Casopis 3 2019
Casopis 3 2019
Casopis 3 2019
1)=861
ISSN 2334-0229 (Online)
3
GRAĐEVINSKI
MATERIJALI I
DIMK
2019.
KONSTRUKCIJE
GODINA
LXII
BUILDING
MATERIALS AND
STRUCTURES
ČASOPIS ZA ISTRAŽIVANJA U OBLASTI MATERIJALA I KONSTRUKCIJA
J O U R N A L F O R R E S E A R C H OF M A T E R I A L S A N D S T R U C T U R E S
GRAĐEVINSKI BUILDING
MATERIJALI I MАTERIАLS AND
KONSTRUKCIJE STRUCTURES
ČАSOPIS ZA ISTRАŽIVАNJA U OBLАSTI MАTERIJАLА I KONSTRUKCIJА
JOURNАL FOR RESEАRCH IN THE FIELD OF MАTERIАLS АND STRUCTURES
Ш
PUBLISHER
Society for Materials and Structures Testing of Serbia, 11000 Belgrade, Kneza Milosa 9
Telephone: 381 11/3242-589; e-mail:dimk@ptt.rs, veb sajt: www.dimk.rs
REVIEWERS: All papers were reviewed
KORICE: Modeli stuba: a) Utegnut presek; b) Efektivno utegnuto jezgro elementa;
c) Efektivno utegnut element prema Evrokodu 8
COVER: Column models: a) Confined volume; b) Effectively confined volume;
c) Effectively confined volume by Eurocode 8
Štampa/Print: Razvojno istraživački centar grafičkog inženjerstva, Beograd
Publikacija: tromesečno
Edition: quarterly
Financial supports: Ministry of Scientific and Technological Development of the Republic of Serbia
ISSN 2217-8139 (Print ) GODINA LXII - 2019.
ISSN 2334-0229 (Online)
DRUŠTVO ZА ISPITIVАNJE I ISTRАŽIVАNJE MАTERIJАLА I KONSTRUKCIJА SRBIJE
SOCIETY FOR MАTERIАLS АND STRUCTURES TESTING OF SERBIА
GRAĐEVINSKI BUILDING
MATERIJALI I MАTERIАLS AND
KONSTRUKCIJE STRUCTURES
ČАSOPIS ZA ISTRАŽIVАNJA U OBLАSTI MАTERIJАLА I KONSTRUKCIJА
JOURNАL FOR RESEАRCH IN THE FIELD OF MАTERIАLS АND STRUCTURES
SАDRŽАJ CONTENTS
1 UVOD 1 INTRODUCTION
Nivo seizmičkog opterećenja, pri elastičnom odgo- The level of the seismic load, at an elastic response
voru konstrukcije, može biti izuzetno visok i zato ga je of the structure, can be extremely high and as such, it
veoma teško konstrukcijski prihvatiti. Jedan od načina can be very difficult for a structure to sustain it. One
smanjenja intenziteta seizmičkog opterećenja jeste option for reducing seismic loads on structure is to allow
dopuštanje kontrolisanih neelastičnih deformacija (ošte- controlled inelastic deformations (damages) to structural
ćenja) elemenata konstrukcije, uz zadržavanje integriteta elements while maintaining the integrity of both the
cele konstrukcije, kao i njenih delova. Ovaj tradicionalni entire structure and all of its parts. This concept of
koncept prihvatanja seizmičkog opterećenja podrazu- sustaining seismic loads presumes that the ductile
meva obezbeđivanje duktilnog ponašanja konstrukcije – behaviour of the structure i.e. global ductility is provided
globalne duktilnosti, kako bi osnovni zahtev, koji in order to fulfil the basic requirement in seismic design –
podrazumeva da konstrukcija mora da izdrži pomeranja the structure must withstand displacements at seismic
pri dejstvu zemljotresa, bio ispunjen. Za procenu ground motions. To evaluate the non-linear behaviour
nelinearnog ponašanja i kapaciteta pomeranja novih i and displacement capacity of new and existing
postojećih konstrukcija usled dejstva zemljotresa, structures due to seismic effects, a variety of methods
moguće je primeniti čitav niz metoda u okvirima linearne can be applied using linear or non-linear structural
i nelinearne analize konstrukcija [1]. Nivo složenosti analysis [1]. The level of complexity of each method
svake metode zavisi od nivoa aproksimacije uticaja depends on the approximation level of the influence of
ključnih faktora na ponašanje armiranobetonskih kon- key factors on the behaviour of reinforced concrete
strukcija pri dejstvu zemljotresa, što se odnosi, pre structures during the earthquake. It relates to the
svega, na modeliranje opterećenja od zemljotresa, modelling of seismic loads, soil-structure interaction,
interakcije konstrukcije i tla, nelinearnog ponašanja non-linear material behaviour and damping. However,
materijala i prigušenja. Međutim, imajući u vidu given the simplicity and robustness it entails, linear
jednostavnost i robusnost koje podrazumeva, u praksi se elastic analysis is most commonly used in practice, with
najčešće koristi linearno-elastična analiza, prema kojoj design of structure based on seismic forces (so-called
se proračun konstrukcije vrši „prema silama” (force- force-based seismic design).
based seismic design).
Da bi se osiguralo duktilno ponašanje u lokalizo- In order to ensure ductile behaviour in the localized
vanim zonama konstrukcije (plastičnim zglobovima), structural zones (plastic hinges), materials must be able
materijali moraju da budu u stanju da postignu odgova- to achieve appropriate deformations. Ductility of the
rajuće deformacije. Lokalna duktilnost armiranobeton- reinforced concrete elements, at the cross-sectional
skih elemenata, na nivou poprečnog preseka, postiže se level, is achieved by the increased elongation of the
povećanim izduženjima čelika (εs), kao i skraćenjima steel (εs), as well as by corresponding concrete
pritisnutog betona (εc), odnosno odgovarajućom compression deformation (εc), i.e. appropriate cross-
duktilnošću krivine preseka. Faktor duktilnosti krivine section ductility curvature. The curvature ductility factor
definisan je kao odnos granične krivine i krivine pri is defined as the ratio of the ultimate curvature and the
tečenju μφ=φu/φy, gde je φy krivina AB preseka pri curvature at yielding μφ=φu/φy, where φy is the curve of
tečenju (armature), a φu granična krivina AB preseka. RC cross-section at yielding (of reinforcement) and φ u is
Prema [3], krivina preseka pri tečenju AB stubova the ultimate curve of RC cross-section.
opterećenih aksijalnom silom pritiska definiše se za According to [3], the yield curvature of cross-section
sledeća dva moguća slučaja: is defined for two possible cases:
a) krivina pri dilataciji na granici razvlačenja a) The curvature with strain at yielding of the
zategnute armature (εs=εyd); tensioned reinforcement (εs=εyd),
b) krivina pri velikim dilatacijama pritiska na gornjoj b) The curvature with large pressure strains on the
(pritisnutoj) ivici betonskog preseka. upper (pressed) edge of the concrete cross-section.
Prema Panagiotakosu i Fardisu [3], usled velike According to Panagiotakos and Fardis [3], due to the
normalne sile, može doći do nelinearnog ponašanja large normal force, a non-linear behaviour of the
pritisnute zone betonskog preseka, pre pojave tečenja compressed zone of the concrete cross-section may
zategnute armature. Autori su za proračun krivine pri occur, before steel yielding. The authors proposed to
pojavi tečenja, u slučajevima visokog nivoa normalne calculate the curvature at yielding, in cases with large
sile u stubovima, predložili gornju granicu dilatacije na normal forces in columns, by limiting the strain of
pritisnutoj ivici betonskog preseka jednaku 1,8·fc/Ec, gde compressed fibre of the concrete cross-section to a
je fc čvrstoća betona pri pritisku, a Ec – modul value of 1,8·fc/Ec, where fc is the compressive strength of
elastičnosti betona. concrete and Ec is the modulus of elasticity of concrete.
Granična krivina AB preseka φu definisana je The ultimate curvature of the RC cross-section φu is
odnosom granične dilatacije pritiska utegutog betona i defined by the ratio of the ultimate strain of the
odgovarajuće visine neutralne ose. Određivanje krivine compressed confined concrete and the corresponding
preseka pri lomu zavisi od nivoa opterećenja, količine depth of the neutral axis. Determination of the cross-
armature, kao i toga da li je dostignuta granica loma sectional ultimate curvature depends on the load level,
betona ili armature, i tako dalje. U zavisnosti od the amount of reinforcement, the failure of the section
vrednosti pomenutih parametara, pri određivanju krivine due to rupture tension reinforcement or compressed
preseka razmatra se ukupni poprečni presek betonskog concrete, etc. Depending on the values of the mentioned
elementa ili samo utegnuti presek (ukupni presek parameters, failure of the section can be achieved
umanjen za neutegnuti zaštitni sloj betona). before spalling of the concrete cover or curvature at the
Raznim eksperimentima je ustanovljeno da duktilnost spalling of the concrete cover.
betona znatno raste kada se dovede u stanje triaksijalne Various experiments have shown that the ductility of
kompresije [7]. Ovakvo stanje može se postići utezanjem the concrete significantly increases when it enters the
elementa poprečnom armaturom u vidu zatvorenih state of triaxial compression [7]. This condition can be
uzengija ili spiralne armature. Na taj način, sprečava se achieved by confining the element with a transverse
bočno širenje elementa usled aksijalne sile. Posledice reinforcement in the form of hoops and ties or spiral
toga su povećanje čvrstoće betonskog elementa i reinforcement. This prevents the lateral expansion of the
razvijanje većih graničnih dilatacija εcu,c, znatno većih od element due to the axial compression force. As a result,
3,5‰, čime se ostvaruje veća granična krivina preseka the strength of the concrete element increases and the
φu. Parametri koji utiču na stepen utezanja jesu: količina development of higher ultimate stain of cross-section
poprečne armature (ρw), čvrstoća čelika (oblik dijagrama compression fibres εcu,c, significantly greater than 3.5‰,
napon–dilatacija), čvrstoća betona na pritisak (oblik which results in a larger ultimate curvature of cross-
dijagrama napon–dilatacija), razmak, oblik i broj section φu. The parameters that affect degree of
uzengija, kao i podužne (vertikalne) armature. confinement are: quantity of transversal reinforcement
Bočne sile, koje se javljaju kao posledica sprečenog (ρw), steel strength (stress-strain diagram), concrete
širenja betonskog elementa, deluju u nivou uzengija. compression strength (stress-strain diagram), distance,
Prema Fardisu [3], smatra se da efekti utezanja dolaze shape and number of stirrups as well as longitudinal
do izražaja pri dostizanju aksijalnog napona pritiska (vertical) reinforcement.
približno jednakom čvrstoći betona pri pritisku, kao i da The lateral forces, which occur as a result of the
ne dolazi do ojačanja armature za utezanje nakon prevented lateral expansion of the concrete element, act
dostizanja granice tečenja, već se za graničnu vrednost at the level of the stirrups. According to Fardis [3], it is
usvaja napon pri tečenju. Najveći bočni pritisak može se considered that the confinement begins at achieving the
razviti samo na onom delu betonskog elementa gde se approximate compression strength of the concrete, and
nalazi armatura za utezanje. Zbog ovakvog delovanja that the stirrups fail to go into hardening when reaching
bočnog pritiska maksimalna vrednost mora biti the ultimate stress and hence the value of stress at
korigovana koeficijentom utezanja. Ovaj koeficijent utiče yielding is adopted as the limit value. The highest lateral
Na slici 1 prikazana je teorijska pretpostavka oblika In Figure 1 the theoretical assumption of the shape
efektivnog dela betonskog elementa, kako pokazuju of concrete element effective area is shown by Sheikh
Sheikh i Uzumeri [8], a kasnije i Mander i ostali [4], u and Uzumeri [8], and later Mander et al. [4], in the cross-
poprečnom preseku (B-B i Z-Z) i duž visine samog section (B-B and Z-Z) and along the height of the
elementa (A-A i Y-Y). Pretpostavljeni oblik efektivno element itself (A-A and Y-Y). The assumed form of the
utegnutog preseka betona smanjuje se na mestima na effective cross-section of concrete is reduced in places
kojima nema uzengija. Oblik promene je parabola s without hoops or ties. The shape of the assumed volume
tangentama u krajnjim tačkama od 45˚, sa žižom od of effective confined element is a parabola with tangents
četvrtine dužine. at the endpoints of 45˚, with apex of a quarter of length
between hoops or ties.
Koeficijent utezanja (α) predstavlja faktor efikasnosti Confinement effectiveness factor (α) represents the
utezanja poprečnom armaturom. Ovaj faktor, prema efficiency factor of the transversal reinforcement. This
propisima Evrokoda 8, sadrži dva činioca αs i αn. Prvi factor, according to Eurocode 8, is defined as a product
član definiše odnos površina preseka 1 i 2 označenih na of two factors αs and αn. First one defines the ratio of the
slici 2 – izrazi (1) i (3). Presek u ravni 1 predstavlja surfaces of sections 1 and 2 shown on Figure 2 -
minimalni poprečni presek koji se može javiti prilikom equations (1) and (3). The cross-section at level 1
otpadanja neefikasno utegnute zone betonskog represents the minimum cross-section which can occur
elementa, dok drugi predstavlja presek u kojem se nalazi after spalling the ineffective area of concrete element,
s s
αs = 1 − 1 − (1)
2·bo 2·ho
n
bi2
αn = 1 − (2)
i =1 6·bo ·ho
Prilikom dostizanja graničnih dilatacija, odlama se When element is reaching the ultimate strains, the
zaštitni sloj betona, pa – shodno tome – efektivni presek, cover of concrete start spalling and, consequently, the
za takva stanja dilatacija, inicijalno postaje umanjen za effective cross-section for such strains initially becomes
debljinu tog sloja, odnosno dobijamo dimenzije smaller for thickness of that layer, i.e. we have
utegnutog preseka: dimensions of the smaller, confined, section:
a) Pravougaoni presek a) For rectangular section:
ho = hc − 2·( c − d bh 2 ) (5)
bo = bc − 2·( c − d bh 2 ) (6)
Do = Dc − 2·( c − d bh 2 ) (7)
Kako bismo shvatili oblik efektivno utegnutog In order to understand the shape of an effectively
elementa duž visine stuba prema izrazima (1)-(4), a confined element along the height of the column
imajući u vidu da koeficijent utezanja predstavlja odnos according to the equations (1)-(4), and taking into
efektivne utegnute površine (slika 3c) i površine account that the confinement effectiveness factor is the
utegnutog preseka (slika 3a), pretpostavljamo da to, ratio of the effective confined area (Figure 3c) and
takođe, može biti odnos zapremina efektivno utegnutog i confined area (Figure 3a), it is assumed that this can
utegutog dela elementa. Pretpostavljamo da izrazi also be the ratio of the effectively confined and confined
Evrokoda 8 efektivnu zapreminu interpretiraju kao volume of the element. It is assumed that the equations
„prizmu” s bazom površine sa slike 3c, tj. da promene of the Eurocode 8 interpret the effective volume as a
efektivne površine po visini elementa nema. "prism" with the base shown on Figure 3c, i.e. that there
are no changes in the effective volume along the height
of element.
