Design for Robustness of Timber Structures

Design for Robustness of Timber Structures F+ΔF

F

F+ΔF

Editors: John Dalsgaard Sørensen, Philipp Dietsch, Poul Henning Kirkegaard and Jochen Köhler

Guideline - Design for Robustness of Timber Structures COST Action E55 “Modelling of the Performance of Timber Structures”

Editors: J.D. Sørensen, P. Dietsch, P.H. Kirkegaard and J. Köhler With contributions by: J.D. Sørensen, P. Dietsch, P.H. Kirkegaard, J. Munch-Andersen, D. Čizmar, L. Neves, J. Branco, B. Zhang, G. Fink, R. Steiger, J. Köhler, V. Rajčić, G. Turk, S. Winter

December 2010

ESF provides the COST Office through an EC contract

COST is supported by the EU RTD Framework programme

Foreword This report is a publication of the European network COST1 Action E55 “Modelling of the Performance of Timber Structures”. The COST Action E55 (website: www.cost-e55.ethz.ch) entitled “Modelling of the Performance of Timber Structures” is a research network established under the aegis of the COST domain “Forests, their Products and Services”. The main objective of COST Action E55 is to provide the basic framework and knowledge required for the efficient and sustainable use of timber as a structural and building material. The Action is structured into three working groups: a) assessment of failures and malfunctions, b) vulnerability of timber structures and c) robustness of timber structures. An important aspect for the assessment of the life cycle performance of timber structures is the interaction of structural components in structural systems. System effects in timber structures are pronounced because of multiscale spatial variability of environmental exposures and material properties. Further, the concept of robustness is an important characteristic of structural systems. Within the scope of Working Group 3, focus was on studying structural robustness of timber structures resulting in the present guideline for assessment of and design for robustness of timber structures. Robustness aspects for timber structures are presented and illustrated by examples. Further, recommendations for robustness design of timber structures are given. John Dalsgaard Sørensen, Chair, Working Group 3, COST E55 Jochen Köhler, Chair, COST E55

1

COST (European Cooperation in Science and Technology) is an intergovernmental European framework for international cooperation between nationally funded research activities. COST creates scientific networks and enables scientists to collaborate in a wide spectrum of activities in research and technology and is subdivided in several thematic domains. COST activities are administered by the COST Office (website: www.cost.esf.org).

Table of Contents 1

Introduction

7

2

Definition of robustness and related terms

8

3

Framework for structural robustness

12

4

System reliability of timber structures, ductility and redundancy

25

5

Robustness in large-span timber structures – structural aspects and lessons learned

36

6

Earthquakes and robustness

49

7

Effect of quality control

59

8

Recommendations

66

9

References

78

10 Authors

83

Annex A. Robustness requirements in codes

85

Annex B. Examples / Case studies

101

1 Introduction This guideline is prepared within the COST Action E55 “Modelling of the performance of timber structures”, WG3 “Robustness of structures”. The main objective of the Action is to provide the basic framework and knowledge required for the efficient and sustainable use of timber as a structural and building material. Focus is directed on the aspects of design, construction, assessment and maintenance of competitive and high performance timber structures. The Action mainly considers high performance structures where the load-bearing capacity is of predominant interest; for example, structures such as timber bridges, large-span halls and roofs, and also load-bearing elements of other types of timber structures. An important aspect, for the assessment of the life cycle performance of timber structures, is the interaction of structural components in structural systems. System effects in timber structures are pronounced because of multiscale spatial variability of environmental exposures and material properties. Further, the concept of robustness is an important characteristic of structural systems. In this guideline, robustness aspects for timber structures are presented and illustrated by examples. Further, recommendations for robustness design of timber structures are given. The guideline is partly based on fact sheets developed in the two COST Actions E55 “Modelling of the performance of timber structures’ and TU601 “Robustness of structures”, see (Köhler et al. 2010). In Chapter 2, a definition of robustness and related terms are presented. Chapter 3 describes a framework for risk- and reliability-based modelling of robustness. In Chapter 4, system reliability aspects are considered and illustrated for timber structures. Structural aspects for primary and secondary structures are considered in Chapter 5. In some countries, seismic design is the main design driver, and therefore robustness aspects are to some degree covered by the seismic design requirements. These aspects are considered in Chapter 6. The effect of quality control is described in Chapter 7. Finally, recommendations are summarized in Chapter 8.

2 Definition of robustness and related terms G. Fink, R. Steiger and J. Köhler Robustness is one of the fundamental terms for civil engineers. It is used frequently in the established codes and in technical literature, as a requirement for sound structural design. However, the meaning of robustness is often not clear and leaves some room for interpretation. The aim of this chapter is to establish an unambiguous definition of robustness and related terms. The importance of robustness in civil engineering is obvious. As it is e.g. written in the Swiss Standard SIA 260 Basis of Structural Design (SIA 2004), “apart from being appropriately integrated, configured and reliable, a structure should be economic, robust and durable.” The respective standard understands robustness as the “ability of a structure and its members to keep the amount of deterioration or failure within reasonable limits in relation to the cause.” However, other definitions exist and to reach a common sense a clarification is needed. As a starting point, definitions for robustness taken from several codes are given below: • ISO 22111 (ISO 2007b): Ability of a structure (or part of it) to withstand events (like fire, explosion, impact) or consequences of human errors, without being damaged to an extent disproportionate to the original cause. • Eurocode 0 (CEN 2002): The ability of a structure to withstand events like fire, explosions, impact or the consequences of human error, without being damaged to an extent disproportionate to the original cause. • SIA 260 (SIA 2004): Ability of a structure and its members to keep the amount of deterioration or failure within reasonable limits in relation to the cause. The similarity of these definitions is obvious. All of them describe robustness based on a relationship between an event and its subsequent consequences (deterioration or failure). The definitions work well if terms


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like, type of event (all or just accidental events), damage, failure, reasonable and disproportionate are used in equal sense. These and other terms are described in more detail below.

Figure 1. Illustration of robustness and related terms. Redundancy: Redundant means not or no longer needed or useful respectively, superfluous (Oxford Dictionaries 2009). Therefore, a structure can only be denoted “redundant” if one particular component failure does not have any destructive influence on the remaining structure. Progressive collapse of structures is characterized by a disproportion in size between a triggering event and the resulting collapse (Starossek 2006). According to (Ellingwood 2002) progressive collapse of a building is a catastrophic partial or total failure that follows from an initiation event that causes local damage and cannot be absorbed by the inherent continuity and ductility of the building structural system. Structural safety/integrity is the ability of a structure and its members to guarantee the overall stability as well as an adequate ultimate

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resistance (including fatigue resistance), corresponding to the assumed actions and the required reliability (SIA 2004). Hazards are any causes that may lead to unwanted events (CEN 2006) and in consequence may call into question the structural safety (SIA 2004). Accidental actions are unlikely to occur with a significant value on a given structure over a given reference period (ISO 2007a), (ISO 2007b), usually of short duration and considerable effect (SIA 2004). Damage/deterioration/defect/failure: In the cited codes, the term damage is often used but never defined. Generally, it can be described as a generic term for the “standardized” definitions as found in (SIA 2004). There, a differentiation between these three terms is made as follows: Deterioration: Possible weakening of the material substance of a structure taking place after its acceptance (take-over by owner). Defect: Missing property, which the structure should exhibit on acceptance according to contract. Failure: Exhaustion of the ultimate resistance due to instability, rupture and fatigue or time-dependent action effects. Consequence classes: In (CEN 2006) a classification of structures and elements of structures is made, whereby the criterion is the importance of the structure in terms of the consequences of its failure: I – Low: Low consequence for loss of human life, or small or moderate economic, social or environmental consequences. II – Ordinary: Medium consequence for loss human life, or considerable economic, social or environmental consequences. III – High: High consequence for loss human life, or very great economic, social or environmental consequences.


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IV – Exceptional: Circumstances where reliability must be set on a case-by-case basis. Tying/segmentation: In (CEN 2002) “tying the structural members together” is mentioned as an opportunity to avoid potential damage. In the opinion of the authors, under certain circumstances it can also be the cause for an extended damage. Monitoring: Determination and assessment of the condition with recommendations on steps to be taken (SIA 2004). Vulnerability of a system is defined as the ratio between the risks due to direct consequences and the total value of the considered asset or portfolio of assets considering all relevant exposures and a specified time frame (JCSS 2008). Human error is often used in codes and technical discussions. However, it is not defined in the below adduced codes.

3 Framework for structural robustness J.D. Sørensen This chapter is based on the fact sheet “J.D. Sørensen, E. Rizzuto and M. H. Faber: Robustness – theoretical framework”, see (Köhler et al. 2010) and (Vrouwenvelder and Sørensen 2009). Robustness of structures has been recognized as a desirable property because of several high system failures, such as the Ronan Point Building in 1968, where the consequences were deemed unacceptable relative to the initiating damage. After the collapse of the World Trade Centre, robustness has obtained a renewed interest, primarily because of the serious consequences related to failure of advanced types of structures and further, that consequences due to structural collapse may exceed the mere rebuilding costs by orders of magnitudes. Furthermore, it was confirmed that robustness is strongly related to internal structural characteristics such as redundancy, ductility and joint behaviour characteristics, but also that the consequences of structural collapse strongly depend on the specific scenario of events starting with some triggering event over a complex series of intermediate events involving more localized damages which finally led to the collapse. In this scenario, the extent to which consequences are generated depends not only on internal structural characteristics but may even more pronounced depend on passive and active measures for damage reduction as well as possible non-conformities with design assumptions due to the quality of execution and or maintenance. In order to minimize the likelihood of failures, as those mentioned above, many modern building codes consider the need for robustness in structures and provide strategies and methods to obtain robustness. In fact, in all modern building codes, one can find a statement (in this or a slightly different form): “total damage resulting from an action should not be disproportional to the initial damage caused by this action.” During the last decades, there have been significant efforts to quantify aspects of robustness. When modelling robustness, system effects are very important. However, the primary criteria in building codes are


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related to design and verification of sufficient reliability of components. It should also be noted that redundancy in systems is closely related to robustness. In principle, redundant system are believed to be more robust than non-redundant systems – but this is not always the case as illustrated by the failures of the Siemens Arena and the Bad Reichenhall Ice Arena, see (Frühwald, Serrano et al. 2007), (Hansson and Larsen 2005) and (Winter and Kreuzinger 2008), see Annex B1. Robustness is related to scenarios where exposures, including unintentional and unforeseen loads and defects, result in local damage to the structural system, and where this damage may lead to further collapse of the structure. In Eurocode EN 1990:2002 (CEN 2002), the basic requirement to robustness is given in clause 2.1 4(P): “A structure should be designed and executed in such a way that it will not be damaged by events such as: • explosion, • impact, and • the consequences of human errors, to an extent disproportionate to the original cause.”

Figure 2. Illustration of the basic concepts in robustness (CEN 2006). An illustration is presented in Figure 2 (CEN 2006). Due to an exposure (a) of any kind, local damage (b) may occur. This local damage is defined

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as the direct consequence of the exposure. Given this local damage, the structure may survive or (a substantial part) may collapse due to: a)

Exposures which could be unforeseen, unintended effects and defects (incl. design errors, execution errors and unforeseen degradation) such as: • unforeseen action effects, incl. unexpected accidental actions • unintended discrepancies between the structure's actual behaviour and the design models used • unintended discrepancies between the implemented project and the project material • unforeseen geometrical imperfections • unforeseen degeneration. b) Local damage due to exposure (direct consequence of exposure). c) Total (or extensive) collapse of the structure following the local damage (indirect consequence of exposure). Robustness is especially related to precautions to prevent/reduce the indirect consequences in step c) in case of a local damage in step b). Robustness rules can also be seen as additional rules/requirements to the basic code-specific checking of individual components/failure modes in order to secure that the structure considered as a system has a satisfactory reliability. The system consists of the structure and the environment where it is situated. Important aspects related to robustness, which will be described in the following, are: • Key elements • Progressive collapse • Redundancy • Ductility

3.1

Risk analysis

During the last decades, there has been a significant effort to develop methods to assess robustness and to quantify aspects of robustness. The basic and most general approach is to use a risk analysis where both


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probabilities and consequences are taken into account. Approaches to define a robustness index can be divided into the following levels with decreasing complexity: • A risk-based robustness index based on a complete risk analysis where the consequences are divided in direct and indirect risks. • A probabilistic robustness index based on probabilities of failure of the structural system for an undamaged structure and a damaged structure. • A deterministic robustness index based on structural measures, e.g. pushover load bearing capacity of an undamaged structure and a damaged structure.

Figure 3. An event tree for robustness quantification (Baker, Schubert et al. 2007). Figure 3 presents the same idea as in Figure 1, however, in a more general way in the form of an event tree, see (Baker, Schubert et al. 2007). The assessment starts with the consideration and modelling of exposures (EX) that can cause damage to the components of the structural system. The term “exposures” refers to extreme values of design loads, accidental loads and deterioration processes but also includes human errors in the design, execution and use of the structure. The term “damage” refers to reduced performance or failure of individual components of the structural system. After the exposure event occurs, the components of the structural system either remain in an undamaged state ( D ) as before or change to a damage state (D). Each damage state can then either lead to the failure of the structure (F) or no failure ( F ). Consequences are associated with each of the possible damage and failure scenarios, and are classified as either direct (Cdir) or indirect (Cind). Direct consequences are considered to result from damage states of individual

16


component(s). Indirect consequences are incurred due to loss of system functionality or failure and can be attributed to lack of robustness (Baker, Schubert et al. 2007) and (JCSS 2008). The basic framework for risk analysis is based on the following equation in which risk contributions from local damages (direct consequences) and comprehensive damages (follow-up/indirect consequences), are added, see (Baker, Schubert et al. 2007) and (JCSS 2008):

R = ∑∑ Cdir,ij P ( D j Ei ) P ( EX i ) + i

j

∑∑∑ C

ind,ijk

k

i

j

(

)

P Sk D j ∩ EX i P ( D j EX i ) P ( EX i )

(1)

where Cdir,ij

consequence (cost) of damage (local failure) Dj due to exposure EXi

Cind,ij

consequence (cost) of comprehensive damages (followup/indirect) Sk given local damage Dj due to exposure EXi

P(EXi) P(Dj|EXi) P(Sk|...)

probability of exposure EXi probability of damage Dj given exposure EXi probability of comprehensive damages Sk given local damage Dj due to exposure EXi

The optimal design (decision) is the one minimizing the sum of costs of mitigating measures and the total risk R. A detailed description of the theoretical basis for risk analysis can be found in (JCSS 2008). It is noted that an important step in the risk analysis is to define the system and the system boundaries. For timber structures, this includes the definition/modelling of the timber structure itself, but also the effect of a possible collapse of the timber structure on the environment/surrounding society. It is noted that in some cases the failure of a (timber) structure can cause extensive indirect consequences for the society. These are important to include when defining the system to be considered in the risk analysis.


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The total probability of comprehensive damages/collapse associated to (1) is:

(

)

P ( collapse ) = ∑∑ P collapse D j ∩ EX i P ( D j EX i ) P ( EX i ) i

(

j

(2)

)

where P collapse D j ∩ EX i is the probability of collapse (comprehensive damage) given local damage D j due to exposure EX i . Note that compared to (1) only one comprehensive damage (collapse) is included in (2). The terms P ( collapse D ) and P ( D EX ) are related to the concepts damage tolerance and vulnerability, respectively. The product P ( collapse D ) P ( D EX ) can be considered as structure dependent measure of the robustness. For damages related to key elements, the probability of collapse is P(collapse D j ∩ EX i ) ≈ 1 . From equation (2), it is obvious that the probability of collapse can be reduced by: • • •

Reducing one or more of the probabilities of exposures P(EXi) – i.e. prevention of exposure or event control. Reducing one or more of the probabilities of damages P(Dj|EXi) – i.e. related to element/component behaviour. Reducing one or more of the probabilities P(collapse D j ∩ EX i ) .

If the consequences are included in a risk analysis, then reduction of direct (local) consequences, Cdir,ij and comprehensive (indirect) consequences, Cind,ij are also important. According to the description above and the robustness definition in (CEN 2002), robustness is mainly related to the reduction of the probabilities P(Dj|EXi) and P(collapse|Dj∩EXj). Increasing the robustness at the design stage will in many cases only increase the cost of the structural system marginally – the key point is often to use a reasonable combination of a suitable structural system and materials with a ductile behaviour. In other cases, increased robustness will influence the cost of the structural system.

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In the next sections, robustness measures are described.

3.2

Robustness measures

3.2.1 Risk-based robustness index (Baker, Schubert et al. 2007) proposed a definition of a robustness index based on risk measures. The approach divides consequences into direct consequences associated with local component damage (that might be considered proportional to the initiating damage) and indirect consequences associated with subsequent system failure (that might be considered disproportional to the initiating damage). An index is formulated by comparing the risk associated with direct and indirect consequences. The index of robustness ( I rob ) is defined as:

I rob =

RDir RDir + RInd

(3)

where RDir and RInd are the direct and indirect risks associated with the first and the second term in equation (1). The index takes values between zero and one, with larger values indicating larger robustness. As mentioned above, the optimal decision is the one which minimizes the total risk obtained by equation (1). This could equally well be by reducing the first or the second term in equation (1). This implies that the definition of a robustness index by equation (3) is not always fully consistent with a full risk analysis, but can be considered as a helpful indicator based on risk analysis principles. It is noted that since the direct risks typically are related to code based limit states, they can generally be estimated with higher accuracy than the indirect risks. A difficult step in the the risk assessment is to model and quantify the probability of the exposures. Therefore, it can be very convenient and helpful to use a conditional index of robustness obtained using risks RDir exposure and RInd exposure conditioned of a given exposure:

I rob exposure =

RDir exposure RDir exposure + RInd exposure

(4)


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3.2.2 Reliability-based robustness index (Frangopol and Curley 1987) and (Fu and Frangopol 1990) proposed some probabilistic measures related to structural redundancy – which also indicates the level of robustness. A redundancy index (RI) is defined by:

RI =

Pf (damaged) − Pf (intact ) Pf (intact)

(5)

where Pf (damaged) is the probability of failure for a damaged structural system and Pf (intact ) is the probability of failure of an intact structural system. The redundancy index provides a measure on the robustness/ redundancy of the structural system. The index takes values between zero and infinity, with smaller values indicating larger robustness. They also considered the following related redundancy factor:

βR =

βintact βintact − β damaged

(6)

where βintact is the reliability index of the intact structural system and

β damaged is the reliability index of the damaged structural system. The index takes values between zero and infinity, with larger values indicating larger robustness. 3.2.3 Deterministic robustness index A simple and practical measure of structural redundancy (and robustness) used in the offshore industry is based on the so-called RIF-value (Residual Influence Factor), (ISO 2007a).

A Reserve Strength Ratio (RSR) is defined as:

RSR =

Rc Sc

(7)

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where Rc denotes characteristic values of the base shear capacity of an offshore platform (typically a steel jacket) and Sc is the design load corresponding to ultimate collapse. In order to measure the effect of full damage (or loss of functionality) of structural member no i on the structural capacity the so-called RIF-value (sometimes referred to as the Damaged Strength Ratio) is defined by:

RIFi =

RSRfail,i RSRintact

(8)

where RSRintact is the RIF-value of the intact structure and RSRfail,i is the

RIF-value of the structure where member no i is failed/removed. The RIF takes values between zero and one, with larger values indicating larger robustness. Other simple measures of robustness have been proposed based on e.g. the determinant of the stiffness matrix of structure with and without removal of elements.

3.3

Robustness in codes

In many codes of practice as e.g. the Eurocodes, the primary design requirements are related to checking that each component/ element/connection has sufficient reliability. A sufficient reliability level is secured by using characteristic values and partial safety factors calibrated to a reliability level which typically correspond to an annual probability of failure of the order 10-6. However, additional requirements/measures are needed to secure that the structure also as a system has sufficient reliability. Further, provisions are needed to reduce/eliminate the effect of design errors, execution errors, unexpected deterioration of components, etc. Robustness requirements in codes of practice should cover these aspects together with quality control systems and application of best practices in design, execution and operation & maintenance as illustrated in Figure 4.


