Prestressed Concrete - 1 Introduction

8/12/2019 Prestressed Concrete - 1 Introduction

1/21

University of Western AustraliaSchool of Civil and Resource Engineering 2004

The University of Western Australia

School of Civi l and Resource Engin eering

CIVL 4111 Design of Structural Systems

Prestressed

Concrete

Developed by

Mr Ken Baker

Presented by

Guowei Ma


2/21

1. Introduction

2. Beam in bending at working load

3. Load balancing and deflections

4. Post-cracking performance of beams

5. Ultimate bending strength of beams

6. Ultimate shear strength of beams

7. Estimation of prestress losses

8. Prestressing anchorages

9. Multi-Span Prestressed Beams and Slabs

10. Deflection and Cracking

PRESTRESSED CONCRETE :

CIVL 4111 Design of Structural Systems


3/21

Basic Principles and Practices

Some options for prestressing a beam Discussion of the options

Materials

Nomenclature

1. Prestressed Concrete:

Introduction


4/21

BASIC PRINCIPLES AND PRACTICES

Why Prestress? Answer: Because concrete is weak in tension

100x100 prism of

concrete, tensile

strength 2.5 MPa

F F

Fractures when F = 2.5x10000/1000 = 25 kN

Same prism, pre-

compressed to 10

MPa

F F

Fractures when F = (10 + 2.5)*10000/1000 = 125 kN

Conclusion: Prestressing increases apparent tensile strength,

5 - fold in th is case!


5/21


How to prestress? 3 examples:

Stress after concrete has hardened

External Post-tensioned

Stress after concrete has hardened

Internal Post-tensioned

Apply stress before concrete is placed, and

release stress after concrete has hardened

Internal Pre-tensioned


6/21

How much prestress? 2 cases:

1. We may require that the prism does not fracture under maximum

working load Fmax for example: aesthetics, durability, vibration.

Then F max < Fcr Fully Prestressed

OR

2. We may be prepared to allow prism to crack under maximum workingload, provided that under sustained load Fsust the cracks are held tightly closed

by the prestress force.

Then Fsust < Fcrand F max > Fcr

Partially Prestressed

In both cases, safety must be assured:

f Fuo >= F*Eh? Surely

its broken !

So what about a beam ? . . . .



7/21

A beam incurs a bending moment under load, and this causes

compression in the top and tension (!) in the bottom thus:

If we introduce an axial force,and a reverse bending moment

thus:

. . . then we can eliminate the tension (or substantially reduce it) thus:

That is the

pr inciple of

prestressing

a beam


8/21

How does the engineer select a prestress force P ? . . .

First there are 2 basic questions:1. Does the original prestress force Poapplied at the end of the member exi st

thr oughout the beam, and persist for the li fe of the structure?

Answer: NO!

Force reduces along the beam due to in itial lossesPo => Pi , and

Force further reduces with time due to long term lossesPi => Pe

2. I s transfer of stress from tendon to concrete simple to achieve?

Answer: NO!

For post-tensioning, we must avoid spall ing and bursting of

concreteat anchor plates.

For pre-tensioning, we must avoid bond failure and spli tting of

concretein transmission zones.



9/21

So how can we introduce

a prestressing force to

take advantage of all this, while

avoiding excessive losses ?

Thats what we must find out.But f ir st :

Some options for prestressing a beam . . . .


10/21

Simple Beam - external , concentr ic prestress

rigidabutments

jack

sliding support

achieves uniform compression throughout beam . . .

so not very efficient, and . . .

dependent on rigidity of abutments

What about the same idea with internal prestress ? . . .


11/21

Simple Beam - concentr ic , internal prestressing :

Post-tensioning

Post- means after

concrete has been placed,

and has hardened.

duct

tendon

jack grips andextends tendon

l ive enddead end

Construction procedure:

Build beam, incl. duct and tendon

Jack against live anchorage

Lock off

Remove jack, trim tendon

Grout duct

Remove formworkEccentr ic prestress? . . .


12/21

Simple Beam- eccentr ic, internal , straight tendon

Post-tensioning

tendon

eccentricity e

belowcentroidal

axis of section

Eccentricity of tendon causes a bending moment action which opposes

bending moment due to applied loading.

Eccentric tendon force causes beam to bend upwards.If self-weight is overcome, then beam lifts off the formwork -

this is virtually always the case.

