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Precast bridges
Design principles
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Course overview
Introduction to the course
Overview on precast systems
In-situ vs precast bridge (example)Design principles
Detailing of girder bridge deck
Girder bridge design (example)
ummary and conclusions
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Presentation overview
Introduction
!alculation flow chart
tructural system
Design graph
"oadfor bridges"oad distribution
!ross section analyses
Design calculation
Detailing
ummary
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Introduction design principles
#ridge beam
#ridge deck
#ridge beam and in-situ deck
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Eurocodes$!% #asis of design
$& '% $urocode #asis of design
$!' General actions $& ''-'-'* $! ' +art '-' Densities* self weight $& ''-'-,* $! ' +art '-, ind actions
$& ''-'-.* $! ' +art '-. /hermal actions $& ''-'-0* $! ' +art '-0 1ctions during execution $& ''-'-2* $! ' +art '-2 1ccidental actions from impact
and explosions $& ''-3* $! ' +art 3 /raffic loads on bridges
$!3 Design of concrete structures $& '3-'-'* $! 3 General rules and rules for buildings $& '3-3* $! 3 4einforced and prestressed concrete
bridges
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Calculation flow chart
element design
Designcalculations
Cross sectional
analysis
Detailing
Pre-tensioning
EC2
Design
graphs
Structural
system
Preliminary design
Loads for bridges
Load distribution
Structural system
FEM or Guyon-
Massonet
EC
Bridge design
!ridge and
dec"
Final preliminary
design
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Co-operation in design
+reliminary general design General design office start with pro5ect - roads and bridges
are drafted6
Detailed prefab design
!oncrete-factory design-office does beam calculations* cross-section drawings* check support nodes etc6
7inal general design General design company finali8es whole bridge and deck
uccesfull bid of the pro5ect 9pdate of drawings
7inali8ing factory drawings of elements
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Structural system
+reliminary design of bridge
pans
support locations
preliminary beam height and cross-section support solutions
dilatation 5oints location
etc
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Inverted T-beam ZIP
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ZIP design graph
#$P%&&
#$P'&&
Span [m]
Variable
load[kN/m2]
(&
&
2&
&
) 2& 2) (& () %& %) )&
#$P&&&
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ZIP design graph
Span [m]
Variableload[kN/m2]
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Design graphs
/he design graph is based on imply supported beams
!entre to centre distance '63 m
Dead weight wear layer is '6. k&:m3* edge line load of ;63
k&:m'
Dutch code &$& 023% (tructural concrete)
Dutch code bridges &$& 023; ("oads for bridges)
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Centre to centre distance
7or larger spans and heights the centre to centre distanceof the
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ules of thumb for ZIP bridges
4oad bridges beams '63% m distance-to-distance deck 3'% mm
beams '6>% m distance-to-distance or more deck3,% mm
4ailway bridges
beams '63% m distance-to-distance deck 30% mm
Other applications
beams '63% m distance-to-distance deckminimum of '>% mm
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!verview of loads
"oads Dead load
/raffic load
7atigue load
1ccidental load
/hermal load
indload
"oad combinations
7or bridges* the simultaneity of actions and the particular
re?uired verifications should be specified
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Traffic load - lanes
Divide bridge deck into lanes
"anes have width of ; m
' lane if w @ .6, m
3 lanes if .6, m @ w @ m
; or more lanes if w A m
"ane ' gives most unfavourable effect
0
lane lane 2
lane (
1emaining area
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Traffic load " load model
"oad model ' of interest
!oncentrated and uniformly distributed load*
normal traffic* for general and local verification
2+& m
2+& m
2+& m
+& m
+& m
+2 m
lane (
lane 2
lane
2+) "/m2
9.0 kN/m2
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#oad $odel %
/wo double axle concentrated loads located at a lane with a weight of BBik consisting of 3 wheels with each %6.
