Design of a 170 m span
bridge over the fjord
Thorskafjordur in Iceland
Jóhannes Helgi Jóhannesson
Avdelningen för Konstruktionsteknik
Lunds Tekniska Högskola
Lunds Universitet, 2010
i Lunds Tekniska Högskola
Box 118 221 00 LUND
Department of Structural Engineering
Lund Institute of TechnologyBox 118
S-221 00 LUND Sweden
Design of a 170 m long bridge over the fjord Þorskafjörður in
Iceland
Dimensionering av 170 m lång bro över fjorden Þorskafjörður på Island
Jóhannes Helgi Jóhannesson
2010
Abstract
Determining the structural type of a bridge is often a difficult task. The purpose of this thesis is to preliminary design three bridge alternatives. The bridge shall cross the fjord Þorskafjörður in Iceland. The goal is to determine the most favorable option. That decision will be based on economy, construction and aesthetics. Following that a more detailed design of the superstructure is performed for the chosen alternative. All calculations are performed according to Eurocode.
Keywords: concrete girder bridge; arch bridge; cable-stayed bridge; concrete; reinforcement; prestress
ii Rapport TVBK-5185
ISSN 0349-4969
ISRN: LUTVDG/TVBK-10/5185+92p
Examensarbete
Supervisor: Dr. Fredrik Carlsson Examinator: Prof. Sven Thelandersson October 2010
iii
This thesis was written under the administration of the Division of Structural Engineering at the University of Lund. It was written during the period September 2009 - September 2010 under the supervision of Dr. Fredrik Carlsson.
I especially want to thank my supervisor, Dr. Fredrik Carlsson, for all his help with making this thesis become real. I also want to thank Einar Hafliðason, the head of the bridge division of the Icelandic Road Administration, for the help with finding a subject for this thesis and for giving me necessary information regarding this subject. For the cost of various structural materials I would like to thank Oskar Bruneby, a site manager at Peab, for his contribution. In addition I would like to thank a good friend from Iceland, Ástþór Ingvason, for making 3D animations of the three bridge alternatives presented in this thesis. Finally, I want to thank my friends at LTH: Bzav Abdulkarim, Daniel Honfi, Ívar Björnsson and Valdimar Örn Helgason for all their help and last but not least other friends and family for their moral support.
Lund, October 2010 Jóhannes Helgi Jóhannesson
v
1 Introduction ... 1
1.1 Background ... 1
1.2 Objectives ... 1
1.3 Outline of the thesis ... 1
2 Bridge types ... 2
2.1 Concrete bridge ... 2
2.2 Arch bridge ... 3
2.3 Cable-stayed bridge... 4
3 The actual project – geometry and boundary conditions ... 5
4 Preliminary design ... 7 4.1 Introduction ... 7 4.2 Loads ... 7 4.2.1 Permanent loads ... 7 4.2.2 Variable loads ... 7 4.2.3 Load combinations ... 8 4.3 Material cost ... 9
4.4 The concrete beam bridge ... 10
4.4.1 Geometry for type 1 ... 10
4.4.2 Size estimation ... 10
4.4.3 Supports ... 11
4.4.4 Construction ... 13
4.4.5 Cost estimation/conclusions ... 13
4.5 The arch bridge ... 16
4.5.1 Geometry for type 2 ... 16
4.5.2 Arch ... 17 4.5.3 Bridge Deck ... 22 4.5.4 Hangers ... 23 4.5.5 Transversal Bracing ... 23 4.5.6 Foundations ... 24 4.5.7 Construction ... 24 4.5.8 Cost estimation/conclusions ... 24
4.6 The cable-stayed bridge ... 26
4.6.1 Aesthetics of cable-stayed bridges ... 26
4.6.2 Geometry for type 3 ... 27
vi 4.6.4 Deck ... 32 4.6.5 Pylons ... 33 4.6.6 Foundation ... 34 4.6.7 Construction ... 34 4.6.8 Cost estimation/conclusions ... 35
4.7 Summary and choice of bridge type... 37
5 Final design ... 38 5.1 Introduction ... 38 5.2 Design ... 39 5.2.1 Building codes ... 39 5.2.2 Loading ... 39 5.2.3 Materials ... 39
5.2.4 Exposure classes and service life ... 40
5.2.5 Tendon alignment and prestress force ... 40
5.2.6 Prestress losses ... 46
5.2.7 Secondary effects of prestress ... 51
5.3 Ultimate moment capacity ... 55
6 References ... 57 6.1 Literature ... 57 6.2 Computer programs... 58 6.3 Other references ... 58 Appendix A ... 59 Appendix B ... 74
1
1 Introduction
1.1 Background
The motivation for writing this thesis is an interest in bridges that the author has acquired during his studies in structural engineering. Many people consider bridges to be state of the art of all civil structures. That can be for many reasons; f. ex. bridges sometimes cross a difficult passing or because of their aesthetic aspects.
During the time the subject for this thesis was under consideration the author decided to contact the bridge division of the Icelandic Road Administration (ICERA). Einar Hafliðason, the head of the bridge division of ICERA, was contacted and he was more than willing to help. He came up with a few options to look into which were all considered. Following that, a decision was made and a bridge that is to be constructed to cross the fjord Þorskafjörður in Iceland was chosen as a subject for this thesis.
1.2 Objectives
The main purpose for a bridge over the fjord Þorskafjörður is to shorten the distance of the route on the way to the northwestern part of Iceland. With this bridge the route will shorten of about 10 km. Another purpose is to increase traffic security by eliminating all one-lane bridges on this 10 km sector. The main objective of this thesis is divided into two parts. First, a preliminary design of three bridge alternatives is made. A rough cost estimation and an estimation of quantity of materials is made based on the preliminary design for these three alternatives. Secondly, a more detailed design is made of the most appropriate bridge type. The choice of a bridge type is based on the conclusions from the first part. These conclusions will primarily be based on economy, aesthetics and construction method.
1.3 Outline of the thesis
Chapter 2 consists of a general discussion about aesthetics, advantages and disadvantages and other aspects for the three bridge types that are chosen to be analyzed.
Chapter 3 displays the bridge location and describes the boundary conditions and geometry at the construction site. It also includes information about why this bridge is to be built.
Chapter 4 includes preliminary design and cost estimations of the three chosen bridge alternatives with respect to the quantity of materials needed for each type. That chapter also includes conclusions of the preliminary design, that is, which type of bridge is chosen for a more detailed design with respect to the limits that are set.
Chapter 5 includes more detailed structural analysis for the superstructure of the chosen bridge alternative.
