MASTER'S THESIS
Assessment of a Connection of a Bridge by Full-Scale Testing
Julia Elhag 2014
Master of Science in Engineering Technology Civil Engineering
Luleå University of Technology
Institutionen för samhällsbyggnad och naturresurser
MASTERS THESIS
Assessment of a connection of a bridge by full-scale testing
Julia Elhag Luleå 2013
Division of Structural and Construction Engineering
Department of Civil, Environmental and Natural resources Engineering Luleå University of Technology
971 87 Luleå
PREFACE
P REFACE
This report is the final part of my civil engineering education at Luleå University of Technology at the division of Structural and Construction Engineering. The work was
conducted between June and November 2013 at the department of Civil, Environmental and Natural resources Engineering.
I would like to thank my supervisor, Thomas Blanksvärd for guidance and counseling along the way. I would also like to thank Peter Collin for input to the work, the staff at the laboratory, Mohammed Salih for having patience with me during the set-ups.
Finally, I would like to thank the people who have been supporting me along my education;
my family and my closest - I'm lucky to be surrounded by such wonderful people in my life.
Luleå, January 2014
Julia Elhag
A BSTRACT
In the beginning of the 20th century there was an expansion of the infrastructural network due to the evolvement of the industry. This expansion included a series of new railway bridges being built and those bridges were designed according to the traffic situation at the time. Many of the bridges are still in use today and as the traffic volume is continuously increasing, replacing of the bridges due to undercapacity would be expensive.
Therefore, it is of interest to investigate the capacity of the bridges to determine their viability. Critical parts in bridges are details which cause stress concentrations and
discontinuities in the geometry such as connections. The longitudinal and transversal beams in floor-systems of old bridges are often connected through their webs by double-angle plates. These connections are designed only to take shear forces since the beams are assumed to be simply supported. The longitudinal beams are in fact continuous and the assumption that they are simply supported is therefore wrong.
A simply supported beam would mean no support moments but a high field moment whereas a fixed beam would mean that there would exist support moments and lower field moments compared to a simply supported beam. If the field moments are proven to be reduced compared to what the beams are designed for, it would mean that there would be end moments acting on the supports which would indicate that the beams would have a certain level of constraint. End moments mean an extra stress on the connections and it would mean that they would be subjected to forces they are not designed to take.
The purpose of this thesis is to investigate if the stringers of an old riveted steel truss bridge are not simply supported by doing a case study. An old railway bridge was monitored during loading with strain gauges, LVDTs and a photometric device, the displacements and strains were measured and analyzed to determine the stresses, moments and as a result of that, the level of restraint. The magnitude of the field moment for the stringers in the bridge proved to be somewhere in between a simply supported and a fixed beam which means that the connections between the floor-beams and the stringers are subjected to both shear forces and moments.
SAMMANFATTNING
S AMMANFATTNING
Den industriella utvecklingen under 1900-talets första hälft innebar en utbyggnad av det infrastrukturella nätverket. Denna utveckling innefattade att en rad nya järnvägsbroar byggdes och sedan den beräknade livslängden för en bro är ca 120 år används många av de broarna än idag. Broarna som byggdes under den industriella expansionen designades med hänsyn till de krav som fanns då men eftersom det sker en ständig ökning av både
trafikintensitet och trafikvolym måste broarnas kapacitet kontrolleras så de håller för de krav som ställs på broar idag.
Kritiska delar av broarna är delar som skapar oregelbundenheter i geometrin och
spänningskoncentrationer till följd av dessa, såsom förband. Golvsystemet i gamla broar består ofta av längsgående och tvärgående balkar i ett rutsystem som är sammanbundna i liven genom vinkelplåtar. Dessa förband är designade för att endast ta skjuvkrafter eftersom långbalkarna antas vara fritt upplagda vid dimensionering. De längsgående balkarna är i själva verket kontinuerliga över flera stöd och antagandet om att de är fritt upplagda är därmed felaktigt.
En fritt upplagd balk saknar stödmoment men har ett relativt högt fältmoment medan en fast inspänd balk har stödmoment men längre fältmoment i jämförelse med en fritt upplagd balk. Kan det bevisas att en balk har längre fältmoment än vad den dimensionerats för betyder detta att balken även bör ha stödmoment, vilket tyder på att det finns en viss
inspänningsgrad. Stödmoment innebär att förbanden utsätts för en extra påfrestning som de ej är dimensionerade för att ta hand om.
Målet med detta examensarbete är att undersöka om förbandet mellan lång- och tvärbalk tar moment genom en fallstudie av en gammal stålfackverksbro med nitade förband.
Förskjutningar och töjningar mäts under lastning med töjningsgivare, lägesgivare och en fotometrisk mätutrustning och resultaten analyseras sedan för att ta fram spänningar, moment och därefter inspänningsgrad. Fältmomenten i långbalken visade sig ligga
någonstans mellan det teoretiskt beräknade fältmomentet för en fritt upplagd balk och en
fast inspänd balk, vilket innebär att förbandet mellan lång- och tvärbalk är utsatta för både
moment och tvärkrafter.
