Module 4D8 Prestressed Concrete Lent Term 2010 … 4D8 Prestressed Concrete Lent Term 2010 Lecture 7...
Transcript of Module 4D8 Prestressed Concrete Lent Term 2010 … 4D8 Prestressed Concrete Lent Term 2010 Lecture 7...
1
Module 4D8Prestressed Concrete
Lent Term 2010
Lecture 7 – Composite Construction
Composite meansPrecast + In-situ
2
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
3
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
4
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
5
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
6
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
7
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
8
Many special cases not covered here!
Always check stresses from first principles
StabilityOften assumed that
concrete too chunky to buckle
10
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