Short description of the semi-probabilistic safety concept

Transcription

1 OVERVIEW Short description of the semi-probabilistic safety concept. Introduction.2 Principles of limit state design.3 Loads and load combinations.4 Base variable.5 Material properties.6 Ultimate limit states design.7 Serviceability limit states design

2 DESIGN. Introduction Short description of the semi-probabilistic safety concept Notes on chapter : This chapter contains a short summary of the currently valid European standards as well as the currently valid design codes for timber structures in Germany and does naturally not claim completeness. It does not replace the detailed regulations of the respective codes and standards, which have to be consulted and perceived as binding during the design of timber structures.. Introduction Timber construction has developed into different regional styles. This development can be attributed to the different building styles of different cultures, regionally differentavailable timber species, and different advancements in research as well as experience [22]. With the increasing unification of Europe and the therein lying wish to reduce restraints and complications in trades, a harmonization of codes and standards has started in the 70 s [22]. With the code series EN 995--:2004/A:2008 [N2] and EN :2006 documents are available today, that are based on proven expertise and allow for a European wide standardized design of timber structures [22]. National annexes expand the base document of the Eurocodes to satisfy regional needs of individual countries. A certain base knowledge is required for the safe application of the semi-probabilistic design concept of Eurocode 5 EN 995--:2004/A:2008 [N2]. The same safety concept is used by the DIN 052:2008 [N6] in Germany, which is part of the reason that the change to the Eurocode 5 is not fully done completed yet. Since the DIN 052:2008 [N6] is an adequate code, some other countries also revert to it for the design of timber structures. Here to however, an adaption has to be done over time. The SHERPA-connector its general construction approval Z from the German Institute for Construction Technology [Deutschen Institut für Bautechnik (DIBt)] [] falls under the regulations of the DIN 052:2008 [N6]. The following sections introduce the methods to design timber structures in accordance the semi-probabilistic safety concept of both codes, EN 995--:2004/A:2008 [N2] and DIN 052:2008 [N6]. Due to the location of the Vinzenz Harrer GmbH in Frohnleiten near Graz, reference is made in certain situations to the Austrian national annex (ÖNORM B 995--:200 [N3]). Afterwards, the ultimate limit sate design and serviceability limit state design according to EN 995--:2004/A:2008 [N2] and DIN 052:2008 [N6] are introduced and compared. The shown calculation models only cover a small part of the respective codes/standards and are under no circumstance to be considered a substitute for the currently valid code documents. Many of the parameters used for the design and sizing of members have underlying natural, statistical deviations. To be able to quantify the therefore arising uncertainties in the calculation models and to minimize the risk of failure, both codes utilize the semi-probabilistic safety concept in their respective design concepts. The European codes for the design of structures are shown in figure. (Abb..). 22

3 . Introduction DESIGN Basis of structural design Structural safety Serviceability Durability Actions (loads) on structures Actions/loads Design of Concrete structures Steel structures Composite structures Design Timber structures Masonry structures Aluminum structures Geotechnical design Design of structures for earthquake resistance Geotechnical and earthquake resistance design Abb..: Overview of the European codes/standards [24] In addition to the definitions of the safety concept in EN 990 Basis of structural design the codes for the loads on structures in the field of timber construction EN 99 Actions (loads) on structures as well as the following specific design codes EN 995 Design of timber structures EN 993 Design of steel structures EN 992 Design of concrete structures EN 998 Design of structures for earthquake resistance are particularly relevant. The design of timber structures is standardized in Europe using the following codes. EN 995--:2004/A:2008 EN :2006 EN 995-2: 2006 Design of timber structures Part -: General Common rules and rules for buildings Design of timber structures Part -2: General rules Structural Fire Design Design of timber structures Part 2: Bridges 23

4 DESIGN.2 Principles of design The respective national code councils have to ability to publish so called national annexes containing specific national regulations, comments and addendums in addition to the afore mentioned base document. All these documents (ÖNORM EN 99x and ÖNORM B 99x) have to be seen and used in conjunction; the mixing other code series (ÖNORM B 4xxx, ÖNORM ENV 99x) is not permitted [N8]..2 Principles of limit state design.2. Preface The on the semi-probabilistic safety concept based family of Eurocodes and other national codes like the DIN 052:2008 [N6], specify the performance of structures through the ultimate, serviceability and durability limit states. If the limit states are exceeded, then the safety and integrity of the structure or the structural system is no longer guaranteed..2.2 Ultimate limit state (ULS) [22] The ultimate limit state describes the state for which an exceeding results in collapse of the structure or to any other type of failure. Indicators of ultimate limit state are: Loss of equilibrium or balance of the entire structure or individual members (assembly/construction stage has to be considered) Loss of stability (especially for slender members) Occurrence of failure mechanisms on the entire structure or individual members.2.3 Serviceability limit state (SLS) [22] Limits of deformation or deflection of a structure due to loads are defined in order to avoid damage (i.e. cracks) in components like ceilings, floors, partition walls, installations/services (mechanical) and others. Specification on usability (deflection, vibration) and appearance of the structure as well as the wellbeing of its users shall also be followed..2.4 Design based on partial safety factors The safety concept followed by the Eurocode and the DIN 052:2008 [N6] is, in contrast to the deterministic safety concept global safety factors ( allowable stress design )[23], based on the design partial safety factors. The safety factors are used to minimize the risk of failure of a structure depending on the assumptions made in the design. Thereby it is to demonstrate that for all significant load combinations, the design loads do not exceed the respective design capacities for any of the limit states. A key advantage of this method is the clear separation of the important parameters in the design of the structure. 24

