examples of original structural solutions and

A R C H I T E C T U R E
C I V I L
E N G I N E E R I N G
E N V I R O N M E N T
T h e S i l e s i a n U n i v e r s i t y o f Te c h n o l o g y
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EXAMPLES OF ORIGINAL STRUCTURAL SOLUTIONS AND METHODS
OF LOAD CARRYING CAPACITY ASSESSMENT FOR EXISTING STRUCTURES
ACCOMPLISHED BY PROFESSOR WITOLD WOŁOWICKI
Janusz KARLIKOWSKI *a, Wojciech SIEKIERSKI *b
* Dr; Faculty of Building and Environmental Engineering, Poznań University of Technology, ul. Piotrowo 5,
61-138 Poznań, Poland
aE-mail address: janusz.karlikowski@put.poznan.pl
bE-mail address: wojciech.siekierski@put.poznan.pl
Received: 10.02.2014; Revised: 15.03.2014; Accepted: 24.03.2014
Abstract
The paper presents several works of Professor Witold Wołowicki completed at the interface of scientific and engineering
activities. The first chapter concerns application of theory of plastic hinges in expert’s activity. An example of original alteration of static scheme of continuous 2-span RC girders to limit shear forces near intermediate support is given.
In the second chapter some original practical structural solutions concerning concrete and steel-concrete composite bridges
are recalled, i.e.:
– precasted post-tensioned girders with thin and wide top flange (solution dated 1978 similar to contemporary VFT system),
– strengthening of listed viaduct of deck made of basin-shape steel plates, achieved by introduction of joint action of girders and new RC slab deck, only within positive bending moment zone,
– strengthening of prestressed concrete spans by introduction of additional steel trusses, that utilized existing deck slab
as top flange.
In the third chapter a method of testing and setting actual influence lines of load transverse spread (ILLTS), worked out by
Professors’ team is presented. The method was applied to the assessment of over 20 bridges in service. An example is shown.
Streszczenie
W artykule przedstawiono szereg prac Profesora Witolda Wołowickiego powstałych na styku nauki i działalności inżynierskiej. Część pierwsza artykułu dotyczy zastosowania teorii przegubów plastycznych w działalności ekspertyzowej. W jednym
z przykładów zaproponowano oryginalną zmianę schematu statycznego dwuprzęsłowych podciągów żelbetowych tak, aby
zmniejszyć siły poprzeczne w strefie podpory pośredniej.
W części drugiej przypomniano kilka oryginalnych praktycznych rozwiązań konstrukcyjnych dotyczących mostów
betonowych i zespolonych, np.:
– prefabrykowane belki kablobetonowe z górną cienką i szeroką półką (rozwiązanie z roku 1978 podobne do obecnego systemu VFT),
– wzmocnienie zabytkowego wiaduktu z pomostem z blach nieckowych przez zespolenie stalowych dźwigarów z nową płytą
żelbetową tylko w strefie dodatnich momentów zginających,
– wzmocnienia przęseł z betonu sprężonego przez wbudowanie dodatkowych stalowych kratownic, dla których pasami
górnymi stała się istniejąca płyta żelbetowa.
W części trzeciej przedstawiono, opracowaną w zespole Profesora, metodykę badań i ustalania rzeczywistych linii wpływu
poprzecznego rozdziału obciążenia (LWPRO). Metoda ta została zastosowana do oceny nośności ponad 20 użytkowanych
mostów. Pokazano przykład zastosowania.
K e y w o r d s : Reinforced Concrete Girders; Prestressed Concrete Girders; Steel-Concrete Composite Girders; Theory Of
Plastic Hinges; Load Transverse Spread; Assessment Of Load Carrying Capacity Of Bridges; Strengthening Of Bridges.
