Institut of Concret Constructions - · PDF fileInstitut of Concret Constructions Bridge Design...
Transcript of Institut of Concret Constructions - · PDF fileInstitut of Concret Constructions Bridge Design...
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Bridge Design 1
Load Bearing Systems
Steffen Marx
Institut of Concret Constructions
Bridge Design
Bridge Design 2
Cross-section design
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Bridge Design 3
Concrete Slabs
• Span up to 20m (maximum 30m) (beyond that uneconomic because of high dead load)
• Slab thickness ≤ 80 cm
• Possible slenderness L/d
rc 15 … 20
pc 18 … 30 (35 in case of continuous beams)
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Concrete Slabs (Transversal gradient)
With side pitch
With roof pitch
inclined bottom side
horizontal bottom side
• less concrete, steel, prestressing
• less concreting effort (plane surface)
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Bridge Design 5
Slab design – street bridge cross sections
Increase of visible slenderness
[F. Leonhardt: Bridges ]
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- usual spans for T-Beams
- 15 m … 40 m … 70 m single span continuous span
T-Beams
rc pc
web without flange
8 ... 10 10 ... 18
web with flange 10 ... 14 12 ... 24 (... 35)
l/d = 15 most economic large increase of costs!
- web thickness ≥ 18 cm rc ≥ 22 cm pc
elements precastfor
- slenderness
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T-Beams
- very favorable for single span! Especially for precast
- advantageous for
- spans 20 ... 35 m - many girders - limitations in falsework (traffic clearance)
- in case of negative moments or high reinforcement or at bearings
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T-Beam cross-sections
Increase of torsion stiffness
Slenderness 14-16 Cross-girder in L/2
Slenderness 20 Very economic variant [F. Leonhardt: Bridges ]
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Box Girders
- very good for cont. girders (good capacity for both, neg. and pos. bending)
- very high torsional stiffness
- very suitable for curved alignment
- Spann 30 m ... 70 m (120 m) constant constr. depth
70 m ... 250 m with haunch - Slenderness (for constant constr. depth)
15 ... 25 ... (30 to 40, depending on ratio of dead / life load (for incremental launching without auxiliary piers)
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Box Girders (design of cross-section)
L
hs hm ≈ 13+2∙L[m] ≥ 20 [cm]
≥ 60cm (internal tendons) ≥ 40cm (external tendons)
≥ 17…20cm (min) In case of free cantilevering up to 2m and more
hs ≈ 2 ∙ hm ≤ 60cm
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Box-girder – typical highway bridge in California
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Box-girder – typical motor way bridge in Europe
> 30m
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Bridge Design 13
Box-girder – typical rail way bridge in Europe
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Basic types of Bridges
[Man-Chung Tang Chairman of the Board T.Y. Lin International San Francisco, USA ]
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Beam Bridges
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Valley Bridges – relation of span and height
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Valley Bridges – relation of span and height
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Box Girders Haunched Systems
Proportioning of spans (optimum for deflection in side- and midspan)
Limit of slenderness ca. l/hs =25 and l/ht =50
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Bridge Design 19
Beam Bridge – favorable and unfavorable haunches
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Beam Bridge – relation of sub- and superstructure
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Bridge Design 21
Beam Bridge – relation of sub- and superstructure
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Frame Bridges
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Frame Structures
• Single span frames (mostly two-hinge-frames, sometimes fixed)
• Max. span ca. 70 m
• Up to 50 m without dilatation joint (with special construction of the approaching structure)
Attainable moment at the corner depending on ratio h/l !
Bridge Design 24
Frame Structures
• Slenderness ca. L/17 at the corner ca. L/30 … L/50 in the field
• Cross-sections: < 25 m: slab 25 – 50 m: corner: box-girder field: T-beam
> 50 m: box-girder
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Bridge Design 25
Frame Structures
• Prestressing of frames:
large span frames are vulnerable of deformations!
creep and shrinkage + displacement of fundation may lead to a loss of H-forces
= increase of field moment
Prestressing of the beam with σ = const for t = ∞ under dead load in center of span
Abutments usually without prestressing
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Frame Structures – strutted Frames
[F. Leonhardt: Bridges ]
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Multi Span Frames
• Monolithic connection between superstructure and piers
Advantages: • No bearings + joints
• Distribution of breaking
forces to all piers
• High slenderness
Disadvantages: • Large constraining
forces (Temp + c + s)
• No regulation of settlements are possible
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Multi Span Frames
Expansion length
Constrain forces mainly depending on pier height L and stiffness EI and expansion length
M = 6∙EI∙u/L²
Important check during preliminary design: Reinforcement practicable???
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Multi Span Frames
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Frame Structures – strutted Frames
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Frame Structures – multi span frames
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Arch Bridges
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Arches
“real” arch
Strut arch with stiffening girder Fixed arch
Two-hinge arch
f/L ≥ 1/7 … 1/3
f/L ≥ 1/10 … 1/6
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Arches
• Conceptual aspects:
Span: 50m … 200 m
Small f/L → large influence of c+s+T and of displacements of
abutment
Girder over the whole length without joints! (joints only at the
bridge ends)
Slenderness of girder in approaching structure ca. 12…15
Construction depth of girder = constant → additional bending
must be carried by the arch
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Arches
• Stiff arch: advantage: quick removal of scaffold possible, free cantilevering possible
• Slender arch: advantage light-weight-scaffold (but must remain until stiffening girder is placed
• Favorable topography: one large span, many small span:
V-shaped valleys
Rivers
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Arches
• Cross-sections:
arch: small span: slab
medium span (up to 150m):
large span: box girder
girder: slab, T-beam, box-girder depending on span and stiffening
• Prestressing: only the girder (no tension stresses for dead load + frequent part of live load)
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Arch Structures – with underlying deck
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Arch Structures
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Arch Structures
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Arch Structures – with deck on top
[F. Leonhardt: Bridges ]
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Arch Structures
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Arch Structures
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Arch Structures – Real Arch
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Arch Structures – Strut Arch
[SBP]
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Fritz Leonhardt:
Kniebrücke over the Rhine,
Düsseldorf, Germany
[D.J. Brown: Brücken]
Tension Systems
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Bridge Design 47
Pùnt da Suransuns, Jürg Conzett, Post tensioning, Stress ribbon, 40 m, 1999