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Figure 4. Code based design.

It is noted that many codes of practice contain some robustness rules, e.g. requirements to tie together concrete elements, but the rules/provisions are not formulated in a consistent way on a rational basis. In countries where structures are designed for seismic loads, the requirements to obtain earthquake resistant structures include many of the same aspects as those considered good for robustness, e.g. redundancy and ductility.

3.4

Structural and reliability models for robustness analysis of timber structures

For the assessment of robustness, the structural behaviour models of timber structures need to be considered with emphasis on modelling of damage scenarios resulting from various foreseen or unforeseen exposures. The risk and reliability based robustness measures require estimation of the probability of total collapse, given some exposure event like a human error in design or execution or an accidental as fire or explosion has occurred. Typical for this type of analysis is that local damage is not considered as the ultimate failure, like in standard design

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for permanent and variable actions. The focus is on the consequences for the structural system after occurrence of a local damage. Therefore, models to be considered are: partly damaged structures; large cracks and/or plastic deformations; large deflections and membrane actions; high temperatures in case of fire; dynamic effects on various scales. Because of several potential means by which a local collapse in a specific structure may propagate from its initial extent to its final state, there is no universal approach for evaluating the potential for progressive collapse (Ellingwood et al. 2007). For reduction of the risk of progressive collapse in the event of loss of structural element(s), the following general structural traits should be incorporated in the design, according to (Ellingwood et al. 2007):

Redundancy: Incorporation of redundant load paths in the vertical load carrying system. Ties: Using an integrated system of ties in three directions along the principal lines of structural framing. Ductility: Structural members and member connections have to maintain their strength through large deformations (deflections and rotations) so the load redistribution(s) may take place. Adequate shear strength: As shear is considered a brittle failure, structural elements in vulnerable locations should be designed to withstand shear load in excess of that associated with the ultimate bending moment in the event of loss of an element. Capacity for resisting load reversals: the primary structural elements (columns, girders, roof beams, and lateral load resisting system) and secondary structural elements (floor beams and slabs) should be designed to resist reversals in load direction at vulnerable locations. Connections (connection strength): connections should be designed in such a way that it will allow uniform and smooth load redistribution during local collapse. Key elements: exterior columns and walls should be capable of spanning two or more stories without bucking, columns should be designed to withstand blast pressure etc. Alternate load path(s): after the basic design of a structure is done, a review of the strength and ductility of key structural elements is


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required to determine whether the structure is able to “bridge” over the initial damage (Ellingwood et al. 2007). In Eurocode 0 (CEN 2002), the following measures to increase structural robustness are mentioned: “Potential damage should be avoided or limited by appropriate choice of one or more of the following: • avoiding, eliminating or reducing the hazards to which the structure can be subjected. • selecting a structural form which has low sensitivity to the hazards considered. • selecting a structural form and design that can survive adequately the accidental removal of an individual member or a limited part of the structure, or the occurrence of acceptable localised damage. • avoiding as far as possible structural systems that can collapse without warning. • tying the structural members together. The basic requirements should be met: • by the choice of suitable materials. • by appropriate design and detailing. • by specifying control procedures for design, production, execution, and use relevant to the particular project.” Next, probabilistic models are needed for modelling and estimation of the risks and probabilities in the risk and reliability based robustness measures. The probabilistic modelling can be based on available information, e.g. in the JCSS Probabilistic Model Code for actions and materials, especially timber, see (JCSS 2002). The JCSS PMC mainly deals with the models for normal design situations and it is noted that for model uncertainties in extreme situations, no data is presently available. Therefore, subjective assessment of the uncertainties is needed. Further, probabilistic models for human errors are difficult to formulate and are under consideration in e.g. the COST Action TU 601, see (Köhler et al. 2010). Estimation of the probabilities themselves requires system models of the failure modes. This aspect is considered in more detail in the next chapter. It requires a system model of the collapse events using series and parallel systems, and careful modelling of the correlation/dependency between the

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stochastic variables and the exposure events. Design and execution errors and unforeseen degradation could in many cases be expected to be present in all similar connections/elements, especially for a new and unconventional structural system, see examples in annex B.1. If an accidental action is the main exposure then this action typically results in an extreme load on one or a few structural elements and then (local) failure of this element. In general, the reliability of a series system is increased if the correlation between the elements in the system is increased, whereas the reliability of a parallel system is increased if the correlation between the elements in the system is decreased. Therefore, if exposures on different structural elements can be considered statistically independent then a parallel system model should be preferred from a reliability point of view. This can be obtained by increasing the redundancy of the structural system. On the other hand, if the exposures on different structural elements can be considered statistically dependent then a parallel system model should be avoided from a reliability point of view. This can e.g. be obtained by using compartmenzation of structural systems. This recommendation deviates from the general recommendations in e.g. Eurocode 0, see above and is further discussed in Chapter 5. Ductility of structural elements increases the reliability of parallel systems and is therefore always an important “tool” to increase the system reliability and the robustness, see Chapter 4.

4 System reliability of timber structures, ductility and redundancy P.H. Kirkegaard, J.D. Sørensen and D. Čizmar

For reduction of the risk of collapse in the event of loss of structural element(s), a structural engineer may take necessary steps to design a collapse-resistant structure that is insensitive to accidental circumstances e.g. by incorporating characteristics like redundancy, ties, ductility, key elements, alternate load path(s), etc., in the structural design. In general, these characteristics can have a positive influence on system reliability of a structure. However, in Eurocodes, ductility is only awarded for concrete and steel structures but not for timber structures. It is well-known that structural systems can redistribute internal forces due to ductility of a connection, i.e. some additional loads can be carried by the structure. The same effect is also possible for reinforced concrete structures and structures of steel. However, for timber structures, codes do not award that ductility, which will result in a semi-rigid behaviour plus higher level of safety due to a lower probability that premature brittle failures occurs and possible redistribution of forces for statically indeterminate structures either internally in the joint or to other structural elements. A redistribution of forces, a so-called statical system effect, will usually increase the reliability of the whole structural system and give an extra safety margin compared to the deterministic code results. In general when a structural system collapses, one or more structural elements have failed. Such a failure mode can, for any mechanical system, be assigned to one of the following three categories: series systems, parallel systems or combination of series and parallel system (also referred as hybrid systems). In series systems, failure of any element leads to the failure of the system. Parallel systems are those systems in which the combined failure of each and every element of the system results in the failure of the system (Madsen, Krenk et al. 1986). Since a redistribution of the load effects takes place in a redundant structural system, after failure of one or more of the structural elements, it becomes very important in parallel systems to describe the behaviour of the failed structural elements after failure has taken place. If the structural element

26


has no strength after failure, the element is said to be perfectly brittle. If the element after failure has a load-bearing capacity equal to the load at failure, the element is said to be perfectly ductile, see Figure 5. Clearly not all kinds of structural elements and material behaviours can be described as perfectly brittle or perfectly ductile. All kinds of combinations in between exist, i.e. some, but not all, of the failure strength capacity is retained.

Figure 5. Perfect brittle and prefect ductile failure mode behaviour.

In the present COST E55 project “Modelling of the Performance of Timber Structures”, existing numerical methods used to assess the reliability of timber structures are evaluated for their possible application to timber systems. Especially consensus on the general characteristics of timber systems regarding redundancy and robustness are established. To reach a better understanding of these aspects, the following activities are considered within WG3:

• • • •

Characterisation of multi-scale variability in timber structures. Analysis of system effects for several types of timber structures. Qualification of robustness as a characteristic of timber structures. Establishing a framework for reliability based design and assessment of timber structural systems based on these considerations.


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Related to these issues, the relationship between robustness, system reliability and the characteristics ductility and redundancy are of great interest.

4.1

System reliability of timber structures – ductility and redundancy

For a structural system, where the system reliability model is a series system of m failure elements, a safety margin as a function of the basic variables X can be written:

M i = gi ( X) , 1, 2,K , m

(9)

where gi is a limit state function. Then the probability failure of the system is given by:

⎛m ⎞ ⎛m ⎞ PfS = P ⎜ U {M i ≤ 0} ⎟ = P ⎜ U{ gi ( X) ≤ 0} ⎟ ≈ Φ (− β S ) ⎝ i =1 ⎠ ⎝ i =1 ⎠

(10)

where Φ is the standard Normal distribution function and β s is the system reliability index for a series system. If a parallel system of m failure elements in one failure mode is considered, then the probability of failure of the parallel system is defined as the intersection of the individual failure events:

⎛ m ⎞ ⎛m ⎞ PfP = P ⎜ I {M i ≤ 0} ⎟ = P ⎜ I { gi ( X) ≤ 0} ⎟ ≈ Φ (− β S ) ⎝ i =1 ⎠ ⎝ i =1 ⎠

(11)

As stated before, it is very important for the calculation of a parallel system reliability to describe the behaviour of the failed element, after the failure has taken place. For the series system, this is not very significant because when one element fails, the failure of the system is inevitable, i.e. a non-redundant system. However, before the reliability modelling in a parallel system of failure elements can be performed, the structural behaviour of the considered failure mode must be clarified. More specifically, the failure of the structural elements and consequences with determination of residual load-carrying capacity and load redistribution in each step in the structural element failure sequence must be described.

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Then the failure functions of the failure elements in the parallel system can be formulated. Failure function no. 1 models failure in parallel system element no. 1 without failure in any other elements. Failure function no. 2 models failure in parallel system element no. 2 with failure in the structural element corresponding to failure element no. 1 (i.e. after redistribution of loads). Failure function no. 3 then models failure of parallel system element no. 3 with failure in the structural elements corresponding to failure element nos. 2 and 1, etc. etc. If a stochastic load S is assumed, and a parallel system consisting of m independently distributed element stochastic strengths Ri, see Figure 6, and a constant modulus of elasticity and perfect equal load sharing among the ideally brittle elements, the system strength R can be calculated as: m

R = max {(m − i + 1) ⋅ Ri } i =1

(12)

where the element strengths Ri are set in a decreasing order, R1 < R2 1.0. In the case of failure due to local damage, such utilization factors will most probably not become critical. But in the case of a higher correlation of damages (all members suffering from the same damage due to global effects), it becomes evident that a structure containing systematic mistakes will not be able to withstand a large load increase due to load distribution from one failing member, meaning it is more fragile to collapse progressively, see (Dietsch and Munch-Andersen 2009). This is further demonstrated in the following sections.

Robustness in large span timber structures – Structural aspects

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5.2.3 Local / global effects in timber structures Failures in structures can range from local failures of structural elements to total (global) collapse. The extent of failure also depends on the type of damaging effects which can be of local nature (e.g. local deterioration from local water ingress) or global nature (e.g. global weakening of elements due to systematic mistakes). Table 1 gives examples for both types of effects which are common in timber structures.

Most robustness strategies given in codes and literature are based on the prevention of a localized effect of short duration (e.g. explosion or impact) leading to a disproportionate collapse of the structure. The given strategies (e.g. load-distribution) will also be beneficial for other types of local effects, as given in Table 1. Table 1. Examples for types of damaging effects and their extent.

Local effects - local failures, e.g. • Local deterioration of element from e.g. local water ingress • Local weakening of element from e.g. holes • Local overloading from e.g. local snow accumulation

Global effects, e.g. • Global weakening of structural elements due to systematic mistakes • Global deterioration of elements from e.g. wrong assumption of ambient climate • Global overloading from e.g. addition of green roof without structural verification

On the other hand have numerous studies on failures in timber structures e.g. (Blaß and Frese 2007; Frühwald, Serrano et al. 2007 and Dietsch and Winter 2009) shown, that global damage from systematic (repetitive) mistakes is much more common than local damage (e.g. local overloading from local snow accumulation) or statistically random occurrences (e.g. low material strength). The reason is that timber structures (primary and secondary structures) are usually composed of repetitive elements which are connected by analogical construction principles. This systematic implies that a mistake, made during the planning or construction phase, will most likely repeat itself in all identical elements. Figure 13 illustrates this statement.

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Robustness in large span timber structures – structural aspects

Failures in Timber Structures - Accountability for Failure n=14; 5% n=30; 11% n=17; 6%

n=84; 31%

n=40; 14% n=14; 5%

Structural Design Construction Planning (environmental cond.) Material (e.g. Production) Execution Changes on-site Maintenance Snow Load (possibly) above Design Load

n=79; 28%

Figure 13. Accountabilities for failures from an evaluation of 214 cases of failed timber structures (Dietsch and Winter 2009).

A project carried out at the Chair for Timber Structures and Building Construction (Dietsch and Winter 2009), evaluating 214 cases of failed timber structures, depicts the accountabilities for evaluated failures as shown in Figure 13. It can be concluded that 70% of the errors (design, planning and maintenance) will, with an utmost probability, have a global effect, while the remaining 30% of failures can either result in global or local damages. These numbers are comparable with the data given in (Ellingwood 1987), comparing multiple studies on failures in structures of all building materials. The mentioned study by Ellingwood reveals an average of 45% failures due to errors in design and planning, 38% due to construction errors and 17% due to errors in the utilization phase (maintenance). 5.2.4 Discussion of robustness strategies Evaluating purlin systems from a structural perspective will highlight continuous systems due to their lowered maximum bending moments, enabling the realisation of larger spacings e at given span and crosssection. Due to this and due to the acceleration of the construction process, purlin systems today are often realized by continuous systems like lap-jointed beams.


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The evaluation from a robustness perspective reveals more debatable results. Continuous systems (due to their redundancy and higher stiffness) will result in an increased load transfer in the case of failure of one structural member. Many publications on robustness mention the redistribution of loads as preferable, which is true in the case of local effects, e.g. local deterioration of element from local water ingress. Nevertheless, as recent studies have revealed, most failures of timber structures are not caused by local defects but by global defects from systematic mistakes such as global weakening of structural elements due to systematic (repetitive) mistakes. Structures suffering from global damaging effects are not able to withstand a large load transfer from neighbour members and will therefore be more prone to progressive collapse. This idea is supported in (Starossek 2006) stating that the “alternate load path” approach (realized by e.g. parallel systems) may “in certain circumstances not prevent but rather promote collapse progression”. Hence, the idea of compartmentalization is introduced which is realized by a deliberate reduction of continuity at chosen compartment borders. For the systems discussed, this approach might be preferable, if the strength and/or stiffness required for the formation of an alternate load path cannot be guaranteed in case of failure of one element. In summary, it can be stated that there is no strategy for the structural designer, which ensures robustness in all cases. When deciding on a robustness strategy, one has to consider different scenarios. The major difference is whether the cause of failure is likely to be a systematic (mostly human) error or an unforeseeable (mostly local) incident. This is subsumed in Table 2 which lists types of damaging effects and possible robustness approaches. Table 2. Preferable robustness approach depending on the type of damaging effect.

Local effects - local failures, e.g. • Local deterioration of element from e.g. local water ingress

Global effects, e.g. • Global weakening of structural elements due to systematic mistakes • Global deterioration of elements from e.g. wrong assumption of

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• Local weakening of element from e.g. holes • Local overloading from e.g. local snow accumulation Robustness approach: • Redistribution of loads to adjacent (undamaged) elements by e.g. redundant secondary system

ambient climate • Global overloading from e.g. addition of green roof without structural verification Robustness approach: • Limiting failure to local level by e.g. determinate secondary systems with “weak/flexible” connections • Compartmentalization/Segmentation

Experience tells that human errors are by far the most common cause. In order to reduce the risk of collapse, and in particular progressive collapse, it is crucial to reduce the number of human errors by e.g. enhanced quality control (see Chapter 7). Against this background, it should be discussed if and how the intensity of quality control should be made dependent upon the number of identical elements used in a structure (Vogel T., pers. comm.).

5.3

Examples

In this chapter, two examples of failed structures are evaluated, both featuring systematic errors in design and construction. The two cases described serve as examples of different design strategies for large-span timber structures and their consequence for robustness. It is demonstrated that robustness is not a straight forward concept because the best strategy depends on the cause of the failure, which is obviously not known during planning and design. Both structures and the effects leading to their failure are described in detail in Annex B1. 5.3.1 Siemens Arena The Siemens Arena, described in detail in (Dietsch and Munch-Andersen 2009) and (Hansson and Larsen 2005) suffered from gross errors in the structural design, reducing the load-carrying capacity of the heel joint of the fish-shaped truss to 25%-30% of its required strength. Due to this, two of the 72 m long trusses collapsed without warning and under very low variable loads, shortly after the opening of the arena (see Figure 14). During design it was decided “that the 12 m long purlins between the trusses should only be moderately fastened to the trusses, so that a failure


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of one truss should not initiate progressive collapse. This strategy proved to work fairly well as “only” two of the 12 trusses collapsed. Considering that all trusses had a much lower strength than required it might be fair to conclude that the extent of the collapse was “not disproportionate to the cause.” (Dietsch and Munch-Andersen 2009). In this case, each truss is a key element. Another - and perhaps more expensive - strategy against progressive collapse could have been to design the trusses, the purlins and their connections so that a failed truss and the roof could hang in the purlins and transfer the load to the neighbouring trusses. Had this strategy against progressive collapse been chosen it is most likely that the progressive collapse would have occurred because the neighbour trusses could not have withstood the extra load from the truss failing first. In this case, the trusses would not have been key elements. But had the cause of the failure been a huge load on one truss or a lone standing mistake in one truss, the second strategy would have been preferable because it significantly reduces the risk of injuries. That strategy might also have worked if e.g. a leaking roof had degraded one truss because it is likely that the other trusses remain unharmed. In that case, large deformations would occur, giving a warning of possible failure.

Figure 14. Top view on Siemens Arena Ballerup, Denmark, collapse of 2 out of 12 main trusses (Photo: Peter M. Thorup).

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5.3.2 Bad Reichenhall Ice Arena The Bad Reichenhall Ice-Arena, further described in (Winter and Kreuzinger 2008), featuring timber box-girders with lateral web boards made from so-called “Kämpf web boards”, suffered from multiple errors and defects, including cumulative degradation processes in the glue-lines and finger joints due to the humidity exposure over the years. This eventually triggered a progressive collapse of the whole roof structure after approximately 34 years of use (see Figure 15) under a large but not exceptional snow load.

The investigation concluded that the failure most probably initiated in one of the three main girders on the east side. Due to the fact that the secondary system, which was realized as a K-bracing to also function against lateral-torsional buckling, was not only strong but also very stiff, the loads were shifted from the girder that failed first to the neighbouring girders. Since these girders suffered from the same errors and degradation processes as the girder failing first, they could not sustain the additional load. Consequently, this developed into a progressive collapse which realized within seconds. The very stiff secondary system also resulted in the fact that a weak girder (containing e.g. general finger joints having lost their adhesion) could transfer its loads to the adjacent girders without large deformations, meaning that this form of advance warning of failure was impeded.


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Figure 15. Top view on Bad Reichenhall Ice Arena after progressive collapse of all main girders (Winter and Kreuzinger 2008). 5.3.3 Conclusions The Siemens Arena was a statically determinate structure, whereas the Bad Reichenhall Ice Arena was a highly statically undeterminate structure, with a very stiff secondary system.

In the Siemens Arena, the weakness was present from the beginning and quite similar in all trusses. The collapse might have been initialized just by the strength reduction over time. The chosen robustness strategy with weak purlins limited the collapse. The design error was so large that it is unlikely that any robustness strategy would have been able to prevent such a collapse, other strategies might even have caused a total collapse. Had it been a local incident which had caused a failure, the collapse might have been restricted to one truss. But nearly 2000 m2 of the roof falling down might in that case have been considered as disproportional to the cause.

