eurocode 1, part 1.7 accidental actions...

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EUROCODE 1, PART 1.7

ACCIDENTAL ACTIONS

BACKGROUND DOCUMENT

FIRST DRAFT January 2005

by

A. Vrouwenvelder U. Stieffel G. Harding


NOTATIONS 3 0. INTRODUCTION 4 1. GENERAL 5 2. ACCIDENTAL ACTIONS 5 2.1 DEFINITION OF ACCIDENTAL ACTIONS 5 2.2 ACCIDENTAL VERSUS VARIABLE ACTIONS 5 2.3 REPRESENTATION OF ACCIDENTAL ACTIONS 6 3. DESIGN FOR ACCIDENTAL ACTIONS 8 3.1. GENERAL 8 3.2. DESIGN FOR UNIDENTIFIED ACCIDENTAL LOADS (Robustness) 11 3.3. DESIGN FOR IDENTIFIED ACCIDENTAL LOADS 14 4. IMPACT 15 4.1. BASICS OF IMPACT ANALYSIS 17 4.2. IMPACT FROM VEHICLES 20 4.3. IMPACT FROM RAIL TRAFFIC 30 4.4 SHIP COLLISIONS 31 5. EXPLOSIONS 37 5.1 NATURE OF THE ACTION 37 5.2 MODEL FOR THE UNCONFINED EXPLOSION 39 5.3 LOADS MODELS FOR GAS EXPLOSION PRESSURES IN BUILDINGS 41 5.4 DESIGN EXAMPLE OF A COLUMN IN A BUILDING FOR AN EXPLOSION 49 5.5 GAS AND FUEL / AIR EXPLOSIONS IN ROAD AND RAIL TUNNELS 53 5.6 DUST EXPLOSIONS IN ROOMS AND SILOS 55 REFERENCES 60


NOTATIONS F = force Fco = compression strength of colliding object Fcs = compression strength of the structure N = number of fatalities per year Pa = probability of not avoiding a collision, given a ship on collision course Pc = probability of collision Pf = probability of failure P(d|f) = probability of a person being killed, given structural failure T = period of time under consideration, mostly a year a = deceleration b = typical dimension of structural object d = distance from structure to the road fs(y) = ship or aircraft position perpendicular to the direction of distribution of initial

propagation k = stiffness m = mass of colliding object n = number of cars, ships, per time unit passing a certain point (traffic intensity) pi = pressure due to explosion r = distance t = time uf = deformation at fracture vo = initial velocity of colliding object vr = velocity of colliding object at impact x,y = coordinates α = angle between rod direction and car direction αs = FORM influence factor β = reliability index λ(x) = probability rate of a ship getting out of control or a car leaving the road

per unit distance α = arctan (d/x) φdyn = dynamic amplification factor Φ = normal distribution φ = venting parameter


1. INTRODUCTION This background document provides explanatory material in support of the draft of Eurocode 1, Part 1.7, Accidental Actions, dated September, 2004. The document is intended for a better understanding of the numbers and rules given in the code. It is envisaged to be of help in setting up National Annexes in the various member states, in applying the document for the design of new structures and for formulating corrections and future improvements. Since the design philosophy for accidental actions differs from the design philosophy for permanent and variable actions, it has been unavoidable to include design principles to a limited extent. It should be noted, however, that later on it should be considered if certain parts ought to be transferred from EN 1991-Part 1.7 to EN 1990. The present version of this background document is a revision of the background document for the ENV.


2. ACCIDENTAL ACTIONS 2.1 Definition of Accidental Actions Accidental actions in the Eurocode system are defined as actions with low probability, severe consequences of failure and usually of short duration. Typical examples are fire, explosion, earthquake, impact, floods, avalanches, landslides, and so on Next to these identified accidental actions, structural members may got damaged for a variety of less identifiable reasons like human errors in design and construction, improper use, exposure to aggressive agencies, failure of equipment, terrorist attacks and so on. In the Eurocode system, fire and earthquake are dealt with in specific parts. The document EN 1991-1-7 deals primarily with impact and explosion. In addition, the document also gives general guidelines how to deal with identified and unidentified accidental actions in general. Because of the nature of accidental loads the design approach may be different from normal loads. Local damage may be acceptable and non-structural measures (e.g. sprinkler installations or vent openings) may prove to be more cost effective than structural ones. The scope of EN 1991-1-7 gives no attention to events, which are generally denoted as accidents, like persons falling through windows or roofs. The reason is that they have no damaging potential for the structural system. 2.2 Accidental versus variable actions Figure 2.1 shows the typical difference between a variable and an accidental load as far as the time characteristics are concerned. The variable load is nearly always present, although its value may be small for a substantial part of the time. However, serious non-zero values will in most cases (wind, snow, traffic) occur many times during the design life of the structure. A typical accidental load, on the other hand, will most probably not occur during the working life of the structure. If the load is present, it normally will take only a short time, varying from a few seconds (explosions) to some days (floods). Figure 2.2 shows a typical probability distribution for the one year maximum of the loads. Accidental loads have a probability of 0.98 per year or more to be zero. Variable loads as wind and traffic have zero probability to be absolutely zero. For snow and earthquake intermediate values may occur. Note that only in a limited number of cases the probability of occurrence of an accidental action and the probability distribution of its magnitude can be determined from statistics. As a result design values in practice often are to some extend nominal values. For some actions in the category variable actions, abnormal values may occur that are not sufficiently taken care of by the normal check of component failure. Special structures may therefore need a check for such abnormal loads. Examples are snow loads in some alpine areas and ice loads on masts and towers. The corresponding safety checks may follow the principles described for accidental situations, even if the loads are not classified as accidental actions according to the present standard.


2.3 Representation of accidental actions Actions on structures can usually be represented as static loads and structural response is usually preformed using a linear elastic analysis. Accidental actions, however, are in general more complex. For instance in the case of impact the action is a truck with random elastic plastic mechanical and geometrical properties that hits a structure at a random angle and velocity. An explosion is a pressure wave where the pressure interacts with the response of the structure. Nevertheless, for structures where the consequences of failure may be considered as limited, there is a need for simplified design rules. The first simplification is that accidental loads are considered as a dynamic force or even as a static equivalent force. Chapter 1 of EN 1991-1-7 gives the following relevant definitions for these quantities:

A dynamic force is a force that varies in time and which may cause significant dynamic effects in the structure; in the case of impact the dynamic forces represents the forces at the point of impact.

A static equivalent force is an alternative representation for a dynamic force and includes the dynamic response of the structure.

In the case of a dynamic force one may start a dynamic analysis, provided that the time dependent behaviour of the load is given. Alternatively one may use dynamic amplification factors as specified in the code for a number of design situations. When a static equivalent force is considered no further dynamic considerations are required. According to chapter 2, clause (2), impact actions indeed are to be considered as free actions, but the set of locations where the forces may apply is nevertheless restricted. Information is presented in Section 4. Note that in Annex A even further simplified representations of the accidental loads are presented. The forces presented in this Annex can directly be applied to dimension floors, columns and connections between them. These forces are of a prescriptive nature and a direct relation with physical entities like impact and explosions should be considered as marginal.


Figure 2.1: Typical time characteristics of (a) accidental and (b) variable load Figure 2.2: Typical probability distribution of (a) accidental and (b) variable loads

(a)

Force

Force

(b)

time

time

f(x)

f(x)

98% 2%

x = load

x = load

(b)

(a)


3. DESIGN FOR ACCIDENTAL ACTIONS 3.1 General 3.1.1 Identified and unidentified accidental design situations According to EN 1990, the term "design situation" is defined to mean the circumstances in which the structure may be required to fulfil its function. The selected design situations have to be sufficiently severe and varied enough to encompass all conditions that can reasonably be foreseen to occur during the execution and use of the structure. The phrase "which can reasonably be foreseen" is somewhat ambiguous in the case of accidental situations, the characteristics of which are that they cannot easily be foreseen in detail or maybe not at all. In particular this holds for accidental actions. IN EN 1991-1-7 therefore a distinction is made between so-called identified and unidentified actions. The identified actions may be analysed using classical (advanced) structural analysis. For the unidentified actions more general robustness requirements (e.g. prescribed tying forces) have been introduced. Note that for low safety class structures the design may be confined to these robustness requirements only, as they also work positively for the identifiable causes. 3.1.2 Objective of design for accidental actions / Acceptance of localised damage The objective of the design is to reduce risks at an economical acceptable price. Risk may be defined as the danger that undesired events represent. Risk is expressed in terms of the probability and consequences of undesired events. Thus, risk-reducing measures consist of probability reducing and consequence reducing measures, including contingency plans in the event of an accident. Risk reducing measures should be given high priority in design for accidental actions, and also be taken into account in design. No structure can be expected to resist all actions that could arise due to an extreme cause, but there is to be a reasonable probability that it will not be damaged to an extent disproportionate to the original cause. As a result of this principle, local failure (which in most cases may be identified as a component failure) may be accepted in accidental design situations, provided that it does not lead to a system failure. The consequence is that redundancy and non-linear effects both regarding material behaviour and geometry play a much larger role in design to mitigate accidental actions than in the case of variable actions. The same is true for a design that allows large energy absorption. 3.1.3 Design Strategies Design with respect to accidental actions may pursue one or more as appropriate of the following strategies, which may be mixed in the same building design:

• Preventing the action occurring or reducing the probability and/or magnitude of the action to a reasonable level. (The limited effect of this strategy must be recognised; it depends on factors which, over the life span of the structure, are commonly outside the control of the structural design process)

• Protecting the structure against the action (e.g. by traffic bollards) • Designing in such a way that neither the whole structure nor an important part thereof

will collapse if a local failure (single element failure) should occur


• Designing key elements, on which the structure would be particularly reliant, with special care, and in relevant cases for appropriate accidental actions

• Applying prescriptive design/detailing rules which provide in normal circumstances an acceptably robust structure (e. g. tri-orthogonal tying for resistance to explosions, or minimum level of ductility of structural elements subject to impact)

3.1.4 Consequences classes Design for accidental situations is in particular implemented to avoid structural catastrophes. As a consequence, design for accidental design situations needs to be included only for structures for which a collapse may cause particularly large consequences in terms of injury to humans, damage to the environment or economic losses for the society. Exempted are thus in particular low-rise buildings, where, compared to high-rise buildings, both the probability of the occurrence of an accidental action and the consequences are small. Nevertheless, protective measures like fire isolation of steel members and design measures like favouring ductile design in earthquake areas are relevant also for low-rise buildings. A convenient measure to decide what structures are to be designed for accidental situations is to arrange structures or structural components in categories according to the consequences of an accident. Eurocode 1991 Part 1.7 arranges structures in the following categories based on consequences of a failure: - Consequences class 1 Limited consequences - Consequences class 2 Medium consequences - Consequences class 3 Large consequences Less important individual structural members or sub-systems may be placed in a lower safety category than the overall structural system. Examples of placing structures in safety categories are shown in the informative annex A. Table 3.1 illustrates the concept of the categorization. Table 3.1. Safety categories suggested in draft for EC 1 Part 1.7

Consequences class Example structures class 1 class 2, lower group class 3, upper group class 4

low rise buildings where only few people are present most buildings up to 4 stories most buildings up to 15 stories high rise building, grand stands etc.