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J. Karlikowski, W. Siekierski
1. INTRODUCTION
Achievements of Professor Wołowicki concern mainly:
– mechanics of bridge structures with plasticity taken
into account,
– shaping and design of concrete bridge structures
and steel-concrete composite structures with new
safety measures (Eurocodes) taken into account.,
– methodology of “in situ” testing of bridge structures,
– diagnostics, load carrying capacity analysis and
strengthening of bridges,
– implementation of new structural materials and
new structural solutions,
– testing and serviceability assessment of railway
bridges for high speed transport.
Results of Professor’s scientific research are presented in various available publications. The paper presents several original achievements created at the
interface of scientific and engineering activities.
Qd = G+Pd – admissible load, i.e. maximal load that
may occur under regular service conditions,
QII = G+PII – upper load for elastic range that is followed by occurrence of the first plastic hinge (point
„i” in the example);
QIV = G+PIV – ultimate bearing capacity of the
structure, i.e. load that triggers destruction mechanism (kinematic chain).
During the increase of load, the bending moment
diagram in the analysed span changes as the curves in
Fig. 1 show.
Beam reinforcement is usually adjusted to the envelope of bending moments. The reinforcement
arrangement implies stair-like lines (Fig. 1), that represent diagram of bending moments M that cause
plasticization at particular cross-sections.
2. THEORY OF ULTIMATE LOAD CARRYING CAPACITY IN EXPERTISE
ACTIVITY
Professor Wołowicki took from his Master, Professor
Ryżyński, the quest for such problems of scientific
research that are able to be applied in the engineering practice. In the sixties of XX century the problems concerned load carrying capacity of reinforced
concrete bar structures (beams, frames, grids) that
was analyzed basing on theory of plastic hinges. The
theory was originally adjusted by Professor Ryżyński
to assessment of load carrying capacity or admissible
service loading of beam and frame structures.
Professor Wołowicki applied the theory to grids. It is
worth recalling.
In statically determinate bar structures occurrence of
single plastic hinge means transformation of a structure into kinematic chain and reaching the state of its
ultimate load carrying capacity. For statically indeterminate structures destruction mechanisms are created by two or three hinges which may occur in particular spans. Thus ultimate load carrying capacity of
whole structure is the same as ultimate load carrying
capacity of the weakest span. Further analysis will be
limited to any span of continuous reinforced concrete
beam (Fig. 1) under load Q, the total of: dead load G
and live load P. Load Q may take a few characteristic
values:
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Figure 1.
Bending moment diagrams for various levels of loading
applied to continuous RC beam [14]
1 – M(Qd), 2 – M(QII), 3 – M(QIV), 4 – plastic hinge
In those days design practice was based on the
method of global safety factor. During regular service
of structure the following conditions concerning load
carrying capacity and serviceability had to be met:
– cross-sections must be protected against plasticization:
Mm
≥ s mw
M m (Qd )
m=(I,i,J)
(1)
– the weakest span must be protected against destruction:
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– displacements, crack widths and main tensile stresses in concrete cannot exceed admissible values.
The symbols in the equations (1) and (2) are:
m, Mm(Qd), M
i0, M
i0(Qd) – bending moments
M
marked in Fig. 1,
smw, sw – bigger than unity, required global safety factors: cross-sectional and structural (for the analyzed
span) respectively.
Some cross-sectional safety factors may be smaller
than the structural safety factor. It means that siw<sw
is possibile. Deficiency of safety reserve at one crosssection must be compensated by its excess at other
cross-sections. The authors of paper [11] assumed the
following values:
siw = 1.3
when sw = 1.6
siw = 1.4
when
sw = 1.8
In the form shown above the plastic hinge theory was
applied in expert’s reports by both Professors. Two
examples will be presented.
s3-4=1.311.3
s3=s4=1.90>1.3
s=1.571.60
Since main tensile stresses also did not exceed admissible values, it was concluded that the service load of
p=5.0 kN/m2 is allowed. In comparison to the
method based on elastic analysis the increase of
admissible service load was 56%.
