Precast Bridges: Design for Time Dependant Effects Precast...

Naples2006/06Camara, J.; Hipólito, A.

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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


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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


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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+


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2.1. Case Study: Base solution

Longitudinal Geometry


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2.1. Case Study: Base Solution

Transversal Geometry

Beam selected for the study


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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


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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


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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


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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


Bottom Beam Fiber Stresses (kPa)Modified Solution

Stresses Control

Less variation in time

Less sensible to variations of

time dependant parameters


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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


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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


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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


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Naples 2006, The Second FIB Congress

Precast Bridges:Design for Time Dependant Effects

Thank you for your time


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( )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

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