TABLE OF CONTENTS
NOMENCLATURE ... IV
1. INTRODUCTION ... 1
1.1 Background ... 1
1.2 Problem discussion ... 1
1.3 Objectives and Purposes ... 2
1.4 Limitations ... 3
1.5 Method ... 3
2. FATIGUE... 6
2.1 Stress conditions and definitions ... 7
2.2 Wöhler ... 10
2.3 Palmgren-Miner ... 11
2.4 Deformation induced fatigue ... 12
2.5 Fatigue calculations according to Eurocode ... 12
2.5.1 Damage equivalent factor ... 12
3. CONNECTIONS ... 17
3.1 Welded connections ... 17
3.1.1 Welds and fatigue ... 18
3.1.2 Hot-spot approach ... 19
3.2 Riveted connections ... 22
3.2.1 Forces in rivets ... 22
3.2.2 Rivet nomenclature ... 23
3.2.3 Shear ... 24
3.2.4 Tension ... 24
3.2.5 Failure of rivets ... 25
3.3 Double angle connections ... 28
3.4 Welded cover-plates ... 30
3.5 Connection detail category ... 31
4. MONITORING METHODS/BRIDGE MANAGEMENT ... 33
CONTENTS
ii
4.1 Bridge assessment ... 33
4.2 Bridge inspection ... 33
4.3 Field testing ... 33
4.3.1 State of the art ... 34
4.4 Monitoring/Strain measurements ... 37
4.4.1 Strain gauges ... 37
4.4.1.1 Bonded foil strain gauges ... 38
4.5 LVDT ... 39
4.6 Optical measuring devices - ARAMIS ... 41
4.6.1 Hardware ... 42
4.6.2 Software ... 42
5. LOADS ... 44
5.1 Load path ... 44
5.2 Load distribution ... 45
5.2.1 Direct Load Model ... 45
5.2.2 Lever Rule Model ... 46
5.3 Traffic loads ... 46
5.3.1 Fatigue load model according to BRO 2004 ... 46
5.3.2 Traffic loads according to Eurocode 1 ... 47
5.3.2.1 Dynamic factors ... 49
6. CASE STUDY ... 51
6.1 Bridge structure ... 51
6.2 Material properties ... 55
6.3 Geometries and stresses ... 56
6.3.1 Cross-sectional properties ... 56
6.3.2 Fatigue stress according to Eurocode ... 60
6.4 Testing procedure ... 61
6.4.1 Preparations ... 62
6.4.1.1 ARAMIS ... 62
6.4.1.2 LVDTs ... 66
6.4.1.3 Strain gauges ... 69
6.5 Loading ... 71
7. RESULTS ... 75
7.1 ARAMIS ... 75
iii
7.1.1 Cyclic loads ... 76
7.1.2 Static loading ... 79
7.2 Strain gauges ... 81
7.3 LVDTs ... 82
8. ANALYSIS ... 84
8.1 Moment and shear force calculations ... 84
8.1.1 Moments calculated by the measured strains ... 84
8.1.2 Theoretic moments and shear forces ... 85
8.2 Level of restraint ... 94
8.3 Displacements, stresses and strains ... 96
9. DISCUSSION ... 100
10. CONCLUSIONS ... 104
FUTURE RESEARCH ... 104
REFERENCES ... 105
APPENDIX A ... 110
APPENDIX B ... 123
APPENDIX C... 234
NOMENCLATURE
iv
N OMENCLATURE
Denotation Definition Unit
Strain %
Deformation m
Stress Pa
E Young's modulus Pa
M Moment Nm
W Bending resistance
Minimum stress Pa
Maximum stress Pa
Mean stress Pa
Stress amplitude Pa
Stress range Pa
R Stress ratio %
Tensile strength of steel Pa
Yield strength of steel Pa
m
Slope of the linear relation between the logarithm of the stress range and the number
of loading cycles -
Constant depending on detail category -
S Stress amplitude Pa
N Number of loading cycles -
Detail category Pa
Constant Amplitude Fatigue Limit at N=5*10
6-
Cut-off limit at N= 10
8-
n The number of times each stress range occurs -
Total damage %
Partial damage %
Resulting equivalent stress range Pa
Damage equivalent factor -
Equivalent stress range Pa
Safety factor for fatigue actions -
Factor accounting the span length - Factor accounting the traffic volume and the
function of the structure type -
v Factor accounting for the design working life
of the structure -
Factor accounting the influence for more than
one load on the structure -
a Ratio between two loaded tracks %
The stress range in the structural detail
created by the LM71 train on track 1 Pa
The stress range in the same structural detail created by the LM71 train on the two tracks
considered. Pa
p Percentage of crossings %
Maximum damage equivalent factor value -
Yield stress Pa
Membrane stress of a weld Pa
Shell bending stress of a weld Pa
Non-linear stress peak of a weld Pa
Nominal stress Pa
Hot-spot stress Pa
Mean stress Pa
Geometric stress concentration factor -
p Pitch m
Back pitch m
Diagonal pitch m
t Plate thickness m
d Rivet hole diameter m
Rivet shank diameter m
Cover plate thickness m
Rivet clamping force N
Shearing load capacity of a rivet N Allowed shear stress in a single lap joint Pa Diameter of rivet hole when calculating for
shear
n Number of rivets in a row -
Tearing capacity of a plate Pa
Tensile capacity of a joint N
Area of the plate to resist tensile forces, where the rivet rows are situated
Area to resist crushing
Allowable bearing/crushing stress of a rivet Pa
NOMENCLATURE
vi
Crushing strength of a joint N
Area to resist margin shear
Permissible shear stress of a plate Pa
Capacity against margin shear N
Rate of change in resistance for a strain gauge %
K Gauge factor -
R Resistance
e Voltage V
Factor to increase or decrease the impact of
traffic loads -
Partial safety factors for load combinations -
D Dynamic factor -
Determining length according to BVS 583.11 m
1
1. I NTRODUCTION 1.1 B ACKGROUND
The industrial development during the first half of the 20th century has led to an expansion of the infrastructure. A series of new railway bridges were built to meet the increasing demands on the infrastructural network (Al-Emrani et al (2009)). Many of those bridges are still in use since the required service life of bridges is normally 100 years or more and traffic development during such a long period is hard to predict (Troive (1998)). In Europe, more than 35 % of the existing railway bridges are more than 100 years old and 50 % of them have reached an age of over 50 years (Olofsson et al (2004)).The traffic loads and the traffic volume is continuously increased and instead of replacing the existing bridges, it is of
interest to investigate the capacity of the existing bridges since there are both economic and environmental profits to be made by avoiding having to replace fully functional bridges(Al- Emrani et al (2009)).
Existing bridges have to be assessed in order to investigate whether they are still viable or not. The analytical methods used in original designs of older bridges were often based on conservative assumptions, meaning that there ought to be more capacity in the bridges than they are originally designed for (Mehrkar et al (1996)). If an assessment of a bridge would indicate that the capacity of the bridge is insufficient, there are four alternatives to deal with the problem (Carlsson et al (2008)):
Replacement of the bridge
Reinforcing the bridge
Limiting the highest allowable axle loads
Proving by another analytical method that the capacity is of the bridge is sufficient
To replace all bridges that are close to reaching their service life would be too expensive and time consuming because of the quantity of old bridges today. Reinforcement of bridges is also a question of cost. At some railways, limiting the axle loads is not an option and it is therefore of importance to identify the critical parts of bridges in use and investigate the capacity of those (Larsson (2009)).
1.2 P ROBLEM DISCUSSION
The iron ore line "Malmbanan", transporting iron ore from northern Sweden to the coast of Norway, has had an increase of the axle loads from 25 tonnes to 30 tonnes per axle
(Olofsson et al (2004)). One of the bridges along Malmbanan is the bridge over Rautasjokk, which is a steel truss bridge with riveted connections.
The old bridge over Åby river, situated adjacent to the border between Norrbotten and
Västerbotten County in the vicinity of Långträsk, is a structure identical to the one over
INTRODUCTION
2 Rautasjokk. The old bridge crossing Åby river was designed for an axle load of 25 tons. It has now been replaced to allow higher axle loads and the old bridge is now to be studied. New riveted structures have not been built in decades, which also means that less attention has been paid to the fatigue lives of the existing riveted structures in service today (Al-Emrani (2002)).
