Ch5 Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Me...Hossam Shafiq II
Plate girders are commonly used as main girders for short and medium span bridges. They are fabricated by welding together steel plates to form an I-shape cross-section, unlike hot-rolled I-beams. Plate girders offer more design flexibility than rolled sections as the plates can be optimized for strength and economy. However, their thin plates are more susceptible to various buckling modes which control the design. Buckling considerations of the compression flange, web in shear and bending must be evaluated to determine the plate girder's load capacity.
This document discusses the design of reinforced concrete deep beams. It defines deep beams as having a span/depth ratio less than 2 or a continuous beam ratio less than 2.5. Deep beams behave differently than elementary beam theory due to non-linear stress distributions. Their behavior depends on loading type and cracking typically occurs between one-third to one-half of the ultimate load. Design considerations include checking for minimum thickness, flexural design, shear design, and anchorage of tension reinforcement.
- Deep beams are defined as beams with a shear span to depth ratio of less than 2. They behave differently than ordinary beams due to two-dimensional loading and non-linear stress distributions.
- Deep beams transfer significant load through compression forces between the load and supports. Shear deformations are more prominent.
- Design of deep beams requires considering two-dimensional effects, non-linear stress distributions, and large shear deformations. Procedures include checking minimum thickness, designing for flexure and shear, and detailing reinforcement.
1) Two-way slabs are slabs that require reinforcement in two directions because bending occurs in both the longitudinal and transverse directions when the ratio of longest span to shortest span is less than 2.
2) The document discusses various types of two-way slabs and design methods, focusing on the direct design method (DDM).
3) Using the DDM, the total factored load is first calculated, then the total factored moment is distributed to positive and negative moments. The moments are further distributed to column and middle strips using factors that consider the slab and beam properties.
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.
Design of column base plates anchor boltKhaled Eid
This document discusses the design of column base plates and steel anchorage to concrete. It covers base plate materials and design for different load cases including axial, moment, and shear loads. It also discusses anchor rod types, materials, and design for tension and shear loading based on calculations of the steel and concrete breakout strengths according to building codes.
1) The document discusses design considerations for columns according to ACI code, including requirements for different types of columns like tied, spirally reinforced, and composite columns.
2) It provides details on failure modes of tied and spiral columns and code requirements for minimum reinforcement ratios, number of bars, clear spacing, cover, and cross sectional dimensions.
3) Lateral reinforcement requirements are discussed, noting ties help restrain longitudinal bars from buckling while spirals provide additional confinement at ultimate load.
The document discusses shear design of beams. It covers shear strength, which depends on the web thickness and h/t ratio to prevent shear buckling. Shear strength is calculated as 60% of the tensile yield stress. Block shear failure is also discussed, where the strength is governed by the shear and net tension areas. An example calculates the maximum reaction based on block shear for a coped beam connection.
Ch5 Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Me...Hossam Shafiq II
Plate girders are commonly used as main girders for short and medium span bridges. They are fabricated by welding together steel plates to form an I-shape cross-section, unlike hot-rolled I-beams. Plate girders offer more design flexibility than rolled sections as the plates can be optimized for strength and economy. However, their thin plates are more susceptible to various buckling modes which control the design. Buckling considerations of the compression flange, web in shear and bending must be evaluated to determine the plate girder's load capacity.
This document discusses the design of reinforced concrete deep beams. It defines deep beams as having a span/depth ratio less than 2 or a continuous beam ratio less than 2.5. Deep beams behave differently than elementary beam theory due to non-linear stress distributions. Their behavior depends on loading type and cracking typically occurs between one-third to one-half of the ultimate load. Design considerations include checking for minimum thickness, flexural design, shear design, and anchorage of tension reinforcement.
- Deep beams are defined as beams with a shear span to depth ratio of less than 2. They behave differently than ordinary beams due to two-dimensional loading and non-linear stress distributions.
- Deep beams transfer significant load through compression forces between the load and supports. Shear deformations are more prominent.
- Design of deep beams requires considering two-dimensional effects, non-linear stress distributions, and large shear deformations. Procedures include checking minimum thickness, designing for flexure and shear, and detailing reinforcement.
1) Two-way slabs are slabs that require reinforcement in two directions because bending occurs in both the longitudinal and transverse directions when the ratio of longest span to shortest span is less than 2.
2) The document discusses various types of two-way slabs and design methods, focusing on the direct design method (DDM).
3) Using the DDM, the total factored load is first calculated, then the total factored moment is distributed to positive and negative moments. The moments are further distributed to column and middle strips using factors that consider the slab and beam properties.
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.
Design of column base plates anchor boltKhaled Eid
This document discusses the design of column base plates and steel anchorage to concrete. It covers base plate materials and design for different load cases including axial, moment, and shear loads. It also discusses anchor rod types, materials, and design for tension and shear loading based on calculations of the steel and concrete breakout strengths according to building codes.
1) The document discusses design considerations for columns according to ACI code, including requirements for different types of columns like tied, spirally reinforced, and composite columns.
2) It provides details on failure modes of tied and spiral columns and code requirements for minimum reinforcement ratios, number of bars, clear spacing, cover, and cross sectional dimensions.
3) Lateral reinforcement requirements are discussed, noting ties help restrain longitudinal bars from buckling while spirals provide additional confinement at ultimate load.
The document discusses shear design of beams. It covers shear strength, which depends on the web thickness and h/t ratio to prevent shear buckling. Shear strength is calculated as 60% of the tensile yield stress. Block shear failure is also discussed, where the strength is governed by the shear and net tension areas. An example calculates the maximum reaction based on block shear for a coped beam connection.
AASHTO T-4 Proposed Guide Specifications for Wind Loads on Bridges During Con...Arkar43
The document summarizes a presentation given at the 2016 AASHTO SCOBS T4 meeting proposing guide specifications for wind loads on bridges during construction. The presentation outlined differences between current AASHTO provisions for completed bridges and those needed for bridges under construction, when the deck is not yet cast. It proposed determining wind loads based on whether work is active or inactive, provided drag coefficients for different girder positions, and recommended reducing wind speeds based on construction duration. The goal is to develop standalone guide specifications to replace Section 3.8 of the design specifications for wind loads during bridge construction.
This document provides an introduction to prestressed concrete bridge design. It discusses how prestressing concrete induces compression to counteract tensile stresses from loading. Prestressed concrete allows for longer concrete bridge spans through precasting units that are lifted into place. The document covers methods of prestressing including pre-tensioning and post-tensioning. It also summarizes design considerations like serviceability limits, stress limitations, prestress losses, and establishes basic inequalities for prestress force and section properties. Magnel diagrams are introduced as a way to determine appropriate prestress force and eccentricity values.
Shear Force And Bending Moment Diagram For FramesAmr Hamed
This document discusses analyzing shear and moment diagrams for frames. It provides procedures for determining reactions, axial forces, shear forces, and moments at member ends. Examples are given of drawing shear and moment diagrams for simple frames with different joint conditions, including pin and roller supports. Diagrams for a three-pin frame example are shown.
The document discusses the design and erection of column base plates. It covers types of base plates for different load cases including axial compression, tension, and combined axial and moment loads. Key topics covered include base plate and anchor rod materials, design for concrete crushing and bending, anchor rod design, and erection procedures. Diagrams illustrate critical sections and design equations for different limit states. Construction tolerances and OSHA standards for base plate design are also summarized.
This document provides an overview of design in reinforced concrete according to BS 8110. It discusses the basic materials used - concrete and steel reinforcement - and their properties. It describes two limit states for design: ultimate limit state considering failure, and serviceability limit state considering deflection and cracking. Key aspects of beam design are summarized, including types of beams, design for bending and shear resistance, and limiting deflection. Reinforcement detailing rules are also briefly covered.
