Lifetime-Oriented Structural Design Concepts- P4 pptx

2.3 Transport and Mobility 47 • information about the influence of the dynamic behaviour of the vehi- cles and the bridge structures including information about the pavement quality, • information about the different types of bridge structures and the corre- sponding influence surfaces, • principles for the model calibration for ultimate limit and fatigue limit states and the damage accumulation under consideration of different ma- terials, methods for the exploitation of the currently available traffic data, • development of large capacity and heavy load transports not covered by the normal traffic models, • the influence of future political decisions with regard to new traffic concepts. 2.3.1.2 Basic European Traffic Data With regard to the cross border trade, load models must be based on traffic data which are representative for the European traffic. For example the devel- opment of the models in Eurocode 1-2 [9] is based on data collected from 1977 to 1990 in several European countries [487, 720, 530, 37, 157, 361, 158]. The main data basis with information about the axle weights of heavy vehicles, about the spacing between axles and between vehicles and about the length of the vehicles came from France, Germany, Italy, United Kingdom and Spain. Most of the data relate to the slow lane of motorways and main roads and the duration of records varied from a few hours to more than 800 hours. Another important point is the medium flow of heavy vehicles per day on the slow lane. In order to analyse the composition of the traffic for the development of the load model in [9] four types of vehicles were defined for the European load model for bridges. Type 1 is a double-axle vehicle, Type 2 covers rigid vehicles with more than two axles, Type 3 articulated vehicles and Type 4 draw bar vehicles. Figure 2.23 shows the typical frequency distribution of these four types resulting from traffic records of the Auxerre traffic in France. The data base of different countries shows that the traffic composition is not identical in various European countries. The most frequent types of heavy vehicles are 1 and 3. Especially in Germany the traffic records in 1984 show that lorries with trailers (Type 4) dominated the traffic composition at that time. The traffic records of the Auxerre traffic (Motorway A6 between Paris and Lyon) gave a full set of the required information for the development of an Euro- pean load model. In addition the Auxerre traffic includes a high percentage of heavy vehicles and gives a representative data base for the development of a realistic European load model. Figure 2.23 shows the distribution of the above explained types of heavy vehicles based on the Auxerre traffic records. Figure 2.24 shows the gross vehicle weight and the axle load distributions for the representative traffic in Auxerre and Brohltal (Germany) where n 30 is the number of lorries with G ≥ 30 kN and n 10 the number of axles with P A ≥ 10 kN. Especially for the development of models for the fatigue resistance 48 2 Damage-Oriented Actions and Environmental Impact Type 1 Type 2 Type 4 Type 3 120 240 360 480 600 720 100 200 300 400 500 600 700 800 N G(kN) 120 240 360 480 600 720 G(kN) 10 20 30 40 50 60 70 80 120 240 360 480 600 720 120 240 360 480 600 720 N 200 400 600 800 1 000 1200 1400 G(kN) G(kN) 20 40 60 80 100 120 140 160 N N Fig. 2.23. Frequency distribution of the total weight G of the representative lorries per 24 hours based on traffic data of Auxerre in France (1986) of structures further traffic records regarding the number of heavy vehicles per day are needed. These data were taken for the load model in [9] from several traffic records in Europe. From all the traffic records only the record locations 1,0 10 -1 10 -2 10 -3 10 -4 150 300 450 600 750 G[kN] Auxerre Brohltal Auxerre Brohltal 1,0 10 -1 10 -2 10 -3 10 -4 50 100 150 200 P A [kN] 30 n n 10 n n total weight of heavy vehicles axle loads Périphérique Doxey Forth Forth Doxey Fig. 2.24. Gross vehicle and axle weight distribution of recorded traffic data from England, France and Germany 2.3 Transport and Mobility 49 Table 2.3. Statistical parameters of the traffic records of Auxerre (1986) 4,1 6,4 3,6 7,2 69 78 45 68 196 443 254 429 Type 4 G o G l 28,0 30,4 17,1 48,1 78 79 60 54 220 463 265 440 Type 3 G o G l 1,3 2,2 0,3 1,0 45 43 46 38 107 257 123 251 Type 2 G o G l 17,2 10,4 13,3 9,4 33 34 35 28 64 195 74 183 Type 1 G o G l Lane 2Lane 1Lane 2Lane 1Lane 2Lane 1 relative frequency % standard deviation V kN mean value P of the total vehicle weight kN 120 240 360 480 600 720 500 1000 1500 N G(kN) Type 3 lane 1 lane 2 22,7 % 27,6 % 1,3 % 3,5 % 65,2 % 58,4% 10,8% 10,5% G 1 G o Type 1 Type 2 Type 3 Type 4 1o GG Fig. 2.25. Histogram of vehicle Type 3 and approximation by two separate distri- bution functions based on traffic