ALTERNATIVE PROCEDURES FOR IMPACT
FORCES IN EUROCODES
Markova J., Jung K.
Klokner Institute, Czech Technical University in Prague, Solinova 7, 166 08 Prague 6, Czech Republic
Abstract: Models for accidental impact forces due to road vehicles recommended in Eurocode
EN 1991-1-7 are analysed. The indicative values of design impact forces recommended for roadways and roads seem to be rather low. It is shown that the upper bound of impact forces should be applied for the design of structures located in the vicinity of traffic routes provided that other safety measures are not taken into account.
1. Introduction
General measures of risk control in the case of accidental design situations due to vehicle impact are given in the Eurocode EN 1991-1-7 1. In this document the impacts are considered from various sources, e.g. from road vehicles, derailed trains and ships. Strategies to be considered in accidental design situation as indicated in the Fig. 1 take into account whereas the accidental actions might be identified or not.
EN 1991-1-7 1 gives general guidance for categorisation of structures regarding the consequences of accidental actions. The static equivalent actions due to impacts are recommended in the main text, advanced impact design concept is given in the informative Annex C. National choice of impact forces may be based on the assumed consequences of failure and particular location of a structure. It is expected that risk analysis will be carried out only in specific situations and needs of a particular project and requirements of the client.
Each Member State of CEN will have to prepare National annex and compare the recommendations of national standards concerning accidental design situations with provisions given in Eurocodes. The aim of this contribution is to compare the alternative procedures for determination of design impact forces facilitating national decision about Nationally Determined Parameters in Eurocode EN 1991-1-7 1.
EN 1991-1-7 1 gives general guidance for categorisation of structures regarding the consequences of accidental actions. The static equivalent actions due to impacts are recommended in the main text, advanced impact design concept is given in the informative Annex C. National choice of impact forces may be based on the assumed consequences of failure and particular location of a structure. It is expected that risk analysis will be carried out only in specific situations and needs of a particular project and requirements of the client.
Fig. 1. Strategies for accidental design situations
Each Member State of CEN will have to prepare National annex and compare the recommendations of national standards concerning accidental design situations with provisions given in Eurocodes. The aim of this contribution is to compare the alternative procedures for determination of design impact forces facilitating national decision about Nationally Determined Parameters in Eurocode EN 1991-1-7 1.
2. Models of impact forces according to standards
In common cases, for the design of structures in accidental design situations due to road vehicle impact, the models of equivalent static forces may be applied. These simplified models may be used for the verification of static equilibrium or for strength verifications, depending on the protection aim. National standards of the Member States of CEN as well as Eurocodes give different guidance including recommended design impact forces due to road vehicles. For example, the Czech standards recommend the impact force 1000 kN for motorways without further criteria concerning location of a structure from the road. In comparison, the British standards recommend accidental design forces about five time greater that are considered for structures within distance less than 4,5 m from the road. The preliminary Eurocode ENV 1991-2-7 [2] recommended the design impact force 1000
kN for motorways and roads. The minimum requirement of 1000 kN is also included in Eurocode EN 1991-2 [6] dealing with all types of traffic actions on bridges.
However, during the development of EN 1991-1-7 1 it was decided to substantially increase the models of impact forces on the basis of national comments. The indicative values of impact forces recommended in the final draft 1 are given in Table 1. These forces represent an indicative (minimum) design requirement that might be exceeded as it is shown in the working drafts and background documents of [1], see the reference upper bound of forces indicated in brackets in Table 1. The reliability of a structure under accidental impact depends on various random aspects including the stiffness of vehicle and structure, their masses, the velocity of a vehicle in the time of impact, space orientation of a structural support, configuration of terrain. Thus, for the assessment of structural reliability, the probabilistic methods may be applied.
The impact forces Fd,x (direction of the traffic) and Fd,y (perpendicular to the traffic
direction) need not to be considered simultaneously according to EN 1991-1-7.