This publication provides guidance on detailed design of single span steel portal frames according to Eurocode standards. It discusses the importance of considering second order effects in portal frame analysis and design. These effects can reduce the frame's stiffness below that calculated from first order analysis. The publication covers analysis and design approaches at the ultimate limit state and serviceability limit state, including imperfections, base stiffness, deflections, cross section resistance, member stability, bracing, connections, and worked examples. Emphasis is placed on using computer software for analysis and design to achieve the most efficient structural solutions.
This document provides an introduction to prestressed concrete, including:
1. The basic principles of prestressing concrete by applying compressive stresses that counteract tensile stresses from loads. This allows for smaller member sizes.
2. The main advantages are smaller sections, reduced deflections, increased spans, and improved durability due to reduced cracking.
3. The two main methods are pre-tensioning, where strands are stressed before casting, and post-tensioning, where strands are tensioned after casting through ducts.
4. Uses include precast beams, slabs, piles, tanks, and bridges constructed with either precast or post-tensioned segments.
This document discusses the design of compression members subjected to axial load and biaxial bending. It introduces the concept of biaxial eccentricities and explains that columns should be designed considering possible eccentricities in two axes. The document outlines the method suggested by IS 456-2000, which is based on Breslar's load contour approach. It relates the parameter αn to the ratio of Pu/Puz. Finally, it provides a step-by-step process for designing the column section, which involves determining uniaxial moment capacities, computing permissible moment values from charts, and revising the section if needed. It also briefly mentions the simplified method according to BS8110.
This document provides an overview of design in reinforced concrete according to BS 8110. It discusses the basic materials used - concrete and steel reinforcement - and their properties. It describes two limit states for design: ultimate limit state considering failure, and serviceability limit state considering deflection and cracking. Key aspects of beam design are summarized, including types of beams, design for bending and shear resistance, and limiting deflection. Reinforcement detailing rules are also briefly covered. Design examples are provided to illustrate bending and shear design of beams.
The document discusses the behavior and design of beam-columns, which are structural elements that experience both axial loads and bending moments. It covers topics such as moment connections for columns, eccentric loads on columns, interaction of axial and bending forces, and moment amplification due to axial loads. Design considerations discussed include checking for adequate strength, using interaction formulas, and verifying sufficient resistance to local buckling. The document appears to be lecture materials on structural steel beam-column design based on Canadian standards.
This document is the preface to the second edition of the book "Earthquake-Resistant Design of Structures" by Shashikant K. Duggal. It discusses updates that have been made to the second edition, including revising and expanding several chapters with new content on topics like dynamics of structures, steel building design, and case studies of earthquakes. The preface provides an overview of the book's contents and approach to introducing concepts of earthquake-resistant design of buildings and structures. It aims to be a comprehensive textbook for students and practitioners. Feedback from the first edition was incorporated to improve the coverage of structural dynamics and code-based design approaches.
This document provides details on reinforcing concrete columns, including:
- Classification of columns as tied, spirally reinforced, or composite
- Minimum reinforcement requirements of 4 bars for tied columns and 6 bars for spiral columns
- Design considerations for tie ratio between 1-8% or 1-6% depending on code
- Clear cover and spacing requirements between bars
- Arrangement and sizing of ties and spirals
- Requirements for bundling, lapping, and hooking of reinforcement bars
This document presents an example of analysis design of slab using ETABS. This example examines a simple single story building, which is regular in plan and elevation. It is examining and compares the calculated ultimate moment from CSI ETABS & SAFE with hand calculation. Moment coefficients were used to calculate the ultimate moment. However it is good practice that such hand analysis methods are used to verify the output of more sophisticated methods.
Also, this document contains simple procedure (step-by-step) of how to design solid slab according to Eurocode 2.The process of designing elements will not be revolutionised as a result of using Eurocode 2. Due to time constraints and knowledge, I may not be able to address the whole issues.
CE 72.52 - Lecture 7 - Strut and Tie ModelsFawad Najam
The document discusses the strut-and-tie approach for analyzing concrete structures. It begins with background concepts such as Bernoulli's hypothesis, St. Venant's principle, and the lower bound theorem of plasticity. It then discusses how axial stresses, shear stresses, and the interaction of stresses affect concrete sections. The document outlines the ACI approach to shear-torsion design and provides equations from ACI 318 for calculating the concrete shear capacity. It introduces the concept of modeling concrete as a truss system and compares this to flexural behavior in beams. The strut-and-tie method is presented as a unified approach for considering all load effects. Guidelines are provided for developing an appropriate strut-and-tie model and
Peer review presentation for the strut and tie method as an analysis and design approach for the mat on piles foundations of the primary separation cell (vessel).
This document provides details of the analysis and design of a multi-storey reinforced concrete building project. It includes the objectives, which are to analyze and design the main structural elements of the building including slabs, columns, shear walls, and foundations. It also summarizes the building being a 12-storey residential building in Gorakhpur, India. The document outlines the various structural elements that will be designed, including flat slab structural systems, column types and design, shear wall design, and pile foundation design.
The document discusses modeling and failure modes of reinforced concrete beams. It covers the following key points:
- Mathematical modeling of reinforced concrete is essential for civil engineering. The three failure modes to investigate are tension, compression, and shear.
- The Whitney rectangular stress distribution model approximates the complex compressive stress distribution with a rectangle. It defines the height of the stress box and calculates the tension and compression forces.
- Models are presented for tension failure based on steel yield strength, compression failure based on the reinforcement ratio, and shear failure based on the concrete and steel contributions.
- An example is given to analyze a reinforced concrete beam and calculate its moment capacity using the Whitney model, given properties of the concrete
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 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.
Ch7 Box Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metw...Hossam Shafiq II
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.
This document discusses composite construction, where a prefabricated beam and cast-in-place concrete slab act together as a unit. It defines composite construction and describes its advantages over non-composite construction, including increased stiffness, strength, and span length. The document discusses how shear connectors interconnect the beam and slab to achieve composite action. It provides equations for calculating the effective slab width, section properties of the composite section, and required strength of shear connectors. An example is given for designing a composite slab on a precast reinforced concrete beam.
AASHTO T-4 Proposed Guide Specifications for Wind Loads on Bridges During Con...Arkar43
The document summarizes a presentation given at the 2016 AASHTO SCOBS T4 meeting proposing guide specifications for wind loads on bridges during construction. The presentation outlined differences between current AASHTO provisions for completed bridges and those needed for bridges under construction, when the deck is not yet cast. It proposed determining wind loads based on whether work is active or inactive, provided drag coefficients for different girder positions, and recommended reducing wind speeds based on construction duration. The goal is to develop standalone guide specifications to replace Section 3.8 of the design specifications for wind loads during bridge construction.
This document provides an introduction to prestressed concrete bridge design. It discusses how prestressing concrete induces compression to counteract tensile stresses from loading. Prestressed concrete allows for longer concrete bridge spans through precasting units that are lifted into place. The document covers methods of prestressing including pre-tensioning and post-tensioning. It also summarizes design considerations like serviceability limits, stress limitations, prestress losses, and establishes basic inequalities for prestress force and section properties. Magnel diagrams are introduced as a way to determine appropriate prestress force and eccentricity values.
Shear Force And Bending Moment Diagram For FramesAmr Hamed
This document discusses analyzing shear and moment diagrams for frames. It provides procedures for determining reactions, axial forces, shear forces, and moments at member ends. Examples are given of drawing shear and moment diagrams for simple frames with different joint conditions, including pin and roller supports. Diagrams for a three-pin frame example are shown.
The document discusses the design and erection of column base plates. It covers types of base plates for different load cases including axial compression, tension, and combined axial and moment loads. Key topics covered include base plate and anchor rod materials, design for concrete crushing and bending, anchor rod design, and erection procedures. Diagrams illustrate critical sections and design equations for different limit states. Construction tolerances and OSHA standards for base plate design are also summarized.