Reliability differentiation is also discussed in EN 1990, Section 2.2. As argued there, there may be various reasons for reliability differentiation, and the choice of categories or classes may to some extent depend on particular needs. Not only the appropriate measures but also the appropriate method of analysis may depend on the safety category, e.g. in the following manner: - Consequences class 1: no specific consideration of accidental actions - Consequences class 2: depending on the specific circumstances of the structure in

question: a simplified analysis by static equivalent load models for identified accidental loads and/or by applying prescriptive design/detailing rules


- Consequences class 3: extensive study of accident scenarios and using dynamic analyses and non-linear analyses if appropriate

It is up to member states to decide what is considered as an appropriate strategy in the various cases.


3.2 DESIGN FOR UNIDENTIFIED ACCIDENTAL LOADS (Robustness) 3.2.1 Background The design for unidentified accidental load is presented in Annex A of EN1991-1-7. Rules of this type were developed from the UK Codes of Practice and regulatory requirements introduced in the early seventies following the partial collapse of a block of flats in east London caused by a gas explosion. The rules have changed little over the intervening years. They aim to provide a minimum level of building robustness as a means of safeguarding buildings against a disproportionate extent of collapse following local damage being sustained from an accidental event [3-1]. The rules have proved satisfactory over the past 3 decades. Their efficacy was dramatically demonstrated during the IRA bomb attacks that occurred in the City of London in 1992 and 1993. Although the rules were not intended to safeguard buildings against terrorist attack, the damage sustained by those buildings close to the seat of the explosions that were designed to meet the regulatory requirement relating to disproportionate collapse was found to be far less compared with other buildings that were subjected to a similar level of abuse. 3.2.2 Summary of the method of Annex A Note that for class 1 there are no special considerations and for class 3 a risk analysis is recommended. So rules are given only for class 2 (both the upper and lower group). A distinction is made between framed structures and load-bearing wall construction. Class 2, Lower Group, Framed structures: Horizontal ties should be provided around the perimeter of each floor (and roof) and internally in two right angle directions to tie the columns to the structure (Figure 3.1). Each tie, including its end connections, should be capable of sustaining the following force in [kN]: -internal ties: Ti = 0.8 (gk + Ψ qk) s L (but > 75kN) (3.1) -perimeter ties: Tp = 0.4 (gk + Ψ qk) s L (but > 75kN). (3.2) In here gk and qk are the characteristic values in [kN/m2] of the self weight and imposed load respectively; Ψ is the combination factor, s [m] is the spacing of ties and L [m] is the span in the direction of the tie, both in m. Edge columns should be anchored with ties capable of sustaining a tensile load equal to 1% of the vertical design load carried by the column at that level. Class 2, Lower group, Load-bearing wall construction: A cellular form of construction should be adopted to facilitate interaction of all components including an appropriate means of anchoring the floor to the walls.


internal ties

perimeter tie

L

s

Figure 3.1 - Example of effective horizontal tying of a framed office building. Class 2 - Upper Group, Framed structures: Horizontal ties as above; In addition one of the following measures should be taken: (a) Effective vertical ties: Columns and walls should be capable of resisting an accidental design tensile force equal to the largest design permanent and variable load reaction applied to the column from any story. Ensuring that upon the notional removal of a supporting column, beam or any nominal section of load-bearing wall, the damage does not exceed 15% of the floor in each of 2 adjacent storeys. The nominal length of load-bearing wall construction referred to above should be taken as a length not exceeding 2.25 H; for an external masonry, timber or steel stud wall, the length measured between vertical lateral supports. (b) Key elements designed for an accidental design action Ad, = 34 kN/m2. Class 2 - Upper Group, Load-bearing wall construction. Rules for horizontal ties similar to those for framed buildings except that the design tensile load in the ties shall be as follows:

For internal ties Ti = 5.7

)qg(F kkt Ψ+ 5z

kN/m (but > Ft) (3.3)

For perimeter ties Tp = Ft (3.4) Where Ft = (20 + 4n) kN with a maximum of 60 kN, where n represents the number of storeys; g, q and Ψ have the same meaning as before, and z = 5h or the length of the tie in [m], whichever is smallest. In vertical direction of the building the following expression is presented:


For vertical tie Tv = 800034A 2

⎟⎠⎞

⎜⎝⎛

th

N (3.5)

but at least 100 kN/m times the length of the wall. In this formula A is the load bearing area of the wall, h is the story height and t is the wall thickness. Load bearing wall construction may be considered effective vertical ties if (in the case of masonry) their thickness is at least 150mm and the height of the wall h < 20 t, where t is wall thickness. 3.2.3 Design Examples (Based on [3-2]) 1. Framed structure, consequences class 2, Upper Group Consider a 5 storey building with story height h = 3.6 m. Let the span be L = 7.2 m and the span distance s = 6 m. The loads are qk = gk = 4 kN/m2 and Ψ=1.0. In that case the required internal tie force may be calculated as: Ti = 0.8 {4+4} (6 x 7.2) = 276 kN > 75 kN For Steel quality FeB 500 this force corresponds to a steel area A = 550 mm2 or 2 ø18 mm. The perimeter tie is simply half the value. Note that in continuous beams this amount of reinforcement usually is already present as upper reinforcement anyway. For the vertical tying force we find: Tv = (4 + 4) (6 x 7.2) = 350 kN/column This correspondents to A = 700 mm2 or 3 ø18 mm. 2. Load bearing wall type of structure, consequences class 2, Upper Group For the same starting points we get Fb = min (60, 40) = 40 and z = 5h = 12m and from there for the internal and perimeter tie forces:

Ti = 60 5.744 +

512

= 110 kN/m and Tp = 40 kN/m

The vertical tying force is given by:

Tv = 8

2.034x 2

2.06.3⎟⎠⎞

⎜⎝⎛ = 300 kN/m

For many countries this may lead to more reinforcement then usual for these types of structural elements.


3.3. DESIGN FOR IDENTIFIED ACCIDENTAL LOADS 3.3.1 Standard design (Sections 4 and 5, Annexes C and D) The general principles for classification of actions on structures, including accidental actions and their modelling in verification of structural reliability, are introduced in EN 1990 Basis of Design. In particular EN 1990 defines the various design values and combination rules to be used in the design calculations. A detailed description of individual actions is then given in various parts of Eurocode 1. The part 1.7 of EN 1991 covers design values for accidental actions and gives rules and values for the following topics:

• -Impact loads due to road traffic, train traffic and ships (Section 4 and Annex C) • -Internal explosions due natural gas (Section 5 and Annex D)

The impact loads are mainly concerned with bridges, but also impact on buildings is covered. Explosions concern explosions in buildings and in tunnels. The design philosophy necessitates that accidental actions are treated in a special manner with respect to load factors and load combinations. Partial load factors to be applied are defined in Eurocode, Basis of Design, to be 1.0 for all loads (permanent, variable and accidental) with the following qualification in: "Combinations for accidental design situations either involve an explicit accidental action A (e.g. fire or impact) or refer to a situation after an accidental event (A = 0)". After an accidental event the structure will normally not have the required strength in persistent and transient design situations and will have to be strengthened for a possible continued application. In temporary phases there may be reasons for a relaxation of the requirements e.g. by allowing wind or wave loads for shorter return periods to be applied in the analysis after an accidental event. As an example Norwegian rules for offshore structures [3-2] are referred to. 3.3.2 Risk analysis (Annex B) For consequences class 3 EN 1990 part 1.7 recommends a risk analysis. A risk analysis may be a valuable tool to study risk scenarios, in particular when accidental situations developing through a complex chain of events have to be considered. However, the complexity needed will be dictated by the problem at hand, and risk analysis in a rigorous form including extensive statistical analyses will be used only in special cases. Risk analysis ideas may, however, also be applied to provide a systematic procedure for identification of risks, and, furthermore, for assessment of accidental actions to be included. The actual assessments may often be made by comparison with known structures, and with risks implied in accepted designs for which experience exists. A severe consequence requires the consideration of extensive hazard scenarios, while less severe consequences allow less extensive hazard scenarios. Consequences are to be assessed in terms of injury to humans, or unacceptable change to the environment, or large economic losses for the society. Accidental design situations are defined in EN 1990 to include "design situation involving exceptional conditions of the structure or its exposure, e.g. fire, explosion, impact or local failure". Thus, accidental actions arising from the natural environment like waves and tides, flooding, tornadoes, extreme erosion or dropping rocks are not included. In accordance with this, the draft for Part 1.7 states that "This part refers to exceptional conditions applicable to the structure or its exposure caused by human activities, e.g. fire, explosion or impact. "


However, in ENV 1990states that "Some actions, for example from seismic actions and snow loads, can be considered as either accidental and/or variable actions ...". The restriction to man-made accidents is thus a choice, presumably motivated by a need to restrict the number of sources of accidental actions to be considered in Part 1.7. Regarding design principles, there is no reason to distinguish between man-made accidents and acts of God, neither in the striving for reducing risks of structural failures, nor in the design philosophy to reach this objective. The logical consequence is that design to mitigate accidental actions should follow the same principles, irrespective of the source of the accidental action. Accordingly, the Project Team has formulated the principles of their draft as generally valid for all categories of accidental actions. Future versions of the standards "Earthquake resistant design of structures" (EN 1998) and "Actions on structures exposed to fire" (ENV 1991-2-2) should thus comply with ENV 1991-1-7, also where this may not fully be the case in the present documents. 3.3.3 Risk acceptance criteria An area that typically is left to the member states is the issue of the risk acceptance criteria. Even Annex B gives only limited guidance. Basicly the ALARP is mentioned, which stands for as low as reasonably practicable. This means that, apart from some lower and upper limits, an economical optimisation is recommended. Whatever the design, there always will be a residual risk which have to be accepted. The residual risk will refer to accidental actions on a low probability level, which are not considered at all in the design, as well as actions that are identified and considered, but for which the design nevertheless will necessitate the acceptance of a residual risk. The residual risk will be determined by the cost of safety measures weighed against the consequences of a serious failure, including the conceivable public reaction after an accident. According to [3-4] the maximum acceptable annual failure probability following from the individual risk constraint can be formulated as:

f)|p(d

10 < P-6

f

Here p(d|f) is the probability of a person being killed, given the collapse of the structure. Among other things this probability depends on the time a person spends in or around a certain building. Also according to [3-4] the maximum annual failure probability following from a societal risk constraint can be formulated as: NA < P k-

f Here N is the expected number of fatalities per year. As practical values for the numbers A = 0.01 to 0.1 and k = 1 to 2 can be suggested. If the number of fatalities N given failure is highly uncertain, the requirement can be replaced by:


P(N > n) < A n-k This relation should hold for all n.