2 Br
There ar main sub 1. 2. 3. 4. These i preferen Safety a principle achieved In this th based on bridge (p based on2.1 C
Concrete concrete of the si for this t These ty longer th they inte alternati sense as with two Desridge typ
re many area bjects consid Safety Serviceabilit Economy Aesthetics ssues and th nce. and serviceab es and thus d through no hesis three b n the four a post tension n the author´Concrete
e slab- or gir e bridges are implest form type of bridg ypes of cros han ca. 25 m egrate to the ives. Neverth s the two typo girders can ign of a 170
pes
as of concern dered in this ty heir order o bility are ac depend on onscientific m bridge types aforemention ed), an arch s interest.bridge
rder bridges an attractive ms for a bridg ge can be see Figure 2-1 s-sections w m. They are ec e surroundin heless, the a es that are co n be seen in f Figur m long bridg n that need t thesis. They of priority m chieved throu the analytic means and de are investiga ned areas of bridge and are by far th e alternative ge with respe en in figure 2 1: A typical cro with prestress conomically ngs on site. T author consid onsidered in figure 2-2. e 2-2: An exam ge over the f 2 to be focused can be listed may though ugh systema cal skills of epend almost ated as optio concern. Th a cable-staye e most comm for long-spa ect to its struc 2-1.oss-section for s reinforcem compatible They are als ders them no
the next cha
mple of a prest fjord Þorskaf d on when d d in order of be criticize atic applicati f the engine t entirely on ons for the pr hese three br ed bridge. T mon of all br an bridges an ctural mode a concrete gir ment in the gi
and can easi o easy to co ot as the stat apters. An ex ressed girder b fjörður in Ice esigning a b f priority as: ed and are ion of scient er. Economy the creativity roject and a ridge types a The choice of ridge types n nd are consid of action. A der bridge. irders are us ily be design onstruct com te-of the-art xample of a c bridge. eland bridge. There merely the
tific and eng y and aesth y of the engi choice is est are; a concre f these altern owadays. Pr dered by man typical cros sually used f ned in the ma mpared to ma bridges in t concrete bea e are four authors´ gineering hetics are neer. tablished ete beam natives is estressed ny as one s-section for spans anner that any other the same m bridge
2.2 A
Arches h in which perfect a impossib to multip For man perspect be very The arch rotation arch itse required at found Arches c risks sucArch bridg
have been us h only comp arch can be ble to have a ple loadings. ny people, an tive and a pl attractive du h type that i possible at elf and the c d since an arc dation; horizo can span up ch as the risk Figurege
sed througho pressive forc thought of a a perfect arch . n arch is con leasure for a uring night. is chosen in supports. T crown of the ch can be sen ontal, vertica to about 55 k for torsiona 2-4: A typicalout the ages a es act at the as the inverse h bridge exce nsidered to b motorist to this paper i The deck wil e arch, so ca nsitive to set al and bendin Figure 2-3: A 50 m and in al buckling o arch bridge w 3 as structural e centroid of e of a hangin ept for one l
be one of the drive over. W is a zero hin ll be located alled half-th ttlements an ng. A model of a ze the case of s of the arches,
with the deck ha
elements. A f each eleme ng chain bet oading cond
e most comp With the app
nged steel ar d at an eleva hrough arch.
d a zero-hing
ero hinge arch. slender struc
must be tak
anging on ties
perfect arch ent of the arc tween abutm dition while i etitive option propriate ligh ch, figure 2-tion between Good found ged arch has
ctures of stee en into consi connected to t h, theoreticall ch. The shap ments. It is pr it is usually s ns from the hting arches -3, which im n the suppor dation condi s high reactio el, various in ideration. the arch. ly, is one pe of the ractically subjected aesthetic can also mplies no rts of the itions are on forces nstability
2.3 C
The con predict. intermed cable-sta the cabl the pylo flexural consump complex Nowada up to ar beautifu a cable-simple c also serv beauty a 2-5. DesCable-stay
ncept of a ca A bridge c diate support ayed bridge es and the p on and the de members. T ption but on x. ays, cable-sta round 1000 ul structures t stayed bridg configuration ve as tourist and visibility ign of a 170yed bridg
able-stayed b carries main ts for the giris a series of pylon are und eck under co This contribut the other ha ayed bridges m and com that appeal to ge and theref n is preferab attractions, y of the bridg Figure 2-5 m long bridg
ge
bridge is sim nly vertical rder so that i f overlapping der predomin mpression. A tes to the eco and larger stare the most me in variou o most peopl fore contribu ble with free for example ge at night. A 5: A cable-stay ge over the f 4 mple althoug loads actin t can span a g triangles th nant axial fo Axially loade onomy of a c tress variatio t common br us forms bec le. The tower ute the most
e standing to when lightin An example o ed bridge with fjord Þorskaf gh the loadin ng on the g long distanc hat connect t orces, with th ed members cable-stayed ons can occu
ridge type fo cause of eco rs, or pylons from an aest owers. Under ng is a part o of a cable-st h two pylons on fjörður in Ice ng mechanis girder. The ce. The basic the deck to t he cables un are generall d bridge. The ur and their s or long-span onomy and s, are the mo thetic point o r special cir of the design ayed bridge n each side. eland sm is not so stay cables c structural f the pylons. T nder tension y more effic ey also have structural be bridges and aesthetics. T st visible ele of view. A c cumstances n which enha can be seen o easy to provide form of a The deck, and both cient than less steel ehavior is can span They are ements of clean and they can ances the in figure
3 Th
The posi Currentl crosses a in each crossing In figure The ligh As was direction necessar acquired The rest sides of fjord wh The larg around maximu minimum rock fill alignmenhe actual
ition of this b ly there is a a river with direction, to g the fjord. e 3-1 the pos ht gray line w mentioned, n. The requ ry area of w d. For full wa t of the distan the bridge. T here the bridg gest possible 1.65 m from um differenc m water ope lings will b nt of the planl project
bridge is in t road that go only one lan o increase trsition of the f where the arro
Figure 3-1: Po the bridge uired length water opening ater changes nce required Therefore the ge is to be po depth of sea m the sea be e between h ning would be at each e nned road lin
– geome
the north-weoes along th ne. The purp raffic safety, fjord can be ow points is osition of the fj will have tw of the brid g needs to be
the water flo to cross the e bridge will ositioned is a a level is arou d. The avera highest and be reduced b end abutmen ne that will b 5
etry and
stern part of he fjord and pose of the ne efficiency aseen. The fig the current r fjord on the no wo traffic la dge, 170 m, e of minimu ow is assume fjord will be l be positione around 1 km. und 6.35 m a age sea leve
lowest sea by a few me nts and eros be considered
boundar
f Iceland pass at the end o ew bridge is and to short gure displays road. rth-western co anes for nor is mainly um 560 m2 s ed to be 2.5 m e achieved by ed in the mid .and the smal el is 4 m fro level is 4.7 ters because ion protectio d is displayed
ry condit
sing a fjord c of the fjord t s therefore to ten the routes the northw oast of Iceland rmal vehicle due to ecol o that full w m/sec. y a road, on ddle of the fj llest possible om the sea b m. It can b of piers and on will be d in figure
3-tions
called Þorska there is a br o have two la e of about 1 estern part o . traffic, one logical reaso water change a rock filling ord. The wide depth of se bed. Hence, be assumed d abutments. at all suppo -2. afjörður. ridge that anes, one 0 km by of Iceland. e in each ons. The s will be g on both dth of the a level is the total that the Guiding orts. The
The soil fundame A sectio The fjor defined greater t Iceland a Figur Des l at the sea b ents will be f on of the fjord Figu rd is not loc as <2% g in than 4% g th are displayed e 3-4: Maximu ign of a 170 Figure 3-2 bed consists founded on c d is displaye ure 3-3: A cros cated in an n this area, he provision d in figure 3-um values of su m long bridg
2: The road lin of sediment cohesive pile ed in figure 3 ss section of th earthquake z see figure 3 s of Eurocod -4. urface accelera ge over the f 6 ne where the br layers. The es. -3. Note that he fjord, the he zone and the 3-4. Accordi de 8 can be ation. (Earthqu Iceland). fjord Þorskaf ridge will be co sediment lay t the height i eight is scaled u e peak value ing to Euroc neglected. T uake Engineer fjörður in Ice onstructed. yers are cohe
is scaled 10 t up of the facto e for surfac code 8 for st The different ring Research C eland esive materia
times the wid
r 10. e acceleratio tructures wit t earthquake Centre, Univer als so all dth. on, ag, is th ag not zones in rsity of
7
4 Preliminary
design
4.1 Introduction
This chapter contains preliminary design of the three bridge types, a concrete girder bridge, an arch bridge and a cable-stayed bridge. The aim of the preliminary design is to determine the most suitable bridge type for the purpose of crossing the fjord Þorskafjörður. The chapter is divided in to two different sections. The first sections (sections 4.2 and 4.3) treat factors that are common for all three bridge types, i.e. loads, load combinations and materials. Sections 4.4 to 4.6 treat the three different bridge types respectively. In these sections are sizes of important bridge elements for each bridge type estimated. These sections also contain rough cost estimations and construction methods for each bridge type. Finally, in the last section of this chapter, the most suitable bridge type is determined based on the preliminary design.
