1. Box girder bridges have two key advantages over plate girder bridges: they possess torsional stiffness and can have much wider flanges.
2. For medium span bridges between 45-100 meters, box girder bridges offer an attractive form of construction as they maintain simplicity while allowing larger span-to-depth ratios compared to plate girders.
3. Advances in welding and cutting techniques have expanded the structural possibilities for box girders, allowing for more economical designs of large welded units.
Design of steel structure as per is 800(2007)ahsanrabbani
It does not offer resistance against rotation and also termed as a hinged or pinned connections.
It transfers only axial or shear forces and it is not designed for moment
It is generally connected by single bolt/rivet and therefore full rotation is allowed
This document provides design aids for reinforced concrete structures based on Indian Standard IS: 456-1978 Code of Practice for Plain and Reinforced Concrete.
The design aids cover material strength and stress-strain relationships, flexural members, compression members, shear and torsion, development length and anchorage, working stress design, deflection calculation, and general tables. Charts and tables are provided for preliminary and final design of beams, slabs, and columns. Assumptions made in developing the design aids are explained. An example illustrates the use of the design aids. Important points regarding the use and limitations of the charts and tables are noted.
The design aids were prepared based on examination of international handbooks and consultation with Indian
This document describes the design of a pile cap by a group of civil engineering students. It defines a pile cap as a concrete mat that rests on piles driven into soft ground to provide a stable foundation. It then provides two examples of pile cap design, showing dimensions, load calculations, reinforcement requirements and construction details. The document concludes that a pile cap distributes a building's load to piles to form a stable foundation on unstable soil. It acknowledges the guidance of professors in completing this project.
The document summarizes a student group's summer training project constructing a box culvert for the North Western Railway in Banswara, India. It describes the project details, components and materials of the box culvert, laboratory and field tests conducted, concrete mix design, construction layout, execution process, and structural analysis considering various loads. The students gained hands-on experience applying their classroom knowledge to the real-world construction of the box culvert.
Combine piled raft foundation (cprf)_Er.Karan ChauhanEr.Karan Chauhan
Combine Piled Raft Foundation(CPRF) is an emerging type of new foundation techniques in High rise buildings and skyscraper which raft as a shallow foundation and pile as deep foundation works sharing the total load and reduce settlement and bending moment. the modern approach of design philosophy is included in post graduation level with soil structure interaction of CPRF and this will use to understand the basic concept regarding it.
The document discusses the balanced cantilever method of bridge construction. It begins by explaining that this method is used for bridges with spans between 50-250m, and involves attaching precast or cast-in-place segments in an alternating manner from each end of cantilevers supported by piers. This method is well-suited for irregular spans, congested sites, and environmentally sensitive areas. It also discusses advantages like determinacy and reduced cracking risks. The document then goes into detail about construction sequences, member proportioning, superstructure types, and analysis of a specific balanced cantilever bridge in Kochi, India.
Design of steel structure as per is 800(2007)ahsanrabbani
It does not offer resistance against rotation and also termed as a hinged or pinned connections.
It transfers only axial or shear forces and it is not designed for moment
It is generally connected by single bolt/rivet and therefore full rotation is allowed
This document provides design aids for reinforced concrete structures based on Indian Standard IS: 456-1978 Code of Practice for Plain and Reinforced Concrete.
The design aids cover material strength and stress-strain relationships, flexural members, compression members, shear and torsion, development length and anchorage, working stress design, deflection calculation, and general tables. Charts and tables are provided for preliminary and final design of beams, slabs, and columns. Assumptions made in developing the design aids are explained. An example illustrates the use of the design aids. Important points regarding the use and limitations of the charts and tables are noted.
The design aids were prepared based on examination of international handbooks and consultation with Indian
This document describes the design of a pile cap by a group of civil engineering students. It defines a pile cap as a concrete mat that rests on piles driven into soft ground to provide a stable foundation. It then provides two examples of pile cap design, showing dimensions, load calculations, reinforcement requirements and construction details. The document concludes that a pile cap distributes a building's load to piles to form a stable foundation on unstable soil. It acknowledges the guidance of professors in completing this project.
The document summarizes a student group's summer training project constructing a box culvert for the North Western Railway in Banswara, India. It describes the project details, components and materials of the box culvert, laboratory and field tests conducted, concrete mix design, construction layout, execution process, and structural analysis considering various loads. The students gained hands-on experience applying their classroom knowledge to the real-world construction of the box culvert.
Combine piled raft foundation (cprf)_Er.Karan ChauhanEr.Karan Chauhan
Combine Piled Raft Foundation(CPRF) is an emerging type of new foundation techniques in High rise buildings and skyscraper which raft as a shallow foundation and pile as deep foundation works sharing the total load and reduce settlement and bending moment. the modern approach of design philosophy is included in post graduation level with soil structure interaction of CPRF and this will use to understand the basic concept regarding it.
The document discusses the balanced cantilever method of bridge construction. It begins by explaining that this method is used for bridges with spans between 50-250m, and involves attaching precast or cast-in-place segments in an alternating manner from each end of cantilevers supported by piers. This method is well-suited for irregular spans, congested sites, and environmentally sensitive areas. It also discusses advantages like determinacy and reduced cracking risks. The document then goes into detail about construction sequences, member proportioning, superstructure types, and analysis of a specific balanced cantilever bridge in Kochi, India.
Suspension Bridges VS Cable-Stayed BridgesHussein Zidan
The document discusses different types of bridges including beam, truss, arch, suspension, cantilever, and cable-stayed bridges. It then focuses on suspension bridges, providing details on their construction and notable examples like the Akashi Kaikyo Bridge in Japan, which has the world's largest suspension bridge main span at 1,991 meters. Cable-stayed bridges are also examined, comparing their construction and forces to suspension bridges. The Russky Bridge in Russia is given as an example of a long cable-stayed bridge type.
Progressive collapse is the result of a localized failure of one or two structural elements that lead to a steady progression of load transfer that exceeds the capacity of other surrounding elements, thus initiating the progression that leads to a total or partial collapse of the structure. The present study is to evaluate the behavior of G+8 reinforced concrete building subjected to potential collapse. The reinforced concrete structure is analyzed by Pushover Analysis using ETABS Software. It shows the maximum storey displacement and a maximum storey drift values of the components are studied. And the potential of the progressive collapse is determined.
This document discusses the design of column braces for structures. It defines braced and unbraced columns, with braced columns having zero sway and stability provided by walls or bracing, while unbraced columns are subjected to sway with stability only from other columns. It describes different types of internal and external bracing patterns and factors to consider in brace analysis, including displacement, base shear, wind loads, maximum shear and bending moments. The document provides guidelines for designing braces based on column moments and explains how bracing type affects seismic resistance parameters through a parametric study.
Two way slabs are slabs that are supported on all four edges and have a ratio of less than 2 between their long and short spans. This causes them to bend in both directions. There are two types: simply supported and restrained. Simply supported slabs have corners that lift up under loading while restrained slabs have corners that are held down, producing torsion. Reinforcement is provided differently depending on the type of slab.
This document discusses different types of bridge foundations. It describes shallow foundations like open foundations and block foundations. It also describes deep foundations such as pile foundations and well foundations. Pile foundations use timber, reinforced concrete, or bored pipe piles below the river bed. Well foundations involve constructing a well structure and sinking it into the ground to transmit heavy loads. The document provides details on the components and advantages of well foundations. It also lists ideal characteristics for selecting a bridge site such as suitable foundation material, straight banks, and minimum obstructions.