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In the Bad Reichenhall Ice Arena, the weakness was initially much smaller but developed over time, and presumably at different rate in different areas of the roof. The collapse was eventually initialized by a severe but nowhere exceptional snow load. Local damages have most likely been present for a long time, but the stiff structure was able to transfer the load to other parts, without significant deformations. A local incident causing a local failure might therefore never have been revealed. A strategy with a less stiff secondary system would presumably have issued a warning both about the general degradation of the strength as well as damage on a local level. These two cases demonstrate that redundancy on its own is not suitable for limiting the consequence of failures due to systematic errors. Compartmentalization/segmentation, ensuring that a collapse does not become progressive appears to be necessary. On the other hand, redundancy on a more local scale would be desirable because it can minimize the consequence of random errors. Such redundant systems must be designed in a way that it becomes evident if redistribution of loads has taken place, e.g. by visible deformations.

6 Earthquakes and robustness J. Branco and L. Neves

Some of the properties sought in seismic design of buildings are also considered fundamental to guarantee robustness of structures. Moreover, some key concepts are common to both seismic and robustness design. In fact, both analyses consider events with a very small probability of occurrence, and consequently, a significant level of damage is admissible. As very rare events, in both cases, the actions are extremely hard to quantify. The acceptance of limited damage requires a system based analysis of structures, rather than an element by element methodology, as employed for other load cases. As for robustness analysis in seismic design, the main objective is to guarantee that the structure survives an earthquake, without extensive damage. In the case of seismic design, this is achieved by guaranteeing the dissipation of energy through plastic hinges distributed in the structure. For this to be possible, some key properties must be assured, in particular ductility and redundancy. The same properties are fundamental in robustness design, as a structure can only sustain significant damage if capable of distributing stresses to parts of the structure unaffected by the triggering event.

6.1

Earthquake design

In order to obtain structures resistant to earthquakes, the following aspects must be considered: structural simplicity; uniformity, symmetry and redundancy; bi-directional resistance and stiffness; torsional resistance and stiffness; diaphragmatic behaviour at the storey level; and, adequate foundations. A clear and direct path for the transmission of the seismic forces is available in simple structures while uniformity allows the inertial forces created in the distributed masses of the building to be transmitted via short and direct paths. Redundancy allows a more favorable redistribution of action effects and widespread energy dissipation across the entire structure. A basic goal of a seismic design is the establishment of

50


diaphragmatic action of the horizontal load bearing systems and the connection (anchorage of the diaphragms) to the vertical load bearing components (walls or frames) in order to transfer the seismic forces to the most rigid ones and tie the whole building. The choice of the methods of analysis depends on the structure and the objective of the analysis: linear static analysis (termed the “lateral force” method of analysis in EN 1998-1 (CEN 2004b); modal response spectrum analysis (also termed in practice “linear dynamic); non-linear static analysis (commonly known as “pushover” analysis); and, non-linear dynamic analysis (time-history or response-history analysis). Most earthquake design codes provide an acceleration response spectrum curve that specifies the design acceleration (which means the horizontal load) based on the natural period of the structure. The basic principle of EN 1998-1 (CEN 2004b) is that when the structure presents a ductile behaviour, the design acceleration and the horizontal force imposed to the building is reduced by division by the so called behaviour factor q. The behaviour factor q is an approximation of the ratio of the internal forces that the structure would experience if its response was completely elastic, to those that may be considered in the design to ensure a satisfactory response of the structure. The behaviour factor is affected by several parameters such as ductility, overstrength and redundancy reduction factors.

6.2

Timber structures under seismic loads

Satisfactory performance of timber buildings, in general, can be partially attributed to the material characteristics of wood itself, and to the lightness and high redundancy of most wood-based structural systems. The lateral redundancy plays an important role in seismic performance of timber structures. A redundant design will almost certainly offer more parallel load paths that can transmit the applied lateral loading on the building down to the foundation. The detailing of connections is very important because the more integrated and interconnected the structure is, the more load distribution possibilities there are. The building’s structural integrity is only as good as the weakest link in the load transmission path, and as a consequence, good performance expectations are contingent on appropriate design, quality workmanship and proper maintenance.


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For timber structures, EN 1998-1 (CEN 2004b) presents upper limit values of the behaviour factor depending on the ductility class, on the structural type (essentially reflecting the greater or lesser redundancy of the structure as a whole) and on the nature of the structural connections (essentially reflecting its ductility and energy dissipation capacity). Semirigid and rigid connections are normally associated with the distinction between dissipative and low-dissipative structures, respectively. EN 1998-1 (CEN 2004b) proposes a classification of timber structures in Ductility Class Medium (DCM) and Ductility Class High (DCH) for dissipative structures and Ductility Class Low (DCL) in the case of nondissipative structures. Besides the general upper limit of q = 1.5 for DCL accounting for overstrength, for DCM and DCH the values indicated for q in Table 8.1 of EN 1998-1 (CEN 2004b) are reproduced in Table 3 with a different arrangement that highlights the influence of the various parameters on the ductility of timber structures (namely the superior behavior of correctly designed and executed nailed connections). Table 3. Maximum values of the behavior factor q for timber structures of DCM and DCH.

Structural type

DCM

DCH

Wall panels with glued diaphragms connected with nails and bolts

Glued panels q = 2.0

Wall panels with nailed diaphragms connected with nails and bolts

-

Trusses

Doweled and bolted joints q = 2.0

Nailed panels q = 3.0 Nailed panels q = 5.0 Nailed joints q = 3.0 -

Mixed structures with timber framing and non-load-bearing infills Hyperstatic portal frame with doweled and bolted joints NOTE: μ is the static ductility ratio.

q = 2.0 μ≥4 q = 2.5

μ≥6 q = 4.0

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6.3


Seismic design and robustness

To analyze the influence of seismic design in the robustness of structures, it is fundamental to define the main strategies to improve robustness. In general, robustness can be improved by reducing the probability of damage, reducing the probability of failure if damage occurs, or by reducing the cost of failure. In the first case, it is paramount to define alternative load paths and to guarantee that: (i) enough resistance exists in these paths to prevent failure; (ii) enough ductility exists to guarantee these paths can be mobilized. If the improvement in robustness is to be achieved through reduction in cost associated with partial failures, then compartmentalization is crucial. In this case, load paths must be cut, in order to limit the extent of failure. The philosophy of designing to limit the spread of damage, rather than to prevent damage entirely, is different from the traditional approach to designing to withstand dead, live, snow, and wind loads, but is similar to the philosophy adopted in modern earthquake-resistant design (FEMA 2002). The guiding principles for a good conceptual design for earthquake resistant buildings have a significant influence on the robustness of structures. In fact, structural simplicity, uniformity, symmetry and redundancy are fundamental in the existence of alternate load paths, a key concept in robustness design. Above all, the seismic design leads to an improvement in ductility and redundancy, as well as ensuring the interconnection of the structure. As a consequence, if a structure is designed according to existing seismic codes, a significant improvement to its resistance in the event of damage might be achieved. On the other hand, the increased redundancy and removal of weak links between elements and parts of the structure will allow damage to propagate through the structure, leading to higher costs in the event of failure. In the particular case of timber structures, seismic design requires a much closer attention to detailing of connections. This can, indirectly, provide enhanced robustness since a significant number of observed failures are associated with errors in connections between elements.


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Lastly, the consideration of earthquakes in some regions has led to significant evolution of engineering practice, leading to significant differences in common practice between countries where earthquakes are likely to occur, if only over long time periods, and those where they are not considered in design. Some of these practices can have a large effect on the robustness of structures, in particular, timber structures. A clear example of this is the use of strong column – weak beam concept in designing buildings, common for seismic resistance. In seismic areas, columns are usually continuous elements, and beams are connected to column at each span. This situation guarantees that key elements, as the columns, are capable of sustaining additional loads, and failure will occur in the beams. This will limit progressive collapse to a single floor and to a bay. If, on the other hand, strong beams or continuous beam are used, failure will progress from bay to bay, increasing the affected area and, consequently, failure costs.

a. Weak beams

b. Strong beams

Figure 16. Strong column – weak beam concept.

6.4

Eurocode 8 and robustness prescriptive rules

At present, few existing codes present significant prescriptive rules to improve robustness of structures. However, there are some general rules

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identified to have a positive influence on the robustness, namely: (i) selective “overstrength” (strong column / weak beam concept); (ii) redundancy (e.g. by providing alternative paths for loads shed from damaged elements); (iii) ductility of response (e.g. by adopting members and connections that can absorb significant strain energy without rupture or collapse). Analyzing the EN 1998-1 (CEN 2004b) provisions, in particular the ones specific to timber structures, several measures can be pointed out to enhance robustness: • [8.6 (4)] In order to ensure the development of cyclic yielding in the dissipative zones, all other structural members and connections should be designed with sufficient overstrength. This overstrength requirement applies especially to: anchor-ties and any connections to massive sub-elements; and, connections between horizontal diaphragms and lateral load resisting vertical elements. • [4.2.1.2 (5)] The use of evenly distributed structural elements increases redundancy and allows a more favorable redistribution of action effects and widespread energy dissipation across the entire structure. • [5.2.3.5 (1)] A high degree of redundancy accompanied by redistribution capacity should be sought, enabling a more widely spread energy dissipation and an increased total dissipated energy. Consequently structural systems of lower static indeterminacy should be assigned lower behaviour factors. • [2.2.4.1 (2)P] In order to ensure an overall dissipative and ductile behaviour, brittle failure or the premature formation of unstable mechanisms should be avoided. To this end, where required in the relevant parts of EN 1998, resort should be made to the capacity design procedure, which is used to obtain the hierarchy of resistance of the various structural components and failure modes necessary for ensuring a suitable plastic mechanism and for avoiding brittle failure modes. Using the capacity design method, it is possible, by choosing certain modes of deformation, to ensure that brittle elements have the capacity to remain intact, while the inelastic deformations occur in selected ductile elements. These “fuses” or energy absorbers act as dampers to reduce force level in the structure (Thelandersson and Larsen 2003). In timber structures, the ductility is concentrated in the joints whereas the timber


55

elements must be regarded as behaving elastically. Therefore, a reliable strength prediction of the joint and its components is essential for applying the capacity design and ensuring the required ductility. This is the possible explanation for the absence of EN 1998-1 (CEN 2004b) provisions for the capacity design method application to the case of timber structures.

6.5

Examples

In this section, several examples of failures are analyzed and the foreseeable influence of considering seismic design on the outcome will be evaluated. The emphasis will be placed on prescriptions defined for areas of moderate or strong seismic risk, in particular when medium or high ductility is required. Prescriptions focused on areas of low seismic risk, in particular, the use of horizontal loads without any further requirements, have little influence of the structural robustness. The first example is the Ronan Point Building failure, triggered by a gas explosion. In this pre-fabricated structure, the consequences of the explosion were amplified by poor workmanship and very limited connection between elements. The existence of strong links between elements is a central requirement in seismic design, and, had earthquake loading been considered, a different, more redundant, structure would have been erected. In principle, this would have reduced the impact of the explosion, limiting the indirect costs associated to the incident.

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Figure 17. Alfred Murrah Federal Building structure.

The Alfred Murrah Federal Building collapsed following the explosion of a car bomb parked in the basement. The building had a structural system composed of regular frames, but, at the ground level, the number of columns was reduced, as shown in Figure 17. This structural system led to an increase in consequences of the explosion, and could have been avoided, had the building been analyzed in a seismic design perspective. In fact, the soft first story failure is prevented by the seismic design. (Corley et al. 1996) pointed out that more than 50% of the collapsed area would have stood if the structure had been designed with special moment frames found in seismic regions as opposed to the ordinary moment frames used in the building. In 1993, a car bomb exploded in the parking lot under World Trade Centre building, causing a significant local damage with a cost of $300,000,000. However, the redundant structure, supported by numerous smaller columns, rather than a central nucleus, significantly reduced the consequences of damages, and no important indirect damages resulted from the explosion.


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At the beginning of the year 2006, 2nd January, the ice arena roof in Bad Reichenhall collapsed under the actual snow load (Figure 18). Fifteen people died, thirty were partly heavily injured. The main reasons for the collapse are: (i) use of urea-formaldehyde glue under moist conditions; (ii) mistakes in the static calculation; (iii) non robust construction and, (iv) lack of maintenance.

Figure 18. Bad Reichenhall Ice Arena collapse.

According to the findings of experts (Winter and Kreuzinger 2008), one of the three main box-girders on the east side failed first. Due to the stiff cross girders, the loads were shifted from the box-girder that failed first to the neighbouring girders. These box-girders, which were already predamaged were also overloaded due to which the entire roof collapsed like a zipper. This transversal stiffness is, however, a desirable property under seismic design, and no real advantage could have been obtained from considering earthquake as a load. In fact, as shown in Figure 18 an increase in stiffness of transversal elements can, in fact, led to an increased risk associated with damage. In the case of the Siemens Arena failure (Figure 19), the first consequence of a seismic design would have been the increase of transversal stiffness. This could have caused progressive failure, following the collapse of one truss, leading to large increases in indirect consequences of damage. In

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fact, the 12 m long purlins between the trusses were only moderately fastened, so that a failure of one truss should not initiate progressive collapse. As all trusses had much lower strength than required by the failure of a neighbour element, it might be fair to conclude that the extent of the collapse was not disproportionate to the cause, as analyzed by (Munch-Andersen 2009). The result of a seismic design could have been an increase in transversal stiffness, which could have caused progressive collapse of the structure. In these last two cases, the only possible advantage of seismic design would have been the closer attention paid to the detailing of connections, required for the definition of the dissipation zones defined in EN 1998-1 (CEN 2004b). In fact, connections played a major role in both incidents, and a more careful design could have avoided the errors.

a)

An intact truss is seen to the right

b) Rupture at the critical cross section in the corner connection Figure 19. Siemens Arena roof after the collapse of two trusses (Munch-Andersen 2009).

7 Effect of quality control P. Dietsch and S. Winter

The term “robustness” and the associated rules for robustness, as presented and discussed in the previous chapters, are generally associated with the phase of structural design for a building. To reliably obtain the anticipated structural safety of a building, it is indispensable that the structure is executed and maintained according to structural calculations and plans. While robustness requirements are established to cover system effects and small defects, quality control is indispensable to eliminate gross errors which can neither be covered by the safety concept incorporated in codes nor by rules for robustness. This fact is constituted in EN 1990:2002 (CEN 2002) paragraph 2.5, stating: “In order to provide a structure that corresponds to the requirements and to the assumptions made in the design, appropriate quality management measures should be in place. These measures comprise: definition of the reliability requirements, organisational measures and controls at the stages of design, execution, use and maintenance.” This chapter will present some essential principles of quality control which should be followed during design, manufacture, construction and use of the building to satisfy above given requirement.

7.1

Structural design

For structural designers, there is one simple rule which will have a significant effect on the quality of the building: a simple design will lead to a simple execution, resulting in fewer errors. Quality control during design is realized by design supervision of calculations, drawings and specifications. The level of design supervision might depend on federal regulations or requirements of the local authorities. According to EN 1990:2002 (CEN 2002), Annex B.4, it is dependent on the consequence class of the building as illustrated in Table 4. The design supervision differentiation according to EN 1990:2002 (CEN 2002) consists of “various organisational quality control measures

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which can be used together. For example, the definition of design supervision level may be used together with other measures such as the classification of designers and checking authorities.” Table 4. Recommended requirements for design supervision, according to EN 1990:2002 (CEN 2002).

Design Supervision Levels

Characteristics

Minimum recommended requirements for checking of calculations, drawings and specifications

DSL3 Relating to RC3

Extended Supervision

Third-party checking: checking performed by an organisation different from that which has prepared the design


Normal Supervision

Checking by different persons than those originally responsible and in accordance with the procedures of the organization


Normal Supervision

Self-checking: checking performed by the person who has prepared the design

7.2

Manufacturing of structural elements

Large-span timber structures are generally realized with structural elements from glued laminated timber, an industrially manufactured wood product. For this product, as well as for most other products used in timber construction, most working processes within the production line are nowadays performed by computer-controlled machinery. A widely accepted basis for quality management measures within production is EN ISO 9001:2008 (ISO 2008). Quality control during production is to be interpreted as the control of correct functioning, correct machine settings and the use of the machine only within its given boundary conditions. Drying chambers, for example,


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should be adjusted to dry the timber slowly enough to avoid internal drying stresses. Grading machines should only be used to grade wood for which the machine has been approved for, since machine settings can differ considerably for different wood species. During the gluing process, the different influencing parameters (temperatures, “pot-time”, pressure magnitude, pressure-time) should not only be constantly controlled and documented but also adjusted to the wood species used. Building authorities require that structural elements/products possess a verification of applicability (e.g. a general technical approval). Depending on the structural importance of the building product and other indicators (e.g. sensitivity to a correct production process and existing experiences with product), different levels of quality control measures are required for the product. This always includes self-inspection (including documentation) and might be extended up to periodical third-party checks by approved inspection agencies, including tests of randomly taken samples.

7.3

Construction / execution

The correct execution is essential to obtain the anticipated structural safety and robustness of a building. Quality control in this phase is intended to check, if the personnel on site has assembled the structural elements according to plans without any errors of structural importance. This includes the control of the proofs of applicability and a check, if the presumed material grades have been used. EN 1990:2002 (CEN 2002), Annex B.5 contains information on inspection during execution. It differentiates between different levels of inspection according to the consequence class of the building as illustrated in Table 5. The code refers to the “material standards” for further guidance on inspection of execution. For timber structures, information is given in paragraph 10 of EN 1995-1-1 (CEN 2004a). The requirements include for example the establishment of a control plan which comprises the production and workmanship control off and on site as well as the control after completion of the structure (inspection maintenance in service). It should be emphasized that the control of the correct execution should be carried out by the structural engineer or the check engineer. The

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German building authorities require, for example, that a technical attestation of the correct execution with regard to the certified structural verifications has to be issued by the check engineer and proven by his signature “execution according to plans”. If the requirements for issuing the attestation are not present, the check engineer has to notify the building authorities. The accomplishment of these assignments is not included in the fees for checking the structural calculations, but they are compensated on an hourly basis. Table 5. Recommended requirements for inspection during execution, according to EN 1990:2002 (CEN 2002).

Inspection Levels

Characteristics

Requirements

IL3 Relating to RC3

Extended Inspection

Third-party inspection

IL2 Relating to RC2

Normal Inspection

Inspection in accordance with the procedures of the organization

IL1 Relating to RC1

Normal Inspection

Self-inspection

7.4

Hand-over to owner / user

A correct hand-over of the building to the owner/user should include the issuing of a comprehensible documentation in form of an instruction manual. At the same time, the owners/users have to be clarified about their responsibility for the structural safety of their building, explaining that this responsibility should be met by e.g. initiating periodic building assessments. The inclusion of notes, e.g. “an engineer has to be consulted in the case of change of use or changes to the building” could be a mean to emphasize items which are crucial for the structural safety of a building over its lifetime. Above given statements are supported in EN 1995-1-1 (CEN 2004a), paragraph 10.7, stating: “All the information required for the use in service and the maintenance of a structure is assumed to be made available to the person or authority who undertakes responsibility for the finished structure.”


7.5

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Use in service

A robust structure can only guard this quality over the intended servicelife of the building, if the correct functionality of the structural elements (especially key elements) of the building is ensured throughout the lifetime of the building. To enable the owner/user to meet this responsibility reliably and costeffectively, a comprehensive maintenance plan should be set up by the structural engineer. Possible outlines of such guidelines are given in the report of WG1 of COST E55 (Köhler and Fink 2011). It should include the clear definition of critical (key) elements. The associated maintenance schedule should define the necessary inspection intervals and detailedness of the respective inspections. Both should be set up with regard to the consequence class (potential for danger and the consequences of failure) of the building. One approach to this, taken by the Bavarian Building Authorities, is given in (Baubehörde 2006). The concept of a “Building Book” has proven very beneficial to combine all necessary documentation and to facilitate the accomplishment of above given objectives. It should contain all necessary information for the person in charge of the building and future inspectors. A possible layout is given in Table 6, further described in (Dietsch and Winter 2009). If it is utilized as a “Building Diary”, i.e. continued by the owner and future inspectors, it guarantees a consistent documentation, even with the change of authorized personnel. The recent developments in monitoring equipment and technologies suggest their consideration as part of an integral maintenance approach. Such technologies could help to identify e.g. the correct flow of loads or to give hints on exceptional influences, e.g. moisture distribution, but they cannot replace conventional maintenance. Monitoring has proven to be beneficial in the case of existing buildings that undergo a change of use or change of boundary conditions, e.g. change of snow loads in the code. In this case, monitoring can be applied to enable the continued use of a building by monitoring the magnitude of the relevant actions, signalizing when the use should be restricted and e.g. the snow be removed from the roof.