The second example concerns factory building where
roof structure was supported by 2-span reinforced
concrete girders. After building completion additional layers were to be placed on the roof that would
result in the increase of dead loads. The strength
analysis was carried out based on the theory of plastic hinges. Sufficient values of cross-sectional and
structural safety factors were obtained:
si=1.54>1.3
sk=1.66>1.3
s=1.581.60
However, admissible value of main tensile stress in
concrete was exceeded over middle support.
Reinforced girders required strengthening against
shear near the support.
a
b
c
d
Figure 2.
Scheme of frame loaded on lower girder (floor of public
utility building [14]
The first example concerns possibility of increase of
service load of ceiling over a hall. The building structure consisted of:
– transverse reinforced concrete frames of H-type,
spaced every 4.6 m, with bottom tips clamped and
upper tips pin-connected to the roof (Fig. 2),
– Akerman type roof, constructed as 3-span continuous slab with cantilevers.
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e
Figure 3.
Scheme of roof strengthening of factory building together
with diagrams of bending moments and shear forces [19]
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(2)
The ceiling over the hall was designed for service
load of p = 2.0 kN/m2. Some alteration introduced
during construction allowed to increase the ceiling
service load based on elastic analysis up to
p = 3.2 kN/m2. The wish of hall governor was to
increase the service load up to p = 5.0 kN/m2. The
middle girder of H frame turned out to be the weakest structural member. Application of the theory presented above led to the following safety factors for
the girder:
C I V I L
M i0
≥ sw
M i 0 (Qd )
e
c
J. Karlikowski, W. Siekierski
Strengthening with external stirrups or steel clamps
would require roof piercing that would be troublesome. Gluing reinforcement to concrete was impossible since side surfaces of girders were covered by roof
structure. Original alteration of static scheme was
suggested to reduce shear forces near the intermediate support (Fig. 3). Four holes were drilled in the
roof near each of ten girders. Two C-beams were then
suspended on bolts inserted through the holes.
Tightening nuts on the bolts introduced additional
force system shown in Fig. 3b. Diagrams of implied
bending moments and shear forces are shown in Fig.
3c. The additional force system caused the following
changes in internal force distribution over the distance 2c:
– decrease of extreme bending moments,
– decrease of shear forces,
– certain increase of internal shear force at the point
of application of concentrated load on span side.
The advantage of described strengthening method
was its simplicity and short execution time without
need to stop production in the hall.
3. PRACTICAL STRUCTURAL SOLUTIONS IN BRIDGES
Several original (at least In Poland) practical structural solutions of Professor’s are scarcely documented. In the authors’ opinion it is worth to recall some
characteristic examples concerning concrete and
steel-concrete composite bridges [1, 3, 813, 1720,
25]. Described solutions have been worked out in cooperation with colleagues, however, with significant
participation of Professor Wołowicki. Some of them
have not been realized in socialistic realities and others have been applied in recent years usually in
altered form.
One of the examples is an innovation registered at
the Patent Office in 19781). Precasted post-tensioned
concrete beams WBS were used for bridge building
in those days. Their main disadvantage was limited
horizontal stiffness which generated a lot of difficulties during prestresing and transport. Moreover,
pouring deck slab concrete required complex formwork. Authors of the utility pattern modified the precast beam. Top thin and wide flange was added
(Fig. 4a) [17]. In this way both disadvantages of the
precasted member were minimized. The flange might
be used as formwork and might be connected to “in
situ” concrete slab creating composite structure.
Unfortunately the concept did not occur interesting
to anybody in those days.
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a
b
c
d
Figure 4.