This document provides an overview of design in reinforced concrete according to BS 8110. It discusses the basic materials used - concrete and steel reinforcement - and their properties. It describes two limit states for design: ultimate limit state considering failure, and serviceability limit state considering deflection and cracking. Key aspects of beam design are summarized, including types of beams, design for bending and shear resistance, and limiting deflection. Reinforcement detailing rules are also briefly covered.
This publication provides guidance on detailed design of single span steel portal frames according to Eurocode standards. It discusses the importance of considering second order effects in portal frame analysis and design. These effects can reduce the frame's stiffness below that calculated from first order analysis. The publication covers analysis and design approaches at the ultimate limit state and serviceability limit state, including imperfections, base stiffness, deflections, cross section resistance, member stability, bracing, connections, and worked examples. Emphasis is placed on using computer software for analysis and design to achieve the most efficient structural solutions.
This document provides an introduction to prestressed concrete, including:
1. The basic principles of prestressing concrete by applying compressive stresses that counteract tensile stresses from loads. This allows for smaller member sizes.
2. The main advantages are smaller sections, reduced deflections, increased spans, and improved durability due to reduced cracking.
3. The two main methods are pre-tensioning, where strands are stressed before casting, and post-tensioning, where strands are tensioned after casting through ducts.
4. Uses include precast beams, slabs, piles, tanks, and bridges constructed with either precast or post-tensioned segments.
This document discusses the design of compression members subjected to axial load and biaxial bending. It introduces the concept of biaxial eccentricities and explains that columns should be designed considering possible eccentricities in two axes. The document outlines the method suggested by IS 456-2000, which is based on Breslar's load contour approach. It relates the parameter αn to the ratio of Pu/Puz. Finally, it provides a step-by-step process for designing the column section, which involves determining uniaxial moment capacities, computing permissible moment values from charts, and revising the section if needed. It also briefly mentions the simplified method according to BS8110.
This document provides an overview of design in reinforced concrete according to BS 8110. It discusses the basic materials used - concrete and steel reinforcement - and their properties. It describes two limit states for design: ultimate limit state considering failure, and serviceability limit state considering deflection and cracking. Key aspects of beam design are summarized, including types of beams, design for bending and shear resistance, and limiting deflection. Reinforcement detailing rules are also briefly covered. Design examples are provided to illustrate bending and shear design of beams.
The document discusses the behavior and design of beam-columns, which are structural elements that experience both axial loads and bending moments. It covers topics such as moment connections for columns, eccentric loads on columns, interaction of axial and bending forces, and moment amplification due to axial loads. Design considerations discussed include checking for adequate strength, using interaction formulas, and verifying sufficient resistance to local buckling. The document appears to be lecture materials on structural steel beam-column design based on Canadian standards.
This document is the preface to the second edition of the book "Earthquake-Resistant Design of Structures" by Shashikant K. Duggal. It discusses updates that have been made to the second edition, including revising and expanding several chapters with new content on topics like dynamics of structures, steel building design, and case studies of earthquakes. The preface provides an overview of the book's contents and approach to introducing concepts of earthquake-resistant design of buildings and structures. It aims to be a comprehensive textbook for students and practitioners. Feedback from the first edition was incorporated to improve the coverage of structural dynamics and code-based design approaches.
This document provides details on reinforcing concrete columns, including:
- Classification of columns as tied, spirally reinforced, or composite
- Minimum reinforcement requirements of 4 bars for tied columns and 6 bars for spiral columns
- Design considerations for tie ratio between 1-8% or 1-6% depending on code
- Clear cover and spacing requirements between bars
- Arrangement and sizing of ties and spirals
- Requirements for bundling, lapping, and hooking of reinforcement bars
This document presents an example of analysis design of slab using ETABS. This example examines a simple single story building, which is regular in plan and elevation. It is examining and compares the calculated ultimate moment from CSI ETABS & SAFE with hand calculation. Moment coefficients were used to calculate the ultimate moment. However it is good practice that such hand analysis methods are used to verify the output of more sophisticated methods.
Also, this document contains simple procedure (step-by-step) of how to design solid slab according to Eurocode 2.The process of designing elements will not be revolutionised as a result of using Eurocode 2. Due to time constraints and knowledge, I may not be able to address the whole issues.
CE 72.52 - Lecture 7 - Strut and Tie ModelsFawad Najam
The document discusses the strut-and-tie approach for analyzing concrete structures. It begins with background concepts such as Bernoulli's hypothesis, St. Venant's principle, and the lower bound theorem of plasticity. It then discusses how axial stresses, shear stresses, and the interaction of stresses affect concrete sections. The document outlines the ACI approach to shear-torsion design and provides equations from ACI 318 for calculating the concrete shear capacity. It introduces the concept of modeling concrete as a truss system and compares this to flexural behavior in beams. The strut-and-tie method is presented as a unified approach for considering all load effects. Guidelines are provided for developing an appropriate strut-and-tie model and
Peer review presentation for the strut and tie method as an analysis and design approach for the mat on piles foundations of the primary separation cell (vessel).
This document provides details of the analysis and design of a multi-storey reinforced concrete building project. It includes the objectives, which are to analyze and design the main structural elements of the building including slabs, columns, shear walls, and foundations. It also summarizes the building being a 12-storey residential building in Gorakhpur, India. The document outlines the various structural elements that will be designed, including flat slab structural systems, column types and design, shear wall design, and pile foundation design.
The document discusses modeling and failure modes of reinforced concrete beams. It covers the following key points:
- Mathematical modeling of reinforced concrete is essential for civil engineering. The three failure modes to investigate are tension, compression, and shear.
- The Whitney rectangular stress distribution model approximates the complex compressive stress distribution with a rectangle. It defines the height of the stress box and calculates the tension and compression forces.
- Models are presented for tension failure based on steel yield strength, compression failure based on the reinforcement ratio, and shear failure based on the concrete and steel contributions.
- An example is given to analyze a reinforced concrete beam and calculate its moment capacity using the Whitney model, given properties of the concrete
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 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.
Ch7 Box Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metw...Hossam Shafiq II
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.
This document discusses composite construction, where a prefabricated beam and cast-in-place concrete slab act together as a unit. It defines composite construction and describes its advantages over non-composite construction, including increased stiffness, strength, and span length. The document discusses how shear connectors interconnect the beam and slab to achieve composite action. It provides equations for calculating the effective slab width, section properties of the composite section, and required strength of shear connectors. An example is given for designing a composite slab on a precast reinforced concrete beam.
Analysis and Design of Composite Beams with Composite Deck Slab.docxAdnan Lazem
This document presents an overview of the theory and design of composite beams with steel decks according to the AISC Specification. It discusses general considerations for composite beam design including that it is most efficient for heavy loading and long spans. It also summarizes provisions for fully and partially composite beams, requirements for shored and unshored construction, and considerations for end reactions, deflection, use of different material strengths, and use of cover plates.
IRJET- A Study on Concrete Filled Steel Tubular Column Steel Beam Connect...IRJET Journal
This document summarizes a study on the behavior of steel beam to concrete filled steel tubular column connections using different types of concrete. Specifically, it examines connections using light weight concrete and normal concrete with an external diaphragm. Two specimens of each concrete type were tested under static loading. The results showed panel zone deformation in the beam-column joints for both light weight and normal concrete. However, light weight concrete connections performed better in terms of seismic performance and energy dissipation compared to normal concrete connections. The aim of the study was to develop a more economical concrete filled steel tubular structure system by utilizing lighter concrete materials.
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.