4.2 Loads
For the preliminary design of this project only three loads are considered. Two permanent loads, self-weight and pavement, and one variable load, traffic load. The loads are determined according to Eurocode 1 (EC1).
4.2.1 Permanent loads
Self-weight for reinforced concrete is set to 25 kN/m3. The self-weight of pavement and structural
steel are set to 2.1 kN/m2and 78.5 kN/m3 respectively.
4.2.2 Variable loads
The variable actions, which are taken into account in this thesis, are traffic loads in vertical direction. After some discussion with the head of the bridge division of ICERA it seemed reasonable to do this simplification in the preliminary analysis.
Traffic Loads
In EC1-2, chapter 4, there are defined four different load models for traffic loads. In this case Load Model 1 (LM1) is used with two partial systems, one including axle loads (Tandem system TS) and the other including uniformly distributed loads (UDL system), see figure 4-1. LM1 is considered to cover most of the effects from traffic of lorries and cars and should be used for general and local verifications while the other load models are considered for dynamic effects, special vehicles and other situations. LM1 should be applied on each notional lane and on the remaining areas. On notional lane number i, the load magnitudes are referred to as αQiQik and αqiqik, axle load and distributed load respectively. On the remaining areas, the load magnitude is referred to as αqrqrk. According to chapter 4.3.2(3) in EC1-2 the recommended minimum values for the adjustment factors are:
≥ 0,8 ≥ 1,0
The national annex for Sweden recommends the following minimum values for the adjustment factors: = 0,9
= 0,9 = 0
Hence, Icelandi characte These lo most unf 4.2.3 Several when a state is m limit sta Des these values c national an eristic vertica oad arrangem favorable res Load comb load combin bridge is ana made for the ate is accordin
ign of a 170
s are used f nnex for this al distributed
Table ments are disp
sult. Figure 4 binations nations need t alyzed and d preliminary ng to EC0, s , m long bridg
for this situa part of Euro d loads, qik, ar e 4-1: Axle load played on fig 4-1: Load arra to be taken i designed. Bu design of al ection 6.4.3. , " + " ge over the f 8 = 1,0 = 1,0 ation. The S ocode 2 is no re summariz ds and uniform gure 4-1 and angements for l nto account, ut for simplif ll bridge type 2: " + " , , fjord Þorskaf Swedish nat ot ready yet. C zed in table 4 mly distributed d should be a load model 1 in in the ultim fication only es. The desig
" + " fjörður in Ice ional annex Characteristi 4-1. d loads. arranged for n EC1-2.
ate and servi y an analysis gn value of a , , , eland is applied ic axle loads each case to iceability lim in the ultim actions in the since an , Qik, and o give the mit states, mate limit e ultimate
where γG,j Gk,J γP P γQ,1 Qk,1 γQ,i ψ0,i Qk,i Here are variable principa
4.3 M
Table 4-not com that hav attended Sweden given. To estim is used necessar from Zh as the o mainten the desig Partial facto Characterist Partial facto Relevant rep Partial facto Characterist Partial facto Factor for co Characterist e γG,j=1.35, γ action resp al action.Material c
-2 summariz mpletely corre e been inves d and other . Workforcemate the price (SEK/kg). T ry to find the huan (1998) a ones that w ance or othe gn of that is r for perman ic value of p r for prestres presentative v r for variable ic value of th r for variable ombination v ic value of th γP=1.0 and γ pectively. Th
ost
zes unit priceect they will stigated. The resources li is included Table e of the steel To come up e unit weight about stay ca were chosen r factors, wi not done in nent action j permanent ac ssing actions value of a pr e action 1 he leading va e action i value of varia he accompan γQ,1=1.5 the p he last term es for the ma give a good basis of the ke discussio in these val 4-2: Unit pric l hangers in t p with a pri t (kg/m) of th ables where here to use ll be estimat the prelimin 9 tion j s restressing ac ariable action able action i nying variabl partial safety in this equa aterials used. d perspective cost estimat ons with con lues and high
ces for various the arch brid ice for the he cables. Un
the unit wei e and that v ted and cost o ary phase. H ction n 1 le action i y factors for ation is not . Even thoug on prices fo tion and pric ntractors and her values a
structural mat dge, see secti
stay cables nit weight fo ght of cables value is 24 of foundatio Here estimatio r permanent required sin gh values of or compariso ces is from c d engineers re chosen w terials. ion 4.5.4, uni of the cable or cables was s that has a s .1 kg/m. No ns is a factor on is used to action, prest nce there is o various expe on of the brid ourses the au both in Ice where a price it price for so e-stayed brid s found in a similar break o lifetime c r of uncertain o calculate th tress and only one enses are dge types uthor has land and range is olid steel dge it is literature king load cost, like nty since he cost of
the subs elements
4.4 T
Bridge t supporti the bridg 4.4.1 This bri continuo down to 4.4.2 As was m spans, tw figure 4-the lengt The firs prestress 290x290 Also an The heig height, L bridge sh economi won’t co The cen Theland where B The thic The estim Des structures wi s. Included inThe concr
type no. 1 is ing the beam ge deck will Geometry idge type w ous girder br the sea bed. Size estim mentioned b wo internal -2. This choi th of the exte st step is to s system is 0 mm. 3 cab additional th ght of the g L/h, of the g hould be cho ic reasons (s ome up probl nter distance dersson (2009 B is the free w ckness of the mated cross-ign of a 170 th a method n the substrurete beam
s a concrete ms. There wil be 10 m, see for type 1 ill have a c ridge with 4 ation efore, the tot spans with t ice of span le ernal spans idecide the p VSL 6-19. bles are chos hickness of 3 irder is dete girder. A rec osen in the ra section 7.2.1 lems later in e between t 9): width of the b slab is chose -section of th m long bridg developed b ucture are the
m bridge
post-tension ll be two ma e figure 4-3. oncrete slab spans, see fi tal span of th the length 4 engths is ma s about 80 % Figure 4-2: Sp prestressing The dimens sen in each r 300 mm is de ermined by t commended ange of 12-3 1 in Menn (1 n the design. ℎ= 20 the two ma = 1,8 ∙ bridge. en to be 250 he bridge, ba ge over the f 10 by Menn (19 e piers and fu ned girder b ain girders w Supports wil b supported igure 4-2. Th he bridge is 1 8 m and tw de to get an % of the lengtpan lengths for system to e sions for an row which r etermined ov the slenderne slenderness 35 and some 1986)) and So the estim ⟹ ℎ =48 20 ain girders, ⟹ =1 1, mm to be ab ased on the m fjord Þorskaf 986) as a 23. undaments. bridge with f with post-tens ll be founded on two cont he girders ar 170 m. The b wo external sp even momen th of the inte r bridge type 1 estimate the chorage blo results in a m ver the suppo
ess, a ratio b ratio for a c lower range a low value mated height b = 2,4 a, is chose 0 ,8= 5,6 ble to resist s methods abov fjörður in Ice .5% of the to four spans an sioning cable d on concrete tinuous gird re supported bridge is divi pans with a nt distributio ernal ones. . size of the cks for that minimum wi orts. between the conventional e should be c e should also becomes: en with the shear forces a ve, can be see
eland
otal cost of s
nd concrete es. The total
e piles.
ders. The bri on concrete
ided into fou length of 3 n. That is ac girders. The t specific sy idth, b, of 10 span length l cast-in-plac onsidered be o be chosen e following and moment en in figure 4 structural columns width of idge is a columns ur smaller 7 m, see chieved if e chosen ystem are 080 mm. h and the ce girder ecause of so there method, ts. 4-3.