Cross-sections of precasted beams with thin and wide flange
1 – thin flange, 2 – „in situ” concrete
The idea, in altered form, was used in construction of
north roadway (independently of construction of
south roadway) of Most Dworcowy in Poznań, completed in 1992. Precast pre-tensioned “PoznańFranowo” beams were used (Fig. 4c). The bridge was
originally designed for class I according to older
bridge loading standard introduced in 1966. After
introduction of new bridge design standards it was
necessary to increase design load carrying capacity up
to class A of the new bridge loading standard. It was
achieved by decreasing thickness of precast beam
flange and increasing total thickness of the flange and
“in situ” concrete slab (Fig. 4d).
It is worth mentioning that the idea of assembling
thin flange and a girder weak in horizontal plane
became popular as construction of steel-concrete
composite beams of VFT type (Fig. 4b). The VFT
system was developed in the 90s of XX century in
Germany.
Precast pre-tensioned „Poznań - Franowo” beams are
also the part of Professor contribution in introduction of 75mm strands and their deep anchorage into
Polish bridge engineering [18]. For this work
Professor Wołowicki received an award from Polish
Federation of Engineering Associations (NOT) in
1976.
An interesting solution was used during modernization of south roadway of Most Dworcowy in Poznań,
built in 1910. Listed steel part of viaduct (spans 35)
over Dworcowa street had deck made of basin-shape
steel plates filled with concrete. As a part of modernization the riveted steel structure was strengthened
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b
Figure 5.
Strenthening of listed steel viaduct by assembling girders
with new RC concrete deck slab in main span [3]
1 – rocking support, 2 – pillar, 3 – girder splice, 4 – hinged
support of next span
by making it a part of steel-concrete composite structure together with new RC deck slab [3]. Basin-shape
steel plates were not removed and shear connectors
were installed over the distance where positive bending moments were expected (Fig. 5). Over the distance where negative bending moments were expected the slab was protected against detachment. Block
shear connectors were used with welded loops made
of reinforcing bars (Fig. 5c). Shear connectors were
attached to top flanges of girders by high strength
friction grip bolts. The bolts were situated in holes
left by removed rivets. Design of modernization of
listed spans was based on the results of earlier tests
carried out for similar spans in Bridge Department of
Poznań University of Technology [2]2) and [5, 6, 16].
Realization of modernization of south roadway of
Most Dworcowy was awarded in the competition
“Bridge Work of the Year 1999”, organized by the
Polish Association of Bridge Engineers (ZMRP).
Figure 6.
Steel arched span connected with inundation spans made of prestressed concrete to create continuous beam [1]
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In mid 80s of XX century Professor presented concepts of: bridge design based on connecting steel and
concrete segment along the bridge and enhancement
of load carrying capacity of existing RC Gerber-type
bridges by replacing concrete inner spans with steel
ones [19, 20]. Attempts to implement the concepts
did not work out in those days. Only in 2004 the St.
Roch Bridge over Warta river was built in Poznań
according to Professor’s concept (Fig. 6).
In the new St. Roch Bridge the prestressed inundation spans made of concrete are connected to steel
arched main span to create one structural system [1].
The inundation spans consist of six concrete beams
that overlap steel beams of main span (arch ties and
longitudinal deck beams) by 5 m. Passive anchorages
of prestressing cables are situated within this distance. Prestressed beams are connected to steel
beams with the use of shear studs welded to webs of
steel beams. Moreover, RC deck slab of inundation
spans is connected by means of anchoring bolts to
steel orthotropic deck of main span. The structure
was awarded in the competition “Bridge Work of the
Year 2004”. It is worth mentioning that thanks to
Professor’s initiative the old arched span was used as
footbridge over Cybina river in Poznań [11].
In multi girder bridges maximum stress level in particular girders is not equal. Difference may reach
even 20%. The highest stress level is present in outermost girders and those adjacent to them. So sometimes it seems possible to increase load carrying
capacity of bridge by strengthening outermost girders
or by appropriate redistribution of loading taken by
particular girders (decreasing loading taken by the
outermost and increasing loading taken by inner girders). The two subsequent examples of structural solutions concern the concept.
