % % Rotational spring of rubber % % % % % % Bridge B (with temporary paving) Basic model % % % % % % Concrete barrier curb stiffness considered % % Rotational spring of rubber % % % * Bottom: comparison of measured and analytical values *2 When the rotating spring of the rubber is considered in addition to the stiffness of the concrete barrier curb.