Failure due to fatigue starts with fatigue cracks and fatigue crack initiation is the most critical in areas which contain flaws and stress concentrations. Connections and other details cause discontinuities in structures, making the connections subject to stress concentrations. As girders, diaphragms, beams, stringers etc must be structurally connected in some way, the level of stress concentration in these details needs to be examined (W.Ryan et al (2006)).
Floor-systems in older bridges are typically designed as grid structures that consist of
longitudinal and transverse elements consisting of stringers and floor-beams. The beams are connected through their web plates by riveted double-angles (Kumar Goel (2006)).
Connections between floor-beams and stringers are known to be particularly prone to fatigue (Righihiotis et al (2010)). Since these connections are designed only to take shear forces and it has been proven that the beams are not simply supported, it is of interest to investigate how much bending the connection takes (Moreno (2013)).
1.3 O BJECTIVES AND P URPOSES
The purpose of this thesis is to investigate the fatigue behavior of a riveted and welded
connection between a floor-beam and a stringer in a steel truss bridge with the objective to
determine the amount of bending the connection takes. The beams are continuous but the
connections are designed as if they were simply supported i.e. with zero moment at the
supports. The riveted connections are not free to rotate in the plane of the stringer axis and
is thus not simply supported. It is therefore of interest to investigate the level of constraint
since the beams have properties somewhere in between a simply supported and a fixed
beam as seen in the bottom image in Figure 1.
3
Figure 1, Moment diagrams for simply supported, fixed and semi-rigid beams
1.4 L IMITATIONS
Only the connections between floor-beams and stringers will be considered in this thesis.
Ambient conditions affect the fatigue life of a steel specimen. Low temperatures, for example have a negative effect on the fatigue life (Nussbaumer et al (2011)). In this thesis, influence from temperature and environment will not be considered, neither will effects of degradation such as corrosion, coatings and other time dependant effects.
1.5 M ETHOD
To get a better understanding and a greater insight into the research area, a literature study is made, focusing on fatigue in general and on welded and riveted connections. In order to find literature, databases such as Google Scholar, Google and Scopus are used. Since a structured observation is made on a real bridge and the data format is numerical, the approach is quantitative (Mack et al (2005)).
To be able to continue using existing bridges it is necessary to prove either that the
structural capacity is higher than assumed in the design codes or that a failure is ductile
enough so that it is detected in time. To prove this, the time dependency of materials,
known size effect of the tensile strength and detailing has to be investigated and that is why
a field test of an older structure will give the most accurate results (Vogel (1996)). Since
there will be measurements made on a real bridge and existing theories will be used for
INTRODUCTION
4 assessment, the research strategy will be a case study. Testing will be made using hydraulic jacks that will induce the load. For measurement of deflections, LVDTs and an optical testing device will be used and strain gauges will measure the strains. Material properties together will the actual measured strains will give results regarding the stresses in the structure.
Results from the testing will thereafter be analyzed and discussed.
Stress is load applied to a unit area and stresses are always accompanied by strain since the stresses produces a deflection or deformation which is referred to as a strain. By measuring the deformations in the connection, shown in Figure 2, the strain is computed according to eq. (1) and the strain will be given in %.
L
P
Δ
Figure 2, deformation of a specimen
(1)
With known material properties, the stresses in the connection can be calculated as the stresses are proportional to the strains according to Hooke's law (eq.(2)) as long as the elastic limit or proportional limit is not exceeded. The relation between stress and strains have been experimentally tested for numerous materials and the stress-strain relation for a typical steel material with elastic- and plastic regions and proportional limits specified is displayed in Figure 3.
Figure 3, graphical relation between stress an d strain for a typical steel (Kyowa)
(2)
5 Where E is the Young's modulus of the material. So if the Young's modulus of the material is known, strain measurements enable calculations of the stress induced by a known applied force. With the stress calculated and the cross-sectional geometry known, the moment can be calculated according to eq, (3).
(3)
To decide the level of constraint, we consider the end moment of a fixed beam as
. The end moment for the stringers in this study are referred to as M. To
determine the level of constraint, , we simply calculate the ratio of M over according to eq. (4).
(4)
FATIGUE
6
2. F ATIGUE
Fatigue is "the tendency of a member to fail at a stress level below its yield stress when subject to cyclical loading" (W.Ryan et al (2006)). Even though the phenomena fatigue has been studied for over 200 years, fatigue is till the far most common reason of failure in structures of metallic materials. (Eriksson (2006)).There are two types of fatigue, low cycle fatigue (up to 10 000 load cycles) and high cycle fatigue ( 10 000 load cycles) (Nussbaumer et al (2011)) .The main acts of load induced fatigue are:
Initiation of microscopic-sized cracks
Crack propagation from microscopic to macroscopic size as a result of a huge amount of loading cycles. An accumulating damage of the material around the crack, which size increases by each loading cycle.
The crack propagation is followed by a sudden increase of crack growth speed which eventually leads to failure when the cracks reach their critical size and the fatigue strength of the specimen has been reached (Boardman (1990)). The geometry of the structural detail determines the crack propagation speed and the crack location. Sharp geometrical changes effect the stress flow and creates stress concentrations.
Fatigue can be cyclic and regular or completely stochastic. Fatigue cracks can take form at elastic load levels and damages due to fatigue are initially at a very local extent. The crack is opened because of the elastic deformation of the structure and is therefore easiest to detect during loading. When the residual cross-section is plasticized, the crack will be permanently opened. At this stage, the structure is usually close to failure (Eriksson (2006)). Fractures can be ductile or brittle. Brittle failures come sudden and without a warning and an example of a brittle failure is shown in Figure 4. A ductile fracture is to prefer since these failures are preceded by distortions which give a visual warning of the upcoming fracture, a ductile failure is shown in Figure 5 (W.Ryan et al (2006)).
Figure 4, brittle (shear) failure of a bolt
7
Figure 5, ductile failure of a plate
The fracture behavior is determined by temperature, loading rate and level of constraint.
Cold temperatures, high loading rates and highly constrained specimens increase the risk of brittle failure in details prone to fatigue (W.Ryan et al (2006)).
2.1 S TRESS CONDITIONS AND DEFINITIONS
The number of load cycles required to initiate a crack is the fatigue-crack-initiation life and the amount of load cycles required to propagate the crack size to critical is called the fatigue- crack-propagation life. The sum of the fatigue-crack-initiation life and the fatigue-crack- propagation life is the total fatigue life (W.Ryan et al (2006)). The initiation phase can represent a large proportion of the total life, especially regarding high cycle fatigue (Andersson (2009)).