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Table 6. Exemplary structure of a building book (Dietsch and Winter 2009).

1

Preface

2

Setup Data (architect, specialist engineers, check engineer, construction firms, …)

3

Building Sheet (building type, structural system, main dimensions, foundations, …)

4

Description and Sketches of Building (position plan, structural materials and dimensions)

5

Superstructure / Loads / Live Loads (e.g. snow loads)

6

Structural Calculations (codes used (edition), programs applied, assumptions, …)

7

Foundation / Subsoil (e.g. water table)

8

Materials / Structural Elements (material characteristics, technical approvals, ...)

9

Changes / Modifications / Renovations (e.g. openings, green roof, ventilation, heat insulation, …)

10

Rehabilitation Measures / Instructions for Inspection (instructions and intervals)

11

Inspections performed (participants, tools utilised, particularities)

12

Planning Documents (documents available, date of document)

13

Copies (set-up information, copies received by, …)

14

Table of Contents


7.6

65

Conclusions

In this chapter, it is illustrated that a structure can only be called “robust”, if the structural design and the design for robustness is correctly implemented during execution and its correct functioning is ensured over the lifetime of the structure. In Chapter 5, it is shown that human errors are by far the most common cause for failures in structures. Combining this knowledge with the fact that timber structures are usually composed of repetitive elements, which are connected by analogical construction principles, it should be discussed if and how the intensity of quality control should be made dependent upon the number of identical elements used in a structure (Vogel, T. pers. comm.). The quality of the construction can also be clearly linked to how much time the planning team and the construction companies can afford to realize this project. This implies that an adequate payment of all people involved has a direct influence on the resulting quality of the construction. To decrease the occurrence of failures during the lifetime of the structure, it has proven very beneficial to introduce guidelines and schedules for assessing and inspecting a structure. The building book, accompanying a structure over its lifetime, customizes these and is therefore a good resource to accomplish abovementioned objectives for each individual structure.

8 Recommendations P. Dietsch, J. Munch-Andersen and J.D. Sørensen

8.1

Robustness measures

Risk- and reliability-based measures of robustness are described and discussed in Chapter 3. These measures require probabilistic models to be formulated for the important failure modes and the uncertain parameters related to loads, strengths and models. Further, for quantification of the risk-based measure of robustness, modelling of the consequences of failures is needed. These probabilistic and consequence models are in general difficult to establish and not directly applicable for recommendations for practical applications. But the risk and reliability based robustness measures can be used as a rational basis for formulating recommendations for practice. Estimation of the probability of extensive failure and collapse requires system models of the failure modes to be formulated, see Chapter 4. Especially the importance of ductility is investigated and shows that the level of ductility should be at least 1.5 - 2.0 before a significant increase in system reliability is observed for redundant structural systems. The system model of collapse events using series and parallel systems requires careful modelling of the correlation/dependency between the stochastic variables and the exposure events. Design and execution errors and unforeseen degredation could in many cases be expected to be present in all similar connections/elements, especially for new and unconventional structural systems. If an accidental action is the main exposure then this action typically results in an extreme load on one or a few structural elements and then (local) failure of this element. If exposures on different structural elements can be considered statistically independent then a parallel system model should be preferred from a reliability point of view. This can be obtained by increasing the redundancy of the structural system. On the other hand, if the exposures on different structural elements can be considered statistically dependent, then a parallel system model should be avoided from a reliability point of view. This can e.g. be obtained by using compartmentalization of structural systems. This recommendation deviates from the general

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recommendations in codes of practice and is further discussed in the next section.

8.2

Proposals towards designing for robustness in large-span timber structures

Robustness strategies can be ambiguous, as outlined in Chapter 5, since the best strategy depends on the failure scenario. In this section, some ideas are outlined with the aim of reducing failures of primary structural elements while decreasing the possibility of a progressive collapse in the case of an element failing. For this reflection, seismic situations have not been considered since they oftentimes require a different treatment (see Chapter 6 for seismic situations). The ideas presented are solely based on structural considerations, not on the objective of efficiency and costeffectiveness. Whereas historical timber roof structures were oftentimes realized as highly indeterminate systems, did the developments in timber engineering lead to the fact that most large-span timber structures today are realized with a statically determinate primary structure (e.g. single-span beams), carrying a statically indeterminate secondary structure. From the background of the statements given in Chapter 5, this scenario of redundancy should be reversed, meaning that primary elements should become more redundant while secondary structures should be designed as determinate systems to achieve the objective of compartmentalization. Nevertheless, redundancy on a local scale could be desirable because it can minimize the consequence of random errors. Such redundant systems must be designed in a way that it becomes evident if redistribution of loads has taken place, e.g. by visible deformations. The fact that most structures are realized with identical, repetitive elements forming statically determinate main structures should activate considerations on how quality control could be adapted accordingly (see also Chapter 7). An alternative approach would be to introduce diversity and indeterminacy into the structure, e.g. by designing a structure with many different elements, thereby avoiding too much symmetry and repetition and possibilities for redistribution of loads. An example of such a structure is shown in Annex B.3. In spite of these advantages, the aim to introduce diversity and indeterminacy into a structure will result in higher

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demands in terms of design, planning, manufacture and execution, and thereby higher costs. 8.2.1 Primary structures Although most primary systems in timber structures are statically determinate systems, there are a few possibilities to realize redundant primary systems. Amongst the most typical statically indeterminate structural systems for timber halls are frame systems, often realized with V-shaped columns, see Figure 20. This approach can be refined by integrating struts as shown in Figure 21.

Another possibility to increase redundancy of primary structural elements is to introduce internal indeterminacy. Examples of this are trusses with diagonal cross members as shown in Annex B4 or beams which are trussed with sag rods (see Figure 22). For such systems it seems feasible to consider the failure of one structural element (e.g. the steel rods), designing the remaining elements to withstand the stress resultants in the changed structural system in the accidental load case. This would, however, usually imply that the key elements need to be over-designed in the ULS. Since timber is a highly anisotropic material, structural elements are sometimes reinforced with e.g. pre-drilled, screwed-in rods to compensate for low strength properties, e.g. tension perpendicular to grain or shear strength (see Figure 23). Due to the fact that both failure mechanisms are very brittle, meaning that the deformations in linear-elastic range are very small, such reinforcements might not be able to activate their full loadcarrying capacity in the undamaged state (especially for shear reinforcements with screwed-in rods). But even though the additional load-carrying capacity, due to the reinforcing elements, might be relatively low in the undamaged state, they should be regarded as beneficial. The reason is that they can be designed to carry the full shear or tension perpendicular to grain stresses in the damaged state, meaning that they prevent a full separation of the upper and lower parts of the beam in the case of a local separation (crack) due to over-stressing. Thereby, they introduce redundancy which represents a second barrier against brittle failure mechanisms.

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Figure 20. Indeterminate frame system with V-shaped frame corner.

Figure 21. Indeterminate system with V-shaped column and struts.

Figure 22. Example of system with internal indeterminacy, beam trussed with sag rod.

Figure 23. Example of a pitched cambered beam with reinforcements.

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8.2.2 Secondary structures Typical purlin systems for timber structures have to fulfil two requirements: a) To carry the vertical loads from the roof structure (e.g. self-weight and snow) and to transfer them to the primary structural elements; b) To perform as part of the bracing system, transferring the horizontal loads (stability and wind loads) to the vertical bracing system (see Figure 24).

Figure 24. Exemplary structural system with purlins performing as part of the bracing system.

This dual function causes the main difficulties when considering robustness and the objective of realizing compartmentalization. To obtain functionality as bracing against wind loads and lateral torsional buckling of the primary members, the purlin systems are realized to transfer horizontal (axial) loads in tension and compression. This implies that, in the case of one main member failing, the purlin systems will develop into a tie member, thereby transferring the vertical loads from the failing member to the adjacent members (see Figure 12 in Chapter 5). It should be noticed that robustness requires at least two vertical bracing elements, one near to each end of the building. This will ensure that the remaining parts of the building are still braced after the failure of one main member.

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8.2.3 Detailing of connections with respect to robustness A first design approach, with regard to the challenges illustrated in the previous section, would be to differentiate between the purlins according to their functions since not every purlin has to act as part of the bracing system. This means that purlins which are not part of the bracing system should be designed as to not transfer axial (horizontal loads) while purlins that act supplementary as part of the bracing system should not “hinge” themselves into the remaining main members in case of failure. The latter could be achieved by not “over-designing” the connections between the determinate purlins for axial forces, meaning that the purlins would only form a tie member until the system reaches the axial design load from horizontal loads. This could be achieved by e.g. matching the amount of nails used in hangers to these forces.

Another connection type which would enable this and potentially lead to a detachment of the purlin system and the main member in case of failure is sketched in Figure 25. Many producers of connectors offer systems which feature illustrated mechanisms since such connector types are also known to decrease assembly time. For such cases, in which vertical loads should basically only be transferable in compression, it is important to check if lifting forces like wind-suction are compensated by the self-weight of the roof. If this is not the case (e.g. in edge regions), these lifting forces have to be locally anchored whereby the anchoring device should adhere to the mentioned requirements (easy detachment in case of failure). It is self-evident that the roof cladding will be constructed so it will not develop into a tie member in the case of failure. While it might be worth considering a roof cladding which can carry the loads on a failing purlin to other purlins, it should definitely not support load transfer in the case of a failing main member.

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Figure 25. Connection to transfer horizontal and vertical loads, potentially enabling detachment in case of failure.

Pushing these ideas further, it seems plausible to consider a clear separation of both functions stated above. This would result in a purlin system, designed to only transfer vertical loads and one separate bracing system to carry all horizontal loads. A possible layout of this detail is sketched in Figure 26. The supports of the purlins on the main members could then be designed to only carry vertical loads, while simply a slight horizontal fastening would be needed to secure their position. The bracing system would still be designed to transfer horizontal loads in tension and compression but due to the separation of both systems - would not transfer any vertical loads to the neighbouring beams in the case of one main member failing. Nevertheless, such a design can only be fully beneficial if easy detachment of main member and bracing system is enabled (as indicated by the channel section, only horizontally stabilizing the main beam) and the purlins and bracing elements are not placed within the same plane. Although only bracing elements perpendicular to the main member are sketched in Figure 26, it is self-evident that cross bracing is needed to transfer the horizontal loads to the vertical bracing elements. Load transfer in case of failure will be more pronounced between two primary members adjacent to a horizontal cross bracing, making these members key elements which should be given special consideration during design.

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Purlins (vert. loads)

Bracing (hor. loads)

Figure 26. Separation of load bearing structure for horizontal and vertical loads, enabling detachment in case of failure.

Modifying the above given possibilities, one could consider a bracing system which is designed to only carry axial (horizontal) loads in compression, meaning that horizontal loads could only be transferred unidirectional as illustrated in Figure 27. Following the requirement of redundancy, this would mean that at least two bracing systems will be realized for each direction of load. Such a system needs exact execution to obtain force-fit connections. Nevertheless, due to the necessary lengths of load transfer and possible problems in meeting the horizontal deflection limits, such a system seems less feasible.

Force-tight connections Figure 27. Connection to transfer axial compression forces and vertical loads, enabling detachment in case of failure.

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The addition of small steel-ties between the purlins would permit the twodirectional transfer of horizontal loads, see Figure 28. The steel-ties need to be designed for axial tension forces. But if they are not “overdesigned", they should fail as soon as significant rotation of one of the purlins starts.

Steel-Tie (symbolized)

Figure 28. Connection to transfer axial tension and compression forces and vertical loads, enabling detachment in case of failure.

A system, comparable to Figure 25 and enabling easy detachment between secondary members, hangers and main members, was applied in the roof structure of an exhibition centre. When one main beam collapsed due to the corrosion failure of its appendant steel suspension cable, the purlins did not develop into tie members but developed hinges at the supports, limiting the failure to one field (see Figure 29).

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Figure 29. Exhibition centre, failure of one main beam, development of hinges at supports of purlins (Photo: MPA BAU, TUM).

A final alternative to realize connections between the primary beams and the purlins which only transfer vertical forces, thereby enabling easy detachment in the case of failure of one element, is to design the primary beams as internally stable against lateral torsional buckling, also being capable to transfer external horizontal loads (e.g. wind loads). This is only achievable, if the primary beams be designed less slender or with a Tsection as sketched in Figure 30.

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Figure 30. Primary beam with cross-section to enable internal stability against lateral torsional buckling, also capable to transfer external horizontal loads (e.g. wind loads). 8.2.4 Summary Large-span timber structures generally consist of primary, long spanning members connected by secondary members. The primary members can e.g. be tapered glulam beams, trussed beams or arches. The secondary system is typically realized by a purlin-type structure. The purlins carry the roof cladding, which can be regarded as the tertiary structure. In most cases, horizontal loads from wind and torsional loads are carried by a bracing system.

All investigations on failures of large-span timber structures conclude that systematic mistakes during design or construction are the primary reason for failure. It is therefore evident that secondary structures, which are able to redistribute loads from a failed main member to neighbouring main members, are likely to cause progressive collapse when a main member fails. Progressive collapse is most efficiently prevented by compartmentalization of the structure. Each compartment can include

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several main members, but it should not cover an area larger than “acceptable” in the case of failure. Within each compartment, the secondary structure can be allowed to redistribute loads in order for local failures not to cause local collapse. But it is important that such a redistribution becomes immediately evident, e.g. in form of large deformations. Therefore, the secondary system should be designed so that it issues a warning if it transfers load, e.g. by visible deflections. Another possibility could be sophisticated, continuous surveillance systems which give warning based on deformations, or sound from cracks. The area of each compartment might depend on the area of the whole structure, but also on the novelty of the structure. A very innovative design is more likely to inherent systematic errors than traditional structures. For traditional structures the prevention of local collapse from local failures can be given higher priority than for innovative structures.

9 References Baker, J. W., Schubert, M. et al. (2007). On the assessment of robustness. Journal of Structural Safety. 30(3): pp. 253-267. Baubehörde (2006). Hinweise für die Überprüfung der Standsicherheit von baulichen Anlagen durch den Eigentümer/ Verfügungsberechtigten. Oberste Baubehörde im Bayerischen Staatsministerium des Inneren. Munich, Germany. Bell, K. (2007). Shear failure in glulam frames - an actual case. Department of Structural Engineering, Norwegian University of Science and Technology. Trondheim, Norway Biondini, F., Frangopol, D. M., et al. (2008). On Structural Robustness, Redundancy, and Static Indeterminacy. Proceedings of the 2008 Structures Congress - Crossing Borders. Vancouver, BC, Canada Blaß, H.-J. and Frese, M. (2007). Failure Analysis on Timber Structures in Germany - A Contribution to COST Action E55", 1st Workshop. Graz University of Technology, Austria. Brunner, M. (2000). On The Plastic Design Of Timber Beams With A Complex Cross-Section. Proceedings of WCTE 2000. Whistler, Canada. CEN (2002). Eurocode 0 - Basis of structural design. European Prestandard ENV 1990. European Committee for Standardization CEN. Brussels, Belgium. CEN (2004a). Eurocode 5 - Design of Timber Structures - Part 1-1: General - Common rules and rules for buildings. European Committee for Standardization CEN. Brussels, Belgium. CEN (2004b). Eurocode 8-1 - Design of structures for earthquake resistance - Part 1: General rules, seismic actions and rules for buildings. European Committee for Standardization CEN. Brussels, Belgium. CEN (2006). Eurocode 1-1-7 - Actions on structures. Part 1-7: General actions - Accidental actions. European Committee for Standardization CEN. Brussels, Belgium. Corley W.G., Sozen M.A., Thornton, C.H. and Mlakar P.F. (1996). The Oklahoma City Bombing: Improving Building Performance through Multi-Hazard Mitigation. Federal Emergency Management Agency Mitigation Directorate. FEMA Report 277. Washington, D.C, USA.

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Daniels, H. E. (1945). The statistical theory of the strength of bundles of threads, Part I. Proceedings of the Royal Society. London, UK. Dietsch, P. and Munch-Andersen, J. (2009). Robustness considerations from failures in two large-span timber roof structures. Proceedings of the Joint Workshop of COST Actions TU0601 and E55. Ljubljana, Slovenia. Dietsch, P. and Winter, S. (2009). Assessment of the Structural Reliability of all wide span Timber Structures under the Responsibility of the City of Munich. Proceedings of the 33rd IABSE Symposium. Bangkok, Thailand. DS/INF-146 (2003). Robustness - background and principles information (In Danish). Danish Standards. Charlottenlund, Denmark Ellingwood, B. R. (2002). Load and resistance factor criteria for progressive collapse design. National Workshop on Prevention of Progressive Collapse. National Institute of Building Sciences. Rosemont, USA. Ellingwood, B. R. and Leyendecker, E. V. (1978). Approaches for design against progressive collapse. J Struct Div ASCE 104: pp. 413423. Ellingwood, B.R. (1987). Design and Construction Error Effects on Structural Reliability. Journal of Structural Engineering. 113/2: pp. 409-422 Ellingwood, B. R., Smilowitz, R., Dusenberry, D. O., Duthinh, D., Carino, N. J. (2007). Best Practices for Reducing the Potential for Progressive Collapse in Buildings. National Institute of Standards and Technology. Gaithersburg, USA. FEMA (2002). NEHRP recommended provisions for the development of seismic regulation for new buildings and other structures. FEMA Rep. No. 368. Federal Emergency Management Agency. Washington D.C, USA. Frangopol D.M. and Curley, J.P. (1987). Effects of damage and redundancy on structural reliability. Journal of Structural Engineering 113(7): pp. 1533-1549. Frühwald, E., Serrano, E. et al. (2007). Design of safe timber structures – How can we learn from structural failures in concrete, steel and timber?. Report TVBK-3053. Div. of Struct. Eng. Lund University, Sweden.

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Fu G. and Frangopol, D.M. (1990). Balancing weight, system reliability and redundancy in a multiobjective optimization framework. Structural Safety 7(2-4): pp. 165-175. Glos, P. (1981). Zur Modellierung des Festigkeitsverhaltens von Bauholz bei Druck-, Zug- und Biegebeanspruchung. Berichte zur Zuverlässigkeitstheorie der Bauwerke. Heft 61. Sonderforschungsbereich 96. München, Germany. Gollwitzer, S. and Rackwitz, R. (1990). On the reliability of Daniels systems. Structural Safety 7: pp. 229-243. Gulvanessian, H. and Vrouwenvelder, T. (2006). Robustness and the Eurocodes. Structural Engineering International 2: pp. 167-172. Hansson, M. and Larsen, H. J. (2005). Recent failures in glulam structures and their causes. Engineering Failure Analysis 12(5): pp. 808818. Hendawi, S. and Frangopol, D. M. (1994). System reliability and redundancy in structural design and evaluation. Structural Safety 16: pp. 47-71. Herzog, T., Natterer, J., Volz, M. (2000). Timber Construction Manual. Birkhäuser Architecture. Basel, Switzerland. Hoffmeyer, P. and Sørensen, J.D. (2007). Duration of Load Revisited. Wood Science and Technology. Vol. 41, No. 8, pp. 687-711. ISO (2007a). ISO 19902 Petroleum and Natural Gas Industries - Fixed Steel Offshore Structures. International Organization for Standardization ISO. Geneva, Switzerland. ISO (2007b). ISO Standard 22111 - Bases for design of structures General requirements. International Organization for Standardization ISO. Geneva, Switzerland. ISO (2008). ISO 9001 - Quality management systems - Requirements. International Organization for Standardization ISO. Geneva, Switzerland.

