Extreme loading situations are often known as ‘accidental loads’ because they occur under circumstances that are typically due to events that are inherently unlikely to occur. They are often referred to as accidental design situations to differentiate them from those of standard or an everyday occurrence. This post is a background to how BS EN 1990: Eurocode – Basis of structural design approaches the effects of extreme loading conditions on structures.

The word “extreme” often associated with something that goes beyond what is usual or reasonable. A list of such event that can be classified as extreme in the context of applied loads include:

• Explosion
• Vehicular Impact
• Seismic Event
• High Wind
• Tsunami etc.

A structure might be exposed to any of these extreme events at some point during its lifetime, therefore some serious consideration must be given to their likelihood at the design stage. Though some of these events are less likely they are certainly extreme. The likelihood of these event occurring is so low that to design for them would, in most instances, be considered unreasonable. For example, it will be considered unreasonable to design a structure against a seismic event in Nigeria. However, there are exceptions where the likelihood of more extreme event must be considered irrespective of the fact that the likelihood of occurrence is so low.

### Consequence Class

Due to the low probability, a vast majority of structures are not typically designed against accidental or extreme loading condition. Instead, structures are classified into a Consequence Class. This classification is based on the significance of how significant the failure of a structure will be rather than the likelihood of it failing. This Consequence Class is defined in Annex A of BS EN 1991-1-7 General Actions -Accidental Action. Designers are to check the structure they’re designing against this section of the code when considering a structure for accidental actions.

### Eurocode Approach to Assessing Accidental Actions

The approach adopted by BS EN 1990 to extreme conditions is based on the manipulation of the partial factors applicable to loads/ actions. Such factors are considerably smaller than those used for permanent conditions. This is based on the premise that the circumstances in which these incidents occur are very rare and, as such, the partial factors that relate to the permanent conditions are not acceptable. To explain the partial factors applied to extreme loading these variables must be defined.

‘A’ is the variable label for accidental actions, which are actions due to extreme events. This has two subscripts: ‘Ad‘ and ‘AEd‘. The former is for all accidental actions, while the latter is for actions generated by seismic events.

The general format of determining the design actions on structures subjected to accidental actions are defined in Table 6.11 of BS-EN 1990-1-1 excluding seismic action. This can be simplified for structures without prestressed elements to the expression

{ E }_{ d }=\left\{ { G }_{ k,j }+{ A }_{ d }+{ \psi  }_{ 1 }{ Q }_{ k,1 }+{ \psi  }_{ 2 }{ Q }_{ k,2 } \right\}
##### Where:
• Ed is the effect of the combined actions
• Gk,j is the permanent action e.g. self-weight of the structure
• Ad is the action due to an accidental event
• Qk,1 is the leading frequent variable action e.g. occupancy and furniture
• Qk,2 is the accompanying quasi-permanent variable action e.g. wind
• ψ1 is the factor for leading frequent value of a variable action*
• ψ2 is the factor for accompanying quasi-permanent value of a variable actions

The values of ψ1 & ψ2 are taken from table A11 of BS EN 1990.

In addition to the partial factors added to loads / actions, the material’s partial factors are adjusted to reflect the circumstances under which the occurrence happens.

For example let us consider a shopping mall building subjected to blast force in addition to permanent actions, imposed loads and wind actions. The building will be subjected to the following load combinations.

{ E }_{ d }={ G }_{ k,j }+{ A }_{ d }+{ 0.7Q }_{ k,1 }+0{ Q }_{ k,2 }
 { E }_{ d }={ G }_{ k,j }+{ A }_{ d }+{ 0.2Q }_{ k,1 }+{ 0.6Q }_{ k,2 }

The first expression considers imposed load as the leading variable action and wind as accompanying variable action. While in the second expression wind is the leading variable action and imposed load is accompanying variable action.

Here, the factors applied to the permanent and variable actions are much lower than that for normal condition. The reason for this is based on the assumption that the likelihood of an accidental event is so low giving that the effect of the load is minima in permanent conditions.

The common forms of extreme or accidental conditions include but is not limited to the following.

#### Blast Force

The magnitude of a  blast is difficult to assess because of the number of factors that need to be considered. The size and location of the explosion are key factors in the estimation of the possible force produced. This can be measured, but a large amount of knowledge has to be understood about the structure, location and access restrictions before any calculation can be carried out.

As a measure against the disproportionate collapse of buildings from blasts, the Eurocode requires all key elements to be designed for a minimum force of 34kN/m2. These elements are to remain intact following the explosion, else a large portion of the structure could collapse.

The partial factors described above apply to the assessment of these elements against this force. It usually results in the key element being able to withstand the blast force without any substantial modification, as it is already designed for even higher forces due to the higher partial factors related to behavior in non-extreme cases.

#### Seismic Events

Seismic events generate actions of very short duration all over a structure. They are rare and are considered as such by BS EN 1990 as a form of accidental action. There is a variation on the partial factors to be applied to seismic events, to reflect the nature of actions generated by seismic events. For structures subjected to seismic events, the value of the design action is given by the expression:

{ E }_{ d }={ G }_{ k.j }+{ A }_{ Ed }+{ \psi  }_{ 2 }{ Q }_{ k,2 }

Note that the leading variable action part of the equation has been removed. This is because it’s mass would be considered to be beneficial to the structure during a seismic event. And, since it’s a variable action, it value varies in magnitude with time, hence, it is best to ignore it completely.

#### Flooding

Sub-structures of buildings including basements are designed to withstand and accommodate flooding. This is done by assuming hydrostatic pressures will be applied to them at some depth. The effects of flowing water around sub-structures is usually covered by applying general robustness requirements.

#### Mechanical Failure of Plant

Consideration must be given to the probability of plant which is part of the building services failing. A common example of this is the collapse of a lift which can result in very high impact forces. Such a force is deemed highly improbable and thus is treated as purely accidental.

#### High Winds

High winds and extreme temperatures are designed for, using normal methods and are not considered to be accidental. The magnitude of wind force is based on a statistical assessment of past records to determine extreme values for a particular return period. These are typically between 50 to 120 years.

### Conclusion

The extreme loading conditions described in this post are the common forms encountered in practice. However, accidental actions are numerous and its consideration requires the design engineer to make a sound judgement on the environment in which the structure is to operate as well as the intended function of the structure.

### Sources

The Institution of Structural Engineers (2010) Manual for the design of building structures to Eurocode 1 and basis of structural design London.

Ingleton J. (Ed.) (1999) Natural Disaster Management Leicester, UK, Tudor Rose Holdings Ltd

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