This document discusses the design of two-way floor slab systems. It compares the behavior of one-way and two-way slabs, describing how two-way slabs carry load in two directions versus one direction for one-way slabs. Different two-way slab systems like flat plates, waffle slabs, and ribbed slabs are described. Methods for analyzing two-way slabs include direct design, equivalent frame, elastic, plastic, and nonlinear analysis. Design considerations like minimum slab thickness are discussed along with examples calculating thickness.
The document discusses bridge types, components, selection criteria, and design considerations. It begins by defining what a bridge is and its purpose in transportation systems. It then covers typical bridge components and various structural forms for bridges based on material, span length, and other factors. Key criteria for selecting bridge types include span length, site conditions, cost, and aesthetics. The document emphasizes that aesthetic design requires considering function, proportion, harmony, order/rhythm, and contrast/texture to create pleasing structures that blend with their environments.
The document discusses limit state design of reinforced concrete structures. It introduces limit states as conditions where the structure becomes unfit for use, including limit states of strength and serviceability. Limit state design involves characterizing loads and resistances as random variables and using partial safety factors on loads and resistances to achieve a target reliability. The document outlines the general principles of limit state design according to Indian Standard code IS 800, including defining actions, factors governing strength limits, and serviceability limits related to deflection, vibration and durability.
Retaining walls are used at the Shraddha Vivanta Residency construction site in Mumbai for two main purposes. Cantilever retaining walls around 3.5 meters deep allow for a basement and four floors of stacked parking underneath the residential building. Additional retaining walls surround underground water tanks for suction and firefighting. The walls are located along the building perimeter and around the tank areas. Proper waterproofing of the retaining walls is important given their underground locations.
This document discusses bolted connections used in structural engineering. It begins by explaining why connection failures should be avoided, as they can lead to catastrophic structural failures. It then classifies bolted connections based on their method of fastening, rigidity, joint resistance, fabrication location, joint location, connection geometry, and type of force transferred. It describes different types of bolts and bolt tightening techniques used for friction grip connections. It discusses advantages and drawbacks of bolted connections compared to riveted or welded connections. The document provides detailed information on design and behavior of various bolted connections.
This document discusses the need for raft foundations. Raft foundations are recommended when:
1) Building loads are heavy or soil capacity is low, so individual footings would cover too much area.
2) Soil contains weak lenses or cavities, making differential settlement hard to predict.
3) Structures are sensitive to differential settlement.
4) Structures like silos naturally suit raft foundations.
5) Floating foundations are needed over very weak soil.
6) Buildings require basements or underground pits.
7) Individual footings would experience large bending stresses.
Raft foundations increase capacity, decrease settlement, and equalize differential settlement compared to individual footings. However,
This document summarizes the key aspects of box culvert design and analysis. Box culverts consist of horizontal and vertical slabs built monolithically, and are used for bridges with limited stream flows and high embankments up to spans of 4 meters. They are economical due to their rigidity and do not require separate foundations. Design loads include concentrated wheel loads, uniform loads from embankments and decks, sidewall weights, water pressure when full, earth pressures, and lateral loads. The culvert is analyzed for moments, shears, and thrusts using classical methods to determine force effects from these various loading conditions.
This document provides information on the structural design of a simply supported reinforced concrete beam. It includes:
- A list of students enrolled in an elementary structural design course.
- Equations and diagrams showing the forces and stresses in a reinforced concrete beam with a singly reinforced bottom section.
- Limits on the maximum depth of the neutral axis according to the grade of steel.
- Examples of analyzing the stresses and determining steel reinforcement for a given beam cross-section.
- A design example calculating the dimensions and steel reinforcement for a rectangular beam with a factored uniform load.
DESIGN OF BOX CULVERT AS PER IRC-112: 2011, INTERNSHIP PROJECT REPORT.
INCLUDES:
1) BASIC DETAILS
2) DESIGN OF 2 CELL BOX CULVERT
3) DESIGN OF WING WALLS (RETAINING WALLS) AS PER IRC
Prestressed concrete is concrete that is placed under compression using tensioned steel strands, cables, or bars. This is done through either pre-tensioning or post-tensioning. In pre-tensioning, the steel components are tensioned before the concrete is poured, while in post-tensioning, the steel components are tensioned after the concrete has hardened. Prestressed concrete provides benefits over reinforced concrete like lower construction costs, thinner structural elements, and longer spans between supports.
This document summarizes the design of a single reinforced concrete corbel according to ACI 318-05. The corbel is 300mm wide and 500mm deep with 35MPa concrete and 415MPa steel reinforcement. It was designed to resist a vertical load of 370kN applied 100mm from the face of the column. The design includes checking the vertical load capacity, calculating the required shear friction and main tension reinforcement, and designing the horizontal reinforcement. The provided reinforcement of 3 No.6 bars for tension and 3 No.3 link bars at 100mm spacing was found to meet all design requirements.
This document discusses shear wall analysis and design. It defines shear walls as structural elements used in buildings to resist lateral forces through cantilever action. The document classifies different types of shear walls and discusses their behavior under seismic loading. It outlines the steps for designing shear walls, including reviewing layout, analyzing structural systems, determining design forces, and detailing reinforcement. The document emphasizes the importance of properly locating shear walls in a building to resist seismic loads and minimize torsional effects.
Seismic Analysis of regular & Irregular RCC frame structuresDaanish Zama
This document discusses seismic analysis of regular and irregular reinforced concrete framed buildings. It analyzes 4 building models - a regular 4-story building, a stiffness irregular building with a soft ground story, and two vertically irregular buildings with setbacks on the 3rd floor and 2nd/3rd floors. Static analysis was performed to compare bending moments, shear forces, story drifts, and joint displacements. Results showed irregular buildings experienced higher seismic demands. The regular building performed best, with the single setback building also performing well. Irregular configurations increase seismic effects and should be minimized in design.
The document discusses large span structures and provides definitions and examples of common structural systems used for large spans. It defines a large span structure as having a span larger than 15-20 meters. Common structural systems described include long span beams, trusses, tensile structures, folded plates, and portal frames. Long span beams are summarized as utilizing parallel beams, composite beams with web openings, cellular composite beams, tapered girders, and haunched composite beams. Long span trusses include Pratt, Warren, north light, saw tooth, Fink, and tubular steel trusses. Tensile structures carry loads only in tension and are used for roofs, with examples of linear, 3D, and
Influence line diagram for model arch bridgekunalsahu9883
The Lupu Bridge in Shanghai, China is a steel box section tied arch bridge with a main span of 550m, making it the largest arch bridge in the world when it was completed. A tied arch bridge design was used because the ground conditions on either side of the river were unsuitable for the large forces from a normal arch bridge. The bridge was analyzed using structural analysis software to determine member forces and deformations under load. The bridge is an impressive engineering feat that helped advance Chinese bridge engineering.
Suspension Bridges VS Cable-Stayed BridgesHussein Zidan
The document discusses different types of bridges including beam, truss, arch, suspension, cantilever, and cable-stayed bridges. It then focuses on suspension bridges, providing details on their construction and notable examples like the Akashi Kaikyo Bridge in Japan, which has the world's largest suspension bridge main span at 1,991 meters. Cable-stayed bridges are also examined, comparing their construction and forces to suspension bridges. The Russky Bridge in Russia is given as an example of a long cable-stayed bridge type.
Progressive collapse is the result of a localized failure of one or two structural elements that lead to a steady progression of load transfer that exceeds the capacity of other surrounding elements, thus initiating the progression that leads to a total or partial collapse of the structure. The present study is to evaluate the behavior of G+8 reinforced concrete building subjected to potential collapse. The reinforced concrete structure is analyzed by Pushover Analysis using ETABS Software. It shows the maximum storey displacement and a maximum storey drift values of the components are studied. And the potential of the progressive collapse is determined.