4. IMPACT 4.1 Basics of impact analysis The mechanics of a collision may be rather complex. The initial kinetic energy of the colliding object can be transferred into many other forms of kinetic energy and into elastic-plastic deformation or fracture of the structural elements in both the building structure and the colliding object. Small differences in the impact location and impact angle may cause substantial changes in the effects of the impact. This, however, will be neglected and the analysis will be confined to the elementary case, where the colliding object hits a structural element under a right angle. Even then, impact is still an interaction phenomenon between the object and the structure. To find the forces at the interface one should consider object and structure as one integrated system. Approximations, of course, are possible, for instance by assuming that the structure is rigid and immovable and the colliding object can be modelled as a quasi-elastic single degree of freedom system (see Figure 4.1.1). In that case the maximum resulting interaction force equals: F = vr √(km) (4.1.1) vr = the object velocity at impact k = equivalent stiffness of the object m = mass of colliding object This result can be found by equating the initial kinetic energy (mvr

2/2) and the potential energy at maximum compression (F2/2k). An alternative model for the colliding object is the continuous elastic rod (see Figure 6.1). Let the rod have mass density ρ, modulus of elasticity E, cross sectional area A and length L. The interaction force between this rod and the structure can then be presented as: F = Z vr (4.1.2) where Z = EA/c is the rod impedance and c = √ (E/ρ) is the wave propagation velocity. Substituting Z and c: F = vr A √(Eρ) (4.1.3) Taking k = EA/L and m = ρAL we arrive again at (4.1.1). So there is no difference between the spring and rod model as far as the maximum force is concerned. There is, however, a difference as far as the load time history is concerned. The results of the two models have also been indicated in Figure 4.1.1. In practice the colliding object will not behave elastically. In most cases the colliding object will respond by a mix of elastic deformations, yielding and buckling. The load deformation characteristic may, however, still have the nature of a monotonic increasing function (see Figure 4.1.2). As a result one may still use equation (4.1.1) to obtain useful approximations. Note that F, of course, will never be larger than the upperbound in Fp in the load deformation curve. Note also that the unloading branch usually has a much steeper slope than the loading branch. This fact has an important effect on the load time history. Let us assume a 100 percent plastic deformation. In that cases there will be an infinite stiffness for the unloading branche. For the spring model this means that at the top load the spring stiffness becomes infinitely great and the interaction force drops down to zero immediately. So the total load duration is:


Δt = 0.5 π √ (m/k) = 1.57 √ (m/k) For the rod model the end of the loading curve is reached as soon as the pressure wave reaches the end of the rod. The reflecting wave will have an infinite propagation velocity. So the load duration in this case is: Δt = L/c = L √ (ρ/E) = √ (m/k) (4.1.4) It can easily be verified that in both cases the total impuls S Fdt = mv as it should. The formula (4.1.1) gives the maximum force value on the outer surface of the structure. Inside the structure these forces may give rise to dynamic effects. An upperbound for these effects can be found if the load is conceived as a step function. In that case the dynamic amplification factor is 2.0. If the pulse nature of the load is taken into account calculations lead to amplification factors ranging from below 1.0 up to to 1.8, depending on the dynamic characteristics of the structure and the object. As the upperbound for the load (equation 4.1.1) and the upperbound to the amplification factors almost exclude each other on physical grounds, the following formula is proposed as a more or less realistic: Fdyn = ϕdyn F 1.0 < ϕdyn < 1.4 (4.1.5) In the approach untill now the structure has been assumed to be infinitely stiff. This assumption leads to conservative estimates for the interaction force. Another relatively simple upperbound may be obtained by assuming that all available kinetic energy is consumed by the structure. If the structure behaves elastically the resulting force in the structure then follows from:

kF

21 = vm

21 2

2 (4.1.6)

If the structure reacts rigid plastic, the maximum displacement follows from:

uF =vm 21

fcs2 (4.1.7)

Fcs = static collapse load of the structure uf = deformation of the structure at fracture In this case failure occurs if uf exceeds the deformation capacity of the structure. Both (4.1.6) and (4.1.7) have the disadvantage that the load depends on the structural properties. For this reason they will not further be used in this document. In Eurocode 1, Part 1.7, equation (4.1.1) has been used to calculate the static equivalent forces. The values of the quasi-static load F and the dynamic factor ϕdyn are represented separately. For users who want to do a proper structural dynamic analysis the time and load duration data are presented.


Figure 4.1.1 Spring and rod models for the colliding objects

Figure 4.1.2: General load displacement diagram of colliding object


4.2 IMPACT FROM VEHICLES 4.2.1. The probability of hitting the structure Consider a structural element in the vicinity of a road or track. Impact will occur if some vehicle, travelling over the track, leaves its intended course at some critical place with sufficient speed (see Figure 4.2.1). Which speed is sufficient depends on the distance from the structural element to the road, the angle of the collision course, the initial velocity and the topographical properties of the terrain between road and structure. In some cases there may be obstacles or even differences in height.

Figure 4.2.1: A vehicle leaves the intended course at point Q with velocity v0 and angle α. A

structural element at distance r is hit with velocity vr. The event that the intended course if left is modelled as an event in a Poison process. In most countries statistics are available for various road types, mainly for highways. To give some indication: according to [4.4] the probability of leaving a highway is about 10-7 per vehicle per km. Higher and lower values will occur in practice, depending on the local circumstances. The main parameters describing the kinematics of a vehicle at the point of departure are the velocity v0 and the angle α. There are no indications that v0 and α are dependent for straight sections of the road. The direction angle α varies from 0 to 30 or 400. The velocity of a vehicle on a road depends on the type of road, the mass of the car, the weather conditions, the local situation and the traffic intensity at the time. Statistics are available in all countries. The distribution of the velocity conditional upon the event of leaving the track, however, is not known. As long as no specific information is available, one might assume the conditional and unconditional velocity distributions to be the same. Confining ourselves to the case of a level track, the vehicle will as a rule slow down after the point of leaving the track, due to roughness of the terrain, obstacles or the driver's action. It is assumed, that the car maintains its direction. Further, assuming a constant deceleration or friction, the speed and the distance can be calculated as a function of t: at - v = v(t) 0 (4.2.1)


221

0 atvr(t) −= (4.2.2) Both formulas hold as long as v(t) > 0. Eliminating t leads to v as a function of r: v <ar 2for ar)2 - v( = v(r) 2

020 (4.2.3)

The deceleration 'a' can be assumed to be a random variable modelled by a lognormal distribution with mean 4 m/s2 and 30% coefficient of variation. This means that in 90% of the cases the deceleration is between 2.0 and 7.0 m/s2, which seems reasonable. Combining the 'leaving model' and the 'speed reduction model', it is possible to calculate the (approximate) probability that a structural element is hit [4.1] [4.2].[4.3] (see figure 4.3.1): Pc(T) = n T λ Δx P(v2 > 2ar) (4.2.4) n = number of vehicles per time unit T = period of time under consideration λ = probability of a vehicle leaving the road per unit length of track Δ = part of the road from where collisions may be expected v = velocity of the vehicle when leaving the track a = deceleration r = the distance from "leaving point" to "impact point" For r we may substitute: r = d/sin α (4.2.5) d = distance from the structural element to the road α = angle between collision course and track direction In (4.2.4) nT is the total number of vehicles passing the structure during some period of time T; λ Δx is the probability that a passing vehicle leaves the road at the interval dx. Note that the distance Δx also depends on α, where α is a random variable. So, in fact, equation (4.24) should be considered as being conditional upon α, and an additional integration over α is needed. We will, however, simplify the procedure and calculate Δx on the basis of the mean value of α: Δx = b / sin μ(α) (4.2.6) The value of b depends on the structural dimensions. However, for small objects such as columns a minimum value of b follows from the width of the vehicle. In our further calculations b = 2.5 m will be assumed. Let us now consider a bridge column at a distance d to a highway track. Assume the data as presented in table 4.2.1. Based on these numbers, figure 4.2.2 gives the probability of a column being hit at a distance d to the track. The result is quite realistic, as indeed many structural objects close to the tracks of a highway are hit once or more during the life time. For buildings in general, the probability of being hit, of course is much lower. For instance, according to [4.6] the number of buildings having a serious impact in The Netherlands is 100 per year. Given a total of 2,000,000 buildings leads to a probability of 5 * 10-5 per year or 0.002 per


life time. This number, however, also includes impacts from falling cranes etc. From [4.4] it can be inferred that the probability of a car collision with a dwelling in Great Britain is about 2 * 10-6 per year, and with other buildings 6 * 10-6. It should be stressed that these numbers are only indications for the average building. Specific circumstances (distance to a road type of road) may lead to much higher or lower values in individual cases. Table 4.2.1: Data for probabilistic collision force calculation

variable designation type mean stand dev

n number of lorries/day deterministic 5000 -

T reference time deterministic 100 years -

λ accident rate deterministic 10-10 m-1 -

b width of a vehicle deterministic 2.50 m -

α angle of collision course rayleigh 10˚ 10˚

v vehicle velocity lognormal 80 km/hr 10 km/hr

a deceleration lognormal 4 m2/s 1.3 m/s2

m vehicle mass normal 20 ton 12 ton

k vehicle stiffness deterministic 300 kN/m -

0

0.2

0.4

0.6

0.8

1

10 20 30 40 50

Collision probability per year

distance [m]

Figure 4.2.2: Probability of a structural element at a distance d from a high way track being hit

for a period of 150 years according to formula (4.2.4) and Table 4.2.1 4.2.2 Mechanical impact model The mechanical impact model according to (Section 4.1) will be compared with experiments by Camillo Popp [4.5] and Chiapetta and Pang [4.6]. Popp [4.5] used 18000 kg lorries, hitting walls and columns with varying speeds. His test number XII (velocity 80 km/hour) has been reproduced in Figure 4.2.3. According to the model (4.1.1) the collision force (exclusive the dynamic effect in the structure) should be:


F = v √ (km) = 22 √ (300 000 * 18000) N = 1600 kN. Figure 4.2.3 gives a maximum force of about 2400 kN (240 ton). This however is a peak of very short duration. Popp also calculated a time average (the dotted line) in the figure).The maximum of this curve is 1250 kN (125 ton). These values can be considered as upper and lower bounds for the design The value of 1600 kN therefore seems to be a reasonable number. The load duration according to (4.1.4) equals: Δt = √(m/k) = √ (1800/300000) = 0.24 s There is good agreement with the experiment (see Figure 4.2.3).

