View source for Design for half-through construction

__SECTIONLINKTOTOP__
The structural configuration of a [[Half-through_bridges|half-through bridge]] generally creates a linear rectangular [[Half-through_bridges#U_frame_configuration|U–shaped trough]], the vertical legs being the main girders and the horizontal being the bridge deck. Design of such bridges requires consideration of the interaction between the transversely spanning action of the deck and the longitudinal spanning of the main beams. The interaction is generally referred to as U-frame action.This article introduces the design considerations for [[Half-through_bridges|half-through bridges]], with references to design standards where appropriate.
{{#image_template:image=File:R5_Fig8.png|caption=General arrangement of a half-through bridge|align=right|wrap=true|width=500}}

==Structural behaviour==
While the structural behaviour is essentially a simple hierarchical progress of slab spanning between cross girders, cross girders spanning between main girders and main girders spanning between supports, the key structural ‘element’ that requires special design consideration is the [[Half-through_bridges#U-frame_configuration|‘U-frame’]] that is created by a cross girder and the two vertical [[Stiffeners|stiffeners]] to which it is connected.  The need for frames is to provide intermediate lateral restraint to the top flanges, which are in compression.  Such intermediate restraint is able to constrain the buckling mode of the top flanges, as shown below left.

The restraint provided by each [[Half-through_bridges#U-frame_configuration|‘U-frame’]] depends on the three components – cross girder, vertical [[Stiffeners|stiffeners]] and the [[Connections_in_bridges|connections]] between cross girder and main girder.  The restraint can be expressed in in terms of a flexibility under unit lateral load, as shown below right.
<gallery mode=nolines widths=380px heights=300px> 
Image:R15_Fig1.png|Constrained buckling mode of top flanges
Image:R15_Fig2.png|Flexibility of a 'U-frame' 
</gallery>
<br>
The influence of this flexible restraint on the design of the main girder is discussed below.

Global analysis to determine load effects is usually carried out using a [[Modelling and analysis of beam bridges#Grallage analysis|grillage model]].  For railway bridges it is usually sufficient to have a line of nodes along the rail lines, as well as along the main girder, and across every cross girder for closely spaced cross girders (up to 1500mm spacing).  For highway bridges, a finer mesh will be needed, similar to that for [[Ladder_deck_composite_bridges|ladder deck bridges]].

==Design basis==
===Loading===
{{#image_template:image=File:R15_Fig3.png|caption=Restraint of loaded [[Half-through_bridges#U-frame_configuration|‘U-frame’]]|align=right|wrap=true|width=500}}
The loading arrangement to give maximum effects in the main girders is easily determined.  A line beam analysis would give adequate results.  Evaluation of the effects on the cross girder and their [[Connections_in_bridges|connections]] require more detailed consideration.  For a railway bridge, an ‘axle load’ (one of the 250 kN point loads in the Load Model 71 of BS EN 1991-2<ref name="No1">BS EN 1991-2:2003. Eurocode 1: Actions on structures. Traffic loads on bridges. BSI</ref>) should be positioned over the cross girder  being considered and the Uniformly Distributed Load (UDL) should be present on both sides.  The effects induced in the cross girder by this loading depends on the stiffnesses of the slab and cross girder and is best determined by the [[Modelling and analysis of beam bridges#Grillage analysis|grillage model]].  

Maximum end moments on a cross girder occur when one cross girder is more heavily loaded than its neighbours.  Under direct load, a cross girder bends and the uprights of the [[Half-through_bridges#U-frame_configuration|‘U-frame’]] want to lean inwards, but they are partially restrained by the top flange, spanning between the adjacent [[Half-through_bridges#U-frame_configuration|‘U-frames’]], as illustrated right.

The loading that gives the most onerous value of force F<sub>c</sub> is with all the loading to one side of the cross girder, as shown below.
{{#image_template:image=File:R15_Fig4.png|caption=Loading for maximum end moment on a cross girder|align=left|width=500}}
Load effects on highway bridge cross girders also depend on the stiffness of the [[Half-through_bridges#U-frame_configuration|‘U-frames’]] and similar dispositions of loading apply.

