57GLASS PERFORMANCE DAYS 2007 | www.gpd.fi

Consequence-based safety requirements for structural glass membersFreek Bos, Fred VeerDelft University of Technology, Faculty of Architecture, Department of Building Technologye-mail: F.P.Bos@tudelft.nl, www.glass.bk.tudelft.nl

Keywords

1= safety 2= risk 3= probability 4= consequence 5= damage6= residual strength

Abstract

Glass is generally considered to be an unsafe material to use in building structures. To limit the risk associated with glass structures, there has been a focus on the probabilistic approach. This is insufcient for structures in general and for glass structures in particular. Much more than common structural materials like steel and reinforced concrete, glass is highly susceptible to a wide range of incidents causing glass breakage. Therefore, one should not (only) ask when will the glass break? (probabilistic approach), but (also) what will happen when is does? (consequence-based approach). Analysis of projects realized in practice show that structural engineers are aware of this, and use varying strategies to limit the consequences of glass failure. However, such strategies are applied to varying extent, depending on the engineers experience and opinion, location, structure type and probably on many more factors. Hence, an explicit consequence-based approach is proposed for structural glass members, in addition to the existing probabilistic approach. This approach sets specic requirements to the residual strength of structural glass members for a certain period of time, at prescribed levels of damage. The concept of Member Consequence Classes (MCC) is introduced, in order to be able to differentiate requirements for members based on their role within a structure and the function and accessibility of the structure at hand. The presented approach allows for an open discussion on the required level of residual strength at varying levels of damage. Furthermore, it provides a basis for comparing design options in terms of safety. Finally, because it sets requirements for the application of structural glass in any (building-) structural application, it provides a fundamental basis for the development of structural glass beyond the existing small scale glass structures like entrances, pavilions and conservatories.

1.Introduction

The brittle failure behavior of glass makes it not an obvious choice as a structural material, even though it has

relevant strength and stiffness. As it yields neither globally nor locally, it is sensitive to peak stresses that may be the result of a wide variety of causes ranging from (micro scale) surface defects to (macro scale) detailing errors. Furthermore, due to the molecular structure of glass there is no mechanism present to stop the growth of a crack once it has started. Finally, glass has an extremely low impact strength because of the electronically polar array of the molecular bonds. The result of these properties is that glass breaks suddenly and completely, and the strength of individual pieces shows a large scatter (the coefcient of variation is typically between 10 and 30 %, [1]). It is generally accepted that specic measures are necessary to ensure the safety of glass structures. In this paper, the authors propose to use a combined probabilistic/consequence-based approach to assess the safety of glass structures, based on existing methods of stress checking extended with quantiable requirements concerning residual strength at certain prescribed levels of damage.

Besides the structurally unsafe behavior of glass, its shards pose an immediate risk to the personal safety of people. Although this should be heeded at all times, such considerations fall outside the direct scope of this article.

2.Safety, risk, probability and consequence

To quantify safety, the notion of risk has been introduced, popularly dened as the product of probability and consequence (Eq. 1). Although the correct mathematical formulation is more complex [2], (Eq. 1) clearly points out that risk is basically dependent on two components: the probability that something will happen and the consequence of it when it does. Thus, risk can be limited by decreasing either or both of these components.

(1)FFF CPR

RF = risk associated with the failure of a piece of engineering.

PF = probability of a failure event.CF = the consequence of a failure event.

Structural (glass) engineering codes tend to focus on the probability component of risk (as will be shown below) although requirements towards the consequence aspect can be found to various extent in different code systems. Developments towards more balanced probabilistic/consequence-based approaches can be observed because it has been shown that a single-sided probabilistic approach, even though it is a powerful tool in assessing and minimizing the risk of structures, has its limits.

For a truly fully probabilistic analysis, it would be required that all relevant data concerning structural properties (e.g. material composition, material quality, geometry) and actions on that structure (self weight, static, semi-static, dynamic, shock/impact) are known, so that they can be described statistically. As this is impossible, approximations are used, based on research and experience. However, in reality failures are hardly ever caused by those actions applied in probability analysis [3]. Technical errors may occur, but prevailing political, nancial, scientic, professional and industrial conditions may also have an overriding effect [4]. Furthermore, actual failure is usually not caused by a single error but the consequence of a conjunction of multiple deciencies. This is virtually impossible to describe statistically. Hence, the calculated reliability of a structure based on a probabilistic approach, is useful to compare structural designs with each other and to a theoretically allowable level of risk, but has limited meaning in terms of real risk.