Figure 4.2.3 Impact forces resulting from a 18000 kg lorry with 80 km/hr


0

500

1000

1500

2000

2500

0 1000 2000 3000 4000 5000

upperlowertheorie

E [kNm]

F[kN]

Figure 4.2.4 Comparison of (4.1.1) and experiments by Popp [4.5] In figure 4.2.4 equation (4.1.1) is compared with the total set of 18 experiments by Popp. For every experiment the time average force and the peak force are presented. It should be mentioned that in all these experiments the velocity is above 50 km/hour. The experiment with impact energy equal to 300 kNm was done with a Mercedes car. All other experiments were performed using trucks. The conclusion for the total set of experiments can be the same as for the experiment XII discussed above. Chiapetta and Pang [4.6] did tests and calculations on car impact. The results for a 30 mph impact of a Plymouth Satellite (4380 lbs) have been shown in figure 4.2.5. The maximum force in the experiment was about 100 kips = 440 kN. According to the models (4.2.1), so again excluding the internal structural dynamic effects, we find: F = v N (km) = 15 N (300 000 * 2000) N = 380 kN This also indicates that the mechanical model gives globally the correct values, although the elastic vehicle model is a fiction. The stiffness parameter ko has the nature of a calibration factor rather than a physical quality. For this reason the document uses the term “equivalent stiffness”. Note that, contrary to the expectation, for trucks and cars the same value for this equivalent stiffness can be maintained.


Figure 4.2.5 Impact forces resulting from a 2000 kg car with 54 km/hr


4.2.3 Theoretical Design values for impact forces We shall calculate the collision force probabilities and derive from there a design value for a bridge column near a highway track. Similar to (4.2.4) we may write [4.2], [4.3]: P(F>Fd) = n T λ Δx P{ 1.4 √ ( m k (v2 - 2ar)) > Fd } (4.2.7) For Δx and r the same approximations as in section 4.2.2 will be used. Figure 4.2.6 gives the force Fd as a function of the distance d. According to EC1, Basis of Design, Annex A, the force Fd has been tuned in such a way that: P(F>Fd) = α(-sβ) = Φ(-0.7*3.8) = 10-3 (4.2.8) Both (4.2.7) and (4.2.8) are life time probabilities.

0

500

1000

1500

2000

2500

3000

eq 4.3.7

10 20 30 40 50

distance [m]

force [kN]

Figure 4.2.6 Design force as a function of the distance to the track Let us finally compare the results with some data from practice. In the Netherlands 216 collisions to superstructures were observed in a set of 3000 bridges over a period of 10 years. This gives a probability of collision of 0.007 per year. Furthermore, based on damage observations and back calculations have been made to estimate the static equivalent forces. The result is presented in Figure 4.2.7. It has been found that 64 % of the collisions have an equivalent force less than 1000 kN and 98 % is less than 4000 kN.


Given these data the following result can be observed (in round numbers):

Force Exceedence probability given the

collision

Exceedence probability for

one year

Exceedence probability for the

life time

2000 kN 0.1 0.7 10-3 0.7 10-1

4000 kN 0.01 0.7 10-4 0.7 10-2

6000 kN 0.001 0.7 10-5 0.7 10-3 It follows roughly that a life time probability of 0.001, corresponding to EN 1990, Basis of Structural Design, α=0.7 and β=3.8, leads to a force close to 6000 kN. If we accept the reduced exceedence probability of 10-4 per year as according to ISO [4.7], one finds about 4000 kN. In both cases the values are higher than the ones calculated in figure 4.2.6. Life time probability [%]

0

10

20

30

40

50

60

70

1 2 3 4 5 6 7 8 force [MN]

Figure 4.2.7 Distribution of collision forces based on observations In addition to the values in this Table the code specifisd more advanced models for nonlinear and dynamic analysis in an informative annex.. For impact loads the reader is referred to the bridge part of this project. The design values in EC1, Part 1.7, Table 4.1, have for political reasons been chosen in accordance with Eurocode 1, Part 3. In the following table some possible corresponding input values for the parameters m1, ko and ν equation 4.2.1 are presented.


Table 4.2.2: Calculation of design values in EC1, Part 1.7, Table 4.1 type of road mass velocity equivalent

stiffness collision force based on (4.2.1)

m [kg]

v [km/h]

k [kN/m] Fstat [kN]

motorway

20000 50 300 1000

urban area

20000 25 300 500

courtyards - only passenger cars - also trucks

1500 20000

8 8

300 300

50 150

The input design values for masses and velocity are relatively low, taking into account the other data in this chapter. As a consequence also the Fd value in Eurocode 1, Part 1.7 are too low. However, if combined with a conservative linear classic static structural model, the overall design could still very well be over designed. 4.2.5 Design examples for a bridge pier Consider the reinforced concrete bridge pier of figure 4.2.8. The cross sectional dimensions are b = 0.50 m and h = 1.00 m. The column height h = 5 m and it is assumed to be hinged to both the bridge deck as to the foundation structure. The reinforcement ratio is 0.01 for all four groups of bars as indicated in figure 4.2.8 right hand side. Let the steel yield stress be equal to 300 MPa and the concrete strength 50 MPa. The column will be checked for impact by a truck under motorway conditions.

x

H h y

Fdy

a b

Figure 4.2.8 Bridge pier under impact loading According to the code, the forces Fdx and Fdy should be taken as 1000 kN and 500 kN respectively and act at a height of a = 1.25 m. The design value of the bending moments and shear forces resulting from the static force in longitudinal direction can be calculated as follows:


Mdx = H

)aH(a −Fdx = 00.5

)25.100.5(25.1 −1000 = 940 kNm

Qdx = H

aH −Fdx =

00.525.100.5 −

1000 = 750 kN

Similar for the direction perpendicular to the diving direction:

Mdy= H

)aH(a −Fdy = 00.5

)25.100.5(25.1 − 500 = 470 kNm

Qxy = H

aH −Fdy =

00.525.100.5 −

500 = 375 kN

Other loads are not relevant in this case. The self-weight of the bridge deck and traffic loads on the bridge only lead to a normal force in the column. Normally this will increase the load bearing capacity of the column. So we may confine ourselves to the accidental load only. Using a simplified model, the bending moment capacity can conservatively be estimated from: MRdx = 0.8 ω h2 b fy = 0.8 0.01 1.002 0.50 300 000 = 1200 kNm MRdy = 0.8 ω h b2 fy = 0.8 0.01 1.00 0.502 300 000 = 600 kNm As no partial factor on the resistance need to be used in the case of accidental loading, the bending moment capacities can be considered as sufficient. The shear capacity of the column, based on the concrete tensile part (say fctk = 1200 kN/m2) only is approximately equal to: QRd = .0.3 bh fctk = 0.3 1.00 0.50 1200 = 360 kN. This is almost sufficient for the loading in y-direction, but not for the x-direction. Additional shear force reinforcement is necessary.


4.3 IMPACT FROM RAIL TRAFFIC EN 1991-Part 1.7, Subsection 4.5, deals with horizontal forces resulting from derailment. This subsection has been written in such a way that the loads are very close to UIC SC 7J report 777-1 (May 1996) [4.8]. Table 4.3.1 presents values in European Codes. Eurocode 1, Part 3 does only specify vertical loads due to derailment. To some extent it is questionable whether an analysis for horizontal impact should be made at all, even for most category 3 types of structures. One might argue that the probability of such an event is so small that no analysis is required. Some research in this direction is recommended. If, however, impact from trains is to be considered, the loads are extremely high. UIC Subcommittee Bridges mentions values up to 10 MN. Recent Swiss research [4.9] reveals values up to 30 MN (see Figure 4.3.1).

Figure 4.3.1 Impact functions of engines on stiff structures (from [4.9])


4.4 SHIP COLLISIONS 4.4.1 Modelling of collision event The probability of a ship colliding with a particular object in the water (offshore platform, bridge deck, bridge piers, sluice) depends on the intended course of the ship relative to the object and the possibilities of navigation or mechanical errors. In order to find the total probability of an object being hit, the total number of ships should be taken into account. Finally, the probability of having some degree of structural damage also depends on the mass, the velocity at impact, the place and direction of the impact and the geometrical and mechanical properties of ship and structure. When discussing ship collisions, it is essential to make a distinction between rivers and canals on the one side and open water areas like lakes and seas on the other. On rivers and canals the ship traffic patterns can be compared to road traffic. On open water, shipping routes have no strict definitions, although there is a tendency for ships to follow more or less similar routes when having the same destination. A typical possible model for the ship distribution within a traffic lane is presented in figure 4.4.1. In general it will be possible to model the position of a ship in a lane as a part with some probability density function. Details will of course depend on the local circumstances. It should be noted that sometimes the object under consideration might be the destination of the ship, as for instance a supply vessel for an offshore structure. Navigation errors are especially important for collisions at sea. Initial navigation errors may result from inadequate charts, instrumentation errors and human errors. The probabilistic description of these errors depends on the type of ship and the equipment on board, the number of the crew and the navigation systems in the sea area under consideration. Given a ship on collision course, the actual occurrence of a collision depends on the visibility (day or night, weather conditions, failing of object illumination, and so on) and on possible radar and warning systems on the structure itself. Mechanical failures may result from the machinery, rudder systems or fire, very often in connection with bad weather conditions. The course of the ship after the mechanical failure is governed by its initial position and velocity, the state of the (blocked) rudder angle, the current and wind forces, and the possibility of controlling the ship by anchors or tugs. These parameters together with the mass and dimensions of the ship should be considered as random. Given these data, it is possible to set up a calculation model from which the course of the ship can be estimated and the probability of a collision can be found. For further discussion a co-ordinate system (x,y) is introduced as indicated in Figure 4.4.1 The x co-ordinate follows the centre line of the traffic lane, while the y co-ordinate represents the (horizontal) distance of the object to the centre. The structure that potentially could be hit is located at the point with co-ordinates x=0 and y=d.