4.4.3 Maximu To estim has to b loads ha To find figure 4-The GD And the Supports um load on a mate the mos be determine ave to be loc GDF, the m -4. Fs for the tw following tr Figu a column wo st unfavorab ed. GDF tells cated in the m moment is ca Figure wo traffic loa raffic loads th ure 4-3: The cr ould be when ble load actin s how the tr most unfavo alculated aro e 4-4: Location ds, axle and = 1,37 = 1 hat act on on 11 ross-section at n the given t ng on a sing raffic load is rable positio ound B with n of traffic load distributed l 7 For the ta 1,16 For U ne beam are: preliminary st traffic load i gle beam the
s distributed on on the bri
the lever ar
ds to determine oads, are det andem system DL system tage. s located as girder distri between the idge deck in rm for each e GDF. termined to b m shown in fig ibution facto e girders. Th the lateral d load as disp be: gure 4-4. or (GDF) he traffic direction. played in
where th analyzed section. the colum The max state. At The wid calculate with the as fck=45 the mini 11 So for a For the p Precaste Des he axle load d in the leng Figure 4-5 s mns and the Figure 4-5: P ximum norm t this stage th dth of a sin ed from a for yield streng 5 MPa, the p imum thickn 1180 10 single suppo piles, given t ed 270x270 p ign of a 170 ds are chan gth direction shows the ac bridge sectio Position of traf mal force in t he concrete q ngle girder o rmula for pre
= gth of the rein
percentage o ess of the su
= 1380 ort the total s that each pile
piles with 12
m long bridg
nged into on n for one gir ctions and th
on in the ulti
ffic loads when the middle su quality is assu over suppor eliminary de 0.44 nforcement a of reinforcem upport should 0.44 45 size is determ e resists 400 11 4 00 mm spaci ge over the f 12 = 1012 = 37 ne concentra rder. Calcula he position o imate limit st n the largest no upport is cal umed to be C rts is 1.380 sign given in + 100 0.6 as fy=500 MP ment p=2% a d be: + 2 100(0.67 mined to be b kN, gives: 180 00 28
ing and a fou
fjord Þorskaf 2 / ated force (a ations are m f actions to tate. ormal force at lculated to be C45/55. mm. The th n the ISE ma 67 − 0.44 Pa, character and Ac as the 7 500 − 0 b x t = 7500 x undation of t fjörður in Ice assumption). made for half
decide the la
the middle sup e 11.180 kN hickness of anual (1985): istic cylinder e gross cross .44 45) ⇒ x 450 mm. the size 5x10 eland Then the b f of the brid argest shear pport occurs. N in the ultim the support : r strength of -sectional ar ⇒ ≥ 311 0 m. bridge is dge cross force for mate limit t wall is f concrete rea. Thus
13 4.4.4 Construction
The construction method of a concrete girder bridge is relatively easy to perform. Concrete girder bridges are one of the most common bridges in Iceland. This bridge alternative is often chosen for similar conditions as are in this case because of economic and constructional reasons, that is, when a shallow fjord is to be crossed.
Supports and columns below the superstructure will be constructed first. They will be founded on piles. Since the level of sea depth at is shallow at the construction site the superstructure of the bridge will be casted in forms that are supported on a temporary filling under the bridge. The filling will finally be removed when the concrete has hardened and can then be used as road material.
4.4.5 Cost estimation/conclusions
To estimate the cost of this bridge type a method from Menn (1986) is used. The following is an explanation of this method.
The superstructure’s costs can be reliably estimated with the help of the geometrical average span length, lm, defined as:
=∑ ∑ where li is the length of span i.
The empirical equations given below give the quantities of concrete, reinforcing steel, and prestressing steel as functions of lm and have been derived from samples of recently constructed bridges.
By this method the volume of concrete in the whole superstructure is obtained by multiplying the total deck surface by the effective girder depth, hm, defined by the following expression:
ℎ = 0.35 + 0.0045 ∙
where hm and lm are in meters. This equation is valid provided the actual girder depth, h, satisfies the following inequality: 1 20≤ ℎ ≤ 1 16
which fulfills the criteria used earlier, l/h=20. The quantity of reinforcing steel is obtained by multiplying the total volume of concrete by the mass of steel per unit volume of concrete, ms. The parameter ms is estimated using the equation:
= 90 + 0.35 ∙
where lm is in meters and ms is in kilograms per cubic meter of concrete (kg/m3). This expression is
valid provided the deck slab is not transversely prestressed. Between 65 and 70 kg/m3 of
reinforcement is required for stability during construction and crack control; this quantity is independent of span length, see Menn (1986). The transverse reinforcement required to resist loads is primarily a function of cross-section dimensions. An additional 20 to 25 kg/m3 is required for
minimum attention The ma construc equation where lm girders multiply The esti obtained (scaffold (tempora into acco material falsewor sea leve increase estimate Here is o is a tab calculati Des m 65 to 70 k n in the desig ss of prestre ction method n: m is in meter that are no ying mp by th imated cost d by multipl ding system ary structure ount the prop l costs, anot rk and formw l the cost pe ed. These va ed using table Table 4 only listed th ble that sum
ions as well ign of a 170 kg/m3 is loca gn and arrang essing steel d. For girders s and mp is i ot transverse he total volum of concrete lying the es ms that are u e used to ret posed constr ther constru work costs yi ercentage of alues are cho e 4-3, from M 4-3: Table from he quantity o marizes tho as the empiri m long bridg ated in the d gement of th per unit vo s that are cas
in kilograms ely prestress me of concre e, reinforcin stimated qua used to tem tain unharden ruction seque uction metho ields the tota
the total cos osen to be 2 Menn (1986) m Menn (1986) of super- and se results. T ical equation ge over the f 14 deck slab. Th he superstruct lume of con sted on conv = 0.4 ∙ s per cubic m ed. The qu ete. ng steel and antities with mporarily su ned concrete ence; if it is g od should b al superstruct st of those st 5% and 23% ). ) to estimate co d substructure These quanti ns above. The fjord Þorskaf he deck slab ture reinforc ncrete, mp, i ventional fals meter of conc uantity of pr d prestressin unit materi upport perma e until harde greater than 6 be considere
ture cost. Sin tructural part % respective
osts for variou e materials th ities are acq e calculated fjörður in Ice should there ement. s a function sework, mp i crete. This ex restressing s ng steel in t ial costs. Th anent structu ened) should 65 percent o ed. Adding nce abutment ts as well as ely. The rem
us structural el hat will be d quired based quantities ar eland efore be the n of span len s estimated u xpression is steel is obta the superstru he cost of f ures) and fo d be estimate f the superst the bridge ts and piers a falsework/fo maining cost lements. determined an d on the pre re given in ta focus of ngth and using the valid for ained by ucture is falsework formwork ed taking tructure´s material, are under formwork ts can be nd below eliminary able 4-4.
For the f sub- and cost for This resu type of b ISK/SEK T figures given d superstruct this bridge ty ult is consist bridge was 6 K. Note that Table 4-4: Amo n in table 4-4 ture and the t ype the total
tent with a d 638.500.000 this draft ass
F
ounts of structu 4, abutments
total cost bas values for th
Table 4-5: T draft for this p ISK which i sumes the tot
Figure 4-6: An 15 ural materials and column sed on the pr he structural Total cost of br project made is around 38 tal length of n overview of th
for the concre s are include rice values f elements are ridge type 1. e by ICERA .700.000 SE f 182 m inste he beam bridg
ete beam bridg ed. Below is from section e doubled. where the e EK with the e ad of 170 m. e. ge. a table with 4.3 and to g estimated cos exchange rat . prices of get a total st for this e of 16.5
4.5 T
Bridge t Each arc will be o deck wil main gir which ar the main 4.5.1 The cho chosen b which w conditio To conn a drawin To deter determin DesThe arch b
type no. 2 is ch will be of of zero hinge ll be of com rders with sh re connected n girders, see Geometry oice of the r between 4 an would result ons on site (nnect the deck ng of the stru rmine the se ned accordin ign of a 170
bridge
a conventio f a steel box ed type with mposite steel/c hear studs. T d to the arch e figure 4-7. F for type 2 rise of the a nd 8 see, Lo in less horiz no rock – only k to the arch uctural mode Figur ction forces ng to figure 4 m long bridgnal steel arc cross-sectio X-bracing b concrete. In To connect th hes with hang
igure 4-7: A cr rch is based oretsen and S zontal reacti y sediment s = 4 ⇒ vertical stee l of the bridg e 4-8: A struct in the arche 4-9. ge over the f 16 h bridge wit on with steel between the a the longitud he two main gers. A reinf ross-section of d on the rati Sundquist (19 ion forces. T soil layers). T ⇒ =17 4 l wire hange ge. tural model of es the GDF n fjord Þorskaf th two separa stiffeners in arches to inc dinal directio n girders ther forced concr
the bridge dec
io between s 995). This ra This ratio is That results i 70 4 = 42,5 ers with c/c 2
the tied arch b needs to be
fjörður in Ice
ate arches ab nside, see fig
rease lateral on of the brid re will be tra rete slab wil
ck.