C I V I L
a
e
c
J. Karlikowski, W. Siekierski
After 1990 Professor worked on strengthening of
bridge by gluing carbon fibres strips (bridge over
Warta river in Śrem) and strengthening of big frame
bridge by introduction of additional tensioning by
external cables over parts of structure length (bridge
over Warta river in Poznań) [12].
a
b
Figure 7.
Strengthening of prestressed concrete bridge with introduced steel trusses [9]
1 – truss girder, 2 – part of roadway closed during rebuilding,
3 – roadway open to traffic during rebuilding
Original solution according to Professor’s concept was
applied to strengthen prestressed concrete beam spans
of the bridge over Warta river in Rogalinek near
Poznań. Two strengthening options were designed. The
option of introducing additional girders was chosen [9].
Steel truss girders were situated between outermost
and adjacent to them prestressed post-tensioned concrete girders (Fig. 7). Existing RC deck slab became top
flange of the trusses. Another strengthening option was
also an original Professor’s concept. It was then suggested for strengthening another viaduct in Konin. It is
based on force redistribution in span cross-section,
implied by additional steel cross beam with appropriately located tensioning bolts (Fig. 8a) [8, 10]. One or
two such cross beams may be introduced to get additional forces shown in Fig. 8b,c. Equalizing stress levels
in all girders is achieved by choice of forces P1 (P2) that
introduce tension in bolts. Redistribution of internal
forces in multigirder structure may also be achieved by
transverse prestressing [13].
a
4. APPLICATION OF EXPERIMENTAL
INFLUENCE LINES OF LOAD TRANSVERSE SPREAD FOR ASSESSMENT OF
LOAD CARRYING CAPACITY OF
BRIDGES
Conditions of bridge service change more and more
often. Application of plastic reserves to assessment of
load carrying capacity of bridges, described in chapter 2, is possible for deterministic excessive loads
(exceptional loads) [23]. However, besides various
analytical methods it is possible to assess load carrying capacity on the basis of “in situ” testing. It is particularly attractive because it enables exploitation of
safety reserves that were not taken into account during design. Such load carrying capacity reserve may
be joint action of main girders and decks that were
designed as independent of girders. Existence of the
joint action must be proved experimentally.
In static analysis of bridges influence lines of load
transverse spread (ILLTS) are often applied. The
lines obtained from experiment differ from those
computed. For this reason, in 1987, Professor’s workgroup developed a method of testing and setting
a
b
c
b
Figure 8.
Method of equalizing loading taken by girders in multi
girder bridge by introduction of steel cross beam [10]
1 – steel cross beam, 2 – tensioning bolts
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Figure 9.
Schemes to compute coordinates ηik:
a) load scheme, b) deflection line of cross-section, c) influence lines of load transverse sprea
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n
Bc = ¦ Bi
s
P1 = (1 + ∆p ) ⋅ ¦ Pr ⋅η 1r
r =1
(6)
where:
s
∆p =
¦ Pr ⋅η 1r ⋅ δη1r
r =1
s
¦ Pr ⋅η 1r
(7)
r =1
(3)
i =1
c) B0 denotes comparative stiffness so the following
symbol was introduced:
βi =
Bi
B0
(4)
Let us assume that for concentrated load of P at position „k” (Fig. 9a) deflections wik of all beams were
recorded (Fig. 9b). Then coordinates ηik may be set
based on equation [4]:
η ik =
β i ⋅ wik
n
¦ β i wik
,
and the following must be true:
i =1
wing must be true:
n
¦η ik = 1
i =1
(5)
(5)
It was proved in [4] that equation (5) may be applied
also when tri-axle lorry is used instead of concentrated load. Bridge testing method and algorithm of test
results development were given. Testing should provide appropriate number of objective results to allow
statistic analysis. To achieve that the following principles should be respected:
– number of „k” positions, where load is applied
should not be less then five,
– in each „k” position load must be applied at least
twice,
– deflection of each beam should by measured with at
least two gauges.