data of Auxerre in France (1986 ) and frequency of the different vehicle types in the lanes 1 and 2 with a high rate of heavy vehicle in the total traffic are of interest, for example the traffic records of Brohltal and Auxerre in Figure 2.24. The histograms acc. to Figure 2.23 can be subdivided into two separated density functions, where the mean values correspond to loaded and unloaded vehicles. The statistical parameters of these distribution functions are given in Table 3.6. For the vehicle of Type 3 the distributions are shown examplarily in Figure 2.25. Furthermore for the development of the load model the frequency of the different vehicle types in the lanes 1 and 2 is needed. The records based on the Auxerre traffic are given in Figure 2.25. The number of axles per vehicle varies widely depending on the differ- ent vehicle manufactures. Nevertheless the frequency distributions of the axle 50 2 Damage-Oriented Actions and Environmental Impact Table 2.4. Relation between gross weight of the heavy vehicles and the axle weights of the lorries of types 1 to 4 in % (mean values and standard deviation) Axle 1 Axle 2 Axle 3 Axle 4 Axle 5 Type of vehicle m V m V m V m V m V G o 50,0 8,0 50,0 8,0Type 1 G l 35,0 7,0 65,0 7,0 G o 40,5 8,4 36,2 8,8 23,7 7,3Type 2 G l 29,4 5,7 42,8 4,2 27,8 5,3 G o 30,6 5,8 27,5 4,4 16,2 3,6 13,6 3,1 12,1 3,1Type 3 G l 17,1 2,4 26,9 4,4 19,9 3,0 19,0 2,8 16,7 3,8 G o 31,7 5,7 31,3 5,8 13,4 4,1 13,7 3,5 9,9 3,3Type 4 G l 18,5 4,1 29,1 4,2 18,9 3,6 18,3 3,4 15,2 4,3 Table 2.5. Distance of axles in [m] of the different types of vehicles (mean values and standard deviation) Axle 1-2 Axle 2-3 Axle 3-4 Axle 4-5 Type of vehicle m V m V m V m V Type 1 3,71 1,1 Type 2 3,78 0,71 1,25 0,03 Type 3 3,30 0,26 4,71 0,78 1,22 0,13 1,23 0,14 Type 4 4,27 0,40 4,12 0,31 4,00 0,42 1,25 0,03 pacings show three cases with peak values nearly constant and very small standard deviations (vehicles of types 2, 3 and 4 with a space of 1.3 m corre- sponding to double and triple axles and with a space of 3.2 m corresponding to tractor axles of the articulated lorries). For the other spacings widely scattered distributions were recorded resulting from the different construction types of vehicles. As mentioned before, the traffic data given in Figures 2.23 and 2.24 are based on the traffic records of the Auxerre traffic in France. These data gave no sufficient information about the distribution of gross vehicle weight G on the single axles. Additional information from the traffic records of the Brohltal -Traffic in Germany (Highway A61) was used to define single axles weights and the spacing of the axles. These data (mean values of axle weight and axle spacing and corresponding standard deviations) are given in Tables 3.7 and 3.8. A further important parameter is the description of different traffic situa- tions. For the development of load models the normal free flowing traffic as 2.3 Transport and Mobility 51 a[m] 200 400 600 0,001 0,002 0,003 0,004 0,005 f(a) 90 D )1( DO a[m] f(a) 20 100 Fig. 2.26. Comparison of measured and theoretical values for the density function of intervehicle distances well as condensed traffic and traffic jam have to be distinguished. The main parameters of the probability density functions for the distance are the lorry traffic density per lane (lorries per hour), the ratio between lorries and mo- torcars, the mean speed and the probability of occurrence of lorry distances less than 100 m to cover the development of convoys. A typical example for the distribution of distances measured at motorway A7 near Hamburg is given in Figure 2.26 and compared with an analytical function for high traffic densities given in [720]. The density function is ap- proximated by a linear increase up to 20 m due to the minimum distance, a constant part up to a distance of 100 m because of convoys and an exponen- tially decreasing part for distances greater than 100 m for covering free flowing traffic. Another possibility is the approximation of the intervehicle distance by a log-normal distribution [305] which is based on new traffic data [314]. In Figure 2.26 the value α of the constant part between 20 and 100 m, giving the probability of occurrence for lorry distances less than 100 m, and the value λ were obtained from traffic records of 24 representative traffics in Germany. Additional information regarding the probability of occurrence of convoys are given in [267]. These accurate models apply mainly to the development of fatigue load models. Regarding load models for ultimate and serviceability limit states simplified models for the vehicle distances can be used on the safe side. In case of flowing traffic the distance between lorries is given by a minimum distance required, which results from a minimum reaction time of a driver to avoid a collision with the front vehicle in case of braking. OnthesafesideaminimumbrakingreactiontimeT s of the driver of one second is assumed. Then the minimum distance a is given by a = v · (T s ) where v is the mean speed of the vehicles. With this assumption also convoys are covered. The distance is limited to a minimum value of 5 m in case of jam situations. 