===Governing criteria===
The design must consider the criteria of :
*[[Design_for_half-through_construction#Fatigue|Fatigue]]
*[[Design_for_half-through_construction#Deformation_performance|Deflection performance]] 
*Strength
<br>
For highway bridges, design is usually controlled by strength, with some details controlled by [[Fatigue_design_of bridges|fatigue]].  For railway bridges, [[Design_for_half-through_construction#Fatigue|fatigue]] and [[Design_for_half-through_construction#Deformation_performance|deformation performance]] are much more significant and strength may be a lesser consideration (because a design that satisfies the other criteria, will usually be strong enough).

Most half-through bridges are replacements for an existing structure, or on the line of an existing railway or road.  Buildability is often the most significant factor in choosing the structural configuration.  For guidance on the considerations needed for railway bridges, refer to [[#Resources|SCI P318]].

==Fatigue and deformation performance==
===Fatigue===
{{#image_template:image=File:R15_Fig5.png|caption=Doubler plate detail|align=right|wrap=true|width=400}}
The principles of [[Fatigue design of bridges|fatigue design]] are the same for [[Half-through_bridges|half-through bridges]] as for other forms of bridge, namely:
*Determine the loading events and their frequency
*Classify the detail under consideration, in terms of its performance under cyclic loading
*Determine the fatigue life of the detail under the design loading history
<br>
The cross girders in [[Half-through_bridges|half-through bridges]] have a particularly onerous loading cycle, since most of the load is a variable action (traffic load) and the effects for each loading event are a high proportion of the maximum design value.  This is particularly true for railway bridges, where Load Model 71 is used for both Ultimate Limit State (ULS) and fatigue loading, and there are four ‘axles’ for each loading event.  The onerous nature of the loading applies also to the [[Connections_in_bridges|connections]] to the main girder.

With onerous loading cycles, there is a strong incentive to use the ‘best’ fatigue details, but there are certain details where only lower class details can be used, notably:
*Doubler plate terminations
*Cross girder [[Connections_in_bridges|connections]].
<br>
A typical doubler plate detail is shown above right.  At its ends, the doubler plate is tapered in plan and in elevation, to smooth the stress flow as much as possible, but a [[Fatigue design of bridges#Detail categories|detail category]] 36 (in accordance with BS EN 1993-1-9<ref name="No2">BS EN 1993-1-9:2005. Eurocode 3: Design of steel structures. Fatigue. BSI</ref>) is inevitable for thick flanges.  The [[Connections in bridges#Fillet welds|fillet weld]] attaching the doubler must be checked as a [[Fatigue design of bridges#Detail categories|detail category]] 80 in shear, for the stress flow transferred.

At cross girder [[Connections_in_bridges|connections]], there is often a plate welded onto the face of the web, as shown below.  Discontinuous plates (i.e. a separate ‘patch plate’ at the end of each cross girder) introduce [[Fatigue design of bridges#Detail categories|detail categories]] 80 and 71 into the web.  Shear is transferred through [[Fatigue design of bridges#Detail categories|category]] 80 fillet welds.  If the plate were continuous, the detail on the web would be [[Fatigue design of bridges#Detail categories|category]] 100, but the shear transfer through the [[Connections in bridges#Fillet welds|fillet weld]] is still [[Fatigue design of bridges#Detail categories|category]] 80.  The [[Connections_in_bridges#Bolted_connections|bolted connections]] use preloaded bolts and provided that the preload is maintained under fatigue loading there is no special concern.  The [[Connections_in_bridges|connections]] at the ends of the cross girders introduce further [[Fatigue design of bridges#Detail categories|category]] 80 in shear; a suitable size [[Connections in bridges#Fillet welds|fillet weld]] must be chosen.
<gallery caption="Cross girder end [[Connections_in_bridges|connection]] details" widths=380px heights=200px> 
Image:R15_Fig6.png
Image:R15_Fig7.png
</gallery>
<br>
Cross girders are usually [[Steel_construction_products|rolled sections]] and free from welding in their midspan regions (except where stud connectors are welded on top).  The fatigue classification is therefore good.  However, it is best to avoid any welded attachments (such as to support services) in these midspan regions as they would introduce lower classes into regions that experience a particularly onerous fatigue loading.