This document discusses the design of column braces for structures. It defines braced and unbraced columns, with braced columns having zero sway and stability provided by walls or bracing, while unbraced columns are subjected to sway with stability only from other columns. It describes different types of internal and external bracing patterns and factors to consider in brace analysis, including displacement, base shear, wind loads, maximum shear and bending moments. The document provides guidelines for designing braces based on column moments and explains how bracing type affects seismic resistance parameters through a parametric study.
Two way slabs are slabs that are supported on all four edges and have a ratio of less than 2 between their long and short spans. This causes them to bend in both directions. There are two types: simply supported and restrained. Simply supported slabs have corners that lift up under loading while restrained slabs have corners that are held down, producing torsion. Reinforcement is provided differently depending on the type of slab.
This document discusses different types of bridge foundations. It describes shallow foundations like open foundations and block foundations. It also describes deep foundations such as pile foundations and well foundations. Pile foundations use timber, reinforced concrete, or bored pipe piles below the river bed. Well foundations involve constructing a well structure and sinking it into the ground to transmit heavy loads. The document provides details on the components and advantages of well foundations. It also lists ideal characteristics for selecting a bridge site such as suitable foundation material, straight banks, and minimum obstructions.
This document discusses the design of two-way floor slab systems. It compares the behavior of one-way and two-way slabs, describing how two-way slabs carry load in two directions versus one direction for one-way slabs. Different two-way slab systems like flat plates, waffle slabs, and ribbed slabs are described. Methods for analyzing two-way slabs include direct design, equivalent frame, elastic, plastic, and nonlinear analysis. Design considerations like minimum slab thickness are discussed along with examples calculating thickness.
The document discusses bridge types, components, selection criteria, and design considerations. It begins by defining what a bridge is and its purpose in transportation systems. It then covers typical bridge components and various structural forms for bridges based on material, span length, and other factors. Key criteria for selecting bridge types include span length, site conditions, cost, and aesthetics. The document emphasizes that aesthetic design requires considering function, proportion, harmony, order/rhythm, and contrast/texture to create pleasing structures that blend with their environments.
The document discusses limit state design of reinforced concrete structures. It introduces limit states as conditions where the structure becomes unfit for use, including limit states of strength and serviceability. Limit state design involves characterizing loads and resistances as random variables and using partial safety factors on loads and resistances to achieve a target reliability. The document outlines the general principles of limit state design according to Indian Standard code IS 800, including defining actions, factors governing strength limits, and serviceability limits related to deflection, vibration and durability.
Retaining walls are used at the Shraddha Vivanta Residency construction site in Mumbai for two main purposes. Cantilever retaining walls around 3.5 meters deep allow for a basement and four floors of stacked parking underneath the residential building. Additional retaining walls surround underground water tanks for suction and firefighting. The walls are located along the building perimeter and around the tank areas. Proper waterproofing of the retaining walls is important given their underground locations.
This document discusses bolted connections used in structural engineering. It begins by explaining why connection failures should be avoided, as they can lead to catastrophic structural failures. It then classifies bolted connections based on their method of fastening, rigidity, joint resistance, fabrication location, joint location, connection geometry, and type of force transferred. It describes different types of bolts and bolt tightening techniques used for friction grip connections. It discusses advantages and drawbacks of bolted connections compared to riveted or welded connections. The document provides detailed information on design and behavior of various bolted connections.
This document discusses the need for raft foundations. Raft foundations are recommended when:
1) Building loads are heavy or soil capacity is low, so individual footings would cover too much area.
2) Soil contains weak lenses or cavities, making differential settlement hard to predict.
3) Structures are sensitive to differential settlement.
4) Structures like silos naturally suit raft foundations.
5) Floating foundations are needed over very weak soil.
6) Buildings require basements or underground pits.
7) Individual footings would experience large bending stresses.
Raft foundations increase capacity, decrease settlement, and equalize differential settlement compared to individual footings. However,
This document summarizes the key aspects of box culvert design and analysis. Box culverts consist of horizontal and vertical slabs built monolithically, and are used for bridges with limited stream flows and high embankments up to spans of 4 meters. They are economical due to their rigidity and do not require separate foundations. Design loads include concentrated wheel loads, uniform loads from embankments and decks, sidewall weights, water pressure when full, earth pressures, and lateral loads. The culvert is analyzed for moments, shears, and thrusts using classical methods to determine force effects from these various loading conditions.
This document provides information on the structural design of a simply supported reinforced concrete beam. It includes:
- A list of students enrolled in an elementary structural design course.
- Equations and diagrams showing the forces and stresses in a reinforced concrete beam with a singly reinforced bottom section.
- Limits on the maximum depth of the neutral axis according to the grade of steel.
- Examples of analyzing the stresses and determining steel reinforcement for a given beam cross-section.
- A design example calculating the dimensions and steel reinforcement for a rectangular beam with a factored uniform load.
DESIGN OF BOX CULVERT AS PER IRC-112: 2011, INTERNSHIP PROJECT REPORT.
INCLUDES:
1) BASIC DETAILS
2) DESIGN OF 2 CELL BOX CULVERT
3) DESIGN OF WING WALLS (RETAINING WALLS) AS PER IRC
Prestressed concrete is concrete that is placed under compression using tensioned steel strands, cables, or bars. This is done through either pre-tensioning or post-tensioning. In pre-tensioning, the steel components are tensioned before the concrete is poured, while in post-tensioning, the steel components are tensioned after the concrete has hardened. Prestressed concrete provides benefits over reinforced concrete like lower construction costs, thinner structural elements, and longer spans between supports.
This document summarizes the design of a single reinforced concrete corbel according to ACI 318-05. The corbel is 300mm wide and 500mm deep with 35MPa concrete and 415MPa steel reinforcement. It was designed to resist a vertical load of 370kN applied 100mm from the face of the column. The design includes checking the vertical load capacity, calculating the required shear friction and main tension reinforcement, and designing the horizontal reinforcement. The provided reinforcement of 3 No.6 bars for tension and 3 No.3 link bars at 100mm spacing was found to meet all design requirements.
This document discusses shear wall analysis and design. It defines shear walls as structural elements used in buildings to resist lateral forces through cantilever action. The document classifies different types of shear walls and discusses their behavior under seismic loading. It outlines the steps for designing shear walls, including reviewing layout, analyzing structural systems, determining design forces, and detailing reinforcement. The document emphasizes the importance of properly locating shear walls in a building to resist seismic loads and minimize torsional effects.
Seismic Analysis of regular & Irregular RCC frame structuresDaanish Zama
This document discusses seismic analysis of regular and irregular reinforced concrete framed buildings. It analyzes 4 building models - a regular 4-story building, a stiffness irregular building with a soft ground story, and two vertically irregular buildings with setbacks on the 3rd floor and 2nd/3rd floors. Static analysis was performed to compare bending moments, shear forces, story drifts, and joint displacements. Results showed irregular buildings experienced higher seismic demands. The regular building performed best, with the single setback building also performing well. Irregular configurations increase seismic effects and should be minimized in design.