Analizu prvo sprovodimo na jednostavnijem obliku The analysis starts with a simpler form of a column,
stuba, odnosno na stubu kružnog poprečnog preseka, i.e. a circular cross-section. The diameter of the cross-
prečnika utegnutog preseka Do=40 cm i razmaka section is Do=40 cm and stirrup spacing s=20 cm. The
uzengija s=20 cm. Prvi parametar za analizu predstavlja first parameter for the analysis is the confinement
koeficijent utezanja prema izrazima Evrokoda 8, tj. effectiveness factor according to the assumptions of the
izrazima (3) i (4), koji nazivamo α[EC8]. Dalje, Eurocodes 8, i.e. equations (3) and (4), which is named
konstruišemo tri trodimenzionalna elementa, od kojih je α[EC8]. Subsequently, three three-dimensional elements
prvi stub prečnika Do (slika 4a). Drugi element are designed, where the first is a column with diameter
predstavlja efektivnu zapreminu prema teorijskoj Do (Figure 4a). The second element represents the
pretpostavci Mander i ostali [4], s bazom efektivno effective volume according to the theoretical assumption
utegnutog jezgra prikazanog na Preseku B-B (slika 1) i of Mander et al. [4], with the base of the effectively
podužnom promenom u svemu prema Preseku A-A. confined core shown in Section B-B (Figure 1), and a
Ovakav model prikazan je na slici 4b. Odnosom vertical change of shape along the height of element
zapremina modela sa slike 4b i 4a dobijamo teorijski according to Section A-A. This model is shown in Figure
Pošto smo s dovoljnom tačnošću zaključili šta Since it is concluded, with sufficient accuracy, what
predstavlja bazu „cilindra”, dalje analiziramo kvadratne is the base of "cylinder", square columns are further
stubove. Izabrano je nekoliko tipičnih načina armiranja analyzed. Several typical reinforcement forms have been
(slika 5). Model A predstavlja presek s najmanjim selected (Figure 5). Model A represents the section with
mogućim stepenom armiranja, koji ne ispunjava least possible reinforcement, which does not meet the
minimalne uslove lokalne duktilnosti Evrokoda 8 u minimum local ductility requirements by Eurocode 8, in
Prilikom modeliranja kvadratnih stubova, nailazimo While modelling the square columns the lack of data,
na nedostatak podataka regulisanih odredbama regulated by the provisions of Eurocode 8, is noticed. It
Evrokoda 8. Reč je o tome da ne znamo koliko is a matter of not knowing how the maximum ineffective
maksimalno neefektivna zona ulazi u stub, po visini, zone enters the column between the two rows of the
između dva reda uzengija, pa su dva razmatrana modela stirrups, along the height of the column, so the two
prikazana na slici 6. models considered are shown in Figure 6.
Na slici 6a usvojena je funkcija parabole sa žižom od In Figure 6a, the parabola function with apex s/4=5
s/4=5 cm, dok je za drugi slučaj (slika 6b) usvojena cm is adopted, while for the second case, Figure 6b,
raspodela konstruisanjem površine ograničene sa četiri surface is designed with bounded four parabolas, using
parabole u programskom paketu AutoCAD, kod koje se software package AutoCAD, in which the 3 cm apex is
Deo tabele 3, koji je označen kao Teorijski, Part of Table 3, which is named Theoretical, is the
predstavlja koeficijente utezanja kvadratnog stuba square-column confinement effectiveness factor for
teorijskom pretpostavkom efektivne zone Mander i ostali theoretical assumption of effective zone by Mander et al.
[4] – α[ACAD] i poređenje dobijenih rezultata s [4] - α[ACAD] and a comparison with obtained results for
koeficijentima uzezanja dobijenih iz izraza (1) i (2) – coefficients calculated from equations (1) and (2) -
α[EC8]. Drugi deo tabele 3 (Prema EC8) predstavlja α[EC8]. The second part of Table 3 (According to EC8)
odnos „prizmatične” pretpostavke efektivno utegnute is the relation between the "prismatic" assumption of the
zone betonskog elementa – α[EC8-ACAD] i izraza (1) i concrete element effective confinement zone - α[EC8-
(2) – α[EC8]. Zaključujemo, prema rezultatima tabele 3, ACAD] and the equations (1) and (2) - α[EC8].
da propisi pojednostavljuju oblik efektivno utegnute zone According to the results shown in Table 3, it is concluded
stuba i da je koeficijent utezanja konzervativan. To se that the regulations simplify the shape of the effectively
uočava u jako maloj razlici (Δ) pretpostavljenog modela i confined zone of the column and that the confinement
izraza (1) i (2) iz Evrokoda 8, koja su oko 0,02 za effectiveness factor is conservative. This is noticeable in
klasične slučajeve armiranja. the very small difference (Δ) between the assumed
model and equation (1) and (2) from Eurocode 8, which
are about 0.02 for usual reinforcement details.
Model / Model A B C D E
α [EC8] 0,1875 0,3750 0,4219 0,4688 0,5625
Teorijski
α [ACAD] 0,2726 0,4922 0,5245 0,5989 0,7512
Theoretical
Δ 0,0851 0,1172 0,1026 0,1301 0,1887
Slika 7. Poređenje koeficijenata utezanja razmatranih modela (napomena: veza između modela A-E nije linearna)
Figure 7. Comparison of the confinement effectiveness factors for considered models (note: the relation between
models A-E is not linear)
Kod stubova kružnog poprečnog preseka, sila In the case of circular cross-section the confining
utezanja ravnomerno deluje duž kružne uzengije i nema force acts equally along the circular hoop and there are
neefektivnih delova utegnutog poprečnog preseka. no ineffective parts of confined cross-section.
Shodno tome, greške pri modeliranju efektivno Consequently, there were no errors in the modelling an
utegnutog elementa, sa osnovom utegnutog elementa effectively confined element, with the basis scaled by the
koja je skalirana izrazima (3) i (4), nije bilo i videli smo factors calculated from equations (3) and (4), and we
poklapanja rezultata prema tabeli 1. To nije slučaj i kod noticed the matching of the results in Table 1. This was
kvadratnih preseka, gde postoji komplikovanija not the case while designing the square cross-section
geometrija i kod koje se zbog greške modela javljaju columns with more complicated geometry and where
određene razlike. Greška se uvećava, takođe, zbog certain differences occur, due to model errors. The error
usvajanja površina koje generiše sam program, sa is also increased by adopting surfaces generated by the
određenom gustinom mreže. software itself, with a certain density of the mesh.
Čest slučaj u praksi jeste da se stubovi dodatno In most cases, in practice, the columns are
utežu na određenim mestima duž visine stuba (npr. u additionally confined at certain levels along the height of
zoni spoja grede i stuba) postavljanjem spoljašnje the column (for example, in the zone of beam and
uzengije na duplo manjem rastojanju. Prema odredbama column joints) by adding an external stirrup between
Evrokoda 8, utezanje preseka radi se uniformno po celoj existing ones. According to the regulations of Eurocode
visini disipativne zone, postavljanjem svih uzengija 8, the cross-section confinement is uniform over the
preseka na istom rastojanju, pa se postavlja pitanje entire height of the dissipative zone by placing all
efikasnosti utezanja preseka progušćenjem samo stirrups at the same distance, so the question of any
spoljne uzengije. Pomenuti slučaj iz prakse analizira se extra efficiency on confined element with that external
dodatnim utezanjem elementa, postavljanjem barem stirrup is to be answered. The mentioned case from the
jedne osnovne uzengije na polovini prethodno usvojenog practice is analyzed by additional confinement of the
Prema rezultatima iz tabele 3 i tabele 4, za teorijski According to the results from Table 3 and Table 4,
koeficijent utezanja, zapažamo da s progušćenjem for the theoretical confinement effectiveness factor, it
uzengija smanjujemo koeficijent, što nije očekivano i da can be noticed that with additional basic stirrup the
dobijeni rezultati odstupaju od razmišljanja u praksi, gde coefficient is reduced, which is unexpected and that the
se progušćene uzengije smatraju vidom dodatnog obtained results deviate from practice where the
utezanja. Greška koja se pravi usvajanjem teorijskog additional stirrup is considered as enhanced
modela jeste ta da parabolu na mestu dodatne uzengije confinement. The mistake in designing the theoretical
mi teorijski usvajamo. Ona ima dužinu d0 i žižu s/4. model was made because we adopted the parabola at
the place of additional stirrup by theory. Parabola have
length do and apex s/4.
Model / Model A B C D E
α [EC8] / 0,3750 0,4219 0,4688 0,5625
Teorijski
α [ACAD] / 0,4128 0,4210 0,440 0,5243
Theoretical
Δ / 0,0378 -0,0009 -0,0288 0,0382
Slika 9. Prikaz razlike modela:a) B; b) BA; c) BA korigovanog; s poprečnim presecima na sredini visine
Figure 9. Model differences: a) B; b) BA; c) BA corrected; with cross-sections in the middle of the height
Na slici 10 prikazan je model sa unutrašnje strane, Figure 10 shows the model from the inside, where it
gde se jasno može uočiti da – zbog ispunjenja can be clearly noticed that in order to fulfil the
preporuka Evrokoda 8 o neefektivnoj zoni između recommendations of Eurocode 8 on the ineffective zone
pridržanih šipki podužne armature – činimo grešku koju between the retained longitudinal reinforcement, an error
nadomešćujemo ograničavanjem neefektivne zone u was made which is corrected by limiting the ineffective
tom preseku. zone in that cross-section.
Slika 10. Minimalni poprečni presek po visini stuba modela: a) E; b) EA; c) EA korigovanog
Figure 10. Minimal cross-section along the height of the models: a) E; b) EA; c) EA corrected
S dovoljnom tačnošću možemo zaključiti da teorijski With sufficient accuracy, it can be concluded that the
pretpostavljen, efektivno utegnut, element, kako su ga theoretically assumed, effectively confined, element by
dali Mander i ostali [4] (α[ACAD]), daje veće koeficijente Mander et al. [4] (α[ACAD]) gives a higher confinement
utezanja od pretpostavke koju definišu izrazi prema effectiveness factor than the recommendations defined
odredbama Evrokoda 8 (α[EC8]). Na slici 11 prikazana by the equations in Eurocode 8 (α[EC8]). Figure 11
je razlika između ovih koeficijenata, s napomenom da shows the difference of these coefficients, with the note
veza između modela A do E nije linearna. Prema that the relation between the A-E model is not linear.
sumiranim rezultatima, na slici 11, zapažamo veoma According to the summarized results, in Figure 11, we
mala odstupanja od koeficijenata utezanja prema notice very small deviations from the confinement
izrazima (1) i (2) (α[EC8]) u odnosu na pretpostavljenu effectiveness factor by equations (1) and (2) (α[EC8]) in
„prizmu” (α[EC8-ACAD]), pa shodno tome smatramo da relation to the assumed "prism" (α[EC8-ACAD]), and
je pretpostavka o obliku efektivno utegnutog elementa, u consequently it is considered that the assumption about
podužnom pravcu, dovoljno tačna. the shape of an effectively confined element in the
longitudinal direction is sufficiently correct.
Slika 12. Poređenje teorijskog i dodatno utegnutog teorijskog modela – tabele 3 i 4 (napomena: veza između modela A-E
nije linearna)
Figure 12. Comparison of the theoretical and additionally confined theoretical model - Table 3 and 4 (note: the relation
between models A-E is not linear)
U radu je predstavljena analiza faktora efikasnosti The paper presents the analysis of the confinement
utezanja armiranobetonskih preseka poprečnom effectiveness factor for the reinforced concrete cross-
armaturom, kao jednog od ključnih parametara koji utiču sections with stirrups, as one of the key parameters that
na obezbeđivanje zahtevanog faktora efikasnosti krivine influence the achievement of the required cross-section
preseka, prema Evrokodu 8 [2]. Objašnjeno je fizičko curvature ductility factor, according to Eurocode 8 [2].
značenje faktora efikasnosti na osnovu grafičkog prikaza The physical meaning of the confinement effectiveness
utegnutog betona elementa kvadratnog, odnosno factor is graphically explained for confined concrete
kružnog poprečnog preseka. Dokazano je da su izrazi za elements of square and circular cross-sections.
sračunavanje koeficijenta utezanja prema Evrokodu 8 [2] Equations for calculating the confinement effectiveness
definisani odnosom: (1) zapremine tela prizmatičnog factor according to Eurocode 8 [2] have been shown and
oblika čija je osnova jednaka najmanjem poprečnom defined by the relation: (1) the volume of a prismatic
preseku efektivno utegnutog jezgra koji se može javiti element with basis equal to the smallest cross-section of
duž elementa; (2) zapremine tela prizmatičnog oblika the effectively confined core that may occur along the
čija je osnova definisana oblikom spoljašnje uzengije. element, and (2) the volume of the element of prismatic
Ovakva definicija daje konzervativne rezultate u odnosu form with basis defined by the form of external stirrup.
na „realni” faktor efikasnosti utezanja, definisan prema This definition gives conservative results with respect to
ukupnoj zapremini efikasno utegnutog betona. Takođe, the "real" confinement effectiveness factor, defined by
dokazano je da dodatno progušćavanje spoljašnje the total volume of effectively confined concrete. In
konturne uzengije na duplo manjem rastojanju ne addition, it has been shown that the added external
uvećava bitno vrednost koeficijenta utezanja. Ovaj stirrup between existing ones insignificantly increases
zaključak odnosi se isključivo na koeficijent utezanja, što the value of the confinement effectiveness factor. This
ne znači da betonski element, povećanjem poprečne conclusion applies only to the confinement effectiveness
armature, nema povećanje kapaciteta duktilosti. factor, which does not mean that the concrete element
will not increase the ductility capacity with increased
transverse reinforcement.