JCSS. (2001). Probabilistic model code. Part 2 - Load Models. JCSS Publication. Zürich, Switzerland. JCSS (2002). Joint Committee on Structural Safety: Probabilistic Model Code. JCSS Publication. Zürich, Switzerland.

JCSS. (2006). Probabilistic model code. Part 3 - Resistance Models. JCSS Publication. Zürich, Switzerland. JCSS (2008). Risk Assessment in Engineering Principles. System Representation & Risk Criteria. JCSS Publication. Zürich, Switzerland.

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Kirkegaard, P. H. and Sørensen, J. D. (2008). A Probabilistic Approach for Robustness Evaluation of Timber Structures. DCE Technical Report Nre. 55. Aalborg University, Department of Civil Engineering, Denmark Kirkegaard, P. H., Sørensen, J. D., et al. (2009). Robustness Evaluation of Timber Structures with Ductile Behaviour. 12th International Conference on Civil, Structural and Environmental Engineering &Computing. Madeira, Portugal. Köhler, J., Narasimhan, H. and Faber, M.H. (ed.) (2010). Proceedings of the Joint Workshop of COST Actions TU0601 and E55. ETH Zurich, Switzerland. Köhler, J., Fink, G. (ed.) (2011). Assessment of Failures and Malfunctions. Report of COST E55 WG1. Shaker Publishing Company. Aachen, Germany Legislation (2010). The Building Regulations 2010 – Building and Buildings, England and Wales. No. 2214. UK Statutory Instruments. London, UK Leijten, A. J. M., Ruxton, S., et al. (2006). Reversed-Cyclic Behavior of a Novel Heavy Timber Tube Connection. Journal of Structural Engineering 132(8): pp. 1314-1319. Madsen, H. O., Krenk, S. et al. (1986). Methods of Structural Safety. Prentice-Hall. Upper Saddle River, USA. McKenzie, W.M.C. and Zhang, B. (2007). Design of Structural Timber to Eurocode 5. Palgrave MacMillan. Basingstoke, UK. Munch-Andersen J. (2009). The Siemens Arena collapse in a robustness perspective. COST E55. 5th Workshop - WG3-Robustness of Systems. Norwegian University of Science and Technology. Trondheim, Norway NKB/SAKO (1999). Basis of design of Structures. Proposal for modification of Partial Safety Factors in Eurocodes. Nordic Council of Ministers. Oslo, Norway. Oxford Dictionaries. (2009). http://www.askoxford.com. Piazza M., Del Senno M., et al. (2004). A pseudo-ductile approach design of glued laminated timber beams. Proceedings of WCTE 2004. Lahti, Finland. Schubert, M., Straub, D. et al. (2005). On the Assessment of Robustness II: Numerical Investigations. Robustness of Structures Workshop organised by the JCSS & IABSE WC 1, November, 28-29. BRE, Garston, Watford, UK.

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SIA (2004). Standard SIA 260 - Basis of Structural Design. Swiss Society of Engineers and Architects. Zurich, Switzerland. Schmidt, H. J. (1974). Überdachung der Eislaufhalle Bad - Reichenhall. Ausstellung Holzbau Konstruktionen der Arbeitsgemeinschaft Holz e.V. als Sonderdruck aus Zeitschrift Detail 6/1974. Düsseldorf, Germany Short, C. (1995). Purlins. in: Timber Engineering STEP 2 - Design, details and structural systems. Centrum Hout, Netherlands. Sørensen, J. D. (1991). PRADSS : Program for Reliability Analysis and Design of Structural Systems. Aalborg University, Denmark. Starossek, U. (2006). Progressive Collapse of Structures: Nomenclature and Procedures. Structural Engineering International 2: pp. 113117. Stehn, L. and Björnfot, A. (2002). Comparison of different ductility measurements for nailed steel-to-timber connections. Proceedings of WCTE 2002. Shah Alam, Malaysia. Stehn, L. and Borjes, K. (2004). The influence of nail ductility on the load capacity of a glulam truss structure. Engineering Structures 24(6): pp. 809-816. Thelandersson S. and Larsen H.J. (2003). Timber Engineering. John Wiley & Sons, LTD. Ney York, USA Vrouwenvelder, T. and Sørensen, J.D. (2009). Robustness of structures, EU COST action TU0601. Proceedings of ICOSSAR. Osaka, Japan. Winter, S. and H. Kreuzinger (2008). The Bad Reichenhall ice arena collapse and the necessary consequences for wide span timber structures. Proceedings of WCTE 2008. Miyazaki, Japan

10 Authors Jorge Manuel Branco

University of Minho, Civil Engineering Department, Campus de Azurém, 4800-058 Guimarães, Portugal

Dean Čizmar

University of Zagreb, Kačićeva 26, 10000 Zagreb, Croatia

Philipp Dietsch

Technische Universität München, Chair for Timber Structures and Building Construction, Arcisstraße 21, 80333 München, Germany

Gerhard Fink

ETH Zurich, Institute of Structural Engineering IBK Group Risk and Safety, HIL E23.1, Wolfgang-Pauli-Str. 15, 8093 Zurich, Switzerland

Poul Henning Kirkegaard

Aalborg University, Department of Civil Engineering, Sohngaardsholmsvej 57, 9000 Aalborg, Denmark

Jochen Köhler

ETH Zurich, Institute of Structural Engineering IBK Group Risk and Safety, HIL E24.1, Wolfgang-Pauli-Str. 15, 8093 Zurich, Switzerland

Jørgen Munch-Andersen

Danish Timber Information Council (TOP), Lyngby Kirkestræde 14, 2800 Kgs. Lyngby, Denmark

Luís Armando Neves

New University of Lisbon, Quinta da Torre, 2829-516 Monte de Caparica, Portugal

Vlatka Rajčić

University of Zagreb, Kačićeva 26, 10000 Zagreb, Croatia

John Dalsgaard Sørensen

Aalborg University, Department of Civil Engineering, Sohngaardsholmsvej 57, 9000 Aalborg, Denmark

René Steiger

EMPA, Swiss Federal Laboratories for Materials Science and Technology, Wood Laboratory, Ueberlandstrasse 129, 8600 Dübendorf, Switzerland

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Authors

Goran Turk

University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, 1000 Ljubljana, Slovenia

Stefan Winter

Technische Universität München, Chair for Timber Structures and Building Construction, Arcisstraße 21, 80333 München, Germany

Binsheng Zhang

Napier University, Centre for Timber Engineering, Merchiston Campus, 10 Colinton Road, Edinburgh EH10 5DT, United Kingdom

Annex A. Robustness requirements in codes J.D. Sørensen, B. Zhang, J. Branco and L. Neves

Annex A1 Eurocodes: EN1990 and EN1991-1-7 In this annex, the basic Eurocode requirements to robustness in EN 1990 (CEN 2002) and EN 1991-1-7 (CEN 2006) are presented. In (Gulvanesian and Vrouwenvelder 2006) the background for the requirements is described. The following text is an extract from this description: “The objective of design in general is to reduce risks at an economical acceptable price. Risk may be expressed in terms of the probability and the consequences of undesired events. Thus, risk-reducing measures consist of probability reducing measures and consequence reducing measures. No design, however, will be able or can be expected to counteract all actions that could arise due to an extreme cause, thus a structure should not be damaged to an extent disproportionate to the original cause. As a result of this principle, given in 4(P) of EN 1990 (CEN 2002), local failure may be accepted. For that reason, redundancy, and non-linear effects play a much larger role in design for accidental actions, than in the case of variable actions. Design for accidental design situations needs to be primarily included 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. A convenient measure to decide which structures are to be designed for accidental situations is to arrange structures or structural components in categories according to the consequences of an accident. The design for unidentified accidental load is presented in Annex A of EN 1991-1-7 (CEN 2006). Rules of this type were developed from the UK Codes of Practice and regulatory requirements introduced in the early 1970s, following the partial collapse of a block of flats at Ronan Point 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

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disproportionate extent of collapse following local damage being sustained from an accidental event”. In the following, the main robustness requirements in EN 1990 (CEN 2002) are described in section A1.1. As mentioned above, EN 1990 provides the general principles, e.g. it is stated that a structure should be “designed in such a way that it will not be damaged by events like fire, explosions, impact or consequences of human errors, to an extent disproportionate to the original cause.” It also states that potential damage should be averted by “avoiding, eliminating or reducing the hazards to which the structure can be subjected; selecting a structural form which has low sensitivity to the hazards considered; selecting a structural form and design that can survive adequately the accidental removal of an individual member or a limited part of the structure, or the occurrence of acceptable localized damage; avoiding as far as possible structural systems that can collapse without warning; tying the structural members together.” Section A1.2 contains the robustness requirements in EN 1991-1-7 (CEN 2006) related to “Design for consequences of localised failure in buildings from an unspecified cause”. EN 1991-1-7 (CEN 2006) provides strategies and methods to obtain robustness. Actions that should be considered in different design situations are, see Figure A1: 1) designing against identified accidental actions, and 2) designing against unidentified actions (where designing against disproportionate collapse, or for robustness, is important). The methods used to design for robustness of a structure are divided into several levels based on potential consequences of structural failure (Consequence Class). CC1 represents low consequence class with no special requirements, CC2 are structures with medium consequences that can be handled using simplified analysis, while CC3 stands for high consequence class where a reliability or risk analysis must be conducted. However, there are no specific criteria which could be used to quantify the level of robustness of a structure which could have a benefit for design and analysis of structures.


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Figure A1. Design situations according to EN 1991-1-7. Annex A1.1 Robustness in EN 1990:2002 “Basis of structural design” In section 2.1 “Basic requirements”, the following basic robustness requirement is formulated:

(4)P A structure should be designed and executed in such a way that it will not be damaged by events such as: • explosion, • impact, and • the consequences of human errors, to an extent disproportionate to the original cause. (5)P Potential damage should be avoided or limited by appropriate choice of one or more of the following: • avoiding, eliminating or reducing the hazards to which the structure can be subjected. • selecting a structural form which has low sensitivity to the hazards considered.

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•

selecting a structural form and design that can survive adequately the accidental removal of an individual member or a limited part of the structure, or the occurrence of acceptable localised damage. avoiding as far as possible structural systems that can collapse without warning. tying the structural members together.

• •

(6) The basic requirements should be met: • by the choice of suitable materials. • by appropriate design and detailing. • by specifying control procedures for design, production, execution, and use relevant to the particular project. (7) The provisions of Section 2 should be interpreted on the basis that due skill and care appropriate to the circumstances is exercised in the design, based on such knowledge and good practice as is generally available at the time that the design of the structure is carried out. Annex A1.2 Robustness in EN 1991-1-7:2005 “Accidental actions” The informative annex A in EN 1991-1-7 contains information for design for consequences of localised failure in buildings from an unspecified cause. It gives rules and methods for designing buildings to sustain an extent of localised failure from an unspecified cause without disproportionate collapse. Whilst other approaches may be equally valid, adoption of this strategy is likely to ensure that a building, depending upon the consequences class, is sufficiently robust to sustain a limited extent of damage or failure without collapse.

(1) Designing a building, so that neither the whole building nor a significant part of it will collapse if localised failure were sustained, is an acceptable strategy, in accordance with Section 3 of this part. Adopting this strategy should provide a building with sufficient robustness to survive a reasonable range of undefined accidental actions. (2) The minimum period that a building need to survive following an accident should be the period needed to facilitate the safe evacuation and rescue of personnel from the building and its surroundings. Longer periods of survival may be required for buildings used for handling


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hazardous materials, provision of essential services, or for national security reasons. Consequence classes of buildings (1) Table A1 provides a categorisation of building types/occupancies to consequences classes This categorisation relates to the low, medium and high consequences classes given in 3.4 (1).

Table A1. Categorisation of consequences classes.

Consequence Class 1

2a Lower Risk Group

2b Upper Risk Group

3

Example of categorisation of building type and occupancy Single occupancy houses not exceeding 4 storeys. Agricultural buildings. Buildings into which people rarely go, provided no part of the building is closer to another building, or area where people do go, than a distance of 1½ times the building height. 5 storey single occupancy houses. Hotels not exceeding 4 storeys. Flats, apartments and other residential buildings not exceeding 4 storeys. Offices not exceeding 4 storeys. Industrial buildings not exceeding 3 storeys Retailing premises not exceeding 3 storeys of less than 1000 m2 floor area in each storey. Single storey educational buildings. All buildings not exceeding two storeys to which the public are admitted and which contain floor areas not exceeding 2000 m2 at each storey. Hotels, flats, apartments and other residential buildings greater than 4 storeys but not exceeding 15 storeys. Educational buildings greater than single storey but not exceeding 15 storeys. Retailing premises greater than 3 storeys but not exceeding 15 storeys. Hospitals not exceeding 3 storeys. Offices greater than 4 storeys but not exceeding 15 storeys. All buildings to which the public are admitted and which contain floor areas exceeding 2000 m2 but not exceeding 5000 m2 at each storey. Car parking not exceeding 6 storeys. All buildings defined above as Class 2 Lower and Upper Consequences Class that exceed the limits on

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area and number of storeys. All buildings to which members of the public are admitted in significant numbers. Stadia accommodating more than 5 000 spectators. Buildings containing hazardous substances and/or processes Recommended strategies (1) Adoption of the following recommended strategies should provide a building that will have an acceptable level of robustness to sustain localised failure without a disproportionate level of collapse.

a) For buildings in Consequence Class 1: Provided a building has been designed and constructed in accordance with the rules given in EN 1990 to EN 1999 for satisfying stability in normal use, no further specific consideration is necessary with regard to accidental actions from unidentified causes. b) For buildings in Consequence Class 2a (Lower Group): In addition to the recommended strategies for Consequences Class 1, the provision of effective horizontal ties, or effective anchorage of suspended floors to walls, as defined in A.5.1 and A.5.2 respectively for framed and load-bearing wall constructions should be provided. c) For buildings in Consequence Class 2b (Upper Group): In addition to the recommended strategies for Consequence Class 1. The provision of: effective horizontal ties, as defined in A.5.1 and A.5 2 respectively for framed and load-bearing wall construction (see 1.5.11), together with effective vertical ties, as defined in A.6, in all supporting columns and walls should be provided, or alternatively, the building should be checked to ensure that upon the notional removal of each supporting column and each beam supporting a column, or any nominal section of load-bearing wall as defined in A.7 (one at a time in each storey of the building) the building remains stable and that any local damage does not exceed a certain limit. Where the notional removal of such columns and sections of walls would result in an extent of damage in excess of the agreed limit, or other such limit specified, then such elements should be designed as a "key element" (see A.8).


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In the case of buildings of load-bearing wall construction, the notional removal of a section of wall, one at a time, is likely to be the most practical strategy to adopt. d) For buildings in Consequences Class 3: A systematic risk assessment of the building should be undertaken taking into account both foreseeable and unforeseeable hazards. NOTE 2 Guidance on the preparation of a risk analysis is included in Annex B NOTE 3 The limit of admissible local failure may be different for each type of building. The recommended value is 15 % of the floor, or 100 m2, whichever is smaller, in each of two adjacent storeys, see Figure A2.

Key (A) Local damage not exceeding 15 % of floor area in each of two adjacent storeys (B) Notional column to be removed a) Plan b) Section Figure A2. Recommended limit of admissible damage.

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Effective horizontal ties Framed structures: (1) Effective horizontal ties should be provided around the perimeter of each floor and roof level and internally in two right angle directions to tie the column and wall elements securely to the structure of the building. The ties should be continuous and be arranged as closely as practicable to the edges of floors and lines of columns and walls. At least 30% of the ties should be located within the close vicinity of the grid lines of the columns and the walls.

(2) Effective horizontal ties may comprise rolled steel sections, steel bar reinforcement in concrete slabs, or steel mesh reinforcement and profiled steel sheeting in composite steel/concrete floors (if directly connected to the steel beams with shear connectors). The ties may consist of a combination of the above types. (3) Each continuous tie, including its end connections, should be capable of sustaining a design tensile load of "T" for the accidental limit state. Annex A1.3 Considerations on robust design of timber structures to Eurocodes In addition to designing a timber structure to support loads from normal use, there should be a reasonable probability that the structure will not collapse catastrophically because of misuse or accident. Buildings should be designed so that they are robust, which is defined in EN 1991-1-7 (CEN 2006) as the ability of a structure to accommodate unforeseen accidental events like fire, explosions, impact or the consequences of human error without being damaged to an extent disproportionate to the original cause. The recommendations for all types of buildings are generally given in the Building Regulations of EU member countries (Legislation 2010). For robust design of timber buildings, EN 1995 Part 1-1 (CEN 2004a) is also required together with EN 1990 (CEN 2002), EN 1991 (CEN 2006) and other Eurocode parts.

A key element should be designed for the accidental loading specified in EN 1990. Structural elements that provide lateral restraint vital to the stability of a key element should also be designed as a key element. The accidental loading should be applied to the member from all horizontal and vertical directions, in one direction at a time, together with the


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reactions from other building components attached to the member that are subject to the same accidental loading but limited to the maximum reactions that could reasonably be transmitted, considering the breaking resistance of such members and their connections. The accidental loads should be considered as acting with the loads given in Equation (8.2). i.e. Equation (6.11b) of EN 1990. The recommended value of Ad for building structures is 34 kN/m2. The capacity of the element and its connections should be calculated in accordance with Equation (8.3), i.e. Equation (6.6a) of EN 1990 together with Equation (2.14) of EN 1995-1-1. Overall structural stability (McKenzie and Zhang 2007) To ensure that a design is robust and stable: (a) the geometry of the structure should be considered. (b) required interaction and connections between timber load bearing elements and between such elements and other parts of the structure should be assumed. (c) suitable bracing and diaphragm effects should be provided in planes parallel to the direction of the lateral forces acting on the whole structure.

In addition, the designer should state in the health and safety plan, any special precautions or temporary propping necessary at each and every stage in the construction process to ensure overall stability of all parts of the structure. Generally, instability problems arise due to an inadequate provision to resist lateral loading (e.g. wind loading) on a structure. There are a number of well established structural forms which, when used correctly, will ensure adequate stiffness, strength and stability. It is important to recognise that stiffness, strength and stability are three different characteristics of a structure. The most common forms of structural arrangements which are used to transfer loads safely and maintain stability are: • braced frames • unbraced frames • shear cores/walls • cellular construction • diaphragm action.

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Annex A2 Eurocodes: EN 1998 “Design for earthquake resistance” According to Eurocode 8 (CEN 2004b), the following aspects are important for design of structures exposed to earthquakes: • Structural simplicity, uniformity and symmetry. • Bi-directional and torsional resistance. • Ductility. • Redundancy which allows for redistribution of actions and widespread energy dissipation across the structure - strong columns/ weak beams principle. • Diaphamic action of floors. Redundancy requirements are described in is clause 5.2.3.5: (1)P A high degree of redundancy accompanied by redistribution capacity should be sought, enabling a more widely spread energy dissipation and an increased total dissipated energy. Consequently structural systems of lower static indeterminacy should be assigned lower behaviour factors (see Table 5.1). The necessary redistribution capacity should be achieved through the local ductility rules given in 5.4 to 5.6. An important descriptor of the behaviour is the “behaviour factor” defined by: • Factor used for design purposes to reduce the forces obtained from a linear analysis, in order to account for the non-linear response of a structure, associated with the material, the structural system and the design procedures. • The “behaviour factor” includes the effect of ductility through the ductility class used to classify different structures with respect to their ability to have ductile failure modes. Further, the “behaviour factor” includes the effect of regularity and failure mode type.