BB
ikweight
9niformly distributed load a??ikon lanes
a??rkon remaining area
1emar"3 defined as /ational Parameter
Loation
!otal load
2 " #ik[kN]
$ik%$
rk&
[kN/m2]
Lane no 2 5 65
(&& 7
5 89&
Lane no 2 2 5 625
2&& 72
5 29)
Lane no ( 2 5 6(5
&& 7(
5 29)
:ther lanes & 7i5 29)
1emaining
area
& 7r5 29)
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Collision forces
Fd;ma;
Fdyma;
C' axle "=' on footways and cycle tracks
C!ollision with kerbs
C Impact load underside deck (headroom @ . m) Inclineerde force at '%
Eori8ontal component ''%% k&Fertical component '% k&
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#oad combinations
erviceability limit state !haracteristic value combination
5'
Gk*5
H + H Bk*'
H iA'
%*i B
k*i
GkH + H BlaststH %*, ?gvb
9ltimate limit state 7undamental combination
5'G*5 Gk*5H p + H B*' Bk*'H iA' B*i %*i Bki
'*;. GkH '*% + H '*;. B laststH '*;. ?gvb
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#oad distribution
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#oad action and reaction
"oad model in centre of deck
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#oad action and reaction
"oad model in centre of deck
"oad model at one side of deck
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#oad distribution
"oad is carried by more than one beam
"oading leads to Deflections and 4otations
"oad distribution is influenced by #ending stiffness /orsional stiffness In both span direction and transversal direction
=ethods to determine transversal load distribution(moment in beams and deck) &umerical finite element model method 1nalytical Guyon-=assonet method
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&umerical method
7inite element modelling of beams and deck
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&umerical displacements
Displacements due to edge load
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&umerically calculated moment
#ending moment due to edge load
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'nalytical method
Guyon-=assonet/ransversal dirstribution coefficient K
KL KoH (K'- K%) at a certain
KoL transversal load distribution for a cross sectionwithout torsional stiffness (L %)
K'L transversal load distribution for a cross section
with full torsional stiffness (L ')
KL transversal load distribution for a cross section
with torsional stiffness (%@@')
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Design curves
Design curves for the effects of concentrated loadson concrete bridge decks KL KoH (K'- K%) at a certain
'o(al)es *or beam b
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Influence lines
Influence of load on beam position
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E(ample load distribution %)*
Deck width '%6> m* ;% m span beams '63 m width
"oad 0%% k&
$ffective width L :>'%6> L '36'. m
(& m
'&& "/
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E(ample load distribution +)*
7ull distribution
=aximum moment = L 7l L 0%%;% L ,.%% k&m for bridge deck
Eence* average ,.%%: L .%% k&m per beam
+&
-b =(%b =2b =%b & %b 2b (%b b
K
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E(ample load distribution ,)*
4eal distribution (case L ' and L %)
=aximum moment = L 7l L 0%%;% L ,.%% k&m for bridge deck
Eence* average of ,.%%: L .%% k&m per beam #eam position % 36;,.%%L ''2% k&m
#eam position b -%62.%% L -;.% k&m
2+(%+8
+&2
&+8
-&+*
P>,
-1
0
1
2
-b =(%b =2b =%b & %b 2b (%b b
K
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E(ample load distribution )*
4eal distribution (case L ' and L %)
=aximum moment = L 7l L 0%%;% L ,.%% k&m for bridge deck
Eence* average of ,.%%: L .%% k&m per beam #eam position ':3b 36,%.%%L '3%% k&m
#eam position b -%6;,.%% L -'2% k&m
&+(8
+,&
2+%&
+,8
+2*
P>,
+&&
&+&2
-&+'-&+(%
-1
0
1
2
-b =(%b =2b =%b & %b 2b (%b b
K
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E(ample load distribution *)*
Fariable load moment of all beams due to loaddistribution
agging moment of '3%% k&m Eogging moment of ;.% k&m
!omposite element prefab beam with in-situtopping
(& m
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Distribution of shear load
pread of tan 3:; is taken into account
tan2( ?EC3 @ %)AB
'&& "/
%&& "/
2&& "/
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$oment in dec.
agging moment
Eogging moment
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Cross section analysis
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Cross sectional properties
8 L centroid MmmN
epL excentricity of pre-tensioning
1 L area Mmm3
N L section modulus Mmm;N
I L moment of inertia Mmm,N
k L kern MmmN
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'nalysis of cross section
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#imit criteria in S#S
tresses and cracking in cross section* influenced
by long term loading !hange of stresses
/ensile stresses (flexural tensile cracking)
!ompressive stresses "ocal stresses
$xcessive crack width
Deflection $xcessive deflection
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"inear behaviour
1 and I are transformed cross sectional properties
=xis bending moment (G and B) at section x
+mis prestressing force (ex:including losses of prestress)
8tand 8bare 8-coordinate of top and bottom fibres
Stresses in cross section
A
Pm
I
zeP tm
I
zeP bm
-
+
-
-
+
I
zM bx
e
dh
Vx Mx
Npz
b
z
t
I
zM tx
A
Pm
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Tensile stresses
7lexural tensile strength of concrete
!racking patterns of pre-tensioned beams
ctmctmflctm ff
hf ,
10006.1max,
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7lexural tensile cracking
!racking of top fibers cracking of bottom fibers
(after release) (after =x)
Tensile stresses
ePz
I
A
P
z
IfM m
t
m
t
flctmr
,
+
-
flctmf ,
flctm
f,
+
-
xm
b
m
b
flctmr MePz
I
A
P
z
IfM
,
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educe head tensile stresses
#eam head stresses are too high (; =pa)
Debonded strand at beam end
Inclination of strands with pressure point
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Compressive stresseschanges under long-term loading
1
10
0,
ttforMMM
tttforMM
PPP
ltgx
gx
rscmtm
APm I
zePm t
I
zePm b
-
+
-
-
+
I
zM bx
e
d
h
Vx Mx
Pmzb
zt
IzM tx
A
Pm
-
-
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Composite/ beam and dec.
