Suggestion of Impact Factor for Fatigue Safety Assessment of Railway Steel Plate Girder Bridges

Transcription

1 Suggestion of Impact Factor for Fatigue Safety Assessment of Railway Steel Plate Girder Bridges 1 S.U. Lee, 2 J.C. Jeon, 3 K.S. Kyung Korea Railroad, Daejeon, Korea 1 ; CTC Co., Ltd., Gunpo, Kyunggi, Korea 2 ; Korea Maritime University, Busan, Korea 3 Abstract In Korea, there are about 1, ballastless steel plate girder railway bridges which are short and simple and have been served for over 3 years. As well known, the fatigue phenomenon, which is caused from accumulation of live load stress, is one of the main factors controlling the life of the bridges. In this paper, appropriate impact factors for fatigue check of such bridges are presented from the parametric study on the dynamic behavior of the bridges and the feasibility of the presented impact factors is substantiated through the comparison with the measured values. Keywords: fatigue, impact factor, steel railway bridge, vibrational analysis 1. Introduction It is reported in the Korean statistical data that there are about 2,6 railway bridges under service, and 1, bridges, among them, are ballastless, short, simple steel plate girder bridges which have been served for over 3 years[8]. From now on, they are called as 'such bridges' in this paper. As well known, the fatigue phenomenon, which is caused from accumulation of live load stress for long time, is one of the main factors controlling the life of the bridge, and the bridge is apt to be subject to fatigue damage as the bridge span shortens because the ratio of stress caused by the live load to the total stress and number of stress cycles become higher[11]. Therefore, it can be easily expected that fatigue will become a main factor which increases the maintenance cost of such bridges highly from now on. Bridge design specifications in most countries recommend using a stress level caused by static live load in addition to an impact factor for the static design of structural members of steel bridges. The impact factors specified are to consider a potential extreme impact condition. However, it should be noted that use of the impact factor may develop an over safety design of the bridges since the fatigue is caused from accumulation of live load stress for long time under a normal condition rather than an extreme condition. Therefore, the Japanese Fatigue Design Guide of Steel Highway Bridge[5] recommends to reduce the fatigue design impact factor by 5% of the value used in the normal design except for the bridge ends where cause higher impact. In addition, the impact factor recommended in AASHTO LRFD[1] for the fatigue limit state is also 5% of the factor for the ultimate or serviceability limit states. Validity of such factors was reviewed in Ref.[1]. The Korean Railway Bridge Design Criteria[7] specifies the fatigue design impact factor as the same one used in the normal static design for the bridge whose span length is under 9m, but, for the bridge longer than 9m as 65% of the static design value. However, its background has not been clearly identified yet. Moreover, research related to impact factor in terms of fatigue has not been performed until now in the field of railway bridge in Korea as far as the authors know although various papers about extreme impact factor are available[2, 4]. In this paper, appropriate impact factors for fatigue check of such bridges are presented from the parametric study on the dynamic behavior of the bridges and the feasibility of the presented impact factors is substantiated through the comparison with the measured values.. 2. Definition of impact factor for fatigue check In general, running train develops larger response in the bridge members than that by normal static analysis due to vibration and interaction of bridge and train. Magnitude of the response is influenced by various factors such as running speed, characteristics of bridge and train and so on. Such ect is considered in the bridge design specifications as impact factor. The Korean Railway Bridge Design

2 Criteria[7] specifies the static design impact factor for steel and composite bridges as Equation (1), however, for fatigue design, it regulates to use 65% of the value for the bridge longer than 9m. 2 L i = 5 for L 24 m (1a) 48 i 18 = + 26 L 9 for L > 24 m (1b) in which, L : span length (m) If a stress time history at center of simple span bridge due to single axle moving load is obtained as shown in Figure 1, then, impact factor is calculated using Equation (2) for normal static design. However, for fatigue design, we are interested in the maximum stress range rather than the maximum stress. Therefore, we defined the impact factor as Equation (3) in this paper considering the maximum stress range. Furthermore, Equation (4) will be used to derive a representative value when the impact factors calculated under various analysis conditions are dealt with statistically. Because i95 % value has 95% confidence level for the sample mean, the value is considered as adequate for analyzing fatigue phenomenon. 1 Stress (kgf/cm ) 2 5 f stat f dyn dyn,r Figure 1: Example of stress time history at center of simple span bridge f dyn i static design = 1 (2) f stat f dyn, r i fatigue design = 1 (3) f stat in which, f : maximum dynamic stress dyn f stat : maximum static stress f : maximum dynamic stress range dyn, r σ i = μ (4) N where, μ : sample mean σ : standard deviation N : number of samples 3. Analysis results 3.1 Methodology The typical cross section of bridge used in this paper is shown in Figure 2. The steel plate girder bridge is ballastless, simple and have been served for over 3 years. Their span lengths are short and weight ratios of superstructure to train are very small as shown in Table 1. The detailed dimensions

