Jankowski Tadeusz Presentation

8/11/2019 Jankowski Tadeusz Presentation

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Post tension in bridgePost tension in bridgePost tension in bridgePost tension in bridge

structuresstructuresstructuresstructures

Author: Engineer Jankowski Tadeusz

Leader: Associate Professor Gi ejowski Marian

Warsaw Universit of Techno!og

"e#art$ent of %ivi! Engineering

&nstitute of 'oad and (ridges

Warsaw )*+,

Master "i#!o$a -e$inar in .oreign Language

Table of ContentsTable of ContentsTable of ContentsTable of Contents

1. The purpose of prestressing

2. General principles of theory

3. Classical designing of tension

4. Continous beam without friction e=const

5. Example of stressed slab

6. Technical details

7. Beam and parabola

8. Friction looses

9. Influence line M=1 for beam

10. Influence line M=1 for 2 spans

11. Construction for example in Poland

12. Constructions for examples abroad


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The purpose of prestressingThe purpose of prestressingThe purpose of prestressingThe purpose of prestressing

Change the tension situation in element (beam, shield, plate or shell).Designer should completely remove the stretching under the loadcombination: dead weight + stress.

Building long span beams made of concrete cheap and strong material.Spans can be as long as trusses.

To master forces in the construction to designer's will.

To reduce costs. Post tensioned beam are 40-50% cheaper than integratedsteel and concrete

Stressing concrete gains the economical advantages in volume of concr(up to 30%) and reinforcement steel (up to 70%) Betonowe konstrukcj

sprone Kalikst Grabiec, Jerzy Kampioni PWN

Conception and realisation of tensioned structures is to form theinternal forces and moments situation inside the structure. Designerof reinforced concrete must take the geometrical parameters only.


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General principles of theoryGeneral principles of theoryGeneral principles of theoryGeneral principles of theory

Differential equation of a beam

Constant cross section and material

Parametric cross section and material

Equation of perpendicular (to beam axis) load from the cable

It is not so simple!Where is friction and forces at the ends?Parabolic path

Classic method of analysing tension in cross section

Compression of concrete

Infinite small part of beam

Stretchingof steel

Excentricity of the cable

Compression

Stretching

3

Classical designing of tension


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ContinousContinousContinousContinous

Beam withoutBeam withoutBeam withoutBeam without

frictionfrictionfrictionfriction

e=conste=conste=conste=const

Bending moments

Shear forces

Axial forces

! "#ample of stressed slab! "#ample of stressed slab! "#ample of stressed slab! "#ample of stressed slab


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$! Technical details$! Technical details$! Technical details$! Technical details

Stressing steel

Reinforcing steel


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Beam with two hinges:- constant cross section- parabolic path of the cable- without friction

Questions from situation:

How cable loads the concrete?

Is it possible to change theparabolic path to cylindricalpath and calculate load on theconcrete with friction looses?

Are friction interactionsadvantages or disadvantages?

Why disadvantages?

Styczna - tangent

%

beam and

parabola


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&&&&

'riction looses'riction looses'riction looses'riction looses

Function of stretching in the cable depands from the angle of the circle path

Angle given in radians

Important in mechanical industry

Differential equation ofequilibrium on cylindricalsurface and rope over it. Leonhard Euler is an

author of the solution

Reactions are contans

(

)nfluence line

*=1 for beam


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Basic system: continous beam

System of simple beams force method.

Areas

Values

1+

)nfluence

line for

2 spans


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Construction for e#ample in PolandConstruction for e#ample in PolandConstruction for e#ample in PolandConstruction for e#ample in Poland

H=7.5m above support H=3.1m in span

Cables 19 wires x150mm2:518 tons Cables for M


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12 Construction for e#ample abroad12 Construction for e#ample abroad12 Construction for e#ample abroad12 Construction for e#ample abroad

Motorway A1 in Italy Lofots bridges in Norway

Raftsund bridge in Norway

Lavant bridge in Austria

Than, you for your attentionThan, you for your attentionThan, you for your attentionThan, you for your attention

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Jankowski Tadeusz Presentation