Safety variations in steel designed using Eurocode 3

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1 JCSS Wokshop on eliability Based Code Calibation Safety vaiations in steel designed using Euocode 3 Mike Byfield Canfield Univesity Swindon, SN6 8LA, UK David Nethecot Impeial College London SW7 2BU, UK Abstact It is established that the diffeent design tasks coveed by a stuctual code should confom to a simila level of eliability. This wok demonstates a wide vaiation in the eliability of selected design tasks taken fom Euocode 3. A simple method of coecting this is poposed. In cetain cases this will poduce significant gains in economy; in othes it will impove safety. Keywods: Calibation, Codes, Design, eliability, Steel Stuctues, Stuctual Safety. 1 Intoduction The stuctual Euocodes contain thousands of design expessions fo pedicting the esistance of diffeent components in a ange of situations fo thei complete set of stuctual mateials. These expessions vay in quality, as measued by thei ability to coelate accuately against test data. Some failue modes ae highly epeatable and easy to model, such as the bending failue of lateally estained beams. Othe modes, often involving a high degee of instability, equie complex design expessions to cove all the contolling paametes and physical effects yet poduce only elatively cude coelation with expeiments. Such modes include the shea buckling esistance of plate gides. The numeical values selected fo patial safety factos on esistance, M -factos, have the potential to significantly affect the economics of one constuction mateial ove anothe. CEN, the body esponsible fo dafting the Euocodes, have adopted what is known as a boxed values appoach to M -factos. The system woks by pemitting each membe state to select its own M values. These ae known as boxed values and ae applied to a whole host of diffeent esistance functions. Fo example, M1 is applied to the ange of design expessions concened with buckling in steel constuction. This system is attactive since it gives each membe state the feedom to adjust the elative economies achieved by the codes to the levels aleady achieved by the existing national standads. Howeve, as this pape will demonstate, the numeous expessions govened by M1 include some highly eliable design tasks, and othes fo which the boxed value poduces eliability levels fa lowe than desied fo safe design. The pobability of the esistance of a stuctual membe falling below the design esistance (not the pobability of failue) is influenced by 4 factos: eliability of mateial popeties eliability of geometic popeties Design expession accuacy 1

2 JCSS Wokshop on eliability Based Code Calibation The value of patial safety facto, M A suvey of the eliability of basic mateial and geometic popeties fo hot olled steel sections has ecently been caied out, based on ove 7000 mill test esults fom two leading EU poduces [1]. The suvey found that steel is poduced to a highe quality than was assumed duing the calibation of the safety factos fo Euocode 3-1 [2]. Vaiability of mateial and geometic popeties was found to have little impact on eliability. Indeed, the wok showed that the assumptions concening vaiability used duing the EC3 calibation ae consevative, being based on suveys caied out in the ealy 1970 s [3]. Subsequent wok [6,7] has indicated that accuacy of the design expession has by fa the geatest impact on design eliability. This pape examines whethe a link exists between design eliability and the complexity of the stuctual phenomenon being consideed. Thus, the pobability of esistance falling below design esistance is established fo thee adically diffeent esistance functions: 1. The tensile load capacity of odinay bolts 2. Bending moment capacity of lateally estained beams 3. Shea buckling esistance of plate gides The analysis shows that eliability levels vay consideably between these thee diffeent esistance functions. This lack of unifomity is due to the inability of the pesent system to accommodate the lage vaiations that exist in the quality of the design expessions. The impotance to each membe state of being able to adjust the elative economics of the codes is ecognised and an adjustment to the Euocodes is poposed that enable eliability levels to become moe unifom. The new method elies on an additional safety facto embedded within the esistance functions, supplementing the existing boxed-value patial safety factos. In situations such as estained beam design, the appoach will lead to substantial design economies. Convesely, safety factos may have to be inceased whee eliability would othewise fall shot of the taget eliability. 2 Basis of M calibation The objective of calibation is to povide a scientific basis fo selecting values fo the - factos that ensue a given (o taget) level of confidence in achieving safe design; i.e. the pobability of esistance () minus load (S) < 0 is suitably small. If the statistical distibutions of and S ae known as illustated in Fig. 1, then the pobability that (-S) will fall below zeo may be epesented in tems of the safety index β. Whee β is the numbe of standad deviations (σ -S ) between the mean of -S (µ -S ) and the oigin, as illustated in Fig. 1. The logaithmic nomal pobability distibution function is used to model both and S. Basic geometic and mateial popeties ae also assumed to be lognomally distibuted [4]. A lognomal distibution has the advantage that it does not poduce negative values. 2