Considering furthermore that glass is much more susceptible to all kinds of incidental actions, deciencies and errors that are difcult to describe statistically, it will be clear that it is extremely important to explicitly reckon with the consequence component of the risk associated with glass structures. Surprisingly, such considerations have practically been absent in most structural glass codes as well as scientic literature concerning structural glass.

3.Risk control in structural (glass) engineering codes

The basic requirements towards building structures in the Netherlands

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are dened in the NEN 6700 [5]. In this code, the maximum allowable level of risk is limited primarily by requiring a structure to meet a minimum reliability index E, which is dened as the probability that an ultimate limit state or a serviceability limit state is exceeded during the reference life time of the structure. Clause 5.3.3 of NEN 6700 also states that collapse of a single component should not lead to excessive damage and thus pays attention to the consequence side of risk. But while extensive rules to check if a structure meets the reliability requirements have been laid down in NEN 6702 [6] (which denes the actions on structures) and several material codes (giving rules on how to check a designed structure against those actions), specications of this consequence-based requirement are much less consistent, often hard to recognize as such and/or not quantiable.

A Dutch code on the structural use of glass does not yet exist, but is most closely approached by prNEN 2608-2:2004 [7] which deals with wind loads, snow and self weight on non-vertical glazing. However, the scope of this code excludes glass in primary load carrying applications like beams, columns and even oors. For evaluating non-vertical glazing it requires a stress check and provides rules to calculate the maximum bending tensile strength of the glass. However, it does not specify any requirements with regard to the consequence of a failure.

In the European context, basic requirements towards building structures have been formulated in NEN-EN 1990 [8]. This code sets requirements to the reliability of structures similar to those in the NEN 6700. With regard to the consequences of failures, the NEN-EN 1990 is more extensive. In 4(P) under clause 2.1, it is stated that a structure should not be disproportionately damaged by explosion, impact or human error. Sub clause 5(P) names several strategies that can be deployed to limit or avoid potential damage, but these are still quite generally formulated. However, part 7 of Eurocode 1 [9], deals with the structural resistance both to identied accidental actions and unspecied failure causes in detail. Especially the acceptance in the code that unspecied failure causes may occur, is important because it calls for a consequence based safety approach. And indeed, clause 3.3 describes strategies to be applied to the design of building structures in order to limit the extent of local failure of whatever cause: key structural elements should be designed to withstand a (large) accidental action and the structure should be designed in a way that failure of a local member will not endanger the stability of the structure or a signicant part of it. The informative annex A of this code gives a guideline to design for consequences of local failure in buildings from an unspecied

cause. It categorizes building types into consequence classes (CC), depending on the severity in case of collapse. The extent of the measures that should be taken to avoid disproportionate collapse is dependent on consequence class.

The quantitative requirements with regard to the consequence of a local failure are still relatively limited compared to all requirements regarding the probability of a failure. Nonetheless, contrary to the Dutch codes, the European codes not only provide general requirements but also rules and guidelines on how those consequence related requirements should be met. However, it should be noted that both general requirements in the NEN-EN 1990 and the rules and guidelines in NEN-EN 1991-1-7 focus solely on the (complete) structure.

On European level, there has only been a provisional code for structural glass: the NEN-EN 13474 [10] (withdrawn early 2007). As the NEN 2608-2, this code focused on checking the design stress against the bending tensile strength of the glass. However, it did not completely ignore the consequence aspect because it stated in clause 5.1 that breakage of the glazing may not result in further damage if the glazing is part of the supporting structure. However, how this general remark was to be interpreted, was not elaborated further.

The German structural glass code DIN 18008 which has been published in March of this year, appears to be the rst to extensively treat the consequence aspect [11], by requiring glazing structures not only to be able to carry actions on it during its reference life time with a certain level of probability but also demanding sufcient residual strength (Resttragfhigkeit) for certain structures or installation situations. It therefore denes residual strength as the capacity of a glazed construction to remain sufciently stable in case of glass breakage and it rightfully states that this can not be realized by applying a safety factor as this would inuence the probability of failure, not the consequences should one occur.

