Structure and Analysis Bridge Design brief

Figure 1

Bridge design

Most suitable bridge forms

· Beam bridge

· Arch bridge

The beam bridge: Beam and slab with ladder decks

This form of bridges comprises of slab which sits on top of steel I-beams. This form is mostly used for mid span highway bridge which is where our required bridge falls in.

Slab in this system is supported on tow main girders with a spacing of about 3.5m and it lies longitudinally between the girders as per the below diagram.

Figure 1

The bridge will use plate girders giving us a scope to vary the flange and web sizes to fit and suit the bridge load carrying capabilities. In the design process, ability of the bridge to carry the maximum load expected and the loading at the various stages of construction will guide on the proportion of girders that is their depth, width of tension and compression flanges and web thickness.

The girders are erected firmly on the ground and have stud connectors welded on the top flange to provide composite action between the slab and girder. The number of studs and spacing vary depending on expected level of shear flow between steel girder and concrete slab.

The girders rest on bearings fastened to the bottom flange. The girders are stiffened to carry the bearing loads at these points. Some cases apply bracing between the girders at support to carry lateral forces and provide torsional restraint.

Bridge description

· The bridge will have a span of 50m.

· The bridge will be raised to a height of 10m on both sides to be in level with the existing highway. The girders will have constant height.

· The bridge cross section will have the reinforced concrete slab sitting on top of two main abutment substructures and an extra substructure which will be on the central reservation. The main substructure will be located at the embarkment of the road.

Construction sequence

Abutment substructure construction

Girder construction

The bridge will consist of two main girder I beams. The girders will be of the same height. To make the I-beam, steel plates will be used. The steel plate is cut into the required sizes for the bottom flange and top flange and for the web. The cut pieces are then fillet welded into the I-section. This is done either by machine manual assembling in jig or through improved pressing machine specially made for the job. And later welded on both sides to make the weld continuous. This form an inverted T repeating the process with the second flange now produces the I-girder.

To increase load carrying capacity of the I-section vertical stiffeners are added to the web (Vayas, & Iliopoulos 2013). They may consist of plate cut of equal or smaller thickness which is controlled by making the web of thicker. The girders are painted except the final coat which is done at the site after erection. On the site the substructure abutment are made ready and given time to heal before taking the girders. The girder sections are joined as per the length of the bridge at the site splice positions. Cranes are used to place the girder on the constructed sub structure. To join two girders, bolted splices using cover plates placed on both sides of the flange to overlap the ends of both girders are used.

A frame work made of glass reinforced plastic panels is made to support concrete. The glass reinforce plastics forms the formwork where the concrete is put. To strengthen it girders and bracers are made adequate and enough to carry the weight of wet concrete. Additionally, temporary cross bracing can be provided in midspan areas to support the girders thus stabilizing the compression flange. The temporary bracing is later removed once the concrete has hardened.

The bridge floor is done as per the design drawing with the reinforcements. The sizes of bar, their cutting length hooks and bents should be maintained. Once the reinforcements are prepared they are placed in their respective positions as per the specified spacing and concrete cover. Binding wires are used to tie shrinkage and distribution reinforcements.

The concrete cover and spacing for floor slabs can be maintained by introducing spacers and bars supporters. Wires are used to tie main reinforcement, shrinkage and temperature reinforcement (distribution reinforcement). Concrete is then poured on the prepared reinforcement starting from one end and ensuring it is not piled at one point but continuously poured. During concrete pouring presence of cracks, excessive deflections maintenance of level and plumbing is done. Vibrations are used to compact the concrete into molds within the forms and around the embedded items and reinforcements and also eliminate stone pockets, entrapped air and honeycombs (Bot, 2003). The slab is then cured.

Construction loads

During design of the bridge some loads should be considered. These include: deck formwork and brackets, walkways, handrails, construction live loads, wind loads on the structure and equipment in use.

The construction equipment used include power screed used for concrete deck placements, bridge mounted erections systems, bridge support concrete delivery systems. The anticipated loads for our bridge will be determined based on member sizes, site location.

The bridge girder should be capable to transmit wind loading during construction to the support location. Alternative to these permanent lateral bracing systems should be placed to resist this load. The magnitude of wind loading should be determined using site data. The wind loads that include friction velocity must be determined, friction length, and wind velocity based on the bridge location and height of the structure.

The site the bridge is to be build the wind load is 1kN/. Bridge attachments should be determined and evaluated and included in dead load effects. Example of temporary attachments include: temporary scaffoldings suspended form the bridge, temporary safety lines and supports, overhanging brackets temporary hand rails and form work.