3 of the bridges are given in the Standard Design Documents' published by the Korea National Railroad[6]. Figure 2: Typical cross section of bridges(unit: mm) Bridge Id. Span length (m) Girder spacing (m) Girder height (m) Sectional area(m 2 ) 2nd moment of area(m 4 ) Total weight at center at support at center at support (tonf) I Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Table 1: Structural properties of bridges Analysis variables included in this paper are described in Table 2 considering the fact that vibrational behavior of the bridge is influenced by various factors, such as train speed, modelling and characteristics of bridge and train and so on. One conventional passenger train(expressed as Saemaeul), one freight train and one high speed train(expressed as KTX) were taken into consideration and their weights and axle spacings are given in Figure 3. The KTX train is also included in this study because the train is running over the conventional line in Korea. In analysis, the train was modelled as multi-axle moving masses and multi-axle moving forces according to Ref.[2], and the results were compared. The multi-axle moving mass model seems to adequate because the weights of superstructure given in Table 1 are very small comparing to those of train. The bridge was modelled as a beam with 6 DOFs. The equations of motion of bridge discretized by finite elements can be written in the form: M u& & + C u& + Ku = P ( t ) (5) in which M, C, and K = the mass, damping and stiffness martices, respectively, and are symmetric; u and P (t) = the vectors of nodal displacements and loads, respectively. A dot represents a derivative with respect to time. The load vector is constructed by transforming an arbitrary point loads at arbitrary positions into joint loads by using the cubic Hermitian interpolation functions. When the moving mass model is used, the point load is calculated summing the axle weight and the inertia force. Then, Equation (5) can be solved in the time domain by the direct integration method[3].

4 Items Variables Bridge Id. Train model Train type Train speed (km/h) Vibrational analysis Span length I, Ⅱ, Ⅲ, Ⅳ, Ⅴ, Ⅵ, Ⅶ Moving mass Saemaeul 5-15 (ΔV=2) Effect of bridge stiffness 1, 11, 1, 13% of stiffness of bridge Ⅲ Ⅲ Moving mass Saemaeul 5-15 (ΔV=2) Effect of train model 2 models I, Ⅱ, Ⅲ, Ⅳ, Ⅴ, Ⅵ, Ⅶ Moving mass, Moving force Saemaeul 5-15 (ΔV=2) Effect of train type 3 types Ⅲ Moving mass Table 2: Analysis variables Saemaeul Freight train KTX 5-15 (ΔV=2) 3-8 (ΔV=2) 5-15 (ΔV=2) (a) Saemaeul (2 locomotives + 6 passenger cars) (b) Freight train (1 locomotives + 19 freight cars) (c) KTX (2 power cars + 18 passenger cars) Figure 3: Axle weights and spacings of trains(unit: m, tonf(1tonf=9.81kn)) 3.2 Eigenvalue and critical speed The eigenvalue analysis was also performed to find out the critical speed due to repeated beatings of train axles and impact factor at that speed. Figure 4 shows a relationship between the calculated natural frequencies and span lengths of the bridges. In Figure 4, the dots represent the calculated values and the solid line was constructed by the regression analysis. From this figure, the natural frequency of bridge constructed using the Standard Design Documents[6] can be calculated by 4 L 1.2, in which L is span length. The critical speeds of train, then, can be calculated by Equation (6), and are given in Table 3 for Seamaeul. The shadowed part in the table represents that the critical speed exists within the maximum operating speed(15km/h) of train. As seen in Figure 3, because the axle arrangement of Saemaeul is not completely regular, 5 kinds of the ective beating interval were considered in Table 3. V cr = f S (6) 1 in which, V cr : critical speed of train(m/s) f 1 : first natural flexural frequency of bridge(hz) S : ective beating interval of train(m)