4.Safety strategies in practice

Although up until the publication of the DIN 18008 there has been little attention in the codes for the behavior of glass structures in case of failure, practicing engineers have certainly not ignored it. In all structural glass projects, strategies are applied to limit the consequences of glass breakage. Combining single glass plies into multiply laminates with adhesive interlayers is the single most important strategy applied in practice to avoid sudden collapse of a structural glass member. The basic argument behind the application of this technique is that if one ply breaks through whatever cause, the remaining ply/plies will still be able to carry a certain load while

simultaneously ensuring that the glass shards will stick to the laminate, thus avoiding personal injuries.

But beyond this basic and valid argument, a number of questions arise, such as: How many layers should be used? Should failure of a single glass ply, multiple plies or perhaps even of the entire glass section be reckoned with? What should be the strength of the remaining ply/plies? Should the glass be prestressed? What kind of interlayer should be used? Should more special measures be applied, like stainless steel reinforcement?

When analyzing realized structural glass projects, it will become clear that these questions are answered differently in each project: the number of glass layers varies, different kinds of foil are used, different levels of prestress are applied, etc. The grounds, on which decisions with regard to these properties are being made, are unclear. Consequence based safety requirements are not formulated a priori (at least not publicly). Thus, it can not be properly assessed whether the required level of safety is achieved in a specic design. Furthermore, design options can not objectively be compared and it is not clear what experiments should be performed to prove the safety of a specic design. Finally, the lack of clearly formulated requirements concerning post-failure behavior, make it difcult to objectively discuss structural safety of glass members.

5.Towards a combined probability/consequence-approach

Therefore, the authors propose a quantiable system of consequence based safety requirements in addition to the existing probability requirements. This approach seeks to limit the consequences of failure of a structural member by requiring the member to retain a certain amount of strength for a certain period of time after the failure has set in. Thus, it can be avoided that failure coincides with collapse.

5.1. Parameters

Failure of a glass member can occur in different forms. A three layer laminate beam (Figure 1) is considered failed when all layers are broken, but also when only one layer is broken. Since the latter is more likely to occur, it is reasonable to differentiate between the post-failure requirements for different failure cases. To be able to make such distinctions, the concept of glass damage Dglass is introduced as the third parameter by which the consequence-based safety requirement is dened (besides post-failure strength and time). It can be dened in terms of loss of structurally functioning glass in the critical cross section of a structural glass member (Eq. 2).

Glass damage, Strength, and Time can now be combined into one

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coordinate system in which a minimum strength can be dened as a three dimensional shape. Figure 2 shows an example. As it will be impossible to asses the full continuous relation between glass damage, strength, and time of a specic member, discrete demarcations along each axis are introduced which should be considered when checking if a member fullls the consequence-based requirements. This allows for more unied ways of testing and checking and also for a more easily readable, two dimensional presentation of the requirements as shown in Figure 3.

5.2. Axis demarcations

5.2.1. DamageWhen glass breaks, the cracks usually run through a piece completely. This cracking behavior allows for a discretization of the amount of damage by formulating it in terms of complete breakage of 1 to n layers of glass, where n = the total amount of layers in the cross section. For the purpose of clarity, the layers are considered to have an equal cross section area. Using Eq. 3, Eq. 2 can be rewritten as Eq. 4, which introduces d as the glass damage factor, i.e. the number of cracked layers.

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Figure 2

Example of a consequence-based safety re-quirement, formulated in terms of a minimum strength in the S, D, t-diagram.

Figure 1

Failure of a three layer laminate glass beam, with different levels of damage: a) One outer layer bro-ken, b) All outer layers broken, c) All layers broken. In all stages the beam can be considered to have failed. In an ordinary PVB-laminate beam, stage c) will also lead to collapse.

Figure 3

Example of how a consequence-based safety requirement might be represented two-dimen-sionally.

