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E.1 Limits of validity of Load Model HSLM
1. Load Model HSLM is valid for passenger trains conforming to the following criteria:
– individual axle load P [kN] limited to 170 kN and for conventional trains also limited to the value in accordance with Equation E.2,
– the distance D [m] corresponding to the length of the coach or to the distance between regularly repeating axles in accordance with Table E.1,
– the spacing of axles within a bogie, dBA [m] in accordance with:
2,5 m ≤ dBA ≤ 3,5 m (E.1)
– for conventional trains the distance between the centres of bogies between adjacent vehicles dBS [m] in accordance with Equation E.2,
– for regular trains with coaches with one axle per coach (e.g. Train type E in Appendix F2) the intermediate coach length DIC [m] and distance between adjacent axles across the coupling of two individual trainsets ec [m] in accordance with Table E.1,
– D/dBA and (dBS − dBA)/dBA should not be close to an integer value, – maximum total weight of train of 10,000 kN,
– maximum train length of 400 m,
– maximum unsprung axle mass of 2 tonnes,
Table E.1 - Limiting parameters for high speed passenger trains conforming to Load Model HSLM
Type of train P [kN] D [m] DIC [m] ec [m]
Articulated 17 0 18 ≤ D ≤ 27 -
-Conv entional Lesser of 17 0 or v alue corresponding to equation E.2 below. 18 ≤ D ≤ 27 -
-Regular 17 0 10 ≤ D ≤ 14 8 ≤ DIC ≤ 11 7 ≤ ec ≤ 10
where:
where:
PHSLMA, dHSLMA and DHSLMA are the parameters of the Universal Trains in accordance with Figure 6.12 and Table 6.3 corresponding to the coach length DHSLMA for:
– a single Universal Train where DHSLMA equals the value of D,
– two Universal Trains where D does not equal DHSLMA with DHSLMA taken as just greater than D and just less than D,
and D, DIC, P, dBA, dBS and ec are defined as appropriate for articulated, conventional and regular trains in Figures E.1 to E.3:
Figure E1 - Articulated train
Figure E2 - Conventional train 141
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Figure E3 - Regular train
2. The point forces, dimensions and lengths of the Universal Trains defined in 6.4.6.1.1 do not form part of the real vehicle specification unless referenced in E.1(1).
E.2 Selection of a Universal Train from HSLM-A
1. For simply supported spans that exhibit only line beam dynamic behaviour and with a span of 7 m or greater a single Universal Train derived from the load model HSLM-A may be used for the dynamic analysis.
2. The critical Universal Train is defined in E.2(5) as a function of:
– the critical wavelength of excitation λc [m] defined in E.2(4) where the critical wavelength of excitation λc is a function of:
– the wavelength of excitation at the Maximum Design Speed λv [m] given in E.2(3), – the span of the bridge L [m],
– the maximum value of aggressivity A(L/λ)G(λ) [kN/m] in the range of excitation wavelength from 4,5 m to L [m] given in E.2(4).
3. The wavelength of excitation at the Maximum Design Speed λv [m] is given by:
λv = vDS/no (E.3) where:
no First natural frequency of the simply supported span [Hz]
vDS Maximum Design Speed in accordance with 6.4.6.2(1) [m/s]
4. The critical wavelength of excitation λc should be determined from Figures E.4 to E.17 as the value of λ corresponding to the maximum value of aggressivity A(L/λ)G(λ) for the span of length L [m] in the range of excitation wavelength from 4,5 m to λv.
Where the span of the deck does not correspond to the reference length L in figures E.4 to E.17, the two figures corresponding to the values of L taken as either just greater than the span or just less than the span of the deck should be taken into account. The critical wavelength of excitation λc should be determined from the figure corresponding to the maximum aggressivity. Interpolation between the diagrams is not permitted.