===Deformation performance===
The comfort and safety of railway traffic is sensitive to the deformation performance of bridges and although [[Half-through_bridges|half-through bridges]] are not intrinsically more susceptible, the structural configuration and high ratio of live to dead load mean that deformation performance is a prime consideration.  Two of the most common aspects that need to be checked are twist and gradient at the end of the span.  The effects are illustrated below.
Deflection limits for railway bridges are given in Annex A of BS EN 1990<ref name="No3">BS EN 1990:2002+A1:2005. Eurocode: Basis of structural design. BSI</ref> and these are adopted in GC/GN5612<ref name="No4">[http://www.rssb.co.uk/rgs/standards/gcgn5612%20iss%201.pdf Guidance on Loading Requirements for the Design of Railway Structures. Railway Group Standard GC/GN5612 (Issue 1, 2014). RSSB.]</ref>, although there is a correction / clarification that for the calculation of vertical deformation, the effects from railway traffic should be multiplied by the dynamic factor (Φ) as well as the load classification factor (∝). 
<gallery caption=" " widths=380px heights=200px> 
Image:R15_Fig8.png|Twist in a skew span
Image:R15_Fig9.png|Change of gradient between adjacent spans under live load
<br>
</gallery>

==Design resistance of main girders==
===Effective section===
It is usual to neglect the contribution of the deck to the resistance of the main girders at ULS but interaction must be considered at the Servicibility Limit State (SLS) – notably in determining shear flow between deck and main girders near the ends of the span and in determining crack widths in the concrete slab.

===Bending resistance===
The main consideration in determining the resistance of the main girders is the stability of the top flange in compression.  As mentioned above, restraint is provided by the [[Half-through_bridges#U-frame_configuration|‘U-frame’]]; it is therefore necessary to consider their effectiveness in preventing buckling of the top flange.

The buckling behaviour of the top flange of a simply supported half-through bridge is actually a distortional buckling phenomenon (the deflected shape of the [[Half-through_bridges#U-frame_configuration|‘U-frame’]] is a distortion of the cross section) but BS EN 1993-2<ref name="No5">BS EN 1993-2:2006. Eurocode 3: Design of steel structures. Steel bridges. BSI</ref> only recognises [[Design_of_beams_in_composite_bridges#Introduction_to_lateral_torsional_buckling|lateral torsional buckling]] slenderness and the rules for determining the parameter [[file:LambdabarLT.png|25px]] need to be followed. 

Clause 6.3.4.2 of BS EN 1993-2<ref name="No5"></ref> offers a method that can be applied to lengths between effective lateral restrains and with flexible intermediate restraints. This method is based on a beam-on-elastic-foundation (BEF) model. This underlying BEF model is of an infinitely long beam/strut subject to axial load and restrained at intervals by lateral springs, as shown diagrammatically below.
{{#image_template:image=File:R15_Fig10.png|caption=Beam on elastic foundation model|align=left|width=600}}
However, the clause rules cannot be used for flexible end restraints (which is the likely situation, since end [[Half-through_bridges#U-frame_configuration|‘U-frame’]] will not be ‘rigid’). To remedy this deficiency, PD 6695-2<ref name="No6">PD 6695-2:2008+A1:2012. Recommendations for the design of bridges to BS EN 1993. BSI</ref> (Section 9) provides an adjustment  to the m parameter in clause 6.3.4.2.

Alternatively, elastic critical buckling resistance can be determined by a finite element buckling analysis and this will lead to the determination of design resistance of the main girder.