span and ris atio is in this suitable bec n 25 m are cho bridge. determined a eland
bove the brid gure 4-11. Th stiffness. Th dge there wi ansversal ste l be casted o e which is g s case chosen cause of geot osen. On figu again. The G dge deck. he arches he bridge ll be two el beams on top of generally n to be 4 technical ure 4-8 is GDFs are
The follo And the 4.5.2 To desig investiga moving moment owing GDFs following tr Arch gn the arch t ated: abutme a point load t, shear force Figure 4 s are acquire raffic loads th the influence ent, ¼ of the d of 100 kN e and normal 4-9: Position of d: = 1,13 = 1 hat act on on e lines for th e arch and t N in 10 m i force. Thes 17 f traffic loads w 3 For the ta 1,00 For U ne girder are: = 694 = 27 he arch need he middle. I intervals ove se influence d when calculati andem system DL system : 4 / d to be determ Influence lin er the deck diagrams can ing GDF. m mined. 3 sec nes for each in the longi n be seen in f ctions in the section are itudinal dire figure 4-10. arch are made by ction for
Design of a 170 m long bridge over the fjord Þorskafjörður in Iceland
18
Figure 4-10: Influence lines for various section forces at most critical placements.
To calculate the important section forces for design of the cross section of the arch the traffic loads are placed on the most unfavorable position corresponding to these influence diagrams in a program called PCFrame. PCFrame is a commercial program for structural analysis of frames.
Cross Section
To design the arch in the ultimate limit state the section forces are required. The highest moment in the arch is reached when the traffic load is located in the middle of the span. The position of the point load at the first quarter of the span gave the highest normal force. So these corresponding section forces are used to design the cross section and are shown in table 4-6.
-1.00 -0.50 0.00 0.50 1.00 0.00 0.20 0.40 0.60 0.80 1.00 M x/L
Influence Lines for Moment in the Arch
Abutment 1/4 of span
Middle of the span
-1.00 -0.50 0.00 0.50 1.00 0.00 0.20 0.40 0.60 0.80 1.00 V x/L
Influence Lines for Shear Force in the Arch
Abutment 1/4 of span
Middle of the span
-1.00 -0.50 0.00 0.50 1.00 0.00 0.20 0.40 0.60 0.80 1.00 N x/L
Influence Lines for Normal Force in the Arch
Abutment 1/4 of span
The mat The follo direction The cro dimensio A. Stability To chec well as w load and terial qualitie owing cross-n across-nd resistacross-n oss-section i ons of the cr y ck for stabili with the help d the maximu
T es of the stee
-section was nce, see figu
F s a welded ross section ( ity in longitu p of PCFram um normal f Table 4-6: Des el are given in Table 4-7: determined ure 4-11: Figure 4-11: Ch box section (moment of udinal direct me. To fulfill force needs to 19 sign section for
n table 4-7.
Material quali after few tria
hosen cross-sec n with trape inertia, secti
tion two inve l the requirem
o be in the ra
rces in the arch
ities of steel. als with resp
ction of the arc ezoidal stiffe ion modulus
estigations a ments for sta ange from 4 h. pect to stabili ch. feners. Furth etc.) can be are made; ca ability the ra to 5, see Lo
ity in the lon
her details a seen in the a alculation by tio between oretsen and S ngitudinal about the appendix y hand as buckling Sundquist
(1995). critical b where S case S is determin From an well wi determin EC3 giv is given with Nd Here χ is with e and α, a stronger ̅, the no Des To calculate buckling load Sis the one-h s 98525 mm ned to be 458 nalysis in PC ith the calc nation of the ves another m in section 5. as the design s the reductio equal to an imperfecti r axis and a w on-dimension ign of a 170 e the bucklin d is given as half length of and k is 0.70 845 kN and t CFrame for th culations by cross section Fi method to de .5.1 in EC3. n normal forc on factor for ion factor, o welded box s nal slenderne m long bridg ng load by ha :
f the arch and 0 for a fixed the ratio betw
his case this y hand. The n. The buckl igure 4-12: Bu etermine the EC3 defines ce and the ca . r the relevant = + = 0,5 obtained from section with b ess, is define ge over the f 20 and formulas = ( ) d k is the effe d arch with a ween the buc
= 4.8 factor is dete ese calculati ling mode sh uckling mode sh buckling res s the followin ≤ . apacity of the = t buckling m 1 − ̅ , 1 + ̅ − 0 m an approp b/tf<30, α be = 0.49 ed as fjord Þorskaf s presented b ) ective length rise-span rat ckling load an ermined to b ions were t hape for this
hape of the arc sistance crite ng criteria: e cross-sectio / ode and is de 1 0,2 + ̅ riate bucklin comes fjörður in Ice by Austin (1 h factor, see A tio as 0.25. F nd the maxim be 5.0. That m the most cr arch is show ch.
eria for comp
on, Nb.Rd, as efined as ng curve. Fo eland 971) were u Austin (1971 For these val mum normal matches cons ritical ones wn in figure 4 pressed mem or buckling a used. The 1). In this lues Pe is l force is siderably for the 4-12. mbers and about the
where βA In this c Table 4-It can be arch. Compre To dete determin In this c The cros Here, Np and Wpl factor is seen in a force are The resu A is dependin ase βA is equ -8 summarize e seen in tabl ession and ermine the c ned. To decid case the cros ss-section ca Npl.Rdis the pl the plastic s defined as appendix A. e made accor ults of this an ng on the cro ual to 1. For r es the results Table le 4-8 that th bending ca compression de the cross s section cla apacities are d lastic design section modu = 1,1 in Next a chec rding to secti nalysis are su ̅ = oss-section a = 1 for Cl = / resistance of s of this anal e 4-8: Criteria he buckling re pacities and bendin section class ass is determi defined in EC . n resistance f ulus. For res n section 5.1. ck for bendin ion 5.4 in EC . ummarized in 21 = / s below: lass 1, 2 or 3 for Class 4 f member to = 1,1 ysis. for buckling r esistance is w ng capacitie s plastic stres ined to be 1. C3 in section . = / = / for compress sistance of C 1 in EC3. Th ng moment, c C3. The follo ≤ . ≤ . + . n table 4-9. , cross sectio 4 cross sectio buckling the resistance from well above th es the class ss distributio ns 5.4.4 and / sion, Mpl.Rdth Class 1, 2 or he calculatio compression owing design Ben Com ≤ 1 Com ons ons e safety facto m EC3. he calculated of the cros on is assumed 5.4.5 respect he plastic re 3 cross-sect ons for Npl.Rd, and combin n criteria are nding mpression mbined bend or is d normal forc ss-section ha d. tively as esistance for tion the parti
Mpl.Rdand W ned bending a
checked:
ing and axia
ces in the as to be bending ial safety Wpl can be and axial l force
All the c so small 4.5.3 The brid work as will only Transve The tran loading them. Th moment cross-se Figure 4 The high these sec given in Des criteria are fu l and are ther
Bridge Dec dge deck wi composite d y make the st ersal beams nsversal beam for these be hese position t and shear ction in the u 4-13: Positions hest moment ction forces n sections 5.4 ign of a 170 Tabl ulfilled. Also refore neglec ck ill consist of deck with st tructure mor s ms will be m eams will be ns are show i force in the ultimate limi s of traffic load t and shear fo the cross-sec 4.5 and 5.4.6 ≤ m long bridg le 4-9: Design v o, the cross-s cted. The arc
f main steel teel shear stu re rigid. Estim made of ste e when the a in figure 4-1 transversal it state. ds and shear- a
force are dete ction can be
in EC3 as
. =
ge over the f
22 values and resi section is ass ch is mostly i
girders, tran uds. The com mated thickn
el and will axle load fro 13. This locat beams. The and moment di determined. ermined to b determined. / fjord Þorskaf
istance for the sumed to res in compressi nsversal beam mposite effe ness of the co be placed w om the traffic tion of the ax ese section f iagrams when e 3025 kNm The design For class 1 o fjörður in Ice arch. ist the shear on. ms and conc ct is not cal oncrete slab i with 5 m spa c is placed e xle load will forces are us the cross-secti m and 1359 kN criteria for s or 2 cross sec eland forces since crete slab. T culated here is 200 mm. acing. Worst exactly abov l generate th sed to determ ions of cross be N respective shear- and m ctions e they are They will e but that t case of ve one of e highest mine the eams are ely. From moment is
where th beams is Main gi The mai hangers. 7241 kN the tran calculati 4.5.4 The han hangers ultimate exactly carbon s 4.5.5 The cho the X-ty analyzed he parameter s shown in fi rders in girders w . The largest Nm respectiv nsversal bea ions can be s Hangers ngers are the
are designe e limit state.