Figure 4.4.1: Ingredients for a probabilistic collision model The occurrence of a mechanical or navigation error, leading to a possible collision with a structural object, can be modelled as an (inhomogeneous) Poison process. Given this Poison failure process with intensity λ(x), the probability that the structure is hit at least once in a period T can be expressed as [4.1][4.2][4.3]: dydx (y)f y)(x,P (x) )P-nT(1 = (T)P scac λ∫∫ (4.4.1) where: T = period of time under consideration n = number of ships per time unit (traffic intensity) λ(x) = probability of a failure per unit travelling distance Pc(x,y) = conditional probability of collision, given initial position (x,y) fs(y) = distribution of initial ship position in y direction Pa = the probability that a collision is avoided by human intervention. For the evaluation in practical cases, it may be necessary to evaluate Pc for various individual object types and traffic lanes, and add the results in a proper way at the end of the analysis. To give some indication for λ, in the Nieuwe Waterweg near Rotterdam in the Netherlands, 28 ships were observed to hit the river bank in a period of 8 years and over a distance of 10 km. Per year 80 000 ships pass this point, leading to λ = 28/(10*8*80000) = 10-6 per ship per km.


4.4.2 Mechanical Models For practical applications, especially in offshore industry, some rules have been developed to calculate the part of the total energy that is transferred into the structure. Some of these rules are based on empirical models, others on a static approximation, starting from so-called load indentation curves (F-u diagrams) for both the object and the structure (see figure 4.5.2). According to this model the interaction force during collapse is assumed to raise form zero up to the value where the sum of the energy absorption of both ship and structure equal the available kinetic energy at the beginning of the impact.

Figure 4.4.2 Recommended indention curve for supply vessel (DNV) For a number of bridge projects figure 4.4.3 (from [4.3]) shows proposed impact forces resulting from various models. The plotted points are added to show the accuracy of the simple model according to (4.1.1). The same holds for the bow-indentation curves in figure 4.4.4.


Figure 4.4.3 Estimated vessel collision forces for various projects; impact speed = 7 m/s (from [4.3])


Figure 4.4.4 Calculated load - bow indentation curves (from [4.3])


4.4.3 Design values If data about types of ships, traffic intensities, error probability rates and sailing velocities are known, a design force could be found from [4.2][4.3]:: dydx (y)f ]F > km)(y)P[v(x, (x) )p-nT(1 = )F>P(F sdad λ∫∫ (4.4.2) v(x,y) = impact velocity of ship, given error at point (x,y) k = stiffness of the ship m = mass of the ship For all other variables, see formula (4.41). Given a target reliability and estimates for the various parameters in (4.4.2) design values for impact forces may be derived. The values in Tables 4.5 and 4.6 of Part 1.7, however, have not been derived on the basis of an explicit target reliability. For inland ships the values in Table 4.5 have been chosen in accordance with ISO DIS 10252. For a particular design it should be estimated which size of ships on the average might be expected, and on the basis of those estimates, design values for the impact forces can be found. Table 4.4 shows a comparison between: the values in Table 4.5 of EN 1991-1-7 the values based on Annex C, equation (C1) (identical to (4.4.1) in this report) the values based on Annex C, equation (C9) The masses for the inland waterways ships should been taken in the middle of the class. The velocity used is 3 m/s and the equivalent stiffness k = 5 MN/m. Table 4.4.1Design forces for inland ships

m [ton] v [m/s] k [N/m] F [MN] F [MN] F[MN]

Table

4.5 eq

(C.1) eq

(C.9) 300 3 5000000 2 4 5 1250 3 5000000 5 8 7 4500 3 5000000 10 14 9

20000 3 5000000 20 30 18 For sea going vessels values in Table 4.6 are based on equation (C11), with v = 3 m/s and ko = 15 MN/m for the smallest ship category and 60 MN/m for the heaviest category. Table 4.4.2 gives a comparison with EN 1991-1-7, Annex C (C11) and (C.1) (or (4.4.1) in this report). Table 4.4.2 Design forces for seagoing vessels

m [ton] v [m/s] k [N/m] F [MN] F [MN] F[MN]

Table

4.6 eq(C.1)eq

(C.11) 3000 5 15000000 50 34 33

10000 5 30000000 80 87 84 40000 5 45000000 240 212 238 100000 5 60000000 460 387 460


5 EXPLOSIONS 5.1. Nature of the action Gas explosions account for by far the majority of accidental explosions in buildings. Gas is widely used and, excluding vehicular impact, the incidents of occurrence of gas explosions in buildings is an order of magnitude higher than other accidental loads causing medium or severe damage [5.1 and 5.2]. Reference [5.2] concluded that “... of the abnormal loads listed [i.e. loads considered as plausible sources of the initial failure which might lead to progressive collapse], only the gas explosion, bomb explosion and vehicular collision constitute a problem for buildings”. Many gas explosions within buildings occur from leakage into the building from external mains. According to [5.1]: “There should be no relaxation ... for buildings without a piped gas supply, since a risk would usually remain of gas leaking into the building from outside”. It would be impractical in most circumstances to ensure gas will not be a hazard to any particular building. Therefore it seems reasonable to take a gas explosion as the normative design accidental action, excluding impact. In this context an explosion is defined as rapid chemical reaction of dust or gas in air. It results in high temperatures and high overpressure. Explosion pressures propagate as pressure waves. The following are necessary for an explosion to occur [5.3]: - fuel, in the proper concentration : - an oxidant, in sufficient quantity to support the combustion : - an ignition source strong enough to initiate combustion The fuel involved in an explosion may be a combustible gas (or vapour), a mist of combustible liquid, a combustible dust, or some combination of these. The most common combination of two fuels is that of a combustible gas and a combustible dust, called a “hybrid mixture”. Gaseous fuels have a lower flammability limit (LFL) and an upper flammability limit (UFL). Between these limits, ignition is possible and combustion will take place. Combustible dusts also have a lower flammability limit, often referred to as the minimum explosive concentration. For many dusts, this concentration is about 20 g/m³. The oxidant in an explosion is normally the oxygen in air. Moisture absorbed on the surface of dust particles will usually raise the ignition temperature of the dust because of the energy absorbed in vaporizing the moisture. However, the moisture in the air (humidity) surrounding a dust particle has no significant effect on an explosion once ignition has occurred. The pressure generated by an internal explosion depends primarily on the type of gas or dust, the percentage of gas or dust in the air and the uniformity of gas or dust air mixture, the size and shape of the enclosure in which the explosion occurs, and the amount of venting of pressure release that may be available. In completely closed rooms with infinitely strong walls gas explosions may lead to pressures up to 1500 kN/m2, dust explosions up to 1000 kN/m2, depending on type of gas or dust. In practice, pressures generated are much lower due to imperfect mixing and the venting that


occurs due to failure of doors, windows and other openings. Windows respond in a brittle manner because the thinness of the glass makes very little deformation possible before there is complete disintegration. For this reason, coupled with their relatively light weight and low static strengths, they make good explosion vents. But venting is also afforded by failure of non-structural relatively weak wall panels. It must be borne in mind that the response in real structures is highly complex: the geometry of the space, obstacles to free expansion producing turbulence, etc. Reference [5.4] comments: “The value of theoretic analyses of structural responses to such [explosive] loadings is limited by the impossibility, at least at present, of determining with any degree of accuracy, even after the event, what they have been at all significant points in any particular case. And it is part of the nature of accidental loading that prediction before the event will always remain impossible. The response of complete structures are, moreover, highly complex.” Reference [5.4] also comments that “... deformations [of typical walls and floors] before major loss of load bearing capacity may correspond to values of the deformation parameter [ratio of total plastic deformation to deformation at the elastic limit] of 10 or more. Such elements (if their response is a purely flexural one with no shear failure) may thus withstand peak pressures up to about twice their static strengths. Though they will suffer permanent deformation, their load bearing capacity will be unimpaired”. Reference [5.4] also points out that such ductility may be possessed by elements that are commonly considered brittle (such as brick walls) by virtue of edge restraints.


5.2 Model for the unconfined explosion An explosion can be defined as "a rapid combustion with a marked and measurable pressure increase" [5.5]. A hemispherical cloud with a volume V0 consisting of a homogeneous combustible gas/air mixture will, after ignition in the centre, expand to a hemisphere with volume V1. The characteristic properties can be calculated as follows: 1) The peak overpressure

• in case of detonation:

7.1

00 )(518.0 −⋅⋅=

LrPPpeak for 088.129.0

0

≤≤Lr

(5.2.1)

3

0

2

0

1

00 )(1194.0)(1841.0)(2177.0 −−− ⋅+⋅+⋅⋅=

Lr

Lr

LrPPpeak (5.2.2)

for 088.10

≥Lr

^

• in the case of deflagration:

1

00 )( −⋅⋅=

LrPPpeak φ (5.2.3)

Ppeak: peak overpressure of shock wave [Pa] P0: atmospheric pressure [Pa] r: distance to the centre of the explosion [m] L0: characteristic explosion length [m], which is given by:

(5.2.4) Ec: combustion energy of mixture per unit volume 2) The positive phase duration tP

0

t0P L

tct ⋅= (5.2.5)

c0: local sound velocity [m/s] 3) The impulse:

∫ −=Pt

0SS )dtp(t)(pi (5.2.6)

31

0

c00 p

EVL ⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅=


Using the schematic simplified pressure-time curve, the impulse, for both shock wave or pressure wave, is then equal to:

PSS tP21i ⋅⋅= (5.2.7)

Finally, the time course of the static overpressure can be approximated during the phase of overpressure by the following equation, known as the Friedlander-Approximation:

tpt

pe t

tptp /exp)1()( α−−= (5.2.8)

Fig 5.2.1. Pressure p against the time t during an explosion.


5.3 Loads models for gas explosion pressures in buildings 5.3.1 Vent Coefficient Numerous empirically methods predicting explosion overpressures based on explosion venting are published in the literature. The empirical relationships produced by Cubbage and Simmonds [5.6], Cubbage and Marshall [5.7] and Rasbash [5.8] are commonly used. They were determined for a limited range of variables such as volume, burning velocity, mass of fuel (air mixture), and vent areas. The empirical correlations Cubbage and Simmonds are based on the concept of a vent coefficient K.

v

s

AAK = (5.3.1)

where As means the area of side of enclosure, and Av the area of the vent opening. The commonly used equations and its ranges of application are listed below:


5.3.2 Cubbage and Simmonds Probably the most widely used of the formulae presented. The Cubbage and Simmonds' equations contain terms expressing the effect of characteristics of both the gas-air mixture and the enclosure in which the explosion occurs. They may be used for any type of gas-air-mixtures since the burning velocity S0 allows for the influence of combustion characteristics of different gases on the pressure generated. This is the velocity with which the flame front moves relative to the unburned mixture immediately ahead of it.