ZAHVALNOST ACKNOWLEDGMENTS
Autori zahvaljuju Ministarstvu prosvete, nauke i The authors thank the Ministry of Education, Science
tehnološkog razvoja Republike Srbije na finansijskoj and Technological Development of the Republic of
podršci u okviru projekata TR-36048 „Istraživanje stanja Serbia for financial support under the projects TR-36048
i metoda unapređenja građevinskih konstrukcija sa "Research on condition assessment and improvement
aspekta upotrebljivosti, ekonomičnosti i održavanja” i methods of civil engineering structures in view of their
451-03-02141/2017-09/49 „Procena seizmičkog serviceability, load-bearing capacity, cost effectiveness
odgovora postojećih objekata u Srbiji i Austriji – ocena and maintenance" and 451-03-02141/2017-09/49
stanja, ojačanje i sanacija”. "Seismic evaluation of existing buildings in Serbia and
Austria – assessment, retrofitting and strengthening".
6 LITERATURA
REFERENCES
[1] Ćosić M., Folić R., Brčić S.: Pregled savremenih [6] Milićević I., Ignjatović I.: Analiza primene
seizmičkih analiza i načina uvođenja prigušenja u sekundarnih seizmičkih elemenata u proračunu
njima, Građevinski materijali i konstrukcije 2017, prema Evrokodu 8, Građevinski materijali i
60(1), 3-30. konstrukcije 2017, 60(3), 15-29
[2] EN 1998-1: 2004: Poračun seizmički otpornih [7] Richart F.E., Brandtzaeg A., Brown R.L.: A study of
konstrukcija - Deo 1: Opšta pravila, seizmička the failure of concrete under combined
dejstva i pravila za zgrade, Građevinski fakultet u compressive stresses, Bulletin No. 185, University
Beogradu, 2009. of Illinois, Urbana, 1928.
[3] Fardis M.N.: Seismic design, assessment and [8] Sheikh S.A., Uzumeri S.M.: Strength and Ductility
retrofitting of concrete buildings based on EN - of Tied Concrete Columns, Journal of the Structural
Eurocode 8, Springer, Dordrecht, 2009. Division, 1980, Vol. 106, Issue 5, Pg. 1079-1102.
[4] Mander J.B., Prestley M.J.N., Park R.: Theoretical [9] Vidic T., Fajfar P., Fischinger M.: Consistent
stress-strain model for confined concrete, Journal inelastic design spectra: strength and
of Structural Engineering, 114(8), 1988, 1804- displacement, Earthquake Engineering and
1825. Structural Dynamics, 23, 1994, 507-521.
[5] Milev J., Problems and their solutions in practical
application of eurocodes in seismic design of rc
structures, Građevinski materijali i konstrukcije
2016, 59(3), 3-25
Fokus ovog rada usmeren je na efekte utezanja This paper is focused on the effects of confinement
armiranobetonskih preseka, odnosno na način na koji of the reinforcement reinforced concrete sections, i.e. in
poprečna armatura utiče na poboljšanje karakteristika – the way that the transverse reinforcement affects the
kako materijala, tako i utegnute zone elementa. improvement of the characteristics of both the material
Pojašnjeno je praktično značenje koeficijenta utezanja iz and the affected zone of the element. The practical
izraza Evrokoda 8. Izvršena je procena veličine dela meaning of the confinement effectiveness factor from the
elementa koji je efektivno utegnut uzengijama na expression of Eurocode 8 was explained. Size of the
primerima različito armiranih kružnih i kvadratnih part of element that is effectively confined by the stirrups
preseka stubova i analizom trodimenzionalnog prikaza is estimated on examples of differently reinforced
efektivno utegnutog betona. Uspostavljena je relacija circular and square sections of the column by analysis of
između koeficijenta utezanja prema izrazima Evrokoda 8 the three-dimensional presentation of effectively
i efektivno utegnutog dela betonskog elementa. confined concrete sections. The connection between
confinement effectiveness factor by Eurocode 8 and real
Ključne reči: Evrokod 8, lokalna duktilnost, effective concrete core is established.
koeficijent utezanja
Key words: Eurocode 8, ductility, confinement
effectiveness factor
STRUČNI RAD
Golubka NECHEVSKA-CVETANOVSKA PROFESSIONAL PAPER
Artur ROSHI UDK:624.012.45.042.7
doi:10.5937/GRMK1903019N
Figure 2.4. Connection of the old to the new reinforcement of the R/C jacket: a) protection of new bar against buckling
with welding; b) protection of new bar against buckling with octagonal ties; 1- existing column, 2- jacket, 3-key, 4-bent
bars, 5-added reinforcement, 6-ties, 7-welding, 8-alternating corners), (P.Gavrilovic [15])
R/C jackets are applied in the case of serious The concrete overlay of the jacket should be at least
damage or inadequate seismic resistance of the column 75–100 mm, to provide sufficient cover of the new
(including here failure of quality of concrete used on the reinforcement and space for 135◦-hooks at the tie ends
site during construction). Depending on the existing local (Fig. 3.2(a)). For this range of thickness, shotcrete is
conditions, jackets are applied along the perimeter of the more convenient. Thicker overlays are normally cast-in-
column, which is the ideal case, or sometimes on one or place.
more sides. − In order to increase the moment resistance of
In the case where the jacket is limited to the storey vertical elements, longitudinal reinforcement should be
height, an increase in the axial and shear strength of the continued to the adjacent storeys through the holes or
column is achieved with no increase in flexural capacity slots in the slab. To avoid perforating the beams on all
at the joints. Therefore, it is recommended that the sides of the cross-section, jacket bars continuing through
jackets protrude through the ceiling and the floor slabs of the slab should be concentrated near the corners of the
the storey where column strengthening is necessary new section, often in bundles (Fig.3.2. (b) and (c)).
(Figure 3.2). Jacket vertical bars may be anchored into a foundation
element either:
Figure 3.2. Concrete jackets in columns: a) the simplest case b) jacket bars bundled near corners, engaged by cross-ties
or orthogonal tie c) jacket bars bundled at corners, dowels at interface with old column d) U-bars welded to corner bars
e) steel plates welded to corner bars f) one-or two-sided jackets g) one-sided concrete overlay with single curtain of two
way reinforcement at exterior face of perimeter walls, (M,Fardis[12])
(a) (b)
Figure 3.4. Steel jackets built-up in situ with corner angles and horizontal straps
Moisture and
Strength Modulus Cost
chemical resistance
Carbon High High Excellent High
Aramid High Intermediate Good High
E-Glass High Low Low Low
Confinement strengthening (Figure 4.3 ) consists of: the volume of the strengthened member. In addition,
(1) Cleaning and repair significant improvements can be achieved in the
(2) Primer capacity and ductility characteristics of the element. In
(3) Adhesive Figure 4.4, beam strengthening in an existing structure is
(4) FRP strips presented.
(5) Last adhesive layer These materials may be used for numerous
purposes such as enhancement of the flexural capacity
Fibre polymer fabrics that can be used to improve of floor slabs and improvement of shear capacity of
bending, shear and axial capacities of the columns and beams, columns, joints and shear walls (Fig. 4.5 and
beams may be manufactured from various materials Fig. 4.6)
such as carbon, glass and aramid without an increase in
5 CONCLUSION
[1] Eurocode 8: Design of Structures for Earthquake [15] Gavrilovic, P. “Repair and Strengthening of
Resistance - Part 1: General Rules, Seismic Building Structures” lecture notes, Institute of
Actions and Rules for Buildings. Earthquake Engineering and Engineering
[2] CEN 2004, European Standard EN 1998-3: 2005 Seismology, Skopje 2005.
Eurocode 8: Design of Structures for Earthquake [16] Yan Z, Pantelides CP (2007), “Design-Oriented
Resistance. Part 3: Assessment and Retrofitting of Model for Concrete Columns Confined with Bonded
Buildings. FRP Jackets or Post-Tensioned FRP Shells”, In:
[3] Folić, R., Zenunović, D. Liolios, A., “ Triantafillou TC (ed) 8th International Symposium
Recommendation for seismic apgrading of on Fiber Reinforced Polymer Reinforcement for
damaged RC Structures”, Int Conf. Structural Concrete Structures (FRPRCS-8), Patras, GR,
Faults and Repair" June 2014, Edinburgh, paper 6-1.
Scotland, Proc. Editor: Professor M C Forde [17] Jones, I.A; Owen, M.J.; Middleton, V; “Integrated
[4] Golubka Nechevska-Cvetanovska, “Non-Linear Design and Manufacture Using Fibre-Reinforced
Analysis and Design of RC Cross-Section Resis- Polymeric Composite”, CRC Press LLC,
tance of RC Buildings”, published September 1998. Cambridge, England, 2000.
[5] Ozcebe, G., Ersoy, U., Tankut, T,, Akyuz, U., and [18] http://www.mdacomposites.org/Manufacturing.htm,
Erduran, E., 2004. “Rehabilitation of Existing RC Market Development Alliance of the FRP
Structures Using CFRP Fabrics”, Proceedings of Composites Industry, Copyright 2000-2001 Market
the 13th World Conference on Earthquake Development Alliance of the FRP Composites
Engineering, Vancouver, Canada, Paper No. 1393. Industry.
[6] Earthquake-Resistant Construction of Adobe [19] Ko, Frank K., Du, George W., “Handbook of
Buildings (available in Spanish and English) EERI Composites-Textile Preforming”, Chapman and
Publication # WHE-2006-01 (published on the web Hall, 1998, London, England.
in 2003; hard copy in 2006). [20] Andrea Prota “Innovative Building Materials”,
[7] M. DI ludovico, A. Prora, G.Manfredi and lecture notes, Department of Structural
E.Gosenza, “Seismic Strengthening of an Under- Engineering, University Federico II, Naples, 2014.
design RC Structure with FRP”, Department of [21] Di Ludovico M. “Design and Retrofit of RC
Structural Engineering, University of Naples Constructions”, lecture notes, Department of
Federico II, Naples, Italy, Published online 24 Structural Engineering, University of Naples
August 2007 in Wiley InterScience; Federico II, 2013.
[8] CNR-DT 200/2004. Guide for the Design and [22] Mazzolani “Protection of Historical Buildings”,
Construction of Externally Bonded FRP Systems PROHITECH 09, 2009 Taylor & Francis Group,
for Strengthening, 2004 (Downloaded free from: London.
http://www.cnr.it/sitocnr/IlCNR/Attivita/Normazionee [23] Folić, R., Radonjanin, V., Prokić, A., Malešev, M.:
Certificazione/NormazioneeCertificazione Earthquake dame to RC bridges and review of
file/IstruzioniCNR DT200 2004 eng.pdf). recommendation for its repair and strengthening
[9] Abbas Moustafa “Earthquake_Resistant Struc- (ID 1594-Folic), 16th European Bridge Conference,
tures-Design, Assessment and Rehabilitation”, 23rd – 25th June 2015, Edinburgh, Scotland, Proc.
Published online February 2012, published in print Editor: Professor M C Forde, pp.18. ,ISBN No: 0-
edition February 2012. 947664-78-4;
[10] “Handbook on Seismic Retrofit of Buildings”, April [24] N. Pojani (2003). "Seismic Engineering". Published
2007, edited by Indian Institute of Technology- at TOENA, Tirana, Albania.
Madras. [25] A. K. Chopra (2003). “Dynamic of Structures” 2nd
[11] Barbara Ferracuti, Marco SAVOLA, Roberto ed. Theory and Application to Earthquake
FRANCIA, Rui PINHO, Stelios ANTONIOU “Push- Engineering. Prentice Hall, New Jersey.
over Analysis of FRP-Retrofitted Existing RC [26] T. Paulay and M. J. Priestly (1992). “Seismic
Frame Structures”, University of Patras, Patras, Design of Reinforced Concrete and Masonry Struc-
Greece, July 2007. tures”. Wiley & Sons, ISBN 0 - 471 - 54915 - 0.
[12] Michael_N.Fardis, “Seismic Design, Assessment [27] G. Necevska-Cvetanovska and R. Petrusevcka
and Retrofitting of Concrete Buildings, (2000). “Methodology for Seismic Design of R/C
Department of Civil Engineering, University of Building Structures “. 12WCEE.
Patras, Greece, 2009. [28] European Committee. “ Eurocode – 2: Design of
[13] L C Hollaway and M B Leeming, “Strengthening of concrete structures”.
Reinforced Concrete Structures Using Externally- Part 1-1: General rules and rules for buildings.
Bonded FRP Composites in Structural and Civil English version, December 2004.
Engineering”, published in North and South America [29] ”NATO SfP 977231 Project: "Seismic Assessment
by CRC Press LLC, 2000 Corporate Blvd, NW. and Rehabilitation of Existing Buildings", NATO
[14] L.C. Hollaway and J.G. Teng, “Strengthening and Science Series.
Rehabilitation of Civil Infrastructures Using Fibre-
Reinforced Polymer (FRP) Composites” published
2008, Woodhead Publishing Limited and CRC
Press LLC.
PRETHODNO SAOPŠTENJE
PRELIMINARY REPORT
Marin VASSILEV UDK:692.232.046.3
doi:10.5937/GRMK1903031
1 INTRODUCTION
Despite the extensive application of portal frames for the selection of adequate criterion for load-carrying
single-storey buildings with steel structures, there are resistance. The application of the geometrical and
still some aspects of their stability that require additional material nonlinear analysis with imperfections (GMNIA)
clarification. No codified practical method is given in is also clarified and discussed in [3]. Some well known
EN 1993-1-1 [1] for lateral-torsional stability verification simplified methods for out-of-plane stability verification of
of rafters in the haunched portions loaded by hogging rafters and haunches are presented as well. However
bending moments. It seems that, within the code, there they consider restraints at the bottom flanges too, and
are only two possible approaches: the general method thus appear unsuitable for local practice. Nevertheless,
for lateral (clarified in details in [5], [6] and [7]) and lateral some brief description of GMNIA is presented.
torsional buckling (§6.3.4 of [1]) and geometrically and The third type of analysis, GMNIA, is also carried out
materially nonlinear analysis with imperfections (GMNIA) automatically. The model with shell FE is generated and
as regulated by §2.5 and Annex C of EN 1993-1-5 [2]. linear buckling analysis is initially performed. The first
However, both methods seem quite complicated and overall out-of-plane buckling mode is used to obtain the
cumbersome for practical use. initial imperfections pattern, scaled according to §5.3.4
The lateral-torsional stability of rafters seems an of EN 1993-1-1 [1]. A revised model is thus generated.
even more complicated problem, taking into account the Material nonlinearity is based on bilinear constitutive law
haunched portions, the negative (hogging) bending with isotropic strain hardening. The load-carrying
moments and the specific restraint conditions with lateral capacity of the frame is assumed to correspond to the
supports at the top (tensile) flange only (the so-called ‘fly ultimate state criterion ‘attainment of the maximum load’.
bracing’ is unconventional for Bulgarian practice). The stressed state and the failure mode are also
Therefore, the author has recently carried out an analysed. The software used is ABAQUS nonlinear FE
extensive research and theoretical analyses in the above software (Abaqus 2016) [6]. A typical picture at limit
context. In a recent publication [3] the general method state is illustrated in Figure 1.
for lateral buckling has been discussed in details with The primary objective of this study was to adapt,
emphasis on the specific issues of its application to the propose and confirm a simplification of widely spread
frame lateral stability, namely the complex modelling, the practical method for calculating buckling capacity of
correct identification of the relevant buckling mode and haunch. The latter is based on buckling verification of
equivalent compressed strut and it is illustrated in Fig. 2.
