Prestressed Concrete - 1 Introduction

The University of Western Australia School of Civil and Resource Engineering

CIVL 4111 Design of Structural Systems Developed by Mr Ken Baker

Presented by Guowei Ma

Prestressed Concrete University of Western Australia School of Civil and Resource Engineering 2004

CIVL 4111 Design of Structural Systems

PRESTRESSED CONCRETE : 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

1. Prestressed Concrete: Introduction • Basic Principles and Practices • Some options for prestressing a beam

• Discussion of the options • Materials • Nomenclature

BASIC PRINCIPLES AND PRACTICES Why Prestress? Answer: Because concrete is weak in tension F

F

100x100 prism of concrete, tensile strength 2.5 MPa

Fractures when F = 2.5x10000/1000 = 25 kN

F

F

Same prism, precompressed to 10 MPa

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

Conclusion: Prestressing increases ‘apparent’ tensile strength, 5 - fold in this case!

Basic Principles and Practices

How to prestress? 3 examples:

External

Post-tensioned

Internal

Post-tensioned

Internal

Pre-tensioned

Stress after concrete has hardened

Stress after concrete has hardened

Apply stress before concrete is placed, and release stress after concrete has hardened

Basic Principles and Practices

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 working load, provided that under sustained load Fsust the cracks are held tightly closed by the prestress force. Then Fsust < Fcr and F max > Fcr

Partially Prestressed

Eh? Surely it’s broken !

In both cases, safety must be assured:

f Fuo >= F*

So what about a beam ? .

.

.

.

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:

That is the principle of prestressing a beam

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

Basic Principles and Practices How does the engineer select a prestress force P ? . . .

First there are 2 basic questions: 1. Does the original prestress force Po applied at the end of the member exist throughout the beam, and persist for the life of the structure?

Answer: NO! • Force reduces along the beam due to initial losses Po => Pi , and • Force further reduces with time due to long term losses Pi => Pe

2. Is transfer of stress from tendon to concrete simple to achieve? Answer: NO! • For post-tensioning, we must avoid spalling and bursting of concrete at anchor plates. • For pre-tensioning, we must avoid bond failure and splitting of concrete in transmission zones.

So how can we introduce a prestressing force to take advantage of all this, while avoiding excessive losses ?

That’s what we must find out.

But first : Some options for prestressing a beam .

.

.

.

Simple Beam - external , concentric prestress

rigid abutments

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 ? . . .

Simple Beam - concentric , internal prestressing : Post-tensioning dead end

duct

live end

jack grips and extends tendon

tendon

Construction procedure: • Build beam, incl. duct and tendon • Jack against live anchorage • • • •

Lock off Remove jack, trim tendon Grout duct Remove formwork

‘Post-’ means after concrete has been placed, and has hardened.

Eccentric prestress? . . .

Simple Beam - eccentric, internal, straight tendon Post-tensioning

tendon eccentricity e below centroidal 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 . . .

Simple Beam - eccentric, internal, straight tendon Pre-tensioning rigid 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

‘Pre-’ = tensioning of steel against rigid forwork BEFORE concrete is placed, and release after concrete has hardened.

What about changing the eccentricity along the beam? Good thinking . . .

Simple Beam - eccentric, internal, draped tendon Post-tensioning Dead end

Duct and tendon Live end

Eccentricity 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 the concrete 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.

So what materials do we

use to make prestressed concrete ?

Answer: Concrete, Prestressing steel, and Reinforcing steel . . . . plus lots of special fitments

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

• tolerate the high stresses which occur, and • minimise creep under sustained load. 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.

MATERIALS Prestressing Steels : Extracts from AS3600-2001 Table 6.3.1 : Material type Nom. dia. Area Min. break. Min. tensile and Standard mm mm 2 load kN strength fp MPa Wire - AS1310 5 19.6 33.3 1700 7 38.5 65.5 1700 7-wire super strand - AS1311

Bars - AS1313 (super only)

9.3 12.7 15.2

54.7 100 143

102 184 250

1860 1840 1750

23 29 etc

415 660

450 710

1080 1080

All these are commonly used for post-tensioning. For pre-tensioning, strand is commonly used, but also wire, which must be crimped or deformed to achieve bond.

dia.

Stress-Strain of prestressing steel : fp = (ultimate) tensile strength (Breaking strength) MPa fpy = yield strength MPa Ep = elastic modulus MPa

stress sp

fp fpy

idealised

Slope = Ep

0.002

>0.050 strain ep

This idealised curve is called elastic/plastic (sometimes bi-linear). It is usually used in calculations thus: Up to epy ,stress sp = Ep ep

Above epy, , stress sp = fpy

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 <= 1500 MPa. Ap required = 1000 x 10^3 / 1500 = 667 mm2 duct Number of f12.7 mm strands (area = 100 mm2) 50f = 667 / 100 = 6.7 i.e. 7 strands. Stress in 7-strand tendon, loaded to 1000 kN 7/12.7f = 1000 x 10^3 / (7 x 100) strand tendon = 1430 MPa. grout NB P must not exceed 0.85 x 700 x 1840 o

= 1095 kN > 1000 kN o.k.

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 fibre 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

sc

= stress in concrete MPa

sp

= stress in tendon MPa

e

= eccentricity of tendon force from centroidal axis mm

( + = compression )

. . . . and our Code is AS3600 - 2001

SUMMARY • Prestressed structures may be Pre-tensioned or Posttensioned. • 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 in design. • Medium to high strength concrete, and high strength, low relaxation steels are used in prestressed structures.