Can we achieve the same result with Pre-tensioning?

Yes, we can . . .


13/21

Pre- = tensioning of steel

against rigid forwork BEFORE

concrete is placed, and

release after concrete hashardened.

Simple Beam - eccentr ic, internal, straight tendon

Pre-tensioning

r igid end forms, to hold

prestress force

Construction procedure:

Build rigid end forms

Install and stress tendon Place concrete, and allow to harden

De-stress, cut and trim tendon

What about changing the eccentr icity along the beam?

Good thinking . . .


14/21

Duct and tendon L ive endDead end

Eccentr icity of tendon varies to match applied bending

moment

Tendon is placed inside the duct, which is carefully

draped within the formwork, and held tightly in position while theconcrete is placed.

For a uniformly distributed applied loading, the shape of the

drape is a parabola, with zero eccentricity at ends, and maximum

eccentricity at mid-span.

Simple Beam - eccentr ic, internal, draped tendon

Post-tensioning


15/21

So what materials do we

use to make prestressed

concrete ?

Answer: Concrete,

Prestressing steel, and

Reinforcing steel . . . .

plus lots of special fitments


16/21

Concrete:

At least medium strength - Grade 32, 40, 50, or 65 to

tolerate the high stresses which occur, and

minimise creep under sustained load.

MATERIALS

Prestressing Steel:

Specially manufactured high strength steel,

to tolerate the very high stresses incurred, and

of low relaxation at high sustained stress.

Reinforcing Steel:

Grade 500N, used to

enhance ultimate strength in bending,

to ensure adequate shear resistance, and

to prevent destructive bursting and spalling at anchorages.


17/21

Prestressing Steels :Extracts from AS3600-2001 Table 6.3.1 :

Material type Nom. dia. Area Min. break. Min. tensileand Standard mm mm

2load kN strength f p

MPa

Wire - AS1310 5 19.6 33.3 1700

7 38.5 65.5 1700

7-wire super 9.3 54.7 102 1860

strand - AS1311 12.7 100 184 1840

15.2 143 250 1750

Bars - AS1313 23 415 450 1080

(super only) 29 660 710 1080

etc

All these are commonly used for post-tensioning.

For pre-tensioning, strandis commonly used, but also

wire, which must be crimped or deformed to achievebond.

dia.

MATERIALS


18/21

Stress-Strain of prestressing steel :

stress s p

strain p

fp

fp = (ultimate)

tensile strength

(Breaking strength)

MPa

>0.050

fpy

fpy = yield strength

MPa

0.002

Slope = Ep

Ep = elastic modulus

MPa

idealised

This idealised curve is called elastic/plastic (sometimes bi-l inear).

I t is usual ly used in calculations thus:

Up to py,stress p= Ep p

Above py, , stress p = fpy


19/21

Multi-strand tendon : Tendon = a single wire, strand or rod,or a bundle of wires, or a bundle of

strands.

Multi-strand tendon comprises a bundle of strands.

Number of strands required is estimated from:

maximum force to be applied Po , and

stress level s p to be adopted.

EXAMPLE: Po = 1000 kN, f 12.7 mm super strand, stress 1000 kN o.k.

duct

50f

7/12.7f

strand

tendongrout


20/21

NOMENCLATURE

Some symbols:

Ap = area of tendon(s) mm2

fp = breaking strength of tendon MPa (N/mm2)

fpy = yield strength of tendon MPa

dp = distance from compressive f ibre to tendon mm

ds = distance from compressive fibre to rebar mm

P = prestress force in tendon kN (Po , Pi , Pe)

fcp = compressive strength of concrete at time of transfer MPa

c = stress in concrete MPa ( + = compression )p = stress in tendon MPa

e = eccentr icity of tendon force from centroidal axis mm

. . . . and our Code is AS3600 - 2001


21/21

Prestressed structures may be Pre-tensioned or Post-tensioned.

Post-tensioned structures may be Internally or Externally

prestressed.

Prestressing is used to increase the apparent tensile

strength of concrete, by causing an internal action opposite to

the action due to applied load.

Prestress losses must be estimated and allowed for indesign.

Medium to high strength concrete, and high strength, low

relaxation steels are used in prestressed structures.

SUMMARY

Documents

Prestressed Concrete - 1 Introduction