5 Fundamental Frequency (Hz) 6 4 f = 4 L Caculated Regression Curve Bridge Id Span Length (m) Figure 4: Relationship between span length and natural frequency of bridge Span length (m) Frequency (Hz) S = 2.6m S = 5.m Critical speed(km/h) S = 7.6m S = 15.9m S = 23.5m I Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Calculated impact factor Table 3: Critical speed of Saemaeul Vibrational analyses were performed using Saemaeul and the bridges shown in Table 1. The train speed was changed from 5 to 15km with 2km/h interval to investigate ect of train speed. An example of moment time history at center of 25.4m bridge is shown in Figure 5(a), and Figure 5(b) shows the history obtained when the train is running with the calculated critical speed over 16.m bridge. As shown in Figure 5, free vibration component exists after train passed the bridge, and such component is considered to increase maximum stress range used in fatigue check. 4E+5 Dynamic (V=15km/h) 3E+5 Dynamic (V=139.7km/h) Bending Moment (kgf-m) 2E+5 E+ Static Bending Moment (kgf-m) 2E+5 1E+5 E+ Static -2E E (a) L=25.4m, V=15km/h (b) L=16.m, V=139.7km/h Figure 5: Examples of moment time history at center of bridge by Saemaeul In order to investigate dynamic response increment by train speed, impact factors for the bridges of Ⅳ, Ⅴ, Ⅵ and Ⅶ are shown with respect to train speed in Figure 6. These bridges have the critical speed within the maximum operating speed as shown in Table 3. As seen in Figure 6, the speeds bringing

6 about large impact factor are similar to the critical speeds given in Table 3. Therefore, it is confirmed that the dynamic response of bridge has close relationship with axle arrangement of train. From the statistical analysis for train speeds, i values with respect to span length of bridge were calculated and compared in Figure 7. The ect of free vibration is also given in the figure. Generally, impact factors are shown to increase in proportion of decrease of span length but increasing ratio is not as much as specified in the Korean Design Criteria[7], especially in bridge shorter than 9m. This means that impact factor is not solely a function of span length. In addition, ect of free vibration is significant, and about 33-43% of impact factor is from the free vibration. Therefore, the free vibration component should be considered in the fatigue check of simple span bridge L=16.m L=19.2m L=22.3m L=25.4m Vcr=77.km/h Vcr=9.1km/h Vcr=139.7km/h Vcr=17.2km/h Vcr=148.1km/h Vehicle Velocity (km/h) Figure 6: Relationship between impact factor and train speed for different bridge length Span Length (m) with Free Vibration without Free Vibration Design Value (Korean) Figure 7: Relationship between calculated impact factor( i ) and span length 3.4 Effect of bridge stiffness The stiffness of bridge seems to affect the dynamic behavior of bridge. The structural properties of bridges were obtained from the Korean Standard Design Documents[6]. However, the properties can vary depending on designer. Therefore, in this paper, ect of bridge stiffness was investigated by changing it from 1 to 13% of the reference value given in Table 1 for 12.9m bridge used widely in Korea. The resulted impact factors and i values are shown in Figures 8 and 9 with respect to train speed and stiffness ratio, respectively. According to Figure 8, distribution patterns of impact factor by train speed are similar, however, the speed giving maximum impact factor moves to right-hand side with increase of bridge stiffness. In addition, as shown in Figure 9, i value decreases with increase of bridge stiffness but its ect is very small, say, stiffness increase of 1% decreases impact factor 1%. 4 K=1% K=11% K=1% K=13% Vehicle Velocity (km/h) Figure 8: Relationship between impact factor and train speed for different bridge stiffness Stiffness Ratio for Basic Model Figure 9: Relationship between impact factor( i ) and stiffness ratio