Permanent attachment includes: inspection walkways and handrails and utilities. All loads combinations must be evaluated to capture all critical conditions during the bridge construction.

Bracers

Main girder requires bracing to avoid buckling. Restraint at in-service stage is provided by knee braces from the cross girder to the bottom of the web. The knee braces often poise challenge of fabricating due to their high cost. Bracing the cross girder is more economical than increasing flange thickness. This can be achieved by pairing the cross girder with channel bracing at midspan.

Stiffener provision Stiffeners help to limit dimension of the web panel to control web buckling, they are also used at support positions and to form connections at positions of cross girder or bracing (Earls and Shah, 2002). Transverse web stiffeners are commonly used. The transverse web stiffeners are provided at the position of each cross girder.

At the support the web stiffeners used are known as bearing stiffeners. They are also provided at positions of jacking for bearing replacements. Example as in the picture below.

Bearing stiffeners are usually thicker than intermediate web stiffeners. This is because they act against additional lateral forces transmitted to the supports. They are 30mm to 50mm thick.

Bridge articulation

Bridge is designed to deal with movements that arise from temperature, wind, traffic loadings and self-weight. Bearings are used to connect the bridge and its supports, they help accommodate movements arising from these effects. Method of bridge construction.

This includes design of the steel work. Construction sequence must be included in the design including erection of the steel work and concreting of the deck.

The bridge is erected in one of the following ways:

· Erection by use of crane

· Launching

· Sliding

· Rolling

· Lifting large preassembled sections.

Erection by use of crane is the most convenient, once the supports have been erected and cured, the girders are lifted with cranes from the ground onto the bridge substructure. The girders can be placed singly for full span after they have been joined.

The drawing below shows girder erection by crane.

Advantages of the beam and slab with ladder decks.

· High strength to weight ratio- steel exhibit less weight in relation to its strength. This has great impact on substructure and foundation cost which is beneficial. In places with lift and swing bridges light weight of girders reduces size of counter weight which means reduced plant costs. It also results in girders with reduced depths which solve the problem of head clearances and minimizing length and height of approach ramps.

· Speed of erection- the light weight of steel makes their workability easy and in conditions of bad weather the girders can be erected with minimal time and joined accordingly. This reduced disruption caused to roads.

· Versatility- during working with steel a number of method and sequences are available in which the installation job can be done. This makes contractor work easy and is able to use the cheapest and safest as he uses machines available. The contractor is able to choose the erection sequence and construction programme that best suites his timeline and machines. This is seen by available ways the main girder can be installed such as by use of cranes, slide-in techniques or by use of transporters (Yabuki, Lebegue, Gual, Shitani, and Zhantao, 2006).

· Workability of steel-steel can be modified to attain different shapes and sizes. Steel have high surface quality which allows attention to details. This makes it possible to shape it in ways to increase aesthetic and appearance of the bridge, modern fabrication methods facilitate curvature in both plan and elevation. Painting introduce colour and contrast to the bridge which can be repainted to refresh it or change appearance.

· Steel durability-steels are mostly affected by rusting. With ability to galvanize the steel and paint the steel and also reinforce the steel the structures are expected to have a lifespan of over 100 years. The structure need not to be overloaded. They should be well designed to ensure that drainage is good. The girders are exposed and visible making it easy to inspect and accessible. Any sign of deterioration can be detected and addressed by repainting, welding or strengthening it. Most structures are designed with provision of access platforms and travelling gantries for ease of maintenance and inspections.

· Durability -Steel bridges now have a proven life span extending to well over 100 years. Indeed, the life of a steel bridge that is carefully designed, properly built, well maintained and not seriously overloaded is indefinitely long.

· Modification demolition and repair- during bridge design provision for modification such as widening to accommodate extra lanes is possible. In bridge building detachable structures are used and are either welded or bolted. This means that when the bridge is no longer needed the girders can be detached into manageable sizes and recycled which is beneficial in terms of sustainability. In case of a section of the bridge worn out it is easy to detach that section and replace or repair it.

Disadvantages of the beam and slab with ladder deck

· Maintenance cost of the structure is high. This is because once steel is repaired it has to be repainted and also anticorrosion applications has to be done on the part worked on. Some common examples of steel preparations include: dry abrasive blasting, water blasting, coal tar coating, painting and alloying. These protecting methods are expensive and also restricted by practical limitations such as accessibility, location and time in case of maintaining an already erected member (Gordon, and May 2007).

