Structural Analysis of Bridges: Transverse Distribution of Internal Forces in Bridge Decks

INTRODUCTION

Bridges are structures related to planar factors that form a stable three-dimensional frame. Equilibrium of this body as assured by means of a bond to the ground through bearings, piers, abutments, and the bridge foundations. Consequently, bridges are spatial structures confined to external loads and movements and restricted in their movement through their support conditions. The calculation of the internal moments and forces is a critical step in qualifying the effects of the one of a kind actions from their factor of the application all the way down to the support. Concrete bridges are exacted to crack within the tensile and extreme deflection provinces, under heavy truckload situations and, consequently, the right reinforcement with great tensile strength material must be supplied. To this motive, the stress and deflection distribution of bridges on transverse and longitudinal direction should be decided. Although many research have been carried out to predict the live load distribution aspect of skewed bridges, only limited numbers focused on determining the maximum distribution of tensile and compressive stress, and deflection of skewed bridges.

In many bridge design approaches, the highest effective and negative stress of bridges is obtain the usage of the corresponding moment distribution factor formulas in corresponding cross-sections. It have to be mentioned that maximum tensile and compressive stress at the cross-phase is indeed localized, at the same time as the moment distribution factors specifications were obtained based on uniform distribution of stress on the bridge cross-section.

The structural analysis is a primary-order elastic linear one. The calculation of the elastic mechanical sections for every cross-section requires the active width of the flanges (shear lag effect) and the distinctive modular ratios within concrete and steel (creep effect). the second step of the global analysis is the estimation of the internal forces and moments distribution alongside the whole girder. The analysis should remember the construction stages and takes under consideration the concrete cracking on internal supports through a simplified method.

Bridge Decks

A bridge deck is the surface of a bridge. A structural element of its superstructure, it could be constructed of concrete, steel, open grating, or timber. sometimes the deck is covered a railroad bed and track, pavement concrete, or different varieties of pavement for ease of vehicle crossing. A concrete deck may be a crucial part of the bridge structure or it could be supported with I-beams or steel girders. while a bridge deck is fitted in a via truss, it is seldom called a floor system. A suspended bridge deck could be suspended from the primary structural components on a suspension or arch bridge. On a few bridges, such as a tied-arch or a cable-stayed, the deck is a primary structural factor, carrying tension or compression to support the span.

Type of bridges

• Cable-Stayed bridge
• Suspension bridge
• Composite bridge
• Steel Truss bridge
• Reinforced Concrete bridge
• Steel Box Girder bridge
• Prestressed Concrete bridge

In choosing the appropriate bridge-type it is essential to find a structure to be able to carry out its required purpose and provide an acceptable look as a minimum cost. Conclusions taken at the initial plan will outline the extent to which the actual structure approximates to the perfect, however so will choices are taken on the detailed design stage. consideration of every of the ideal characteristics, in turn, will provide a few indication of the significance of initial bridge design.

The structure depth available should be estimated. The budgetary implications of raising or lowering any approach embankments have to then be analyzed. by lowering the embankments the cost of the earthworks may be reduced, however, the resulting reduction in the construction depth may also cause the deck to be more expensive. Headroom conditions have to be sustained under the deck. If the bridge is to cross a road that is on a curve, then the width of the opening may also need to be extended to provide an adequate site line for transports on the curved road. it's far vital to outline the condition of the bridge site through carrying thorough site investigation

Deck Analysis

For decks with skew less than 25°, a simple unit strip approach of examination is typically good enough. For skews greater than 25° then a grillage or finite element method will be required for the examination. In Skew decks twisting moments will broaden in the slab. This grows to be greater considerable with higher skew angles. Automated system evaluation will return values for Mx, My and Mxy where Mxy outlines the twisting moment in the slab. due to the impact of this twisting moment, The slab's most cost-effective reinforcing way could be to install the reinforcing steel in the direction of the principal moments. These directions modify over the slab and directions have to be determined in which the reinforcing bars should lie. wood and Armor’s detailed equations of  the moment of resistance to be provided in predetermined directions to resist the involved moments Mx, My and Mxy. Various steel arrangements significant check on have given the best positions as follows

Reinforced Concrete Decks

The common types of reinforced concrete bridge decks are classified in to three categories:

• Solid Slab reinforced concrete bridge deck
• Voided Slab Reinforced Concrete Bridge deck
• Solid Slab reinforced concrete bridge deck