The document discusses large span structures and provides definitions and examples of common structural systems used for large spans. It defines a large span structure as having a span larger than 15-20 meters. Common structural systems described include long span beams, trusses, tensile structures, folded plates, and portal frames. Long span beams are summarized as utilizing parallel beams, composite beams with web openings, cellular composite beams, tapered girders, and haunched composite beams. Long span trusses include Pratt, Warren, north light, saw tooth, Fink, and tubular steel trusses. Tensile structures carry loads only in tension and are used for roofs, with examples of linear, 3D, and
Influence line diagram for model arch bridgekunalsahu9883
The Lupu Bridge in Shanghai, China is a steel box section tied arch bridge with a main span of 550m, making it the largest arch bridge in the world when it was completed. A tied arch bridge design was used because the ground conditions on either side of the river were unsuitable for the large forces from a normal arch bridge. The bridge was analyzed using structural analysis software to determine member forces and deformations under load. The bridge is an impressive engineering feat that helped advance Chinese bridge engineering.
This document provides an overview of box girder bridges. It discusses the key features and advantages of box girder bridges, including their high torsional stiffness and structural efficiency. The document also examines the general behavior of curved box girder bridges, noting the effects of bending, torsion, and warping stresses. Finally, it reviews several past studies that have analyzed box girder bridges through experimental testing, finite element analysis, and varying parameters like curvature, span length, and cross-sectional depth.
Retrofitting of Bridge with Voided Slab to raise the Deck LevelIRJET Journal
The document discusses retrofitting an existing bridge by casting a voided slab over the existing deck slab. A voided slab is lighter than a solid slab and can reduce the self-weight and cost of the structure. Polystyrene boxes are placed on the deck slab and filled with concrete to form voids above. This allows increasing the road level without overloading the bridge girders. The voided slab is modeled in STAAD Pro to analyze bending moments and check the design is adequate. The voided slab reduces the weight and cost of construction compared to a solid slab.
This document provides details on the design of a cable-stayed bridge project over the Suez Canal. The key aspects are:
1) The bridge has a total length of 730m with a 165m side span and 400m main span. It consists of a concrete box girder deck, H-shaped concrete pylons that are 150m tall, and 16 pre-tensioned steel strand cables on each side.
2) Analyses were conducted to determine cable forces, member forces and deformations due to self-weight, live loads, wind, and earthquakes. The bridge was found to meet design criteria.
3) The main components of the deck, pylons, and cables are
This document provides details on the design of a cable-stayed bridge project over the Suez Canal. It includes the following key points:
1) The bridge has a main span of 400m and two side spans of 165m each for a total length of 730m. It uses an H-shaped reinforced concrete pylon that is 150m tall to support 36 stay cables arranged in a semi-fan configuration.
2) The bridge deck is a 3m deep concrete box girder 20m wide to accommodate 4 lanes of traffic. Finite element analysis was used to model the bridge and optimize the cable tensions to minimize deformations.
3) Analysis considered dead loads, live loads, wind loads,
Different forms of steel intensive structures, shape optimisation,stability,p...SanjibKumarMandal1
THE FRAME GEOMETRY MATCHES THE SHAPE OF THE BENDING MOMENT DIAGRAM FOR OPTIMAL DESIGN, THUS MINIMIZING MATERIAL WASTE AND REDUCING THE TOTAL WEIGHT OF FRAMES
This document discusses reinforced concrete (RC) girder bridges. It begins by defining girder bridges as the simplest bridge type, consisting of horizontal beams supported at each end. RC girder bridges are comprised of deck slabs that vehicles drive on, supported by main girders. There are three main types of girder bridges: box girders, which can handle twisting forces and are suitable for longer spans; concrete girders made of pre-stressed concrete; and I-beam girders made of steel. RC girder bridges must be designed to support dead loads from the structure itself, live loads from traffic, and dynamic loads from wind and weather.
Ch8 Truss Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...Hossam Shafiq II
This chapter discusses truss bridges. It begins by defining a truss as a triangulated assembly of straight members that can be used to replace girders. The main advantages of truss bridges are that primary member forces are axial loads and the open web system allows for greater depth.
The chapter then describes the typical components of a through truss bridge and the most common truss forms including Pratt, Warren, curved chord, subdivided, and K-trusses. Design considerations like truss depth, economic spans, cross section shapes, and wind bracing are covered. The chapter concludes with sections on determining member forces, design principles, and specific design procedures.
This document discusses steel-concrete composite construction. It describes shear connectors, which provide composite action between steel beams and concrete slabs. There are three main types of shear connectors: rigid connectors made of steel bars or angles that resist shear through bearing pressure; flexible stud connectors that bend and fail through yielding; and bond-type connectors that rely on bond and anchoring. The document discusses the design of shear connectors according to Indian codes IRC 22-1986 and IS 11384-1985, providing methods to calculate the design strength of shear connectors.
This document summarizes a seminar presentation on stress ribbon bridges. It defines a stress ribbon bridge as a tension structure similar to a simple suspension bridge, where the suspension cables are embedded in the deck which follows a catenary arc between supports. This provides stiffness to prevent excessive swaying. Such bridges use pre-tensioned concrete reinforced by steel cables. The document outlines the history and theory behind stress ribbon bridges, describes their construction process, and provides examples of existing stress ribbon bridges along with their advantages and disadvantages.
The document discusses rigid frame systems used in high-rise buildings. It provides a history of rigid frames, an introduction to what they are, and examples of their applications. It describes the material properties and connections used. It discusses considerations for rigid frame design like behavior under lateral loads. It notes advantages like architectural freedom but also disadvantages like increased drift. It concludes with a case study on using hybrid rigid/semi-rigid frames to improve seismic performance.
Running Head BRIDGE DESIGN1BRIDGE DESIGN31.docxtoddr4
Running Head: BRIDGE DESIGN 1
BRIDGE DESIGN 31
Title:
Student Name:
Institution:
Course:
Date:
BRIDGE DESIGN FOR THE MOTOR WAY BELOW
8m
Embankment
A
Motorway
16m
10m
Central Reservation
Motorway
16m
Grass Verge
Existing Factory Units
Footway
A
Carriagewaym
Existing Factory Units
Fixed Factory Entrance
Fixed Factory Entrance
3m
2m
3m
2m
10mm
Existing Highway to Proposed Bridge
Existing Development
Proposed Development
Existing Development
Existing Retaining Wall – 500mm thick rc construction indicated by old record drawings
Central Reservation
10m
10m
Section A-A
2m footway
1.2m high parapets
10m carriageway
Bridge Deck Section
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 .
This document provides an introduction and literature review on concrete filled steel tube (CFST) columns. Some key points:
1) CFST columns utilize the advantages of both steel and concrete by using a steel hollow section filled with concrete. They are widely used in building construction.
2) Previous research has shown CFST columns have improved structural performance due to confinement of the concrete core by the steel tube. They also have construction advantages due to their simple erection sequence.
3) The literature review covers the behavior of CFST under different load cases like axial, bending, and combined loads. It also discusses design concepts, analytical methods, and codes/standards for CFST columns.
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2. Steel Bridges
CHAPTER 7
BOX GIRDER BRIDGES
7.1 INTRODUCTION
Box girders have two properties which can offer substantial advantages in
certain circumstances over plate girders:
1- they possess torsional stiffness, and
2- their flanges can be made much wider, thus solving the problem of
providing a large steel area within a narrow width of plate.
As well as being advantageous in the completed condition of the bridge,
these properties can also make box girder bridges simpler in principle to
erect. The problems of lateral torsional buckling, for example, do not arise,
and if a bridge is to be erected by cantilevering, very long unsupported spans
can be adopted.
For medium span bridges, box girders offer an attractive form of
construction. Design and construction techniques already popular and
common for plate girder bridges can be utilized to produce box girder bridges
of clean appearance whilst maintaining relative simplicity and speedy
construction procedures. The scope of application of such designs could
cover the medium span range from about 45 m to 100 m.
