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Module 4D8Prestressed Concrete

Lent Term 2010

Lecture 7 – Composite Construction

Composite meansPrecast + In-situ

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For domestic buildings

e

P

Prestress

iZPe

AP

+

+

Load applied to precast beam

i

pre

ZM

−

+

i

comp

ZM

′−

Load applied to composite beam

=

Stress on precast beam alone

=

Final stress on composite beam

These stresses do not alter because of addition of in-situ concrete Discontinuity

e always measured from axis of precast section

Centroid

Precast

Composite

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e

P

PrecastCentroid

y

Fibre 1

Fibre 2

Composite centroid

y′

Fibre 3

Fibre 4 (in-situ)Fibre 1 (precast)

Fibre 2

Precast properties

Eprecast

Iprecastfor bending about precast centroid

Zi = Ιprecast/y(i=1,2)

b

Ein-situ < Eprecast

bEEb

precast

situineff

−=

Composite properties

Z′i = Ιcomposite/y′(i=1,2,3,4)

Icompositefor bending about precast centroid

Propped construction1. Install precast beam

5. Apply load

Normally used for buildings

2. Insert props

4. Remove props when cured

3. Add in-situ – weight carried on props

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Propped construction• Weight of in-situ concrete carried by

props, not by precast

• In-situ concrete cures, so section now behaves compositely

• Props removed, so weight of in-situ now carried by composite action

Unpropped ConstructionUsually used for bridges where propping would be impossible or where it would interfere with access

Precast beam has to carry the full weight of the in-situ concrete without benefit of composite action

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Propped Construction• Precast carries:-

• Own weight• Prestress

• Composite carries:-• Wt of in-situ• Live loads

Unpropped Construction• Precast carries:-

• Own weight• Prestress• Wt of in-situ

• Composite carries:-• Live loads

Design of composite beams• Manufacturers have standard shapes and

recommendations for sizes of in-situ flanges

• Usually no need to design section

• May need to design the prestress in the precast section

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For an unpropped beam with composite centroid within the precast section (usual case for bridge beams)

Critical cases:-• At transfer, under precast self-weight,

check compression in bottom (fibre 2) and tension in top (fibre 1)

• At working prestress, under full dead weight plus live load, compression in top (fibre 1) and tension in bottom (fibre 2)

Mg1 Moment in beam due to self weight of the precast beam

Mq Moment in beam due to maximum live load

Mg2 Moment in beam due to self weight of the in-situ concrete

Other notation as for normal beams

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t

g

t

tt

PM

PfZ

AZe 111 ++−≤

Fibre 1, tension, precast self weight, transfer

t

g

t

ct

PM

PfZ

AZe 122 ++−≤

Fibre 2, compression, precast self weight, transfer

t

qgg

t

cw

RPMZZMM

RPfZ

AZe

)/( 112111′++

++−≥Fibre 1, compression, full load, working prestress

t

qgg

t

tw

RPMZZMM

RPfZ

AZe

)/( 222122′++

++−≥Fibre 2, tension, full load, working prestress

Eccentricity inequalities

Plot Magnel diagram in the normal way

What is the Moment Range?

Ma

Mb Moment range at one section

But same section and prestress must work everywhere in the beam,so effective moment range applies to whole beam

Most precast beams have straight tendons and uniform prestress

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Many special cases not covered here!

Always check stresses from first principles

StabilityOften assumed that

concrete too chunky to buckle

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Steel girders most susceptible

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Lateral-Torsional Buckling• No top flange until deck complete• Torsional restraint at support critical• Transportation a problem

Hanging Beams can Topple

Lack of torsionalrestraint means that beam can rotate as a rigid body and bend about its minor axis

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