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UNCERTAINTIES IN CHARACTERISTIC STRENGTHS
OF HISTORIC STEELS USING NON-DESTRUCTIVE TECHNIQUES
Mi osla SÝKORA1, Jan MLČOCH1, Pa el RYJÁČEK2
1Depa men o S uc u al Reliabili y, Klokne Ins i u e, Czech Technical Uni e si y in P ague,
Šolíno a 7, P ague, Czech Republic
2Depa men o S eel and Timbe S uc u es, Facul y o Ci il Enginee ing, Czech Technical Uni e si y in P ague,
Tháku o a 7, P ague, Czech Republic
mi osla [email p o ec ed], [email p o ec ed], pa el. yjacek@ s .c u .cz
DOI: 10.35181/ ces-2019-0022
Abs ac . The use o a ious non- o mino -des uc i e
es s (NDTs) is o en p e e ed o educe he cos o
s uc u al su eys o his o ic s uc u es made o cas and
w ough i ons o old ca bon s eels. This con ibu ion hus
explo es he measu emen e o s associa ed wi h common
NDT echniques and quan i ies unce ain ies in
cha ac e is ic s eng h es ima es based on NDTs only. I
appea s ha a uni y mean and coe icien o a ia ion o
12% migh be adop ed o he measu emen unce ain y
o he me hods unde s udy (B inell, Leeb, Poldi, Vicke s,
Rockwell). On a e age, he ue cha ac e is ic ul ima e
s eng h is by ~15% la ge han ha based on many
NDTs. This ep esen s he expec ed gain when he
cha ac e is ic alue is es ima ed om i e DTs ins ead o
a la ge numbe o NDTs. In p ac ice de ailed eliabili y
assessmen s should always be based on esul s o DTs o
a leas on NDTs p ope ly calib a ed by DTs.
Keywo ds
His o ic s eel, cha ac e is ic s eng h, i on,
measu emen e o , non-des uc i e es , unce ain y.
1. In oduc ion
The mechanical p ope ies o his o ic me al ma e ials
such as cas and w ough i ons o old ca bon s eels
exhibi a conside able sca e dependen on pe iods o
cons uc ion and he egion o a p oduce , esul ing in
di e ences in he p oduc ion p ocedu e, i s quali y and
alloy composi ion [1] and [2]. Commonly, he design
documen a ion o his o ic s uc u es is missing and he e
is no clea ela ionship be ween ma e ial s eng hs and
yea o execu ion o his o ic s eel b idges in he Czech
Republic [3]. This is why he in o ma ion o hei
assessmen s needs o be based on measu emen s and es s
only [4] and [5]. The use o a ious non- o mino -
des uc i e es s (NDTs) is o en p e e ed o e o
des uc i e es s (DTs) o educe he cos o s uc u al
su ey and damage o he s uc u e.
Howe e , limi ed a en ion has been paid o he
in es iga ion o unce ain ies in cha ac e is ic s eng h
es ima es based on NDTs only. This is why he submi ed
con ibu ion explo es he measu emen e o s associa ed
wi h common NDT ha dness echniques and quan i ies
unce ain ies in cha ac e is ic s eng h es ima es. The
measu emen unce ain y is assessed conside ing he
da abase o pai s o NDTs and DTs aken om his o ic
s uc u es om he 19 h cen u y.
2. Expe imen al Da abase
The da abase con ains 119 pai s o NDT and DT esul s
ob ained om mos ly ailway b idges and some buildings
om he second hal o he 19 h cen u y. Mos o he es
esul s we e published in p e ious scien i ic
con ibu ions [6], [7], [8], [9] and [10]. The es s o
ensile s eng h we e conduc ed by he ollowing
me hods:
1. DT esul s a e based on ensile es s acco ding o
ISO 6892 o ensile es ing o me allic ma e ials
unde no mal empe a u es. The es unce ain y
is negligible (coe icien o a ia ion, “CoV”,
V < 1%) [11].
2. The ollowing NDT me hods we e used o
de e mine ul ima e s eng h o his o ic s eels on
he basis o empi ical ela ionships wi h
ha dness o he ma e ial:
• s a ic (B inell, Rockwell, Vicke s),
• dynamic (Poldi hamme , Leeb).
The ma e ials unde in es iga ion include w ough i ons
and his o ic s eels.
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3. Measu emen Unce ain y
In line wi h common p ac ice, he measu emen s aken a
a s uc u e a e assumed o be independen obse a ions.
The da abase con ains no ob ious ou lie s; o ins ance,
measu emen s beyond he limi s o calib a ion cu es o
e y small/ high NDT s eng hs in pai s wi h mode a e
DT s eng hs ha could explained as measu emen s a
local non-homogenei ies.