5 .2 Principles of design DESIGN Some of the important parameters are: Loads: live loads, snow, wind, temperatures,... Material properties: strength, stiffness,... Geometric parameters: dimensions, geometries,... All these parameters are random variables that are subject to statistical variations. Figure.2 (Abb..2) is a graphical representation of the relation between the demand/action E and the resistance R of a member based on typical distribution functions. Both random variables are of varying nature. Failure in this case can be defined by the relationship R E < 0. The limit state is reached in the case where R E = 0. Based on the fact that there is not enough empirical knowledge for both distribution functions, especially for the distribution ends, the semi-probabilistic safety concept is applied to ensure a sufficient, safe distance between prescribed values (characteristic values and design values respectively) of each distribution function. Through the consistent concept of the Eurocodes partial safety factors, the design of structures can be done material independent. The material dependent part of the design can then be done based on the same concepts. With: Nominal safety zone E E mean E k E d R R mean R k R d demand/action mean value of the demand characteristic values of the demand design values of the demand resistance mean value of the resistance characteristic values of the resistance design values of the resistance Abb..2: Semi-probabilistic safety concept Due to the in some cases considerably varying properties of the raw material wood regard to its mechanical properties, the orthotropic (different properties axial, tangential and radial) material and moisture properties (shrinkage and swelling in the afore mentioned directions) as well as the inhomogeneous nature of the material structure, some additional modification factors are introduced to the semi-probabilistic safety concept for the design of timber structures. These additional modification factors allow for example the consideration of different moisture contents, load durations, reduction of the cross-sectional area due to cracks or the time-dependent deformation behavior of timber structures. 25

6 DESIGN.3 Loads and load combinations.3 Loads and load combinations.3. Terms and definitions related to loads/demands Loads/actions under the European code concept means: a group or range of forces (loads) acting on a structure (direct loads) (.5.3. a) [N]), as well as a group or range of imposed deformations or acceleration, for example due to temperature changes, moisture changes, uneven settlement or earthquakes (indirect loads) (.5.3. b) [N]). The following figure gives on overview of loads/actions that have to be considered if necessary in accordance EN 99. Actions (loads) on structures General loads Weights, self-weights, live loads for buildings Live loads for bridges Loads due to cranes and machinery Loads on silos and fluids containers Fire loads on structures Snow loads Wind loads Temperatur effects Loads during construction Extreme loads Abb..3: EN-codes to reflect the effects of loads [24].3.. Effects of loads on structures The loads/actions on a structure cause stresses on members (i.e. internal forces, stresses, strains) or responses of the structure as a whole (i.e. deflections, rotations/torsion). 26

7 .3 Loads and load combinations DESIGN.3..2 Classification of loads/actions Permanent loads (G) ( [N]) Loads that are assumed to always be acting in the same direction and their time dependent variation can be neglected (direct loads/actions, i.e. self-weight of structures, services, and others; indirect loads/actions i.e. shrinkage, uneven settlement and others). Variable loads (Q) ( [N]) Loads that are assumed to not always act in the same directions and their time dependent variation cannot be neglected (i.e. live loads on floors, snow loads, wind loads and others). Extreme or unusual loads (A) ( [N]) Loads that are usually of short duration but significant order of magnitude and their occurrence throughout the live span of the building is of insignificant probability (i.e. fire, explosion, impact, earthquake and others). Design value of loads (G d oder Q d ) ( [N]) Value of the load/action, which is established by multiplying the representative value the partial safety factor. Characteristic value of loads (G k oder Q k ) ( [N]) Most important representative value of loads/actions..3.2 Load combinations (excluding fatigue) Loads on a structure usual occur in combination other (variable) loads, thus combinations under consideration of their respective occurrence probabilities have to be applied. The design situations can be differentiated into permanent situations that correspond to normal usage conditions of the structure; temporary situations that relate to temporary states of the structure (construction, maintenance and others); extreme situations that relate to unusual conditions of the structure, i.e. fire, explosion, impact or results of localized failures; situations during earthquakes that includes earthquake conditions on the structure [23]. The chosen design situations must include all conditions that can reasonably be expected during the construction and use of the structure sufficient accuracy (3.2 (3) [N]). The combination rules follow the general principle: Each load combination should include one dominant variable load (primary load maximum value) or one extreme load (earthquake, impact, others). The effects of other loads (secondary loads) should be considered if deemed meaningful by physical or operational reasons. Each variable load should be considered a primary load. This means that the number of different load combinations equals to the number of the independent of each other occurring variable loads. Out of all load combination, the load combination the least favorable effects on the structural behavior of the structure is governing for the design. The integration of the loads is done using the partial safety factors g G and g Q and combination factors y. 27

8 DESIGN.3 Loads and load combinations.3.2. Combination rules for ultimate limit state design Load combination for permanent (normal situation) and temporary (construction situation) design situations (= base combinations) [N] > (.) E d S G k,j g G,j Q k, g Q, Q k,i g Q,i ψ design value of the load combination joint impacts of (summation) is to be combined design value of permanent load j partial safety factor for permanent load j characteristic value of the dominant variable load partial safety factor for the dominant variable load characteristic value of the accompanying variable load i partial safety factor for the accompanying variable load i combination factor of variable load Since the setting up of the load combinations is connected a relatively large computational effort, simplified rules are presented in the DIN 052:2008 [N6] equation (.2) for the use in building construction. (.2) Note: No simplifications for the load combinations are provided in EN 990. Load combinations for extrem/unusual design situations (fire, explosions,...) [N] (.3) E d A d ψ, ψ 2, ψ 2,i design value of the load combination for extreme/unusual design situations design value of extreme load factor for the frequent dominant variable load factor for the quasi-permanent dominant variable load factor for the quasi-permanent accompanying variable load 28