52 2 Damage-Oriented Actions and Environmental Impact 2.3.1.3 Basic Assumptions of the Load Models for Ultimate and Serviceability Limit States in Eurocode As mentioned before, the load model in Eurocode 1 is mainly based on the traffic records of the A6 motorway near Auxerre with 2 × 2 lanes because these measurements were performed over long time periods in both lanes of the Highway and because these data represent approximately the current and future European traffic with a high rate of heavy vehicles related to the total traffic amount and also with a high percentage of loaded heavy vehicles (see also Figure 2.24). The European traffic records had been made on various locations and at various time periods. For the definition of the characteristic values of the load model therefore the target values of the traffic effects have to be determined. For Eurocode 1-2 it was decided, that these values correspond to a probability p = 5% of exceeding in a reference period R T =50years which leads to a mean return period of 1000 years. For the determination of target values of the traffic effects additional as- pects have to be considered. The measurements of the moving traffic (e.g. by piezoelectric sensors) include some dynamic effect depending on the rough- ness profile of the pavement and the dynamic behaviour of the vehicles which has to be taken into account for modelling the traffic. The dynamic effects of the vehicles can be modelled acc. to Figure 2.27 taking into account the mass distribution of the vehicle, the number and spacing of axles, the axle characteristic (laminated spring, hydraulic or pneumatic axle suspension), the damping characteristics and the type of tires [720, 530, 238, 99, 330, 331]. The normal surface roughness can be modelled by a normally distributed station- ary ergodic random process. The roughness is a spatial function h(x) and the relation between the spatial frequency Ω and the wave length L is given by Ω =2π/L [1/m]. In the literature many surfaces have been classified by power spectral densities Φ h (Ω) acc. to Figure 2.27. Increasing exponent w results in a larger number of wave length and increasing Φ h (Ω) results in larger ampli- tudes of h(x). For modelling the surface roughness of road bridges w =2can be assumed. The quality of the pavement of German roads can be classified for motorways as ”very good”, for federal road as ”good” and for local roads as ”average”. While for the global effects of bridge structures an average roughness profile can be assumed, for shorter spans up to 15 m local irregularities (e.g. located default of the carriageway surface, special characteristics at expansion joints and differences of vertical deformation between end cross girders and the abutment) have to be taken into account. These irregularities were modelled in Eurocode 1-2 by a 30 mm thick plank as shown in Figure 2.27. As mentioned above, the axle and gross weights of the vehicles of the Aux- erre traffic were measured by piezoelectric sensors. The calculations with fixed base and the vehicle model acc. to Figure 2.27 showed for good pavement quality, that the characteristic values determined from the measured gross and axle weights include a dynamic amplification of approximately 15% of 2.3 Transport and Mobility 53 S x z M m A ,T A spring and damper of the vehicle body mass of the axle spring and damper of the tyre h(x) unevenness of the carriageway 200 200 300 30 Model for irregularities Modelling of the vehicles 10 2 10 1 10 0 10 -1 10 -2 spatial frequency :=2S/L [m -1 ] power spectral density ) h (: ) [cm -3 ] 10 2 10 1 10 0 10 -1 10 -2 10 3 10- 3 PSD- spectras acc. to ISO-TC 108 a ve r a ge pa ve me n t ) h ( : o )=16 go o d pa v e me nt ) h ( : o ) =4 ve r y goo d pave m e nt ) h ( : o ) = 1 w o ohh )()(  » ¼ º « ¬ ª : : :) :) : o =1 m -1 w=2 +h -h +x[m] L Fig. 2.27. Model for the vehicles and local irregularities and power spectral density of the pavement the axles weights and 10% of the vehicle gross weight. The filtering of the dynamic effects leads in comparison to the measured values to a reduced stan- dard deviation. The corrected data of the static vehicle weights are given in Table 3.9. The dynamic behaviour of the bridge structure is mainly influ- enced by the span length and the dynamic characteristics of the structure [169] (eigenvalues acc. to Figure 2.28 and the damping characteristics). With the vehicle model and the modelling of the roughness of pavement surface acc. Table 2.6. Statistical parameters of the corrected static traffic records of Auxerre (1986) mean value P of the