===Toughness===
BS EN 1993-1-10<ref name="No7">BS EN 1993-1-10:2005. Eurocode 3: Design of steel structures. Material toughness and through-thickness properties. BSI</ref> gives rules for limiting thickness of elements to avoid [[Material selection and product specification#Fracture toughness|brittle fracture]] and these rules are amplified by the UK National Annex<ref name="No8">NA to BS EN 1993-1-10:2005. UK National Annex to Eurocode 3: Design of steel structures. Material toughness and through-thickness properties. BSI</ref> and PD 6695-1-10<ref name="No9">PD 6695-1-10:2009 Recommendations for the design of structures to BS EN 1993-1-10. BSI</ref>.  In most cases, these rules lead to the selection of ‘ordinary’ [[Material selection and product specification#Fracture toughness|sub grades of J2 or K2]] quality.  However, when doubler plates are terminated on a tension flange, the detail is ‘severe’ (i.e. the adjustment of reference temperature is −30&deg;C) and, coupled with significant tensile stress and the use of thick material, would require the use of the highest [[Material selection and product specification#Fracture toughness|toughness quality]] (ML or NL) – and even those sub-grades may not be tough enough.  Doublers on tension flanges should therefore be taken the whole length of the span in a simply supported bridge or into a compressive region in a multiple span bridge.

==Design resistance of cross girders==
The cross girders usually act compositely with the slab, or with a steel deck plate.  For composite girders, adequate [[Shear_connection_in_composite_bridge_beams|shear connection]] must be provided.  In most cases, the deck will be in tension due to global effects and bond should not be relied upon to provide the connection.  Reinforcement passed through holes in the web or [[Shear_connection_in_composite_bridge_beams#Headed stud shear connectors|shear connectors]] on top of the girders will achieve the necessary connection.  Since the cross girders are predominantly in sagging bending (there are only small end restraint moments arising from [[Half-through_bridges#U-frame_configuration|‘U-frame’]] effects) there are no [[Design_of_beams_in_composite_bridges#Introduction_to_lateral_torsional_buckling|lateral torsional buckling]] considerations, even when the slab or plate is on top of the girder (rather than encasing or partly encasing it).

==Best practice details==
In the drafting of [[#Resources|SCI P318]], a range of preferred details was drawn up, based on advice from designers and fabricators.  Comments were given on their suitability in terms of [[Fatigue_design_of_bridges|fatigue]] endurance, [[Design_for_steel_bridge_construction#Fabricating_the_steelwork|fabrication]], [[Design_for_steel_bridge_construction#Bridge_erection|installation]] and [[Corrosion_protection|durability]].  Refer to that publication for detailed advice.

An example of a preferred detail is shown below.
{{#image_template:image=File:R15_Fig11.png|caption=Preferred detail for cross girder connection in a half-through railway bridge|align=left|width=600}}

==References==
<references/>

==Resources==
*[[Media:SCI_P318.pdf|Iles, D.C. (2004) Design guide for steel railway bridges (P318) SCI]]
*[[Media:BCSA_51-10.pdf|Steel Bridges: A practical approach to design for efficient fabrication and construction. (51/10). BCSA]]
*[[Media:SCI_P185.pdf|Hendy, C.R.; Iles, D.C. (2015) Steel Bridge Group: Guidance Notes on best practice in steel bridge construction (6th Issue). (P185). SCI]]
**[[Media:GN_1-10.pdf|Guidance Note 1.10 Half through bridges]] 
**[[Media:GN_2-10.pdf|Guidance Note 2.10 Steel deck plate for footbridges]]

==See also==
*[[Half-through bridges]]
*[[Material selection and product specification]]
*[[Modelling and analysis of beam bridges]]
*[[Shear connection in composite bridge beams]]
*[[Fatigue design of bridges]]
*[[Stiffeners]]
*[[Connections in bridges]]
*[[Bridge articulation and bearing specification]]
*[[Skew bridges]]
*[[Design for steel bridge construction]]
*[[Design of steel footbridges]]

==External links==

*[https://www.standardsforhighways.co.uk/dmrb/ Highways England DMRB (Design Manual for Roads and Bridges)]
*[http://www.standardsforhighways.co.uk/ha/standards/mchw/index.htm Highways England MCDHW (Manual of Contract Documents for Highway Works)]
*[http://www.steel-sci.com/the-steel-bridge-group.html The Steel Bridge Group (SBG)]

[[Category:Bridges]]
[[Category:Index of main articles]]