Annex A3 Denmark – Robustness requirements in national annex to EN 1990 According to Danish design rules, robustness should be documented for all structures where consequences of failure are serious. Robustness is related to scenarios where exposures result in damage to structural


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system. This means that a robust structure can be achieved by means of suitable choices of materials, general static layout and structural composition, and by suitable design of key elements. Robustness should be distinguished from accidental loads although some of the design procedures and measures are similar; structures should be robust regardless of the likelihood of accidental loads. A key element is defined as a limited part of the structure, which has an essential importance for the robustness of the structure so that any possible failure of the key element implies a failure of the entire structure or significant parts of it, (DS/INF146 2003). Examples of unintentional loads and defects are e.g. unforeseen load effects, geometrical imperfections, settlements and deterioration, unintentional deviations between the actual function of the structure and the applied computational models and between the executed project and the project material. The requirements to robustness of a structure should be related to the consequences of a failure of the structure. Therefore, documentation of robustness is only required for structures in high consequence class. Robustness is assessed by preparation of a technical review where at least one of the following criteria should be fulfilled: a) by demonstrating that those parts of the structure essential for the reliability only have little sensitivity with respect to unintentional loads and defects. b) by demonstrating a load case with ‘removal of a limited part of the structure’ in order to document that an extensive failure of the structure will not occur if a limited part of the structure fails. c) by demonstrating sufficient safety of key elements, so that the entire structure with one or more key elements has the same reliability as a structure where robustness is documented by b). The design procedure to document sufficient robustness can be summarized in the following steps: 1. Review of loads and possible failure modes/scenarios and determination of acceptable collapse extent. 2. Review of the structural systems and identification of key elements. 3. Evaluation of the sensitivity of essential parts of the structure to unintentional loads and defects. 4. Documentation of robustness by “failure of key element” analysis; 5. Documentation of robustness by increasing the strength of key elements if Step 4 is not possible.

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The robustness requirement used in Denmark is formulated in an informative annex in the Danish National Annex to Eurocode EN 1990.

Annex A4 Offshore: Robustness requirements in ISO 19902 This section describes robustness related requirements in ISO19902 Petroleum and Natural Gas Industries — Fixed Steel Offshore Structures (ISO 2007a) 3.2.10 Robustness

Ability of a structure to withstand events with a reasonable likelihood of occurring without being damaged to an extent disproportionate to the original cause. 7.9 Robustness

A structure should incorporate robustness through consideration of the effects of all hazards and their probabilities of occurrence, to ensure that consequent damage is not disproportionate to the cause. Damage from an event with a reasonable likelihood of occurrence should not lead to complete loss of integrity of the structure. In such cases, the structural integrity in the damaged state should be sufficient to allow a process system close down and/or a safe evacuation. Robustness is achieved by either: a) Designing the structure in such a way that any single load bearing element exposed to the hazard can become incapable of carrying its normal design load without causing collapse of the structure or any significant part of it; or b) Ensuring (by design or by protective measures) that no critical component exposed to the hazard can be made ineffective. A.7.9 Robustness

The robustness concept is closely related to accidental actions, consequences of human error, and failure of equipment. Following ISO


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19900, these situations are denoted “hazardous circumstances” or briefly “hazards”. Robustness is also important in the event of serious but unidentified fatigue damage. Robustness is achieved by considering accidental limit states that represent the structural effects of hazards. Ideally, all such likely hazards should be identified and quantified by means of rational analyses. However, in many cases it is possible based on experience and engineering judgement to identify and reasonably quantify the most important accidental limit states. They will often be those from ship impact, dropped objects, explosions and fires. The design should follow ISO 19900 which uses the following approach: • careful planning of all phases of development and operation. • avoiding the structural effects of the hazards by either eliminating the source or by bypassing and overcoming them. • minimising the consequences. • designing for hazards. When the hazard cannot reliably be avoided, the designer has a choice between minimising the consequences (i.e. the consequences of loosing an element due to a hazard), or designing for the hazard (i.e. making the element strong enough to resist the hazard). In the first case, the structure should be designed in such a way that all primary load elements that can be exposed to hazards are non-critical components. In the second case, critical components that can be exposed to hazards are made strong enough to resist the hazards considered. It should be emphasised that robustness requirements do not imply that all structures should be able to survive removal of any structural element, if no hazards are likely to occur. The starting point is a hazard that is more unlikely to happen than the usual design situations, but not unlikely enough to be neglected. If there is no hazard, then there is no requirement in relation to robustness. Also, only one hazard at the time should be considered.

Annex A5 Robustness requirements in JCSS In the Probabilistic Model Code (JCSS 2002) robustness requirement is

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also formulated as: “A structure should not be damaged by events like fire, explosions or consequences of human errors, deterioration effects, etc. to an extend disproportionate to the severeness of the triggering event”, see also annex A5. In order to attain adequate reliability in relation to accidental loads, two basic strategies are proposed: nonstructural (prevention, protection and mitigation) and structural measures (making the structure strong enough to withstand the loads limiting the amount of structural damage or limiting the amount of structural damage). The robustness requirement in the JCSS Probabilistic Model Code (JCSS 2002) is in section 3.1 and Chapter 8. Below the text from Chapter 8: Annex A: The robustness requirement

A.1 Introduction In clause 3.1, the following robustness requirement has been formulated:

“A structure shall not be damaged by events like fire explosions or consequences of human errors, deterioration effects, etc. to an extent disproportionate to the severeness of the triggering event”. This annex is intended to give some further guidance. No attention is being paid to terrorist actions and actions of war. The general idea is that, whatever the design, proper destructive actions can always be successful. A.2 Structural and nonstructural measures In order to attain adequate safety in relation with accidental loads one or more of the following strategies may be followed: 1. reduction of the probability that the action occurs or reduction of the action intensity (prevention). 2. reduction of the effect of the action on the structure (protection). 3. making the structure strong enough to withstand the loads; 4. limiting the amount of structural damage. 5. mitigation of the consequences of failure.

The strategies 1, 2 and 5 are so called non-structural measures. These measures are considered as being very effective for some specific accidental action. The strategies 3 and 4 are so called structural measures. In general, strategy 3 is extremely expensive in most cases. Strategy 4, on the other hand accepts some members to fail, but requires that the total


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damage is limited. This means that the structure should have sufficient redundancy and possibilities to mobilise so called alternative load paths. In the ideal design procedure, the occurrence and effects of an accidental action (impact, explosion, etc.) are simulated for all possible action scenarios. The damage effect of the structural members is calculated and stability of the remaining structure assessed. Next, the consequences are estimated in terms of number of casualties and economic losses. Various measures can be compared on the basis of economic criteria. A.3 Simplified design procedure The approach sketched in A2 has two disadvantages:

(1) it is extremely complicated. (2) it does not work for unforeseeable hazards. As a result, other more global design strategies have been developed, like the classical requirements on sufficient ductility and tying of elements. Another approach is that one considers the situation where a structural element (beam, column) has been damaged, by whatever event, to such an extent that its normal load bearing capacity has vanished almost completely. For the remaining part of the structure, it is then required that for some relatively short period of time (repair period T) the structure can withstand the "normal" loads with some prescribed reliability: P(R < S in T | one element removed) < ptarget The target reliability in (A1) depends on: • the normal safety target for the building. • the period under consideration (hours, days or months). • the probability that the element under consideration is removed (by other causes then already considered in design). The probability that some element is removed by some cause, not yet considered in design, depends on the sophistication of the design procedure and on the type of structure. For a conventional structure it should, at least in theory, be possible to include all relevant collapse origins in the design. Of course, it will always be possible to think of failure causes not covered by the design, but those will have a remote

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likelihood and may be disregarded on the basis of decision theoretical arguments. For unconventional structures this certainly will not be the case. A.4 Recommendation For unconventional structures, as for instance large structures, the probability of having some unspecified failure cause is substantial. If in addition new materials or new design concepts are used, unexpected failure causes become more likely. This would indicate that for unconventional structures the simplified approach should be recommended.

For conventional structures there is a choice: (1) one might argue that, as one never succeeds in dealing with all failure causes explicitly in a satisfactory way, it has no use to make refined analyses including system effect, accidental actions and so on; this leads to the use of the simplified procedure. (2) one might also eliminate the use of an explicit robustness requirement (A1) as much as possible by taking into the design as many aspects explicitly as possible. Stated as such, it seems that the second approach is more rational, as it offers the possibility to reduce the risks in the most economical way, e.g. by sprinklers (for fire), barriers (for collision), QA (for errors), relief openings (for explosions), artificial damping (for earth quake), maintenance (for deterioration) and so on.

Annex B. Examples / Case studies Annex B1 Siemens Arena and Bad Reichenhall Ice Arena P. Dietsch and J. Munch-Andersen

Two large-span timber roof structures and their failures are presented since the different robustness strategies applied are considered to having significantly influenced the type of failure. One is the Siemens Arena in Ballerup, Denmark and the other the Bad Reichenhall Ice Arena in Germany. The principal structures are described as well as the flaws that are believed to have caused the failures. The robustness of the structures is discussed, including the consequences of the one structure to be statically determinate and the other to be in-determinate. The two cases described serve as examples of different design strategies for large-span timber structures and their consequence for robustness. It is demonstrated that robustness is not a straight forward concept because the best strategy depends on the cause of the failure - which is obviously not known during planning and design. This finding is further described and evaluated in Chapter 5. The structures and their failures Siemens Arena The cycling arena was built in 2001. The main roof structure consisted of 12 trusses, each truss composed of two glulam timber arches with vertical connectors, see (Hansson and Larsen 2005). The upper arch was mainly exposed to compression, the lower to tension. The horizontal component of the tension and compression forces were neutralised at the corner connections, realized with concealed steel plates which were connected to both arches by embedded dowels and a few bolts, see Figure B2. The structure appeared as an elegant slim construction with a free span of 73 metres across the arena. The distance between the trusses was 12 metres. The secondary structure consisted of simply supported purlins.

Two of the trusses collapsed without warning at a time with almost no wind and only a few millimetres of snow. The partial collapse happened

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just a few months after the inauguration of the arena. No people were present in the arena during the collapse.

Figure B1. The Siemens Arena roof structure after the collapse of two trusses. An intact truss can be seen on the right.

Figure B2. Corner connection with concealed steel plates, connecting the timber parts through bolts (visible) and dowels (not visible).

Figure B3. Rupture at the critical cross section in the corner connection. Note the dowels and steel plates.


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An investigation showed that the cause of the failure could be localised to one critical cross-section in the tension arch near the support, where the load-bearing capacity was found to be between 25 and 30% of the required capacity. By mistake, this cross-section was not considered at all in the design. Three critical design errors were identified: • The design strength used for the timber part was almost 50% too high. • The reduced height of the cross section near the ends of the arches, see Figure B2., was not considered. • The reduction of the timber cross section due to steel plates, bolts and dowels, see Figure B3., was not considered. The expected short term load-carrying capacity at the critical cross section happened to be only slightly larger than the loads from the self weight of the structure. Because the strength of timber is reduced over time when it is loaded (the kmod-effect), it is likely that the collapse took place when the strength was reduced to the stresses caused by the self weight. According to Eurocode 5, and confirmed by Hoffmeyer and Sørensen (2007), the reduction factor for medium duration loads (1 week to 6 months) is kmod = 0,8. Such a reduction is enough to explain how the collapse could take place at a time with no special external load. The investigation also revealed that the stability of the trusses was not ensured sufficiently and that the quality of the gluing of the glulam was not as specified. These problems, nevertheless, did not contribute to the actual failure. The collapse did not occur due to an unknown phenomenon. The design of the trusses was not checked by the engineer responsible for the entire structure due to unclear specification of the responsibility and duties of that engineer. This might explain why such a vital error could pass the quality assessment of the design. The demands to the quality assessment of such structures in the Building Regulations have been increased after the incident. An independent third party control is now required. Bad Reichenhall Ice Arena The contents of the following are derived from: Winter, S., Kreuzinger, H., 2008 “The Bad Reichenhall Ice Arena collapse and the necessary

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consequences for wide span timber structures” (Winter and Kreuzinger 2008). The Bad Reichenhall Ice Arena, built in 1971/1972, was a structure of approx. 75 m in length and approx. 48 m in width, see Figure B4 and Figure B7. The roof was supported by 2.87 m high main girders, which were produced as timber box-girders, see Figure B7. The box-girders featured upper and lower glulam members and lateral web boards made from so-called “Kämpf web boards” - a type of cross laminated timber. The 48 m long girders were produced from three 16 m long sections, which were joined with general finger joints.

Figure B4. The Ice Arena in Bad Reichenhall.


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Figure B5. Partial view of the collapsed roof structure.

The secondary system was fixed to the sides of the girders and acted both as purlins and as lateral bracing (K-bracing) for the main box-girders, see Figure B6. This enabled the roof structure to redistribute loads between the girders. On January 2nd 2006, the entire roof collapsed without warning during a period of significant snowfall, see Figure B5. However, the snow load was not above the characteristic snow load used in the design.

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Figure B6. Layout of the roof of the Ice Arena and side view of the girders (Schmidt 1974).


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The design and construction of the girders were identified as one cause for the failure. There were several contributions to the failure: • The review of the structural calculations revealed two important errors. For the assessment of the load-bearing capacity of the box girder, the bending strength of the glulam was applied, rather than the tensile and compressive strength of the lower and upper girder. In addition, the weakening of the cross-sections due to the general finger-joints between the girder parts as well as the web-boards was also not taken into account in the structural calculations. Comparative calculations, based on the technical rules applicable at the time of the construction of the Bad Reichenhall Ice Arena, have shown that the safety factor was only of a magnitude of around 1.5, whereas the required factor was about 2.0. • For the box girder with Kämpf web-boards, a general technical approval was available, which however, limited the height of the web-girders to 1.20 m. Therefore, a so-called “Approval for an Individual Case” by the Supreme Building Authority would have been necessary for executing this special structure. According to the findings to date, such an approval was not applied for. An application in 1971 to extend the general approval to larger heights was not granted by the German Institute for Building Technology. Further, the production of the vertical general finger joints of the web-boards must be regarded as difficult and not very robust. The quality of the glue lines in these finger joints differed significantly. • The box girders were produced using urea-formaldehyde glue. The technical rules both then and now allow the use of this type of glue for load-bearing components only in a dry ambient climate because that glue is not permanently moisture-resistant. Today, it is known that unheated and non-air-conditioned ice arenas represent a particularly critical climate for moisture-sensitive components. Besides, a relative high humidity, the thermal radiation between the ice surface and the roof parts facing the ice surface leads to cooling and thereby increased condensation on these parts of the roof structure. Since that knowledge did not exist in 1972, the use of ureaformaldehyde glue for bonding the load-bearing components did not generally violate the state-of-the-art of technology at that time. However, the general technical rules for using the Kämpf web-boards required the connections between the glulam-girders and the web

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•


boards to be carried out with the significantly more elastic resorcinol glue (RF), due to the thick bonding gaps. The gluing of the blocking between girders and web-boards at the supports did not correspond to the recognised rules at the time as gluing secured by nails was and is limited to a board thickness of max. 35 – 50 mm.

Figure B7. Cross-section of the box-girders in the Ice Arena (Schmidt 1974).

Due to the humidity exposure over the years, the glue-lines and finger joints were significantly damaged. This primarily affected the general finger joints in the lower girder and the bonding between the girders and the web-boards. It was found, that in some cases, there was no adhesive effect to a depth of 50 mm to 80 mm in the lower girders. In combination


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with the errors in the structural calculations, this represents the most significant cause for the collapse of the Bad Reichenhall Ice Arena. In addition, there were repeated cases of water penetration as a result of leaks in the roof membrane and in the area of the roof drainage. These were not permanently rectified and the roof structure did not receive renovation paint during the use of the arena. Whether such measures would have significantly delayed the damage to the glue lines of the roof structure, cannot be answered. The structural calculations for the roof structure appear not to have been examined by a check engineer, even though this was obligatory for special buildings, e.g. assembly or sport halls. Further, it is not documented that any professional examination of the structural integrity has been carried out as part of the maintenance of the building. The arena was initially open on two sides. It is not believed that there were any disadvantageous effects from the subsequent enclosure. Neither is a settlement of the concrete structure thought to have caused significant impact on the roof structure. Robustness considerations Siemens Arena During design, it was decided that the 12 m long purlins between the trusses should only be moderately fastened to the trusses, so that a failure of one truss should not initiate progressive collapse. Each truss then becomes a key element. This strategy proved to work fairly well as “only” two of the 12 trusses collapsed. Considering that all trusses had a much lower strength than required it might be fair to conclude that the extent of the collapse was not disproportionate to the cause.

Another, and perhaps more expensive, strategy against progressive collapse could have been to design the trusses, the purlins and their connections so that a failed truss and the roof could hang in the purlins and transfer the load to the neighbouring trusses (when considered an accidental load case). Had this strategy against progressive collapse been chosen it is most likely that progressive collapse would have occurred because the neighbour trusses could not have withstood the extra load

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from the truss failing first. In this case, the trusses would not have been key elements. Nevertheless, had the cause of the failure been a huge load on one truss or a lone standing mistake in one truss, the second strategy would have been preferable because it significantly reduces the risk of injuries. This strategy might also have worked if e.g. a leaking roof had degraded one truss because it is likely that the other trusses remain unharmed. In that case, large deformations would occur, giving a warning of possible failure. There were two bracing systems in the longitudinal direction, one at each gable. This ensures stability of the remnant part of the building when one truss has failed. This strategy also proved successful, even though there was no wind or snow to call for big demands to the bracing system. Bad Reichenhall Ice Arena Robustness has not been considered, neither during design nor during the lifetime of the building.

The investigation showed that the first failure occurred in one of the three main girders on the east side. Due to the stiff cross bracing, the loads were shifted from the girder that failed to the neighbouring girders. Because these girders suffered from the same mistakes and degradation processes as the girder failing first, they could not sustain the additional load. Consequently, this developed into a progressive collapse which realized within seconds. The ability to redistribute loads, often called redundancy, is generally regarded as favourable for the robustness of a structure because a random local failure will not cause total collapse. This also means that the boxgirders are not key elements in the usual meaning of the term. But since the secondary structure was not only strong but also very stiff, a weak girder would transfer its loads to the adjacent girders without any warning from large deformations. This means that e.g. some general finger joints could have lost their strength long ago. A more robust system could have been achieved in various ways: • A strong but softer secondary system could give warning about redistribution of load taking place due to increasing deformations.


•

111

Since the secondary structure also had to fulfil the purpose of bracing against lateral-torsional buckling of the main girders, it needed to be stiff. If both requirements should have been fulfilled, a different bracing system would have been needed. A statically determinate secondary system with connections, which would allow for one girder to collapse, without increasing the load on the adjacent girders.

A discussion of both structures from a robustness point of view is included in Chapter 5.

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Annex B2 Exemplary comparative calculations on typical purlin systems in timber P. Dietsch

The requirement for a robust structure is often defined as a structure being “designed in such a way that it will not be damaged by events like fire, explosions, impact or consequences of human errors, to an extent disproportionate to the original cause” (CEN 2002). A structure should be insensitive to local failure (disproportionate collapse), thereby including the design against progressive collapse. There are several approaches to demonstrate this, e.g. given in (DS/INF-146 2003). One of these approaches is to demonstrate that a load case “removal of a limited part of the structure” will not lead to extensive failure. This chapter contains exemplary comparative calculations of typical secondary systems for timber roof structures. Comparing the results against typical reasons for damages and failure, it becomes obvious that the objective of load transfer - often mentioned as preferable - should be critically analysed. This finding is further described and evaluated in Chapter 5, including proposals for structural systems and details towards a robust design of wide-span timber structures. Evaluated system

To enable an evaluation of different purlin systems, it was decided to present comparative deterministic calculations based on an exemplary roof geometry as shown in Figure B8 and B9. The chosen roof, featuring an angle of 10° and covering an area of ℓ/w = 30.0/20.0 m2 is supported by 6 primary beams at a distance of e = 6.0 m. It is assumed that the beams be designed to have a utilization factor of η ≈ 0.95. The dead load be gk = 0.5 kN/m2, the snow load be sk = 0.8 kN/m2, the wind load, acting as wind suction should be neglected for this evaluation. The purlins, featuring a cross section of b/h = 100/200 mm2 should be realized with grade C24 timber. Their spacing eP be chosen so that each purlin system has a utilization factor (ULS) of 0.9 < η < 1.0. A possible change in cross section over the roof length (to adapt to the different bending moments) should be neglected. Regarding the ULS verification for bending around both axes, this leads to the spacings e, given in Table B1.