total vehicle weight [kN] standard deviation V [kN] lane 1 lane 2 lane1 lane 2 Type 1 G o G l 74 183 64 195 31 23 29 28 Type 2 G o G l 123 251 107 257 40 31 39 35 Type 3 G o G l 265 440 220 463 51 42 68 65 Type 4 G o G l 254 429 196 443 37 55 60 64 54 2 Damage-Oriented Actions and Environmental Impact span length in [m] 10 20 30 40 50 60 70 80 90 2 4 6 8 10 Hz81,0 L 1 4,95f 933,0 r V f [Hz] Eigenvalues (1. mode) Comparison of calculated and measured dynamic amplification 10 20 30 40 50 60 70 80 vehicle speed [km/h] calculated values measured values dynamic amplification in [%] 10 20 30 40 50 60 70 36,95 41,0m 32,35 Fig. 2.28. Measurements of the eigenvalues of the first mode of steel and concrete Bridges [169], and comparison of theoretically determined dynamic amplifications with measurements to Figure 2.27 results can be obtained by dynamic calculations of the bridge and be compared with measurements at bridges. Figure 2.28 shows an exam- ple of the calculated and measured dynamic amplification of the Deibel-Bridge [720]. With the assumptions and models explained above, a realistic determina- tion of the dynamic and static action effects due to traffic loads is possible. In a first step random generations of load files and roughness profiles of the pave- ment surface can be produced. Each load file consists of lorries with distances based on constant speed per lane. The main input parameters are the number and types of lorries, the probability of occurrence of each lorry type, the his- togram of the static lorry weights of each type, the distribution of lorries to several lanes. For the load files simply supported and continuous bridges with one, two and four lanes and different span lengths between 1 and 200 m with a representative dynamic behaviour (mass, flexural rigidity, mean frequency acc. to Figure 2.28 and damping) have to be investigated in order to get re- sults which are representative for the dynamic amplification of action effects of common bridges. Three different types of bridges with cross-sections with one, two and four lanes were investigated for the load model in Eurocode 1-2. For the different lanes the traffic types acc. to 3.10 were assumed, where traffic type 1 is a heavy lorry traffic for which motorcars were eliminated from the measured Auxerre traffic. The traffic type 2 is the measured traffic of lane 2.3 Transport and Mobility 55 Table 2.7. Different cross-sections and traffic types for the random generations number of lanes type of cross section traffic types of the different lanes 1 3,0 m Type 1 2 3,0 m 3,0 m Lane 1: Type 1 Lane 2: Type 2 4 3,0 m 3,0 m 3,0 m 3,0 m Lane 1: Type 1 Lane 2: Type 3 Lane 3:Type 3 Lane 4: Type 2 1 in Auxerre, including motorcars and traffic type 3 is the measured traffic of lane two in Auxerre. Detailed information about the generation of these load files are given in [720, 530]. With random load files the static and the dynamic action effects of the different bridge types can be determined. The comparison of the static and dynamic action effects gives information about the dynamic amplification and the dynamic factor Φ, influenced by the dynamic behaviour of the lorries, the bridge structure and by the quality of the pavement. The results of the simulations can be plotted in diagrams which give the cumulative frequency of the action effects. A typical example is given in Figure 2.29 for a bridge with 50 97 99,9 M E [kNm] 1000 1300 700 convoy v= 80 km/h convoy v= 60 km/h convoy v= 40 km/h traffic jam cumulative frequency [%] action effect M E Fig. 2.29. Cumulative frequency of the action effects for different vehicle speeds [530] 56 2 Damage-Oriented Actions and Environmental Impact 1,2 1,4 1,6 1,8 1,0 0,8 2,0 2,2 10 20 30 40 50 60 70 80 L [m] flowing traffic and good pavement quality flowing traffic and average pavement quality pavement irregularities (30 mm thick plank) M Fig. 2.30. Influence of the quality of the pavement on the dynamic amplification factor ϕ[530] one lane, good pavement quality and a span of 20 m. It can be seen that for this example the increase of the vehicle speed leads also to an increase of the dynamic action effects. Furthermore the dynamic amplification is extremely influenced by the roughness of the pavement and also by the span of the bridge. The influences of the pavement quality and traffic in more than one lane are shown in Figures 2.30 and 2.31. The results of the simulations show for condensed traffic no significant influence of the span length and the number of loaded lanes on the dynamic amplification. In case of flowing traffic the dynamic amplification of action effects depends significantly on the quality of the pavement, the number of loaded lanes, the span length and the type of the influence line of the action effect considered. 