7 3.5 Effect of train model Three kinds of train model can be used for vibrational analysis of bridge, say, multi-axle moving force model, multi-axle moving mass model, and multi-degree-of-freedom system model. The moving force model considers axle weight only, however, inertia force in addition to axle weight is also considered in the moving mass model. And, the multi-degree-of-freedom system model considers the suspension system of car body and bogie, so it has an advantage to be able to represent the real behavior of train if its exact mechanical properties used in the model are available. Unfortunately, such exact data does not exist in Korea. If we perform dynamic analysis using the multi-degree-of-freedom system model without exact mechanical data of train, it can lead to a useless result. Therefore, in this paper, dynamic analysis is performed modelling Saemaeul by moving force and moving mass models, and resulted impact factors are compared. It is described in Ref.[2] that moving mass model can estimate the dynamic behavior of bridge reasonably. Impact factors calculated for the shortest and lightest one among bridges of Table 1 are shown in Figure 1 with respect to train speed. Two models show quite different results as seen in Figures 1 and 11. This seems because weight ratio of train to bridge is very large. However, the difference becomes small with increasing span length as shown in Figure 11 because the ratio becomes smaller with increasing span length. In general, it is known that impact factor decrease with span length increasing. However, the moving force model does not show such trend. Therefore, moving mass model seems to be an appropriate train model at this stage. 6 Moving Mass 4 Moving Mass Moving Force Moving Force Vehicle Velocity (km/h) Figure 1: Relationship between impact factor and train speed depending on train model(l=6.6m) Span Length (m) Figure 11: Relationship between impact factor( i ) and span length depending on train model(l=6.6m) 3.6 Effect of train type In this section, ect of train type on impact factor of the bridge was investigated for the bridge of 12.9m. Three types of train shown in Figure 3 were considered. Then, speed of train was changed from 5 to 15km/h for Saemaeul and KTX, and 3 to 8km/h for Freight train with 2km/h increment in order to consider dynamic ect and normal condition in the conventional railroad. Figure 12 shows examples of moment time history calculated by 3 trains modelling as multi-axle moving mass at center of the bridge. It is known from Figure 12 that negative moment occurs regularly by Saemaeul and KTX running, but not by Freight train. Such phenomenon takes place because maximum axle spacings of Saemaeul(13.3m) and KTX(15.7m) are greater than bridge length(12.9m) and then bridge is no loaded temporarily. This phenomenon is more clear by KTX than by Saemaeul owing to difference of axle spacing. Therefore, it can be understood that short span bridge is placed at a disadvantage in terms of fatigue and why the Korean Design Criteria[7] regulates for fatigue check to use the same impact factor as used in normal static design for bridge less than 9m. From the statistical analysis for train speeds, as seen in Figure 13, % 95 i values for Saemaeul and KTX are similar but for Freight train it is about half of them. The reason of this fact seems difference of train speed considered and the negative moment ect mentioned above.

8 2E+5 3E+5 Bending Moment (kgf-m) 1E+5 E+ Bending Moment (kgf-m) 2E+5 1E+5 E+ -1E (a) Saemaeul(V=15km/h) -1E (b) Freight train(v=8km/h) 2E+5 Bending Moment (kgf-m) 1E+5 E+ -1E (c) KTX(V=15km/h) Figure 12: Examples of moment time history at center of bridge(l=12.9m) % 1.6% 22.15% Saemaeul Freight Car KTX Type of Vehicle Figure 13: Effect of train type on impact factor( 4. Suggestion of impact factor for fatigue check As well known, running train develops larger stress ranges in the bridge members than that by normal static load due to various factors such as train speed and interaction of bridge and train and so on. Therefore, dynamic ect should be considered as impact factor for fatigue check. However, such factor is different depending upon design regulations[1, 5, 7, 1]. For example, the Korean Railway Bridge Design Criteria[7] specifies to use 65% of the static design impact factor for fatigue design for the bridge longer than 9m, and the Japanese Fatigue Design Guide of Steel Highway Bridge[5] recommends to reduce the fatigue design impact factor by 5% of the value used in the normal design except for the bridge ends where cause higher impact. In addition, the impact factor recommended in AASHTO LRFD[1] for the fatigue limit state is also 5% of the factor for the ultimate or serviceability limit states. Reduction of impact factor for fatigue check can be understood considering the fact that fatigue is caused from accumulation of live load stress for long time under a normal condition rather than an i )

9 extreme condition. However, we can not say that reduction ratio and its background are clearly identified. In this section, calculated impact factors are compared with field test results and appropriate value is suggested for fatigue check of such bridges. 4.1 Comparison of calculated and measured impact factors Validity of calculated impact factors is confirmed through the comparison with measured values for 11 bridges. Structural types of those bridges are identical to that used in this paper. Bridge list and measured impact factor are given in Table 4[9]. But, because free vibration component was not considered in measured value, the values are compared with calculated i in which the component is not included. Comparison of impact factors with respect to span length of bridge is shown in Figure 14. Among 32 cases, measured value exceeds calculated one slightly in 2 cases only. Therefore, it can be said that analytical approach used in this paper is appropriate and i can be a representative impact factor for fatigue check. Classification Span length (m) A 16. Measured impact factor for various train speeds(%) 4km/h 5km/h 6km/h 7km/h 8km/h 9km/h 1km/h Average (%) B C D E F G H I J K Table 4: Measured impact factor