!omposite action between
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Change of stresses
!hange of stresses in strands and concrete dueto time dependent loss of pre-stressp*cHsHr byshrinkage* creep and relaxation
P.Q at time after release of prestress P '%Q at time of erection of elements and
imposed loading P 3.Q at infiniy (.% years)* but more
indicative
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Design calculation
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$ain design parameters
Depth of unit
trand pattern
Degree of prestress
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"ongitudinal strands anchored by bond +restressed steel wires or strands
"ongitudinally placed in bottom and web of unit
2-wire Rhelical strandS of '36. or '.62 mm diameter
9ltimate tensile strength is '2% k& and 3>% k&* respectively&o longitudinal reinforcement bars
hear reinforcement tirrups
+ro5ecting reinforcementEead reinforcement
ZIP reinforcement
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Some characteristic strengths
!oncrete !,%:.% to !0%:2. utili8ed
!haracteristic compressive strength is ,%T0% =pa
trands
!haracteristic tensile strength for strands is '2%%T'%% =pa
+re-stress level is ';.% U ',.% =+a
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0ailure modes in 1#S
!racking and failure of concrete
#alanced failure design
7lexural compression failure
7ailure of prestress
Vielding (rupture) of the strands
1nchorage failure of strands
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Good design is balanced failure design
1t increased loading from " to 9" #eam starts cracking followed by
yielding of strands such that extensive cracking occurs and largedeflections
finaly followed by failure of concrete compression 8one
2alanced failure design
Ncu
= 0.8bxfcd
Npu
cu
pu
1t 9" strain and stress distribution are
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2alanced failure design
p [N/mm2]
p []
FeP1860
1570
1260
6.5 20.0
p in SLS
pu = p + p
pu in ULS
&cu L &pu
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0le(ural compression failure!rushing of concrete compression 8one prior to
failure (over-reinforced cross-sections)
p in SLS
pu in ULS
p [N/mm2]
p []
FeP1860
1570
1260
6.5 20.0
pu = p + p
Npu > Npu
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3ielding 4rupture5 of strands
Vielding of strands prior to failure (under-reinforced cross-sections)
p [N/mm2]
p []
FeP1860
1570
1260
6.5 20.0
p in SLS
pu in ULS
pu = p + p
Npu < Ncu
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'nchorage failure of strands
1nchorage failure capacity (rotational model)
hear force affects crack due to bending moment so that it
forms an angle xto the strands
00
0 90 V
Vxx
ca
pa
VV
xdNM
4.0
()H 8&H
crackeduncracked
&p
&cu
Fc
a aH
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'nchorage failure of strands
1nchorage and tensile capacity of strands
bpd
pmpdptbpd
fll )(
22
bpt
pm
pt
ptptptpt
fl
llll
021
21 2.1,8.0
lpt1
atreleae
Pi
Pd at ULS
P
lpt2 lbpd
Np!(Pi, P)
Np
dista!"
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$ain design parameterstandardised strand pattern
#$P ma;imumnumber 2+)mm
)&& )&
'&& )(
*&& )'
,&& )8
8&& '2
&&& ')
&& ',
2&& *
(&& *%
%&& **)&& ,&
'&& ,(
*&& ,'
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Shear force
Shear
stress
area
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Interface ZIP beam-dec.
i i f
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Stirrup reinforcement
tandardisation of stirrups
S i i f
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Stirrup reinforcement
tandardisation of stirrups
P 6 i i
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Pro6ecting stirrups
Sti d d ti
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Stirrups and production
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Detailing
# l t
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#ocal stresses
1nchorage stresses in the transmission 8one #ursting and spalling* related to distribution of
prestress force over cross-section
plitting due to bond action
splitting
spalling
b)rsting
e0
spalling
Bond stress
slip
strand
Ribbed bar
C t d t
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Concrete product
!oncrete cover
/olerances of product
S
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#ridge deck
#ridge beam and in-situ deck
#ridge beam
Summary