at hanger nu steel with the
Transversa oice of X-typ
ype, see Bun d as a truss sy rs are explain igure 4-14. F Fi will be conne t shear force vely. Here the
ms. The de seen in appen Fig elements th ed to resist t This force umber 1 clo e design yield al Bracing e bracing rat nner and Wr ystem. Later
ned in the las For detailed c igure 4-14: Est ected to the t e and momen e same criter etermined cr ndix A. gure 4-15: Dete hat connect th he largest te is acquired osest to the d strength as
ther than Vie right (2006) ral braces wi 23 ≤ . = st section. Th calculations, timated size of transversal b nt in the mai ria are check ross-section ermined size of he bridge de ension force, when the ax support. The s 3605 kN. erendeel brac , which resu ll not be calc ( √ )/ he determine see appendix
f the cross beam
beams which in girders ar ked, shear- an
can be see
f the main gird
eck to the arc , which is d xle force fro e chosen ma cing is that th ults in less l culated at thi ed cross-sect x A. ms. h are hangin re determined nd moment r en in figure ders. ch. They are determined to om the traff aterial of the he system wi lateral deflec is time.
tion of the tra
ng from the a d to be 2087 resistance, as e 4-15 and e vertical cab o be 3393 k fic load is po ese hangers ill be more r ctions and w ansversal arches in 7 kN and s was for detailed bles. The kN in the ositioned is M100 igid with would be
4.5.6 The soil concrete (2010). length o estimate for each be 35 pi fundame support direction 4.5.7 My prop First, fou be place segment segment placed in Next the beams th welded casted. 4.5.8 In table quantitie on the m Des Foundatio l under the e piles that w The piles wi of the piles w ed amount of h arch. The sp iles under eac ent itself. Th
the fundam n and the app
Constructi posal of a co undations fo ed under the ts, sizes that t at a time, su n right positi e deck is co hat are hang together and Cost estim 4-10 the to es are based method in sec ign of a 170 ns foundations will be drive ill have an in will be 14 m. f piles is pacing betwe ch abutment he filling beh ments. A con proximate siz Fig ion onstruction m r the arches e bridge. The are possible upported by ions the temp onstructed. T ging in the ha d finally, wh mation/conc tal quantity on the preli ction 4.4.2 fo m long bridg s is sedimen en down to nclination do . The largest 12 4 een the piles . The piles w hind the brid ntinuous foun ze of it will b gure 4-16: Plac method for th will be const en the arche e to transpor falsework st porary worki The main gir angers. The hen all the w
clusions of materials minary calcu or bridge type ge over the f 24 nt layers. Th the ground. own in the di t reaction for 601 00 32 will be 1.2 will also be a dge will also ndation is ch be 7.2 x 4 x 1
cing of piles at
his bridge typ tructed and t es will be ra rt. These seg tanding on th ing plane is r rders come hangers con work with the
s for the arc ulations. The e one. These fjord Þorskaf he foundatio Each pile r irection to th rce in the arc
m. The total able to resist o be able to
hosen under 16.8 m, see f
the arch suppo
pe is similar then a tempo aised. Each a gments will b he working p removed and in segments nnect the arch
e structural s
hes and brid e cost estima e cost figures fjörður in Ice n will be fo resists about he arch’s dire ch’s direction number of p the risk of tu resist some r the whole figure 4-16. orts. r to the meth orary working arch will be be welded to plane. When d can be used s and are co hes to the de steel is done
dge deck are ation for the s are given in eland ounded on p 400 kN, Ha ection. The e n is 12601 k piles is deter urning along external act bridge in th
hod for bridg g plane of gr divided into ogether in ste the arches h d as a road fil onnected to t eck. Each se , the concret e summarize foundations n table 4-11. precasted afliðason estimated kN so the rmined to g with the tions and he lateral ge type 1. ravel will o several eps, each have been lling. the cross egment is te slab is ed. These is based
To get a This brid steel cos a total cost th dge type is l st and compl Table 4-10: he total mater
little less tha exity of the s F Quantities of rial cost is do Table 4-11: an twice as ex structure. An Figure 4-17: An 25 structural mat oubled, whic Total cost of b xpensive as n overview o n overview of t
terials for the ch is a rough
bridge type 2. the first brid of the arch br
the arch bridg
arch bridge. estimation.
dge type. Thi ridge can be ge. is mainly dep seen in figur pends on re 4-17.
4.6 T
Bridge t pylons steel/con about th cable-sta 4.6.1 Bridge t cable st configur 4-20. Th stabilize Nowada orthotrop Many co for conc construc construc yard. Th weight o because A prope Howeve except f concrete Althoug composi composi Most po Howeve end span In this conditio there is transferr and a co cable sy DesThe
cable-type no. 3 is on each sid ncrete deck. he choice of t ayed bridges Aesthetics type no. 3 is tayed bridge rations, see f he pylons ca ed by the cabays the pylon pic or as a co oncrete cable crete cable-st ction is a f ction it is po he segments, of the segme it is stiffer a erly designed er, with incr for very long e. Thus the re gh the steel or ite deck wit ite with the ortions of th er, tensile str ns. Post-tensi a self-ancho ons on site, th a so called red to the su ombination ystem can be ign of a 170
-stayed b
s a back and de, similar The cross s the superstru s are discusse s of cable-s s a cable stay is to be de figure 4-18. T an either be bles that are aFigure 4-18 ns are most omposite ste e-stayed brid tayed bridge further deve ossible to use , however, sh ent is limited and easier to d and fabric reasing labor g spans. The educed self-w rthotropic de th a concrete steel girder he girder ar resses may o ioning is usu oring system he foundation earth anchor upports at th of self-anch seen on figu m long bridg
bridge
front cable-to the Öres section of th ucture is in th ed. stayed brid yed bridge. T esigned. The The number rigid, work anchored into : Configuratio often made el/concrete d dges have be es: cast-in-pl elopment of e a more com hould all be d by the tran erect. cated orthotr r costs, the use of steel weight of the eck is too expe slab on a by shear stu re under hig occur in the m ually used in m is prefera ns will be be red system w e ends of th oring and ea ure 4-19. ge over the f 26 -stayed bridg sund bridge he deck is si he next chap dges There are se e cables can of spans can k as a cantile o the ground
ons of the cable e of concrete deck. een built. In lace construc the free ca mplicated cro similar to av nsportation c ropic deck is orthotropic l in the deck e deck slab m pensive for c steel frame uds reduces gh compress middle portio these areas t able, see fig elow sea leve where the ho he bridge wh
arth anchorin
fjord Þorskaf
ge, see figure e. The bridg imilar to brid pter where ae everal types n be arrange n either be tw ever, or the d. es for cable-sta e. The deck general, the ction or prec antilever co oss-section b void adjustm capability. B s a good sol deck becom k is, today, tw must result in construction can be very the steel qua sion, which on of the cen to keep the c gure 4-19. T el and sedim orizontal com hich requires ng system. T fjörður in Ice e 4-21. This ge will con dge type 2. esthetics and
that can com ed in a harp
wo or three, deck is stif
ayed bridges. k can be mad
ere are two c cast construc onstruction m because prec ment in the p Box is the pr lution for a mes less com
wo to four ti n appreciable in most coun y competitiv antity of the is good for nter span an concrete unde That depend ment layers ar mponents of favorable fo The principl eland bridge type sist of a co A further di d structural s me into mind p-, fan- or c see figures ff and the py de of concre construction ction. A cast method. For casting is don precasting for referred cros cable-stayed mmercially a imes as expe e savings. ntries at this ve. Making e girder sign r concrete m nd at both en er compressi s on the fo re the main s f the cable fo foundation co le of a self-a e has two omposite iscussion system of d when a combined 4-19 and ylons are ete, steel methods t-in-place r precast ne in the rms. The s section d bridge. attractive ensive as time, the the deck nificantly. members. nds of the ion. oundation soil. Also orces are onditions anchored
Let us co be a goo seen on But, an a self-an 4.6.2 Based o Here, a h and deli the view in the py The oute stays wo modelle analysis two pyl bridge d horizont 4.6.3 In this se onsider an as od choice wit figure 4-20. asymmetrica nchoring syst Geometry on the discus harp shape c cate appeara wing angle. It ylon begin a er spans leng on’t exceed d in SAP200 of structures ons are conn deck to each tal.