3 JCSS Wokshop on eliability Based Code Calibation β.σ -S Loading (S) µ -S - S esistance () 0 Fig. 1: Assumed distibutions of, S and -S 3 The taget eliability The Stuctual Euocodes aim to povide a pobability of the esistance of stuctual components falling below the design esistance (P(< d )) of This is known as the taget eliability and is not the pobability of failue. The design esistance is given by: n d = (1) M Whee M is the patial safety facto on esistance and the nominal esistance n is calculated using manufactue s values of geometic and mateial popeties. This is sometimes called the chaacteistic esistance, which is misleading. Whilst manufactues specify chaacteistic values (95% confidence limit) fo mateial stength, they specify mean values fo geometic popeties such as web thickness. Fo this and othe easons esistances calculated using nominal mateial and geometical popeties ae not chaacteistic values, i.e. they do not epesent the 95% confidence limit. Ln[ d ] u d.ζ λ fequency log esistance (ln[]) Fig. 2: The statistical basis of the eliability calculations 4 The calculation of P(< d ) Fig. 2 shows the basis of the eliability calculations, with the log design esistance, Ln( d ), located u d numbe of standad deviations ( ˆζ ) fom the mean of log esistance ( ˆλ ) i.e: 3

4 JCSS Wokshop on eliability Based Code Calibation ln d = λˆ ˆ u dζ (2) λˆ ln d eaanging, u d = (3) ζˆ The taget eliability is achieved when u d = 3.04 with a sample size n. This coelates to a P(< d ) of If u d 3.04 and the sample size is small then fom Student s t-distibution we can detemine the pobability of esistance falling below design esistance, i.e: ( ) λˆ ln d P < d = Φ n 1 ζˆ (4) Whee: 2 Standad deviation of log esistance, ζ ˆ = ln( 1+ vˆ ) (5) ˆ 2 And the mean value of log esistance, ˆ ζ λ = ln( bm ) 2 (6) Vˆ is the coefficient of vaiation of esistance is the esistance calculated using mean values of basic vaiables. m b is a measue of any diffeence between expeimental and pedicted esistances; i.e, a b of 1.10 epesents a esistance function that on aveage undeestimates esistance by 10%. Altenatively the safety facto equied to achieve the taget eliability (known as detemined diectly fom: n = 0.5 exp λˆ n + 1 / n t ζˆ [ (( ) ) ] n 1 ) can be Whee the t n-1 facto is deived fom student s t-distibution fo a pobability of This poduces essentially the same esult as the method used fo calibating the Euocodes [4]. 5 The eliability analysis Using the method outlined above thee diffeent esistance functions have been calibated. Each of these utilises eadily available test data to illustate the main contention of the pape; it is not claimed that this illustative teatment is compehensive in tems of calibating against all suitable test data. These include: 1. Tensile esistance of odinay bolts. This was based on 135 diect tensile tests on 20mm diamete gade 8.8 odinay bolts [5]. 2. Bending esistance of estained beams. This was based on 20 tests caied out specifically fo the pupose of calibating the plastic moment of esistance design function [6]. Lateal estaints wee positioned and section sizes selected to poduce what may be consideed as a wost case scenaio. 3. Shea buckling esistance of plate gides. This was based on a suvey of 35 diffeent tests on plate gides [7]. esistance calculations wee caied out using the simple post-citical design method, using fomulae elating to gides with web slendeness > 1.2. In all cases the design expessions wee taken fom Euocode 3-1 [2]. The esults fom the analysis ae listed in Table 1. (7) 4