3101

V

28)WK(4.3SP +⋅⋅⋅= (5.3.2)

KS58P 02 ⋅⋅= P1: pressure of the vent removal phase [mbar] P2: pressure of the venting phase [mbar] S0: burning velocity [m/s] (natural gas 0.45 m/s) K: vent coefficient, dimensionless W: weight per unit area of the vent cladding [kg/m2] V: volume of room [m3] Range of application: • Max and minimum dimensions of room have a ratio less then 3:1: Lmax : Lmin ≤ 3 : 1 • The vent area coefficient; K, is less then 5: K ≤ 5 • The weight per unit area of the vent cladding W must not exceed 24 kg/m2

Cubbage and SimmondsP1 = S (4.3 KW + 28) / V0.333

01234567

0,000 0,020 0,040 0,060 0,080

A/V

P1 [k

N/m

2 ] volume 80 m3volume 120 m3volume 160 m3volume 200 m3

Figure 5.3.1: Gas and fuel / air explosions in rooms and closed sewage bassins (Cubbage, Simmonds) 5.3.3 Rasbash et al


The equation of Rasbash et al. can be expected to predict the maximum overpressure generated in a given situation, irrespective of whether this relates to P1 or P2.

77.7K}]V

28)W(4.3K{[S1.5PP310vm ++⋅

+= (5.3.3)

Pm: maximum overpressure [mbar] Pv: uniformly distributed static pressure at which venting components will response [mbar] S0: burning velocity K: vent coefficient W: weight per unit area of the vent cladding V: volume of room Range of application: • Maximum and minimum dimensions of room have a ratio less than 3:1: Lmax : Lmin ≤ 3 : 1 • The vent area coefficient; K, is between 1 and 5: 1 ≤ K ≤ 5 • The weight per unit area of the vent cladding does not exceed 24 kg/m2: W ≤ 24 kg/m2 • The response pressure of the vent cladding, overpressure required to open it, does not

exceed 70 mbar: Pv ≤ 70 mbar

RasbashPmax = 1.5 Pv + S{[4.3 KW + 28) / V0.333] + 77.7 K

020406080

100

0,000 0,020 0,040 0,060 0,080

A/V

Pmax

[kN

/m2 ]

volume 80 m3volume 120 m3volume 160 m3volume 200 m3

Figure 5.3.2: Gas and fuel / air explosions in rooms and closed sewage bassins (Rasbash)


5.3.4 NFPA 68 Guide for Venting of Deflagrations for low strength buildings The Guide for Venting of Deflagrations of the National Fire Protection Association proposes for low strength buildings the following equation to determine the maximum pressure developed in a vented enclosure during a vented deflagration of a gas- or vapour-air-mixture:

Pred = (C2 x As2) / Av

2 (5.3.4) Pred: maximum pressure developed in a vented enclosure during a vented deflagration in bar Av: vent area in m2 AS: internal surface area of enclosure in m2 C: venting equation constant in (bar)1/2 The maximum pressure Pred can not be larger than the enclosure strength Pes. Pred should not be greater than 0.1 bar.

0

0,1

0,2

0,3

0,4

0,5

0 20 40 60 80 100

Av [m2]

As=250 m2, C=0.013 (bar)1/2 As=250 m2, C=0.037 (bar)1/2 As=250 m2, C=0.045 (bar)1/2 Figure 5.3.3: Gas and fuel / air explosions for low strength buildings (NFPA 68, Guide for

Venting of Deflagrations, 2002 Edition) From the following table the values for the venting equation constant can be seen: gas- or vapour-air-mixture

constant C in (bar)1/2

anhydrous ammonia 0.013 methane 0.037 gases with fundamental burning velocity < 1.3 that of propane 0.045 hydrogen not available There are no dimensional constraints on the shape of the room besides that the shape is not extremely one dimensional. As a check the following equation should be used:

l3 < 8 x (A / U) (5.3.5) where l3 : is the longest dimension of the enclosure, A the cross-sectional area in m2 normal to the longest dimension and U the perimeter of cross section in m. The vent closure should weight not more than 12.2 kg/m2.


5.3.5 NFPA 68, Guide for Venting of Deflagrations, 2002 Edition for high strength

buildings The required vent area for rectangular enclosure is determined according to the following equation: A = [ (0.127 * log10 KG - 0.0567) * pBem.

-0.582 + 0.175 * pBem.-0.572 (pstat. - 0.1)] * V0.667 (5.3.6)

A vent area [m2] pmax maximum explosion overpressure of the dust KG deflagration index of gas [bar m s-1] pBem design strength of the structure [bar] pstat: static activation overpressure with size of existing vent areas [bar] V: volume of enclosure [m3] This equation is valid for the following conditions:

• V ≤ 1'000 m3 • L/D ≤ 2, where L greatest dimension of enclosure, D = 2 * (A / π )0.5 , A is cross-

sectional area normal to longitudinal axis of the space • pstat ≤ 0.5 bar, pstat < pBem. • 0.05 ≤ pBem. ≤ 2 bar • KG ≤ 550 bar m s-1

0

5

10

15

20

25

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

V [m3]

KG=300 bar m/s, p stat=0.15 bar, p Bem=0.5 bar KG=300 bar m/s, p stat=0.20 bar, p Bem=0.6 bar KG=300 bar m/s, p stat=0.35 bar, p Bem=1.5 bar KG=300 bar m/s, p stat=0.50 bar, p Bem=2.0 bar

Figure 5.3.4: Gas and fuel / air explosions for high strength buildings (NFPA 68, Guide for Venting of Deflagrations, 2002 Edition) For elongated rooms with L/D ≥ 2 the following increase for the vent area has to be considered:

∆AH = A * KG (L/D - 2)2 / 750 ∆AH increase for vent area [m2]


5.3.6 European standard EN 1991-1-7 The pressure model in the Eurocode is based on [5.2, 5.9, 5.10] and is given by the maximum of pd= 3 + pv (5.3.7) pd = 3 + 0.5 pv+0,04/(Av/V)2 (5.3.8) Av: area of venting components [m2] V: volume of room [m3] Range of application: • The equations are valid in rooms up to 1000 m3 total volume: V ≤ 1000 m3 • The ratio of the area of venting components and the volume are valid: 0.05 (1/m) ≤ Av/V

≤ 0.15 (1/m) The explosive pressure acts effectively simultaneously on all of the bounding surfaces of the room. An important issue is further raised in clause D.XXX. It states that the peak pressures in the main text may be considered as having a load duration of 0.2 s. The point is that in reality the peak will generally be larger than given by (5.3.7 and 8), but the duration is shorter. So combining the loads from the above equations with a duration of 0.2 s seems to be a reasonable approximation. In [5.9] and [5.10] a series of explosive tests in a simulated kitchen are reported. A typical time-pressure diagram from one of the tests is shown here in Figure 5.3.5. After ignition the pressure rises to the venting pressure, p0. Following this a slight pressure increase occurs followed by a drop in pressure. After a further half a second or so, pressure again increases in a high frequency oscillatory pattern. Considering these test findings, [5.2] states: “Since the frequency of the oscillations is so much higher than the natural frequency of the bounding surfaces, their effect can be essentially ignored in comparison to the mean pressure part p2. Moreover, since the frequency of p1 and p2 is roughly 2 Hz, while the resonant frequencies of masonry walls and concrete panels and floors are about 30 Hz-60 Hz, p1 and p2 may be treated effectively as static loads for design purposes. A dynamic analysis would be considerably more involved, and does not appear to be warranted in view of the limited data. Within experimental limitations, it appears that p1 and p2 are attained simultaneously in all parts of the room and the gas explosion thus may be considered to be uniform on all bounding surfaces. “Although p1 and p2 may be considered as static loads in terms of the dynamic response of the structure the loading rate is still sufficiently accelerated that most structural materials would exhibit some apparent increase in strength. This may be as high as 20-30 percent over those values specified for design”. With regard to venting pressure afforded by windows, [5.2] suggests that venting pressure pv may be determined from tests or may be calculated from uniformly loaded plate bending formulae. Guidance can also be obtained in reference [5.4].


Figure 5.3.5 Load time history (from [5.9])


In Figure 5.3.6 the design pressure is presented as a function of A/V.

ENV 1991-2-7:1998Pd = 3 + Pv/2+0.04/(Av/V)2

Pd: static pressure of design value

020406080

100

0,000 0,020 0,040 0,060 0,080

A/V

Pd [k

N/m

2 ] volume 80 m3volume 120 m3volume 160 m3volume 200 m3

Figure 5.3.6: Natural gas explosion in rooms (ENV 1991-2-7:1998)


5.4 Design example of a column in a building for an explosion Consider a living compartment in a multi-storey flat building. Let the floor dimensions of the compartment be 8 x14 m and let the height be 3 m. The two small walls (the facades) are made of glass and other light materials and can be considered as venting area. These walls have no load bearing function in the structure. The two long walls are concrete walls; these walls are responsible for carrying down the vertical loads as well as the lateral stability of the structure. This means that the volume V and the area of venting components Av for this case are given by: Av = 2 x 8 x 3 = 48 m2 V = 3 x 8 x 14 = 336m3 So the parameter Av / V can be calculated as: Av / V = 48 / 336 = 0.144 m-1 As V is less then 1000 m3 and Av / V is well within the limits of 0.05 m-1 and 0.15 m-1 it is allowed to use the loads given in the code. The collapse pressure of the venting panels pv is estimated as 3 kN/m2 , Note that these panels normally can resists the design wind load of 1.5 kN/m2. The equivalent static pressure for the internal natural gas explosion is given by: pEd= 3 +pv = 3 + 3 = 6 kN/m2 or pEd = 3 + pv/2+0,04/(Av/V)2 =3 + 1.5 + 0.04 / 0.1442 = 3 + 1.5 + 2.0 = 6.5 kN/m2 This means that we have to deal with the latter. The load arrangement for the explosion pressures is presented in Figure 5.4.1. According to Eurocode EN 1990, Basis of Design, these pressures have to be combined with the self weight of the structure and the quasi-permanent values of the variables loads. Let us consider the design consequences for the various structural elements.