Design ection the ele
symmetrical th respect to al system ha tem. for type 3 ssion above configuration ance because t also allows at a lower ele gths should b its limits. Fi 00 for 3D ana s. The deck, nected toget h pylon. Eac ements in the Figure 4-1 system with foundation c Figure 4-2 s earth-anch self-anchori n of the cable e an array of an earlier st evation so th be around 30 igure 4-21 d alysis. SAP2 see figure 4-ther with on ch cable wil Figure 4-21 e following t 27 19: Self anchor h only one py construction 20: Asymmetri ored cables ing cable sy es is chosen. parallel cabl tart of the de hat fastening 0-40% of the isplays the g 2000 is a com -26, is 10 m ne cross-beam ll be connec 1: Model for br table will be red system. ylon as can b n. An exampl ical system. and requires ystem is pref Harp shape les will alwa eck construct of cables ca e main span geometry of mmercial fini wide with fo m for stabil cted to trans ridge type 3. checked in t be seen in fig le of that stru s better found ferable in th configuratio ays appear pa tion because an start befor length so the the chosen m ite element p our pylons, tw
ity. Ten cab sversal beam the ultimate gure 4-19. Th uctural system dation condi his specific s on offers a ve arallel irresp the cable an re the pylon e stresses in model. The program for s wo on each s bles will con ms with 30° limit state. hat could m can be tion than situation. ery clean pective of nchorages is ready. the back bridge is structural side. The nnect the angle to
To begi elements traffic lo is move displaye indicate Des in with the s of the brid oads are plac d in 5 m inc ed for those the position ign of a 170 Tab necessary s ge that are u ced by using crements alon parts of the of the pylon m long bridg ble 4-12: Eleme section force under investi these influen ng the bridg e bridge that ns. ge over the f 28 ents that will b es and react gation. SAP2 nce lines. To ge deck. On f t will be an fjord Þorskaf be checked in U tions are de 2000 is used o create influ figures 4-22 nalyzed at th fjörður in Ice ULS. etermined fo d to create in uence lines a to 4-24 are his stage. Th eland or the corres nfluence line point load o these influe he dark verti sponding s and the f 100 kN nce lines ical lines
29
Figure 4-22: Influence lines for moments in the deck and at pylon supports. -1.00 -0.90 -0.80 -0.70 -0.60 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 M x/L
Influence Lines for Moment in the main girders @Pylon Center -1.00 -0.90 -0.80 -0.70 -0.60 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 M x/L
Influence Lines for Moment in Pylon Supports
Design of a 170 m long bridge over the fjord Þorskafjörður in Iceland
30
Figure 4-23: Influence lines for normal forces in pylon support and moment at 55% of the height of the pylons. -1.00 -0.90 -0.80 -0.70 -0.60 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 N x/L
Influence Lines for Normal Force in Pylon Supports
Left Pylon Right Pylon
-1.00 -0.90 -0.80 -0.70 -0.60 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 M x/L
Moment in 55% of the Height of the Pylons
31
Figure 4-24: Influence lines for various parts of the structural system of the cable-stayed bridge.
After the influence lines have been created the bridge is modeled as a 3D model in SAP2000 with the forces positioned at the corresponding positions. The slab is modeled as area section elements with a meshing of 0.5 m so that the axle traffic loads can be positioned right. Main girders and cross beams in the bridge deck are modeled as frame elements as well as the pylons. The cables are modeled as cable elements with high tensional stiffness. The only supports of the model are the fixed supports under the pylons because the pylons and cables should be able to carry its self-weight under construction. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 N x/L
Axial Force in cables - Back Stays
Cable 1 Cable 2 Cable 3 Cable 4 Cable 5 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 N x/L
Axial Force in cables - Front Stays
Cable 1 Cable 2 Cable 3 Cable 4 Cable 5
4.6.4 Concre The con concrete shear stu Cross B The cro designed loads for When th the cross of the fl see appe Main G Largest span and reached is chosen the widt calculati Des Deck te Slab ncrete slab w e casted on s uds will be w Beams ss beams w d to resist th r the largest Figu he largest mo s beams. The anges is 300 endix A. irder moment in t d is determin
when the tra n. From thes th of the flan ion, see appe
ign of a 170 will be 250 m ite and a me welded on cro will be made he self-weigh moment can ure 4-25: Posit oment and sh e cross sectio 0 mm and the
the main gir ned to be 73 affic loads ar se design val nges is 400 m endix A. Figu m long bridg mm thick and etal deck ben
oss beams an
of steel and ht of the co n be seen in f
ion of the traff hear force are on of the bea e thickness o
rders is when 11 kNm. Th re applied w lues the size mm and the ure 4-26 disp ge over the f 32 d the concret neath of trape nd main girde d are placed ncrete slab figure 4-25.
fic loads to esti e determined am is I shape of the web an
n the traffic he largest she where the pylo of the girder thickness of plays the cho
fjord Þorskaf
te quality is ezoidal profil
ers.