Final effect of test recordings are ILLTS for particuη ik
lar beams, given as average values of coordinates and respective values of relative accidental uncertainty δ η ik (Fig. 10).
Let us assume that number of “s” concentrated loads
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1
Figure 10.
Experimental ILLTS (
η ik) and respective diagram of relative uncertainties of recorded displacements [4]
The described testing method was applied for an
assessment of load carrying capacity of over 20 steel
road bridges with deck slab of two kinds [5, 6, 7]:
– RC slab assembled with steel beams with no intention of joint action (flexible connection of unknown
parameters),
– basin-shape or cylindrical-shape steel plates filled
with concrete.
As an example of method application a 9-beam
bridge of 17.6 m span with deck slab of basin-shape
steel plates filled with concrete [5, 6] is chosen. The
bridge was loaded with tri-axle lorry. Deflections of
all girders and strains of three outermost girders were
recorded at span centre. Recorded strains allow finding neutral axis of cross-section. Results proved joint
action of main girders and basin-shape steel plates
filled with concrete (flexible shear quasi-connection).
Thanks to the joint action of deck and girders
extreme bending moments caused by live loads might
be increased by over 6%.
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a) flexural stiffness of beams Bi=EIi vary from beam
to beam, but stiffness distribution along span does
not change,
b) total flexural stiffness of bridge cross section Bc is
given as:
Pr may be applied in bridge cross-section. Then the
load taken by outermost beam „i=1” is given as:
C I V I L
actual ILLTS, that may be applied to compute actual
load carrying capacity of bridges.
Fig. 9 shows the schemes used for setting coordinates
ηik of ILLTS in multibeam bridge. The following
assumptions were made:
e
c
J. Karlikowski, W. Siekierski
materials.
REFERENCWES
[1]
Jusik M., Urbaniak A., Wołowicki W.; Przebudowa
mostu św. Rocha w Poznaniu (Rebuilding of St. Roch
Bridge in Poznań). Inżynieria i Budownictwo, No.3,
2006; p.126-131 (in Polish)
[2]
Karlikowski J., Madaj A., Wołowicki W.; Badanie
skutków zarysowania płyty w belkach zespolonych
(Research on results of concrete slab cracking in
steel-concrete composite beams), Inżynieria i Budownictwo, No.7, 2002, p.381-383 (in Polish)
[3]
Karlikowski J., Madaj A., Wołowicki W.; Zwiększenie
nośności zabytkowego wiaduktu stalowego przez
zespolenie z płytą pomostową (Increase of load carrying capacity of listed steel viaduct due to creation of
steel-concrete composite structure), Konferencja
naukowo-techniczna “Mosty zespolone”, Kraków,
1998; p.163-170 (in Polish)
Figure 11.
Experimental ILLTS in multibeam bridge [6]
1 – joint action of deck and girders taken into account, 2 –
joint action of deck and girders neglected, 3 – analytical,
neglecting deck
[4]
Karlikowski J., Wołowicki W.; Wyznaczanie linii
rozdziału poprzecznego w mostach wielobelkowych
na podstawie pomiarów in situ (Setting influence line
of load transverse spread in multigirder bridges on
the basis of in situ testing), Archiwum Inżynierii
Lądowej, No.1-2, Vol.XXXV, 1990; p.63-79 (in
Polish)
Joint action of deck and girders caused favorable
change of transfer spread of live loads. Fig. 11 shows
experimental ILLTS for outermost beam and the one
near it for two variants – with and without joint action
taken into account – continuous and dashed lines
respectively. It can be seen that actual transverse
rigidity of span is larger than the one that neglects
joint action of deck and girders. Live load spread
over girders is even more.
For the beam next to the outermost one the ILLTS
based on analytical method of equivalent orthotropic
plate (dotted line), that had been used several years
earlier to set load carrying capacity of the bridge, is
given. Taking into account roadway live load according to PN-85/S-10030 and experimental ILLTS the
loading taken by the beam no.8 is about 40% smaller
than the one computed on the basis of analytical line.