IRJET- Effects of Different Parameters on Inelastic Buckling Behavior of ...IRJET Journal
This document discusses a study that analyzed the buckling behavior of composite concrete-filled steel tube columns with different parameters. The study used finite element analysis to model composite columns with double I-beam cross sections. It investigated the effects of eccentric loading, slenderness ratio, and distance between steel profiles on buckling capacity. The results showed that filling steel sections with concrete delays steel yielding and increases column capacity. Greater concrete surface area and lower slenderness ratio also led to higher strength due to increased confinement effects.
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 study that models a reinforced concrete beam-column joint under cyclic earthquake loading. The study conducted nonlinear static and dynamic analyses of the joint model. Under nonlinear static analysis, the joint was subjected to cyclic earthquake loading. Under nonlinear dynamic analysis, the joint was subjected to three real historic earthquakes. Crack pattern analysis identified the worst cracking scenario. Seismic analysis identified critical response times when maximum forces, displacements and stresses occurred. The model sustained all earthquakes, but failed during the third cycle of cyclic loading. Crack size and location varied between earthquakes. Cracks developed and increased with additional loading cycles, leading to failure. The study compared results to previous work and found reinforcement bar size significantly impacts load capacity.
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.
CONCRETE-ENCASED CFST BEAM-COLUMN JOINTS: A REVIEWIRJET Journal
This document reviews concrete-encased concrete-filled steel tubular (CFST) beam-column joints. It discusses how beam-column joints are the most seismically affected part of framed structures, so understanding their seismic performance is important. Concrete-encased CFST beam-column joints consist of a CFST core surrounded by reinforced concrete. The document reviews the properties and performance of these joints, including different types of connections, experimental investigations that have been conducted, and the results of one experimental program that tested seismic performance and found three main failure types. In summary, concrete-encased CFST beam-column joints demonstrate favorable seismic behavior and strength due to the composite action of the steel tube and concrete.
This document discusses reinforced concrete design. It covers topics such as constituent materials and properties, basic principles, analysis methods, strength of concrete, stress-strain curves, modulus of elasticity, assumptions in design, failure modes, design philosophies, safety provisions, structural elements, and analysis of reinforced concrete sections. Flexural failure modes and equations of equilibrium for reinforced concrete design are also presented.
This document discusses composite construction, specifically composite steel and concrete beams. It provides definitions and examples of composite construction, explaining that it aims to make each material perform the function it is best suited for. It then describes the differences between non-composite and composite beam behavior. The document goes on to discuss elements of composite construction like decking and shear studs. It also summarizes the design process for composite beams, covering moment capacity, shear capacity, shear connector capacity, and longitudinal shear capacity calculations.
IRJET- Experimental Analysis of Buckling Restrained Brace Under Cyclic LoadngIRJET Journal
This document discusses the experimental analysis of buckling restrained braces (BRBs) under cyclic loading. BRBs are a type of bracing system used in structures to resist lateral forces like earthquakes. They have advantages over conventional bracing systems in providing a more stable hysteretic response. The study involved fabricating BRB models and testing them under static ultimate and cyclic loading. One model was tested to determine ultimate strength, while another was used to study behavioral characteristics under loading and unloading cycles. The results showed that BRBs can undergo considerable yielding in both tension and compression and dissipate more energy than conventional braces.
Effect of creep on composite steel concrete sectionKamel Farid
Creep and Shrinkage are inelastic and time-varying strains.
For Steel-Concrete Composite beam creep and shrinkage are highly associated with concrete.
Simple approach depending on modular ratio has been adopted to compute the elastic section properties instead of the theoretically complex calculations of creep.
#2 2006 improving seismic performance of concrete filled tube to base connec...jothi boominathan
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2. Steel Bridges240
CHAPTER 6
COMPOSITE PLATE GIRDER BRIDGES
6.1 GENERAL
6.1.1 Composite Action
Steel structures supporting cast-in-place reinforced concrete slab construction
were historically designed on the assumption that the concrete slab acts
independently of the steel in resisting loads. No consideration was given to the
composite effect of the steel and concrete acting together. This neglect was
justified on the basis that the bond between the concrete deck and the top of
the steel girder could not be depended upon. However, with the wide use of
structural welding, it became practical to provide mechanical connectors
between concrete and steel to resist the horizontal shear which develops
during bending, Fig 6.1. Composite action is developed when the concrete
deck and the supporting steel girder are integrally connected so that they
deflect as a single unit.
3. Chapter 6: Composite Plate Girder Bridges 241
Fig. 6.1 Composite Deck Bridges
In developing the concept of composite behavior, consider first the non-
composite girder of Fig. 6.2, wherein if friction between the slab and the
girder is neglected the girder and slab each carry separately a part of the load.
The strain distribution corresponding to this case is shown in Fig.6.2. There
are two neutral axes; one at the slab mid surface and the other at the girder
centroid. When the slab deforms under vertical loads, its lower surface is in
tension and elongates; while the upper surface of the girder is in compression
and shortens. Thus a discontinuity will occur at the plane of contact. Since
friction is neglected, only vertical internal forces act between the slab and
girder.
When complete interaction between the slab and girder is developed by the
introduction of mechanical connectors, no relative slippage occurs between
the slab and girder and the resulting strain diagram is shown in Fig. 6.3. Under
this condition a single neutral axis occurs which lies below that of the slab and
above that of the girder. Horizontal forces (shears) are developed that act on
the lower surface of the slab to compress and shorten it, while simultaneously
they act on the upper surface of the girder to elongate it.
4. Steel Bridges242
Fig. 6.2 Stress and Strain Distributions in Non-Composite Girders
Fig.6.3 Stress and Strain Distributions in Composite Girders
5. Chapter 6: Composite Plate Girder Bridges 243
6.1.2 Advantages and Disadvantages:
The basic advantages resulting from composite design are:
1. Reduction in steel weight.
2. Shallower steel girders.
3. Increased stiffness.
A weight saving in steel between 20 to 30 % is often possible by taking full
advantages of composite action. Such a weight reduction in the supporting
steel girders permits the use of a shallower section which is better from the
traffic clearance point of view. The stiffness of the composite bridge is
substantially greater than that of the concrete floor with its supporting steel
girders acting independently. Normally the concrete slab acts as one-way plate
spanning between the supporting girders. in composite design, an additional
use is made of the slab by its action In a direction parallel to and in
combination with the supporting steel girders. The net effect is to greatly
increase the moment of inertia of the floor system in the direction of the steel
girders. The increased stiffness considerably reduces the live load deflections.
Assuming full composite action, the strength of the section greatly exceeds the
sum of the strengths of the slab and the girder considered separately,
providing high overload capacity.
While there are no major disadvantages to using composite construction, some
limitations should be recognized. In continuous bridges, the negative moment
region will have a different stiffness because the cracked concrete slab in
tension is not participating. Also, long-term deflection caused by concrete
creep and shrinkage could be important when the composite section resists a
substantial part of the dead load, or when the live load is of long duration.
These two points shall be dealt with in later sections.
6.2 COMPONENTS OF COMPOSITE GIRDERS
6.2.1 Steel Girder
Composite construction is more economic when the tension flange of the steel
section is larger than the compression flange. The ratio of the girder span, L,
to the girder overall depth including concrete slab, h, lies generally between
16 and 22. For limited girder depth, L/h may exceed 22 provided that
deflection due to live load without impact does not exceed the allowable value
specified by the Code as L/800.
6. Steel Bridges244
Fig. 6.4 Composite Section Parameters
6.2.2 Concrete Slab
Concrete: The concrete used for composite construction shall comply with the
current Egyptian Code of Practice for Design of Reinforced Concrete
Structures. The minimum accepted value for the characteristic cube concrete
strength, fcu, is 300 kg/cm2
for bridges. For deck slabs subjected directly to
traffic (without wearing surface) , the value of fcu shall not be less than 400
kg/cm2
.