The pattern of the fracture surface describes the loading history of the specimen. On the surface, striations occur and the specimen develops one striation distance per loading cycle for loads above a certain threshold value (Eriksson (2006)). To characterize the fatigue the fatigue cycle, a few parameters are introduced:
is the minimum stress
is the maximum stress
If
the load is vibrant/pulsating and repeated ( , See b), Figure 7 .
If the load is referred to as alternating or completely reversed ( )., see a), Figure 7 .
I.e. if
and
have the same sign the load is pulsating. If they have different signs the load is alternating (Nicholas (2006) ). c) in Figure 7 , an alternating tensile stress is displayed and d) in Figure 7 displays a stress alternating between a compressive and tensile value (Boardman (1990)).
Stress conditions and definitions (Boardman (1990)):
FATIGUE
8 The mean stress, , is the average of the maximum stress and the minimum stress in one cycle: σ
m
(5)
The range of stress, , is the difference between the maximum stress and the minimum stress:
(6)
The stress amplitude, is defined as half of the range of stress:
(7)
The stress ratio, R is the ratio of the minimum and maximum the stress:
(8)
Definitions above are displayed in Figure 6.
Figure 6, definition of stresses, tensile residual stresses (Nussbaumer et al (2011))
9
Figure 7, load cycle notations (http://www.asminternational.org/content/ASM/StoreFiles/06181G_Sample.pdf)
Tensile forces give a high contribution to fatigue and compressive forces cause less damage than tensile forces (Eriksson (2006)). A fatigue critical member in a steel bridge is a steel member in tension, or with a tension element, whose failure would cause a portion of the bridge to collapse (W.Ryan et al (2006)). In the normal case, without any impact from environment and temperature, the life length of a specimen rarely depends on the
frequency or wave shape of the loading. Life length substantially depends on the number of load cycles, independent of the shape of the sine waves (Eriksson (2006)).
In the standards, there is a fatigue limit at 10
8load cycles. At stress ranges below the
constant amplitude fatigue limit (CAFL) shown in Figure 8, cyclic loading can be applied a
large number of times (> times) without reaching fatigue failure, meaning a fatigue life
FATIGUE
10 tending to infinity (Nussbaumer et al (2011)). As the fatigue strength of steel is roughly proportional to f
u, high strength steel have better fatigue properties than soft steels, but this does not apply for welded sections. Surface and environment affects the fatigue properties of a steel specimen and ideal conditions would be highly polished rods in vacuum (Eriksson (2006)).
Fatigue cracking rarely occurs in base material and is most common to start in a detail, from welds or connections (Nussbaumer et al (2011)). Geometric imperfections give stress
concentrations. A crack results in a large stress concentration and the stress concentration is the most intense at the tip of the crack. Every change in the shape of a body gives a local increase of stress. Local plastic deformation limits stress concentration at static loading. At varying loading, the most affected area is deformed plastic varying in tension and
compression. With this type of loading, damage is accumulated in the material and fatigue cracks eventually appears (Eriksson (2006)).
There is no reliable non-empirical formula for determining the number of load cycles before fatigue cracks are initiated. High strength steels are more sensitive to sharp changes in geometry than softer steels (Eriksson (2006)).
2.2 W ÖHLER
One of the earliest to address the topic fatigue was August Wöhler (Nicholas (2006)). Wöhler came to the conclusion that the stress range ( ) is the most important parameter when it comes to fatigue. (Eriksson (2006)).For a given detail there is a linear relation between the logarithm of the stress range and the number of loading cycles with the slope 1/m. Different details are assigned different constant values ( ) depending on its geometric properties and what kind of structural detail it is (Al-Emrani (2002)).
The results of fatigue testing are often plotted as
, or the stress amplitude (S) versus the number of load cycles (N), to fracture using a logarithmic scale for N. The curve is referred to as an S-N-curve (Stress-Number-curve) or a Wöhler curve (Boardman (1990)). The
relationship between the logarithms of the stress range and the number of loading cycles is:
(9) or
(10)
The three main variables controlling fatigue performance of structural steel details are thus
the stress range, the number of loading cycles and the properties of the structural detail. The
slope constant of all fatigue-design curves is m=3 up to five million load cycles. At five million
load cycles, the Constant Amplitude Fatigue Limit (CAFL) is fixed (Al-Emrani (2002)). For
11 constant amplitude stress ranges over or equal to the CAFL, the fatigue life is infinite. All curves are parallel and each curve is characterized by , which is the value of the fatigue strength at load cycles in MPa (Nussbaumer et al (2011)). Figure 8 displays fatigue- design curves by Eurocode 3. Point 1 in the image displays the detail-category factor C, point 2 displays the CAFL and point 3 displays the cut-off limit at N=10
8cycles.
Figure 8, fatigue strength curves for normal stress range from Eurocode 3. Numbers of curves indicate detail catecory (Zamiri Akhlaghi (2009))
The fatigue curves are based on experimental trials and include effects of expected crack location, imperfections, residual stresses, stress directions, welding procedures, detail geometry and stress concentrations due to the detail geometry, metallurgical conditions and local stress concentrations because of the shape of the weld (Nussbaumer et al (2011)).
2.3 P ALMGREN -M INER
The Palmgren-Miner's rule stems from the assumption of linear damage accumulation. The
total damage,
is the sum of a series of partial damages. When
= 1 is reached, failure
occurs. The partial damages are represented by the ratio of and . is defined as the
times each stress range occurs and the number of load cycles to failure is referred to as
(Nussbaumer et al (2011)):
FATIGUE
12
(11)
The Palmer-Miner rule does not take the order of loading into account, but the equation together with suitable safety factors is reliable enough to be used for design (Nussbaumer et al (2011)). The Palmgren-Miner's rule is not exact but it will, in most cases, give a safe fatigue life estimation. For situations with high mean stresses combined with repetitive stress
releases, the rule can overestimate the fatigue life (Larsson (2009)).
2.4 D EFORMATION INDUCED FATIGUE
Appears in the weaker of two connected parts in a structure (for example a stiff primary beam connected to a less stiff secondary beam in a structure will force its deflection upon the secondary beam).
The phenomena is most commonly noticed in railway bridges with riveted connections.
The life length of the structure decreases in proportion to the number of axles but in the cube of the axial pressure, meaning that doubling the load will decrease the life length to 1/8 (Eriksson (2006)).