H = 3m pd

B = 8 m

Figure 5.4.1: Load arrangement for the explosion load


Bottom floor Let us start with the bottom floor of the compartment. Let the self weight be 3 kN/m2 and the live load 2 kN/m2. This means that the design load for the explosion is given by: pda = pSW + pE + ψ1LL pLL = 3.00 + 6.50 + 0.5*2.00 = 10.50 kN/m2 The design for normal conditions is given by: pd = γG ξ pSW + γQ pLL = 0.85 * 1.35 * 3.00 + 1.5*2.00 = 6.4 kN/m2 We should keep in mind that for accidental actions there is no need to use a partial factor on the resistance side. So for comparison we could increase the design load for normal conditions by a factor of 1.2. The result could be conceived as the resistance of the structure against accidental loads, if it designed for normal loads only: pRd = 1.2*6.4 = 7.7 kN/m2 So a floor designed for normal conditions only should be about 30 percent too light. If, however, we take into account the increase in short duration of the load we may increase the load bearing capacity by a factor ϕd given by (see end of section):

ϕd = 1 + Rd

SW

pp

2max

)t(gu2Δ

where Δt = 0.2 s is the load duration, g = 10 m/s2 is the acceleration of the gravity field and umax is the design value for the midspan deflection at collapse. This value of course depends on the ductility properties of the floor slab and in particular of the connections with the rest of the structure. It is beyond the scope of this paper to discuss the details of that assessment, but assume that umax = 0.20 m is considered as being a defendable design value. In that case the resistance against explosion loading can be assessed as:

pREd = ϕd pRd = [1 + 7.7

32)2.0(10

20.0*2]* 7.7 = 12.5 kN/m2

So the bottom floor system is okay in this case. Upper floor Let us next consider the upper floor. Note that the upper floor for one explosion could be the bottom floor for the next one. The design load for the explosion in that case is given by (upward value positive!): pda = pSW + pE + γQ ψ pLL = - 3.00 + 6.50 + 0 = 3.50 kN/m2 So the load is only half the load on the bottom floor, but will give larger problems anyway. The point is that the load is in the opposite direction of the normal dead and live load. This means that the normal resistance may simply be close to zero. What we need is top reinforcement in the field and bottom reinforcement above the supports. The required resistance can be found by solving pRd from:


ϕd pRd = [1 + Rd

SW

pp

2max

)t(gu2Δ

] pRd = 3.50

Using again pSW = 3 kN/m2, Δt = 0.2 s, g=10 m/s2 we arrive at pRd = 1.5 kN/m2. This would require about 25 percent of the reinforcement for normal conditions on the opposite side. An important additional point to consider is the reaction force at the support. Note that the floor could be lifted from its supports, especially in the upper two stories of the building where the normal forces in the walls are small. In this respect edge walls are even more vulnerable. The uplifting may change the static system for one thing and lead to different load effects, but it may also lead to freestanding walls. We will come back to that in the next paragraph. If the floor to wall connection can resist the lift force, one should make sure that the also the wall itself is designed for it. Walls Finally we have to consider the walls. Assume the wall to be clamped in on both sides. The bending moment in the wall is then given by: m = 1/16 p H2 = 1/16 6.5 3^2 = 4 kNm/m If there is no normal force acting in the wall this would require a central reinforcement of about 0.1 percent. The corresponding bending capacity can be estimated as: mp = ω 0.4d2 fy = 0.001 0.4 0.22 300.000 = 5 kNm/m Normally, of course normal forces are present. Leaving detailed calculations as being out of the scope of this document, the following scheme looks realistic. If the explosion is on a top floor apartment and there is an adequate connection between roof slab and top wall, we will have a tensile force in the wall, requiring some additional reinforcement. In our example the tensile force would be (pE – 2 pSW) B/2 = (6.5-2x3) * 4 = 2 kN/m for a middle column and (pE – pSW) B/2 = (6.5-3) * 4 = 14 kN/m for an edge column. If the explosion is on the one but top story, we usually have no resulting axial force and the above mentioned reinforcement will do. Going further down, there will probably be a resulting axial compression force and the reinforcement could be diminished ore even left out completely. Derivation of ϕd Consider a spring mass system with a mass m and a rigid plastic spring with yield value Fy. Let the system be loaded by a load F>Fy during a period of time Δt. The velocity of the mass achieved during this time interval is equal to: v = (F - Fy ) Δt / m The corresponding kinetic energy of the mass is then equal to: E = 0.5 m v2 = 0.5 (F-Fy)2 Δt2 / m By equating this energy to the plastic energy dissipation, that is we put E = F Δu ,we may find the increase in plastic deformation Δu. Δu = 0.5 (F-Fy)2 Δt2 / m Fy


As mg = FSW we may also write: Δu = 0.5 (F-Fy)2 g Δt2 / FSW Fy Finally we may rewrite this formula in the following way:

F = Fy (1 + Rd

SW

FF

2max

)t(gu2Δ

)

For the slab structure we have replaced the forces F by the distributed loads p.


5.5 Gas and fuel / air explosions in road and rail tunnels According to Annex B of ENV 1991-1-7 for the case of detonation, the following pressure time function should be taken into account (see Figure 5.6.1)

0t)p(x,

})/tcx

2cx

(exp{pt)p(x,

})/tcx

(texp{pt)p(x,

012

0

01

0

=

−−=

−−=

212

121

cx

tcx

cx

for

cx

cx

tcx

for

≤≤−

−≤≤

(5.5.1)

for all other conditions p0: peak pressure (=2000 kN/m2) c1: propagation velocity of the shock wave (~1800 m/s) c2: acoustic propagation velocity in hot gasses (~800 m/s) t0: time constant (=0.01s) ¦x¦: distance to the heart of the explosion t: time [s] c1 1800c2 800 p1 p2 x/c1 x/c2-x/c1 x/c2 H1 H2 H3 H4po 2000 t pto 0,01 0,0005 0 4377,51 1623,87 0,008 0,010417 0,019 0 1 0 1x 15 0,001 0 4164,02 1623,87 0,008 0,010417 0,019 0 1 0 1

0,0015 0 3960,94 1623,87 0,008 0,010417 0,019 0 1 0 10,002 0 3767,76 1623,87 0,008 0,010417 0,019 0 1 0 1

0,0025 0 3584 1623,87 0,008 0,010417 0,019 0 1 0 10,003 0 3409,21 1623,87 0,008 0,010417 0,019 0 1 0 1

0,0035 0 3242,94 1623,87 0,008 0,010417 0,019 0 1 0 10,004 0 3084,78 1623,87 0,008 0,010417 0,019 0 1 0 1

0,0045 0 2934,33 1623,87 0,008 0,010417 0,019 0 1 0 10,005 0 2791,22 1623,87 0,008 0,010417 0,019 0 1 0 1

0,0055 0 2655,1 1623,87 0,008 0,010417 0,019 0 1 0 10,006 0 2525,6 1623,87 0,008 0,010417 0,019 0 1 0 1

0,0065 0 2402,43 1623,87 0,008 0,010417 0,019 0 1 0 10,007 0 2285,26 1623,87 0,008 0,010417 0,019 0 1 0 1

0,0075 0 2173,81 1623,87 0,008 0,010417 0,019 0 1 0 10,008 0 2067,79 1623,87 0,008 0,010417 0,019 0 1 0 1

0,0085 1966,943 1966,94 1623,87 0,008 0,010417 0,019 1 1 0 10,009 1871,014 1871,01 1623,87 0,008 0,010417 0,019 1 1 0 1

0,0095 1779,764 1779,76 1623,87 0,008 0,010417 0,019 1 1 0 10,01 1692,963 1692,96 1623,87 0,008 0,010417 0,019 1 1 0 1

0,0105 1623,873 1610,4 1623,87 0,008 0,010417 0,019 1 0 1 10,011 1623,873 1531,86 1623,87 0,008 0,010417 0,019 1 0 1 1

0500

1000150020002500

0 0,01 0,02 0,03

t [s]

p [k

N/m

2]

p

Figure 5.5.1: pressure in case of detonation


In case of deflagration the following pressure time characteristic should be taken into account (see Figure 5.6.1)

)1)((4)(00

0 tt

ttptp −= for 0tt0 ≤≤ (5.5.2)

p0: peak pressure (=100 kN/m2) t0: time constant (=0.1 s) t: time [s]

0

20

40

60

80

100

0 0,05 0,1

t [s]

p0=100 kN/m2, t0=0.1 s Figure 5.5.2: Pressure in case of deflagration


5.6 Dust explosions in rooms and silos Dust explosions are treated in Annex B, Section B.3, based on the ISO 6184-a, published in the [5.5]. These references are based on work of [5.15, 5.16]. The three basic conditions for a dust explosions are:

• combustible dust • dispersive air • ignition source

Under conditions of complete confinement most common inflammable dusts mixed with air, at atmospheric pressure, may produce a maximum explosion pressure in excess of 14 bar. [5.17]. Dust explosions occurring at elevated initial temperatures tend to show lower maximum explosion pressures than those occurring at ambient temperatures. [5.16] gives a linear relationship between the reciprocal temperature and the Pmax:

initial

max

initial

max

TT~

PP

(5.6.1)

The cubic law is an important tool in estimating the explosion severity of dusts in vessels. Dusts are classified according to their Kst-value (Kst is the VDI designation; the ISO designation for the same quantity is Kmax).The cubic law is given by (see [5.16]:

max31

)(dtdPVK

st= (5.6.2)

where V is the volume of the vessel [m3] and )(dtdp

max is the maximum value of the rate of

pressure increase during explosion For the standardisation of the dust explosion classes Bartknecht developed an explosion vessel [Bartknecht, 1993]. In his 1 m3 explosion vessel. [Bartknecht (1971)] used a dust dispersion system by which the dust was forced at high velocity by high pressure air through a number of 4-6 mm diameter holes in a U-shaped tube of 19 mm in diameter. Bartknecht's 1 m3 vessel and dust dispersion system has later been adopted as an ISO standard (International Organisation for Standardisation (1985)). Definition of dust explosion classes according to [5.16], (1m3 apparatus, 10 kJ ignition source)

Dust explosion class Kst [bar m/s] Characteristics St 0 0 Non-explosible St 1 0 < Kst ≤ 200 Weakly to moderately explosible St 2 200 < Kst ≤ 300 Strongly explosible St 3 Kst > 300 Very strongly explosible


Vent sizing methods Numerous methods for vent sizing have been proposed. The process of choosing the most effective method of vent sizing can be complex, depending on several factors like Kst, Pmax, vessel volume and length to diameter ratio. The vent ratio in general is defined as:

Vent ratio = Area of vent / Volume of the vessel A method for scaling vent areas for rooms and silos is the Radandt Scaling Law. [5.18] [5.15], Appendix 8.1 indicated the Equation, derived by Radandt:

cVba ⋅⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

redPA (5.6.3)

A: vent area [m2] Pred: maximum explosion pressure in the vented vessel [bar] V: volume of vessel [m3] a, b, c: empirical constants depending on the dust explosion class (see Tables 1 and 2) Pstat: static relief pressure and size of existing vent areas [bar] Pred: reduced maximal explosion pressure [bar]