The measu emen unce ain y ε is ea ed he e as a
andom a iable. A widely adop ed mul iplica i e o ma
o measu emen unce ain y is aken in o accoun :
DT = ε NDT, (1)
whe e deno es s eng h o he ma e ial.
Following he obse a ions ela ed o model
unce ain y [12], he mul iplica i e o ma is mo e
app op ia e when he di e ence be ween measu emen s
and ue alues – DT s eng hs he e – is p opo ional o
he la e . When he di e ence is independen o he
magni ude o a ue alue, he addi i e o ma becomes
mo e app op ia e.
The mul iplica i e o ma is assumed he ea e o be
ep esen a i e o NDT measu emen s. Ou lie s a e
de ec ed by he signi icance es (G ubb’s es [13]) and
excluded om u he analyses (one NDT esul o
B inell, Vicke s, and Leeb es s). The measu emen
unce ain y cha ac e is ics – mean με and CoV Vε – a e
gi en in Tab. 1. NDT esul s a e compa ed wi h
espec i e DTs o a) B inell, b) Leeb, and c) all ha dness
me hods in Fig. 1.
Conside ing b oadly di e en sample sizes o he
NDT me hods, he measu emen unce ain y
cha ac e is ics in Tab. 1 indica e ha he same mean and
CoV migh be adop ed o he me hods unde s udy in a
i s app oxima ion, με ≈ 1 and Vε ≈ 12%. This
assump ion is also suppo ed by:
• he same p inciple o he me hods, based on he
ela ionship o ha dness and ma e ial s eng h,
• simila ac o s in luencing he measu emen
unce ain y and hus by he simila expec ed magni ude o
associa ed unce ain y.
Tab.1: Measu emen unce ain y cha ac e is ics o a ious NDT
me hods.
Me hod Sample size n Mean με CoV Vε
B inell 35 0.98 12 %
Leeb 51 1.01 12 %
Poldi 18 1.01 12 %
Vicke s 10 0.89 18 %
Rockwell 5 1.00 7 %
All 119 0.99 12 %
Fig. 1: Compa ison o NDTs and DTs o a) B inell, b) Leeb, and c) all
ha dness me hods (ou lie s ma ked).
No e ha hese ac o s include skills and expe ience
o he wo ke , quali y o specimen su ace, s i ness and
mass o he specimen, epea abili y o he es ing de ice,
homogenei y o ha dness o he ma e ial, numbe o
measu emen s o es ima e ha dness in one loca ion, and
200
300
400
500
600
700
200 300 400 500 600 700
NDT [MPa]
DT [MPa]
a) B inell
200
300
400
500
600
700
200 300 400 500 600 700
NDT [MPa]
DT [MPa]
b) Leeb
200
300
400
500
600
700
200 300 400 500 600 700
NDT [MPa]
DT [MPa]
c) all
Leeb B inell
Poldi Vicke s
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pa ly also he slope o he in es iga ed membe
(ho izon al s. e ical measu emen s hough commonly
compensa ed when con e ing ha dness o s eng h).
Fu he , a logno mal dis ibu ion ha is commonly
adop ed in conjunc ion wi h he mul iplica i e o ma o
he model o measu emen unce ain y [14] is assumed
o he measu emen unce ain y.
4. Unce ain y in Cha ac e is ic
S eng h Es ima e
The e ec o he measu emen unce ain y on he
es ima e o cha ac e is ic ul ima e s eng h is in es iga ed
by means o simula ions:
1. Ul ima e s eng h o w ough i ons and his o ic
s eels is o en simila o ha o he mode n s eel
S235, [3], [15] and [16]. The au ho s’ da abase
indica e ha a ue ul ima e s eng h o he
ma e ial o a pa icula in es iga ed his o ic
s uc u e could be desc ibed by:
• cha ac e is ic ul ima e s eng h
uk = 350 MPa, V u =
5%, and µ u = 380 MPa, and
• a logno mal dis ibu ion.
These assump ions a e in a b oad ag eemen wi h he
in o ma ion on his o ic me als gi en in ČSN 73 0038 –
he Czech s anda d on he assessmen o exis ing
s uc u es – as well as wi h he gene ic models o
mode n s eels p o ided in [14] and wi h empi ical
expe ience [17]. I is emphasised ha hese cha ac e is ics
apply o a homogeneous ma e ial – i is o en obse ed
in su eys o his o ic b idges ha ma e ial p ope ies
di e amongs a ious membe s such as be ween main
gi de s and seconda y membe s, beam and pla e membe s
e c.
