- Interior girders: The live load shear for interior beams shall be determined by applying the lane fractions specified in Table
Table -Distribution of Live Load per Lane for Shear in Interior Beams
- Exterior girders: The live load shear for exterior beams shall be determined by applying the lane fractions specified in Table
Fundamental of Bridge Design 36
Table Distribution of Live Load Per Lane for Shear in Exterior Beams Where: S = spacing between girders (mm)
L = Length of Girder (mm) ts = thickness of slab (mm)
The lever rule involves summing moments about one support to find the reaction at another support by assuming that the supported component is hinged at interior supports.
When using the lever rule on a three-girder bridge, the notional model should be taken as shown in Figure 13-1. Moments should be taken about the assumed, or notional, hinge in the deck over the middle girder to find the reaction on the exterior girder.
Figure 13-1 Notional Model for Applying Lever Rule to Three-Girder Bridges
Multiple presence factors shall not be used with the approximate load assignment methods other than statical moment or lever arm methods because these factors are already incorporated in the distribution factors.
Box Girder Bridge:
Concrete box girder bridges are economical for spans of above 25 to 45m. They can be reinforced concrete or prestressed concrete. Longer span than 45m will have to be prestressed.
They are similar to T-beams in configuration except the webs of T-beams are all interconnected by a common flange resulting in a cellular superstructure. The top slab, webs and bottom slab are built monolithically to act as a unit, which means that full shear transfer must be provided between all parts of the section.
Reinforced concrete box girders have high torsional resistance due to their closed shape and are particularly suitable for structures with significant curvature. This construction also lends itself to aesthetic treatment.
Concrete box girder bridges have several advantages over other types;
Fundamental of Bridge Design 37 1. The relatively shallow depth of box girders is all advantage where headroom is limited like in urban overpasses.
2. Monolithic construction of the superstructure and substructure offers structural as well as aesthetic advantage. The pier caps for continuous box girders can be placed with in the box, facilitating rigid connection to the pier.
3. They provide space for utilities such as water and gas lines, power, telephone and cable ducts, storm drains and sewers, which can be placed in the hollow cellular section.
Typical cross section is shown in Fig. below. While the interior webs are all vertical the exterior webs may be vertical, inclined or curved. When the exterior webs are inclined their slope should preferably be IH: 2V.
Design Consideration:
The structural behavior of box girders is similar to T-beams. Box girders are essentially T-beams with transverse bottom flange resulting in a closed, torsionally stiff multi-cell configuration.
The interior webs resist shear and often only a small portion of girder moments. Consequently they are usually thinner than the webs of T-beams. This is so because, in the case of continuous T-beams, the webs must resist the negative girder moments as well as all the shear, and contain all the reinforcement for positive moments.
The bottom slab (soffit) contains reinforcement for the positive moment and also acts as a compression flange in the negative moment regions of continuous spans. The bottom slab also affords a superstructure considerably thinner than a T- beam bridge of the same span and permits even longer spans to be built.
Cross-sections are taken as shown in Fig. below a and b for analysis for exterior and interior girders respectively. The structural analysis is same as for T-beams. Section analysis is also same except the compression bottom flange for continuous spans. The entire slab width is assumed effective for compression.
a. Exterior girder b. Interior girder Continuous RC bridge:
Advantages
Fundamental of Bridge Design 38 - Less number of bearings than simply supported bridge since one line of bearings is
used over the piers
- Reduced width of pier, thus less flow obstruction and less amount of material
- Requires less number of expansion joints due to which both the initial cost and maintenance cost become less. The rigidity quality over the bridge is thus ~proved.
- Lesser depth of girder, hence economical supports.
- Better architectura1 appearance - Lesser vibration and deflection Disadvantages
- Analysis is laborious and time consuming - Not suitable on yielding foundations RC rigid frame bridges:
In rigid frame bridges, the deck is rigidly connected to the bridge and piers. All the advantages of a continuous span bridge are present here.
Additional advantages of rigid frame bridges over continuous ones are - More rigidity of the structure
- Less moments in deck being partly transferred to the supporting members - No bearings are required
- Better aesthetic appearance than the continuous span structure
As in continuous span bridges, these structures also require unyielding foundation materials. The analysis is however, more laborious than the former.
Steel Bridge:
Steel bridge construction consists of rolled steel beams, plate girders or trusses with reinforced concrete deck or steel plate deck-beam bridges.
- Steel has got several advantages.
- It is a high quality, homogeneous, isotropic material that is perfectly elastic to its yield point.