In this well-known simplified model from literature [4], 2 NUMERICAL ANALYSIS OF METHODOLOGY FOR
an equivalent compressed strut is defined in section 1 as HAUNCH VERIFICATION
illustrated in the figure. The axial compression force on
the strut is determined in the same section. The lateral An analysis is made, independently upon the
buckling verification of the haunched portion is then simplified methodology with an equivalent compressed
replaced by out-of-plane flexural buckling check of the strut, of haunched zones consisting a profile of type IPE
strut. Buckling length coincides with the geometric length and a haunch cut from the base profile, with an initial
of the member. The method seems very simple, height coinciding with the initial height of the beam
however requires a fly-brace restraint at the haunch end projected on the column. Examined lengths for the
[4](both flanges at both ends of element must be haunched section are between 1 cm and 500 cm. Thus,
restraint for out-of-plane movement). Nevertheless, the it can be said that all possible cases are considered in
method is also applied in this study with a view to be full-wall frames made of rolled profiles (for example, if
eventually adapted to the typical practice in Bulgaria, we decide that the haunch length is 10% of the frame
where fly bracing is absent. Imperfections are opening and is 4 meters long, it means that the frame
considered according to [1] when calculating buckling should have an opening of40 meters– on such an
compression capacity of T-strut. Considered haunches opening a IPE-type rolled profile can hardly be applied).
are identical and composed of steel grades – S235, The geometry of the options considered is shown
S275 and S355. schematically in Figure 3.
The purpose of the upcoming analysis is to draw out
simplified formulas to apply the simplified method with
an equivalent pressed rod, especially for the IPE-type
beam and the haunch with the same profile described in
Figure 3.
2.1 Analysis of haunch buckling capacity In Figure 4, the illustrated dependence is done for a
350 cm long haunched section, but for practically
We will initially evaluate the effect of the size of the different lengths, the tendency remains. Only the small
equivalent compressed strut. Its magnitude depends on eccentricities have some effect on the load bearing
the compressed part of the stem, respectively the capacity of the element – at e <200. The typical
eccentricity of the force, reduced at some distance from eccentricity of the frames examined by about 10% slope
the center of gravity of the cross section: is about 300 cm (eg 1000 kNm bending moment and
approximately 300 kN pressure in section of the third).
e = M / N [cm] (1)
Although the eccentricity does not have an enormous
Figure 4 illustrates a relationship between the importance – about 10% (maxNb,Rd,z / minNb,Rd,z~ 1,1), in
bearing capacity of the T-section equivalent order to be safe for the next reasoning, we will perform a
profile(Nb,Rd,z) for the various rolled profiles, in function of detailed analysis with an eccentricity value of about 300
eccentricity. cm (this way we will work with the “lower” values of the
load bearing capacity).
Fig. 5. Compression capacity of equivalent T-struts with different lengths composed of steel grade S235
Fig. 6. Compression capacity of equivalent T-struts with different lengths composed of steel grade S275
Fig. 7. Compression capacity of equivalent T-struts with different lengths composed of steel grade S355
2.2 Compression force in equivalent T-profile force which is checked and deducted to this equivalent
T-profile should be known. Therefore, the different
Formula (5) is valid for all the haunched zones listed geometric characteristics of the described profiles will be
at the beginning of the current subsection (fig.3). analyzed at the different eccentricities, respectively.
Naturally, if it is used in calculations, the compression
5 REFERENCES
[1] EN 1993-1-1: Eurocode 3: Design of steel [6] Penelov Č., A. Stojkov, P. Cvetkova. The
structures. Part 1-1: General rules and rules for application of the general method of EN1993-1-1 to
buildings, CEN, 2005. stability evaluation of steel members which are
[2] EN 1993-1-5: Eurocode 3: Design of steel within the scope of application of the standard
structures. Part 1-5: Plated structural elements, method for members in compression and bending.
CEN, 2006. Annual of UACEG, vol. XLVI-V, Sofia, 2013-14.
[3] Vassilev M., N. Rangelov. Stability problems of [7] Penelov Č., A. Stojkov, P. Cvetkova. The
single storey steel frames (Part 1). Annual of application of the general method of EN1993-1-1 to
UACEG, vol. 51(4), Sofia, 2018. stability verification of steel tapered members in
[4] Koschmidder D.M., D.G. Brown. Elastic design of compression and bending. Annual of UACEG, vol.
single span steel portal frame buildings to XLVI-V, Sofia, 2013-14.
Eurocode 3, SCI Publication P397, 2012. [8] Abaqus, 2016. Dassault Systems / Simulia,
[5] Simões da Silva, L., Simões, R., Gervásio, H. Providence, RI, USA
2010. Design of Steel Structures. ECCS.
Recently the author have conducted an extensive Autor je sproveo opsežnu teorijsku analizu bočne
theoretical analysis programme on lateral stability of stabilnosti čeličnih portalnih okvira toplo valjanih profila.
steel portal frames of hot-rolled profiles. Specific Razvijen je poseban softver za automatsko modelovanje
software has been developed for automatic modelling i primenu GMNIA metode s ciljem da se predlože
and applying the GMNIA method with a view to propose jednostavna i pouzdana pravila projektovanja za
simple and reliable design rules for practical use. praktičnu upotrebu. Dokazano je da je pojednostavljena
A simplified method with equivalent compressed strut metoda sa ekvivalentnim pritisnutim podupiračima u zoni
regarding haunched area was proven to be reliable. vute pouzdana. Metod je analiziran i pojednostavljen
Therefore the author has analysed and simplified the kako bi bio lakši za primenu.
method to make it easier to use.
Ključne reči: Čelični portalni okviri , ekvivalentni
Key words: Steel portal frames, Equivalent pritisnuti podupirač, vuta
compressed strut, Haunch
1 UVOD 1 INTRODUCTION
Problematika ispitivanja integriteta šipova u posled- The problem of pile integrity testing has expanded
njih dvadesetak godina doživela je ekspanziju u pogledu: over the last twenty years in terms of: test methodology,
metodologije ispitivanja, tehnike i instrumentalizacije test technique and instrumentalization, diversity of test
ispitivanja, raznovrsnosti tipova testova ispitivanja, types, software-hardware test support, and signal theory
softversko-hardverske podrške ispitivanju i teorije i and processing. In this sense, being a civil engineer or
obrade signala. U tom smislu, biti građevinski inženjer ili geotechnical engineer with experience in the field of
inženjer geotehnike sa iskustvom u oblasti projektovanja foundation design and construction is insufficient; a
i izgradnje fundamenata nije dovoljan uslov, već se rather multidisciplinary consideration of pile testing is
zahteva multidisciplinarnost u razmatranju problematike required. In addition to standard scientific disciplines,
ispitivanja šipova. Pored standardnih naučnih disciplina, such as: theory of elasticity, soil mechanics, soil
kao što su teorija elastičnosti, mehanika tla, dinamika tla, dynamics, rock mechanics, foundations, structural
mehanika stena, fundiranje, ispitivanje konstrukcija, testing requires a good knowledge of relatively recent
zahteva se i dobro poznavanje relativno novije naučne scientific topics of soil-structure interactions, but also
tematike interakcija konstrukcija–tlo, ali i drugih naučnih other scientific topics which are not primarily studied in
tematika (koje se primarno ne izučavaju u građe- construction or geotechnics, such as: wave theory,
vinarstvu ili u geotehnici), kao što su: talasna teorija, method of characteristics, theory and signal processing,
metoda karakteristika, teorija i obrada signala, termo- thermodynamic theory, etc. The degree of reliability of
dinamička teorija i slično. U zavisnosti od stepena the applied methodology and interpretation of test results
poznavanja određenih naučnih disciplina, zavisi i stepen also depends on the degree of knowledge of particular
pouzdanosti primenjene metodologije i interpretacije scientific disciplines. The experience of the authors of
rezultata ispitivanja. Iskustva autora ovog rada pokazuju this paper indicates that there is often an inadequate
da se neretko nailazi na neadekvatnu interpretaciju interpretation of the pile testing standards, even of the
standarda ispitivanja šipova, pa i kompletne metodolo- complete testing methodology. In this sense, the focus of
gije ispitivanja. U tom smislu, težišta ovog rada jesu da this paper is to present some of the authors' experiences
se predstave određena iskustva autora rada i da se and to indicate the need for consistency in the
ukaže na potrebu za doslednošću u primeni metodolo- implementation of the pile testing methodology
gije ispitivanja šipova, koja je prikazana u radu [6]. S presented in [6]. On the other hand, the application of
druge strane, primena nekoliko metoda u ispitivanju several methods in pile integrity testing allows a better
integriteta šipova omogućava bolje sagledavanje understanding of the final test solution. All of these
finalnog rešenja ispitivanja. Sve ove metode, primarno, methods are primarily based on the wave theory, but
zasnivaju se na talasnoj teoriji, ali i na procesiranju also on signal processing and numerical analyses.
signala i na numeričkim analizama.
Dr Mladen Ćosić, Institut za ispitivanje materijala IMS, Dr Mladen Cosic, Institute for testing of materials IMS,
Beograd, Srbija, mladen.cosic@institutims.rs Belgrade, Serbia, mladen.cosic@institutims.rs
Mr Kristina Božić-Tomić, Institut za ispitivanje materijala Mr Kristina Bozic-Tomic, Institute for testing of materials
IMS, Beograd, Srbija, kristina.tomic@institutims.rs IMS, Belgrade, Serbia, kristina.tomic@institutims.rs
Dr Nenad Šušić, Institut za ispitivanje materijala IMS, Dr Nenad Susic, Institute for testing of materials IMS,
Beograd, Srbija, nenad.susic@institutims.rs Belgrade, Serbia, nenad.susic@institutims.rs
Test integriteta šipa sa senzorom (SIT) u praksi se Sonic Integrity Test (SIT) is in practice also called the
zove i test eha zvuka (SET) ili test eha šipa (PET), a Sonic Echo Test (SET) or Pile Echo Test (PET), and it
pripada grupi niskodilatacionih testova (LST). Test belongs to the group of Low Strain Tests (LST). SIT is
integriteta šipa sa senzorom (SIT) zasniva se na teoriji based on the theory of one-dimensional wave
jednodimenzionalne propagacije talasa kroz šip, s ciljem propagation through the pile, with the aim of
utvrđivanja: stvarne dužine šipa, postojanje defekata i determining: the actual length of the pile, existence of
diskontinuiteta i redukcije poprečnog preseka šipa [6]. defects and discontinuities and reduction of the pile
Takođe, analiziraju se: promena signala u domenu glave cross-section [6]. In addition, it analyzes variation of
šipa, kvalitet odziva signala u bazi šipa, promena signal in the pile head domain, signal response quality at
a) b)
Slika 1. Opreme za ispitivanje integriteta šipova testom integriteta šipa sa senzorom (SIT): a) SIT+ oprema holandske
firme Profound [15]; b) PIT-QFV oprema američke firme Pile Dynamics [12]
Figure 1. Equipment sets for pile integrity testing using SIT: a) SIT + Dutch Profound company equipment [15], b) PIT-
QFV U.S. Pile Dynamics company equipment [12]
a) b)
Na slici 3 prikazani su reflektogrami SIT integriteta Figure 3 shows SIT reflectograms of pile integrity
šipova dobijeni SIT+ holandskom opremom: regularan obtained by the Dutch equipment SIT+: regular pile, pile
šip, šip sa značajnijim redukcijama impedance u with significant impedance reductions in certain cross-
određenim presecima, nejasan odziv baze šipa i nakon sections, a vague pile toe response even after appli-
primene eksponencijalnog filtera, redukcija impedance cation of an exponential filter, the impedance reduction
Pile : 322 11.1.2019. Pile : 1215 18.2.2019.
v = 2,5 mm/s v = 1,8 mm/s
t50% = 0,56 ms t50% = 0,69 ms
a)Pile : 180 5 10 15 20
31.1.2019. b)Pile : 6 0 5 10 15 20 25 30 35
14.2.2019.
