precast bridges: design for time dependant effects precast...
TRANSCRIPT
Naples2006/06Camara, J.; Hipólito, A.
Pre
cast
bridg
es
Desig
n f
or
Tim
e D
epe
nda
nt
Eff
ects
Naples 2006, The Second FIB Congress
Precast Bridges:Design for Time Dependant Effects
Camara, José – Associated Professor at Instituto Superior Técnico, Lisbon
Hipólito, António – Msc in Structural Engineering, Project Dept. Manager at
Mota-Engil, Lisbon
Naples2006/06Camara, J.; Hipólito, A.
Pre
cast
bridg
es
Desig
n f
or
Tim
e D
epe
nda
nt
Eff
ects
Objectives
1. Present a mathematical tool to take into account time
effects in a simply and rational way
2. Study the influence of prestress layout on structural
behaviour and economy
3. Study the influence of construction procedure on the
prestress value
Naples2006/06Camara, J.; Hipólito, A.
Pre
cast
bridg
es
Desig
n f
or
Tim
e D
epe
nda
nt
Eff
ects
1. Mathematical Tool
( )121 SS1
SS −χϕ+
ϕ+=∞
Usual Formula
L
q
Structural System 1
L
q
Structural System 2
Long Time Analysis
Deformations
Curvatures
Stresses
Efforts
( )[ ]( )i,1i,2
ef1
'1
i,1'1
σ−σχϕ+
ϕ∆+σ=σ∞
( )2
'1
1
'0,1
R
1
R
11
R
1
⋅ϕ∆+
⋅ϕ+=
∞
( ) 2'11
'0,11 δ⋅ϕ∆+δ⋅ϕ+=δ∞
( )[ ]( )12
ef1
'1
1 MM'1
MM −χϕ+
ϕ∆+=∞
Basis
Proposed Formula
∆ϕ’1 = ϕ’1 (t∞, t0) - ϕ’1 (t1, t0)
( )[ ] ( )[ ]1t,1
0t,11ef1
E
E'1'1 χϕ+=χϕ+
Naples2006/06Camara, J.; Hipólito, A.
Pre
cast
bridg
es
Desig
n f
or
Tim
e D
epe
nda
nt
Eff
ects
2.1. Case Study: Base solution
Longitudinal Geometry
Naples2006/06Camara, J.; Hipólito, A.
Pre
cast
bridg
es
Desig
n f
or
Tim
e D
epe
nda
nt
Eff
ects
2.1. Case Study: Base Solution
Transversal Geometry
Beam selected for the study
Naples2006/06Camara, J.; Hipólito, A.
Pre
cast
bridg
es
Desig
n f
or
Tim
e D
epe
nda
nt
Eff
ects
Longitudinal structural system Span section Support section
Phase 1: Positioning of the prefabricated beams
and phase 2: Execution of the beams connection giving continuity to the system.
Phase 3: Concreting of the top slab for 6.0m to each side of the supports
Phase 4: Execution of the remaining slab deck
Phase 5: Finalising the bridge deck (non structural elements).
2.1. Case Study: Base Solution
Construction Procedure
Naples2006/06Camara, J.; Hipólito, A.
Pre
cast
bridg
es
Desig
n f
or
Tim
e D
epe
nda
nt
Eff
ects
2.2. Cable Layout Study
Effective prestress strand number
0,00 26,00 61,00
0
10
20
30
40
50
60
70
0,0 10,0 20,0 30,0 40,0 50,0 60,0 70,0
N
Supports Base solution Cable layout modification
Bigger Sheave Lengths
Smaller Prestress Value
Naples2006/06Camara, J.; Hipólito, A.
Pre
cast
bridg
es
Desig
n f
or
Tim
e D
epe
nda
nt
Eff
ects
2.2. Cable Layout Study
0,00 26,00 61,00 96,00 122,00
fctm = 3800
-18000
-16000
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
4000
6000
0,00 20,00 40,00 60,00 80,00 100,00 120,00
Supports ENVE min ENVE max fctm
Bottom Beam Fiber Stresses (kPa)Base Solution
Naples2006/06Camara, J.; Hipólito, A.
Pre
cast
bridg
es
Desig
n f
or
Tim
e D
epe
nda
nt
Eff
ects
0,00 26,00 61,00 96,00 122,00
fctm = 3800
-18000
-16000
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
4000
6000
0,00 20,00 40,00 60,00 80,00 100,00 120,00
Apoios Service - min Service - max fctm
2.2. Cable Layout Study
Bottom Beam Fiber Stresses (kPa)Modified Solution
Stresses Control
Less variation in time
Less sensible to variations of
time dependant parameters
Naples2006/06Camara, J.; Hipólito, A.
Pre
cast
bridg
es
Desig
n f
or
Tim
e D
epe
nda
nt
Eff
ects
2.3. Construction Procedure Study
Case C� Position of the pre-slabs, 0.10m thick, while in a simple
supported system
� Complementary concrete as in the base solution
Case D� Slab deck totally built on a simple supported system
� Both cases with increased sheave lengths
Naples2006/06Camara, J.; Hipólito, A.
Pre
cast
bridg
es
Desig
n f
or
Tim
e D
epe
nda
nt
Eff
ects
2.4. Results
Long Term Prestress
134.5%10800D
111.5%8950C
100.0%8030B
111.5%8950A
P/PBP [kN]
A: Base solution
B: Base solution + increased sheaves
C: Increased sheaves + precast slabs over simply supported system
D: Increased sheaves + slab deck over simply supported system
Naples2006/06Camara, J.; Hipólito, A.
Pre
cast
bridg
es
Desig
n f
or
Tim
e D
epe
nda
nt
Eff
ects
Conclusions
� The mathematical tool presented, gives a very rational and feasible procedure for structural behaviour evaluation
� Careful design of cable layout, particularly sheave lengths, can grant better structural behaviour and economy
� Construction procedure can influence significantly the prestress values
� For the type of structures studied, beam continuity during construction, is favourable for the prestress value
Naples2006/06Camara, J.; Hipólito, A.
Pre
cast
bridg
es
Desig
n f
or
Tim
e D
epe
nda
nt
Eff
ects
Naples 2006, The Second FIB Congress
Precast Bridges:Design for Time Dependant Effects
Thank you for your time
Naples2006/06Camara, J.; Hipólito, A.
Pre
cast
bridg
es
Desig
n f
or
Tim
e D
epe
nda
nt
Eff
ects
( )121 SS1
SS −χϕ+
ϕ+=∞
Deformations
Curvatures
Stresses
Efforts
1. Mathematical Tool
� Aging Coefficient Method:ϕχ+
=1
EE c
adj,c
� Known simplified formula:
( )[ ]( )i,1i,2
ef1
'1
i,1'1
σ−σχϕ+
ϕ∆+σ=σ∞
( )2
'1
1
'0,1
R
1
R
11
R
1
⋅ϕ∆+
⋅ϕ+=
∞
( ) 2'11
'0,11 δ⋅ϕ∆+δ⋅ϕ+=δ∞
( )[ ]( )12
ef1
'1
1 MM'1
MM −χϕ+
ϕ∆+=∞
( )[ ] ( )[ ]1t,1
0t,11ef1
E
E'1'1 χϕ+=χϕ+
aj,1t,1
aj,1t,chom
E
Ek =
Proposed Formula
Basis of Formulation
Scales creep’s
influence