[5]
Karlikowski J., Wołowicki W.; Doświadczalne określenie współpracy płyty pomostowej z blach
wypełnionych betonem z dźwigarami stalowymi
mostu drogowego (Experimental assessment of joint
action of deck made of basin-shape steel plater filled
with concrete and steel beams of roadway bridge).
XXXVI Konferencja Naukowa KILiW PAN i KN
PZITB. Wrocław – 1990 – Krynica, Vol. III, 1990;
p.47-52 (in Polish)
[6]
Karlikowski J., Wołowicki W.; The experimental – analytical assessment of carrying capacity of the quasi –
composite multibeam bridge. Proceedings of the 4th
international conference “Safety of bridge structures”, Wrocław, September 9-12, 1992; p.435-442
[7]
Karlikowski J., Wołowicki W.; Ocena nośności małych
mostów drogowych o niepełnym zespoleniu
(Assessment of load carrying capacity of small road
bridges with partial joint action of deck and girders).
III Konferencja Naukowo – Techniczna „Problemy
projektowania, budowy i utrzymania mostów
małych”, Wrocław – Szklarska Poręba, 1994;
p.135-142 (in Polish)
[8]
Madaj A., Ratajczak G., Wołowicki W.; The reinforcement of concrete bridge structure by means of steel
truss. Colloqium on actual problems of concrete
structures, Bratislava 1991; p.160-165
[9]
Madaj A., Ratajczak G., Wołowicki W.; Wzmocnienie
wielodźwigarowego przęsła mostu kablobetonowego
(Strengthening of multigirder prestressed post-tensioned bridge span). Inżynieria i Budownictwo, No.6,
5. CONCLUSION
On the occasion of 75th birthday anniversary some
characteristic structural solutions and original methods of assessment of load carrying capacity of authorship or co-authorship of Professor Witold Wołowicki
were recalled. In the authors’ opinion they may by
used nowadays in modified form that takes into
account cotemporarily available technologies and
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[10] Madaj A., Ratajczak G., Wołowicki W.; Wzmacnianie
wielodźwigarowych mostów z betonu (Strengthening
of multigirder concrete bridge span). Drogownictwo,
No.9, 1993; p.126-131 (in Polish)
[11] Madaj A., Sturzbecher K., Wołowicki W.; Kładka dla
pieszych nad Cybiną w Poznaniu (Footbridge over
Cybina river in Poznań). Inżynieria i Budownictwo,
No.1 2, 2009; p.89-92 (in Polish)
[12] Madaj A., Wołowicki W., Węgrzynowska M.;
Wzmocnienie sprężonego mostu ramowego
budowanego metodą wspornikową (Strengthening of
prestressed frame bridge erected according to cantilever method). Inżynieria i Budownictwo, No.7-8,
2006; p.418-422 (in Polish)
[13] Madaj A., Wołowicki W.; Podstawy projektowania
budowli mostowych (Basic of bridge structure
design). WKiŁ, 2007 (in Polish)
[14] Ryżyński A., Wołowicki W.; Zastosowanie teorii
przegubów plastycznych do oceny dopuszczalnych
obciążeń ustrojów z betonu zbrojonego (Application
of theory of plastic hinges to assessment of admissible
loads on reinforced concrete structures). Inżynieria
i Budownictwo, No.3, 1969; p.94-102 (in Polish)
[15] Ryżyński A., Wołowicki W.; Przykład wzmocnienia
podciągu żelbetowego z wbetonowanymi belkami
prefabrykowanymi (An example of strengthening of
reinforced concrete girder with encased precasted
beams). Zeszyty Naukowe Politechniki Poznańskiej,
Budownictwo Lądowe, No.19, 1974; p.75-81 (in
Polish)
[16] Wołowicki W., Apanas L., Ratajczak G.; Badania