9 .3 Loads and load combinations DESIGN Load combination for the design situation earthquake [N] (.4) E dae design value of the load combination for the design situation earthquake A Ek characteristic value of loads due to earthquake g I weighting factor (per EN 998) Combination rules for serviceability limit state design The load combinations should be adapted to the structural behavior and the use of the building and the associated serviceability requirements. In general, the condition according to [N] (.5) has to be satisfied. E d C d design value of load at the serviceability limit state design value of limit for the governing serviceability limit state criteria Characteristic combination [N] For non-reversible impacts on a structure (.6) Frequent combination [N] For reversible impacts on a structure (.7) Quasi-permanent combination [N] For long-term impacts (i.e. appearance) on a structure (.8) 29

10 DESIGN.3 Loads and load combinations.3.3 Partial safety factors for loads With the help of partial safety factors, model uncertainties and variations in the loads and their impacts can be considered. Ultimate limit states for verification of equilibrium (EQU) and load-carrying capacity (STR) for members out geotechnical loads Combination Permanent loads Variable loads Unfavorable Favorable Dominant Load Accompanying Load Base combination g G,j,sup G k,j,sup g G,j,inf G k,j,inf g Q, Q k, g Q,i y 0,i Q k,i g G,j,sup =,35 g G,j,inf =,00 g G,j,sup =,0 g G,j,inf = 0,90 g G,j,sup =,35 g G,j,inf =,5 g Q, =,50 g Q,i =,50 g G,j,sup / g G,j,inf G k,j,sup / G k,j,inf y A d A Ed for verifications STR for verifications STR for verifications EQU (i.e. uplift due to wind sucktion; structure is considered a rigid body) for verifications EQU (i.e. uplift due to wind sucktion; structure is considered a rigid body) for verifications EQU (resistances on the member side are taken into account; for combined verifications EQU/STR) for verifications EQU (resistances on the member side are taken into account; for combined verifications EQU/STR) for verifications STR and EQU for unfavorable loads (0 for favorable loads) for verifications STR and EQU for unfavorable loads (0 for favorable loads) partial safety factors for calculations upper / lower bound design values upper / lower bound characteristic value of a permanent load combination factor design value of extreme/unusual load design value of loads due to earthquakes A Ed = g A I Ek (g I... weighting factor) Main Extreme/unusual G k,j,sup G k,j,inf A d (y, or y 2, ) Q k, Other y 2,i Q k,i Earthquake G k,j,sup G k,j,inf g f A Ek oder A Ed y 2,i Q k,i Serviceability limit states Kombination Permanent loads Variable loads Unfavorable Favorable Dominant Accompanying Characteristic G k,j,sup G k,j,inf Q k, y 0,i Q k,i Frequent G k,j,sup G k,j,inf y, Q k, y 2,i Q k,i Quasi-permanent G k,j,sup G k,j,inf y 2, Q k, y 2,i Q k,i Note: For extreme design situations and earthquakes in the ultimate limit state as well as the serviceability limit state design, the partial safety factors are considered as,0. Tab..: Design values for loads and suggested partial safety factors according to EN 990:2003 [N] (summary) 30

11 .3 Loads and load combinations DESIGN.3.4 Combination factors y 0, y and y 2 The combination factors y 0, y and y 2 consider the reduced probability of the simultanious occurance of unfavorable impacts of multiple unrelated variable loads. The loads are divided into Characteristic value of a load [N] The characteristic value of a load is chosen, so that it is not exceeded during the reference period of time. Rare value [N] The combination factor of a rare occurring variable load is used in conjunction a variable load. Frequent value of a variable load [N] The combination factor of a frequently occurring variable load is chosen in such way, that the frequency of exceeding it during the service life is limited to a certain value. Quasi-permanent value of a variable load [N] The combination factor for a quasi-permanently occurring variable load is chosen in such way, that the time frame of exceeding it is a substantial part of the reference period. Loads y 0 y y 2 Live loads for buildings a) Category A: residential buildings 0,7 0,5 0,3 Category B: office buildings 0,7 0,5 0,3 Category C: gathering places 0,7 0,7 0,6 Category D: retail areas 0,7 0,7 0,6 Category E: storage areas,0 0,9 0,8 Category F: vehicle traffic in building construction, vehicle weight 30 kn 0,7 0,7 0,6 Category G: vehicle traffic in building construction, 30 kn < vehicle weight 60 kn 0,7 0,5 0,3 Category H: roofs Snow loads for buildings (per EN 99--3) b) Finland, Iceland, Norway, Sweden 0,7 0,5 0,2 Locations in CEN-member countries an elevation above 000 m above sea-level 0,7 0,5 0,2 Locations in CEN-member countries an elevation below 000 m above sea-level 0,5 0,2 0 Wind loads for buildings (per EN 99--4) c) 0,6 0,2 0 Temperature applications (except fire) for buildings, per EN d) 0,6 0,5 0 Notes: The establishment of the combination factors is given in the national annex. a) Live loads for buildings per EN 99-- b) Snow loads per EN For not explicitly mentioned countries the relevant local conditions should be considered. c) Wind loads per EN d) Temperature variations per EN Tab..2: Suggested partial safety factors according to EN 990 [N] 3