Thickness: The thickness for the deck slab shall not be less than 16 cm. If the
slab is subjected directly to traffic with no wearing surface, the minimum
thickness shall be 20 cm.
The slab may rest directly on the steel girder or on concrete haunch to increase
the moment of inertia of the composite section, see Fig. 6.4. It is also possible
to use formed steel deck with the deck ribs oriented parallel or perpendicular
to the steel girder. The concrete slab may also be prestressed.
6.2.3 Shear Connectors
Since bond strength between concrete slab and steel girder is not dependable,
mechanical shear connectors must be provided. They are connected to the top
flange of the steel girder and embedded in the concrete slab to transmit the
longitudinal shear and prevent any slippage between the concrete slab and the
steel girder. There are several types of the shear connectors such as: anchors,
hoops, block connectors, studs, channels and angle connectors as will be
discussed in details in section 6.4.
7. Chapter 6: Composite Plate Girder Bridges 245
6.3 DESIGN CONSIDERATIONS:
6.3.1 Effective Width
In ordinary girder theory the bending stress is assumed constant across the
girder width and is calculated from the bending formula, f = M * y / I. Since
the composite girder has a wide top flange, plate theory indicates that the
stress in the concrete slab is not uniform across the girder width. Referring to
Fig. 6.5, the stress is maximum over the steel girder and decreases non-
linearly as the distance from the supporting girder increases. Similarly to the
treatment of T-sections in reinforced concrete design, an effective width is
used in place of the actual width, so that the ordinary girder theory can be
used. The effective width of the slab bE is computed from the condition that bE
times the maximum stress fc equals the area under the nonlinear stress curve.
Fig. 6.5 Effective Width Concept
For design purposes, ECP defines the portion of the effective width of the
concrete slab on each side of the girder centerline bEL or bER as the smaller of
the following values; see Fig. 6.6:
8. Steel Bridges246
1. One-eighth of the girder span,(center-to-center of supports), L/8.
2. One half the distance to the center-line of the adjacent girder, b.
3. Six times the thickness (t) of the slab neglecting haunch.
4. the distance to the slab edge, b*
(for exterior girders)
For girders having a slab on one side only, the effective slab width bE shall not
exceed the smaller of 1/12 of the span length of the girder or six times the
thickness (t) of the slab neglecting haunch.
Fig. 6.6 Effective Width of Concrete Slab
The span lengths to be used in continuous beams are shown in Fig. 6.7. If the
two adjacent spans in a continuous beam are unequal, the value of bE to be
used in calculating bending stresses and longitudinal shear in the negative
moment regions shall be based on the mean of the values obtained for each
span separately.
Fig. 6.7 Effective Spans for Continuous Beams
9. Chapter 6: Composite Plate Girder Bridges 247
6.3.2 Computation of Section Properties
The section properties of the composite section can be computed by the
transformed section method. In contrast to reinforced concrete design where
the reinforcing steel is transformed into an equivalent concrete area, the
concrete slab in the composite section is transformed into an equivalent steel
area. As a result, the concrete area is reduced by using a reduced slab width
equal to be/n, where n is ratio of the steel modulus of elasticity Es to the
concrete modulus of elasticity Ec. While as the steel modulus is equal to a
constant value at 2100 t/cm2
Concrete Characteristic
Cube Strength, f
, the concrete modulus varies according to the
concrete grade. Consequently, the value of the modular ratio n varies with the
concrete grade as follows:
Table (6.1) Recommended Values of the Modular Ratio (n)
cu (kg/cm2
Modulus of Elasticity
of Concrete, E
)
c (t/cm2
Modular
Ratio, n)
250
300
400
≥ 500
220
240
280
310
10
9
8
7
With this transformation, the composite girder may be considered as a steel
girder to which has been added a cover plate on the top flange. It should be
noted that this cover plate, being concrete, is considered to be effective only
when the top flange is in compression. In continuous girders, the concrete slab
is in tension and thus composite action does not exist. Referring to Fig. 6.7,
the following section properties can be calculated.,
As = Cross-sectional area of steel girder,
Ac = Cross-sectional area of slab only,
Ar
Av = Cross-sectional area of transformed section = As + Ac / n ,
= Cross-sectional area of steel reinforcement,
Is = Moment of inertia of steel girder @ its own central axis s – s,
Ic = Moment of inertia of effective slab @ its own central axis c – c,
lv = Moment of inertia of transformed section @ its own central axis v – v,
= Is + As * ev
2
+ (Ic + Ac * yc
2
) / n
10. Steel Bridges248
Fig. 6.7 Composite Section Properties
Section Moduli:
Steel Section: Upper Steel Zus = Is / yus
Lower Steel Zls = Is / yls
Composite Section: Upper Steel Z'us = Iv / y'us
Lower Steel Z'ls = Iv / y'ls
Upper Concrete Z'uc = Iv / y'uc
5.3.3 Stress Calculations
Bending stresses in the composite section (steel girder, concrete slab, and
longitudinal reinforcement) shall be calculated in accordance with the elastic
theory, ignoring concrete in tension and assuming no slippage between the
steel girder and concrete slab. The actual stresses that result in the composite
section due to a given loading depend on the manner of construction. Two
different methods of construction may be used:
Case I: Without Shoring:
The simplest construction occurs when the steel girders are placed first and
used to support the concrete slab formwork. In this case the steel girder, acting
11. Chapter 6: Composite Plate Girder Bridges 249
noncompositely, supports the weight of the forms, the wet concrete and 'its
own weight. Once the forms are removed and concrete has cured, the section
will act compositely to resist dead loads placed after concrete curing (e.g.,
wearing surface) and live loads. Such construction is said to be without
temporary shoring or unshored. Referring to Figs. 6.8 and 6.10a; the stresses
in steel and concrete are computed as:
fus = MD / Zus + ML / Z'us
flS = MD / Zls + ML / Z'ls
fuc = ML / ( n * '
ucZ )
where MD= bending moment due to dead load and ML =bending moment due
to additional dead load and live load plus impact.
Fig. 6.8 Unshored Construction
12. Steel Bridges250
Case II: With Shoring
Alternatively, the steel girders may be supported on temporary shoring. In
such a case, the steel girder, forms, and wet concrete are carried by the shores.
After curing of concrete, the shores are removed and the section acts
compositely to resist all dead and live loads. This system is called shored
construction. Referring to Fig. 6.9 and 6.10b; the stresses in steel and concrete
are computed as follows:
fus = ( MD + ML ) / '
usZ
fls = ( MD + ML ) / '
lSZ
fuc = ( MD + ML ) / n '
ucZ
13. Chapter 6: Composite Plate Girder Bridges 251
Fig. 6.9 Shored Construction
Figure 6.10 illustrates the distribution of bending stresses for composite
girders constructed with or without shoring. Maximum bending stresses in the
steel section shall comply with the allowable bending stresses of the used
materials. The compression flange of the steel girder and its connection to the
web must be designed for the shear flow calculated for the composite section.
During construction, the compression flange must satisfy local buckling and
lateral torsional buckling requirements. After construction, however, the
composite section shall be exempt from such requirements.
The maximum bending stresses in the concrete slab shall not exceed the
allowable limits permitted by the Egyptian Code of Practice for Design of
Reinforced Concrete Structures. The steel web alone shall resist vertical shear
stresses of composite girder, neglecting any concrete slab contribution.
14. Steel Bridges252
Fig. 6.10 Stress Distributions in Composite Sections
6.3.4 Design for Creep and Shrinkage
If shoring provides support during the hardening of concrete, i.e. Case II, the
total deflection will be a function of the composite section properties. Account
must be taken of the fact that concrete is subject to creep under long-time
loading (i.e, dead load) and that shrinkage will occur, see Fig. 6.11.