Table 1. Horizontal static equivalent design forces due to impact on vertical members of supporting structures over or adjacent roadways
Category of traffic Force Fd,x [kN] * Force Fd,y [kN] *
Motorways, country national and main roads
1000 (2500) 500 (1250)
Country roads in rural areas 750 (2500) 375 (1250)
Roads in urban areas 500 (2500) 250 (1250)
Courtyards, parking garages 50 (100) Cars
150 (300) Lorries
25 (50) 75 (150)
* Values of impact forces introduced in bracket are based on working drafts of 1.
The values of design impact forces given in Table 1 are left open for the national choice as Nationally Determined Parameters. The National Annex may prescribe the force as a function of the distance d of the centraline of the nearest trafficked lanes to the structural member. Further information on the effect of the distance d, where applicable, can be found in Annex C. For the determination of impact forces and preparation of background documents for the development of National annex of EN 1991-1-7 1, it is necessary to analyse various provisions. Eurocode EN 1991-1-7 1 gives basic information concerning accidental models for impact forces in Section 4, general guidance for risk analyses may be found in the informative Annex B, advanced impact models in Annex C. Selected alternative provisions for determination of accidental impact forces due to road vehicle are analysed as follows.
3. Analysis of impact models
Eurocode EN 1991-1-7 1, Annex C gives alternative procedures for specification of impact forces due to road vehicles. The maximum resulting interaction force F is given as
Fvr km (1)
where vr is the vehicle velocity at impact, k is the equivalent elastic stiffness of the
vehicle, m is its mass. Expression (1) gives the maximum force value on the outer surface of the structure. Inside the structure these forces may give rise to dynamic effects. In case of a vehicle impacting a structure, the velocity vr in (1) can be taken equal to
vr v20 2as (2)
where v0 is the velocity of the vehicle leaving its track on the traffic lane, a
is the average vehicle deceleration after leaving the traffic lane, s is the distance from the point where the vehicle leaves the road to the structural member. The design forces due to vehicle impact can be assessed as
Fd = F0 b 1 d d (3)
where F0 is the collision force and the braking distance db = (v2o /2a) sin , where is the angle between the trafficked lane and the course of the impacting vehicle. Recommended values of the vehicle mass m, velocity v, deceleration a, collision force F0 and braking
distance as given in EN 1991-1-7 1 are shown in Table 3.
Table 3. Design values for mass, velocity and collision force
Type of road Mass
m [kg] Velocity v [km/h] Deceleration a [m/s2] Collision force F0 [kN] Braking distance db [m] Motorways 30 000 90 3 2 400 20 Urban areas 30 000 50 3 1 300 10 Courtyards 30 000 15 3 400 2
Resulting design impact forces for three types of roads taking into account different distances d of a structure from the road are indicated in Table 4, based on formulae (1), (3) and data of Table 3.
Table 4. Design values of impact force Fd
Type of road Design impact force Fd,x [kN]
d = 3 m d = 6 m d = 9 m
Motorways 2200 2000 1800
Urban areas 1200 1100 950
Eurocode EN 1991-1-7 1 gives information enabling to consider effects of the different slope of the terrain. The resulting impact forces Fd,x versus increasing distance d of the
structural member for the vehicle velocity of 90 km/h are indicated in Fig. 2. For the impact force F0 it is considered the flat terrain, for F1 downhill and for F2 uphill, based on
the assumptions given in Annex C.
0 500 1000 1500 2000 2500 3000 3500 4000 3 5 7 9 11 13 15 17 Fd,x [kN] [kN] F0 F2 F1 d [m]
Fig. 2. The impact force Fd,x versus increasing distance d of a structural
member, for v0 = 90 km/h and three types of terrain (F0 for flat terrain, F1 downhill, F2 uphill)
The probabilistic methods of the reliability theory are applied for the determination of impact forces. Two alternative procedures given in EN 1991-1-7 1, Annexes B and C are analysed.