12 DESIGN.4 Base variable.4 Base variable.4. Design value of a strength property (capacity) The design load-carrying capacity of a cross-section, member or connection is determined equation (.9) in timber construction. or (.9) X k or R k characteristic of the strength property or load-carrying capacity k mod modification factor for duration of load and service class per Tab..8 and.9 g M partial safety factor of a material property, per Tab..6 and.7 The modification factor k mod is a safety factor, Is a safety factor, which considers the effect of load duration and moisture content on the capacity of a structure. The safety factor g M is a partial safety factor that consideres unfavorable variations of material properties, model uncertainty and size tolerances..4.2 Loads and environmental influences.4.2. Load-duration classes (KLED) The classification of the duration of load on a building or structure is given in Tab..3 and.4 KLED Order of accumulated duration of characteristic load Beispiele permanent more than 0 years self-weight of structures, equipment, fixed installations and building services long-term 6 month to 0 years storage goods medium-term week to 6 month live loads, snow loads for elevations above 000 m above sea-level short-term less than one week snow loads for elevations up to 000 m above sealevel, wind loads instantaneous less than minute extreme/unusual loads, impact loads, earthquake loads Tab..3: Assignment of structures to KLED according to EN 995--:2004/A:2008 [N2] and ÖNORM B 995--:200 [N3] 32

13 .4 Base variable DESIGN Loads Weights and distributed loads according to DIN 055- Vertical live loads according to DIN A attics, living and habitable spaces B office spaces, work spaces, hallways C rooms, meeting rooms and spaces, serving the accumulation of people ( exception of the categories established in A, B, D and E) D retail spaces E factories and work-shops, stables, storage spaces and access, areas significant accumulation of people F traffic and parking spaces for light vehicles (gross-weight 25 kn) access ramps to such areas G areas for the operation of counterweight forklifts H non-accessible roofs, except for usual maintenance, repairs K helicopter-regular loads T stairs and landings Z entrances, balconies and similar Horizontal live loads according to DIN horizontal loads due to people on balustrades, handrails and other structures that serve as a barrier horizontal loads to achieve adequate lengthwise and cross bracing horizontal loads for helicopter landing pads on roofs - for horizontal live loads - for roll-over protection Wind loads according to DIN Snow loads and ice loads according to DIN building site elevations 000 m above sea-level building site elevations > 000 m above sea-level Impact loads according to DIN Horizontal loads due to the operation of cranes and equipment according to DIN a according to the associated loads KLED permanent medium-term medium-term short-term medium-term long-term medium-term short-term medium-term short-term short-term short-term short-term a short-term short-term instantaneous short-term short-term medium-term instantaneous short-term Tab..4: Assignment of structures to KLED according to DIN 055-, DIN 055-3, DIN 055-4, DIN 055-5, DIN 055-9, DIN and DIN Service classes (NKL) The hygroscopic properties of wood cause an adjustment of the moisture content to the ambient humidity due to moisture absorption and moisture release. The resultant equilibrium moisture content of the wood influences the technological properties of wood ( increasing humidity comes a decrease in strength and E-modulus). Because of the environmental influence on wood components, it is necessary to divide the structures into service classes. They characterize the climatic conditions around the building during its lifetime. Service class Ambient climate temperature relative humidity a Moisture content of common soft-woods Structure or building type 20 C 65 % 2 % interiors of residential, school and administrative buildings 2 20 C 85 % 20 % interiors of utility buildings like storage halls, riding arenas and industrial buildings as well as covered structures outside, of which members are not exposed to the elements (30 angle of rain) > 20% members in the constructive wood protection a The relative humidity in service classes and 2 can exceed the indicated value for a maxium of a few weeks per year. Tab..5: Assignment of structures to service classes according to ÖNORM B 995--:200 [N3] and DIN 052:2008 [N6] 33

14 DESIGN.5 Material properties To reduce cracks due to shrinkage and dimensional changes, wooden members for service classes and 2 should be limited to a moisture content u 20 % at the time of construction and to u 25 % for service class 3 (per DIN 052:2008 [N6])..4.3 Partial safety factors for material properties and resistances Ultimate limit state g M Ultimate limit state g M Base combination Solid timber Glued laminated timber LVL, plywood, OSB Particle boards Fibreboard, hard Fibreboard, medium MDF-fibreboard Fibreboard, soft Connections Nail-plates (steel properties) extreme/unusual combinations,30,25,20,30,30,30,30,30,30,25 General,00 Serviceability limit state General,00 g M permanent and temporary design situations Wood and wood-based materials,30 Steel in connections - dowel-type fasteners loaded in bending - parts loaded in shear and tension for design to the yield strength of the net-section - plate design in load-carrying capacity for nail-plates extreme/unusual combinations,0,25,25 General,00 Serviceability limit state General,00 g M Tab..6: Suggested partial safety factors for material properties according to ÖNORM EN 995--:2009 [N2] Tab..7: Suggested partial safety factors for material properties according to DIN 052:2008 [N6].5 Material properties.5. Strength modification factors to consider the service class and load-duration class Notes from EN 995--:2004/A:2008 [N2] and DIN 052:2008 [N6]: The value of k mod for the shorter load-duration is typically used if a load combination is made up of different load-durations. Notes from EN 995--:2004/A:2008 [N2]: If a connection made of wood parts different time-dependent behavior, then k mod k mod, and k mod,2 of both wood parts is to be established. 34