c = 4200 m/s l = 18,00 m fil = 0,31 ms exp : 10 V 7.98 auto cv = 3950
v = 2,3 mm/s = 2,3m/s
mm/sl = 30,00 m fil = 0,31 ms exp : 10 V 7.98 auto
t50% = 0,66 ms t50% = 0,49 ms
e) 0 5 10 15 20 25 f) 0 5 10 15 20 25
c = 4150 m/s l = 20,00 m fil = 0,31 ms exp : 5 V 7.98 auto c = 3800 m/s l = 23.50 m fil = 0.31 ms exp : 10 V 7.98 auto
Slika 3. Reflektogrami SIT integriteta šipova dobijeni SIT holandskom opremom: a) regularan šip; b) šip sa značajnijim
+
redukcijama impedance u određenim presecima; c) nejasan odziv baze šipa i nakon primene eksponencijalnog filtera; d)
redukcija impedance znatnije pre baze šipa; e) varijacija signala iz pozitivne u negativnu vrednost - posledica niskog
modula elastičnosti glave šipa; f) značajna redukcija impedance u početnom delu šipa - defekat/diskontinuitet
Figure 3. SIT reflectograms of pile integrity obtained by the Dutch equipment SIT +: a) regular pile, b) pile with significant
impedance reductions in certain cross-sections, c) vague pile toe response even after application of an exponential filter,
d) impedance reduction significantly before the pile toe, e) signal variation from positive to negative value - consequence
of low modulus of elasticity of the pile head, f) significant impedance reduction in the initial part of the pile -
defect/discontinuity
a) b)
c) d)
Slika 4. Reflektogrami SIT integriteta šipova dobijeni PIT-QFV američkom opremom: a) regularan šip; b) šip s redukcijom
impedance u početnom delu; c) efekat povećanja impedance i krutosti tla; d) šip izgrađen kraći nego što je projektom
predviđeno
Figure 4. SIT reflectograms obtained by the U.S. PIT-QFV equipment: a) regular pile, b) pile with impedance reduction in
the initial part, c) effect of increasing the impedance and soil stiffness, d) pile built shorter than designed
Prilikom sprovođenja SIT integriteta šipa, kod During the implementation of pile integrity SIT, in
određenih reflektograma, mogu se pojaviti značajnije certain reflectograms, considerable impedance
redukcije impedance, što može biti jedan od pokazatelja reductions may occur, which may be one of the
defekta i/ili diskontinuiteta šipa. Da bi se detaljnije indicators of a defect and/or discontinuity of the pile. In
analizirao stepen defekta i/ili diskontinuiteta, sprovodi se order to analyze in more detail the degree of the defect
dodatna analiza koja se zasniva na talasnoj teoriji i and/or discontinuity, an additional analysis is conducted,
metodi karakteristika. Softver SITWAVE ima mogućnost which is based on the wave theory and method of
analize promene impedance duž stabla šipa, tako da se characteristics. The SITWAVE software has the ability to
efikasno može dobiti oblik šipa izgrađen u tlu, dok analyze the impedance variations along the pile shaft, so
softver PIT-S ima mogućnost analize oblika šipa that the pile shape built in the soil can be effectively
primenom β metode. S obzirom na veću pouzdanost obtained, while the PIT-S software has the ability to
rešenja koje se dobija primenom SITWAVE softvera, jer analyze the pile shape using the β method. Due to the
je, između ostalog, matematička analiza promene higher reliability of the solution obtained by the
impedance kompleksnija i naučno utemeljenija, ovaj application of SITWAVE software, because, among
softver se i češće koristi za ovakve situacije. Jednačina other things, the mathematical analysis of impedance
propagacije talasa putem elastičnog medijuma, u variation is more complex and scientifically founded, this
opštem slučaju, jeste hiperbolična parcijalna software is more often used in such situations. The wave
diferencijalna jednačina drugog reda [23]: propagation equation through an elastic medium is, in
the general case, a hyperbolic partial differential
equation of the second order [23]:
(1)
,
gde je v brzina talasa, u pomeranje, t vreme. Ukoliko je where v is the wave velocity, u displacement, t time. If
dužina talasa veća od prečnika šipa ili jednaka prečniku the wavelength is higher than or equal to the pile
šipa, tada se propagacija talasa u šipu može razmatrati diameter, then the wave propagation in the pile can be
primenom jednodimenzionalne teorije rasprostiranja analyzed by applying the one-dimensional theory of
talasa u čvrstom medijumu [11]. Jednodimenzionalna wave propagation in a solid medium [11]. The one-
(2)
,
a opšte rešenje ove jednačine glasi: and the general solution of this equation is:
. (3)
Brzina propagacije longitudinalnih talasa u čvrstom The velocity of propagation of longitudinal waves in a
medijumu v jeste funkcija karakteristika materijala tog solid medium v is the function of material characteristics
medijuma i određuje se prema: of that medium and it is determined according to:
, (4)
gde je E Young-ov modul elastičnosti, ρ zapreminska where E is the Young modulus of elasticity, ρ is density.
težina. Sada se jednačina (2) može pisati kao: Now equation (2) can be written as:
, (5)
pri čemu se rešenje traži tako da su vreme i pomeranje whereby solution is sought so that time and
nezavisne promenljive: displacement are independent variables:
, (6)
a zatim zamenom izraza (6) u (2) dobija se: and then, by the substitution of expression (6) in (2) is
obtained:
i / and . (7)
Rešenje problema (7) moguće je dobiti za The solution of the problem (7) can be obtained for
jednostavnije sisteme i konturne uslove u zatvorenom simpler systems and contour conditions in a closed form,
obliku, međutim kod kompleksnijeg modeliranja šipa s however, in more complex modelling of a pile with
diskontinuitetima i defektima potrebno je primeniti discontinuities and defects, it is necessary to implement
metodu konačnih elemenata. S druge strane, ukoliko se the finite element method. On the other hand, if the
problem propagacije talasa u šipu razmatra u diskretnim problem of wave propagation in a pile is considered in
segmentima, tada je rešenje jednačine (2) moguće discrete segments, then the solution to the equation (2)
odrediti metodom karakteristika, pri čemu se izraz (3) could be determined using the method of characteristics,
može pisati kao [24], [18]: whereby expression (3) can be written as [24], [18]:
, (8)
gde je ↓ oznaka za talas koji se kreće od glave ka bazi where ↓ is the designation for the wave propagating from
šipa, a ↑ oznaka za talas koji se kreće od baze ka glavi the head to the toe of the pile, and ↑ the designation for
šipa. Odgovarajuća brzina talasa vp i sila F koja se the wave propagating from the toe to the head of the
indukuje u šipu, za diskretan element šipa, određuju se pile. The corresponding wave velocity vp and force F
iz: induced in the pile, for the discrete element of the pile,
are determined from:
, (9)
, (10)
gde je A površina poprečnog preseka šipa. Pošto su vp↓ i where A is the area of the pile cross section. Since vp↓
F↓ samo funkcije od (x-vt) i vp↑ i F↑ samo funkcije od and F↓ are only functions of (x-vt) and vp↑ and F↑ only
(x+vt), brzina i sila mogu se pisati kao: functions of (x+vt), the velocity and force can be written
as:
i / and , i (11)
,
Bilo koja promena A, E ili ρ parametra generiše Any variation of A, E or ρ parameters generates a
promenu u odzivu brzina na reflektogramu. U slučaju variation in the response of velocities in the
diskontinuiteta, kada je na jednom delu prečnik šipa reflectogram. In case of a discontinuity, when a section
manji, jednačine ravnoteže za granicu dva medijuma of the pile has a smaller cross section, equilibrium
glase: equations for the interface of two media are:
i / and , i (13)
,
gde se indeksi 1 i 2 odnose na medijume. Zamenom where indices 1 and 2 refer to the media. Substituting
(11) u (13) dobija se: (11) for (13) the following is obtained:
(14)
,
Kada je šip pobuđen na vibracije u tlu postoji When a pile is excited to soil vibrations, there is a
kompleksna interakcija šip–tlo, gde se sila trenja po complex soil-pile interaction, where the friction force
omotaču šipa W uzima u razmatranje kao: along the pile surface W is taken into consideration as:
, (15)
i / and . i (16)
,
Komponente sila za medijume se sada određuju Force components for media are determined
prema: according to:
i / and . i (17)
,
U bazi, na kontaktu šipa i tla, jednačine ravnoteže At the toe, on the contact of the pile and the soil,
glase: equilibrium equations are:
i / and i (18)
,
,
gde je L dužina šipa, a Fg sila reakcije tla. Ukoliko se šip where L is the pile length, and Fg soil reaction force. If
diskretizira po dužini na n delova, pri čemu je dužina the pile is discretized along its length to n sections,
jednog diskretnog elementa ΔL=vΔt, a vreme whereby the length of one discrete element is ΔL=vΔt,
propagacije talasa kroz šip razmatra se u diskretnim and the time of wave propagation through the pile is
intervalima Δt, tada se za sile u diskretnim elementima considered in discrete intervals Δt, then, for the forces in
f↓n,i i f↑n,i može pisati: the discrete elements f↓n,i and f↑n,i it can be written:
, (19)
, (20)
gde je ZN impedanca diskretnog N elementa šipa, ZN+1 where ZN is the impedance of a discrete N element of
impedanca diskretnog N+1 elementa šipa. Model the pile, ZN+1 impedance of the discrete N+1 element of
interakcije šip-tlo jeste jednodimenzionalni kontinualni the pile. The soil-pile interaction model is a one-
diskretan model, kod koga se tlo modelira kontinualno dimensional continuous discrete model, in which the soil
raspodeljenim oprugama duž šipa i koncentrisanom is modelled by continuously distributed springs along the
oprugom u bazi šipa. Konstitutivni model ponašanja tla pile and concentrated spring at the pile toe. The
je linearno-elastičan, a dodatno se modelira i prigušenje constitutive model of soil behaviour is linear-elastic, and
tla. Usklađivanje signala (odgovora), dobijenog soil damping is additionally modelled. When matching
primenom proračunskog modela i reflektograma in-situ the signals (responses) obtained by applying the
SIT ispitivanja, sprovodi se iteracijama, a ovaj postupak calculation model and from reflectograms of in-situ SIT
je poznat kao kompatibilizacija. Prvo se iteriraju testing is carried out through iterations, and this
parametri tla, a zatim, nakon postizanja konvergencije procedure is known as signal matching. The soil
rešenja putem ovih iteracija, sprovodi se iteriranje parameters are first iterated, and then, after achieving
geometrijskih parametara (poprečnog preseka) šipa. the convergence of the solutions through these
Takođe, intervencija se sprovodi i korekcijom modula iterations, iteration of the geometric parameters (cross-
a) b)
c) d)
Slika 5. Reflektogrami šipova 1 i 2: a) reflektogram šipa 1; b) reflektogram šipa 2; c) kompatibilizovani signal
šipa 1 - finalna iteracija; d) kompatibilizovani signal šipa 2 - finalna iteracija
Figure 5. Piles 1 and 2 reflectograms: a) pile 1 reflectogram 1, b) pile 2 reflectogram, c) pile 1 matched signal
(final iteration), d) pile 2 matched signal (final iteration)
Na slici 6 prikazani su oblici defektnih šipova dobijeni Figure 6 shows defective pile shapes obtained using
primenom softvera SITWAVE: oblik šipa 1 dobijen putem the SITWAVE software: pile shape 1 obtained through
početnih iteracija (slika levo) i oblik šipa 1 dobijen u initial iterations (figure left) and pile shape 1 obtained in
poslednjoj iteraciji (slika desno), oblik šipa 2 dobijen the final iteration (figure right), pile shape 2 obtained
putem početnih iteracija (slika levo) i oblik šipa 2 dobijen through initial iterations (figure left) and shape pile 2
u poslednjoj iteraciji (slika desno). Dobijeni oblici su obtained in the final iteration (figure right). The resulting
zapravo funkcija promene impedance, gde – pored shapes are, in fact, a function of the impedance
promene geometrijskih karakteristika – učestvuju i variation, where in addition to variation of the
mehaničke karakteristike šipa. To znači da se redukcija geometrical characteristics, the mechanical
poprečnog preseka odnosi na promenu prečnika šipa i/ili characteristics of the pile also participate. This means
na promenu modula elastičnosti betona. Na osnovu that the reduction in cross-section refers to the change in
ovako sprovedenih analiza, primenom softvera pile diameter and/or the change in modulus of elasticity
SITWAVE, naknadno su izvedena bušenja i vađenja of concrete. Based on the analyzes performed in this
uzoraka šipova 1 i 2, tako da su ova ispitivanja potvrdila way, by using the SITWAVE software, the drilling and
da postoje defekti u zonama koje su prethodno extraction of piles 1 and 2 samples were subsequently
identifikovane kao domeni redukcije impedance šipova. performed, and these tests confirmed that there were
defects in the zones previously identified as domains of
pile impedance reduction.
Numeričke analize integriteta šipa sprovode se Numerical SIT analyses are conducted by varying
promenom metode konačnih elemenata (FEM – Finite the finite element method (FEM), whereby the pile and
Element Method), pri čemu se šip i tlo modeliraju 2D the soil are modelled using 2D surface finite elements or
površinskim konačnim elementima ili se koriste konačni finite elements for rotational symmetry. In the procedure
elementi za rotacono simetrično stanje. U postupku of determining acceleration, velocity and displacement of
određivanja ubrzanja, brzine i pomeranja šipa the pile, differential motion equations are observed:
posmatraju se diferencijalne jednačine kretanja:
, (21)
gde je [M] matrica masa, {A} vektor ubrzanja, [C] matrica where [M] is mass matrix, {A} acceleration vector, [C]
prigušenja, {V} vektor brzine, [K] matrica krutosti, {U} damping matrix, {V} velocity vector, [K] stiffness matrix,
vektor pomeranja i {Q} vektor spoljašnjeg opterećenja. {U} displacement vector and {Q} external load vector.
Rešavanje jednačina (21) se sprovodi numeričkom Solving equations (21) is conducted using step-by-step
integracijom korak po korak Hilber-Hughes-Taylor-ovim numerical integrations using the Hilber-Hughes-Taylor
(HHT) postupkom u modifikovanom obliku [10]: (HHT) procedure in a modified form [10]:
, (22)
. (23)
Numeričko modeliranje defekata šipa sprovodi se Numerical modelling of pile defects is performed by
analizom šipa kroz faze oštećenja (SDA). SDA analiza pile stage degradation analysis (SDA). SDA analysis is
se konstruiše tako da se povezivanjem individualnih constructed in such a way that the effects of pile defects
analiza generišu i simuliraju uticaji defekata šipa. Ove are generated and simulated by linking individual
analize se sukcesivno sprovode korišćenjem matrica analyses. These analyses are successively performed
krutosti sistema na kraju prethodne analize stanja using the system stiffness matrix at the end of the
defekata, kao inicijalne matrice krutosti sistema naredne previous defect state analysis as the initial stiffness
analize stanja defekata. Matematička formulacija SDA matrix of the subsequent defect state analysis. The
analize izvedena je polazeći od izraza za stanje potpune mathematical formulation of SDA was derived from the
integralnosti šipa [8]: expression for the state of the complete pile integrity [8]:
, (24)
, , (25)
gde je matrica krutosti eliminisanog domena Where is the stiffness matrix of the eliminated
konačnih elemenata šipa (simulacija defekata), [M0] domain of finite elements of the pile (defect simulation),
matrica masa integralnog šipa (bez defekata), [M0] mass matrix of the integral pile (without defects),
matrica masa eliminisanog domena konačnih elemenata mass matrix of the eliminated domain of finite pile
šipa (simulacija defekata). U i-toj fazi analize defekata elements (defect simulation). In i-th phase of pile defect
šipa, proračun se sprovodi prema: analysis, the calculation is conducted according to:
, , (26)
dok za n-tu fazu važi: while for the n-th phase, it is:
, , (27)
gde je [Kn] matrica krutosti defektnog šipa u finalnoj fazi where [Kn] is the stiffness matrix of the defective pile in
proračuna, [Mn] matrica masa defektnog šipa u finalnoj the final calculation phase, [Mn] the defective pile mass
fazi proračuna. Na slici 7 prikazani su modeli šipova s matrix in the final calculation phase. Figure 7 shows pile
defektima i bez njih, dok su na slici 8 prikazani models with and without defects, while Figure 8 shows
reflektogrami numeričkih modela šipova i tla: integralni reflectograms of the numerical pile and soil models:
šip (bez defekata), šip s redukovanim kvalitetom integral pile (without defects), pile with reduced quality of
materijala glave, šip s proširenjem prečnika na polovini head material, pile with a diameter expansion at half-
dužine stabla, šip s diskontinuitetom na polovini dužine length, pile with a discontinuity at half-length (a crack
stabla (prslina bez zatvaranja), šip u višeslojnoj sredini without closure), pile in a multilayered medium (the layer
(sloj ispod baze šipa je boljih geomehaničkih below the pile toe has better geomechanical
karakteristika) i šip s randomiziranim diskontinuitetom characteristics) and pile with randomized discontinuity of
prečnika duž stabla. diameter along the shaft.