NOTE It can be seen from Figures E.4 to E.17 that in many cases λc = λv but in some cases λc corresponds to a peak value of aggressivity at a value of λ less than λv (For example in Figure E.4 for λv = 17m, λc = 13m)
Figure E.4 - Aggressivity A(L/λG(λ) as a function of excitation wavelength λ for a simply supported span of L = 7,5 m and damping ratio ζ = 0.01
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https://law.resource.org/pub/eur/ibr/en.1991.2.2003.html 97/113 Figure E.5 - Aggressivity A(L/λG(λ) as a function of excitation wavelength λ for a simply supported span of L = 10,0
m and damping ratio ζ = 0.01
Figure E.6 - Aggressivity A(L/λG(λ) as a function of excitation wavelength λ for a simply supported span of L = 12,5 m and damping ratio ζ = 0.01
Figure E.7 - Aggressivity A(L/λG(λ) as a function of excitation wavelength λ for a simply supported span of L = 15,0 m and damping ratio ζ = 0.01
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Figure E.8 - Aggressivity A(L/λG(λ) as a function of excitation wavelength λ for a simply supported span of L = 17,5 m and damping ratio ζ = 0.01
Figure E.9 - Aggressivity A(L/λG(λ) as a function of excitation wavelength λ for a simply supported span of L = 20,0 m and damping ratio ζ = 0.01
Figure E.10 - Aggressivity A(L/λG(λ) as a function of excitation wavelength λ for a simply supported span of L = 22,5 m and damping ratio ζ = 0.01
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https://law.resource.org/pub/eur/ibr/en.1991.2.2003.html 99/113 Figure E.11 - Aggressivity A(L/λG(λ) as a function of excitation wavelength λ for a simply supported span of L = 25,0 m and damping ratio ζ = 0.01
Figure E.12 - Aggressivity A(L/λG(λ) as a function of excitation wavelength λ for a simply supported span of L = 27,5 m and damping ratio ζ = 0.01
Figure E.13 - Aggressivity A(L/λG(λ) as a function of excitation wavelength λ for a simply supported span of L = 30,0 m and damping ratio ζ = 0.01
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Figure E.14 - Aggressivity A(L/λG(λ) as a function of excitation wavelength λ for a simply supported span of L = 32,5 m and damping ratio ζ = 0.01
Figure E.15 - Aggressivity A(L/λG(λ) as a function of excitation wavelength λ for a simply supported span of L = 35,0 m and damping ratio ζ= 0.01
Figure E.16 - Aggressivity A(L/λG(λ) as a function of excitation wavelength λ for a simply supported span of L = 37,5 m and damping ratio ζ = 0.01
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https://law.resource.org/pub/eur/ibr/en.1991.2.2003.html 101/113 Figure E.17 - Aggressivity A(L/λG(λ) as a function of excitation wavelength λ for a simply supported span of L = 40,0 m and damping ratio ζ = 0.01
5. The critical Universal Train in HSLM-A is defined in Figure E.18:
Figure E.18 - Parameters defining critical Universal Train in HSLM-A as a function of critical wavelength of excitation λc [m]
NOTE For values of λc < 7 m it is recommended that the dynamic analysis is carried out with Universal Trains Al to A10 inclusive in accordance with Table 6.3.
Where:
D Length of intermediate and end coaches defined in Figure 6.12 [m]
d Spacing of bogie axles for intermediate and end coaches defined in Figure 6.12 [m]
N Number of intermediate coaches defined in Figure 6.12
Pk Point force at each axle position in intermediate and end coaches and in each power car as defined in Figure 6.12 [kN]
λc Critical wav elength of excitation giv en in E.2(4) [m]
6. Alternatively the aggressivity A(L/λ)G(λ) [kN/m] is defined by equations E.4 and E.5:
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05.06.2013 Eurocode 1: Actions on structures - Part 2: Traffic loads on bridges where i is taken from 0 to (M-1) to cover all sub-trains including the whole train and:
L Span [m]
M Number of point forces in train Pk Load on axle k [kN]
Xi Length of sub-train consisting of i axles
xk Distance of point force Pk from first point force P0 in train [m]
λ Wav elength of excitation [m]
ζ Damping ratio