2. The numbe o NDTs, nNDT (s udy pa ame e
he e) is ypically de e mined by he need o ha e
a easonable su ey o he s uc u e, o o i s
la ge pa ; i is commonly ela i ely la ge, say
a ound 25. NDT esul s a e sampled as ollows:
• A andom ealisa ion o a ue s eng h, u,i (i =
1..nNDT), is simula ed om a logno mal dis ibu ion wi h
he assumed mean and CoV.
• Using Eq. (1), he NDT esul is simula ed as u,NDT,i =
u,i / εi whe e he denomina o is a andom alue ob ained
om he logno mal dis ibu ion wi h με = 1 and Vε = 12%.
• The es ima e o cha ac e is ic s eng h based on nNDT
esul s, uk,NDT, is ob ained using he app oach in Annex D
o EN 1990:2002 (assuming a logno mal dis ibu ion and
“unknown CoV”).
• The e o in he es ima e hen becomes θj = uk /
uk,NDT,j = 350 MPa / uk,NDT,j.
3. This p ocedu e is epea ed nsim- imes (j =
1..nsim), o ob ain mean and CoV o he e o
una ec ed by s a is ical unce ain y. In his s udy
nsim is 1000.
4. To highligh he e ec o he measu emen
unce ain y, simila simula ions a e gene a ed
conside ing ha a numbe o DTs, nDT, is
a ailable. In his si ua ion he measu emen
unce ain y is negligible and DT esul s a e
assumed o be equal o u,i. The es ima e o
cha ac e is ic s eng h, uk,DT, is again ob ained
using Annex D o EN 1990:2002. The e o in
he es ima e hen becomes θj = 350 MPa / uk,DT,j.
The a iabili y o he mean, CoV and con idence
in e als o he e o θ wi h a numbe o es s is displayed
in Fig. 2. While he mean μθ al eady app oaches uni y
e ec i ely o a e y small numbe o DTs, say up o
i e, he measu emen unce ain y esul s in a sca e o
NDT esul s and μθ is a om uni y (con e ging o abou
1.15). This sugges s ha , on a e age, he ue
cha ac e is ic s eng h is by ~15% la ge han ha based
on a e y la ge numbe o NDTs while al eady o nDT = 5
he uk es ima e becomes easonably unbiased, μθ = 1.03.
The simila ends a e obse ed o he CoV o he
e o θ. Bo h mean and CoV a e hen e lec ed by he
con idence in e als plo ed in Fig. 2c). I is obse ed ha
o highe numbe s o es s, say nNDT > 15 and nDT > 5,
he expec ed di e ence be ween uk,NDT and uk,DT is
a ound 15%. This ep esen s he expec ed gain when he
cha ac e is ic alue is es ima ed based on i e DTs
ins ead o a la ge numbe o NDTs.
5. Discussion
The p esen s udy p o ides he backg ound in o ma ion
o u he esea ch ha will be aimed o deli e he
me hodology o es ima ing design s eng h alues o
his o ic me als based on NDTs and a small numbe o
DTs. When de i ing he pa ial ac o , he unce ain y in
geome y and model unce ain y need o be conside ed in
addi ion o he a iabili y o a ma e ial p ope y [2], [7]
and [18].
Acco ding o he bes p esen p ac ice, ma e ial
p ope ies based on NDTs only a e only used in
p elimina y eliabili y assessmen s (see ISO 13822:2010
o he assessmen o exis ing s uc u es and he
backg ound ma e ial o de eloping he guidance on
exis ing s uc u es in Eu ocodes [19]). The de ailed
assessmen s should always be based on esul s o DTs o
a leas on NDTs p ope ly calib a ed by ew DTs. This is
also in pa ial ag eemen wi h he s udy on w ough i on
b idges by Go don and Knop [20] who concluded ha ,
as a consequence o he composi e na u e o he ma e ial,
he e is a poo co ela ion be ween s eng h and ha dness
and he s anda d con e sions be ween di e en measu es
o ha dness do no apply.
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Fig. 2: Va iabili y o he cha ac e is ics o he e o θ wi h a numbe o
es s: a) mean, b) CoV, c) con idence in e als.
In p ac ice, he ul ima e s eng h is ypically u ilised
in a limi ed numbe o cases; e.g. when assessing
esis ance o i e s, join s o o sec ions wi h holes.
Mos ly u needs o be con e ed o yield s eng h, y. The
au ho s’ la ge da abase consis s o 265 pai measu emen s
o a io α = y / u o his o ic b idges da ed back o 1865-
1940. The p elimina y analysis indica es ha he a io α:
• exhibi s no end wi h ime, yield o ul ima e s eng h,
• could be desc ibed by he mean alue o 0.8 and CoV
o 10 %.