a) b) c) d) e) f)
Slika 7. Modeli šipova s defektima i bez njih: a) integralni šip (bez defekata); b) šip s redukovanim kvalitetom materijala
glave; c) šip s proširenjem prečnika na polovini dužine stabla; d) šip s diskontinuitetom na polovini dužine stabla
(prslina bez zatvaranja); e) šip u višeslojnoj sredini (sloj ispod baze šipa je boljih geomehaničkih karakteristika);
f) šip s randomiziranim diskontinuitetom prečnika duž stabla
Figure 7. Models of piles with and without defects: a) integral pile (without defects), b) pile with reduced quality of head
material, c) pile with a diameter expansion at half-length, d) pile with a discontinuity at half-length (a crack without
closure), e) pile in a multilayered medium (the layer below the pile toe has better geomechanical characteristics),
f) pile with randomized discontinuity of diameter along the shaft
c) d)
e) f)
Slika 8. Reflektogrami numeričkih modela šipova i tla: a) integralni šip (bez defekata); b) šip s redukovanim kvalitetom
materijala glave; c) šip s proširenjem prečnika na polovini dužine stabla; d) šip s diskontinuitetom na polovini dužine
stabla (prslina bez zatvaranja); e) šip u višeslojnoj sredini (sloj ispod baze šipa je boljih geomehaničkih karakteristika);
f) šip s randomiziranim diskontinuitetom prečnika duž stabla
Figure 8. Reflectograms of numerical models of piles and soil: a) integral pile (without defects), b) pile with reduced
quality of head material, c) pile with a diameter expansion at half-length, d) pile with a discontinuity at half-length (a crack
without closure), e) pile in a multilayered medium (the layer below the pile toe has better geomechanical characteristics),
f) pile with randomized discontinuity of diameter along the shaft
S obzirom na to što se prilikom sprovođenja testova Given that when conducting SITs and numerical
integriteta šipa sa senzorom (SIT) i numeričkih analiza analyzes of pile integrity (simulations), original
integriteta šipova (simulacija) dobijaju originalni (uncorrected) reflectograms are obtained, they are
(nekorigovani) reflektogrami, to se oni dodatno further processed in order to make certain corrections
procesiraju s ciljem sprovođenja određenih korekcija i and filtering. Most often, filtering and scaling procedures
filtriranja. Najčešće se sprovode procedure filtiranja i are performed directly in the time domain, however,
skaliranja direktno u vremenskom domenu, međutim frequency filtering methods are also used. Filtration
koriste se i metode filtriranja u frekventnom domenu. adjusts the reflectogram to more clearly detect possible
Filtriranjem se koriguje reflektogram radi jasnijeg defects in the pile by eliminating less significant and
uočavanja eventualnih defekata u šipu eliminacijom conserving essential discrete peak velocity values of the
manje bitnih i konzervacijom bitnih diskretnih vrednosti reflectograms, while scaling increases the signal
pikova brzina reflektograma, dok se skaliranjem reflection intensity, primarily at the pile toe, for an easier
povećava intenzitet refleksije signala, prevashodno u identification of the pile length. A n-times weight filter is
bazi šipa s ciljem lakše identifikacije dužine šipa. most commonly used to filter the signal directly in the
Najčešće se primenjuje n-tostruki težinski filter kojim se time domain [27]:
signal direktno filtrira u vremenskom domenu [27]:
, (28)
, (29)
, (30)
gde je vo(t) brzina originalnog (nefiltriranog) where vo(t) is the velocity of the original (unfiltered)
reflektograma u vremenu (t), dok su vf,1(t), vf,i-1(t), vf,i(t), reflectogram in time (t), while vf,1(t), vf,i-1(t), vf,i(t), vf,n-1(t),
vf,n-1(t), vf,n(t) brzine korigovanog (filtriranog) vf,n(t) are velocities of corrected (filtered) reflectogram in
reflektograma u vremenu (t). Na slikama 9 i 10 prikazani time (t). Figures 9 and 10 show characteristic examples
su karakteristični primeri reflektograma i 2D of reflectograms and 2D spectrograms of piles with
spektrograma šipova s manjim diskontinuitetima i većim smaller discontinuities and larger defects in the middle of
defektom u sredini šipa: bez primenjenog filtera i s the pile: with no filter applied and with a filter applied.
primenjenim filterom. Spektrogrami su konstruisani Spectrograms are constructed using the Short Time
primenom kratkotrajne Fourier-ove transformacije Fourier transform (STFT), so that in the frequency
(STFT), tako da se u frekventnom domenu jasno može domain one can clearly observe the variation in
a) b)
c) d)
Slika 9. Reflektogrami i 2D spektrogrami šipa s manjim diskontinuitetima: a) reflektogram šipa bez primenjenog filtera;
b) reflektogram šipa s primenjenim filterom; c) 2D spektrogram šipa bez primenjenog filtera; d) 2D spektrogram šipa
s primenjenim filterom
Figure 9. Reflectograms and 2D spectrograms of a pile with smaller discontinuities: a) pile reflectogram without applied
filter, b) pile reflectogram with applied filter, c) 2D pile spectrogram without applied filter, d) 2D pile spectrogram with
applied filter
a) b)
c) d)
Slika 10. Reflektogrami i 2D spektrogrami šipa s većim defektom u sredini šipa: a) reflektogram šipa bez primenjenog
filtera; b) reflektogram šipa s primenjenim filterom; c) 2D spektrogram šipa bez primenjenog filtera; d) 2D spektrogram
šipa s primenjenim filterom
Figure 10. Reflectograms and 2D spectrograms of a pile with larger defects in the middle of the pile: a) pile reflectogram
without applied filter, b) pile reflectogram with applied filter, c) 2D pile spectrogram without applied filter, d) 2D pile
spectrogram with applied filter
Test integriteta šipa sa sondama (CSL) zasniva se Crosshole Sonic Logging (CSL) is based on wave
na propagaciji talasa, primenom sondi s razdvojenim propagation using separate transmitter and receiver
transmiterom i risiverom. Ovim testom se interaktivno i sensor. With this test, the integrity of the pile can be
simultano, između instaliranih cevi u šipu, detaljno može thoroughly examined interactively and simultaneously,
ispitati integritet šipa celom dužinom po svim poprečnim between the installed pipes in the pile, along entire
presecima [6]. Ispitivanje integriteta sprovodi se kod svih length and across all cross sections [6]. Integrity testing
tipova armiranobetonskih bušenih šipova. Metodologija is performed on all types of bored reinforced concrete
ispitivanja integriteta šipa sa sondama (CSL) definisana piles. The testing methodology of CSL is defined by
je standardom ASTM D6760 [2]. Centar za puteve i ASTM D6760 [2]. The Centre for Roads and
geotehniku Instituta IMS poseduje licenciranu opremu za Geotechnics of the IMS Institute possesses the licensed
test integriteta šipa sa sondama američke firme Pile CSL equipment manufactured by the US Pile Dynamics
Dynamics. Korišćenjem ove opreme moguće je sprovesti company. Using this equipment, it is possible to perform
analizu ultrazvučnih profila u vremenskom domenu ultrasonic time domain analysis (TDA), as well as
(TDA), ali i dodatnu tomografsku analizu integriteta šipa additional Crosshole Sonic Logging Tomography
(CSLT). Oprema poseduje integrisane softverske (CSLT). The equipment has integrated software modules
module za: procesiranje, skaliranje, korekciju i filtriranje for: signal processing, scaling, correction and filtering.
signala. CHAMP-Q oprema [14] za test integriteta šipa The CHAMP-Q equipment [14] for CSL, of the U.S. Pile
sa sondama (CSL), američke firme Pile Dynamics, Dynamics company, consists of: a meter with a weight
sastoji se iz: metra s tegom za preliminarnu proveru for preliminary checking of the length and possibility of
dužine i nezapušenosti instaliranih cevi, sondi - installed pipes, probes - transmitters (generating
transmitera (generišu ultrazvučni signal nominalne ultrasonic signal of 45kHz nominal frequency), probes -
frekvencije 45 kHz), sondi - risivera (nominalne receivers (nominal frequencies 45kHz), 4 sets of cables
frekvencije 45 kHz), četiri seta kablova za povezivanje for connecting 4 probes, tripods for cables with sensors
četiri sonde, tripoda za kablove sa senzorima za analizu for analyzing the position of probes in the pipes,
pozicije sondi u cevima, hardverskog sistema za hardware system for acquisition, storage, processing
akviziciju, memorisanje, procesiranje i vizuelizaciju and visualization of data and software CHA-S, CHA-W
podataka i softvera CHA-S, CHA-W i PDI-Tomo. and PDI-Tomo. AD signal conversion is conducted using
Konverzija AD signala sprovodi se primenom 12-bitnog the 12-bit converter (sampling frequency is from 500kHz
konvertera (frekvencija semplovanja je od 500 kHz do 2 to 2MHz). Figure 11 shows the CHAMP-Q equipment for
MHz). Na slici 11 prikazana je CHAMP-Q oprema za CSL by the U.S. Pile Dynamics company.
ispitivanje integriteta šipova testom integriteta šipa sa
sondama (CSL) američke firme Pile Dynamics.
Slika 11. CHAMP-Q oprema za ispitivanje integriteta šipova testom integriteta šipa sa sondama (CSL) američke firme
Pile Dynamics [14]
Figure 11. CHAMP-Q CSL equipment of the U.S. company Pile Dynamics [14]
Pravilno sprovođenje testa integriteta šipa sa A proper procedure of CSL requires the preliminary
sondama (CSL) zahteva prethodnu pripremu cevi u koje preparation of pipes into which test probes are lowered.
se spuštaju sonde za ispitivanje. Ove cevi se ugrađuju u These tubes are embedded in the body of the pile and
telo šipa, a naknadno se mogu injektirati nakon they can be subsequently injected after testing. Figure
sprovedenog ispitivanja. Na slici 12 prikazane su čelične 12 shows the steel pipes connected and welded to the
cevi spojene i zavarene za unutrašnju stranu armaturnog inside of the pile reinforcement cage and the ends of the
koša šipa i krajevi cevi koji vire nakon betoniranja. pipes protruding after concreting.
Na slici 13 prikazani su: tripod za kablove sa Figure 13 shows: tripod for sensor cables,
senzorima, uređaj za akviziciju, memorisanje, acquisition, storage, processing and data visualization
procesiranje i vizuelizaciju podataka i povezane i device and connected and placed probes in tubes. The
postavljene sonde u cevima. Sonde na svojim krajevima probes have weights at their ends, so the total length of
imaju tegove, tako da je ukupna dužina sondi i tegova the probes and weights is a little over 30 cm. In this
nešto veća od 30 cm. U tom smislu, da bi se adekvatno sense, in order to adequately carry out the analysis of
sprovela analiza integriteta glave šipa, potrebno je the integrity of the pile head, it is necessary to make the
ispustiti cevi dovoljno izvan glave šipa, kako bi se i pipes sufficiently protrude outside the pile head to allow
sonde izvukle izvan glave šipa, a ostale u cevima. the probes to be pulled out of the pile head and remain
Budući da prilikom krajcovanja glave šipa vrlo često in the pipes. Since during the trimming of the pile head
nastupi oštećenje cevi za ispitivanje integriteta šipa sa the pipe for CSL is very often damaged, it is almost
sondama (CSL), to je gotovo nemoguće sprovesti impossible to perform an adequate analysis of the
adekvatnu analizu integriteta glave šipa. integrity of the pile head.
a) b)
Slika 13. a) tripod za kablove sa senzorima, uređaj za akviziciju, memorisanje, procesiranje i vizuelizaciju podataka
povezan sa sondama; b) povezane i postavljene sonde u cevima
Figure 13. a) tripod for sensor cables, device for acquisition, storage, processing and visualization of data connected to
probes, b) probes connected and placed in pipes
Na slici 14 prikazani su specifični slučajevi pozicija i Figure 14 shows specific cases of positions and
dužina cevi izvan glave šipa: cevi su adekvatne dužine, lengths of pipes outside the pile head: the pipes are
čak je i beton nedovoljno okrajcovan, što je povoljno u adequate in length, even the concrete is insufficiently
smislu ispitivanja integriteta glave šipa, cevi nisu trimmed, which is advantageous in terms of testing the
adekvatne dužine i krajevi cevi se završavaju na integrity of the pile head, the pipes are inadequate in
različitim visinama, cevi su adekvatne dužine, glava šipa length and the ends of the pipes end at different heights,
je dobro okrajcovana i naknadno obrađena (najpovoljnija the pipes are of adequate length, the head of the pile is
situacija) i krajevi cevi se završavaju u ravni glave šipa, well-trimmed and finished (the most favourable situation)
što je nepovoljno, jer se sonde ne mogu izvući and the ends of the pipe end flush with the pile head,
kompletno, pa se samim tim ne može sprovesti which is unfavourable, since the probes cannot be pulled
adekvatna analiza integriteta glave šipa. out completely, and thus, it is impossible to carry out an
adequate analysis of pile head integrity.