Figure -Voided Slab Reinforced Concrete Bridge

Figure -Solid Slab reinforced concrete bridge

Figure -Beam and Slab reinforced concrete bridge

Solid Slab reinforced concrete bridge decks are most beneficial for small, individual or multi-span bridges. These are effortlessly adaptable for great skew. Voided Slab Reinforced Concrete Bridge and Beam and Slab reinforced concrete bridge decks are used for more extensive, individual or multi-span bridges. In circular voided decks the ratio of [depth of void] / [depth of slab] should be smaller than 0.79, and the highest area of a void needs to be smaller than 49% of the deck section.

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Prestressed Concrete Decks

The term pre-tensioning is explained as it is a technique of prestressing wherein the tendons are tensioned before the concrete is placed, and the prestress is conveyed to the concrete when proper cube strength is reached. Post-tensioning is a technique of prestressing wherein the tendon is tensioned after the concrete has reached a appropriate force. The tendons are tied in opposition to the hardened concrete quickly after prestressing.

Pre-tensioned Bridge Decks

Varieties of beams in general use are inverted T-beams, M-beams and Y beams. Inverted T-beams are typically used for spans between 7 and 16 meters and the voids among the beams are loaded with in situ concrete as a result of forming a solid deck. M-Beams are used for spans between 14 and 30 meters and have a thin slab cast in situ fording among the top flanges to form Voided  Slab Reinforced Concrete Bridge deck. The top surface of the bottom flange of M-Beams cannot be effortlessly inspected; additionally, the constrained access makes bearing rearrangement hard. As a final result of these obstacles, the Y-beam was introduced in 1990 to replace the M-beam. This lead to the manufacturing of an SY-beam that's used for spans between 32 and 40 meters. The U-beam is used for spans between 14 and 34 meters and is generally selected in which torsional strength is needed.

Post-tensioned Bridge Decks

This is another kind of bridge desks which is called as Post-tensioned bridge decks commonly composed using concrete and ducts have been cast in the required positions.

When the concrete has got adequate strength, the tendons are joined via the ducts and tensioned by using hydraulic jacks acting in the end direction  of the member. The ends of the tendons are then anchored. Tendons are then bonded to the concrete by adding grout into the ducts after the stressing has been carried out. it is feasible to use pre-cast concrete units that are post-tensioned mutually on-site to form the bridge deck.

Composite Decks

Composite Decks are kind of bridge decks which constructed using the composite construction normally related to the interaction using the reinforced concrete and structural steel.

Steel Box Girders

Box girders have a clean, continuous design line and need much less renovation because most of the of surface area is protected from the climate conditions . The box pattern could be very sturdy torsionally and is consequently consistent during execution and in service; unlike the plate girder which commonly requires further strengthening to obtain adequate stability.

Steel Truss Decks

The usually used bridge spans are among 30m and 150m in steel Truss decks, where the construction depth is limited. The small construction depth decreases the duration and height of the method embankments that might be required for some other deck form. This will have a notable impact on the overall expense of the structure, especially where the method gradients cannot be steep as for railway bridges.

Cable Stayed Decks

Cable-stayed bridges, under the category in which the bridge spans between 150m and 1000m. Cable-stayed bridges are generally affordable for spans in excess of 250m.  Straight cables are connected directly to the deck and result in important axial forces into the deck. Consequently, the structure is self-anchoring and relies less on the ground conditions than the suspension bridge.

Suspension Bridges

Suspension bridges are another type in which used bridge spans more than 350m. Numerous early suspension bridges have been designed without the sensitivity of wind effects. Large deflections have been formed in the flexible decks and wind loading formed weak oscillations. The problem changed into largely solved by using tilted hangers. The suspension bridge is a catenary cable prestressed through absolute weight. The cables are led over the support towers to ground anchors. The strengthened deck is supported particularly through vertical or inclined hooks.

Bridge Deck Comparisons

The factors affecting life-span of bridge deck are Thermal expansion, Fatigue, overloads, Wear and abrasion

Methodology

In common, the method to compute site-specific bridge traffic loading consists of the following steps:

Traffic data collection: This presents the idea for the evaluation. It traditionally includes truck weight and axle information, and more recently vehicle acceleration and time headways, generally good enough for short-span bridges. however, reasonable premises need to be made during congestion, because of the shortage of congested traffic data.