15 .5 Material properties DESIGN Material (reference standard) Service class Material (reference standard) Service class Solid timber (EN 408-) Glued laminated timber (EN 4080) LVL (EN 4374, EN 4279) Plywood (EN 636-, EN 636-2, EN636-3) OSB/2 a (EN 300) Particle board Typ P4 a, P5 (EN 32) Fibreboard, hard: HB.LA a, HB.HLA, HB.HLA2 (EN 622-2) Load-duration 2 3 Load-duration 2 permanent 0,60 0,60 0,50 permanent 0,30 0,20 long-term 0,70 0,70 0,55 long-term 0,45 0,30 medium-term 0,80 0,80 0,65 medium-term 0,65 0,45 short-term 0,90 0,90 0,70 short-term 0,85 0,60 instantaneous,0,0 0,90 instantaneous,0 0,80 Material (reference standard) Service class Material (reference standard) Service class OSB/3, OSB/4 (EN 300) Particle board Typ P6 a, P7 (EN 32) Fibreboard, medium: MBH.LA a, MBH.LA2 a (EN 622-3) MBH.HLS, MBH.HLS2 (EN 622-3) Fibreboard, MDF: MDF.LA a, MDF.HLS (EN 622-5) Load-duration 2 3 Load-duration 2 permanent 0,40 0,30 permanent 0,20 long-term 0,50 0,40 long-term 0,40 medium-term 0,70 0,55 medium-term 0,60 short-term 0,90 0,70 short-term 0,80 0,45 instantaneous,0 0,90 instantaneous,0 0,80 a Applicable to service class only Tab..8: Suggested modification factors k mod according to EN 995--:2004/A:2008 [N2] Material Service class Material (reference standard) Service class Solid timber Glued laminated timber Laminated wood beams LVL X-lam Plywood Resin bonded particle board Cement bonded particle board Fibreboard, Typ HB.HLA2 (DIN EN 622-2: ) Load-duration 2 3 Load-duration 2 permanent 0,60 0,60 0,50 permanent 0,30 0,20 long-term 0,70 0,70 0,55 long-term 0,45 0,30 medium-term 0,80 0,80 0,65 medium-term 0,65 0,45 short-term 0,90 0,90 0,70 short-term 0,85 0,60 instantaneous,0,0 0,90 instantaneous,0 0,80 Material (reference standard) Service class Material (reference standard) Service class OSB-sheets, Typen OSB/2 a, OSB/3 und OSB/4 (DIN EN 300: ) Fibreboard a, Typ MBH.LA2 (DIN EN 622-3: ) Gipsum board, Typen GKB a, GKF a, GKBI and GKFI (DIN 880) Load-duration 2 3 Load-duration 2 permanent 0,40 0,30 permanent 0,20 0,5 long-term 0,50 0,40 long-term 0,40 0,30 medium-term 0,70 0,55 medium-term 0,60 0,45 short-term 0,90 0,70 short-term 0,80 0,60 instantaneous,0 0,90 instantaneous,0 0,80 a service class only Tab..9: Suggested modification factors k mod according to DIN 052:2008 [N6] 35

16 DESIGN.5 Material properties Material (reference standard) Solid timber (EN 408-) Glued laminated timber (EN 4080) LVL (EN 4374, EN 4279) Plywood (EN 636-, EN , EN 636-3) OSB/3, OSB/4 (EN 300) Particle board, Typ P6, P7 (EN 32) Application in service class only 2 Application in service class and 2 only Service class Service class Material (reference standard) ,60 0,80 2,00 0,80,00 2,50,50 2,25 OSB/2 (EN 300) Particle board, Typ P4, Typ P5 (EN 32) Fibreboard, hard: HB.LA, HB.LA, HB.LA2 (EN 622-2) Fibreboard, MDF: MDF.LA, MDF.HLS (EN 622-5) Fibreboard, medium: MBH.LA, MBH.LA2, MBH.HLS, MBH.HLS2 (EN 622-3) 2,25 3,00 3,00 4,00 Note: Universally finger jointed members according to EN 387 for which in connection the grain direction changes, can not be used in service class 3. Tab..0: Suggested deformation factor k def according to EN 995--:2004/A:2008 [N2] Notes to EN 995--:2004/A:2008 [N2]: For connections made of wood members the same time-dependent behavior, then the value of k def has to be doubled. Is a connection made of wood members different time-dependent behavior, then the value of k def the deformation factors k def, and k def,2 of both mambers has to be established Material Solid timber a Glued laminated timber LVL b Laminated wood beams X-lam Plywood LVL c Service class Service class Material (reference standard) ,60 0,80 2,00 0,80,00 2,50 Resin bonded particle board Cement bonded particle board Fibreboard, Typ HB.LA2 (DIN 622-2: ) Fibreboard, Typ MBH.LA2 (DIN 622-3: ) OSB-sheets,50 2,25 Gipsum board 2,25 3,00 3,00 4,00 a The values of k def for solid timber, a moisture content of fibre saturation or higher at the time of installation and that can dry out after installation have to be increased by,0. b all veneers parallel to the grain c perpendicular veneers Tab..: Suggested deformation factor k def according to DIN 052:2008 [N6] Notes to DIN 052:2008 [N6]: If the permanent load portion > 70 % of the total load, then the stiffness of members loaded in compresion has to be reduced by a factor of / (+k def ). For structures made of members different time-dependent behaviors, the stiffness of the individual members should be reduced by a factor of / (+k def ). For structures made of wood or wood-based materials different k def -values, the arithmetic mean is to be used. The deformation factor of the wood has to be used for steel plate-wood connections. 36