I hus appea s ha he CoV o α is compa able o ha o
measu emen unce ain y and i is conside ably la ge
han V u. As he a io α la gely depends on he chemical
composi ion o he alloy, u he in es iga ions a e
needed o imp o e he in o ma ion on i s s a is ical
p ope ies and p opose a p ocedu e on how o include he
unce ain y in α in p ac ical eliabili y assessmen s.
Fu he esea ch will also be ocused on:
• in es iga ing he abili y o NDTs in iden i ying
non-homogenei y o he ma e ial,
• de ailed analysis o NDT unce ain y wi h espec
o he ype o he me hod and ype o an
in es iga ed ma e ial,
• c i ical compa ison o he addi i e and
mul iplica i e o ma s o measu emen
unce ain y,
• p o iding a me hodology o es ima ing esis ance
cha ac e is ics o his o ic me al s uc u es,
conside ing also p e ious s udies in his ield [21]
and [22]; see also he i s esul s in [23].
6. Concluding Rema ks
As he mechanical p ope ies o his o ic me al ma e ials
exhibi a conside able sca e , he in o ma ion o
eliabili y assessmen s needs o be commonly based on
measu emen s and es s only. This con ibu ion explo es
he measu emen e o s associa ed wi h common NDT
ha dness echniques and quan i ies ela ed unce ain ies
in cha ac e is ic s eng h es ima es. The nume ical
analysis indica es ha :
• Uni y mean and coe icien o a ia ion o 12% migh
be adop ed o he measu emen unce ain y o he
me hods unde s udy (B inell, Leeb, Poldi, Vicke s,
Rockwell) as a i s app oxima ion.
• While he mean o he e o in he es ima e o
cha ac e is ic ul ima e s eng h (5% ac ile) app oaches
uni y e ec i ely o a e y small numbe o DTs, he
measu emen unce ain y esul s in a sca e o NDT
esul s and he mean o he es ima e is a om uni y. On
a e age i is expec ed ha he ue cha ac e is ic s eng h
is by ~15% la ge han ha based on a e y la ge numbe
o NDTs. This ep esen s he expec ed gain when he
mean o e o , μ
θ
a)
numbe o es s, n
NDT
o n
DT
1
1.1
1.2
1.3
0 5 10 15 20 25
1.4
1.5
DTs
NDTs
CoV o e o , V
θ
b)
numbe o es s, n
NDT
o n
DT
0%
5%
10%
15%
0 5 10 15 20 25
20%
25%
NDTs
DTs
E o , θc)
numbe o es s, n
NDT
o n
DT
1
1.2
1.4
1.6
0 5 10 15 20 25
1.8
0.8
75% con idence in e al - NDTs
75% con idence in e al - DTs
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cha ac e is ic alue is es ima ed based on i e DTs
ins ead o a la ge numbe o NDTs.
• To de i e he design alue, he es ima e o a 5%
ac ile needs o be di ided by a pa ial ac o ha
accoun s o he unce ain y in geome y and model
unce ain y in addi ion o he a iabili y o s eng h (and
possibly o he ac o s such as a ge eliabili y o ela i e
impo ance o he esis ance a iables wi h espec o he
limi s a e unde conside a ion).
I is emphasised ha de ailed eliabili y assessmen s
should always be based on esul s o DTs o a leas on
NDTs p ope ly calib a ed by DTs.
Acknowledgemen s
This wo k was suppo ed by he Minis y o Cul u e o
he Czech Republic unde G an DG18P02OVV033 ‘‘The
Me hods o Achie ing he Sus ainabili y o Indus ial
He i age S eel B idges”.
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Abou Au ho s
Mi osla SÝKORA was bo n in České Budějo ice,
Czech Republic. He ecei ed his M.Sc. in 2001 and Ph.D.
in 2005 om Facul y o Ci il Enginee ing, CTU in
P ague. His esea ch in e es s include basis o s uc u al
design, s uc u al eliabili y, p obabilis ic op imisa ion,
load modelling, isk assessmen o echnical sys ems, and
applica ions o p obabilis ic me hods in s uc u al design.
Jan MLČOCH was bo n in Mladá Bolesla , Czech
Republic. He ecei ed his M.Sc. in 2015 om Facul y o
Ci il Enginee ing, CTU in P ague. His esea ch in e es s
include unce ain y quan i ica ion and p obabilis ic
eliabili y analysis o ein o ced conc e e s uc u es.
Pa el RYJÁČEK was bo n in Plzeň, Czech Republic.
He ecei ed his M.Sc. in 2000 and Ph.D. in 2003 om
Facul y o Ci il Enginee ing, CTU in P ague. His
esea ch in e es s include s eel b idges (connec ions,
s abili y, composi e ac ions), FRP in he b idge
enginee ing, b idge assessmen and ein o cing, a igue
assessmen and b idge – ack in e ac ion.