Jankowski Tadeusz Post Tensioning in Concrete Bridge Structures

8/11/2019 Jankowski Tadeusz Post Tensioning in Concrete Bridge Structures

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Warsaw University of TechnologyDepartment of Civil EngineeringInstitute of Roads and Bridges

Warsaw 2!"

Foreign language Master Diploma Seminar

Post tensioning in

concrete bridge structures

Author: Engineer Jankowski Tadeusz

eader: Associate Pro!essor "i#e$owski Marian


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%& Purpose o! stressing

The main purpose of stressing is to deform structure due to designers will) Ideale+ample is function with values opposite to dead weight) It could #e write ,wg-+./ws-+. in caseof #eam 0 one dimension element) Desired deformation is get as every other deformation of

structure) Designer should put the load in e+act places on construction and ma*ecalculations) In other words( $tress is effectuated programmed state of tension inside theelement) Descri#ed state of tension is characterised #y no,stretching concrete along elementunder the load( dead weight 1 stress)

The a#ility of #uilding concrete medium,length spans -32m. is also the purpose ofstressing) Building such spans from reinforced concrete is impossi#le) $teel truss is moree+pansive than stressed concrete) $tressing gains ",45 savings in reinforcing steel)

6Initial stressing leads to savings in material) In many cases in stressed structuresusage of concrete is 75 and reinforcing steel 85 in comparison to reinforcedconcrete9:position 8 page !4;

t enough to solve pro#lem completely)Continuous technological progress and collected e+perience have lead to diffuse

advanced technologies in stressing concrete in many #ranches of engineering) ?owadays steelanchorages constructed from cones are most common)

$tressing ca#les are often use to increase carrying capacity of e+isting old #ridges andstructures)

'& (asic assumptions to calculations

The first step of calculations is determine type of stressed element) In this essay#eams are considered) There are two types of differential e'uation connected to #eam(

the first is commonly *nown for #eams with constant cross section

the second for #eams with parametric cross section often used in cantilevercontinuous #ridges :position " page @;

In further part of an essay only the constant cross section will #e considered)The second assumption to design is eccentricity of stressing force in every cross

section) The path of a ca#le determines the e'uivalent load from stressing put on the #eamelement) The path imprecates to straight line or some function e-+.) Aor e+ample e'uivalent

vertical load from para#olic path is e'ual p-+.) The form of e'uivalent load e'uation is similarto e'uation of #eam I-+./constant)


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)& *lassic method o! stressed cross section calculations

Classic method advised #y standard


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,& E-ample o! calculation o! two span continuous beam with constanteccentricit. and !orce

n the picture #elow there is an e+ample of two span continuous #eam under the loadfrom ca#le with constant eccentricity and force) Aorce method was used to calculate #ending

moment= shear and a+ial forces in every point of structure)Fraph of #ending moments is not o#vious) Designer must ta*e care a#out stretchinga#ove ca#le on #oundary supports and #elow ca#le in the middle support) Goreover veryimportant is great opposite reaction in middle support which may cause a lot of trou#les withstretching concrete a#ove #earing) $uch opposite reactions weren>t considered in FdaHs*$outh overpass and lead to destroy concrete a#ove #earings)


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/& E-ample o! modelling and FEM results o! stressed round slab

Round sla# model in Ro#ot structural AEG software shows the #ehaviour of structureunder load from ca#le with constant eccentricity and force along one of diameters) The ca#le

was replaced with a+ial force$-+./$/const andcontinuous #endingmoment G-+./$e/const=#ecause it>s impossi#le tomodel ca#le in this software)It>s a general rule oftheoretical mechanic= if onemove vector #y section)

There were values ta*enar#itrarily( $/4*?Jm and G/,!*?mJm -stretching inupper fi#ers.) Upliftingcalculated #y AEG enginee'uals ! cm in direction dueto e+pectations)

0& Technical and realisation details

$tressing techni'ues in #ridge structures can #e separate into several types(

.