In approximately 90 % of all reported damage cases for steel- and composite bridges, the damages are deformation induced (Al-Emrani et al (2009)).
2.5 F ATIGUE CALCULATIONS ACCORDING TO E UROCODE
2.5.1 D AMAGE EQUIVALENT FACTOR
When controlling a structure that is going to be subjected to a load history, the procedure is
complex and the engineer needs knowledge about the loads that are going to act on the
structure during its lifetime. Assumptions have to be made and the damage accumulation
calculations follow those assumptions. To simplify the work, the concept of fatigue damage
equivalent factor was introduced. First, real traffic and displacement is modeled over the
structure. Thereafter, the corresponding stress history is deducted and the resulting stress
range histogram is calculated. Then the resulting equivalent stress range,
is calculated
and compared with the detail category. The procedure is explained in Figure 9.
13
Figure 9, Damage equivalent factor (Nussbaumer et al (2011))
The resulting stress range is though not representative of the fatigue effect on the bridge due to real traffic and must be corrected with a damage equivalent factor, , in order to achieve a value that corresponds to the equivalent stress range,
(Nussbaumer et al (2011)).
(12)
FATIGUE
14 The recommended value for the factor
is 1,0 (Eriksson (2006)). In the Eurocodes, the procedure splits the factor into four different partial factors in order to take more parameters into account:
But
(13)
where:
λ
1is a factor accounting the span length as shown in Figure 10 and Figure 11.
λ
2is a factor accounting the traffic volume and the function of the structure type as shown in Figure 12.
λ
3is a factor accounting the design working life of the structure, which is calculated according to (14):
(14)
λ
4is a factor accounting the influence for more than one load on the structure calculated according to (15) . Eurocode only deals with bridges with two tracks loaded at the same time
(15)
Where
- the ratio between two loaded tracks
- the stress range in the structural detail created by the LM71 train on track 1
- the stress range in the same structural detail created by the LM71 train on the two tracks considered.
p - percentage of crossings
λ
maxis the maximum damage equivalent factor value, which is a function of the structure type. For Railway bridges, the limiting value is bound by the CAFL, , and can be calculated according to (16) before it tends to 1,4 (Nussbaumer et al (2011))
(16)
15
Figure 10, partial damage equivalent factor λ1 for road and rail bridges as a function of the critical influence line length L (Nussbaumer et al (2011))
Figure 11, damage equivalent factor λ1 for railway bridges (Nussbaumer et al (20111))
FATIGUE
16
Figure 12, damage equivalent factor λ2 for railway bridges (Nussbaumer et al (2011))
After calculating the different - factors,
can be calculated by breaking it out in eq. (12)
17
3. C ONNECTIONS
Parts in structures need to be connected in some way and there are different ways to connect these joints, for example bolting, riveting and welding. In this chapter, welding and riveting will be first be described since these are the connection methods used in the double angle and cover plate connection to be analyzed in this thesis.
3.1 W ELDED CONNECTIONS
Welds are metal parts connected and joined together by heating of the surfaces to a fluid, plastic state with or without addition of a filler (weld) material. The parts to be joined are referred to as the base material and the filler material is referred to as the weld. The whole connection is referred to as the weldment. There are four common types of welds; groove welds (butt welds), plug welds, fillet welds and tack welds. (Tamboli (2009)).
Figure 13, groove weld (W.Ryan et al (2006))
Figure 14, fillet weld (W.Ryan et al (2006))
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18
Figure 15, plug weld (W.Ryan et al (2006))
Figure 16, tack weld (W.Ryan et al (2006))
3.1.1 W ELDS AND FATIGUE
Welds are designed for fatigue strength and the fatigue limit for non welded or affected
material is approximately 0,5f
u(Eriksson (2006)). The load concentration is the biggest at the
weld toe, which is the boundary between the weld and the base material (Nussbaumer et al
(2011)). Even weld edges give moderate stress concentrations and fatigue cracks are often
initiated at the weld toe where intrusions are common. In non-penetration welds, stress
19 concentrations appear at the root of the weld. If cracks are initiated at the root of these types of connections, they grow outwards through the weld (Eriksson (2006)).
When subjected to fatigue loading, welds have some characteristic properties which differ from the base material. The amount of load cycles before crack initiation is reduced in a weld compared to the amount of load cycles required to initiate a crack in a base material (Nussbaumer et al (2011)). The majority part of the life time of a base material is the
initiation period whilst the initiation period takes up an insignificant part of the life time of a welded material (Eriksson (2006)).
A welded connection does not have to carry or transfer any outer load to give a stress concentration, the connection is not a defined unit, like a rivet in a riveted connection, but an integrated part of its surroundings. Residual stresses are stresses which do not depend on outer loads (Eriksson 2006)). All welding result in high built-in residual tension stresses (W.Ryan et al (2006)). Tension in one area is compensated by compression in another area.
The heat source used when welding gives a thermal deformation (expansion when heating, shrinking when cooling) in the material. When heated, the specimens are deformed
plastically closest to the weld and during cooling, remaining tensile stresses are forced because of the shrinking (Eriksson (2006)).
When subjected to a varying cyclic outer stress (0
), the longitudinal stress in the weld will vary between the yield stress, , and
. If the stress is compressive (0 to
), the stress in the weld will vary between the yield stress and the maximum stress.
This means that for a given nominal stress with a stress range , the stress in the weld will vary between and
independent if the stress is compressive or tensile. At stresses near the yield limit, fatigue can occur even at pure nominal compressive loading and the fatigue strength of a welded connection only depends on the stress range of the outer load. Therefore, design of welded connections can be based on the nominal stress range and the design S-N-curve can be used independent on the
of the applied load (Eriksson (2006)).
The size of the residual stresses in the weld depends on material properties. For soft steels, the yield limit of the welds is stronger than the base material. For mid-strength steels, weld and base material will be about the same strength and for high-strength steels, alloying materials are needed to achieve evenly strong weldments. (Eriksson (2006)).
3.1.2 H OT - SPOT APPROACH
The hot spot approach is a method based on geometrical stresses (Al-Emrani et al (2009)).
The method was mainly developed for welded connections but it does not take local stresses
near the weld toe into account. It is still a new method and has not been used as wide as the
nominal stress method. The method is suited to be used in situations when fatigue design or
fatigue assessment of a detail is required and the detail is not a standard details to be found
in tables provided by the design code, for complex details where a clear definition for the
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20 nominal stress cannot be made or when modeling a component with a detailed FEM-model (Zamiri Akhlaghi (2009)).