Generation of a database: As the traffic data is generally not large good enough to identify the rare loading events used for bridge design and assessment, an extended garage of invented motors may be formed the usage of common Monte Carlo methods based on the recorded information.

Simulation of load effects: The traffic database is taken over a bridge and the essential load effects are calculated, for situation using influence principles or finite element analysis; if applicable, dynamic effects are also calculated

Extrapolation: As it may be still considerably computationally requiring to simulate traffic for very long intervals, load effects are moreover extrapolated to find appropriate values with the security level needed by the codes of practice. These values can be then compared to the resistance of similar members

Model calibration: When the objective is to develop a code to be implemented for a range of conditions, then a notional pressure model is found which envelopes the considered load effects. The calibration process often includes reliability examination to derive proper partial security factors

British Standard’s Traffic Load Models (HA and HB)

The first approved vehicle load for highway bridges in the UK was launched in 1922. There are many kinds of research carried on the permanence of highway bridges in conducting numerous traffic loadings as the initial source of stress on the structure. These traffic loads are analyzed in bridge examination and design according to the specific design code used in the country of practice.  Type HA uniformly distributed loading represented typical traffic loads and HB represents heavy unusual loads. These have been replaced in the current Eurocode with HA modified to Load Model 1 and HB modified to Load Model 3. Nevertheless, for this assignment, we will be examining the outcomes of the British standard model.

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Type HA Loading

The Type HA loading is the official design loading for Great Britain and adequately meets the effects of all allowed normal vehicles other than those used for unusual indivisible loads. In  the Road Vehicles Regulations 1998 (Authorised Weight), pointed to as the AW Vehicles and cover vehicles up to 44-tonne gross vehicle weight. Loads from those AW vehicles are described by a Knife Edge Load and a Uniformly Distributed Load.

 The loading has been enhanced to cover:

• overloading which means an excessive load.
• Impact load which means load applied with short duration. 
• Lateral bunching which means that the width of a lane is occupying by more than one vehicle 

The loaded length is associated with the quantity of the Uniformly Distributed Load as defined from the impact line for the member under consideration. For simply supported single span decks this usually associates to the span of the deck. Notational lane holding  HA UDL +KEL  load are shown below,

The Uniformly Distributed Load (W kN/m) is multiplied by a lane factor β to obtain the value to be implemented to each notional lane. If the Uniformly Distributed Load is claimed in kN/m2 then W will required to be divided by the notional lane width bL.

The knife-edge load referred to as KEL is also populated by the lane factor β. The knife-edge load may be placed anywhere along the loaded length to reach the worst effect in the member being considered. A single wheel load of 100 kN also needs to be examined as a choice to the Uniformly Distributed Load and knife-edge load as part of the HA loading design. The wheel load can produce more severe effects than the UDL+KEL on short span members. 

Type HB Loading

The Type HB loading conditions determine from the nature of extraordinary loads mainly concerning industrial transportation possible to handle the roads in the area such as electrical transformers, generators, pressure vessels, machine presses, etc...

The vehicle load is specified by a four-axle carrier with four wheels equally aligned on each axle. The load on each axle  is represented by several units which are dependent on the class of  road and is specified in BD 37/01 Chapter 4 conditions. Motorways and trunk roads require 45 units, Principal roads require 37.5 units and other public roads require 30 units. One unit of HB is similar to 10kN per axle. There are five HB vehicles to check although most vehicles can be allowed by inspection. The spacing between the inner two axles of the vehicle has five different values which provide the range of HB wheels to consider. These are shown below

Figure – Type HB loading of one unit.

Only one HB vehicle is considered to load anyone superstructure. The vehicle is placed within one notional lane or balances two notional lanes to obtain the most consequential effect on the member. HA loading is placed in any remaining lane not occupied by the HB vehicle. Also, if the deck is long enough, the HA UDL only is placed in the lane occupied by the HB vehicle and also is prohibited from the length of lane within 25m from the front and back of the HB vehicle.

Design

The purpose of the design procedure is to analyse the bridge for HA and HB load effects applying the appropriate load factors. The member is then designed for the worst impacts of HA or HB loading.

REFERENCES

• Bridge Deck Behaviour by E.C. Hambly covers methods of analysis of various types of bridge decks.
• Eurocode Design Guides for Bridges