· Steel is not fire proof and in incidences of fire the structure is damaged. Exposing steel to high temperatures it loses its properties. Steel structures strength reduces at high temperatures incase of fire. Heat conductivity of steel is high which makes it contribute in spreading the fire. Fireproof coating of steel involves expanded mineral coating, concrete and intumescent materials. Gypsum blocks and clay tiles may be used to protect steel from heat. These enclosures are expensive and require regular maintenance.

· Buckling-increase in the length of steel in use increases the chances of buckling of the steel, high temperatures also weakens the steel making it susceptible to buckling.

· Fatigue and fracture- during loading of the steel structure, large variations in tensile strength expose steel to excessive tension. This reduces the overall strength of the structure making it susceptible to brittle fracture when its limit is exceeded. This also makes the steel susceptible to buckling. To counter this, steel needs to be stiffened. Steel columns are added to counter balance which makes the structure very expensive to maintain.

· The bridge can be susceptible to sagging- the bridge has no weight transfer occurring on support structure of the beam, this means heavy weight being applied at a specific point repeatedly can lead to sagging at that point. This can lead to bridge collapsing with time if no support and maintenance is carried out.

· The bridge weakens as it gets old

The weight from the deck leads to wear and tear of the bridge support.

· Beam bridge has no aesthetic value compared to arch bridges

Beam bridges are simply cheap and effective; their building does not get around basic aesthetics of its construction.

· Beam has limited placement options

This is seen in water ways where large ships are required to pass. The beam bridge will not be applicable.

· The deck span width of a beam bridge is limited.

Most beam supports two lanes of traffic. For more lanes there will be two bridges built instead of one.

· Beam bridges offer little flexibility

The beam bridges are not designed to handle difficult atmospheric conditions. Cases of high wind conditions vehicles in a beam bridge experience movement when crossing the bridge. Also, the wind accelerates wear and tear on the bridge supports.

Arch bridges

The bridges structural elements are curved members that carry loads. In this compressive force act at the centroid of each element of the arch. In some cases, arch bridges also carry asymmetric loading and point loading, carried by ribs by bending (Lu, Usami and Ge, 2004). This is seen in some arch bridges like the masonry bridge when line of thrust is displaced from its mean path under dead load.

The shape of the true arch can is seen as the inverse of a hanging chain between abutments. The arch bridge is usually subjected to multiple loading that is dead load, live load and temperature all of which produces bending moment stresses in the arch rib that generally less compared to the axial compressive stress (Cai, Xu, Feng & Zhang, 2012).

The arch bridges are generally competitive with the other bridges though their cost may be a bit higher for the same span and are chosen for their aesthetic value.

Construction sequence

In arch fabrication one factor considered is stiffening, should the arch be stiffened longitudinally or not. Considering loss of efficiency when thin plates are used b/t>24 and the additional fabrication cost of stiffened panels. Arches are normally fabricated from weathering steel; the exterior is painted and interior left unpainted.

Tubes are normally used and are left sealed or vented with provisions for drainage.

Bracing between the arches can take a number of forms, and can even be omitted in small to medium spans (Lonetti, Pascuzzo & Aiello, 2019). Tubes are commonly used, and are generally too small for man access. They can either be sealed, or vented into the arch boxes with provision for drainage. Note that hot rolled sections are not available in weathering steel.

Hangers are also applied to support the bridge. The hangers may take the form of round bars. The hangers require to be placed at closer centres since they are of lower strength. Ropes locked coils are also applicable for arch bridges just like for the cable stayed bridges.

A steel orthotropic deck is made or even a concrete one though concrete pose problems when interacting with tensions developed in the tie beam. A ladder deck may be used for support with cross girders.

Arch shape

Parabolic arch is the best shape for structural efficiency. When uniform loading, only axial forces act on the members. Addition of tie beam contributes to stiffness of the system which brings about some moments around the arch springing. Circular arch have greater bending moments in the arch members.

Influence lines

Maximum axial forces are generated when the whole span is loaded, however maximum bending will occur when just part of the span is loaded. Example of an influence line for bending in the arch is given below.

· Influence lines

·

Influence line for axial force in arch member

·

Influence line for force in a hangerIn studying influence line, there are both positive and negative parts. The influence line for a vertical hanger usually comprises a single positive peak as shown above right.