- It has high tensile and compressive strengths.
- Past the yield point it offers considerable ductility to provide a large reserve of strength.
- Steel bridges can be built faster than reinforced concrete or prestressed concrete bridge.
Fundamental of Bridge Design 39 - They can be erected with ease and this minimizing construction costs.
- Steel superstructures are usually lighter than concrete superstructures which translate into reduced substructures costs, which can be significant when soil conditions are poor.
- Steel superstructures can be designed with shallower depth than RC, which is an important consideration when overhead clearance is required.
- Steel bridges are easy and faster to repair than RC.
Steel bridges have some major disadvantages that make then much less favorable than RC or PSC bridges
- Corrosion of steel is the major drawback which requires prohibitively high maintenance cost.
- Corrosion can reduce cross section of structural members and weaken the superstructure also.
Some steel bridge types:
- Rolled steel beam bridge
- Plate girder and steel box girder bridges - Steel truss bridges
- Plate Deck-Stringer Bridges Arch Bridge:
Arches are generally characterized by the development of inclined rather than vertical reactions under vertical loads.
Cross-sections are designed for thrust, moment and shear, with magnitudes depending on the location of the pressure line as shown in Figure below.
Fundamental of Bridge Design 40 If the pressure line coincides with the axis of structure, (as in a uniformly loaded parabolic arch), all cross sections will be subjected to compression, with no moment or shear. If the pressure line falls with in the kern, there will not be tension. But if shape of structure and pressure line differs moment may become dominant. Figure below shows parts of arch bridges.
Compared to the girder bridges, arch bridges are economical because the dead load moments in arch bridges are almost absent when the arch is properly design.
The loads on the arch are carried by the arch ribs mainly through direct axial thrusts, the bending moment and shear forces being small compared to Girder Bridge which requires larger section.
This is due to the hogging moment which balances the sagging moment created by the horizontal force, H, at the support.
The main parameter of an arch is the rise to span ratio, r/l (1/6 to 1/10).
From economic point of view it is attempted to coincide the center of pressure of a given load with center of line of the arch.
Cable Stayed Bridge:
Cable stayed bridges are ideal for spanning natural barriers of wide rivers, deep valleys and for vehicular and pedestrian bridges crossing wide interstate highways because they can provide long spans unobstructed by piers.
Span arrangement types:
- Two span (symmetrical or asymmetric) - Three spans
- Multi Span
Fundamental of Bridge Design 41 The arrangement of the cable stays is one of the fundamental items in the design of cable-stayed bridges. It influences, in fact not only the structural performance of the bridge but also the method of erection and economies.
Longitudinal cable arrangement:
- Radiating (converging)
- Harp
- Fan /Modified fan/
Suspension Bridge:
The twin main cables from the tower of a suspension bridge form a catenary from which the hangers are suspended and fixed to the deck.
Sag ratio for cables should be L/9-L/13
Suspension bridges are economical when the span exceeds 300m. Suspension bridges consist of one main span and two side spans.
L1/L =0.17100.50
Fundamental of Bridge Design 42 The cables being very flexible do not take any bending moment and arc subjected only to tensile forces. The stiffening truss stiffens the deck and distributes the live load of the deck on to the cables. Otherwise the cables would be subjected to local sag due to action of concentrated live load and thus causes local angle change in the deck system.
The stiffening trusses arc hinged at the towers and suspended at node points from suspenders, which are usually high tensile cables.
Vertical suspenders have been used in many bridges but diagonal suspenders have the advantage of increasing the aerodynamic stability
Simple Suspension Bridge
Suspension Bridge with Stiffening Truss
Suspension Bridge with Braced Chain
Fundamental of Bridge Design 43
Fundamentals of Bridge Design 43
6. SUBSTRUCTURE
Piers
Piers provide vertical supports for spans at intermediate points and perform two main functions:
• transferring superstructure vertical loads to the foundations
• resisting horizontal forces acting on the bridge
Although piers are traditionally designed to resist vertical loads, it is becoming more and more common to design piers to resist high lateral loads caused by seismic events.
Generally piers are subjected to:
• Dead loads
• Live loads and impact from the superstructure
• Wind loads on the structure and the live loads
• Centrifugal force from the superstructure
• Longitudinal force from live loads (vehicular braking force)
• Drag forces due to the friction at bearings
• Earth pressure
• Stream flow pressure
• Ice pressure
• Earthquake forces
• Thermal and shrinkage forces
• Ship impact forces
• Force due to prestressing of the superstructure
• Forces due to settlement of foundations