The method is appropriate to use if the fluctuating principal stress mainly acts transverse to the weld toe or in situations when the nominal stress is hard to estimate because of
geometric and/or loading complexities and the approach is only possible to use for fatigue failures starting from the weld toe (Aygül (2012)).
Both macroscopic effects (stress concentrations) and microscopic effects (weld shape, weld type, flaws etc.) are taken into account. Macroscopic effects are included in the calculated geometric stress range and the microscopic effects are taken into consideration in a set of hot spot S-N curves given in EN 1993-1-9 annex B (Nussbaumer et al (2011)). The resulting geometric stress is calculated and is thereafter compared to the fatigue strength according to Wöhler curves corresponding to the current connection type (Andersson (2009)). The notch effect of the weld has an impact on the stress distribution through the thickness of a plate near the weld toe. Since the notch stresses are higher than the nominal stresses in the weld toe, see Figure 17, they control the fatigue cracking of plates (Zamiri Akhlaghi (2009)).
Figure 17, stress through the plate thickness at the weld toe (Zamiri Akhlaghi (2009))
From the non-linear stress distribution in Figure 17, three stress components are recognized;
the membrane stress (
), the shell bending stress (
) and the non-linear stress peak (
). The membrane stress is constant throughout the thickness and equal to the average stress and the shell bending stress distribution is zero in the mid plane and linear through the thickness of the plate. What remains of the stresses is the non linear stress peak, which is in self-equilibrium and which depends on size and form of the weld and weld toe (Zamiri Alhlaghi (2009)).
The stresses at a weld toe that is about to crack are shown in Figure 18, where the increase of stress at the plate surface near the weld toe can be explained by two different factors.
The first factor is the change of macro geometry, which is a stress raiser near the weld toe.
The second factor is the local geometry of the weld, which results in a notch stress (Zamiri
Akhlaghi (2009)).
21
Figure 18, variation of stresses perpendicular to weld toe near the weld toe before fatigue cracking has occurred (Zamiri Akhlaghi (2009))
Since the geometry of the weld is not known in the design phase, the idea of the hot spot approach is to exclude the non-linear notch effect from the structural stress, which is included in the S-N curves. Only the two linearly distributed stress components build up the structural hot spot stress (
) (Zamiri Akhlaghi (2009)):
(17)
When using the hot spot method the fatigue critical points, referred to as the "hot spots", i.e. the points where fatigue stress can be determined using the method, are recognized by for example a FE-analysis of the specimen (Aygül (2012)). Thereafter, the identified hot spot- points are examined using the hot-spot approach (Zamiri Akhlaghi (2009)). When
determining the hot spot stress using furmulas, the nominal stress,
, is multiplied with a geometric stress concentration factor which depends of the detail analyzed according to (18) (Nussbaumer et al (2011)).
(18)
where
is the geometric stress concentration factor
is the nominal stress value from the detail
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22 In case of complex geometries and loadings, a combination of basic load cases is used
(Nussbaumer et al (2011)):
(19)
3.2 R IVETED CONNECTIONS
Until the 1930's, riveting was the most common joining method in Sweden, thereafter it was gradually replaced by bolting and welding. Many of the riveted bridges built before the middle of the last century are still in service (Al-Emrani (2002)).
The riveting procedure is performed according to the following steps (Al-Emrani (2002)):
Rivet holes are drilled and aligned
One rivet head is pre-formed on one side of the rivet, see Figure 19.
Rivet is heated to approximately 1000 C and inserted into rivet hole
Second rivet head is produced by hammering or squeezing the free end of the rivet
Figure 19, rivet inserted into rivet hole before second head is formed (Unit 3 (2013)).
3.2.1 F ORCES IN RIVETS
The diameter of a rivet before it is driven is known as the nominal diameter. The rivet hole is usually made about one millimeter larger than the undriven rivet in order to allow an
increase of the rivet diameter after it has been driven. 1,5 mm for rivets with diameters 24 mm ≤and 2 mm for rivets with diameters >24 mm (Kumar Jain et al (2005)). When the rivet cools down, it will shrink longitudinally as well as radially, a shrinkage which will be restricted by the connected plates (Larsson (2009)). The connected plates will then be subjected to compression stresses through their thickness, a compression stress that will be
counterbalanced by a residual tensile force in the rivet shank,
as shown in Figure 20.
The rivet clamping force will in turn create radial and circumferential compressive stresses
adjacent to the rivet hole, which in their turn are balanced by circumferential tensile stresses
at a distance from the rivet hole (Al-Emrani (2002)). If there is no outer force applied, the
clamping force from the rivet acting on the plate and the contact force from the plate acting
on the rivet will be equal (Larsson (2009)).
23 The rivets in stringer-to-floor-beam- connections are expected to have a lower clamping stress since these connections are constructed on-site with conditions that often results in faults (Kumar Goel (2006)).
Figure 20, rivet with clamping forces (Al-Emrani (2002))
3.2.2 R IVET NOMENCLATURE
There are different types of riveted joints. The arrangement when plates are riveted
together simply by positioning the edges of the plates over each other and sealed by riveting is called a lap joint. When the plates are placed end-to-end and jointed through cover plates, they are referred to as butt joints. If there is only one row of rivets passing through the connected plates, the joint is single riveted and if there are two rows of rivets passing through the plates, the joint is double riveted. Dimensions and notations important in riveted joints are described in Table 1 below and displayed in Figure 21 (Unit 3).
Table 1 , rivet nomenclature
Dimension Description Notation
Pitch Center distance between two
adjacent rivet holes in a row p Back pitch Center distance between two
adjacent rivet rows Diagonal pitch
Smallest distance between the centre of two rivet holes in
adjacent rows of zigzag riveted joints Plate thickness Thickness of plates to be
joined t
Rivet hole diameter Diameter of rivet hole d Rivet shank diameter Diameter of the rivet shank
Cover plate thickness Thickness of the cover plate
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24
Figure 21, different types of riveted joints: (a) Single Riveted Lap Joint; (b) Single Riveted Cover Butt Joint; (c) Single Riveted Double Cover Butt Joint; (d) Double Riveted Lap Joint; (e) Double Riveted Single Cover Butt joint and (f) Double Riveted Double Cover Butt Joint (Unit 3 (2013)
3.2.3 S HEAR
Riveted connections with normal clamping forces transfer moderate shear forces through friction between connected components. The magnitude of these shear forces depends on the clamping force in the rivet, the coefficient of friction between the connected plates and the deformation ability of the joint before the rivets and plates are put into bearing. Since there are a few uncertainties regarding the frictional shear resistance of riveted joints, the frictional shear resistance is commonly neglected in design.(Al-Emrani (2002)).