Loading

In designing for loading, dead loads carry a large portion of design stresses for main elements thus its necessary to allow fully for the erection method. This applies to bending in the arch, locked in bending moments which is controlled by adjusting hanger’s length. Special vehicles are chosen to suit influence lines since loaded lengths and positions of tandem axles are different and changing. Aerodynamic instability is minimal but for bridges with long spans it is necessary for wind tunnel tests. Inter arch bracing designing is done with consideration of wind loading. Accidental loss of a hanger is also considered in arch bridge design. This is to prevent collapse of the whole span in case of such an incidence. Hangers should be routinely inspected and replaced.

Arch/ tie connections

Plating arrangement is confirmed by some local finite element modelling. Careful considerations are given to how fabrication of the pieces is done for efficiency and also to cut on cost.

Hangers

As a rule of thumb, cables are best sized under SLS loading that is limiting tensile stress to 45% of breaking load. The manufacturers can provide data on various forms of ropes, strands and bars. This ensures that under accidental loss of a hanger the remaining hangers can work at higher stress level (Lonetti, Pascuzzo & Aiello, 2019). Cable sockets are made such that their fixings are sized with their strengths exceeding the breaking load of cables. Hangers can be terminated inside the arch. Though internal connections require installation and subsequent inspection and maintenance inside a confined place. Hangers are adjusted to allow for geometrical tolerances between arch and tie and for initial stressing and subsequent adjustments.

Internal hanger connection

Splices

The splices can be bolted or welded. Welding is considered for its efficiency in terms of design since no loss in section from bolt holes occurs.

Fabrication process

An arch box is made comprising four plates joined along their edges. The weld can be an internal fillet weld plus an external part penetrating weld. This is because shear is generally low in arches.

The fabricator may add ring frames at the ends to maintain the square shape. Butt weld is used to join arch and tie beam units. The welding sequence must be adhered to or else cracking may be experienced.

Erection

Method used is determined by the size of bridge, type, obstacle to be closed and other side conditions.

Site accessibility, the cranes available for lifts is also considered. Support availability and necessity is also considered.

Advantages of arch bridges

· Arch bridges can be constructed from any material- most modern arch bridges are constructed with steel and concrete. Materials such as stones when properly build can last long in arch bridges. Aluminium has also been used to build arch bridges.

· Arch bridges can span greater distances- the arch bridges are mostly constructed where there is long distance required to span with the structure. This design option often goes further between two points of vertical support than a straight beam because of the way it handles downward load vectors. This makes the bridge to be in a position to carry more load than horizontal support designs.

· The arch design provide support without distorting over time.

The half circle shape of the arch bridge ensures that no distortion happens downward when load is applied. This applies to both dead load and live loads. This feature reduces greatly the cost of long-term maintenance of the bridge since consistency of the structure is maintained.

· The arch bridge is stronger than other bridges of the same span

In case of something heavy passing over the bridge its weight will modify the bridge with a downward sagging force. The support columns weight is transferred to the entire structure with consistency. Equal displacement in the bridge reduces incidences of wear and tear reducing maintenance cost. The bridge is able to handle thermal and user change effectively.

· The arch bridge becomes stronger with age

With time compression force acting on the bridge acts to flatten it. This gives it added strength. As the arch bridge gains U shape with less rounding, weight is distributed better to the deck, abutments which provide more stability in the crossing surface.

· The arch bridge adapts to local environmental factors better

The shape allows more water to pass under it compared to straight bridge in case its build over a river, this reduces chances of the bridge being swept away.

· Multiple arches can be built to provide more stability

With multiple arches built and tied to each other, a stronger deck that can handles a high level of traffic vehicles can be built. This also increases ability of the bridge to handle most environmental conditions.

· The arch bridges provide a variety of forms that it can take.

Designers when thinking of the aesthetics of the bridge have many options to choose from. They can choose a lighter, thinner design with trussed arch, masonry arch, equilateral points, parabolic, elliptical and Tudor design elements.

Disadvantages of arch bridges

· Tie girders have to be constructed before the arch ribs can function compared to the cable stayed bridge where deck elements and cables are erected simultaneously during the construction process.

· The arch bridges require regular maintenance

Flexibility of the arch bridges makes them susceptible to cracking and tearing when exposed to harsh conditions. This means regular inspections are require to ensure the structure is intact. To ensure that the supports are distributing weight as require to the abutments, maintenance have to be regularly done. Even modern materials wear with time, the structures have to be constantly inspected to ensure intervention and repair is done on time.

