Module 4D8
Prestressed Concrete
Lent Term 2010
Lecture 7 – Composite
Construction
Composite means
Precast + In-situ
1
For domestic
buildings
These stresses do not alter because
of addition of in-situ concrete
Discontinuity
Composite
Centroid
+
Precast
=
+
=
e
P
e always measured
from axis of precast
section
P Pe
+
A Zi
Prestress
−
M pre
Zi
Stress on
precast
beam alone
Load applied to
precast beam
−
M comp
Z i′
Final stress
on composite
beam
Load applied to
composite beam
2
Precast
properties
Eprecast
Composite
properties
b
Fibre 3
Fibre 1
Iprecast
for bending
about precast
centroid
Composite
centroid
y′
Precast
Centroid
Fibre 2
Icomposite
for bending
about precast
centroid
e
y
Fibre 4 (in-situ)
Fibre 1 (precast)
P
Fibre 2
Zi = Ιprecast/y
(i=1,2)
Ein-situ < Eprecast
beff
Z′i = Ιcomposite/y′
(i=1,2,3,4)
E
= in − situ b
E precast
Propped construction
1. Install precast beam
Normally used for buildings
2. Insert props
3. Add in-situ – weight carried on props
5. Apply load
4. Remove props when cured
3
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 Construction
Usually 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
4
Propped Construction
• Precast carries:• Own weight
• Prestress
Unpropped Construction
• Precast carries:• Own weight
• Prestress
• Wt of in-situ
• Composite carries:• Wt of in-situ
• Live loads
• 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
5
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
Mg2
Moment in beam due to self weight of the
in-situ concrete
Mq
Moment in beam due to maximum live load
Other notation as for normal beams
6
Eccentricity inequalities
Fibre 1, tension, precast self
weight, transfer
e≤−
Z1 Z1 f tt M g1
+
+
A
Pt
Pt
Fibre 2, compression, precast
self weight, transfer
e≤−
Z 2 Z 2 f ct M g1
+
+
A
Pt
Pt
Fibre 1, compression,
full load, working
prestress
Fibre 2, tension, full
load, working prestress
Z1 Z1 f cw M g1 + M g 2 + ( Z1 / Z1′) M q
+
+
A
RPt
RPt
M g1 + M g 2 + ( Z 2 / Z 2′ ) M q
Z f
Z
e ≥ − 2 + 2 tw +
A
RPt
RPt
e≥−
Plot Magnel diagram in the normal way
What is the Moment Range?
Most precast beams have straight tendons and uniform prestress
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
7
Many special cases not
covered here!
Always check stresses from
first principles
Stability
Often assumed that
concrete too chunky to
buckle
8
Steel girders most susceptible
9
Lateral-Torsional Buckling
• No top flange until deck complete
• Torsional restraint at support critical
• Transportation a problem
Hanging Beams can Topple
Lack of torsional
restraint means that
beam can rotate as a
rigid body and bend
about its minor axis
10
11