17 .5 Material properties DESIGN.5.2 Material characteristics Material properties are specified by characteristic values that correspond to an assumed percentile value of a statistical distribution. In general, these are 5 %-percentile for strength values and densities, and 5 %-percentile or mean value for stiffness Solid timber Strength properties [N/mm²] Soft-wood C4 C6 C8 C20 C22 C24 C27 C30 C35 C40 C45 3 C50 3 bending f m,k tension parallel f t,0,k tension perpendicular f t,90,k 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 compression parallel f c,0,k compression perpendicular f c,90,k 2,0 2,2 2,2 2,3 2,4 2,5 2,6 2,7 2,8 2,9 3, 3,2 shear,4,a,b f v,k 3,0 3,2 3,4 3,6 3,8 4,0 4,0 4,0 4,0 4,0 4,0 4,0 Stiffness properties [kn/mm²] mean value of the modulus of elasticity parallel E 0,mean ,5 0, %-percentile of the modulus of elasticity E 0,05 4,7 5,4 6,0 6,4 6,7 7,4 7,7 8,0 8,7 9,4 0,0 0,7 parallel mean value of the modulus of elasticity E 90,mean 0,23 0,27 0,30 0,32 0,33 0,37 0,38 0,40 0,43 0,47 0,50 0,53 perpendicular mean value of the shear modulus G mean 0,44 0,50 0,56 0,59 0,63 0,69 0,72 0,75 0,8 0,88 0,94,00 Density [kg/m³] density r k mean value of the density r k,mean Notes to EN 338:2009: The vaues presented above for tension-, compression- and shear strength, the 5%-percentile of the modulus of elasticity, the mean value of the modulus of elasticity perpendicular to the grain and the mean value of the shear modulus were calculated the equations of appendix A of EN 338: The tabulated properties are valid for wood common moisture content at 20 C and 65% relative humidity. 3 It is possible that timber of the class C45 and C50 are not always available. 4 The characteristic values for shear strength according to EN 408 are established for wood out cracks. The effect of cracks should be described in the design stnadards/codes. Notes: a In DIN 052:2008 differnt from EN 338:2009 a shear strength of f v,k = 2,0 N/mm² is defined for all strength classes. b In ÖNORM B 995--:200 different from EN 338:2009 a characteristic values for the shear strength of f v,k = 3, N/mm 2 is defined for all strength classes (is currently being investigated scientifically and is in discussion). Tab..2: Characteristic strength values for soft-wood according to ÖNORM EN 338:2009 [N4], ÖNORM B 995--:200 [N3] and DIN 052:2008 [N6] 37

18 DESIGN.5 Material properties Glued laminated timber Glued laminated timber (BSH) consists of lamellae, from kiln dried wood, glued together. The rigid planar bond of the lamellas does not have to be verified in the design. Cross-sections homogeneous (h) and combined (c) lay-ups (see figure (Abb.).4) are available. Strength properties [N/mm²] Strength classes of glued laminated timber homogeneous glulam combined glulam GL 24h GL 28h GL 32h GL 36h GL 24c GL28c GL 32c GL 36c bending f m,g,k tension parallel f t,0,g,k 6,5 9,5 22, ,5 9,5 22,5 tension perpendicular a f t,90,g,k 0,4 0,45 0,5 0,6 0,35 0,4 0,45 0,5 compression parallel f c,0,g,k 24 26, ,5 29 compression perpendicular f c,90,g,k 2,7 3,0 3,3 3,6 2,4 2,7 3,0 3,3 shear,b f v,g,k 2,7 3,2 3,8 4,3 2,2 2,7 3,2 3,8 Stiffness properties [N/mm²] mean value of the modulus of elasticity parallel 5%-percentile of the modulus of elasticity parallel mean value of the modulus of elasticity perpendicular mean value of the shear modulus Density [kg/m³] E 0,g,mean E 0,g, E 90,g,mean G g,mean density r g,k Notes to ÖNORM B 995--:2009: Different to the specifications in EN 994:999 for all glued laminated timber stregth classes a strength value for shear of f v,g,k = 3,0 N/mm² has to be used. The effect of cracks has to be considered in the shear design verification factor k cr. Notes to DIN 052:2008: a In DIN 052:2008 different to EN 94:999 for all glued laminated timber strength classes a characteristic value for the tension perpendicular to the grain strength of f t,90,g,k = 0,5 N/mm² is specified. b In DIN 052:2008 different to EN 94:999 for all glued laminated timber strength classes a characteristic value for the shear strength of f v,g,k = 2,5 N/mm² is specified. Tab..3: Characteristic strength values for glued laminated timber according to ÖNORM EN 94:999 [N5] and DIN 052:2008 [N6] Abb..4: Example of the cross-section configuration for upright rectangular cross-section loaded in bending homogeneous section combined section GL 28c 00 38