5 JCSS Wokshop on eliability Based Code Calibation Design task EC3 Boxed value P (< d ) M value equied to achieve the taget eliability ( ) Tensile esistance of odinay bolts Bending esistance of estained beams Shea buckling esistance of plate gides Mb = 1.25 < M0 = x M1 = x Table 1: esults fom eliability analysis of 3 sepaate design tasks It is clea that a significant vaiation in eliability levels exists between these thee design tasks. Excessive eliability is pesent fo the tensile capacity of bolts and the bending stength of lateally estained beams. In both cases it would actually be possible to achieve the taget eliability with a M value of less than unity. Convesely, the shea buckling esistance of plate gides is a design situation whee the pobability of design esistance not being achieved is of the ode of 1 in 100. To meet the basic taget eliability, Μ1 should be inceased fom 1.10 to It seems no coincidence that the most complex design task equies the highest safety facto. Moeove, it is likely that this vaiation in design eliability is not esticted to the 3 examples consideed heein. Wee the pesent study to be extended then the vaiability in eliability levels might be expected to be of the fom shown in Fig. 3. Clealy, damatic vaiations in eliability is both uneconomic and potentially unsafe. 1.0E E E E E E E E E E E E-06 P(< d ) Individual esistance functions P(< d ) 1.0E E E E E E+00 Individual esistance functions Fig. 3: An idealised view of the vaiations in eliability between diffeent design tasks Fig. 4: An idealised view of the vaiations in eliability, using the system of supplementay safety factos poposed heein A moe ational method fo applying the esistance functions contained in the codes would be to detemine a M facto fo each esistance function. The facto would take the fom of a numeical constant incopoated into the design expession, with the designe being lagely unawae of the oigin of the facto. No othe safety factos on esistance would be applied. 5

6 JCSS Wokshop on eliability Based Code Calibation It is appeciated that nation states may be unwilling to give up the feedom povided by the boxed value system of safety factos. Given this, it would be possible to embed a supplementay safety facto into each esistance function, whilst etaining the boxed value system of M factos. The supplementay safety facto would take the fom of a numeical constant, whose pupose is to unify eliability levels. The boxed values selected by nation states would meely adjust design economy and taget eliability, with the vaiations in eliability between design tasks being close to the patten shown in Fig. 4. The concept is illustated as follows: M Supplementay facto, SF = Whee M is the boxed value And is the safety facto output fom eliability analysis, such as fom equation 7. Thus the design esistance, d = SF. n / M 1.10 In the case of the plastic moment capacity of estained beams, SF = = Theefoe, M pl.d = 1.17Wplf y / M0, this would epesent a 17% incease in the design moment, whilst still achieving the taget eliability. 6 Conclusions The ole of calibation in seeking to ensue consistency of eliability in design pedictions acoss a ange of diffeent stuctual phenomena has been discussed. Using 3 topics fom steel design and the expessions fom EC3, it has been shown that the pocesses adopted fo calibating the Euocodes lead to widely diffeent levels of eliability. A simple coection, including the intoduction of an additional (hidden) facto whose value depends diectly on the closeness with which the associated design expession fits the suppoting test data has been poposed. 7 Acknowledgements The pape was oiginally published in the poceedings of the IABSE confeence on safety, isk and eliability, held in Malta in 2001 [8]. 8 efeences [1] Byfield, M.P. and Nethecot, D.A., Mateial and geometic popeties of stuctual steel fo use in design, The Stuctual Enginee, vol. 75/No. 21, Nov. 1997, pp [2] CEN, Euocode 3: Design of steel stuctues - Pat 1.1: Geneal ules and ules fo buildings, Bitish Standads Institution, London, [3] Alpsten, G., Vaiations in mechanical and coss-sectional popeties of steel, E.C.C.S., Second Intenational Colloquium on stability, Intoductoy epot, Leige, [4] CEN, ENV : Euocode 3 Tiel 1-1: Annex Z - Detemination of design esistance fom tests, Euopean Committee fo Standadisation, Bussels, [5] Tizani, W., Assessment of the Quality of Impoted Bolts fo Use in Tensile Applications, The Univesity of Nottingham, UK, efeence no. SC (G0629), [6] Byfield, M.P. and Nethecot, D.A., An analysis of the tue bending stength of steel beams, Poceedings of the Institution of Civil Enginees, ISSN , May 1998, pp

7 JCSS Wokshop on eliability Based Code Calibation [7] Nethecot, D.A. and Byfield, M.P () Calibation of design pocedues fo steel plate gide design, Advances in Stuctual Engineeing, Vol. 1 No. 2, 1997, pp [8] Byfield, M.P. and Nethecot, D.A. (2001). eliability of Steelwok Designed to Euocode 3. Poceedings of IABSE Confeence on Safety, isk and eliability in Engineeing Malta,