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is filled with patented wa+es to reduce friction #etween stressing steel and concrete tominimum 0 practically Kero) Ca#le tu#e is often made from high endurance polyethylene toreduce friction for every weave separately :position ! page ;)In real structures friction can>t#e reduce to Kero= #ut it has so small level= that designer can calculate it as e'ual Kero) That isthe reason why this type of stressing is called Lwithout friction9)

C) Ca#le in concrete with friction 0 it>s the same situation as a#ove #ut tu#e is filled withcement,#ase= #ituminous or synthetic resin su#stances :position 2 page !"";)

D. E+ternal ca#les -inside or outside cross section. without friction -E+tra,dosed ifoutside. 0 ca#les touch concrete only in specified places called deviators) Deviator is anelement specially formed to transfer clamp and to construct enough #ig eccentricity) nalysisof structure is made without friction #ut with dynamic and non,linear aspects) The longestspans can #e #uilt with this technology of stressing)

Drawing !) $tressing steel -from left( !+ wire= 4+ weaves= !+ stay ca#le. :position 2 page @;

1& Simple support beam stressed with parabolic path o! cable 2 !indingthe path


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3& Friction and tension looses

Tension loose along the ca#le is e+treme important in calculations) They are caused #ymany reasons :position 7 page !;(, immediate( friction #etween ca#le and ca#le tu#e or concrete is given #y function f-+. along

whole element, immediate( elastic deformation of pressed concrete constant along whole element

, immediate( cones slip inside active anchorage differ along section +o from anchorage, rheological( shrin*age and creeping of concrete, rheological( stressing steel rela+ation


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The loss of stressing force from friction #etween steel and concrete is shown on thedrawings #elow) It depends from friction coefficient= angle of the path and unintentional

waves of ca#le tu#e along the path) E'uation descri#ing friction loss was proposed #y Eulerfor the first time :position 2 page !;)

4& *alculation o! in! luence line !rom mo5ing bending moment M6% onsimple support beam

In case of traditional loading of influence line= uniform '-+. and point forces < aremultiplying #y proper fieldsJordinates of influence line of given static value) This method of

design is the #est for #ridges #ecause of massive moving load from vehicles) Designer has toplace the vehicle a#ove ma+imumJminimum ordinates of the influence line for static valuesof every cross section along the #ridge)

Influence lines frommoving point force areuseless for uniform or point#ending moment) If we havesuch a load on a #eam weshould find the influence linefrom moving point #ending

moment G/!) It>s necessary#ecause there is alwaysmoments with eccentricity ofthe force)


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%7& *alculation o! in! luence line !rom mo5ing bending moment M6% ontwo spans beam

Calculations are o#vious for one span simple support #eam) s &ump in the place is e'ual toG/!) Calculations are made for every #eam interval) There are local coordinates for every#eam to simplify calculations) Rotation can #e calculated from Ga+well,Gohr graphical rule)

ll local coordinates must #e imprecated to one glo#al at the #eginning of the #eam)

Drawing charts for /!m EI/! G/! in Gathematica software is the last chapter ofcalculations)


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%'& E-amples o! stressed bridge constructions in Europe

#road= stressed concrete has #een using for a longest time and for longer spans) Aore+ample in ?orway Raftsund Bridge ma+/2@m and ofots Bridges -interesting #ecause ofits curved shape.= in ustria avant #ridge ma+/!m -!m high a#ove valley.) ist could#e longer and richer for e+tra,dosed #ridges #ut it isn>t a su#&ect of this article)

Summar.Designing strains and ca#les in concrete is very responsi#le and 'uite difficult #ut

economically validate what is shown #y statistics of #uilt o#&ects) Calculations enclosed inthis article may seem to #e vast and difficult= #ut it>s only the top of ice#erg) Completeinformations a#out stressing is in the #oo* L$tressed structures V #ridges9 and LTheory ofstressing9 prof) $tefan Paufman) Gentioned #oo*s are 'uite old -!@44,!@4. #ut give answersto many 'uestions= which L#lac* #o+9 in the shape of AEG software doesn>t answer)

evel of technical *nowledge a#out stressing is still rising)


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Jankowski Tadeusz Post Tensioning in Concrete Bridge Structures

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