6.3.4.1 Influence of Creep
i) General:
For the usual concrete dead loads, concrete does not behave as an elastic
material. Actually, concrete is a plastic material subjected to progressive
permanent deformation under sustained loads. This permanent deformation is
known as creep. For a constant permanent load the creep will vary from 1 to 4
times the elastic deformation under the same load, see Fig. 6.11.
It is known that only permanent loads causing compressive stresses in
concrete produce creep. Moving loads have little effect, as they do not last
long. The amount of creep varies with the magnitude of the permanent
compressive stresses. Low concrete stresses produce very little plastic flow,
which may be neglected.
15. Chapter 6: Composite Plate Girder Bridges 253
Fig. 6.11 Creep in Concrete
Creep in composite beams causes tensile stresses in concrete, compressive
stresses in the top flange and relatively small tensile stresses in the bottom
flange of the steel beam, see Fig. 6.12.
The creep of concrete depends on the curing conditions of the concrete at the
time the stresses are applied, on the intensity and duration of their effect, on
the quality of the concrete and the degree of humidity of its surroundings.
Assuming that deformation of the concrete with creep is directly proportional
to the prevailing stress and assuming a uniform modulus of elasticity EC, the
basic relationship between deformation & constant stress is :
ε = (fc / Ec) / (1 + φ)
where φ = elastic expansion / creep expansion and ε = strain.
Fig. 6.12 Effect of Creep and Shrinkage on Composite Sections
ii) Design for Creep:
The influence of creep is different according to the method of erection of the
composite beam.If the erection is done by case I, the concrete dead load is
carried by steel alone thus no appreciable creep. If the erection is done by
case II, the entire dead load is carried by the composite section causing creep.
16. Steel Bridges254
Hence for case I, the stresses in the composite section may be computed
neglecting creep. However, for case II, stresses in the composite section are
computed using a modular ratio 3n for all dead loads and using a modular
ratio of n for live loads, as to get more stresses in the steel section in
agreement with the phenomena of creep.
Concrete stresses in composite beams are reduced by creep. Therefore the
maximum concrete stress should be determined by neglecting creep.
6.3.4.2 Shrinkage
If the concrete slab is restrained from shrinkage by the steel girders, internal
stresses in concrete and steel independent of external loads will be produced.
Similar to the effect of creep, the shrinkage of concrete creates internal tensile
stresses in the concrete slab, compression in the top flange and tension in the
bottom flange of the steel beams, similar to the effect of creep. The ultimate
shrinkage strain in concrete shall be estimated to be equal to 0.0003.
6.3.5 Design For Temperature Effect
The variation of temperature shall be assumed according to the Egyptian Code
of Practice for Calculating Design Loads and Forces on Structures. In general,
a 30o
c uniform variation of the overall temperature of the structure is assumed.
Due consideration shall be given for the fact that although the coefficient of
thermal expansion for both steel and concrete is identical, the coefficient of
thermal conductivity of concrete is only about 2 % of that of the steel.
Therefore the top of the concrete slab and other levels through the depth of the
girder shall be assumed as shown in Fig. 6.13c .
Such difference in temperature of steel and concrete will create internal
stresses similar to those due to shrinkage and creep, Fig. 6.14. These stresses
result from the jump of temperature at the area of contact between steel and
concrete.
Due consideration of this phenomenon by appropriate method of calculation is
recommended.
17. Chapter 6: Composite Plate Girder Bridges 255
Fig. 6.13 Temperature Distribution
Fig. 6.14 Stress Distribution due to Effect of Temperature
6.3.6 Deflections
If the construction is shored during construction, Case II, the composite
section will support both the dead load and the live load deflections. However,
if the construction is not shored, Case I, the total deflection will be the sum of
the dead load deflection of the steel girder and the live load deflection of the
composite section. The deflection allowable limit due to live load without
impact is equal to L/800.
18. Steel Bridges256
6.3.7 Composite Construction in Continuous Span Bridges
i) General:
When the total bridge length is sufficiently long to require multiple spans,
the designer can either select a series of simple spans or he can use continuous
spans. Simple beam spans has the advantages of:
1) simpler analysis and design,
2) less field splices leading to faster erection,
3) no stresses due to support settlement.
Continuous span construction has the advantages of:
1) less steel weight,
2) less deflection,
3) Fewer number of bearings.
Before a system is selected for a particular bridge, the designer has to study
the advantages of both systems and decide accordingly. A two-span
continuous bridge has only slight economy over simple spans. The usual
bridge structure has three or more spans with the intermediate spans 20 % to
30 % longer than the end spans.
In continuous span bridges, the top concrete slab is subjected to tensile
stresses in the negative moment regions. Accordingly, the slab does not
contribute to the resistance of the cross section. However, benefit can be taken
from the presence of the slab by considering that the longitudinal
reinforcement bars, see Fig. 6.15, remain active within an effective width of
the slab.
Fig. 6.15 Composite Cross-Section at Interior Supports
19. Chapter 6: Composite Plate Girder Bridges 257
This effective width is related to the length of the negative moment region as
shown in Fig. 6.7.
ii) Design Considerations:
The area of reinforcement bars within the effective width is added to the steel
section of the negative moment region. Geometrical properties of both steel
section only and the composite section are calculated and then used to check
the bending stresses as explained before in section 6.3.3. In the negative
moment regions, the lower flange of the steel girder is subjected to
compression and therefore should be checked against lateral and local
buckling provisions.
6.4 SHEAR CONNECTORS
6.4.1 Horizontal Shear Force
The horizontal shear force transferred by the connector shall be computed at
the interface between concrete and upper flange of the steel girder utilizing the
virtual section properties. This horizontal shear must be resisted so that the
slip between both materials at the concrete-steel interface will be restrained.
Friction between the concrete slab and the steel girder can not be depended
upon to provide the required interface shear strength. Instead, the horizontal
shear force at the interface between the concrete slab and the steel girder shall
be transferred by shear connectors, as shown in Fig. 6.16 to Fig. 6.18,
throughout simple spans and positive moment regions of continuous girders.
In negative moment regions, shear connectors shall be provided when the
reinforcing steel embedded in concrete is considered as part of the composite
section, see section 6.3.7.
6.4.2 Connector Capacity
Ideally, to obtain a fully composite section, the connector should be stiff
enough to provide the complete interaction; i.e., no slip at the interface. This,
however, would require that the connectors be infinitely rigid. Also, since the
shear force varies along the girder length, the distribution of the shear
connectors should be such that more connectors are used at high shear
locations.
20. Steel Bridges258
6.4.3 Connector Design
If the dead load stresses are carried by the steel section, e.g., unshored
construction, the connectors may be designed to carry the shearing forces due
to live loads only. But to allow for shrinkage and creeping effects and to give
better security against slip, it is recommended to design the connector to carry
shearing forces due to half the dead load in addition to the live load. For
shored construction, the connectors are to be designed to carry the shearing
forces due to dead and live loads.
To design the connector, the longitudinal shearing force per unit length of the
girder is calculated as:
τc = Q Ac yc / Iv
where:
Ac = Area of concrete section without haunches
yc = Distance between central axis of concrete section and that of
the composite section.
If the spacing between the connectors is equal to "e", then the total horizontal
shear to be transmitted by one connector along a pitch “e” is :
e * τc = e * (Q Ac yc / Iv )
This value should be less than the allowable load the connector can carry,
denoted by Rsc, i.e.,
e * (Q Ac yc / Iv ) < Rsc
From this equation, the connector spacing e can be calculated as:
e = Rsc * Iv / (Q Ac yc)
Thus the pitch “e” is inversely proportional to Q and the connectors are to be
arranged closer to each other at the supports and at bigger intervals near the
middle of the girder.