Transmiterom se emituju talasi kroz telo šipa, a s Transmitters emit waves through the body of the pile,
obzirom na to što su transverzalni talasi znatno sporiji, and since transversal waves are considerably slower,
od interesa za ispitivanje su samo longitudinalni talasi, only longitudinal waves, which are much faster and carry
koji su dosta brži i nose u sebi informaciju o stanju šipa. information about the state of the pile, are interesting for
Merenje se zasniva, zapravo, na analizi promene: testing. In fact, the measurement is based on an
vremena (FAT) ili brzine propagacije talasa od analysis of variation: of time (FAT) or the wave
transmitera do risivera, a za poznato rastojanje između propagation speed from the transmitter to the receiver,
cevi po dubini šipa i količine relativne energije po dubini for the known distance between the pipes along the
šipa. Signali primljeni risiverom sempluju se i beleže kao depth of the pile and the quantity of relative energy along
promene amplitude u funkciji vremena, a zatim the depth of the pile. The signals received by the
procesiraju po dužini ispitanog šipa. Dobijeni podaci receiver are sampled and recorded as variation in
koriste se za potvrdu kvaliteta betona i za identifikaciju amplitude as a function of time and then processed
zona lošeg kvaliteta. Kompletna obrada (procesiranje) along the length of the test pile. The data obtained are
signala sprovodi se primenom teorije i obrade signala, used to confirm the quality of concrete and identify poor
pri čemu se zapis signala prikazuje u digitalizovanom quality zones. Complete signal processing is performed
formatu, a sam signal prikazuje u vremenskom domenu. by applying theory and signal processing, whereby the
Merenje se sprovodi za vertikalni interval od 2 cm do 5 signal record is displayed in a digitized format and the
cm. Kriterijumi za analizu oštećenja šipa definisani su signal itself is displayed in the time domain. The
prema [13]: measurement is carried out for a vertical interval of 2cm
− zadovoljavajuće (G), (odlično): povećanje FAT od to 5cm. Criteria for pile damage analysis are defined
0 do 10% (mada se može tolerisati i do 15%) i/ili according to [13]:
redukcija energije < 6 db (mada se može tolerisati i do − satisfactory (G) (good): increase of FAT from 0 to
7.5 db); 10% (even though up to 15% can be tolerated) and/or
− odstupanje (Q), (devijantno): povećanje FAT od energy reduction < 6db (even though up to 7.5db can be
11% do 20% i/ili redukcija energije od 6 db do 9 db; tolerated),
− prslina/pukotina (P/F), (lošije): povećanje FAT od − deviation (Q) (questionable): increase of FAT from
21% do 30% i/ili redukcija energije od 9 db do 12 db; 11% to 20% and/or energy reduction from 6db to 9db,
− defekat (P/D), (defekat/diskontinuitet): povećanje − flaw (P/F) (poor/flaw): increase of FAT from 21%
FAT > 31% i/ili redukcija energije > 12 db. to 30% and/or energy reduction 9db to 12db,
S obzirom na to što se ispitivanje integriteta šipova, − defect (P/D) (poor/defect): increase of FAT > 31%
testom integriteta šipa sa sondama (CSL), sprovodi s and/or energy reduction > 12db.
četiri sonde, simultano se u šest pravaca dobijaju Since the pile integrity test, CSL, is performed with 4
ultrazvučni profili. Na slikama 15, 16 i 17, za jedan probes, ultrasonic profiles are obtained simultaneously in
pravac, prikazani su ultrazvučni profili integralnog šipa 6 directions. For one direction, Figures 15, 16 and 17,
(bez defekata), šipa s diskontinuitetom u domenu baze i show ultrasonic profiles of an integral pile (without
defektnog šipa - dijagrami promena: brzina propagacije defects), a pile with discontinuity at the toe and a
talasa, relativne energije, vremena dolaska signala defective pile – variation diagrams: of wave propagation
a) b)
Slika 16. Ultrazvučni profili šipa s diskontinuitetom u domenu baze: a) dijagrami promena brzina propagacije talasa,
relativne energije i vremena dolaska signala (FAT); b) dijagrami povećanja vremena dolaska signala (FAT) i redukcije
relativne energije duž stabla šipa
Figure 16. Ultrasonic profiles of a pile with a discontinuity at the toe: a) diagrams of variations in wave propagation
velocities, relative energy and signal first arrival time (FAT), b) diagrams of increase of time of signal first arrival time
(FAT) and reduction of relative energy along the pile shaft
(FAT), povećanja vremena dolaska signala (FAT) i velocity, relative energy, first arrival time (FAT) increases
redukcije relativne energije duž stabla šipa, respektivno. in first arrival time (FAT) and reductions in relative
U konkretnom slučaju, kod integralnog šipa, analizom energy along the pile shaft, respectively. In the specific
ultrazvučnih profila za sve pravce (nisu svi prikazani, s case of the integral pile by analyzing the ultrasonic
obzirom na obimnost ispitivanja), može se konstatovati profiles for all directions (not all of them are shown,
a) b)
Slika 17. Ultrazvučni profili defektnog šipa: a) dijagrami promena brzina propagacije talasa, relativne energije i vremena
dolaska signala (FAT); b) dijagrami povećanja vremena dolaska signala (FAT) i redukcije relativne energije duž stabla
šipa
Figure 17. Ultrasonic profiles of a defective pile: a) diagrams of variations in wave propagation velocities, relative energy
and signal first arrival time (FAT), b) diagrams of increase of time of signal first arrival time (FAT) and reduction of
relative energy along the pile shaft
Na osnovu sprovedenih ispitivanja i prikazanih Using PDI-Tomo tomography software, the identified
ultrazvučnih profila integralnog šipa (bez defekata), šipa characteristic zones of variation of increase and
s diskontinuitetom u domenu baze i defektnog šipa, decrease of wave propagation velocity in concrete were
primenom softvera PDI-Tomo za tomografiju, dodatno su additionally analyzed based on the performed tests and
analizirane identifikovane karakteristične zone promena presented ultrasonic profiles of an integral pile (without
povećanja i smanjenja brzina propagacije talasa u defects), pile with a discontinuity at the toe and defective
betonu. Ove zone prikazane su primenom izopovrši, čije pile. These zones are shown using isosurface, the
boje odgovaraju brzinama propagacije talasa u betonu. colours which correspond to the wave propagation rates
Na slici 18 prikazani su poprečni preseci za integralni šip in concrete. Figure 18 shows the cross sections for the
(bez defekata), šip sa diskontinuitetom u domenu baze i integral pile (without defects), the pile with the
defektni šip, kod kojih se najviše identifikuju povećanja discontinuity at the toe, and the defective pile, where
FAT i redukcije energije, a prikazane su takođe i FAT increases and energy reductions are mostly
odgovarajuće proračunate efektivne površine ovih identified. In addition, the corresponding calculated
poprečnih preseka šipova. Efektivna površina poprečnog effective surfaces of these pile cross sections are shown
preseka proračunata je kao odgovarajući procenat as well. The effective cross-sectional area was
površine poprečnog preseka šipa, kod kojeg je brzina calculated as the corresponding percentage of the pile
propagacije talasa u betonu veća od 3600 m/s. cross-sectional area where the wave propagation
velocity in concrete is higher than 3600m/s
Ispitivanje integriteta šipova metodološki se može Pile integrity testing can be methodologically
prikazati u nekoliko faza: priprema ispitivanja, in-situ presented in several stages: test preparation, in-situ pile
ispitivanje šipova na gradilištu, analiza i odlučivanje testing at the construction site, analysis and decision-
tokom ispitivanja, analiza, interpretacija i prezentacija making during testing, analysis, interpretation and
rezultata ispitivanja, dodatne numeričke analize presentation of test results, additional numerical integrity
integriteta, donošenje odluke o integralnom stanju šipa i analysis, decision on the integral condition of a pile and
pisanje izveštaja o integritetu šipa. S obzirom na pile integrity report writing. Given the cost of testing, SIT
troškove ispitivanja, najčešće se za ispitivanje integriteta is the most commonly used pile integrity test. However,
šipova koristi test integriteta šipa sa senzorom (SIT). CSL pile integrity test is also available depending on the
Međutim, u zavisnosti od stepena važnosti objekta, pa i degree of importance of the structure and even the
pouzdanost rešenja na raspolaganju je ispitivanje reliability of the solution. In practice, SIT is applied for
integriteta šipova testom integriteta šipa sa sondama almost all structural piles given the efficiency and speed
(CSL). U praksi, za gotovo sve šipove objekata, of testing, but it is often neglected that it is an indirect
primenjuje se test integriteta šipa sa senzorom (SIT), s method. The research has shown characteristic models
obzirom na efikasnost i brzinu ispitivanja, ali se često i of reflectograms on the basis of which it is possible to
zanemaruje to da je ovo indirektna metoda. Istraživa- make decisions on the state of pile integrity. However,
njem su pokazani karakteristični modeli reflektograma, there are often debatable situations in practice where it
na osnovu kojih se lako mogu doneti odluke o stanju is impossible to immediately provide an answer
integriteta šipa. Međutim, veoma često se u praksi concerning the pile integrity state, so it is recommended
pojavljuju diskutabilne situacije u kojima nije moguće to use additional methods based on wave theory, signal
odmah dati odgovor o stanju integriteta šipa, pa je matching, and numerical analyses.
preporuka da se koriste dodatne metode koje se When there is a large number of piles in a structure,
zasnivaju na talasnoj teoriji, kompatibilizaciji signala i it is more reliable to make a test plan before building the
numeričkim analizama. piles. A quality test plan can define the test piles on which
Kada je u pitanju veliki broj šipova objekta, CSL will be conducted and the construction technology
pouzdanije je napraviti plan ispitivanja pre izgradnje and/or the arrangement and/or number of piles can be
šipova. Kvalitetnim planom ispitivanja, mogu se definisati corrected. Subsequently, all working (service) piles can
probni (testni) šipovi na kojima će se sprovesti testovi be tested with SIT. The biggest problem arises when all
integriteta šipa sa sondama (CSL) i uticati na korekciju the piles of a structure are built, and then subsequently
tehnologije izgradnje i/ili dispozicije i/ili broja šipova. the pile integrity test is applied. In that case the space for
Naknadno se svi radni (eksploatacioni) šipovi mogu corrections is limited, both in terms of the structural level
ispitati testom integriteta šipa sa senzorom (SIT). and the dynamical construction plan of the structure. In
Najveći problem pojavljuje se kada se svi šipovi objekta many cases the integrity and load-bearing criteria of
izgrade, pa se nakon toga zahteva sprovođenje piles are considered independently when test results
ispitivanja integriteta šipova, jer se stvara ograničen presented in the reports are interpreted by the
prostor za korekcije – kako na konstruktivnom nivou, contracting party. In addition, very often one criterion is
tako i na nivou dinamičkog plana izgradnje objekta. U favoured or another criterion is completely excluded. The
velikom broju slučajeva, kada naručioci ispitivanja only correct engineering solution is that both criteria are
interpretiraju rezultate ispitivanja prikazane u observed and the conditions under which these criteria
izveštajima, kriterijumi integriteta i nosivosti šipova are met are considered. All this, in addition to knowledge
razmatraju se nezavisno. Takođe, vrlo često se jedan and experience, requires continuous improvement in this
kriterijum favorizuje ili se potpuno isključuje drugi multidisciplinary pile testing problem which goes beyond
kriterijum. Jedino i inženjerski ispravno rešenje jeste da the usual domains of construction and geotechnical
se oba kriterijuma poštuju i da se uvažavaju uslovi pod practice.
kojima se ispunjavaju ovi kriterijumi. Sve to, pored
ACKNOWLEDGEMENT
ZAHVALNICA
This paper is a part of the research within the project
Ovaj rad je deo istraživanja u okviru projekta TR TR 36014 supported by the Ministry of education,
36014, koje finansira Ministarstvo prosvete, nauke i science and technological development of the Republic
tehnološkog razvoja Republike Srbije. of Serbia.
6 LITERATURA
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[10] Hilber H., Hughes T., Taylor R.: Improved [22] Rausche F., Ren-Kung S., Likins G.: Comparison
Numerical Dissipation for Time Integration of Pulse Echo and Transient Response Pile
Algorithms in Structural Dynamics, Earthquake Integrity Test Methods, Transportation Research
Engineering and Structural Dynamics, Vol. 5, No. Board Annual Meeting, Washington, USA, 1991,
3, 1977, pp. 283–292. pp. 21–27.
[11] Holeyman A.: Technology of Pile Dynamic Testing, [23] Richart F., Hall J., Woods, R.: Vibrations of Soils
Application of Stress-Wave Theory to Piles, F. and Foundations, Prentice Hall, New Jersey, USA,
Barends ed., Balkema, 1992, pp. 195–215. 1970.
[12] https://www.pile.com/download/brochure/english-
pit-w.pdf
REZIME SUMMАRY
ISPITIVANJE INTEGRITETA ŠIPOVA: TESTIRANJE I PILE INTEGRITY TESTING: TESTING AND RESULTS
ANALIZA REZULTATA ANALYSIS
U radu su prikazani karakteristični primeri ispitivanja The paper presents typical examples of pile integrity
integriteta šipova sa analizom rezultata, pri čemu se testing and the results analysis, whereby the testing
metodologija ispitivanja oslanja na postojeće ASTM methodology relies on existing ASTM standards, as well
standarde, ali i na metodologiju ispitivanja prikazanu u as on the testing methodology presented in the scientific
naučnom radu „Ispitivanje integriteta i nosivosti šipova: paper Pile Integrity and Load Testing: Methodology and
metodologija i klasifikacija”, koji je publikovan u ovom Classification, published in this journal. The pile tests
časopisu. Ispitivanja šipova sprovedena su primenom were conducted using licensed equipment for Sonic
licenciranih oprema za test integriteta šipa sa senzorom Integrity Test (SIT) and Crosshole Sonic Logging (CSL).
(SIT) i test integriteta šipa sa sondama (CSL). The tests have shown the correct and problematic
Ispitivanjima su prikazane korektne i problematične situations that arise when analyzing pile integrity. Some
situacije, koje se pojavljuju prilikom analize integriteta aspects of the wave theory implementation, but also of
šipova. Ukazano je na aspekte primene talasne teorije, signal processing and numerical analysis have been
ali i na procesiranja signala i numeričke analize. Takođe, indicated. Also, the need to develop a plan for testing the
posebno je skrenuta pažnja na potrebu izrade plana integrity of piles in structures with a large number of piles
ispitivanja integriteta šipova kod objekata s velikim has been emphasized.
brojem šipova.
Key words: pile, testing, integrity, reflectogram, SIT,
Ključne reči: šip, ispitivanje, integritet, reflektogram, ultrasonic profile, CSL
SIT, ultrazvučni profil, CSL
Ovog leta, 17. jula, preminuo je akademik Nikola Academician Nikola Hajdin, Doctor of Technical
Hajdin, doktor tehničkih nauka, diplomirani građevinski Sciences, Bachelor of Civil Engineering, full professor
inženjer, redovni profesor (u penziji) Građevinskog (retired) at the Faculty of Civil Engineering, University of
fakulteta Univerziteta u Beogradu. Pored predmeta na Belgrade passed away this summer, on July 17. In
osnovnim studijama – Teorije konstrukcija, Otpornosti addition to the subjects in basic studies: Structural
materijala i Teorije površinskih nosača na Građevin- Mechanics, Strength of Materials, and Theory of Plates
skom fakultetu u Beogradu, predavao je i na posle- and Shells at the Faculty of Civil Engineering in
diplomskim studijama – Teoriju plastičnosti, Nelinearnu Belgrade, he also delivered lectures at postgraduate
elastičnost i Teoriju tankozidnih nosača. Dekan studies in subjects Theory of Plasticity, Nonlinear
Građevinskog fakulteta bio je u mandatu 1975/76 – Elasticity, and Theory of Thin-Walled Members. Within
1976/77. godine. Za dopisnog člana SANU izabran je the period 1975/76 - 1976/77, he held the position of the
1970. godine, a za redovnog člana – 1976. godine. Dean of the Faculty of Civil Engineering. He was elected
Potpredsednik SANU bio je od 1994. do 2003. godine, a a corresponding member of Serbian Academy of
predsednik SANU – od 2003. do 2015. godine. Science and Arts (SANU) in 1970 and a full-time
Tokom svoje profesionalne karijere, Nikola Hajdin member in 1976. From 1994 to 2003 he was the vice-
obavljao je naučne i stručne funkcije u različitim doma- president of SANU, and its president from 2003 to 2015.