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It is proposed to consider the following stages of damage:

One outer layer broken, d = 1. Breakage of one layer is a relatively likely stage of damage, because of the susceptibility of glass to all kinds of failure causes. Because of its unprotected position, breakage of an outer layer is the most likely. All outer layers broken, d = m, with m = the number of outer layers (mwill usually be 2, unless the member has a more complex cross section). Although less likely than the breakage of one layer, the outer layers are more susceptible to sustaining all kinds of damage than the protected inner ones. Both accidental or purposeful (vandalism) mechanical damage may occur. All layers broken, d = n. The basis of a consequence-based approach is that this scenario should also taken into account. It may not be ignored just because it seems unlikely, although only limited post-failure strengths may be required at this level of damage.

5.2.2. StrengthRelating to action levels dened in the codes, several required levels of post-failure strength can be recognized:

Ssw, Strength equal to the self weight of the member. Smom, Strength equal to the momentary load.Ssls, Strength equal to the serviceability limit state action.Suls, Strength equal to the ultimate limit state action.Srep, Strength equal to the representative strength of the member.

The last level of strength can be desired not only for undamaged members, but also for damaged members (even up to the level of d = n) which are used for applications where the consequences

of a collapse (caused by failure) would be severe. Steel shows this kind of behaviour as its ultimate strength after yielding of the complete section (failure) can still exceed the representative pre-failure strength (before yielding).

5.2.3. TimeFew handholds were found to determine the duration at which the required strength levels should be maintained. The following provisional proposal is made:

0:00:30 h (30 s). Time necessary to immediately ee from a damaged structural member.2:00 h. More extensive time to evacuate and close off a space surrounding a damaged member, as well as to remove the loads on the member.24:00 h (1 day). Time to take structural measures (shoring).72:00 h (3 days). Time to take extensive structural measures. The reference life time.

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5.3. Member Consequence Classes

Not all structural glass members need to have the same post-failure strength; a differentiation according to the consequences of a collapse is reasonable. Similar to the redundancy requirements formulated in Eurocode 1 part 7, Consequence Classes can be introduced. To distinguish between the Consequence Classes in that code, which are formulated on the scale of the complete structure, and the ones proposed here, focusing on the scale of individual members, they are named Member Consequence Classes (MCC). We suggest to distinguish between 6 Member Consequence Classes based on a differentiation in a) the type and accessibility of the building in which the glass member is applied, and b) the hierarchical function of the member within the structure (Table 1).

5.4. Minimum post-failure strengths

Now that six Member Consequence Classes have been dened, different requirements can be formulated for each class. The requirements are numerically listed in Table 2. They are graphically presented in the S, D, t-diagram in Figures 4 to 9.

6. Conclusions

In addition to the existing probability based safety analyses of structural glass members, a consequence-based approach has been proposed in this paper. Combined, these approaches make it possible to formulate a priori the level of safety that is desired and to objectively evaluate and compare design alternatives for a specic application.

The consequence-based approach is based on a required level of residual strength for a certain period of time, at prescribed levels of damage. The damage levels are quantied in terms of the number of broken glass layers. The concept of Member Consequence Classes (MCC) has been introduced, in order to be able to differentiate requirements for members based on their role within a structure and the function and accessibility of the structure at hand. The consequence-based approach does not exclude any type of structure or structural member, and thus sets an objective in terms of post-failure behavior to develop structural glass members that can be applied in any structure.

The proposed formulation of consequence-based safety requirements makes it possible to develop standard structural glass members for specic applications, based on standardized testing sequences which by virtue of their standardized nature can be much more extensive than the usual safety testing of structural glass members.

The presented method is novel, and thus still requires elaboration. A more extensive discussion of this subject will appear in HERON [12] . Further research

MCC

Required strength and period of time for certain amount of damage (number of broken layers)

d < 1 (pre-failure) d = 1 (outer) d = m (all outer) d = n (all)

Str. time Str. time Str. time Str. time

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Function of member within structure Accessibility / Building type MCC

Key member High Public 6

Key member Medium Semi-public/ofce 6

Key member Low Private 5

Primary member High Public 4

Primary member Medium Semi-public/ofce 3

Primary member Low Private 2

Secondary member High Public 3

Secondary member Medium Semi-public/ofce 2

Secondary member Low Private 1

Table 1

Member Consequence Classes for combinations of building type and member function.

