In engineering design the general principle is that the resistance of a cross section has to exceed the effects come from the applied loads. That is
Resistance ≥Effect of Loads
When a particular loading condition reaches and just exceeds the resistance capacity of the provided section failure is the result. Such a condition is referred to as a Limit State.
A limit state is a condition beyond which a bridge system or bridge component ceases to full fill the function for which it is designed.
Preventing a limit state from being reached is the central goal of design of bridges. In addition to this function, appearance and economy must get due attention.
Safety is achieved by using reasonable margin of safety factors. These factors are results of collective experience and judgment of qualified group of engineers and officials.
In Highway Bridge design AASHTO LRFD provision is used for bridge design. The resistance side of the inequality of Equation above is multiplied by a statistically based resistance factor, whose value is usually less than one, and the load side is multiplied by a statistically based load factor, whose value is usually greater than one.
The load effect at a particular limit state involves a combination of a different load types (Qi) that have different degrees of predictability. Due to this reason the load effect side is written in a summation form. The equation is
Φ∗Rn≥
∑
γi∗QiAnd this equation involves both load factors and resistance factor due to this the design method is called load and resistance factor design method. In AASHTO LRFD bridge design specification the equation is given by
η∗
∑
γi∗Qi≤Φ∗RnThe additional parameter η is known as load modifier which is incorporated to consider ductility, redundancy and operational importance of the bridge.
Under the umbrella of the LRFD the strength limit state, extreme event limit state, service limit state and fatigue and fracture limit state exist.
Load Factors and Load Combinations:
Fundamental of Bridge Design 24 The total factored force effect shall be taken as:
Q = Ση
iγiQ
iWhere:
ηi= load modifier
Qi = force effects from loads specified herein γi = load factors specified in Tables B and C below Rn= is resistance
Components and connections of a bridge shall satisfy the above equation for the applicable combinations of factored extreme force effects as specified at each of the limit states presented in Table A:
Table A Limit States STRENGTH
I
Basic load combination relating to the normal vehicular use of the bridge without wind.
A reduced value of 0.50, applicable to all strength load combinations, specified for uniform temperature (TU), creep (CR), and shrinkage (SH), used when calculating force effects other than displacements at the strength limit state, represents an expected reduction of these force effects in conjunction with the inelastic response of the structure. The calculation of displacements for these loads utilizes a factor greater than 1.0 to avoid undersized joints and bearings.
STRENGTH II
Load combination relating to the use of the bridge by ERA-specified special design or permit vehicles, without wind.
The permit vehicle should not be assumed to be the only vehicle on the bridge unless so assured by traffic control. Otherwise, the other lanes should be assumed to be occupied by the vehicular live load as specified herein. For bridges longer than the permit vehicle, the presence of the design lane load, preceding and following the permit load in its lane, should be considered.
STRENGTH III
Load combination relating to the bridge exposed to wind velocity exceeding 90 km/h.
Vehicles become unstable at higher wind velocities. Therefore, high winds prevent the presence of significant live load on the bridge.
STRENGTH IV
Load combination relating to very high dead load to live load force effect ratios.
The standard calibration process for the strength limit state consists of trying out various combinations of load and resistance factors on a number of bridges and their components. Combinations that yield a safety index close to the target value of β = 3.5 are retained for potential application. From these are selected constant load factors γ and corresponding resistance factors ϕ for each type of structural component reflecting its use.
This calibration process had been carried out for a large number of bridges with spans not exceeding 60 m. For the primary components of large bridges, the ratio of dead and
Fundamental of Bridge Design 25
live load force effects is rather high, and could result in a set of resistance factors different from those found acceptable for small- and medium-span bridges. It is believed to be more practical to investigate one additional load case than to require the use of two sets of resistance factors with the load factors provided in Strength Load Combination I, depending on other permanent loads present. For bridges with up to 180 m spans, Load Combination IV will govern where the dead load to live load force effect ratio exceeds 7.0.
STRENGTH V
Load combination relating to normal vehicular use of the bridge with wind of 90 km/h (25 m/s) velocity
EXTREME EVENT I
Load combination including earthquake
This limit state includes water loads, WA. The probability of a major flood and an earthquake occurring at the same time is very small. Therefore, consideration of basing water loads and scour depths on mean discharges shall be warranted. Live load coincident with an earthquake is discussed elsewhere in this chapter.
SERVICE I Load combination relating to the normal operational use of the bridge with a 90 km/h (25 m/s) wind and all loads taken at their nominal values. Also related to deflection control in buried metal structures, tunnel liner plate, and thermoplastic pipe and to control crack width in reinforced concrete structures. This load combination should also be used for the investigation of slope stability.