pomostowych płyt stalowo-żelbetowych pod obciążeniem powtarzalnym (Testing of steel-concrete deck
slabs under repeatable loading). Inżynieria i Budownictwo, No.7, 1981; p.263-265 (in Polish)
[17] Wołowicki W., Karlikowski J.; Niektóre zagadnienia
konstruowania betonowych mostów zespolonych
(Some problems of constructing concrete-concrete
composite bridges). Konferencja NaukowoTechniczna „Zagadnienia budownictwa mostów
betonowych”, Kielce, 1977; p.380-387 (in Polish)
[18] Wołowicki W., Sturzbecher K.; Niektóre wnioski z badań belki mostowej sprężonej splotami 75 (Some
conclusions from testing of bridge beams prestressed
with 75 tendons). Drogownictwo, No.7-8, 1978;
p.237-241 (in Polish)
[21] Wołowicki W.; Nośność graniczna rusztów mostowych
z betonu zbrojonego (rozprawa doktorska) (Ultimate
limit load carrying capacity of bridge grids of reinforced concrete; doctoral dissertation). Poznań, 1971
(in Polish)
[22] Wołowicki W.; O wpływie okresowego przeciążenia na
wytrzymałość zmęczeniową stali zbrojeniowej mostów
żelbetowych (On the influence of periodic overloading on fatigue strength of reinforced concrete
bridges). Archives if Civil Engineering, No.1, 1977 (in
Polish)
[23] Wołowicki W.; Problemy obliczania mostów żelbetowych na quasi-statyczne obciążenia wyjątkowe,
Rozprawy nr 100 (Problems of computing reinforced
bridges for quasi-static excessive loads, Dissertations
no.100), Wydawnictwo Politechniki Poznańskiej,
Poznań 1979 (in Polish)
[24] Wołowicki W.; Analiza doświadczalna rusztów żelbetowych w stanach pozasprężystych (Experimental
analysis of plastic behaviour of RC grids). Archiwum
Inżynierii Lądowej No.4, Vol.XXIII, 1977; p.419-436
(in Polish)
[25] Wołowicki W.; Wybrane problemy użytkowania
zabytkowych wiaduktów drogowych nad torami kolejowymi (Some problems of exploitation of listed road
viaducts over railway tracks). VII Konferencja
naukowo-techniczna: Inżynierskie problemy odnowy
staromiejskich zespołów zabytkowych. PAN Oddz.
Kraków, Politechnika Krakowska, MOIIB, Krakow
2006 (in Polish)
1)
Świadectwo autorskie o dokonaniu wzoru
użytkowego nr 30725 pt. Prefabrykowany dwuteowy
dźwigar betonowy (Conformation of authorship of
innovation no. 30725: Precasted concrete girder of
I-section). 17 kwietnia 1978r. (autorzy: W. Wołowicki,
J. Karlikowski)
2)
Karlikowski J., Madaj A., Wołowicki W., Badania wpływów zarysowania płyty betonowej oraz redukcji sił
rozwarstwiających na stany graniczne mostowych
belek zespolonych typu beton-stal (Research on influence of concrete slab cracking and reduction of shear
forces at the steel-concrete interface on ultimate limit
states of steel-concrete composite beams). Grant
KBN, Projekt nr 7TO7E01113, 2000
[19] Wołowicki W.; Grossberechnungen von Brucken in
der Beton-Stahlsegmentbauweise. International
Symposium “Composite steel-concrete structures”,
Bratislava, Vol.III, 1987; p.73-77 (in Polish)
[20] Wołowicki W.; Studium modernizacji mostów
betonowych (Study of modernization of concrete
bridges).
Konferencja
Naukowo-Techniczna
„Naprawa i wzmacnianie betonowych i zespolonych
konstrukcji mostowych”, Kielce, 1988; p.293-298 (in
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1992; p.207-210 (in Polish)
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