1,2 1,4 1,6 1,8 510 15 20 25 3035 1,2 1,4 1,6 1,8 M 10 20 30 40 50 60 70 80 L [m] L [m] bending moment vertical shear bending moment M Fig. 2.31. Influence of the span length and the number of loaded lanes on the dynamic amplification factor ϕ [...]... representative values for serviceability limit states acc to [9] Load Model 1 uniform distributed tandem system loads infrequent design situations frequent design situations quasi permanent design situations Load Model 2 single axle 0,8 0,8 0,8 0,75 0,4 0,75 0 0 0 bridge design As mentioned above the load model in Eurocode 1-2 is based on the Auxerre traffic which covers heavy European continental traffic... strength curve (slopes m1 and m2 and the fatigue strength ΔσD and ΔσD respectively) and the relevant numbers NT o of lorries during the design life assumed for λ2 = 1.0 Therefore the factor differs for structures and structural members with different materials (e.g structural steel, reinforcement, shear connectors) Figure 2.49 shows the λ1 values for steel bridges which are an envelope of the most adverse... corresponds to the traffic category 2 in Table 3.14 Furthermore for the design life a reference value Tso = 100 years was assumed In case of another traffic category or design life the damage equivalent factor 72 2 Damage-Oriented Actions and Environmental Impact has to be modified with the factors λ2 for the traffic category and λ3 for the design life Regarding the traffic category it also has to be considered,... which are in the range of 0.8 for the infrequent and 0.7 for the frequent design situations of bridges with small spans up to 40 m where the single axle loads dominate the actions effects For spans exceeding 40 m the flowing traffic with mainly uniform distributed loads gives values Ψ ≈ 0.8 for the infrequent and 0.45 for frequent design situations These values correspond to the values in Eurocode 1-2 (Table... in Eurocode 1-2 (Table 3.13) 2.3.1.4 Principles for the Development of Fatigue Load Models Fatigue is the progressive, localized and permanent structural change occurring in materials subjected to fluctuating stresses initiating and propagating cracks through a structural part after a sufficient number of load cycles Fatigue is induced in bridges mainly by heavy vehicles The development of appropriate load... 2630 245 397 527 811 France Angers 1987 1272 192 340 456 670 France Lyon 1987 1232 267 450 475 930 country location year Germany Brohltal Belgium France Table 2.9 Different design situations and corresponding return periods and fractiles Design situation Return period TR infrequent frequent quasi - permanent 1 year 1 week 1 day Fractile of the distribution of action effects in % 99,997 99,891 99,240 taking... are the design fatigue life, the type and number of lorries crossing the bridge, the traffic composition and the number of lanes with heavy traffic and in addition the quality of the pavement and the dynamic behaviour of the vehicles and the bridge For fatigue problems of bridges only the traffic situation of flowing traffic has to be considered because the number of traffic jams is negligible during the design. .. serviceability limit states like limitation of deflections, crack width control and limitation of stresses to avoid inelastic behaviour, different design situations have to be distinguished The Eurocodes distinguish between infrequent, frequent and quasi permanent design situations characterised by different return periods The return periods and the corresponding fractile of the distribution of the dynamic... R for frequent design situations acc to [37] for average pavement quality with Φ(Ωh ) = 16 Figure 2.27, the composition of the traffic (100% lorries in the first lane) and a probability of traffic jam of 100% The combination values taking into account these assumptions lead to values ΨT R , which only cover the influence of the return period TR Figure 2.37 shows an example for the frequent design situation... limit NL= 108 type of reinforcement N* Rsk at N* cycles [N/mm2] m1 m2 5 9 straight bars 106 162,5 welded bars and wire fabric 107 58,5 3 5 splicing devices 107 35 3 5 Fig 2.40 Fatigue strength curves for structural steel and reinforcement The main issues in the development of fatigue load models is the damage accumulation hypothesis In civil engineering normally a linear damage 2.3 Transport and Mobility . distributed loads single axle infrequent design situations 0,8 0,8 0,8 frequent design situations 0,75 0,4 0,75 quasi permanent design situations 0 0 0 bridge design. As mentioned above the load. avoid inelastic behaviour, different design situations have to be distinguished. The Eurocodes distinguish between in- frequent, frequent and quasi permanent design situations characterised by different. progressive, localized and permanent structural change occur- ring in materials subjected to fluctuating stresses initiating and propagating cracks through a structural part after a sufficient number