10 i 95% (w/o Free Vib.) Bridge A (L=16.m) Bridge B (L=19.2m) Bridge C (L=19.2m) Bridge D (L=13.2m) Bridge E (L=12.9m) Bridge F (L=19.2m) Bridge G (L=19.2m) Bridge H (L=22.3m) Bridge I (L=12.9m) Bridge J (L=25.4m) Bridge K (L=25.4m) Span Length (m) Figure 14: Comparison of measured impact factor with calculated i neglecting free vibration component 4.2 Suggestion of impact factor for fatigue check The present Korean design curve and the newly suggested one for fatigue design impact factor of railway bridge are shown in Figure 15 together with calculated i values with respect to span length. Effect of free vibration component is included in the calculated i value, and the newly suggested curve was determined in the same manner as the Japanese and LRFD of AASHTO regulations, say 5% of the value used in the ordinary static design. As mentioned before, the present Korean Design Criteria[7] specifies, for fatigue check of bridge longer than 9m, to use 65% of impact factor for static design. As seen in Figure 15, calculated impact factors have a tendency to increase with span length decreasing like the present Korean Design Criteria[7], but no sudden change at short span bridge of length 9m. In addition, we can see that the criteria overestimate it. From these considerations, it can be concluded that 5% of the impact factor used for ordinary static design is enough for fatigue check of steel plate girder railway bridge. 6 4 i proposed =.5 X Equation (1) Proposed Impact Factor Calculated i 95% Present Korean Design Criteria Span Length (m) Figure 15: Impact factor suggested for fatigue check 5. Conclusions In this paper, appropriate impact factors for fatigue check of ballastless, short, simple steel plate girder railway bridges which have been served for over 3 years are investigated, and following conclusions were obtained. (1) Because the present Korean Railway Bridge Design Criteria has a tendency to overestimate impact factor in terms of fatigue, it is enough for fatigue check of steel plate girder railway bridge to use 5% of the impact factor used for ordinary static design.

11 (2) Simple and short span bridge whose span length is shorter than maximum axle spacing of train is placed at a disadvantage in terms of fatigue because negative moment increasing stress range occurs regularly when train is passing over. (3) Impact factor for fatigue check of simple span bridge is increased by free vibration component. (4) Dynamic behavior of bridge whose mass is very small comparing to train's can be estimated reasonably by modelling the train as multi-axle moving mass. (5) Fundamental natural frequency of simple span ballastless steel plate girder bridge constructed using the Korean Standard Design Documents can be calculated by 4 L 1.2, in which L is span length. References [1] AASHTO, "LRFD Bridge Design Specifications", 2nd Edition, (1998). [2] D.I. Chang, K.H. Choi, and H.H. Lee, "A Study on Analysis of Real Response of Steel Railway Bridges", Journal of KSCE, Vol.9, No.2, pp.43-54, (1989) (in Korean). [3] D.I. Chang, and H.H. Lee, "Impact Factor for Simple-Span Highway Girder Bridges", Journal of Structural Engineering, ASCE, Vol.1, No.3, pp , (1994). [4] D.I. Chang, J.D. Lee, and H.H. Lee, "Reasonable Estimation of Steel Railway Bridge Vibrations", Journal of KSSC, Vol.4, No.1, pp.11-18, (1992) (in Korean). [5] Japan Road Association, "Fatigue Design Guide of Steel Highway Bridges", Maruzen, (2) (in Japanese). [6] Korea National Railroad, "Standard Design Documents(Steel Girder)", (in Korean). [7] Korea Rail Network Authority, "Railway Bridge Design Criteria", (4) (in Korean). [8] Korea Railroad, "Annual Report on Railway Statistics", (2) (in Korean). [9] Korea Railroad, "Reports on Safety Assessment of Simple Steel Plate Girder Railway Bridges", (1994-6) (in Korean). [1] H.H. Lee, J.C. Jeon, K.S. Kyung, and T. Mori, "Influence of Moving Vehicle on Fatigue of Steel Bridge", International Journal of Steel Structures, KSSC, Vol.6, No.4, pp , (6). [11] T. Mori, M. Kajihara, and Y. Hasegawa, "Development and Application of an Interactive Program for Fatigue Assessments of Steel Structures Based on JSSC Recommendations", Proceedings of Asia-Pacific Symposium on Bridge Loading and Fatigue, pp , (1996).