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Consequence-based safety requirements for MCC 1. Only in case of one layer breaking should there be signicant post-failure strength.

Figure 5

Consequence-based safety requirements for MCC 2. The primary difference of this MCC with the previous one, is fact that it is required to maintain signicant post-failure strength after the outer layers of the member are broken.

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Consequence-based safety requirements for MCC 3. Because members of this class can be applied in publicly accessible space or for pri-mary members in semi-public spaces, quick col-lapse is unacceptable at a random moment even in case all glass layers break.

Figure 7

Consequence-based safety requirements for MCC 4. In case of MCC 4, the post-failure strength requirement after breakage of the complete section is increased to the service-ability limit state, thus making it sudden collapse unlikely at any moment (as opposed to a ran-dom moment as with MCC 3).

Table 2

Numerical formulation of the proposed post-failure requirements for each of the six Member Conse-quence Classes.

* If n = m, than the requirement for d = m still applies. ** tref = reference life time.

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Figure 9

Consequence-based safety requirement for MCC 6. These members not only play a vital role in the structure, but are also applied in commonly accessible buildings likely to contain many people at a given moment. Therefore, their be-haviour should be inherently safe (comparable to steel), independent on the loading it was calculated for. Thus, they are required to have a post-failure strength equal to their pre-failure strength.

will include evaluating the chosen axes demarcations and MCC criteria, as well as developing relevant experimental test methods. The authors would welcome any remarks or suggestions to further develop the proposed approach.

7.References[1] Veer, F.A., J. Zuidema, F.P. Bos, T. Romein, The

strength and fracture behaviour of annealed and tempered oat glass, Proceedings of the 11th international conference on Fracture, Turin, Italy, 2005.

[2] Vrouwenvelder, A., B.M. Holicky, C.P. Tanner, D.R. Lovegrove, E.G. Canisius (Eds.), Risk Assesment and risk communication in civil engineering, CIB Working Commission TG32, 2001.

[3] Popovic, P.L., W.J. Nugent, Common causes of structural collapses, In: IABSE (Ed.), Proceedings of the International conference on Safety, Risk and Reliability Trends in Engineering, Malta, 2001.

[4] Standing Committee on structural safety, Structural Safety 1996-99: Review and recommendations, SETO, London, United Kingdom, 1999.

[5] Nederlands Normalisatie Instituut, NEN 6700 Technische grondslagen voor bouwconstructies TGB 1990 Algemene basiseisen, Delft, The Netherlands, 2005.

[6] Nederlands Normalisatie Instituut, NEN 6702 Technische grondslagen voor bouwconstructies TGB 1990 Belastingen en vervormingen, Delft, The Netherlands, 2001.

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Figure 8

Consequence-based safety requirements for MCC 5. Because of the structural importance of MCC 5 members (key), they are required to be able to carry the ultimate limit state load for a signicant amount of time load even in case of breakage of the complete glass section.

[7] Nederlands Normalisatie Instituut, 3e Ontwerp NEN 2608-2:2004 Vlakglas voor gebouwen Deel 2: Niet-verticaal geplaatst glas Weerstand tegen windbelasting, sneeuw, eigen gewicht Eisen en bepalingsmethode, Delft, The Netherlands, 2004.

[8] Nederlands Normalisatie Instituut, NEN-EN 1990 Eurocode Grondslag van het constructief ontwerp, Delft, The Netherlands, 2002.

[9] Nederlands Normalisatie Instituut, NEN-EN 1991-1-7 Eurocode 1: Belastingen op constructies Deel 1-7: Algemene belastingen Buitengewone belastingen: stootbelastingen en ontplofngen, Delft, The Netherlands, 2006.

[10] Nederlands Normalisatie Instituut, NEN-prEN 13474-1:1999 Glass in building Design of glass panes Part 1: General basis of design, Delft, The Netherlands, 1999. Withdrawn.

[11] Schneider, J., DIN 18008 Erluterungen und Anwendung, In: Weller, B. (Ed.), Glasbau2007, Dresden, Germany, 2007.

[12] Bos, F.P., Towards a Combined Probabilistic/Consequence-based Safety Approach for Structural Glass Members, HERON, no. 2006-2, Delft, the Netherlands. Publication expected summer 2007.

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