In the following section, different types of shear connectors used in composite
construction are described. In addition, it applies to the calculation of the
allowable horizontal shear load, Rsc, for one connector. The value of Rsc
21. Chapter 6: Composite Plate Girder Bridges 259
computed from the following formulas shall not exceed the allowable
horizontal load, Rw, provided by the connector connection to the girder flange.
6.4.4 Connector Types
Various types of such connectors are shown in Figures 6.16 thru 6.18. The
most common types are the anchor and hoop connectors, the block connector,
the angle and channel connectors, and the stud connectors.
6.4.4.1 Anchors and hoops
a- Anchors and hoops (Fig. 6.16) designed for longitudinal shear should point
in the direction of the diagonal tension. Where diagonal tension can occur in
both directions, connectors pointing in both directions should be provided.
b- Hoop connectors (diameter = φ shall satisfy the following:
r ≥ 7.5φ L ≥ 4r concrete cover ≥ 3 φ
c- Development length and concrete cover of anchors shall be based on the
allowable concrete bond stresses as per the Egyptian Code of Practice for
the Design of Reinforced Concrete Structures.
d- The allowable horizontal load for each leg of anchors and hoops shall be
computed as follows:
Rsc = 0.58 As Fys cos β / (1 + sin2
α) ½
≤ Rw
Where
As = Cross sectional area of anchor or hoop
Fys = Yield stress of anchor or hoop material
β = Angle in horizontal plane between anchor and longitudinal axis
of the girder.
α = Angle in the vertical plane between anchor or hoop and the girder
upper flange.
22. Steel Bridges260
Figure (6.16) Anchor & Hoop Shear Connectors
6.4.4.2 Block Connectors
Block connectors (Fig. 6.17) such as bar, T-section, channel section and
horseshoe can be used as shear connectors. The front face shall not be wedge
shaped and shall be so stiff that uniform pressure distribution on concrete can
be reasonably assumed at failure.
a- Block connectors shall be provided with anchoring devices to prevent
uplift of concrete slab.
b- The height of bar connectors shall not exceed four times its thickness.
c- The height of T-sections shall not exceed ten times the flange thickness
or 150 mm, whichever is the least.
d- Channel sections shall be hot rolled with a web width not exceeding 25
times the web thickness. The height of the connectors shall not exceed 15
times the web thickness nor 150 mm, whichever is the least.
e- The height of horseshoe connectors shall not exceed 20 times the web
thickness nor 150 mm, whichever is the least.
f- The allowable horizontal load (Rbe) transmitted by bearing can be computed
from the following Equation:
24. Steel Bridges262
Rbl = 0.3 η A1 fcu
Where
η = (A2/A1)1/2
A1
≤ 2
= Area of connector front face
A2 = Bearing area on concrete, shall be taken as the front area of the
connector, A1, enlarged at a slope of 1:5 (see Fig. 6.17) to the rear
face of the adjacent connector. Only parts of A2 falling in the
concrete section shall be taken into account.
g- Block connectors shall be provided with anchors or hoops sharing part of
the horizontal load supported by the connector, provided that due account
shall be taken of the differences of stiffness of the block connector and the
anchors or hoops. The allowable horizontal load per connector can be
computed from the following:
Rsc = Rbl + 0.5 Ran ≤ Rw
And Rsc = Rbl + 0.7 Rh ≤ Rw
Where
Ran = Horizontal load supported by anchor
Rh = Horizontal load supported by hoop
6.4.4.3 Channel Shear Connectors
The allowable horizontal load, Rsc, for one channel shear connector, Fig. 6.18,
shall be computed from the following Equation:
Rsc = 0.12 ( tf + 0.5tw) Lc ( fcu Ec ) 1/2
≤ Rw
where: tf , tw = flange and web thicknesses, cm,
Lc = connector length, cm.
25. Chapter 6: Composite Plate Girder Bridges 263
Fig. 6.18 Channel Shear Connectors
5.4.4.4 Angle Connectors
The height of the outstanding leg of an angle connector shall not exceed ten
times the angle thickness or 150 mm, whichever is the smaller. The length of
an angle connector shall not exceed 300 mm (Fig. 6.19).
The allowable horizontal load for an angle connector shall be computed as
follows:
Rsc = 4 Lc tc
3/4
fcu
2/3
≤ Rw
where
Lc = Length of the angle connector ,cm.
tc = Width of the outstanding leg of the angle connector, cm.
And fcu in kg/cm2
26. Steel Bridges264
Fig. 6.19 Angle Shear Connectors
It is recommended to provide a bar welded to the angle to prevent uplift of the
concrete slab, the minimum diameter of the bar shall be computed from the
following:
Φ ≥ 0.45 (Rsc / Fys)1/2
Where
Φ = Diameter of the bar, cm
Fys = Yield stress of the bar, kg/cm
Rsc
2
= Allowable shear load for one angle connector.
The length of the bar on each side of the angle connector standing leg shall be
computed based on the allowable bond strength of concrete following the
provisions of the Egyptian Code of Practice for Design of Reinforced
Concrete Structure.
27. Chapter 6: Composite Plate Girder Bridges 265
6.4.4.5 Stud Connectors
Despite this wide range of connector types, the stud connector, Fig. 6.20 and
6.21, has now become the primary method of connections for composite
beams. The stud can be forge welded to the steel section in one operation
using a special hand held welding machine, see Fig. 6.20. These machines
allow operators to weld approximately 1000 studs per day. Fig. 6.21 shows a
typical shear stud before and after welding.
Fig. 6.20 Automatic Welding of Stud Shear Connectors
The length of the stud connector shall not be less than four times its diameter,
ds, after installation. The nominal diameter of the stud head shall not be less
than one and half times the stud diameter, ds. The value of ds shall not exceed
twice the thickness of the steel girder top flange. Except where formed steel
decks are used, the minimum center-to-center spacing of studs shall be (6ds)
measured along the longitudinal axis of the girder ; and (4ds) transverse to the
longitudinal axis of the supporting composite girder , (Fig. 6.22). If stud
connectors are placed in a staggered configuration, the minimum transversal
spacing of stud central lines shall be 3ds. Within ribs of formed steel decks, the
minimum permissible spacing is 4ds in any direction.
29. Chapter 6: Composite Plate Girder Bridges 267
The allowable horizontal load, Rsc, for one stud connector shall be computed
from the following formula:
Rsc = 0.17 Asc ( fcu Ec ) ½
≤ Rw
≤ 0.58 Asc Fy
where:
Asc = Cross sectional area of stud connector, cm
6.4.5 General Requirements for Shear Connectors
2
Fy = The yield stress of stud steel connectors
6.4.5.1 Connection to Steel Flange
The connection between the shear connectors and the girder flange shall be
designed to resist the horizontal shear load acting on the connector; section
6.4.4.
6.4.5.2 Concrete Cover
a- In order to ensure adequate embedment of shear connectors in concrete
slab, the connector shall have at least 50 mm of lateral concrete cover. On the
other hand, the minimum concrete cover on top of the connector shall not be
less than 20 mm.
b- Except for formed steel slab; the sides of the haunch should lie outside a
line drawn at maximum of 45o
• 60 cm
from the outside edge of the connector. The
lateral concrete cover from the side of the haunch to the connector should be
not less than 50 mm.
6.4.5.3 Placement and Spacing
Except for stud connectors, the minimum center-to-center spacing of shear
connectors shall not be less than the total depth of the slab including haunch,
do. The maximum center-to-center spacing of connectors shall not exceed the
least of the following:
• Three times the total slab thickness (do)
• Four times the connector height including hoops or anchors, if any.
30. Steel Bridges268
However, the maximum spacing of connectors may be exceeded over supports
to avoid placing connectors at locations of high tensile stresses in the steel
girder upper flange.