Until 1940 the structural possibilities for box girders were limited; most
bridge girders were assembled from rolled sections, plates and riveted
connections. With the development of electric welding and precision flame
cutting, the structural possibilities increased enormously. It is now possible to
design large welded units in a more economical way.
3. Chapter 7: Box Girder Bridges 277
A bridge box girder consists of, see Fig. 7.1 :
1. a concrete deck or an orthotropic steel deck serving as the top flange.
2. a stiffened plate as a bottom flange.
3. Web plates, vertical or inclined.
4. stiff diaphragms or cross bracings at supports, and lighter diaphragms
or cross bracings at distances of about 2.5 times the construction depth.
Fig. 7.1 Components of a Box Girder
Clearly, the feature which differentiates the behavior of box girder bridges
from plate girder bridges is the much greater torsional stiffness of the closed
section. The prime effect this has on global bending behavior is to share the
vertical shear more equally between the web plates. Consequently upon this
equal sharing, bending stresses in the flange plates are also more evenly
shared. As a result, box girders behave more efficiently – there is less need to
design for peak load effects which occur on only one plate girder at a time.
Box girders, in addition, have other advantages over plate girders which
make their use attractive; such as:
i- a much neater appearance since the stiffening can remain invisible inside
the box.
ii- the use of inclined webs provides an efficient aerodynamic shape which
is important for long span bridges, see Fig. 7.2.
4. Steel Bridges
Fig. 7.2 Box Girder Section for Long Span Bridges
UUUsual Span Ranges:UU Box girders are suitable for longer span than plate
girders and allow larger span-to-depth ratios. The span to depth ratio will
normally be around 20 to 25 for simple girders and around 25 to 35 for
continuous girders. It is possible to reduce the depth, if necessary, at the
expense of additional steel. The above ratios are valid for roadway bridges.
For railway bridges the ratios should be smaller, say 15 and 20. The
following table gives the economic span limits for roadway bridges:
Composite concrete
deck
Orthotropic
deck
Simple span 20 – 100 70 – 120
Continuous spans 30 – 140 100 – 250
The longest span so far is 300 m achieved in 1974 by costa de silva bridge
in Rio de Janeiro.
7.2 CROSS SECTION ARRANGEMENTS
Box girder bridges can be constructed with single, twin or multiple box
girders. Generally, single box forms, Fig. 7.3 are limited to bridges of fairly
narrow width (although some very wide shallow single boxes have been used
in long span suspension bridges which are outside the scope of this book).
5. Chapter 7: Box Girder Bridges 279
Fig. 7.3 Box Girder Bridge Sections with One Box
6. Steel Bridges
Typical width of the boxes themselves would be between about 2 m and 4
m although both wider and narrower boxes have been used (it is common
practice for the box to be made complete in the fabricator's works in order to
minimize site assembly; boxes much in excess of 4 m in width, whilst
perfectly practical to design and fabricate, can cause problems in transport).
Cantilever brackets would normally be made between about 3 m and 5 m
long, and cross girders between 10 m and 15 m in length (again, of course,
these are not absolute limits, merely common practice). Using these figures
gives total bridge widths of between 8 m and 14 m for a single box with
cantilevers either side, and between 20 m and 33 m for twin boxes with cross
girders between them and cantilevers outside the outer webs.
The most usual layout for bridges of medium span consists of two
longitudinal box girders, interconnected by cross girders which are usually
fabricated plate girders and having also fabricated plate cantilever brackets
projecting beyond their outer webs (Fig.7.4). The deck can either be of
reinforced concrete or of orthotropic stiffened steel plate. If the deck is of
concrete, it will act compositely with the main box girders and also with the
transverse plate girders and cantilevers; if of steel plate, it forms parts of the
flanges of the boxes. As general guidance, a reinforced concrete deck would
be used if the bridge span is less than about 150 m, and an orthotropic steel
deck if it is over 200 m. Between these limits consideration should be given
to either form of construction. It must always be remembered that special
considerations may require the use of a particular type of deck outside the
suggested span ranges quoted above.
An alternative solution to two lane bridges involves carrying each lane on
its own individual single box girder. Such a layout has a number of
advantages in addition to overcoming the problem of fitting a cross girder
accurately between two longitudinal girders present in plate girder bridges.
The use of separate structures for the two lanes of a dual lane bridge ensures
that even if one superstructure is damaged or even destroyed the bridge can
continue to be used whilst it is being repaired or replaced, by diverting two
way traffic on to the remaining structure.
Multiple boxes are needed for wider roads. Alternatively, wide roads can
be carried on twin box sections with cross girders, so that the deck slab works
longitudinally, rather than transversally between the lines of the box webs.
7. Chapter 7: Box Girder Bridges 281
Fig. 7.4 Box Girder Bridge Sections with Two Boxes
When a reinforced concrete slab is used for the deck, the steel girders may
be closed box sections or may be open sections (U – shaped) which are
closed when the slab is cast. In this case separate (and relatively small) flange
plates are provided at the top of each web. These flanges need to be stabilized
laterally by upper horizontal bracing during construction. Shear connectors
are arranged on the top of these flanges to ensure composite action.
When the bridge deck is steel, the top flange plates are stiffened
orthotropically to carry traffic wheel loads as well as acting as the top flange
of the box girder. This stiffening usually takes the form of longitudinal
trapezoidal ribs supported at regular intervals by transverse beams.
8. Steel Bridges
In the descriptions above it has been implicitly assumed that the steel
boxes themselves are of rectangular cross-section. Whilst this is probably the
commonest cross-section, there is no reason in principle why the webs should
be vertical; many boxes from the smallest to the largest have had sloping
webs. In some cases of very large boxes this provides an expedient by which
a two lane deck maybe carried on a single box. The loading on the deck may
be transferred to the webs through deck slab action or through cross girders
inside the box bearing on transverse stiffeners on the webs. If the depth of the
web varies according to the bending moment requirements, the use of non-
vertical webs should be avoided since this combination would give rise to
extremely awkward detailing problems, and could sometimes result in ugly
appearance of the bridge
7.3 BEHAVIOUR OF BOX GIRDER BRIDGES
7.3.1 Structural Analysis
A global structural analysis of the bridge is usually required in order to
establish the maximum forces and moments at the critical sections of the
bridge under the variety of possible loading conditions. Local analysis of the
deck slab is usually carried out separately from the global analysis. For
proper and efficient evaluation of bending and torsion effects, it is necessary
to use computer analysis.
7.3.2 Bending, torsion and distortion
The general case of an eccentric load applied to a box girder may be
resolved into two components, see Fig. 7.5:
1- A symmetrical component with both webs subjected to two equal
vertical loads; and
2- An anti-symmetrical component with the two webs subjected to two
equal and opposite forces forming a couple.
The symmetric component causes the box girder to be subjected to:
1- shear and bending in a vertical plan
2- distortion from bending if the girder section is open
The anti-symmetric component causes the box girder to be subjected to:
1- shear stresses from torsions
2- distortion from torsion.
9. Chapter 7: Box Girder Bridges 283
Fig. 7.5 Effect of Eccentric Loading on Box Girder Sections:
10. Steel Bridges
7.4 Effect Bending
Bending moments produce longitudinal normal stresses in the box girder
given by:
y
I
M
f
x
x
=
Since box girders contain wide flanges, the distribution of the bending
stresses is non-uniform because the flange distorts in its own plane; i.e., plane
sections do not remain plane. This phenomenon is known as "Shear Lag".