Figure B8. Typical roof geometry.

Figure B9. Isometric sketch of typical timber roof structure.

113

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Table B1. Realizable spacings eP between the purlins at 0.9 < η < 1.0 for different purlin systems and given boundary conditions.

Purlin system

Spacing e

Purlin System

Distance e

Simply supp. beam Gerber beam

1.0 m

Continuous beam

1.3 m

1.3 m

Lap jointed purlin

1.6 m

Comparative deterministic calculations It should now be assessed, how the removal of a limited part of the structure will affect the remaining structure.

Two cases are evaluated: a) Removal of a purlin between two supports (equivalent to the failure/rupture of one purlin). b) Removal of one support (equivalent to the failure of one main beam). Table B2 (given on next page) lists the purlin systems and evaluated case of failure (column 1), indicating the removed member and additional members failing due to system instability (column 2). The increases in bending stress in the remaining purlins (column 3) as well as the load increase on the main beams (column 5) are compared. Columns 4 respectively 6 list the resulting utilisation factors in the accidental load case “situation after an accidental event” (γG = γQ = γM = 1.0; ψ1,snow = 0.5; kmod,acc). Since the system is symmetrical, only elements 1 – 3 are listed. Evaluation of results Damaged area The comparison of damaged area(s) shows that – in the case of simply supported purlins as well as continuous and lap jointed purlin systems failure of one purlin will result in local damage (no other field than the one covered by the failing member will fail due to system instability). The failure of one purlin in a gerber system will – because of system instability - in the worst case result in the additional failure of the two adjacent purlins. This extends the damaged area by 200%, compared to the area covered by the failed member.


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In the case of one main member failing, simply supported purlins as well as continuous and lap jointed purlin systems result in the failure of the adjacent purlins (damage restricted to two fields). In the case of gerber beams, the failure of one main member will in the worst case result in the failure of 3 purlins, thereby extending the damaged area by 50%. Table B2. Evaluated purlin systems, removed members and increase in bending stresses on remaining members.

1 1 Purlin system removed member

2

Max. stress incrAdditional failing members ease due to system instability for

/ Removed Member

2

3

4

5

6

Max. utilisation η

Max. stress increase

Max. utilisation η

remaining purlins 3 Simply supp. beam 4 a) Removal of purlin - no additional purlins failing due to system instability 5 b) Removal of supp. 6 Gerber beam 7 a) Removal of purlin (worst case) 8 b) Removal of supp. (worst case)

for remaining main beams (supports)

--

--

--

--

25% 57%

--

(field 1) 25% 57% 1

(field 1)

--

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9 Continuous beam 10 a) Removal of purlin - no additional purlins (worst failing due to system case) instability 11 b) Removal of supp. - no purlins failing due to (worst system instability, case) - possible failure due to significant overloading of remaining purlins 12 Lap jointed beam 13 a) Removal of purlin (worst case) 14 b) Removal of supp. - no purlins failing due to (worst system instability, case) - possible failure due to significant overloading of remaining purlins

19% 54%

10% 50%

(supp. 2)

(supp. 2)

475% 228% 82% 83% (supp. 2)

(supp. 2)

60% 77% (field 1)

10% 50% (supp. 4)

520% 250% 82% 83% * * (field 1) (supp. 2) * beams designed for field moment, assumed overlap of 0.10*ℓ, resp. 0.17*ℓ.

Load transfer / additional load on remaining members A determinate purlin system, e.g. realized by simply supported purlins has the advantage that failure of one member will not result in substantial overloading of other than the failing members. To achieve this, it is important to design the connections in such a way, that they will not transfer large additional loads in the case of failure (failing member “hinging” itself into the remaining members). This subject is further evaluated in Chapter 5. Likewise, the remaining purlins in gerber systems are subjected to a comparatively small stress increase (max. 25%) after failure of a purlin or main member.


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Redundant systems as continuous and lap jointed purlin systems are more critical in that aspect. A failing purlin will increase the bending stress in the remaining purlin system as well as the loads on the main beams by up to 50%. A failing main beam, hinging itself into the purlin system, will theoretically increase the utilisation factor of the purlins by up to 475% resp. 520%, due to the doubled span. If the purlins will be designed to enable load distribution, the realizable distance e between the purlins would decrease from 1.60 m to 0.70 m to stay below a utilization factor of η ≤ 1.0 (accidental load case). This calculation includes a system factor ksys = 1.1 permitted by EN 1995-1-1 (CEN 2004a), applicable for systems that enable load distribution. A failing main member, hinging itself into a continuous secondary system, will result in an additional loading of the remaining main members of up to 82%, depending on the remaining strength and stiffness of the purlin system (achievable utilisation factor before rupture of the purlins). Applying the accidental load case, this will not result in an utilisation factor η > 0.83. In the case of failure due to local damage, this utilization factor is not critical. But if all members suffer from the same damage due to global effects, it becomes evident that a structure containing systematic mistakes will not be able to withstand a large load increase due to load distribution from one failing member, meaning it is more fragile to collapse progressively. A discussion of the effect of the extent of damage on preferable robustness strategies, including proposals for structural systems and details towards a robust design of large-span timber structures is given in Chapter 5.

Annex B3 Norwegian sports hall P.H. Kirkegaard, D. Čizmar and J.D. Sørensen

A probabilistic based robustness analysis has been performed for a glulam frame structure supporting the roof over the main court in a Norwegian sports centre. The robustness analysis is based on the framework for robustness analysis introduced in the Danish Code of Practice for the Safety of Structures and a probabilistic modelling of the timber material proposed in the Probabilistic Model Code (PMC) of the Joint Committee on Structural Safety (JCSS 2002). Due to the framework in the Danish Code, the timber structure has to be evaluated with respect to the following criteria where at least one should be fulfilled: a) demonstrating

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that those parts of the structure essential for the safety only have little sensitivity with respect to unintentional loads and defects, or b) demonstrating a load case with “removal of a limited part of the structure” in order to document that an extensive failure of the structure will not occur if a limited part of the structure fails, or c) demonstrating sufficient safety of key elements, so that the entire structure with one or more key elements has the same reliability as a structure where robustness is documented by b). Based on investigations with respect to criteria a) and b), the timber frame structure has one column with a reliability index a bit lower than an assumed target level. By removal of three columns one by one, no significant extensive failure of the entire structure or significant parts of it are obtained. Probabilistic model for the Norwegian Sports Arena The Norwegian sports centre has a structural system consisting of 14 glulam frames supporting the roof over the main court, see Figure B10. Each frame consists of one 17.5 m long tapered main beams between two beams with approximately constant cross section. The beams are carried by 5 columns, see Figure B11. The frames are spaced 3 m apart and they support purlins which in turn support a wooden ceiling on which insulation, tar paper, plastic, gravel and turf are placed, see Figure B11. The sports centre was erected in 1999 and had severe shear cracking in three of the 14 glulam frames in March 2003. An analysis of theses damages together with detailed data describing the structure are given in (Bell 2007).

Figure B10. Plan of Norwegian Sports Centre.


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Figure B11. Sections of Norwegian Sports Centre. Failure modes, limit state functions, stochastic model The following sections outline the modelling used for the probabilistic calculations of the Norwegian sports centre by using First-Order Reliability Methods (FORM) where a reliability index βe is estimated based on limit state function g (⋅) for each failure mode, see e.g. (Madsen, Krenk et al. 1986). The probabilistic analysis will be performed with a stochastic model for the glulam frame number 3 with respect to the strength parameters for whole structural elements, and not to the strength for the single laminates and the glue (JCSS 2002).

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Axial Force

Shear Force

Bending

Figure B12. Section forces in glulam frame number 3 due to permanent load and snow load.

Further, second order effects have been neglected for beams subjected to compression and combined compression and bending, respectively. Buckling problems in the beams are assumed to be prevented by purlins


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and other secondary structural components attached to the main structural frame system. For the structural analysis, a linear FEA has been performed where the glulam frame has been modelled by beam elements assuming hinges in joint 3 and 8, respectively. Figure B12 presents section forces for the glulam frame number 3 due to permanent load and a variable snow load. These loads will be described in the next section. The magnitude of the section forces as well as the distribution corresponds to results presented in (Bell 2007). Failure modes Related to ultimate limit state failure for the glulam frame, 10 different failure modes are assumed, due to compression (N), tension (T), bending (M), combination of bending and compression (M+N), shear (V) and combination of tension perpendicular to the grain and shear. Also one service limit state failure mode is considered, i.e. deflection in the main beam. The 11 failure modes have been selected based on the section forces presented in Figure B12 and the conclusions in the report (Frühwald, Serrano et al. 2007) where a survey of a number of structural failures in large timber structures are given. The ultimate limit state failures are assumed to be brittle. This assumption and other failure modes which could be generated due to gross errors, e.g. failure in joints, will be discussed below.

The following failure elements are considered for these failure modes: 1. Failure in column 2-4 (N) 2. Failure in column 6-7 (N) 3. Failure in column 7-9 (N) 4. Failure in column 10-11 (N) 5. Failure in the main beam at point 5 (N+M) 6. Failure in the main beam at point 6 (N+M) 7. Failure in beam 9-11 (M+N) 8. Failure in the main beam at point 4 (V) 9. Failure in the main beam at point 6 (V) 10. Failure due to a combination of tension perpendicular to grain and shear at point 5 11. Failure in the main beam at point 5 due to deflection. These 11 failure modes will be modelled according to the failure criteria stated in (CEN 2004a).

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Limit state functions The short-term ultimate limit state function is given for the failure elements 1-4:

gi = X R −

⎛ a ⋅ G + bi ⋅ Q ⎞ NS ⎟ = XR −⎜ i ⎜ k ⋅k ⋅ f ⋅ A⎟ NR ⎝ mod c c , 0 ⎠

(B1)

where A is the cross section area, fc,0 the compressive strength along grain, XR the model uncertainty , G the permanent load and Q the variable load. kmod is a modification factor taking into account the effect of the duration of load and moisture content. kc is a column instability factor. If the failure function is evaluated in section i, then the internal normal force NS can be divided into a linear combination of the variable load Q, and the permanent load G. This gives N = aiG+biQ where ai and bi are constants depending on the geometry. These constants are obtained by a FEanalysis. The failure elements 5-7 will be modelled with following short-term ultimate limit state function:

⎛ a ⋅ G+bi ⋅ Q ⎛N M⎞ c ⋅ G+ di ⋅ Q ⎞⎟ + km ⋅ i =0 gi = XR −⎜⎜ S + km ⋅ S ⎟⎟ = XR −⎜ i ⎜k ⋅k ⋅ f ⋅ A MR ⎠ kmod⋅ fm,α ⋅W⋅ kh ⎟⎠ ⎝ NR ⎝ mod c,z c,0 (B2) where W is the section modulus. MS and NS are the internal bending moment and normal force, respectively given by linear combinations of the variable load Q and the permanent load G. MR and NR are the capacity values for bending moment and normal compressive force, respectively. fm,α is the bending strength at an angle α to the grain, modelled fm,α =km,α fm where km,α is a reduce factor due to the tapered beam shape. The factor km makes allowance for re-distribution of stresses and the effect of homogeneities of the material in a cross-section and kh is a size effect factor (CEN 2004a).


123

The shear failure elements 8-9 will be modelled with following short-term ultimate limit state function:

gi = X R −

VS 3 ⎡ e ⋅ G + fi ⋅ Q ⎤ = XR ⋅− ⋅⎢ i ⎥=0 VR 2 ⎣ k mod ⋅ A ⋅ f v ⎦

(B3)

where VS is the internal shear force and VR is the capacity value for shear force. VS is given by a linear combination of the variable load Q and the permanent load, G. fv is the shear strength. The failure element 10 for combined tension perpendicular to grain and shear has a short-term ultimate limit state function given by:

⎛V M ⎞ g10 = XR −⎜ S + km ⋅ S ⎟ ⎜V MR,90 ⎟⎠ ⎝ R

⎛ 3 e ⋅ G+ f10 ⋅ Q (c10 ⋅ G+ d10 ⋅ Q) ⋅ kp ⎞⎟ + kp ⋅ = XR −⎜ ⋅ 10 =0 ⎜2 k ⋅ f ⋅ A kdis ⋅ kvol ⋅ kmod⋅ ft,90 ⋅W ⋅ kh ⎟⎠ mod v ⎝

(B4)

where MR,90 is the capacity value for bending moment related to tensile stress perpendicular til the grain. ft,90 is tension strength perpendicular to the grain. kdis is a factor which takes into account the effect of the stress distribution in the apex zone and kvol is a volume factor, respectively (CEN 2004a). The greatest tensile stress perpendicular to the grain is related to the bending moment by the factor kp (CEN 2004a). The deflection failure element 11 is given by the short-term serviceability limit state function:

gi = X R −

wnet , fin

δL

⎛ δ (G ) ⋅ (1 + k def ) + δ ( S ) ⎞ ⎟⎟ = 0 = X R − ⎜⎜ δL ⎝ ⎠

(B5)

where δL is an allowable deflection limit given in (CEN 2004a) and wnet,fin the net deflection given as a linear combination of permanent load G and variable load Q . The deflection contribution from permanent load is multiplied with the deformation factor (1+ kdef) where kdef is a factor for the evaluation of creep deformation due to permanent load.

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Stochastic model The stochastic model is given in Table B.3 and is mainly based on information in (JCSS 2002), (Bell 2007) and (NKB/SAKO 1999). For the calculations permanent load G due to self weight and a variable snow load Q are taken into account. The permanent load of the roof structure, excluding the frame is Normal distributed with an expected value µG = 2.5 kN/m2 and a coefficient of variation (COV) VG= 0.1, respectively. The load width per frame is 3 m. The self-weight of the frame is estimated during the FEA and added to the load from the roof structure and modelled by a Normal distribution with a COV at 10%.

For the region in Norway where the structure is located the annual maximum snow load at the ground Qgk is Gumbel distributed with a characteristic value Qgk = 6.5 kN/m2 corresponding to a 98% quantile in an annual maximum distribution. The snow load at the roof Qgk is determined from:

Qgk = S g ⋅ C

(B6)

where C is a deterministic ground to roof snow load shape factor. Assuming the COV for ground snow load to be VQg=0.4 the expected value μQg is determined from the Gumbel cumulative distribution function FQg(·):

FQg (Qgk ) = exp(− exp(−α (Qgk − β )))

μQg ≈ β +

0.577216

α

, σ Qg =

π α⋅ 6

, VQg =

(B7)

σ Qg μQg

(B8)

which gives μQg=3.13 kN/m2 This value has to be multiplied by 3m to determine the total expected ground snow load per frame. The strength variables fc,o, fv and ft,90 are given as functions of the μfm and Vfm for the bending strength and the expected value for the density μρ (JCSS 2002). The initial (short term) bending strength is assumed to be Lognormal distributed with Vfm=0.15. Assuming a glulam material L40


125

with a characteristic value fm,k=40 MPa corresponding to a 5% quantile value the parameters μ ln fm and σ ln fm of the Lognormal distribution can be determined from the equations:

⎛ ln f m ,k − μ ln fm ⎞ ⎟ F fm ( f mk ) = Φ⎜ ⎜ ⎟ σ ln fm ⎝ ⎠

(B9)

where Φ (⋅) is the cumulative standard normal distribution. Based on the parameters of the Lognormal distribution the expected value for the bending strength becomes μ ln fm =49.9 MPa. The density of the glulam is assumed to have an expected value μρ = 490 kg/m3. The different strength variables are mutually correlated as presented in Table B4. Table B3. Statistical characteristics (N:Normal, G:Gumbel, W:2-pWeibull, D:Deterministic ).

LN:Lognormal,

Variable Distri- Expected bution value

COV

Designation

fm

LN

49.9

0.15

Bending strength (Bell 2007)

fc,0

LN

5 μ ln fm

fv

LN

0.2 μ fm 0.8 Vfm

Bending strength (JCSS 2002)

ft,90

W

0.015 μρ

2.5Vρ

Shear strength (JCSS 2002)

XR

LN

1

0.05

Model uncertainty on short-term bearing capacity (JCSS 2002)

G

N

2.5 kN/m

0.1

Permanent load (Bell 2007) (load width 3 m)

Qg

G

3.13 kN/m 0.4

Variable load – snow (Bell 2007) (load width 3 m)

A

N

1*

0.01

Area, *) multiplied with design value (NKB/SAKO 1999)

W

N

1*

0.01

Modulus,*) multiplied with design

0.45

0.8Vfm Compression strength along grain (JCSS 2002)

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value (NKB/SAKO 1999) kc

N

1*

0.01

Instability,*) multiplied with design value (NKB/SAKO 1999)

C

D

0.8

-

Shape factor for snow (Bell 2007)

kh

D

1*

-

Size effect factor,*) multiplied with design value (CEN 2004a)

km

D

0.7

-

Re-distribution of stresses factor (CEN 2004a)

kdis

D

1.4

-

Stress distribution factor in apex zone (CEN 2004a)

kvol

D

1*

-

Volume factor in apex zone,*) multiplied with design value (CEN 2004)

kmod

D

0.9

-

Strength modification factor (CEN 2004a; JCSS 2002)

kdef

D

1

-

Stiffness modification factor (CEN 2004a; JCSS 2002)

kp

D

0.007

-

Tensile stress perpendicular to the grain factor (CEN 2004a)

δL

D

0.089 mm -

Deflection limit (CEN 2004a)

Table B4. Correlation coefficient matrix for strength parameters.

fm fc,0 fv ft,90

fm 1 0.8 0.4 0.4

fc,0 0.8 1 0.4 0.2

fv 0.4 0.4 1 0.6

ft,90 0.4 0.2 0.6 1

Cross sections area A, cross section modulus W and the instability factor kc are assumed normally distributed with a coefficient of variation of 1 %. All other parameters are assumed to be deterministic as presented in Table B3.


127

Reliability analysis of the glulam frame - identification of key elements For each of the failure elements, formulated in section 3, element reliability βi as well as system reliability βs is estimated using first-order reliability methods (FORM) (Madsen, Krenk et al. 1986). The reliability analysis is performed using the software PRADSS (Program for Reliability Analysis and Design of Structural Systems) (Sørensen 1991).

The element reliability indices βi given in Table B5 indicate that failure element 2 and 11 are the most significant failure modes for the glulam frame. The relative ratio between the different reliability indices corresponds very well to the results from a deterministic analysis in (Bell 2007) where coefficients of utilisation for each failure mode were estimated. E.g. the column 6-7 was found to be over-stressed with approximately 20 % compared with design criterion in the Norwegian building code while another failure mode had coefficients of utilisation in the region 75-90 %. The failure element corresponding to a deflection failure mode has also a relatively low reliability index. However, this estimate is strongly related to the choice of design criterion δL. In the following analysis only ultimate limit state failure modes will be considered. Table B5. Element reliability indices βi, reference period 1 year.

1

2

3

4

5

6

7

8

9

10

11

5.58 3.40 6.55 5.76 6.58 5.37 6.05 4.96 4.81 6.31 3.18

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Table B6. Tentative target reliability indicies β (and associated target failure rates) related to one year reference period and ultimate limit state (JCSS 2002).