Compression in prestressed concrete components is investigated using this load combination. Service III is used to investigate tensile stresses in prestressed concrete components.
SERVICE II Load combination intended to control yielding of steel structures and slip of slip critical connections due to vehicular live load.
This load combination corresponds to the overload provision for steel structures, and it is applicable only to steel structures. From the point of view of load level, this combination is approximately halfway between that used for Service I and Strength I Limit States.
SERVICE III Load combination relating only to tension in prestressed concrete structures with the objective of crack control.
The live load specified in these Specifications reflects, among other things, exclusion weight limits. The statistical significance of the 0.80 factor on live load is that the event is expected to occur about once a year for bridges with two traffic lanes, less often for bridges with more than two traffic lanes, and about once a day for bridges with a single traffic lane.
FATIGUE Fatigue and fracture load combination relating to repetitive gravitational vehicular live load and dynamic responses under a single design truck having a constant axle spacing of 9.0 m between 145 kN axles.
The load factor, applied to a single design truck, reflects a load level found to be representative of the truck population with respect to a large number of return cycles of stresses and to their cumulative effects in steel elements, components, and connections.
Fundamental of Bridge Design 26 The load factors for various loads comprising a design load combination shall be taken as specified in Table B. All relevant subsets of the load combinations shall be investigated. For each load combination, every load that is indicated to be taken into account and that is germane to the component being designed, including all significant effects due to distortion, shall be multiplied by the appropriate load factor and multiple presence factor specified in, if applicable..
The factors shall be selected to produce the total extreme factored force effect. For each load combination, both positive and negative extremes shall be investigated.
In load combinations where one force effect decreases another effect, the minimum value shall be applied to the load reducing the force effect. For permanent force effects, the load factor that produces the more critical combination shall be selected from Table C.
Where the permanent load increases the stability or load-carrying capacity of a component or bridge, the minimum value of the load factor for that permanent load shall also be investigated.
The larger of the two values provided for load factors of Uniform Temperature (TU), Creep (CR), and Shrinkage (SH) shall be used for deformations and the smaller values for all other effects.
Table B - Load Combinations and Load Factors Load
Fundamental of Bridge Design 27 Where (see following text):
BR = vehicular braking force CE = vehicular centrifugal force CR = creep
CT = vehicular collision force
DC = dead load of structural components DD = downdrag
DW = dead load of wearing surfaces and utilities EH = horizontal earth pressure load
EL = accumulated locked-in effects resulting from the construction process
EQ = earthquake load ES = earth surcharge load
EV = vertical pressure from dead load of earth fill
FR = friction
IM = vehicular dynamic load allowance LL = vehicular live load WS = wind load on structure
Table C - Load Factors for Permanent Loads, γp
Type of Load Load Factor (γp)
Maximum Minimum
DC: Component and Attachments 1.25 0.90
DD: Downdrag 1.80 0.45
DW: Wearing Surfaces and Utilities 1.50 0.65
EH: Horizontal Earth Pressure
EL: Locked-in Erection Stresses 1.0 1.0
EV: Vertical Earth Pressure
• Overall Stability
• Retaining Structure
• Rigid Buried Structure
• Rigid Frames
• Flexible Buried Structures other than Metal Box Culvert
• Flexible Metal Box Culverts
1.35 load can cause a negative reaction, the load combination would be:
0.9DC + 0.65DW + 1.75(LL+IM)
Fundamental of Bridge Design 28 If both reactions were negative, the load combination would be:
1.25DC + 1.50DW + 1.75(LL+IM).
Load Modifiers, ηi = ηD ηR ηI :
ηD = a factor relating to ductility, as specified below ηR = a factor relating to redundancy as specified below
ηI = a factor relating to operational importance as specified below
Ductility, redundancy, and operational importance are significant aspects affecting the margin of safety of bridges.
• Ductility: The structural system of a bridge shall be proportioned and detailed to ensure the development of significant and visible inelastic deformations at the strength and extreme event limit states prior to failure.
For the strength limit state:
ηD ≥ 1.05 for non-ductile components and connections
ηD = 1.00 for conventional designs and details complying with these Specifications
ηD ≥ 0.95 for components and connections for which additional ductility-enhancing measures have been specified beyond those required by these Specifications
For all other limit states:
ηD = 1.00
• Redundancy: Multiple load-path structures should be used unless there are compelling reasons not to use them.
For the strength limit state:
ηR ≥1.05 for nonredundant members
=1.00 for conventional levels of redundancy ≤0.95 For exceptional levels of redundancy For all other limit states:
ηR = 1.00
Fundamental of Bridge Design 29
• Operational importance: This definition shall apply to the strength and extreme event limit states only. Some bridges or structural components and connections shall be declared to be of operational importance.