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

V [m3]

St1, P red=0.2bar St1, P red=0.5bar St2, P red=0.2bar St2, P red=0.5bar Figure 5.6.1: Dust explosion, vessel (5.18)


Table 1: Factors for the calculation of the vent area A in relation of the cubical volume V. Pstat is assumed to equal 0.1bar, Pmax = 9 bar and Pred must not exceed 2 bar. Dust explosion class pred, max (bar) a b c St 1 < 0.5 0.04 0.021 0.741 ≥ 0.5 0.04 0.021 0.766 St 2 < 0.5 0.048 0.039 0.686 ≥ 0.5 0.048 0.039 0.722 Table 2: Factors for the calculation of the vent area A in relation of the silo volume V. Pstat is assumed to be equal 0.1bar, Pmax = 9bar. Dust explosion class pred, max (bar) a b c St 1 ≤ 2 0.011 0.069 0.776 St 2 ≤ 2 0.012 0.114 0.720 Cubic and elongated vessels, silos and bunkers according VDI, 1995 The sizing of the vent area of cubic vessel is based on experimental investigations that were carried out under conditions that represent the actual situation. The equations should cover unfavourable conditions. For a inhomogeneous dust distribution the size of the vent is smaller than for homogeneous distribution. Therefore only the homogenious situation is considered: A = [ 3.264 * 10-5 * pmax * Kst * pred.max

-0.569 + 0.27 * (pstat - 0.1) * pred.max-0.5 ] * V0.753 (5.6.4)

A vent area [m2] pmax maximum explosion overpressure of the dust Kst dust specific characteristic [bar m s-1] pred.max anticipated maximum reduced explosion over pressure in the vented vessel [bar] pstat: static activation overpressure with size of existing vent areas [bar] V: volume of vessel, silo, bunker [m3] This equation is valid for the following conditions:

• 0.1 m3 ≤ V ≤ 10'000 m3 • H/D ≤ 2, where H high and D diameter of elongated vessel • 0.1 bar ≤ pstat ≤ 1 bar • 0.1 bar ≤ pred.max ≤ 2 bar • 5 bar ≤ pmax ≤ 10 bar for 10 bar m s-1 ≤ Kst ≤ 300 bar m s-1 • and

5 bar ≤ pmax ≤ 12 bar for 300 bar m s-1 ≤ Kst ≤ 800 bar m s-1


0

50

100

150

200

250

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

V [m3]

p max= 5 bar, Kst= 10 bar m/s, p stat=0.1 bar, p red max=0.1 barp max=10 bar, Kst=300 bar m/s, p stat=0.1 bar, p red,max=0.1 bar p max= 5 bar, Kst=300 bar m/s, p stat= 1 bar, p red,max=2 bar p max=12 bar, Kst=800 bar m/s, p stat= 1 bar, p red,max=2 bar

Figure 5.6.3: Dust explosion, cubic and elongated vessels, silos and bunkers [5.5] Rectangular enclosure according VDI, 1995 The required vent area for rectangular enclosure is determined according to the following equation: A = [ 3.264 * 10-5 * pmax * Kst * pBem

-0.569 + 0.27 * (pstat - 0.1) * pBem.-0.5 ] * V0.753 (5.6.5)

A vent area [m2] pmax maximum explosion overpressure of the dust Kst dust specific characteristic [bar m s-1] pBem design strength of the structure [bar] pstat: static activation overpressure with size of existing vent areas [bar] V: volume of vessel, silo, bunker [m3] This equation is valid for the following conditions:

• m3 ≤ V ≤ 10'000 m3 • L3/DE ≤ 2, where L3 greatest dimension of enclosure, DE = 2 * (L1 * L2/ π )0.5 , L1 , L2

other dimensions of enclosure • bar ≤ pstat ≤ 1 bar • 0.02 bar ≤ pBem. ≤ 0.1 bar • 5 bar ≤ pmax ≤ 10 bar für 10 bar m s-1 ≤ Kst ≤ 300 bar m s-1

and • 5 bar ≤ pmax ≤ 12 bar für 300 bar m s-1 ≤ Kst ≤ 800 bar m s-1


0

100

200

300

400

500

600

700

800

900

1000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

V [m3]

p max= 5 bar, Kst= 10 bar m/s, p stat= 0.1 bar, p Bem=0.02 bar p max=10 bar, Kst=300 bar m/s, p stat= 0.1 bar, p Bem=0.02 bar p max= 5 bar, Kst=300 bar m/s, p stat= 1 bar, p Bem=0.1 bar p max=12 bar, Kst=800 bar m/s, p stat= 1 bar, p Bem=0.1 bar

Figure 5.6.4: Dust explosion, rectangular enclosure (VDI, 1995) For elongated rooms with L3/DE ≥ 2 the following increase for the vent area has to be considered:

∆AH = A * (- 4.305 * log pBem + 0.758) *log L3/DE ∆AH increase for vent area [m2]


REFERENCES [3.1] Safety in tall buildings and other buildings with large occupancy by the Institution of

Structural Engineers. [3.2] Stufib Studiecel, Incasseringsvermogen van bouwconstructies (Robustness fo

building structures, in Dutch), Delft, October 2004. [3.3] Norwegian Petroleum Directorate:

Regulations concerning load bearing structures in the petroleum activities 1992 [3.4] DIS2394] [4.1] CIB W81, General Report, Publication 160, CIB, Rotterdam, 1991 [4.2] CIB .W81, Accidental Actions, Publication 167, CIB, Rotterdam, 1993 [4.3] T. Vrouwenvelder

Stochastic modelling of extreme action events in structural engineering Probabilistic Engineering Mechanics 15 (2000) 109-117

[4.4] Moore, J.F.A. , "The incidence of accidental loads on buildings 1971-1981" BRE Information, UK, May 1983 [4.5] Popp, dr.-ing. Camillo. "Der Quersto� beim Aufprall" (in German), Forschungshefte aus

dem Gebiete des Stahlbaues, Deutschen Stahlbau Verband, Köln am Rhein, 1961 [4.6] Chiapella, R.L., Costello, J.F., "Automobile Impact Forces on Concrete Walls", Transactions of the 6th International Conference on Structural Mechanics in Reactor Technology, Vol. J(b), Paris, 1981 [4.7] ISO TC98/SC3/WG4, "Accidental actions due to human activities", Draft July 1987 [4.8] UIC Subcommittee bridges, Structures built over railway lines, OBB-GD 8.4 Draft

May 1992 [4.9] Grob,J., Hajdin,N., “Train Derailment and Its Impact on Structures”, Structural

Engineering International 2/93. [4.10] Larsen, O.D. "Ship Collisions with Bridges" IABSE, Structural Engineering Document 4, ETH, Zürich, Switzerland [4.11] ISO DP 10252 "Accidental Actions due to Human Activities" ISO 1995. [5.1] Mainstone, R.J., Nicholson, H.G., Alexander, S.J., Structural Damage in Buildings

caused by Gaseous Explosions and Other Accidental Loadings, 1971 - 1977, Building Research Establishment, England 1978.

[5.2] Leyendecker, E.V. and Ellingwood, B.R., “Design Methods for Reducing the Risk of Progressive Collapse in Buildings” ; US National Bureau of Standards, Washington ; April 1977.

[5.3] Venting of Deflagrations, National Fire Protection Association, 1988. [5.4] Mainstone, R.J., The Response of Buildings to Accidental Explosions, Building

Research Establishment, England, 1976. [5.5] VDI, 1995, VDI 3673, Part 1, Pressure Venting of Dust Explosions, Juli 1995 [5.6] Cubbage, P.A., Simmonds, W.A., An Investigation of Explosion Reliefs for Industrial

Drying Ovens - I Top Reliefs in Box Ovens. Trans. Inst. Gas Eng., 105, 470, 1995 [5.7] Cubbage, P.A., Simmonds, W.A., An Investigation of Explosion Reliefs for Industrial

Drying Ovens - II Back Reliefs in Box Ovens, Reliefs in Conveyor Ovens, Trans. Inst. Gas Eng., 107, 1997

[5.8] Rashbash, D.J., The Relief of Gas and Vapour Explosions in Domestic Structures. Fire Research Note No. 759, 1969


[5.9] Dragosavic, M., Research on Gas Explosions in Buildings in the Netherlands. Notes Reference No. 354/72, Symposium on Buildings and the Hazards of Explosion, Building Research Station, Garston, England (1972).

[5.10] Dragosavic, M., Structural Measures Against Natural-Gas Explosion in High-Rise Blocks of Flats, Heron, Vol. 19, No. 4 (1973).

[5.11] Harris, R.J., Marshall, M.R., Moppett, D.J., “The Response of Glass Windows to Explosion Pressures”, British Gas Corporation. I.Chem.E. Symposium Serious No. 49, 1977.

[5.12] TNO, 1979, TNO, Prins Maurits Laboratory, Methods for the calculation of the physical effects of the escape of dangerous materials, chapter 8, vapour cloud explosion, TNO, 1979

[5.13] FMB 7714, FMB 7714, Forschungsinstitut für Militärische Bautechnik [5.14] GRD, 1998, Gruppe Rüstung, AC-Laboratorium Spiez, 3700 Spiez: LS 2000,

Luftstossphänomene infolge nuklearer und konventioneller Explosionen, Januar 1998 [5.15] Bartknecht, W.: Staubexplosionen, Ablauf und Schutzmassnahmen, Springer-Verlag,

1987 [5.16] Bartknecht, W.: Explosionsschutz, Grundlagen und Anwendung, Springer-Verlag,

1993 [5.17] Bussenius, S.: Wissenschaftliche Grundlagen des Brand- und Explosionsschutzes,

Kohlhammer, 1996 [5.18] Radandt, Bestimmung der Explosionsdruck-Entlastungsflächen in Übereinstimmung

mit den am häufigsten angewendeten Richtlinien innerhalb und ausserhalb Europas. Europex-Seminar: "Druckentlastung von Staubexplosionen in Behältern", 1986,

[x] Eckhoff, R. K. Dust Explosions in the process industries, Second Edition, 1997 [x] Harris, 1989, Harris, R. J.: Gas explosions in buildings and heating plant, 1989 [x] Lunn, G.: Dust Explosion Prevention and Protection, Part 1 - Venting, Second

Edition, 1992 [x] Nasr, T.: Druckentlastung bei Staubexplosionen in Siloanlagen, Karlsruhe 2000 [x] Van der Wel, P.: Ignition and propagation of dust explosions, 1993 [x] EN 26 184, Teil 1, Explosionsschutzsysteme, Teil 1: Bestimmung der

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