3.2.4 T ENSION
Stringer-to floor-beam connections, amongst other connections, are places in bridges which are subjected to tensile forces. Tensile loaded riveted connections are greatly affected by the clamping force in the rivet. To reach an equilibrium, the initial tensile force in the rivet (
) must be counterbalanced by compressive stresses in the connecting plates acting on a contact area. Since the stiffness of the plates is of greater magnitude than the axial stiffness of the rivet, the components of the connection will have different displacements in the self-equilibrated state (Al-Emrani (2002)).
The stiffness of angles in double-angle connections determines the behavior of the
connection subjected to bending. A stiff connection will have limited bending deformation of
the outstanding legs, meaning that prying forces and bending in the rivets will be almost
25 absent (Larsson (2009)). For less stiff double-angle connections where the outstand legs are able to deform, prying forces will develop and additional axial and bending stresses are produced in the rivet due to the prying action (Al-Emrani (2002)).
The magnitude of the clamping force in the rivet results in need of a higher load to separate the connected plates, meaning that the occurrence of prying will be delayed if the clamping force is increased. Connections with stiff outstanding legs are expected to have a higher clamping force than those with flexible outstanding legs (Al-Emrani (2002)). For a given applied load, an increase of the clamping force will result in a smaller increase of the axial force developed in the rivet (Kumar Goel (2006)).
Tensile overloads of riveted connection may result in partial or total loss of the initial clamping force in the rivet due to local yielding of the rivet in tension, which will affect the fatigue performance of the connection. Reduction of the clamping force will increase the tensile stress range as shown in Figure 22 (Al-Emrani (2002)) .
Figure 22, demonstration of how the reduction in clamping force will increase the stress range of a connection (Al-Emrani (2002))
3.2.5 F AILURE OF RIVETS
In old riveted connections, rivet failure is very common (Haghani et al (2012)). There are
different types of failure that can occur in riveted connections. The failures described below
are calculated with a few assumptions. There is no consideration of bending of the rivets,
friction between plate surfaces is neglected, the tensile loads are assumed to be equally
distributed over pitch lengths, loads are equally distributed over all rivets in the joints, rivet
holes are assumed not to produce stress concentrations, the plate is not weakened at the
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26 hole due to an increase of diameter during formation of the second rivet head and the crushing pressure is assumed to be uniformly distributed over the rivet area (Unit 3 (2013)).
When all rivets in one row shear off simultaneously, a shear failure will occur and the shearing load capacity of a rivet, , can be defined according to eq. (20), where is the allowable shearing stress in a single lap joint (Unit 3 (2013)).
(20)
where
(21)
If ,failure will occur.
If n defines the number of rivets in a pitch row, the shearing load capacity can be defined according to eq.(22).
(22)
For connections with two shearing planes, as in image b) in Figure 23, the allowed stress is 1,75 times the permissible shearing stress for single shear. The shearing load capacity for double shear is defined according to eq. (23) (Unit 3 (2013)).
(23)
Figure 23, shearing of rivet. A) single shear, B) double shear (Unit 3 (2013))
27
Figure 24, single riveted lap joint subjected to shear (Unit 3 (2013))
The plate is weaker in the area where the row of bolts is located. If the plate would tear, it would therefore be in the weakest area of the plate. The area to resist the tensile force is (Unit 3 (2013)):
(24)
If the tearing capacity of the plate in tension is denoted , then the tensile capacity of the joint is defined according to eq.(25) with the condition that if P is the applied tensile strength per pitch length, then failure will occur if (Unit 3 (2013)).
(25)
Due to the compression of the rivet against the rivet hole, the of rivet or the inner plate surface may be crushed. The area to resist crushing is defined according to eq.(26) (Unit 3 (2013)):
(26)
The crashing strength of the joint is defined according to eq.(27) where is the allowed bearing/crushing stress of a rivet and n is the number of rivets in a pitch length (Unit 3 (2013)).
(27)
If , failure will occur.
There can be a shearing of the plate along the margin near a rivet hole as shown in Figure 25. The plate can shear along a-b and c-d and the area to resist the failure is expressed as in eq.(28) (Unit 3 (2013)):
(28)
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28 If the permissible shear stress of the plate is
, then the capacity against margin shear is defined as (Unit 3 (2013)):
(29)
And if
, then failure will occur.
Figure 25, shear of plate margin (Unit 3 (2013))
The fatigue strength of riveted connections are highly dependent on the bearing ratio, which is the ratio of nominal bearing stress of the rivet shank on the plate to the average net- section tensile stress in the plate. The bearing ratio is calculated according to eq.(30) for a single lap joint (Al-Emrani (2002)):
(30)
Where b is the plate width and d is the rivet diameter.
It has been shown that the fatigue strength of riveted connections decreases when the bearing ratio is increased, particularly for riveted connections with reduced or absent clamping force (Al-Emrani (2002)).
3.3 D OUBLE ANGLE CONNECTIONS
The main function of stringer-to-floor-beam-connections is to transfer the end reactions of the stringers to the floor-beams by shear action. The floor-beams and stringers in old bridges are commonly connected through their web by riveted double angles as shown in Figure 26.
It is assumed that the rotational flexibility of these connections is enough to allow the end
rotation of the stringer without developing an end moment, meaning that the assessment of
the fatigue strength of these connections are made assuming that the connection is only
affected by shear forces (Kumar Goel (2006)).
29
Figure 26, Riveted double-angle connection between floor-beam and stinger on the bridge over Åby river
The stringer is not really simply supported but it is not rigid enough to be considered fixed at the supports either. It is in a semi-rigid state, requiring some rotational stiffness that
partially restrains the rotation of the stringer ends, which will lead to the development of negative bending forces in the stringer ends as shown in Figure 27. The negative bending moments will subject the fasteners and double angles to load effects that are not considered in design of the connections (Haghani et al (2012)).
The rotational stiffness of the double-angle connection is mainly a function of the stiffness of the outstanding legs of the angles and the gauge distance has shown to have a great
influence on the behavior of the double-angle connections. The moment acting on the
outstanding legs of the double angles will cause an out-of-plane distortion, shown in Figure
27, that will generate high flexural, non uniform stresses along the depth of the connection
(Kumar Goel (2006)).
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30
Figure 27, Secondary bending of stringer-to-floorbeam connection (Haghani et al (2012))
3.4 W ELDED COVER - PLATES
To increase allowable traffic loads and bridge spans, the moment capacity of the bridge needs to be increased. To increase the moment capacity of a steel bridge, it is possible to weld partial-length cover plates on the upper flange of the girders as shown in Figure 28. The ends of the cover-plates are the bridge details with the least fatigue strength and fatigue cracks are initiated at the weld toe, begins developing in the web and eventually propagates through the entire flange width as shown in Figure 29 (Haghani et al (2012)).