· The arch bridge is expensive

Building of arch bridges is labour intensive and it also takes more time. In addition to that the level of expertise require is more due to its complexity in structure. To obtain high quality bridge material quality is also require meaning high Quality Bridge require more expensive material.

· Arch bridge has to be built in grounds that can support them.

Ground on which the arch bridge is built must be in a position to hold the forces that will be distributed along the bridge up to the abutments. Modern bridges are using materials that can tolerate pressure allowing the bridge to be built on weaker grounds.

· Arch bridges have limited span

By nature, the longer the arch the weaker it is. This means that arch have starting and end points unlike other designs. This forces the designer to use a lot of reinforcing material in case of a long arch or to build several arches to cover the span of the bridge. When the ends of arch bridge are too far spaced from one another, weight transference reduces with distance. The structure also weakens when tension and radius are added.

· Arch bridges are difficult to build.

In designing the bridge, a lot of factors have to be considered, this makes the design work challenging. Building them is also time consuming and they are labor intensive making them expensive to build. To design the bridge the designer must understand interior and exterior pressure that the abutments must handle. Enough strength in material and supports processes for sufficient weight transfer must be observed.

· The arch bridges require stronger supports

The structural integrity of the arch bridges to a great extent is determined by how sturdy the abutments are. This contribute to long time and cost used in building the bridges.

· Constraint in locations

The bridge requires solid and stable supports on both sides. There must be two placement points regardless of the bridge span, that are successful in their support. Though modern materials can withstand more tension and stress, the bridge must be two sided.

· Arch bridges need additional support

This kind of bridges require more side support than other bridge types due to nature of settling and movements that occur within the structure. Artificial pillars provide a finite amount of strength which is not sufficient to reach the weight tolerance necessary for the bridge.

· Excess flexibility on the arch bridge

For the two-hinged and three-hinged arch bridge flexibility can greatly benefit the surrounding communities where thermal changes are frequent. In some design flexibility of the arch is too much for the deck to handle, this happens if too much movements are allowed especially in different directions simultaneously. This can lead to the bridge failure.

The arch design has to be perfect in design for it to work as intended.

The design of the bridge must be perfect for the weight distribution to be balanced the strength of the steel, concrete and other building material must be correct for the structure to stand. Discrepancies may create weaknesses that are too difficult to overcome.

Bridge selection

For this project beam and slab with ladder deck was selected. This is because they are the most cost-effective considering fabrication and erection. The bridge is supposed to be built on a land with limited space, this means excessive supports like would be required in arch bridges can not be made. This makes the ladder deck bridge most suitable for the section. The equipment to use for erection of the bridge must also be considered. The ladder deck only require space for the crane to place the girders.

Minimum time is provided for interrupting the motor way where the bridge will be placed. This means a bridge that will require minimum time to erect and complete the operation. The only operation of ladder deck bridge that will interrupt the motor way is during placing of the girder. The other operations can be carried on with minimum interruption of the motor way.

· From this the most suitable choice for our bridge is the ladder deck.

The bridge will have a length of 50m and the width will be 14m. It will use the ladder deck with main girder space been 4m. This means the girder will have a spacing of 3m and overhang of 3m on both sides.

The bridge framing plan has cross girder with uniform spacing of 6m which are governed by the construction requirements in positive bending and moments redistribution requirements in negative bending.

The bridge will have a cross section as shown

The bridge will have provisions for water, gas and cable passage beneath the foot path as per the drawing.

The bridge will be subjected to

Dead load and live load

In live load the bridge will be subjected to a load 5kN/

Assume a vehicle of 600kN/

1.2m wheel spacing where each wheel carry 150kN/

The vehicle is in constant motion thus the load is shifting along the span of the bridge (Yousif, Z., & Hindi, 2007).

During design the bending moments and shear force are considered.

Bending moments increases as the vehicle moves toward bridge midpoint as shown in the figure

The shear force on the bridge is highest at bridge support and reduces as the weight shifts toward bridge midpoint. This is as illustrated below

The bridge will being a two-lane bridge will have 3 notion lines which are line where weight is experienced

9m/3=3 notion lines with foot paths on both sides

The deck will be ladder deck

The cross girder spacing will be 4m apart. Since the girder used are 3 the bridge will be a double ladder deck.

The plate girder design

The depth rule of thumb will be used span 15 to 20

The full length is 50m

m

Design calculations

Assume concrete thickness 250mm

Force exerted by concrete will be

The bending moments representation will be

Foot path notion lane 1 notion lane 2 foot path