Fig. 7.6 Actual Bending Stress Distribution in a Box Girder.
7.4.1 Shear Lag Phenomenon
When the axial load is fed into a wide flange by shear from the webs, the
flange distorts in its plane and plane sections do not remain plane. The
resulting stress distribution in the flange is not uniform as shown in Fig. 7.6.
In very wide flanges, shear lag effects have to be taken into account for the
verification of stresses, especially for short spans, since it causes the
longitudinal stress at a flange/web intersection to exceed the mean stress in
the flange.
Shear lag can be allowed for in the elementary theory of bending, by using
an effective flange breadth (less than the real breadth) such that the stress in
the effective breadth equals the peak stress in the actual flange, see Fig.7.7.
This effective flange breadth depends on the ratio of width to span.
11. Chapter 7: Box Girder Bridges 285
Fig. 7.7 Effective breadth for shear lag effects
The effective width is a function of the ratio of the span L to the width b of
the box, the cross-sectional area of the stress carrying stiffeners, and the type
and position of loading. For continuous girders, the effective widths are
obtained separately for the individual equivalent simple spans between the
points of inflection. Fortunately, in most situations the span/breadth ratio is
not sufficiently large to cause more than 10-20% increase in peak stress, on
account of shear lag.
According to British Standards UBS5400 : 3/2000:U The effective
width bRB
eRB should be taken as follows:
a) bRB
eRB = ψb for portions between webs:
where
b = half the distance between centers of webs measured along the
mid-plane of the flange plate;
b) bRB
eRB = kψb for portions projecting beyond an outer web;
where
b = distance from the free edge of the projecting portion to the centre
of the outer web; measured along the mid-plane of the flange
plate;
k = (1 – 0.15b/L);
L = span of a beam between centers of support,
or in the case of a cantilever beam, between the support and the
free end;
12. Steel Bridges
ψ = appropriate effective breadth ratio taken from Tables 7.1 – 7.3
for uniformly distributed loads;
a = 0 if there are no stiffeners on the flange within the width b in the
span direction, otherwise:
a =
bwidthinplateflangeofareasectional
bwidthinstiffenersflangeofareasectional
Values of ψ for intermediate values of b/L and a and for intermediate
positions in the span may be obtained by linear interpolation.
The value of ψ at an interior support should be taken as the mean of the
values obtained for adjacent spans. For end spans of continuous beams the
effective breadth ratios may be obtained by treating the end span as a propped
cantilever of the same span.
For the purpose of calculating deflections of beams, the values of ψ given
in these may be adopted for all sections in the span.
Table 7.1 – Effective breadth ratio ψ for simply supported beams
b/L
Mid-span Quarter span Support
a = 0 a= 1 a = 0 a = 1 a = 0 a = 1
0.00 1.00 1.00 1.00 1.00 1.00 1.00
0.05 0.98 0.97 0.98 0.96 0.84 0.77
0.10 0.95 0.89 0.93 0.98 0.70 0.60
0.20 0.81 0.67 0.77 0.62 0.52 0.38
0.30 0.66 0.47 0.61 0.44 0.40 0.28
0.40 0.50 0.35 0.46 0.32 0.32 0.22
0.50 0.38 0.28 0.36 0.25 0.27 0.18
0.75 0.22 0.17 0.20 0.16 0.17 0.12
1.00 0.16 0.12 0.15 0.11 0.12 0.09
13. Chapter 7: Box Girder Bridges 287
Table 7.2 – Effective breadth ratio ψ for interior spans of continuous beams
b/L
Mid-span Quarter span Support
a = 0 a = 1 a = 0 a = 1 a = 0 a = 1
0.00 1.00 1.00 1.00 1.00 1.00 1.00
0.05 0.96 0.91 0.85 0.76 0.85 0.50
0.10 0.86 0.72 0.68 0.55 0.41 0.32
0.20 0.58 0.40 0.42 0.31 0.24 0.17
0.30 0.38 0.27 0.30 0.20 0.15 0.11
0.40 0.24 0.18 0.21 0.14 0.12 0.08
0.50 0.20 0.14 0.16 0.11 0.11 0.07
0.75 0.15 0.10 0.10 0.08 0.09 0.06
1.00 0.13 0.09 0.09 0.07 0.07 0.05
Table 7.3 – Effective breadth ratio ψ for cantilever beams
b/L
Fixed end Quarter span near
fixed end
Free end
a = 0 a = 1 a = 0 a = 1 a = 0 a = 1
0.00 1.00 1.00 1.00 1.00 1.00 1.00
0.05 0.82 0.76 1.00 1.00 0.92 0.86
0.10 0.68 0.61 1.00 1.00 0.84 0.77
0.20 0.52 0.44 1.00 1.00 0.70 0.60
0.30 0.42 0.35 0.95 0.90 0.60 0.48
0.40 0.35 0.28 0.88 0.75 0.52 0.38
0.50 0.30 0.25 0.76 0.62 0.40 0.33
0.75 0.22 0.18 0.52 0.38 0.34 0.23
1.00 0.18 0.14 0.38 0.27 0.27 0.18
7.4.2 Effect of Local Buckling
In addition, web and flange plates of a box girder must satisfy the
requirements of ECP code for local plate buckling resulting from:
1- Axial compression in compression flange.
2- Bending compression in web.
3- Shear in web.
14. Steel Bridges
7.4.2.1 Local Buckling of Compression Flange:
The compression flange is non-compact if
yF
64
t
b
≤ for stiffened
elements and
yF
21
t
b
≤ for unstiffened elements
If (b/t) exceeds these limits then either:
(1) provide longitudinal flange stiffeners to satisfy these requirements; or
(2) base design on effective width bRB
eRB calculated as follows :
bRB
eRB = ρ b,
( ) )1(/05.015.0 p
2
p =ψλψ−−λ=ρ
σ=λ k/F
44
t/b
yp
7.4.2.2 Web Buckling due to Bending :
Web is non-compact in pure bending (ψ = -1 )
if:
yw
w
F
190
t
d
≤
For the case FRB
allRB = 0.58 fRB
yRB gives dRB
wRB/tRB
wRB = 100 for st. 52
If
yw
w
F
190
t
d
〉
Either :
1- provide longitudinal web stiffeners at d/5 from compression flange such
that:
yw
w
F
320
t
d
≤
(= 168 for st. 52) and, if need ,
Use another stiffener at d/2 such that
yw
w
F
370
t
d
≤
(= 195 for st. 52)
15. Chapter 7: Box Girder Bridges 289
Or
2- base design on effective width dRB
eRB calculated as follows:
( )
==λ
==λ
−=ψλΨ−−λ=ρ
ρ=ρ=
σσ
4.113
t/d
9.23
6.3
44
t/d
52.stfor
)9.23k(,k/F
44
t/d
)1(,/05.015.0
2/ddde
p
yp
p
2
p
c
7.4.2.3 Web Buckling due to Shear:
Web is non-compact in shear if
yF
105
tw
dw
≤
For the case qRB
allRB = 0.35 FRB
yRB d/t = 55 for St. 52
If
yF
105
t/d 〉 then reduce allowable shear stress to qRB
bRB given by :
( )
)2.1()F35.0(
9.0
)2.18.0(F35.0625.05.1q
qy
q
qyqb
〉λ
λ
=
〈λ〈λ−=
Where:
)1(/434.5
)1(/34.54k
k
F
57
t/d
2
2
q
q
y
q
〉αα+=
〈αα+=
=λ
For vertically unstiffened webs : (α >> 1)
70
t/d
F
5.132
t/d
34.5k
q
yq
q
=λ
=λ
=
this gives :
( )( )( )
( )
( ) yy
y
yyyb
F/159
t
d
forF35.0
Ft/d
119
F/159
t
d
forF35.0212/Ft/d5.1q
〉=
≤−=
16. Steel Bridges
7.4.3 Combined Shear & Bending
In general, any cross-section of a box girder will be subjected to bending
moment in addition to shear. This combination makes the stress conditions in
the girder web considerably more complex. The stresses from the bending
moment will combine with the shear stresses to give a lower buckling load.