19 .6 Ultimate limit state design DESIGN.6 Ultimate limit state design.6. Preface As part of the design of structures / buildings the following verifications according to EN 990 (6.4. [N]) have to be provided: EQU (equilibrium) Loss of equilibrium of the structure or any of its members, which can be considered a rigid body [24] STR (structural failure) Failure or excessive deformation of the entire structure or individual parts, were the load-carrying capacity and strength of the members becomes governing (stability) [24] GEO (geotechnic) Failure and/or excessive deformation of the ground [24] FAT (fatique) Fatigue failure of the entire structure or individual members [24] (.0) (.) (.2) E d,dst R d,stb E d R d design value of the impact of destabilizing loads design value of the impact of stabilizing loads design value of the impact of the loads design value of the corresponding load-carrying capacity The ultimate limit state design can be done through the stress states (.3) or through the comparison of the internal forces the resistances of the materials. (.4) 00 39

20 DESIGN.6 Ultimate limit state xxxxxx design structure, construct / materials, connections engineering modeling: support conditions, node definition demands/loads: permanent and variable loads characteristic loads strength: material properties, strength parameter characteristic capacities determination of the characteristic internal forces by I. or II. order theory verification of equilibrium (EQU) at ultimate limit state: cross-section and stability (STR/GEO) design design values of load from load combinations partial safety factors γ G or γ Q respectively and the combination factor y 0 design value of material property partial safety factors γ M and the combination factor k mod determination of the governing design situation depending on the load-duration class (KLED) design value of the load E d design value of capacity R d Abb..5 : Flow diagram of the ultimate limit state design.6.2 Cross-section design according to [N3] and [N6].6.2. Tension parallel to the grain With the characteristic values of the permanent loads G k and the variable loads Q k together the relevant load combination, the design value of the tension load s t,0,d can be established. It is then compared to the design value of the tension strength f t,0,d. During the design of the cross-section capacity, any existing cross-section reductions have to be considered (A Netto ~ 0,3 A Brutto to 0,8 A Brutto (depending on the connection type)). The stresses have to satisfy the following condition: (.5) design value of the tension stress design value of the tension strength 00 40

21 xxxxxx.6 Ultimate limit state design DESIGN Compression parallel to the grain The design values for compression parallel to the grain s c,0,d of the relevant load combination, has to be compared to the design value of the compression strength f c,0,d. The stresses have to satisfy the following condition: (.6) design value of the compression stress design value of the compression strength Compression perpendicular to the grain Due to the anisotropic properties, wood has different properties depending on the direction it is stressed. Furthermore, the resistance and the deformation behavior of members out a projection beyond the end- grain in the area of load application is worse than in situations a load application in areas protruding wood fibers. If a wooden member loaded over the entire surface, then the wood fibers behave like pipes stacked on top of each other and are squeezed together in the plastic range [22]. If instead only a partial area is loaded, the stiffness increases. This can be explained the so called linking-effect of the fibers that are protruding the loaded area [25]. 00 4

22 DESIGN.6 Ultimate limit state design Material continuously supported l 2 h type of load application local supported l < 2 h Solid timber from soft-woods,25,50,00 Glued laminated timber from soft-wood,50,75 a,00 a Provided the following applies: l 400 mm, otherwise l = 400 mm or k c,90 =,00 can be assumed. : l... contact length l... spacing of loads h... height of the member Note: Should the factor k c,90 be not know, a conservative value of,00 can be applied. Tab..4: Factor for compression perpendicular to the grain k c,90 according to EN 995--:2004/A:2008 [N2] The stresses have to satisfy the following condition: (.7) design value of the compression perpendicular to the grain stress design value of the compression perpendicular to the grain strength k c,90 factor for compression perpendicular to the grain per Tab..4 For the effective compression area A ef perpendicular to the grain it is permitted to increase the actual contact length by up to 30 mm on each side due to the link-effect parallel to the grain Compression at an angle to the grain For 0 < a < 90 the following verification have to be done: Verification according to EN 995--:2004/A:2008 [N2] (.8) 42

23 .6 Ultimate limit state design DESIGN Verification according to DIN 052:2008 [N6] (.9) (.20) (.2) design value of the compression stress a angle between the load direction and the grain direction of the wood k c,90 factor for compression perpendicular to the grain per Tab..4 Note: The design value of the shear strength f v,d for soft-wood solid timber, glued laminated timber and laminated wood beams can be increased by 40% (0.2.5 [N6]) Bending For beams adequate dimensions and support conditions, for which the risk of lateral torsional buckling can be excluded, the bending stresses may be calculated using the linear elasticity theory. For beams that may tip over, additional stability verifications against lateral torsion buckling have to be carried out. Note: In order to consider the stress re-distributions due to the inhomogeneous character of the material, the EN 995--:2004/A:2008 uses the modification factor k m. In DIN 052:2008 the modification factor for the inhomogeneous character of the material is called k red, whereas the factor k m is used as instability factor. The stresses have to satisfy the following condition: (.22) design value of the bending stress for rectangular cross-section (.23) k m = 0,7 k m =,0 factor for rectangular cross-sections of solid timber, glued laminated timber and laminated wood beams (Note: In DIN 052:2008 the ratio h/b 4 has to be satisfied). factor for other cross-sections 43

24 DESIGN.6 Ultimate limit state design Bending and tension For combinations of bending and tension, the following conditions according equation (.24) and (.25) have to be satisfied: (.24) (.25) k m as per Bending and compression For combinations of bending and tension, the following conditions according equation (.26) and (.27) have to be satisfied: (.26) (.27) k m as per Shear due to shear force For shear and rolling shear equation (.28) as to be satisfied: (.28) design value of the maximum shear stress for rectangular cross-section For the design in shear of members loaded in bending, the effect of possible cracks according to EN 995--:2004/A:2008 [N2] should be done by reducing the cross-section width factor k cr. This factor is already included in the shear strength values found in DIN 052:2008 [N6]. 44