d in 5 m int and the traff
imate the size d in ULS, it’s ed with the to nd flanges is
loads are ap ear force is d ons are posit r is determin f the web an osen bridge d fjörður in Ice C35/45. The les. To achie tervals along ffic loads. Lo of the cross be s possible to otal height of 30 mm. For pplied at the determined t tioned. An I-ned. The tota nd flanges is deck. eland e slab will c eve composit g the deck. T ocation of th eams. determine th f 860 mm. T r detailed cal middle of th to be 1247 k -shaped cros al height is 1 30 mm. For consist of te effects They are he traffic he size of The width lculation, he bridge kN and is ss section 200 mm, r detailed
4.6.5 The pyl C40/50. beams. normal determin pylons i interacti design p appendix The cho Figure 4-26 Pylons lons will be The towers Each pylon force were d ned 1.5 x 2.0 is determine ion diagram t point for the
x A. sen cross-sec N( kN ) 6: Configuratio a concrete s have two v is designed determined t 0 m with a w d to be 1.2 to estimate th e above men Figu ction of the p -30,000 -20,000 -10,000 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 0 N (k N ) on of the deck hollow secti vertical cable for combin to be 27292 wall thicknes x 2.0 m wit he capacity o ntioned sect re 4-27: N-M i pylon is show 5,000 10, N 33 and girders w
ion. The con e planes and ned moment kNm and 5 ss as 0.3 m. T th a wall thi of the pylon. tion forces. interaction dia wn in figure ,000 15,000 2 M (kN N-M Diagram
with shear studs
ncrete qualit d are connec and normal 5121 kN resp The size of t ickness of 0 The star on Calculations
agram for the p 4-28. 20,000 25,000 Nm) m s and trapezoi ty in the py ted together l force. The pectively. Th the cross-bea 0.25 m. Figu the inside of s of the pylo pylon. 0 30,000 35,0 dal profiles. lons is chos r with two tr design mom he size of a ams that con
ure 4-27 dis f the curve s ons are disp
000 sen to be ransverse ment and pylon is nnects the splays an hows the played in
4.6.5.1 Where t main gir tension f 2000 wi Finally a 4.6.6 The foun bridge ty kN and pylon. T 4.6.7 The foun pylon w the deck construc main gir the beam main gir of the sp Des Cables the cables ar rders. The c force in the th tendon un a model of th Foundatio ndation unde ypes. The lar 27292 kNm The fundamen Constructi ndations are will be constru k can start w cted further u rders and cro ms. Finally th rders welded pan. This wa ign of a 170 Figure 4 re connected cables are m cables was d nits as 6-61 w he bridge tha Figure 4-2 n er each pylon rgest vertical m respectivel nt along with ion to be constr ucted up to a where the dec
up. During t oss-beams ar he slab is cas d togeather u
ay, the struct
m long bridg 4-28: Cross sec d to the bridg modeled as c determined to with a design at was constru 29: 3-D model n will consis l reaction for ly. That imp h the piles is
ructed first. A a height whe
ck is connec this the cros re in place th sted. This pr until the top r
ture works a
ge over the f
34 ction of the pyl
ge deck cros cable elemen o be 15888 k n capacity of ucted in SAP of the cable-st st of concret rce and mom plies that app
assumed to After that, th re the lowest cted to the c s-beams are he trapezoida ocess is done row is reache as a self-anch fjord Þorskaf
lon with reinfo
ss beams are nts with high kN. A propo 17019 kN. P2000 is disp tayed bridge in te footings an ment under on proximately
resist the ris
he work with t cable is con cables in seg also set in al profiles ar e for each ca ed and the de hored system fjörður in Ice orcement. e placed to r h tensional s osal of a cabl played in figu n SAP2000. nd cohesive ne pylon is d 13 piles are k for overtur h the pylons nnected. The gments mean place. After re fastened o able row with
eck structure m with the de eland reduce torsio stiffness. Th le system is V ure 4-29. piles as for determined to e needed un rning. can start wh en the constru nwhile the py r the segmen on the upper h the segmen e meets in th eck hanging on in the he largest VSL SSI the other o be 5121 nder each here each ruction of ylons are nts of the edges of nts of the he middle from the
cables o stayed b Figure 4.6.8 The tota price va substruc calculati bridge ty Finally t on each side bridge in the w 4-30: The Ston Cost estim al quantities alues given i cture are lis ions but the ype one.
T the total cost
of the pylon world that di necutters Brid mation/conc of materials in section 4. sted for the cost estimat Table 4-13: Am t of this bridg ns. Below, f isplays how dge (currently t clusions are summar 3. In table 4 cost estim tion for the
mounts of struc ge type is sum Table 4-14: 35 figure 4-30, i this principl
the largest cab
rized in table 4-14 the mai mation. Thes foundations ctural materia mmarized in Total cost of b is an examp e works. ble-stayed brid e 4-13 and co in materials e quantities is based on
als for the cable n the table 4-bridge type 3. le from one ge in the world ost estimatio and quantiti are based n the method e-stayed bridg 14. of the large d) under const on made base ies of the su on the pre d in section e. est cable-truction. ed on the uper- and eliminary 4.4.2 for
This bri depends there is q also a la Des idge type is s on the same quite much q arge factor. A ign of a 170 little less th e factors as f quantity of co An overview Figure 4-31 m long bridg
han three tim for bridge ty oncrete and r of the arch b : An overview ge over the f 36 mes as expe ype 2, steel c reinforcemen bridge can be of my proposa fjord Þorskaf ensive as th cost and com
nt that is use e seen in figu al of a cable-st fjörður in Ice he first bridg mplexity of th ed in the pylo ure 4-31. tayed bridge. eland ge type. Thi he structure. ons and the c
s mainly But also cables are
37
4.7 Summary
and
choice of bridge type
From the total cost estimations for the bridge types it is clear that the cable-stayed bridge is the most expensive one. Also the arch bridge is quite expensive compared to the prestressed concrete bridge that is the least expensive one. From a construction point of view the prestressed bridge is also the most favorable. From these perspectives a concrete girder bridge is the obvious choice.
But, there are also other aspects that need to be taken into consideration when choosing a bridge type; aesthetics, method of construction and construction time are obvious factors that can affect which choice is made. The author will leave those decisions for others to make at later stages but chooses to design the concrete beam bridge in a more detailed manner. In the following chapter more detailed calculations will be performed for the superstructure of bridge type 1. Calculations of the post-tensioned cables are performed where the prestress force and eccentricity of the cable profile are determined. Following that all cable losses are determined and then the secondary effects of prestress. Finally the ultimate moment capacity is determined for relevant members of the superstructure.
Design of a 170 m long bridge over the fjord Þorskafjörður in Iceland
38
5 Final
design
5.1 Introduction
Prestressed concrete structures, using high-strength materials to improve serviceability and durability, are an attractive alternative for long-span bridges, and have been used worldwide since the 1950s. The presence of cracks that can develop in tensile members can lead to corrosion of the reinforcement due to its exposure to water and chemical contaminants. Corrosion is generally only a problem for structures in aggressive exterior environments (bridges, marine structures, etc.) and is not critical in the majority of buildings. The effect of cracking of members can lead to substantial loss in stiffness which occurs after cracking and the second moment of area of the cracked section is far less than the second moment of area before cracking. Thus, allowing cracks to develop can cause a large increase in the deformation of the member. For prestressed concrete, compressive stresses are introduced into a member to reduce or nullify the tensile stresses which result from bending due to the applied loads. The compressive stresses are generated in a member by tensioned steel anchored at the ends of the members and/or bonded to the concrete.
There are two types of prestressing systems: pre-tensioning and post-tensioning systems. Pre-tensioning systems are methods in which the strands are tensioned before the concrete is placed. This method is generally used for mass production of prefabricated members. Post-tensioning systems are methods in which the tendons are tensioned after concrete has reached a specified strength. This technique is often used in projects with very large elements. The main advantage of post-tensioning is its ability to post-tension cast-in-place members. Mechanical prestressing jacking is the most common method used in bridge structures.
The post-tensioning process involves three fundamental stages. In the first stage of the process, the concrete is cast around a hollow duct. After the concrete has set or hardened, a tendon, consisting of a number of strands, is pushed through the duct (alternatively, the tendon can be placed in the duct before casting). Thus, the tendon can be fixed in any desired linear or curved profile along the member. By varying the eccentricity of the tendon from the centroid, the maximum effectiveness of a constant prestressing force can be utilized by applying the prestress only where it is required. Once the concrete has achieved sufficient strength in compression, the tendon is jacked from one or both ends using hydraulic jacks, thus putting the concrete into compression. When the required level of prestress is achieved, the tendon is anchored at the ends of the member. After anchorage, the ducts are usually filled with grout under pressure. The grout is provided mainly to prevent corrosion of the tendon but it also forms a bond between the tendon and the concrete which reduces the dependence of the beam on the integrity of the anchor and hence improves its robustness.
When prestressed concrete elements are designed the following factors need to be considered: • The prestressing reinforcement is determined by concrete stress limits under service load. • Bending and shear capacities are determined for the ultimate limit state
