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  Arch Bridges Software

Case study & Reseach
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Case Study Double Arches vs. Diagonal Arch




This case study applies ICDAS AS 2014.00R and compares deformations of two arch bridges. The reference model has traditional double

arches of cross section 500x300x20. The other diagonal arch has cross section 600x1200x20. Both models carry the same deck of 35.1m

span used as a roadway. The main dimensions are as shown below.




Alternative Text

Main dimensions

  

Arch height to span ratio, H/L = 17874/35100 = 0.509

Arch cross section to span ratio, h/L = 500/35100 = 0.014

Deck depth to span ratio, d/L = 645/35100 = 0.018


Alternative Text

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Reference model

Thickness of plates 10 and 16mm (Top plate not shown)
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Diagonal Arch model

Equivalent thickness top of deck (incl. stiffening ribs)

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123456789_123456789_1123456789Vertical deformation 

123456789_123456789_1123456789 ArchRef.gif
Reference model, vertical deformed values (m)
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Diagonal model, vertical deformed values (m)
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Figure: Animated deadload deformation (m)

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123456789_123456789_1 123456789Reference model

The centre of the deck has a 42mm vertical deflection. The arches deform 30mm at the top points. The top diagonal deforms only 38mm at the centre when its weight is delivered to the arches. The regular deformed values of the arches and the deck confirm a good system for carrying gravity loads.




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Diagonal Arch model (linear analysis vs. non linear)

Irregular deformations occur in this situation. The deck is deformed 61/10 ~ 6 times the arch, and 61/42 ~ 1.45 times the case of double arches.

This effect appears due to the fact that the 3D hanger system does not support the deck vertical effectively. The longest inclined hanger has a big sag of 2.042m due to its self weight. Thus, geometric non linear analysis should be applied when the load and deflection are no longer increasing proportionally at the deck location of the long inclining hangers. Prestressed hangers (cables) can be used to increase system stiffness of the hangers and to reduce the vertical deflection of the deck. In this case the vertical component of the hanger force should be equal to the weight of the hanger segment of the deck (multiplied by 9.82m/s2). Knowing the segment weight, one can calculate the tension force F in the hanger needed in the non linear analysis. The hanger in this case must be cable element with an initial prestressing force F as input.

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Diagonal Arch with Cross-Ties model, 
vertical deformed values (m)
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   One possible method to reduce the vertical deflection of the hangers is to increase the in-plane stiffness of the
hangers by connecting them together with a set of cross-ties as shown in the figure above.

To keep the calculation simple the linear analyse being used. The cross-ties are modelled as beam 

elements carrying both tension and compression. No prestressing forces introduced, 

i.e. the deflections of the deck and the arches will keep unchanged as the model without the cross-ties.

The vertical deformation of the longest hanger is now reduced by a factor 844/2029=0.42

From a dynamic perspective, the properties of the single hangers are modified by 
the presence of the lateral constraints that influence their oscillation characteristics too.


123456789_123456789_1123456789Longitudinal deformation 

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Diagonal model, Top view
 DX DiaArchTra.jpg

Diagonal model with Cross-Ties, Top view

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Longitudinal DX deformation, Deadload (m)
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123456789_123456789_1123456789Lateral deformation 

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Diagonal model, Top view 
 DY DiaArchTra.jpg

Diagonal model with Cross-Ties, Top view

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 Lateral DY deformation, Deadload (m)
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Because the cross-ties are assumed to carry both compression and tension, the longitudinal deformation DX now reduces by a factor

341/1866 ~ 0.18 at the longest hanger. On the other hand, the lateral deformation DY increases by a factor 1198/1010 ~ 1.19. 

I.e. about 19% more gravity from the hangers system now deliver to the bridge center when they are tied together. Note that figures with

cross-ties show significant deformations compared to the model without cross-tiesIt is due to the deformed scale in the cross-ties 

system is in relation to DZ of 844mm, while the other system to DZ of 2029mm.

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123456789_123456789_1123456789Mz about vertical axes perpendicular to the arch 

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ArchRef.gif
Animation of Deadload deformation in Top View (hangers are not shown)

Animation above shows bendfing moment Mz about vertical axes pependicular to the arch element (kNm)

The hangers on one side cause bending for the arch about its vertical axes of max Mz=1733kNm. 

Note that the so called "vertical axes" is perpendicular to the arch elements which are curved. 

I.e. Mz = 3100kNm at the foundation is about the axes perpendicular to the arch, but not vertical.

The same for the hangers on the other haft of the arch.

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123456789_123456789_1123456789My about horizontal axes 

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DY DiaArchTra.jpg
My about horizontal axes of the arch element, Deadload (kNm)

My = 45kNm is found on top of the arch at deadload, where the vertical deformation here is only 10mm.
Mz = -558kNm at the foundation.
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123456789_123456789_1123456789Hulme Arch Bridge, England 1997 

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Participants


Owner

·   Manchester City Council


Architecture

·   Chris Wilkinson Architects

·   Keith Brownlie (architect)


Consulting engineers

·   Ove Arup & Partners


Contractor

·   Henry Boot Construction


Steel construction

·   Watson Steel Ltd.


Cable steel supplier

·   Bridon International (suspenders)



Road Bridge

Raise 25m
Total length 52m
Deck width 18m

cf. 
http://structurae.net/



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