6.4.5.4 Dimensions of Steel Flange
The thickness of steel flange to which the connector is fastened shall be
sufficient to allow proper welding and proper transfer of load from the
connector to the web plate without local failure or excessive deformations.
The distance between the edge of a connector and the edge of the girder flange
to which it is welded should not be less than 25 mm .
6.4.5.5 Concrete Slab Edges
Concrete slab edges shall be provided with end closures, e.g. channels, angles,
or plates, as shown in Fig. 6.23. End closures have to be fixed to the steel
girders before casting the concrete slab. Besides minimizing grout loss during
casting of concrete, end closures enhance the shear connectivity between
concrete slab and steel girders at zones of maximum shear forces. End closures
also help in resisting forces arising from shrinkage and creep.
Fig. 6.23 End Closure for Concrete Slab
31. Chapter 6: Composite Plate Girder Bridges 269
6.5 DESIGN EXAMPLE:
The design example presented in chapter 5 is used here to illustrate the
method of design of composite plate girders. The example uses the same
values of the straining actions at the middle section.
The selection of the girder cross section is essentially a trial-and-error
procedure in which a trial section is assumed and used to check the resulting
stresses in both steel and concrete:
The following section is assumed:
a) Web 2250 × 14
b) Top Flange 400 × 12
(bf / 2tf = 40 / (2 ×1.2) = 16.667 > 21 / yf = 11
No problem since flange is prevented from local buckling by deck slab)
c) Bottom Flange 600 × 32
Section properties are then computed for the following cases:
a) Steel section only:
Centroid Yus = 143.391 cm
Intertia Is = 3953428 cm4
Section Moduli Zus = 27571 cm3
Zls = 45965 cm3
b) Effective Slab Width:
For the right girder:
bER = b* = 150 cm (Side Walk Slab)
bEL = smaller of:
1) Span/8 = 27.5 /8 = 3.4375 m
2) Spacing /2 = 7/2 = 3.5 m
3) 6 ts = 6 * 22 = 132 cm governs
Total effective width bER + bEL = 150 + 132 = 282 cm
32. Steel Bridges270
c) Composite section with n = 9 (Fcu = 300 kg / m2
)
Centroid Y'us = 57.862 cm
Intertia Iv = 11309956 cm4
Section Moduli Z′us = 195465 cm3
Z′ls = 65933 cm3
Zuc = 141619 cm3
d) Composite section with n = 3 × 9 = 27 (Effect of Creep)
Centroid Y'us = 98.186 cm
Intertia Iv = 7836139 cm4
Section Moduli Z′us = 79809 cm3
Z′ls = 59720 cm3
Zuc = 65200 cm
Load
3
Check of Bending Stresses:
a) Non-Shored Construction:
Upper Steel (-)
t/cm
Lower Steel (+)
t/cm2
Upper Concrete
kg / cm2 2
DL 1 Fus = 385 × 100/27571
= 1.396
Fls = 385 × 100/45965
= 0.838
= 0 for non-shored
construction
DL 2 Fus = 115 × 100/79809
= 0.144
Fls = 115 × 100/59720
= 0.193
Fuc = (115 × 100/65200)
*(1000/27) = 6.533
LL + I Fus = 700 × 100/195465
= 0.358
Fls = 700x100/65933
= 1.062
Fuc = (700/141619)
*(1000/9) = 54.92
Total 1.899 2.092 61.453
Checks:
1- Compression at Upper Steel :
a) Total stress: Fus = 1.899 < Fb = 2.1 t/cm2
(compression flange is laterally supported by deck slab)
b) Due to D.L. only Fus = 1.396 t / cm2
compression flange is laterally supported by upper bracing with
Lu = 4.5 m, rT= 8 cm
Lu/rT = 450 / 8 = 56.25
33. Chapter 6: Composite Plate Girder Bridges 271
y
Tu
F
C
188r/L b
≤ = 99
yy
b
5
y
2
Tu
F58.0F)
C10x176.1
F)r/L(
64.0(2ltbF ≤−= = 1.955 t/cm2
Fus < FLTB
2. Tension at Upper Steel :
O.K.
a) Total Tension: fls = 2.092 < Fb = 2.10 t/cm2
b) Fatigue fsr = 0.5 × 1.062 = 0.531 < Fsr = 1.02 t/cm2
{The allowable fatigue stress range (Fsr) is obtained as follows:
* From ECP Table 3.1.a: ADTT >2500, Number of cycles = 2 ×106
Detail Class = B′ (case 4.2 of Table 3.3)
Table 3.2 gives Fsr = 1.02 t/cm2
3. Compression on Upper Concrete:
> fsr }
Concrete fuc = 61.453 < 70 kg/cm2
b) Shored Construction:
DL1 + DL2 LL + I
Upper Steel fus= 50000 / 79809 + 70000 / 195465 =
= 0.626 + 0.358 = 0.985 t/cm2
Lower Steel fls = 50000 / 59720 + 70000 / 65933 =
= 0.837 + 1.062 = 1.899 t/cm2
Upper Concrete: fuc=50000*1000 / (65200*27) + 70000*1000 / (141619*9)
= 28.403 + 54.92 = 83.323 kg/cm2
Code recommends to neglect creep in computing concrete stresses:
Upper Concrete: fus=50000*1000 / (141619*9) + 70000*1000 / (141619*9)
= 39.229 + 54.92 = 94.149 kg/cm2
Note that shored construction results in decrease of steel stresses and increase
in concrete stresses.
34. Steel Bridges272
Design of Shear Connectors
Assuming non-shored construction, the shear force to be carried by the
connectors at the support is:
Qc = 0.5 * QDL1 + (QDL2 + QLL+I)
= 0.5 × 62+ (18 + 100) = 149 tons
The shear / unit length is τ = Qc Sc / Iv
Where Sc = first moment of area of the concrete slab about the neutral axis of
the composite section = Ac * yc
= (282 × 22/9) * (57.862+11) = 47469 cm3
τ = 149 × 47469 / 11309956 = 0.625 t / cm'
a) Stud Connecters:
i) Stud Capacity:
The allowable load of one stud connector is computed as:
Rsc = 0.17 Asc (fcu Ec)1/2
≤ 0.58 ASC Fy
≤ Rw
using φ 24 mm studs, Asc = π / 4 (2.4)2
= 4.52 cm2
Fcu = 300 kg / cm2
= 0.3 t/cm2
Ec = 240 t/cm2
Rsc = 0.17 × 4.52 (0.300 × 240)1/2
= 6.52 t
OR = 0.58 Asc × Fy = 6.29 t
ii) Stud Connection Capacity:
The allowable stress range in shear on the nominal area of the stud (case 26 of
table 3.3) is equal to 0.4 t/cm2
according to table 3.2; i.e.,
Rw = Shear range / stud = π / 4 (2.4)2
× 0.4 = 1.808 t governs
τsr = (0.5 × 100) ×47469 / 11309956 = 0.210 t/cm'
35. Chapter 6: Composite Plate Girder Bridges 273
Using 3 studs per row:
Spacing e ≤ R/τsr = 1.808 × 3/ 0.21 = 25.846 cm
Use studs at 20 cm (check: e ≥ 6d = 14.4 cm)
b) Channel Connector:
The allowable load on one channel connector is calculated from:
Rsc = 0.12 (1 + 0.3) × 20 (0.3 × 200)1/2
= 24 t
However, the design is usually governed by the fatigue capacity of the welded
connection between the channel and the top flange computed as follow:
According to Case 24 of table 3.3 → Fatigue Class E′
From Table 3.2 → τsr = 0.41 t/cm2
Assuming 2 x 20 cm length of 5 mm weld, then
Rw = 2 × 20 × 0.5 × 0.41 = 8.2 t
Connector Spacing = 8.2/0.21 = 39.05 cm
Use Channel C12 spaced at 30 cm.