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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)

Bridge Design 4

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 ]

Bridge Design 6

- 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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Bridge Design 7

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

Bridge Design 8

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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Bridge Design 9

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)

Bridge Design 10

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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Bridge Design 11

Box-girder – typical highway bridge in California

Bridge Design 12

Box-girder – typical motor way bridge in Europe

> 30m

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Bridge Design 13

Box-girder – typical rail way bridge in Europe

Bridge Design 14

Basic types of Bridges

[Man-Chung Tang Chairman of the Board T.Y. Lin International San Francisco, USA ]

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Bridge Design 15

Beam Bridges

Bridge Design 16

Valley Bridges – relation of span and height

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Bridge Design 17

Valley Bridges – relation of span and height

Bridge Design 18

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

Bridge Design 20

Beam Bridge – relation of sub- and superstructure

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Bridge Design 21

Beam Bridge – relation of sub- and superstructure

Bridge Design 22

Frame Bridges

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Bridge Design 23

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

Bridge Design 26

Frame Structures – strutted Frames

[F. Leonhardt: Bridges ]

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Bridge Design 27

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

Bridge Design 28

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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Bridge Design 29

Multi Span Frames

Bridge Design 30

Frame Structures – strutted Frames

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Bridge Design 31

Frame Structures – multi span frames

Bridge Design 32

Arch Bridges

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Bridge Design 33

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

Bridge Design 34

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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Bridge Design 35

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

Bridge Design 36

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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Bridge Design 37

Arch Structures – with underlying deck

Bridge Design 38

Arch Structures

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Bridge Design 39

Arch Structures

Bridge Design 40

Arch Structures – with deck on top

[F. Leonhardt: Bridges ]

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Bridge Design 41

Arch Structures

Bridge Design 42

Arch Structures

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Bridge Design 43

Arch Structures – Real Arch

Bridge Design 44

Arch Structures – Strut Arch

[SBP]

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Bridge Design 45

Fritz Leonhardt:

Kniebrücke over the Rhine,

Düsseldorf, Germany

[D.J. Brown: Brücken]

Tension Systems

Bridge Design 46

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Bridge Design 47

Pùnt da Suransuns, Jürg Conzett, Post tensioning, Stress ribbon, 40 m, 1999