1. Probability of a structural member being impacted by a lorry leaving its traffic lane may be assumed to be 0,01 per year. The target failure probability for a structural member, given a lorry approaching in its direction, is 10-4/10-2 = 0,01 [3, 4]. The accidental
design force Fd is possible to be assessed on the basis of the following condition
P mk
v2 2as
F 0,01 d (4)where all probabilistic models of basic variables may be based on the recommendations of working documents of JCSS [5]. The values of accidental impact forces are analysed and given in Table 5 for the three assumed distances d.
Table 5 Design values of impact forces based on the probabilistic approach
Type of road Design impact force Fd,x [kN]
d = 3 m d = 6 m d = 9 m
Roadways 2910 2850 2810
Urban areas 1580 1500 1430
2. The design impact force may be assessed on the basis of the following condition of Annex B, EN 1991-1-7 1
Pf = n T x P[
km
(
v
2
2
a
s
)
}
Fd] (5)where n is a number of vehicles per time unit, T the period of time under consideration, is a probability of a vehicle leaving the road per unit length, x is a part of the road from where the collision may be expected, other variables are mentioned above. The variable x may be assessed as follows
xsinb( ) (6)
where the variable b depends on the structural dimension. For structural members such as columns a minimum value of b follows from the width of the vehicle (b = 2,5 m may be considered). The angle of a collision is assumed to be 10°C (Rayleigh distribution). The resulting impact forces taking into account formula (5) are given in Table 6.
Type of road Design impact force Fd,x
d = 3 m d = 6 m d = 9 m
Roadways 2950 2880 2800
Urban areas 1900 1800 1740
Figure 3 indicates the range where should be selected the design impact forces Fd for the
recommended target value of reliability index t about 2,3 (corresponding to the target
probability 0,01).
Fig. 3. Design impact force Fd,x versus distance d for target reliability index for roadways (probability of failure 10-2)
The resulting impact forces determined on the basis of above introduced alternative probabilistic procedures are considerably greater than the minimum (indicative) requirement for impact forces given Section 4 of EN 1991-1-7 [1] (see Table 1). For roadways, the impact forces are in a range from 2,9 to 2,8 MN, for roads in urban areas, the impact forces are in a broader range from 1,9 to 1,4 MN (depending on the applied probabilistic approach) for three study cases of distances d from 3 to 9 m.
Presented study indicates that for the design of structural members located nearby the traffic routes the upper bound of the accidental impact forces should be recommended in the National annex of EN 1991-1-7 [1] provided that no other safety measures are accepted.
5. Concluding remarks
The final draft of Eurocode EN 1991-1-7 gives indicative (minimum) requirements for accidental design forces due to vehicle impacts. Alternative procedures for determination of forces are given in informative Annexes B and C.
The impact forces determined on the basis of probabilistic methods are up to three times greater than the recommended indicative values. Final guidance concerning magnitude of design forces is left open for the national decision by the CEN Member States. It is expected that safety as well as economical aspects should be taken into account during the national application of this Part of EN 1991.
It is shown that the alternative procedures for probabilistic assessment of design impact forces given in EN 1991-1-7 leads to similar results. The resulting forces are in a good agreement with advanced impact models of Annex C. Thus, provided that no other safety measures are undertaken, the structures designed for indicative values of impact forces only may have insufficient reliability. Probabilistic methods of theory of structural reliability and methods of risk assessment should be applied for structural safety assuring.
Acknowledgements
This research has been conducted in the Klokner Institute of the Czech Technical University in Prague, Czech Republic as a part of the project No. 103/06/1521“Reliability and risks of structures in extreme conditions” supported by the Grant Agency of the Czech Republic.
References
1. EN 1991-1-7: Basis of design and actions on structures: Actions on structures – Accidental actions. Final working draft, CEN/TC250/SC1, 08/2005
2. ENV 1991-2-7: Basis of design and actions on structures: Actions on structures – Accidental actions due to impact and explosions, 1998
3. ISO DP 10252: Accidental actions due to human activities, 1994
4. Background documents to EN 1991-1-7 and EN 1991-2-7, (1995 – 1998), CEN. 5. JCSS (2001): Probabilistic model code. JCSS, http://www.jcss.ethz.ch.