Relative cost of safety measure

Minor Moderate Large consequences of consequences of consequences failure failure failure

Large (A)

β = 3.1

β = 3 .3 −3

Normal (B)

( p f ≈ 10 )

( p f ≈ 5 ⋅ 10 )

( p f ≈ 10− 4 )

β = 3 .7

β = 4 .2

β = 4.4

−4

Small (C)

β = 3 .7 −4

−5

( p f ≈ 10 )

( p f ≈ 10 )

( p f ≈ 10− 6 )

β = 4 .2

β = 4.4

β = 4 .7

( p f ≈ 10− 5 )

( p f ≈ 5 ⋅ 10− 6 )

( p f ≈ 10− 6 )

The requirements to the safety of the glulam structure can be expressed in terms of an accepted minimum reliability index, i.e. a target reliability index. The Joint Committee on Structural Safety (JCSS) has proposed target reliability values for ultimate limit states for different type of structures. The values presented in Table B6 (JCSS 2002) are obtained based on cost benefit analyses for the society at characteristic and representative but simple example structures and are compatible with calibration studies and statistical observations. The value in the middle of Table B6 should be considered as the most common design situation. However, it should be noticed that the failure consequence also depend on the type of failure classified as a. Ductile failure with reserve strength capacity. b. Ductile failure with no reserve capacity. c. Brittle failure. Consequently, a structural element likely to result in an un-warned collapse should be designed for a higher reliability level than a structure with a more ductile like collapse scenario. Since the glulam frame is assumed to behave in a brittle mode one could argue for a higher


129

reliability target level. Further, the reliability indices in Table B4 are proposed for a structure with one dominant failure mode, i.e. for a structure with equally important failure modes a higher target reliability level should be considered. The reliability indices in Table B5 indicate only one significant failure mode in ultimate limit state and therefore a target reliability index βt = 4.2 is selected. Compared with a recommend target value the reliability analysis of the glulam frame indicates a structure with a bit too high probability of failure for the column 6-7. So far only reliabilities of individual failure modes or limit states have been considered. Assuming the individual failure modes are combined in a series system of failure elements gi the overall generalised system reliability for the glulam frame is given by: 10

β s ≈ −Φ −1 ( PfS ) , PfS = U ( g i ≤ 0) ≈ 1 − Φ10 ( β , ρ ) i =1

(B10)

The combination of failure elements in a series system can be understood as the glulam frame is non-redundant. In the present paper the generalised system reliability is estimated by the Hohenbichler approximation (Madsen, Krenk et al. 1986) after the element reliability indices have been organised in the vector β and the corresponding correlation between each failure element in the correlation matrix ρ. For the 10 ultimate limit states the generalised system reliability index βS =3.32 is estimated.

130

Annex B. Examples / Case studies s

s

∂β __ μs __ ∂μ β

fm f c,0 fv f t,90 XR

∂β __ σs __ ∂σ β

G Qg A W kc

C kh km k dis k vol k mod k def kp 0.025

0.020

0.015

0.010

0.005

0.005

0.010

0.015

0.020

0.02

Figure B13. Sensitivity of the system reliability to variations of the parameters of the stochastic and deterministic variables.

In order to analyse the sensitivity of the system reliability with respect to stochastic as well as deterministic parameters a sensitivity analysis has been performed. Figure B13 shows the sensitivity of the systems reliability index βS to variations of the expected values µ of the stochastic S S variables ∂β ⋅ μ and standard deviations ∂β ⋅ σ respectively. This ∂μ

βS

∂σ

βS

sensitivity measure, the reliability elasticity coefficient, gives the change in the reliability index in percentages due to 1 % change of one of the parameters. The sensitivities of the system reliability to variations in deterministic parameters are estimated by modelling the deterministic parameters as fixed stochastic variables as presented in Table B3. From Figure B13 it is seen that the largest contribution to the overall uncertainty is due to the compression strength along grain fc,0, column instability factor kc and the cross section area A. Besides that, the model uncertainties turn out to be


131

important. The systems reliability is also seen to be sensitive to variations of the snow load. Reliability analysis of the glulam frame – removal of key elements In the following section, damage scenarios assuming columns with brittle failure modes are considered, see Figure B14. Only three failure modes will be considered due to a potential significant failure of the sports arena.

Figure B14. Four different failure scenarios.

Collapse of column 10-12 is assumed to give a minor significant failure. Horizontal stability is assumed to be fulfilled by the primary structure during failure of one element. This means that following failure scenarios will be considered: 1. 2. 3.

Failure of column 1-4. Failure of column 6-7. Failure of column 7-9.

132


Each failure mode will be considered for the permanent load G, permanent load and extreme snow G+Q and permanent load combined with a daily snow load G+Qd. The assumed daily snow load will be estimated using the Ferry-Borges-Castanheta load model. Figures B15-B17 show the reliability indices for failure of columns 1-4, 6-7 and 7-9, respectively. Notice in Figure B15, that failure element 1 is related to a failure mode with compression in column 1-3. This failure mode will only be considered related to failure scenario 1 where there will be compression in column 1-3, else it is a tension element. From the results in Figure B15-B17, it is seen that the timber structure can be characterised as robust with respect to the robustness framework used for the evaluation. By removal of three different columns one by one, extensive failure of the entire structure or significant parts of it was not observed. However, it is noted that this conclusion is strongly related to the choice of target reliability, the stochastic model of the daily snow load and the modelling of the joints. 18

x: Un-damaged (G+Q) o: Failure column 2-4 (G) +: Failure column 2-4 (G+Qd) *: Failure column 2-4 (G+Q)

16 14 12

βi

10 8 6 t

β s β

4 2 0

0

1

2

3

4 5 6 Failure element

7

8

9

Figure B15. System reliability indices for failure scenario 1.

10


18

133

x: Un-damaged (G+Q) o: Failure column 6-7 (G) +: Failure column 6-7 (G+Qd) *: Failure column 6-7 (G+Q)

16 14 12

βi

10 8 6 t

β s β

4 2 0

0

1

2

3


7

8

9

10

Figure B16. System reliability indices for failure scenario 2. 18

x: Un-damaged o: Failure column 7-9 (G) +: Failure column 7-9 (G+Qd) *: Failure column 7-9 (G+Qe )

16 14 12

βi

10 8 6 t

β s β

4 2 0

0

1

2

3


7

8

9

Figure B17. System reliability indices for failure scenario 3.

10

134


Summary The aim of the present example was to investigate the robustness characteristics of timber structures. The robustness analysis is based on the framework for robustness analysis introduced in the Danish Code of Practice for the Safety of Structures and a probabilistic modelling of the timber material proposed in the Probabilistic Model Code (PMC) of the Joint Committee on Structural Safety (JCSS 2002). The approach has been used for a case considering a glulam frame structure supporting the roof over the main court in a Norwegian sports centre. Compared with a recommend target value, the reliability analysis of the glulam frame indicates a structure with a bit too high probability of failure for one out of 11 considered failure modes. Progressive collapse analyses are carried out by removing three columns one by one implying that the timber structure can be characterised as robust with respect to the robustness framework used for the evaluation. However, the results are obtained based on a simplified modelling of the timber structure which does not consider a non-linear behaviour of the joints. Future investigations should also consider redistribution of load effects, system effects and a modelling of possible gross errors, i.e. unintentional load and defects.

Annex B4 Croatian truss structure D. Čizmar, V. Rajčić, P.H. Kirkegaard, and J.D. Sørensen

The present example discusses robustness of structures in general and the robustness requirements given in the codes. Robustness of timber structures is also an issue, as this is closely related to Working group 3 (Robustness of systems) of the COST E55 project. Finally, an example of a robustness evaluation of a large-span timber truss structure is presented. This structure was built few years ago near Zagreb and has a span of 36,5 m. Reliability analysis of the main members and the system is conducted and based on this a robustness analysis is preformed. Sport Centre in Samobor Many recent structures in Croatia, especially sports halls, swimming pools, tourist objects, passages and pedestrian bridges were built using wood (mainly glulam timber). The total area of the considered sport centre is 5910 m2. It consists of three main parts: 1) main hall with dimensions 36,5x45 m, 9 m height for 600 visitors, 2) swimming pool with dimensions 12, 5x25, 10 m height and depth from 1,8 m to 2,4 m and


135

3) two smaller halls with dimensions 20x15 m. This Chapter will focus on the main hall. The main hall of this sport center was erected in 2005 and it is a plane frame truss spaced equally at 5 meters. The structure was calculated according to Eurocode 5. The design was performed by the Chair for the timber structures at the Faculty of Civil Engineering (Prof. Rajcic), University of Zagreb. Figure B19 shows the built structure while Figure B18 shows the static system. For design characteristic values of permanent load g= 6.38 kN/m, snow load s=7.5 kN/m and wind load w=0.9 kN/m are used. The material is timber GL32k. Based on the design, the following cross section dimensions were chosen: upper chord 20/52 cm, lower chord 20/69 cm and diagonal elements 20/24 cm.

Figure B18. Main structure of the sport centre in Samobor.

Figure B19. Details of tensile and compressive elements.

136


Figure B20. Timber truss structure of the sport hall in Samobor. Probabilistic model In this Chapter, probabilistic calculations were done by First-Order Reliability Methods (FORM) where a reliability index is estimated based on limit state functions for each of the considered failure modes. The probabilistic analysis is performed with a stochastic model for the strength parameters for whole structural elements, and not to the strength for the single laminates and the glue. Second order effects are neglected for beams subjected to compression and combined compression and bending, respectively. Buckling problems and lateral buckling is taken into account as in Eurocode 5 with deterministic coefficients. For the structural analysis, a linear Finite Element analysis has been performed where the glulam truss has been modelled by beam and truss elements. Furthermore, only permanent and snow loads are considered in this probabilistic analysis.

Identification of the significant failure modes of this structure is difficult to perform, since there are many possible failure elements. Based on the deterministic structural analysis four different failure modes are considered: 1) combination of bending and compression (M+N) in the upper chord, 2) combination of bending and tension (M+N) in the lower


137

chord, 3) compression (N) and 4) tension in diagonal elements (N). The ultimate limit state failures are assumed to be brittle i.e. when an element fails there is no possibility for load redistribution. The following failure elements are considered for these failure modes: 1. 2. 3. 4.

Failure in bottom cord (N+M) Failure due to tension in diagonal element (N) Failure due to compression in diagonal element (N) Failure in top chord (N+M)

The stochastic model is shown in Table B7 and is mainly based on information in (Kirkegaard and Sørensen 2008). For the calculations, permanent load G due to self weight and a variable snow load are taken into account. The permanent load of the roof structure, is assumed Normal distributed with an expected value µG = 6.8 kN/m1 and a coefficient of variation COV = 0.1. For the region in Croatia where the structure is located, the annual maximum snow load at the ground is Gumbel distributed with a characteristic value sg,k= 1.5 kN/m2 (7.5 kN/m as the distance between the trusses is 5 meters) corresponding to a 98% quantile in the annual maximum distribution function. Based on this, snow load Qgk on roof can be modelled by: Qgk = S g ⋅ C

(B11)

where Sg refers to snow on ground and C (modelled as deterministic variable according to EC1) is the roof snow load shape factor. It is assumed that the coefficient of variation for the region near Zagreb is COV = 0.58. The following equations show how to calculate the mean value. If COV for ground snow load is assumed to be VQg, then the expected value μQs can be determined from the Gumbel cumulative distribution function FQg(·) as: FQg (Qgk ) = exp(− exp(−α (Qgk − β )))

(B12)

138


μQg ≈ β + VQg =

0.577216

α

, σ Qg =

π α⋅ 6

, (B13)

σ Qg μQg

The strength variables f c , f m and f t (compression strength parallel to grain, bending strength and tensile strength, respectively) are calculated based on the reference properties (JCSS 2002). Table B7 shows all probabilistic variables taken into account (designation, distribution, mean value and coefficient of variation). Correlations between the stochastic variables are taken as in (JCSS 2002). Table B7. Lables, designation of stochastic variables, respective distributions, mean values and COV.

Label

Variable

Distribution

Mean value

COV

Es

MOE

LN

11700

13%

X

Model uncertain.

LN

1.00

10%

a b_d

Joint distance Width of diagonals

N N

304.10 200

1% 4%

h_d

Height of diagonals

N

240

4%

b_dp h_dp b_gp h_gp fc fm ft g s

Width bottom chord Height bottom chord Width top chord Height top chord Compression strengt Bending strength Tension strength Permanent load Snow load

N N N N L L L N G

200 690 200 520 26.6 41.4 24.8 6.80 3.00

4% 4% 4% 4% 12% 15% 18% 10% 58%


139

Reliability analysis of the glulam truss

Table B8. Beta indices for corresponding failure elements (reference period: one year).

Element number

1

2

3

4

Reliability index

4.99

7.76

7.04

4.46

For each of the failure elements, the element reliability index βi is estimated using the first-order reliability method (FORM). The element reliability indices shown in Table B11 indicate that the significant failure modes are 1 and 4. The relative ratio between the different reliability indices corresponds very well to the results from a deterministic analysis. The requirements to the safety of the structure can be expressed in terms of an accepted minimum reliability index, i.e. a target reliability index. The Joint Committee on Structural Safety (JCSS) has proposed target reliability values for ultimate limit states (JCSS 2002). For the normal design situations, the reliability index βi (with a reference period equal to one year) should be larger or equal to 4.2. For the considered failure elements the reliabilities of the components are slightly larger (the lowest beta index is approximately 6% higher than target value given by JCSS). Any mechanical system may be assigned to one of the following three categories: series systems, parallel systems or combination of series and parallel system (also referred to as a hybrid system). In series systems, failure of any element leads to failure of the system. Parallel systems are those systems in which the combined failure of each and every element of the system results in failure of the system. If a system does not satisfy these strict definitions of ‘‘series’’ or ‘‘parallel’’ systems, the system is classified as a hybrid system. Calculation of the reliability of the hybrid structures is not an easy task to perform. It is assumed in this paper (based on the structural analysis) that failure elements 1 and 4 are connected in parallel meaning that only failure of both elements will lead into failure of the structure. The same assumption is made for failure elements 2 and 3, effectively meaning that a simplified system is a union of a two parallel systems as given in Figure B21.

140


Figure B21. System model of the structure.

If we consider a parallel system of n failure elements, then the probability of failure of the parallel system is defined as the intersection of the individual failure events: ⎛ n ⎞ ⎛ n ⎞ p f = P ⎜ I { M i ≤ 0} ⎟ = P ⎜ I{ g i ( X ) ≤ 0} ⎟ ⎝ i =1 ⎠ ⎝ i =1 ⎠

(B14)

The FORM approximation of a parallel system can be written: ⎛n ⎞ p f ≈ P ⎜ I {βiJ − α iT ⋅ U ≤ 0} ⎟ = Φ n , A (− β j , ρ ) ⎝ i =1 ⎠

(B15)

where Φn,A is the multivariate n-dimensional normal distribution function and ρ is the correlation coefficient matrix where the correlation coefficients are obtained from the alpha vectors αi and αj:

ρij = α iT ⋅ α j

(B16)

Equations for the parallel system reliabilities are solved numerically in Mathematica. The probability of failure of the series system is assessed using upper and lower bounds: Pf ≥ max[ P( Fi )] in=1

(B17)


141

n

Pf ≤ 1 − ∏ (1 − P( Fi ))

(B18)

i =1

where a lower and upper bounds correspond respectively to fully correlated and un-correlated safety margins. An estimate of the failure probability is obtained as the arithmetic mean of the upper and lower probability bounds. The system reliability index of the intact structure becomes 5.33, see Figure B22.

β par = 5.33

Pf = 2.23 × 10 −16

Pf = 5 × 10 −8

β sys = 5.33 Pf = 5 × 10 −8

Figure B22. System reliability of the intact structure. Robustness analysis of the glulam truss The structure is statically indeterminate, meaning that a loss of one (or more) structural element(s) will not result in collapse of a whole structure i.e. if any of the inner (truss) elements fail, force redistribution will occur and the whole system will not necessarily collapse. For illustration, the simplified approach explained in detail in (Kirkegaard and Sørensen 2008) is used. For each of the failure elements defined previously failure is assumed (a failed element is assumed to fail in a brittle manner) and the reliability of the remaining failure elements is calculated. It is noted that only one failure element is assumed to fail at a time. In Figure B23, robustness indices are shown for the remaining components after each

142


assumed failure. Generally, after failure of one component, reliability of the other components is decreased (as the redistribution of the forces implies that the other elements have a higher utilization ratio). However, for an assumed failure of element 1 (e.g. failure in the middle of lower chord) the reliability indices for the tensile and compressive truss elements are slightly increased. In this case, redistribution slightly decreased the load effect for elements 2 and 3, but load effect for element 4 is highly increased and it can be concluded that the reliability is, for this scenario, insufficient. It is seen that removal of the four different elements one by one, only for this failure scenario, a significant extensive failure of the entire structure or significant parts of it can be expected. This can be seen in the Figure B23 where the lowest robustness index is 0.3 in case of failure of element 1. For the remaining assumed failures, no significant extensive progressive failures can be expected (robustness indices are very high).

Figure B23. Robustness indices (components).

As given in equation 3, index of robustness is based on the reliability of the system. The same model as given in Figure B22 is assumed. System reliabilities for the damaged state are calculated according to the equations B14-B18.


β par = 2.85

143

Pf = 2.23 × 10 −16

Pf = 2.18 × 10 −3

β sys = 2.85 Pf = 2.18 ×10 − 3

Figure B24. System reliability with damaged element 4.

β par = 1.67 Pf = 4.79 ×10

β par = 8.12 −2

Pf = 2.23 ×10 −16

β sys = 1.67 Pf = 4.79 ×10− 2


144


β par = 5.36

β par = 5.09

Pf = 3.98 × 10

−8

Pf = 1.79 × 10− 7

2.18 ×10 −7 ≥ Pf ≥ 1.79 × 10 −7 Pf ≈ 1.99 ×10 − 7

β sys ≈ 5.07


β par = 5.5 Pf = 1.88 ×10

β par = 5.28 −8

Pf = 6.46 ×10 −8

8.33 ×10 −8 ≥ Pf ≥ 6.46 ×10 −8 Pf ≈ 7.38 ×10 − 7

β sys ≈ 5.25



145

Table B9. System reliability indices.

System Intact Failure of element 1 Failure of element 2 Failure of element 3 Failure of element 4

Reliability index 5.33 1.67 5.07 5.25 2.85

Figure B28. Robustness indices.

In Figures B24 to B27, the reliability indices of the system are shown. Results are summarized in Table B9. It is seen that the lowest system reliability occurs when element 1 has failed. Due to load redistribution, the top chord is heavily loaded implying that the system reliability is relatively low. The same conclusion can be drawn for assumed failure of element 4 - but in this case, the system reliability is much higher. For the assumed damages in the elements 2 and 3 (e.g. tensile and compressive elements), no significant effect on the system reliability is observed, so the robustness index is high. Summary The example considered robustness of structures in general and probabilistic approaches for robustness quantification. Special attention is made with respect to timber structures. The robustness analysis in this chapter is based on the general framework for robustness analysis

146


introduced in the Danish Code of Practice for the Safety of Structures and a probabilistic modelling of the timber material proposed in the Probabilistic Model Code (PMC) of the Joint Committee on Structural Safety (JCSS 2002). Two different approaches were considered: first, reliabilities of the remaining components are compared with the reliability indices of the intact structure, and second, a robustness index is formulated at system level. Compared with a recommend target value, the reliability analysis of the structure shows low probabilities of failure for each of the considered failure modes. Progressive collapse analyses are carried out by removing four elements one by one. The results show that the timber structure for three of the failure scenarios can be characterized as robust with respect to the robustness framework used for the evaluation. However, for one of the failure scenarios the robustness can be considered as relatively low. Robustness analysis made on system level also shows similar results. For assumed damage in two of the truss elements, the structure can be considered robust. Failures of the bottom and top chord of the structure result in a lower robustness index (minimal index is calculated for assumed failure of the lower chord). It is noted that the results obtained here are based on a simplified modelling of the timber structure which does not consider a non-linear behaviour of the joints or non linear behaviour of timber. Future, investigations should also consider system effects and a modelling of possible gross errors, i.e. unintentional loads and defects.

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Design for Robustness of Timber Structures

Design for Robustness of Timber Structures

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