Figure 28, cover-plate on Åby bridge
31
Figure 29, crack in welded cover-plate (Andersson (2009))
Eurocode 3 describes detail category classes between C=36 and C=56 depending on the thickness of the main plate, t and the thickness of the cover-plate, (mm). The categories are divided into two categories; and . The fatigue strength decreases with increasing plate thickness. If the slope of the connection is limited to maximum 1:3 as displayed in Figure 30,the connection class can be increased (Andersson (2009)).
Figure 30, cover-plate (Andersson (2009))
3.5 C ONNECTION DETAIL CATEGORY
Connections are grouped into cross-section classes from which the corresponding Wöhler- curves can be calculated. The connection category is defined as the fatigue strength in MPa for at 2 million stress changes in Eurocode 3 it is denoted as (Andersson (2009)). In Figure 31 to Figure 33 the a few of the detail categories are illustrated.
Figure 31, detail category 160 - rolled or extruded products (Nussbaumer et al (2011))
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32
Figure 32, detail categories 36, 40, 45, 50 and 56 - welded cover-plates (Table 8.5 in EN 1993-1-9) (Nussbaumer et al (2011))
Figure 33, Detail categories for use with the hot-shot method (Table B.1 in EN-1993-1-9) (Nussbaumer et al (2011))
Testing of riveted truss girders have been conducted at different stress ranges by Helmerich
et al, Zhou et al, Al Emrani, DiBattista, Mang and Brühwiler. The girders were tested for
bending, tension and cantilever tests were made (Al-Emrani (2002)). By these tests and with
the rivet clamping force, material properties, corrosion and hole preparing technique taken
into account, it can be stated that a safe estimation of the fatigue life of riveted girders can
be made using detail category C71. If the conceptual design provides high bearing stresses,
detail category C63 is more suitable (Larsson (2009)).
33
4. M ONITORING METHODS /B RIDGE MANAGEMENT
4.1 B RIDGE ASSESSMENT
When determining the condition of a bridge, a simplified structural analysis is first made using the original drawings and the information they provide. Thereafter, a site inspection follows to inspect the rate of the degradation. Small cracks are hard to detect visually and sometimes physical or advanced inspection techniques are needed, for example corrosion sensors, accelerometers, strain measurements, vibration measurement or measurement of loads (W.Ryan et al (2006)). Physical tests are made to investigate the strength of the materials in the bridge such as the strength of the steel and the Young's modulus.
Sometimes improved analytical methods are used for assessment. (Mehrkar et al (1996)).
To improve the understanding of the actual behavior of structures, monitoring of structures is necessary (Sustainable bridges). It is also of importance to monitor bridges to have an up- to-date product model of the bridge with the right structural properties (Schlune et al (2008)). The design of the monitoring system has to be based on the bridge model and there are different types of monitoring systems that can be used (Sustainable bridges).
4.2 B RIDGE INSPECTION
Inspections are on-site examinations that are mostly non-destructive with the objection to investigate the present condition of the structure (Sustainable bridges). Inspections are planned and repeated in predetermined intervals (Schlune et al (2008)). Failure critical members in bridges should be inspected on a regular basis, on intervals that does not exceed twenty-four months. Inspections of steel bridges are primarily visual and the inspections include cleaning the area to be examined, brushing off paint if necessary and using of a magnifying unit (W.Ryan et al (2006)).
4.3 F IELD TESTING
Testing of a bridge is made to check and improve the simplified structural models and the analytical methods used. Testing can be done statically or dynamically. In a static test, the measured load is applied in predefined, fixed positions. Static tests are often used to examine the load distribution between main load-carrying members and support restrains (Schlune et al (2008)). Static loading can be performed in different ways (Young et al (2002)):
Short-time static loading - Load applied gradually until failure occurs and total time to reach failure is a few minutes in testing. If in service, then the load is gradually increased to the maximum value end maintained at that top value for a certain time without being reapplied often enough for fatigue consideration.
Long-time static loading - maximum load is applied gradually and, for testing,
maintained for long enough to enable to predict the final effect. If in service, then
the maximum load is maintained continuously or intermittently during the life of
the loaded structure.
MONITORING METHODS AND BRIDGE ASSESSMENT
34 Dynamic testing can be done by forced vibration testing or ambient vibration testing
(Schlune et al (2008)). In repeated loading, a load or stress is applied and then wholly or partially removed or reversed repeatedly. When loading dynamically, the rate of change of momentum must be taken into account (Young et al (2002)).
Analysis methods for bridge assessment according to the codes are often conservative leading to bridges being restricted even though their capacity is sufficient. By performing load testing, the engineer is given information that can be used for avoiding premature repairing or strengthening (Packham (1993)). Full-scale testing of a railway bridge is both complex and expensive. Therefore, the amount of bridges that are tested are limited to a few especially important cases each year (Pietraszek et al (1990)). Since stresses are accompanied by strains and strains are directly related to deflections, measurement of deflections are a common way to determine strains (Young et al (2002)).
4.3.1 S TATE OF THE ART
Through the years, the need of knowledge about the effects of traffic on existing structures has led to a number of studies with associated load tests. Here is a brief synopsis of a few of them.
Mehrkar et al (1996)
Mehrkar-Asl and CL Brookes from Southampton UK conducted supplementary load tests by static and moving loads. Mehrkar has tested over 50 deck-spans since 1989 using different loading systems and by his tests, he has demonstrated that supplementary load tests enable improved assessments to be made.
Chladny et al (1993)
E. Chladny and I. Baláz from Slovak Technical University in Slovakia wrote a paper about the inspection, imperfection measurement, evaluation and strengthening of a 20-year old steel bridge, which was designed according to former codes with lower loading actions in which shear lag was not taken into account. Damage and deterioration were noted and listed from inspection and it was noted that suitable expansion joints were needed and many parts needed cleaning and repainting.
Critical sections were investigated by test loading and comparison was made between
theoretical values and test load values. The comparison indicated a good correlation
between the theoretical and load test values as shown in Figure 34.The rating factors
calculated were very low and zero. Chadny and Baláz takes a look at the design criteria and
compares the rating factors computing them with both the original code and with the same
code with some changes in it. They discuss the plausibility of the values of the impact factors
in the codes in a critical way and compare the British code with the Czechoslovak code.
35
Figure 34, Normal and shear stress distribution in critical section by test loading (Chladny et al (1993))