The interaction between shear and bending can be conveniently represented
by the diagram shown in Fig. 7.8, where the allowable bending stress is
plotted on the vertical axis and the allowable buckling shear stress of the
girder is plotted horizontally. The interaction represents a failure envelope,
with any point lying on the curve defining the co-existent values of shear and
bending that the girder can just sustain. The equation representing this
interaction diagram is :
( )[ ] yba c tb Fq/q3 6.08.0F −=
The interaction diagram can be considered in 3 regions. In region AB, the
applied shear stress qRB
actRB is low (< 0.6 qRB
bRB) and the girder can sustain the full
bending stress FRB
bRB based on the effective width bRB
effRB for the compression flange.
At the other extreme of the interaction diagram in region CD, the applied
shear stress is high (=qRB
bRB) then the allowable bending stress is reduced to 0.44
FRB
yRB to allow for the high shear. In the intermediate region BC the allowable
bending stress is reduced linearly from 0.58 FRB
yRB to 0.44 FRB
yRB.
Shear Stress
BendingStress
0.44 Fy
0.58 Fy
0.6 q b
qb
A B
C
D
Fig. 7.8 Interaction between Shear and Bending
17. Chapter 7: Box Girder Bridges 291
7.5 Effect of Torsion
The torsion component is shown in Figure 7.5 simply as a force couple.
However, torsion is in fact resisted in a box section by a shear flow around
the whole perimeter. The couple should therefore be separated into two parts,
pure torsion and distortion, as shown in Figure 7.5. The distortion component
comprises an internal set of forces, statically in equilibrium, whose effects
depend on the behavior of the structure between the point of application and
the nearest positions where the box section is restrained against distortion.
At supports, bearings will be provided, see Fig. 7.9. Where a pair of
bearings is provided, they are usually either directly under each web or just
inside the line of the webs. To resist forces reacting on the bearings as a
result of the bending and torsion components, bearing support stiffeners will
be required on the web. In addition, a diaphragm (or at least a stiff ring
frame) will be required to resist the distortional effects consequent in
transmitting the torsion from the box to a pair of bearing supports.
Fig. 7.9 End Bearings of a Box Girder
In some cases only a single bearing is provided; a stiffened diaphragm will
be needed to resist the reaction and to distribute the force to the webs.
Between points of support, intermediate transverse web stiffeners may be
provided to develop sufficient shear resistance in a thin web. Intermediate
diaphragms or cross frames, see Fig. 7.10, may be provided to limit the
distortional effects of eccentrically applied loads; they are particularly
effective where concentrated eccentric effects are introduced, such as from a
cantilever on the side of the box. Intermediate cross-frames may also be
provided to facilitate construction.
18. Steel Bridges
Fig. 7.10 Diaphragms and Cross Frames in Box Girders
7.5.1 Torsion and Torsional Warping
The theoretical behavior of a thin-walled box section subject to pure torsion
is well known and treated in many standard texts. For a single cell box, the
torque is resisted by a shear flow which acts around the walls of the box. This
shear flow (force/unit length) is constant around the box and is given by q =
T/2A, where T is the torque and A is the area enclosed by the box. (In Figure
7.5 the torque is QB/2 and the shear flow is Q/4D). The shear flow produces
shear stresses and strains in the walls and gives rise to a twist per unit length,
Ө which is given by the general expression :
∫ =θ=θ
GJ
T
,or
t
ds
GA4
T
2
where J is the torsion constant.
However, it is less well appreciated that this pure torsion of a thin walled
section will also produce a warping of the cross-section, unless there is
sufficient symmetry in the section as shown in Figure 7.11.
19. Chapter 7: Box Girder Bridges 293
Fig. 7.11 Warping of a Rectangular Box subject to Pure Torsion.
For a simple uniform box section subject to pure torsion this warping is
unrestrained and does not give rise to any secondary stresses. But if for
example, a box is supported and torsionally restrained at both ends and then
subjected to applied torque in the middle, warping is fully restrained in the
middle by virtue of symmetry and torsional warping stresses are generated.
Similar restraint occurs in continuous box sections which are torsionally
restrained at supports.
This restraint of warping gives rise to longitudinal warping stresses and
associated shear stresses in the same manner as bending effects in each wall
of the box. The shear stresses effectively modify slightly the uniformity of
the shear stress calculated by pure torsion theory, usually reducing the stress
near corners and increasing it in mid-panel. Because maximum combined
effects usually occur at the corners, it is conservative to ignore the warping
shear stresses and use the simple uniform distribution.
The longitudinal effects are, on the other hand greatest at the corners. They
need to be taken into account when considering the occurrence of yield
stresses in service and the stress range under fatigue loading. But since the
longitudinal stresses do not actually participate in the carrying of the torsion,
the occurrence of yield at the corners and the consequent relief of some or all
of these warping stresses would not reduce the torsional resistance. In simple
terms, a little plastic redistribution can be accepted at the ultimate limit state
and therefore there is no need to include torsional warping stresses in the
ultimate limit state checks.
20. Steel Bridges
7.5.2 Distortion
When torsion is applied directly around the perimeter of a box section, by
forces exactly equal to the shear flow in each of the sides of the box, there is
no tendency for the cross section to change its shape.
If torsion is not applied in this manner, a diaphragm or stiff frame might be
provided at the position where the force couple is applied to ensure that the
section remains square and that torque is in fact fed into the box walls as a
shear flow around the perimeter. The diaphragm or frame is then subject to a
set of distortional forces as shown in Figure 7.5.
Provision of such diaphragms or frames is practical, and indeed necessary,
at supports and at positions where heavy point loads are introduced. But such
restraint can only be provided at discrete positions. When the load is
distributed along the beam, or when point loads can occur anywhere along
the beam such as concentrated axle loads from vehicles, the distortional
effects must be carried by other means.
To illustrate how distortion occurs and is carried between effective
restraints, consider a simply supported box which is subject to a point load
over one web at mid-span. If a flexible intermediate cross-frame (a ring
stiffener without any triangulated bracing in its plane) is placed at the point of
application of the load, it tends to resist the distortion of the cross section by
'sway bending' of the form shown in Figure 7.12. Obviously, the stiffer the
frame the less the distortion of the cross section. (Cross bracing or a plated
diaphragm would be even more effective).
Figure 7.12 Distortion of Box Girder with Stiff Corners or Cross-Frames
21. Chapter 7: Box Girder Bridges 295
The bending of cross-frames and the walls of a box, as a result of the
distortional forces, produces transverse distortional bending stresses in the
box section.
In general the distortional behavior depends on interaction between the two
sorts of behavior, the warping and the transverse distortional bending. The
behavior has been demonstrated to be analogous to that of a beam on an
elastic foundation, BEF, representing the transverse distortional bending
resistance. The BEF model is used as the basis for the rules in Appendix B of
BS 5400 Part 3 for calculating distortion and warping stresses in box girders.
This Appendix is shown in the next section.
It must be emphasized that distortional effects are UUprimaryUU effects – they are
an essential part of the means of carrying loads applied other than at stiff
diaphragms – and they should not be ignored.