25 .6 Ultimate limit state design DESIGN k cr = 0,67 for solid timber k cr = 0,67 ) for glued laminated timber k cr =,00 for other wood based products according to EN 3986 and EN 4374 ) According to ÖNORM B [N3] the design for all strength classes of glued laminated timber is to be done using the crack factor k cr = 0,83, in combination the constant characteristic strength value for shear of f v,k = 3,0 N/mm². In accordance DIN 052:2008 [N6] for design sutiations of double bending for rectangular cross-sections, the following condition has to be satisfied: (.29) Note: In EN no information about this type of loading and design is provided Torsion For cross-sections loaded in torsion, it is permitted to determine the torsion stresses the same way as it is done for isotropic materials. For the design according to DIN 052:2008 [N6] the equation (.30) has to be satisfied: (.30) For the design according to EN 995--:2004/A:2008 [N2] equation (.3) applies: (.3) for a circular cross-section for a rectangular cross-section (.32) tor,d f v,d k shape h b design value of the torsion stress design value of the shear strength factor depending on the shape of the cross-section larger cross-section dimension smaller cross-section dimension 45

26 DESIGN.6 Ultimate limit state design Shear due to shear force and torsion According to DIN 052:2008 [N6] the condition of equation (.33) (.33) has to be satisfied. Note: In EN 995--:2004/A:2008 no information about the type of loading is provided..6.3 Member design (verification of stability).6.3. Preface Members loaded in compression can become instable before reaching their cross-sectional capacity and lose their capacity due to large deformations. Therefore they have to be dimensioned and designed accordingly. Following the design per DIN 052:2008 [N6] for compression members according the so called substitute member method is shown. For the design according to EN 995--:2004/A:2008 [N2] it is referred to the specifications of section 6.3 of the mentioned standard Compression members normal centric compression load The following condition has to be satisfied: (.34) The buckling factor k c is (.35) and (.36) b c = 0,2 b c = 0, for solid timber and laminated wood beams for glued laminated timber and wood based materials related slenderness ratio (.37) 46

27 .6 Ultimate limit state design DESIGN Here is: s c,crit l = l ef / i i l ef = b s oder b h b s or h critical compression stress, established the 5%-percentile of the stiffness parameters slenderness ratio radius of inertia substitute member length buckling length factor member length Bending member out compression force Bending members have to be secured against rotation at the supports. The following condition has to be satisfied: (.38) The instability factor k m is (.39) the related instability slenderness ratio (.40) Here is: s m,crit critical compression stress, established the 5%-percentile of the stiffness parameters J z second moment of inertia about the z-axis, J t torsional moment of inertia section modulud W y For bending memebers rectangular cross-section of width b and height h, the related instability slenderness ratio can be established (.4) For bending memebers from glued laminated timber it is permitted to establish the related instability slenderness ratio l rel,m and the critical bending stress s m,crit respectively, as the product of the 5%-percentile values of the stiffness parameters multiplied by the factor,4. 47

28 DESIGN.6 Ultimate limit state design For a single span beam on fixed supports constant bending moment, is the substitute member length l ef equal to the clear span l of the beam. The substitute member length l ef for other loads and support conditions can be calculated according to appendix E of DIN 052:2008 [N6]. For bending members that are secured against lateral displacement of the compressed edge along the entire beam, k m = can be used. For bending members rectangular cross-section and, k m = can be used. Here b is the member width Members in bending and compression The following conditions have to be satisfied: (.42) and (.43) k c,y buckling factor per equation (Glg. (.35)) for buckling about the y-axis k c,z buckling factor per equation (Glg. (.35)) for buckling about the z-axis k m instability factor per equation (Glg. (.39)) k red factor per section Members in bending and tension The following conditions have to be satisfied: (.44) and (.45) k m instability factor per equation (Glg. (.39)) k red factor per section

29 .7 Common serviceability limit states design DESIGN.7 Serviceability limit states design.7. Deflection limits for bending members The allowable deformations and deflections of structures should be tailored to the planned use. In Tab..5 suggestions for allowable deflections of bending members are made. Value of deflection bending member Deflection limit cantilever beam characteristic design situation quasi-permanent design situation w Q,inst l / 300 l k / 50 w fin - w Q,inst l / 200 l k / 00 w fin - w 0 a) l / 200 l k / 00 a) In ÖNORM B the limits are given as l/250 and l k /25 respectively. Tab..5: Suggested deflection limits accordin to ÖNORM B 995--:200 [N3] and DIN 052:2008 [N6] Here is: w G w Q w 0 deflection due to permanent load deflection due to variable load camber (if available) Abb..6: Deflection components To account for creep, the factor k def per Tab..0 and Tab.. respectively have to be used. 49

30 DESIGN.7 Common serviceability limit states design.7.2 Serviceability limit state design The deflection according to DIN 052:2008 [N6] can be established using the following equation: ) Equation to establish the final deflection w G,fin due to permanent loads (.46) 2) Equation to establish the final deflection w Q,fin due to variable loads (a) for the characteristic (rare) design situation - dominant variable loads (.47) - additional variable loads (b) for the quasi-permanent design situation - for all variable loads (.48) (.49) For vibration design of residental floors/ceilings the specifications provided in section 9.3 of DIN 052:2008 [N6] and section 7.3 of EN 995--:2004/A:2008 [N2] respectively as well as the information provided in section 5.7 of the national annex of ÖNORM B 995--:200 [N3] have to be followed