ćim i stranim društvima. Između ostalog, bio je pred- During his professional career, Nikola Hajdin held
sednik Jugoslovenske grupe Međunarodnog udruženja scientific and professional positions in various domestic
za mostove i visokogradnju, predsednik Jugoslovenskog and foreign associations, including president of the
komiteta Međunarodne unije za teorijsku i primenjenu Yugoslav Group of the International Association for
mehaniku i predsednik Jugoslovenskog društva građe- Bridges and Structural Engineering, president of the
vinskih konstruktera. Yugoslav Committee of the International Union for
Nikola Hajdin bio je član Atinske akademije nauka, Theoretical and Applied Mechanics and president of the
Prvi period odnosno prva oblast – metod integralnih First period - first field: the integral equations
jednačina method.
Nikola Hajdin je predložio (1954) i razradio jedan In 1954, Nikola Hajdin proposed and developed a
metod za numeričko rešavanje graničnih zadataka method for numerically solving boundary problems of
teorije elastičnosti, koji se pokazao prikladnim – kako u Theory of Elasticity, which proved to be suitable in both
teoriji linijskih nosača, tako i u teoriji površinskih nosača. Linear Beam Theory and Theory of Plates and Shells.
Metod je zasnovan na osnovnim diferencijalnim The method is based on basic differential equations of
jednačinama teorije elastičnosti, primenjenim na dvo- the Theory of Elasticity applied on two-dimensional
dimenzionalne probleme. Pretvarajući osnovne diferen- problems. By converting the basic differential equations
cijalne jednačine u integralne, duž usvojenih linija mreže in integral equations along the adopted lines of the net
i njihovim približnim rešavanjem numeričkim putem, and their approximate solving by numerical means, a
dobija se sistem linearnih jednačina, koji vodi ka rešenju system of linear equations is obtained which leads to the
problema. Metod je našao široku primenu u različitim solution of the problem. The method found widespread
granama tehnike, posebno u građevinskom konstruk- application in various branches of engineering,
terstvu, hidrotehnici, analizi saobraćajnih vozila, analizi particularly in civil engineering, hydraulic engineering,
Nikola Hajdin posvetio je jedan deo svoje aktivnosti Nikola Hajdin dedicated a part of his activity to
spregnutim konstrukcijama od betona i čelika. Osnovni composite structures of concrete and steel. The basic
naučni problem – koji je počeo ozbiljnije da se proučava scientific problem that attracted the attention of
posle Drugog svetskog rata – bio je izučavanje feno- engineers in the field after the World War II was the
mena puženja i skupljanja betona, koji dovodi tokom phenomenon of creep and shrinkage of concrete, which
vremena do preraspodele naprezanja u spregnutoj over time leads to the redistribution of stresses in
konstrukciji. Pored više naučnih radova iz oblasti composite structures. In addition to several scientific
spregnutih konstrukcija, Nikola Hajdin je i projektovao papers in the field of composite structures, Nikola Hajdin
spregnute mostove, od kojih se izdvaja most Orašje also designed composite bridges. The Orašje Bridge
preko reke Save, na kome je prvi put u svetu primenjeno over the Sava River is the most important one. What
tzv. dvostruko sprezanje, gde je kod kontinualnog makes this bridge outstanding is the first application of
nosača mosta, pored betonske kolovozne ploče gore, the so-called double composite action, where in the case
primenjena i betonska ploča u donjoj zoni nosača iznad of a continuous girder, in addition of the surface concrete
oslonaca. Most Orašje, osim toga, imao je najveći slab, a concrete slab was also applied in the bottom
raspon za spregnute mostove u to vreme u svetu. Ovde zone of the girder above the supports. Moreover, the
treba dodati i izvedene projekte nadvožnjaka u Ljubljani, Orašje Bridge had the largest span in the world for
sa originalnim načinom sprezanja u donjoj zoni na celoj composite bridges at the time. Here, we should mention
dužini nadvožnjaka, kao i most preko reke Ibar kod the overpass projects in Ljubljana, with the original
Rožaja i most preko akumulacije za hidroelektranu method of composite action in the bottom zone along the
Špilje. Sve ove konstrukcije mostova imale su poneku entire length of the overpass, as well as the bridge over
svojevrsnu inovaciju u našem građevinskom konstruk- the Ibar River near Rožaje and the bridge over the
terstvu, upravo zahvaljujući autoru-projektantu – Nikoli reservoir for the Špilje hydroelectric power plant. All
Hajdinu. these bridge structures contained some kind of
innovation in our structure engineering thanks to the
author-designer Nikola Hajdin.
Naučna oblast Teorije konstrukcija, u kojoj je Nikola The scientific field of Theory of Structures in which
Hajdin takođe dao izuzetan doprinos, jesu tankozidne Nikola Hajdin made a remarkable contribution is thin-
konstrukcije koje se zbog svojih osobina upotrebljavaju u walled structures that, due to their properties, are used
više grana tehnike, kao što su: građevinarstvo, in many branches of engineering, such as civil
mašinstvo, brodogradnja, aeronautika i druge. Radovi engineering, mechanical engineering, shipbuilding,
Nikole Hajdina iz ove oblasti objavljeni su uglavnom u aeronautics and others. Nikola Hajdin's papers in this
inostranstvu u više časopisa i stručnih publikacija; a field were published, for the most part abroad, in a
citirani su i korišćeni u brojnim objavljenim radovima number of journals and professional publications, and
stranih i domaćih naučnih radnika. Izuzetnu vrednost iz were cited and used in many published papers by
ovog opusa predstavljaju dve monografije – foreign and domestic scholars. Two monographs:
Dünnwandige Stäbe, Bd. 1 i 2 (s koautorom Kurtom "Dünnwandige Stäbe", Bd. 1 and 2 (with C.F.
Kolbrunerom), objavljene u prestižnoj izdavačkoj kući Kollbrunner) published by the prestigious Springer
Springer (1972. i 1975). Prema sadržaju, te monografije Publishing House (1972 and 1975) have exceptional
su jedinstveno delo i na originalan način, sa čitavim value in this opus. The monographs are unique in their
nizom priloga, izlažu oblast kojom se Nikola Hajdin bavio contents, presenting in an original way the scientific
više od 20 godina. Kako su ovi radovi bili među prvima fields on which Nikola Hajdin was focused for more than
koji su se na širokom planu bavili ovom problematikom, 20 years with a series of contributions. As these papers
Slika 1. Železnički most preko Save u Beogradu (autori – projektanti: Nikola Hajdin i Ljubomir Jevtović)
Figure 1. Railway Bridge over the Sava River in Belgrade (authors-designers: Nikola Hajdin and Ljubomir Jevtović)
Posle ovog beogradskog mosta, Nikola Hajdin je After this bridge in Belgrade, Nikola Hajdin designed
isprojektovao Most slobode preko Dunava u Novom the Liberty Bridge over the Danube in Novi Sad. With its
Sadu. S rasponom od 351 metar, ova mostovska span of 351 m, at the time of construction this bridge
konstrukcija, u trenutku građenja, predstavljala je svetski structure represented a world record for cable-stayed
rekord za mostove s kosim kablovima, kod kojih su piloni bridges, with the pylons and stay cables being situated
i kosi kablovi u srednjoj ravni mosta. Most je završen i in the central plane of the bridge. The bridge was
Slika 2. Most slobode preko Dunava u Novom Sadu (autor – projektant Nikola Hajdin)
Figure 2. Liberty Bridge over the Danube River (author-designer: Nikola Hajdin)
Nikola Hajdin (s koautorom Bratislavom Stipanićem) Nikola Hajdin (co-authored with Bratislav Stipanić)
isprojektovao je most preko reke Visle u poljskom gradu designed the bridge over the Wisla River in the Polish
Plocku, koji je nagrađen prvom nagradom na city of Plock, which was awarded the first prize in the
međunarodnom konkursu za projekat. S rekordnim international design competition. With the record range
rasponom od 375 metara, za mostove s kosim of 375 meters for cable-stayed bridges (with cables in
kablovima (s kablovima u srednjoj ravni i pilonima the central plane and pylons fixed in beam), it
uklještenim u gredu), predstavlja napredak u odnosu na represented a further improvement in relation to the
most u Novom Sadu. Ukupna dužina mosta jeste 1.200 bridge in Novi Sad. The total length of the bridge is 1200
metara, od čega je 615 metara dužina glavnog dela m, of which 615 m accounts for the length of the main
mosta nad koritom reke Visle, a 585 metara je dužina part of the bridge over the riverbed of the Vistula River,
prilaznog dela spregnutog mosta nad inundacijom. and 585 m is the length of the access part of the
Glavna mostovska konstrukcija je simetrična kon- composite bridge over the inundation. The main bridge
strukcija od čelika – most s kosim kablovima, koji čine: structure is a symmetrical steel structure, a cable-stayed
kontinualna greda, kosi kablovi i dva pilona. Ovo je most consisting of a continuous girder, stay cables, and two
s najvećim rasponom u Poljskoj i predstavlja korak dalje pylons. The bridge represents a step further in the
u razvoju mostova s kosim kablovima. Most je završen development of cable-stayed bridges. It is the bridge
2005, a sa pristupnim vijaduktom otvoren je za with the largest span in Poland. The bridge was
saobraćaj 2007. godine (slika 3). completed in 2005 and open for traffic with the approach
viaduct in 2007 (Figure 3).
Slika 3. Most solidarnosti preko Visle u Plocku (autori – projektanti: Nikola Hajdin i Bratislav Stipanić)
Figure 3. Solidarity Bridge in Plock over the Vistula River (authors-designers: Nikola Hajdin and Bratislav Stipanic)
Prof. dr Bratislav Stipanić, dipl.inž.građ. Professor Bratislav Stipanic, Ph.D. M.Sc. B.C.Eng.
U časopisu Materijli i konstrukcije štampaće se neobja- The Building Materials and Structures journal will
vljeni radovi ili članci i konferencijska saopštenja sa odre- publish unpublished papers, articles and conference reports
đenim dopunama, iz oblasti građevinarstva i srodnih with modifications in the field of Civil Engineering and
disciplina (geodezija i arhitektura). Vrste priloga autora i similar areas (Geodesy and Architecture).The following
saradnika koji će se štampati su: originalni naučni radovi, types of contributions will be published: original scientific
prethodna saopštenja, pregledni radovi, stručni radovi, papers, preliminary reports, review papers, professional
prikazi objekata i iskustava (studija slučaja), kao i diskusije papers, objects describe / presentations and experiences
povodom objavljenih radova. (case studies), as well as discussions on published papers.
Originalni naučni rad je primarni izvor naučnih informa- Original scientific paper is the primary source of scien-
cija i novih ideja i saznanja kao rezultat izvornih istraživanja tific information and new ideas and insights as a result of
uz primenu adekvatnih naučnih metoda. Dobijeni rezultati original research using appropriate scientific methods. The
se izlažu sažeto, ali tako da poznavalac problema može achieved results are presented briefly, but in a way to
proceniti rezultate eksperimentalnih ili teorijsko numeričkih enable proficient readers to assess the results of experi-
analiza, tako da se istraživanje može ponoviti i pri tome mental or theoretical numerical analyses, so that the
dobiti iste ili rezultate u okvirima dopuštenih odstupanja, research can be repeated and yield with the same or results
kako se to u radu navodi. within the limits of tolerable deviations, as stated in the
Prethodno saopštenje sadrži prva kratka obaveštenja o paper.
rezultatima istraživanja ali bez podrobnih objašnjenja, tj. Preliminary report contains the first short notifications on
kraće je od originalnog naučnog rada. the results of research but without detailed explanation, i.e.
Pregledni rad je naučni rad koji prikazuje stanje nauke u it is shorter than the original scientific paper.
određenoj oblasti kao plod analize, kritike i komentara i Review paper is a scientific work that presents the state
zaključaka publikovanih radova o kojima se daju svi neop- of science in a particular area as a result of analysis, review
hodni podaci pregledno i kritički uključujući i sopstvene and comments, and conclusions of published papers, on
radove. Navode se sve bibliografske jedinice korišćene u which the necessary data are presented clearly and
obradi tematike, kao i radovi koji mogu doprineti rezultatima critically, including the own papers. Any reference units
daljih istraživanja. Ukoliko su bibliografski podaci metodski used in the analysis of the topic are indicated, as well as
sistematizovani, ali ne i analizirani i raspravljeni, takvi papers that may contribute to the results of further research.
pregledni radovi se klasifikuju kao stručni radovi. If the reference data are methodically systematized, but not
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poznate spoznaje koje doprinose širenju znanja i prila- as technical papers.
gođavanja rezultata izvornih istraživanja potrebama teorije i Technical paper is a useful contribution which outlines
prakse. the known insights that contribute to the dissemination of
Ostali prilozi su prikazi objekata, tj. njihove konstrukcije i knowledge and adaptation of the results of original research
iskustava-primeri u građenju i primeni različitih materijala to the needs of theory and practice.
(studije slučaja). Other contributions are presentations of objects, i.e.
Da bi se ubrzao postupak prihvatanja radova za their structures and experiences (examples) in the construc-
publikovanje, potrebno je da autori uvažavaju Uputstva za tion and application of various materials (case studies).
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LPDNVLPDOQDIOHNVLELOQRVWSULOLNRPPHÿXVREQRJNRPELQRYDQMDNRG
VSHFLMDOQLKREMHNDWDLQRYDWLYQLGL]DMQRGOLþQDPHKDQLþNDVYRMVWYDL 2SODWH
6NHOH
SUDNWLþQLGHWDOMLL]UDÿHQLSUHPDYLVRNLPVWDQGDUGLPDNYDOLWHWDNRMLVX
,QåHQMHULQJ
LGHDOQL]DWHãNHXVORYHUDGDQDJUDGLOLãWX
6D]QDMWHYLãHR3(5,VLVWHPLPDLUHãHQMLPDQDQDãHPVDMWX ZZZSHULUV