22. Steel Bridges
7.6 DESIGN EXAMPLE:
The design example presented in chapter 5 and chapter 6 is used here to
illustrate the method of design of composite box girders. The same
roadway is carried by two box girders as shown below:
1480
1500 7000
2150 2700 2150
1500
320
220
2525 1450
The example uses the same values of the straining actions as shown
next:
7.6.1 Web Plate Design:
Web Plate Height: The web plate height shall be assumed at 148 cm which
corresponds to an inclined web plate length of 150 cm (standard plate width).
Web Plate Thickness: The minimum thickness for a web without transverse
stiffeners is obtained from:
tPP
2
PP = Q / (41.65 yF )
Since the total shear force is carried by two webs, each web carries
Q = 180/2 = 90 ton (at support). This gives:
tPP
2
PP = 90 / 41.65 6.3 ) = 1.135 i.e., t = 1.065 cm
Use t = 12 mm (next even integer) without transverse stiffeners.
Action
Load Case
At Support Mid section
Q
(t)
M
(m.t.)
Q
(t)
M
(m.t.)
Dead Load DL1 62 0 0 385
Add. Dead Load DL2 18 0 0 115
Live Load LL+I 100 0 25 700
Sum 180 0 25 1200
23. Chapter 7: Box Girder Bridges 297
Check of web buckling due to shear:
Allowable Buckling Shear Stress = qRB
b RB= ( 119 / (d/t) yF ) (0.35 FRB
yRB)
qRB
b RB= ( 119 / (150/1.2) yF ) (0.35 FRB
yRB) = 0.632 t/cmPP
2
PP
Actual Shear Stress:
i.e., Web Plate is safe against buckling due to shear at support
.)K.O(qcm/t514.0
2.1146
90
q b
2
act <=
×
=
24. Steel Bridges
7.6.2 Main Girder Design:
The section properties of the proposed cross section are as follows:
The following section is assumed:
a) Two Webs 1500 × 12
b) Top Flange 300 × 12
(bRB
fRB / 2tRB
fRB = 30 / (2 ×1.2) = 12.5 > 21 / yf = 11
(No problem since flange is prevented from local buckling by deck slab)
c) Bottom Flange 1500 × 22
UUSection properties are then computed for the following cases:
a) Steel section only:
Centroid YRB
usRB = 99.336 cm
Intertia IRB
sRB = 2360156 cmPP
4
PP
Section Moduli ZRB
usRB = 23759 cmPP
3
PP
ZRB
lsRB = 49310 cmPP
3
PP
b) Effective Slab Width:
For the exterior web:
bRB
ERRB = b* = UU150UU cm (Side Walk Slab)
bRB
ELRB = smaller of:
1) Span/8 = 27.5 /8 = 3.4375 m
2) Spacing /2 = 2.15/2 = UU1.075UU m governs
3) 6 ts = 6 * 22 = 132 cm
For the interior web:
bRB
ERRB = smaller of:
1) Span/8 = 27.5 /8 = 3.4375 m
2) Spacing /2 = 2.15/2 = UU1.075UU m governs
3) 6 ts = 6 * 22 = 132 cm
bRB
ELRB = smaller of:
1) Span/8 = 27.5 /8 = 3.4375 m
2) Spacing /2 = 2.70/2 = 1.35 m
3) 6 ts = 6 * 22 = UU132 UUcm governs
Total Effective Slab Width = (150 + 107.5) + (107.5+132) = 497 cm
25. Chapter 7: Box Girder Bridges 299
c) Composite section with n = 9 (FRB
cuRB = 300 kg / mPP
2
PP)
Centroid Y'RB
usRB = 31.372 cm
Intertia IRB
vRB = 8123595 cmPP
4
PP
Section Moduli Z′RB
usRB = 258941 cmPP
3
PP
Z′RB
lsRB = 70153 cmPP
3
ZRB
ucRB = 152206 cmPP
3
PP
d) Composite section with n = 3 × 9 = 27 (Effect of Creep)
Centroid Y'RB
usRB = 60.896 cm
Intertia IRB
vRB = 5608461 cmPP
4
PP
Section Moduli Z′RB
usRB = 92098 cmPP
3
PP
Z′RB
lsRB = 64985 cmPP
3
ZRB
ucRB = 67656 cmPP
3
PP
Check of Bending Stresses:
UUa) Non-Shored Construction:
Load Upper Steel (-)
t/cmPP
2
PP
Lower Steel (+)
t/cmPP
2
PP
Upper Concrete
kg / cmPP
2
PP
DL 1 FRB
usRB = 385 × 100/23759
= 1.620
FRB
lsRB = 385 × 100/49310
= 0.781
= 0 for non-shored
construction
DL 2 FRB
usRB = 115 × 100/92908
= 0.125
FRB
lsRB = 115 × 100/64985
= 0.177
FRB
usRB = (115 × 100/67656)
*(1000/27) = 2.575
LL + I FRB
usRB = 700 ×
100/258941
= 0.270
FRB
lsRB = 700x100/70153
= 0.998
FRB
usRB = (700/152206)
*(1000/9) = 51.10
UUTotalUU UU2.016UU UU 1.956UU UU53.676UU
Checks:
1- Compression in Upper Steel :
a) Total stress: FRB
usRB = UU2.016UU < FRB
bRB = UU2.1UU t/cmPP
2
PP
(compression flange is laterally supported by deck slab)
b) Due to D.L. only Fus = UU1.620UU t / cmPP
2
PP
Assume compression flange is laterally supported by upper bracing
with
LRB
uRB = 4.5 m, rRB
TRB= 8 cm LRB
uRB/rRB
TRB = 450 / 8 = 56.25
y
Tu
F
C
188r/L b
≤ = 99
26. Steel Bridges
yy
b
5
y
2
Tu
F58.0F)
C10x176.1
F)r/L(
64.0(2ltbF ≤−= = UU1.955UU t/cm2
FRB
usRB < FRB
LTBRPBP PPO.K.
2. Tension in Upper Steel :
a) Total Tension: fRB
lsRB = 1.956 < FRB
bRB = 2.10 t/cmPP
2
PP
b) Fatigue fRB
srRB = 0.5 × 0.998 = 0.499 < FRB
srRB = 1.02 t/cmPP
2
PP
{The allowable fatigue stress range (FRB
srRB) is obtained as follows:
* From ECP Table 3.1.a: ADTT >2500, Number of cycles = 2 ×10PP
6
PP
Detail Class = B′ (case 4.2 of Table 3.3)
Table 3.2 gives FRB
srRB = UU1.02UU t/cmPP
2
PP > fRB
srRB }
3. Compression in Upper Concrete:
fRB
ucRB = 53.676 < 70 kg/cmPP
2
PP
7.6.3 Comparison between Different Designs:
The following table shows a comparison between the total weight of steel
needed for the bridge according to the three designed presented in Chapter 5
using non-composite plate girders, in Chapter 6 using composite plate
girders, and in Chapter 7 using composite box girders. It should be note that
the total weight of the first two cases should include the weight of the
stringers and cross girders, not present in the third case. The comparison
shows that the composite box girder solution uses the least weight followed
by the composite plate girder solution.
Section Weight
of Main
Girder
Weight of
Floor Beams
Total
Weight
Web Flanges
1- Non-Composite
Plate Girder
2250*14 600*36
600*36
31.665 15.596 47.261
2- Composite
Plate Girder
2250*14 400*12
600*32
23.526 15.596 39.122
3- Composite
Box Girder
2(1500*12) 2(300*12)
1500*22
32.302 0 32.302