Such classification should be based on social/survival and/or security/defense requirements.
For the strength limit state:
ηl ≥ 1.05 for important bridges
= 1.00 for typical bridges
≤ 0.95 For relatively less important bridges For all other limit states:
ηl = 1.00
For Conventional Construction, Resistance Factors Ф shall be taken as
For flexure and tension of RC = 0.9 For flexure and tension of PSC = 1.0 For shear and torsion = 0.9 For bearing on concrete = 0.7 For compression in strut-and-tie model = 0.7 For compression in anchorage zones = 0.8 For tension in steel in anchorage zones = 1.0 For resistance during pile driving = 1.0 5. Superstructure Types
An efficient design of bridge superstructure is essential to achieve overall economy in the whole bridge structure in that the superstructure dead weight may form a significant portion of the gravity load the bridge must sustain and transmit to the foundation. A light superstructure is economical not _only material requirements of the superstructure but also requires smaller size for substructure and foundations. A clear understanding of the structural behavior of structural behavior under loads is essential for efficient design.
A bridge superstructure is an integrated body of various members of reinforced concrete, prestressed concrete, steel, composite, diaphragms, trusses, arches, etc. Determination of' forces in theses components is essential for design purposes.
The following types of bridges are discussed as follows.
RC Bridge, Steel Bridge, Arch Bridge, Cable Stayed Bridge and Suspension Bridge
Fundamental of Bridge Design 30 Reinforced concrete bridges:
Steel and concrete are construction materials.
Reinforced concrete bridges possess several advantages over steel bridges.
- adaptability of concrete wide variety of structural shapes - Low maintenance cost
- Long life and better resistance to temporary overloads and dynamic loads than steel bridges.
- Cast-in-place Reinforced concrete structures are continuous and monolithic, attributes, which translate into easy construction, low cost and good seismic resistance. They can also be given the desired aesthetic appearance.
The disadvantage
- large dead weight - difficulty to widen - longer construction time
- requires formwork and false work
Bridge live loads occupy partial area of the decks unlike live loads in buildings which is taken uniformly distributed all over the floor area. Live load on bridges can occupy random positions both longitudinally and transversely, and this affects the live load shared by various beams. This aspect of live load distribution is one of the primary concerns in the analysis of bridge decks.
Influence lines will be used to determine load position for maximum effect and the magnitude of these effects.
The following RC bridges will be discussed.
Slab bridge T-girder bridge Box girder bridge Continuous RC bridge RC rigid frame bridges Slab Bridge:
Slab Bridge may be in the form
Fundamental of Bridge Design 31
Uniform thickness
Voided slab
Slab Bridge normally requires more concrete and reinforced steel than Girder Bridge of the same span but the formwork is simpler and less expressive, hence they are economical when these cast factor balance favorably.
The structural configuration of bridge is shown below.
Typical Cross-section of Slab Bridge
Slab bridges are most commonly used to span short spans up to 12 meters. The load carrying mechanism is by plate action, i.e., by bending and twisting due to continuity in all directions.
Application of a load on the portion make the slab deflect into a dish shape locally, causing a two-dimensional system of bending and twisting moments, the mechanism through which the load is transferred to the adjacent elements of the deck, which are less severely loaded.
Slab Notch
Edge beam Post & raining
Curb
Fundamental of Bridge Design 32 Where: Z is the downward deflection of the plate
q is intensity of uniform load D is flexural rigidity of tile plate
In the absence of closed form solution to the above equation, approximate methods are developed.
One method is the method of influence surfaces, which uses design charts. These charts have been prepared by Pucher or slabs of various shapes and support conditions (1964),and by Rusch and Heregnroder (1961) and Dalas and Hanuska (1964) for simply supported skew slabs.
Grillage method is also used for analysis and softwares are available for this. Another method that AASHTO recommends is the Strip Method.
Load distributions:
The equivalent width of longitudinal strips per lane for both shear and moment with one lane, i.e., two lines of wheels, loaded shall be determined as:
The equivalent width, E of longitudinal strips per lane for both shear and moment with more than one lane loaded shall be determined as:
Where: E = equivalent width (mm)
L1 = modified span length taken ≤ of the actual span or 18,000 (mm)
W1 = modified edge-to-edge width of bridge taken to be ≤ of the actual width or 18,000 mm for multilane loading, or 9,000 mm for single-lane loading (mm)
W = physical edge-to-edge width of bridge (mm) NL = number of design lanes as specified
Where decks span primarily in the direction of traffic, the effective width of a strip, with or without an edge beam, shall be taken as the sum of the distance between the edge of the deck and the inside face of the barrier, plus 300 mm, plus one-half of the strip width. The effective width shall not exceed either the full strip width or 1800 mm.