This document discusses concepts related to the design of concrete beams including:
1. It introduces concepts like bending, shear, tension and compression as they relate to beam design.
2. It provides formulas for calculating reactions, shear forces, and bending moments in simply supported beams under different loading conditions.
3. It explains concepts like the neutral axis, stress blocks, and strain diagrams that are important to beam design.
4. It discusses factors that influence the strength of beams like the moment of inertia and reinforcement ratio.
5. It compares working stress and limit state methods of design.
This document provides an overview of the design of steel beams. It discusses various beam types and sections, loads on beams, design considerations for restrained and unrestrained beams. For restrained beams, it covers lateral restraint requirements, section classification, shear capacity, moment capacity under low and high shear, web bearing, buckling, and deflection checks. For unrestrained beams, it discusses lateral torsional buckling, moment and buckling resistance checks. Design procedures and equations for determining effective properties and capacities are also presented.
This document section describes design considerations for precast pretensioned concrete girders. It discusses typical girder sections and common span ranges. The key stages in precast girder design are described as transfer (when prestressing force is transferred to the concrete), service (when self-weight and permanent loads are considered), and ultimate (to resist factored loads). Three stages of stress development are discussed: transfer when prestressing occurs, stage IIA when the girder is erected and before the composite deck is cured, and stage IIB when the composite section develops. Standard precast girder types used in California include I-girders, bulb-tees, bath-tubs, and wide-flange sections,
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 provides information about pile foundations. Piles are long, slender members used to transmit foundation loads through weak soil layers to stronger layers below. They can be made of timber, concrete, steel, or other materials. Factors that influence pile selection include soil conditions, load requirements, availability of materials, and costs. Pile foundations allow buildings and bridges to be supported in places with poor soil by transmitting loads to deeper, stronger layers. The document discusses different types of piles and pile driving methods.
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.
The document provides notes on masonry structures from a course at the University of Illinois. It discusses lateral strength and behavior of unreinforced masonry (URM) shear walls, including design criteria, failure modes, and examples. Key points include allowable stresses for flexure, shear, and axial loading; effects of perforations on stiffness and force distribution; and checking stresses in piers between openings.
The document discusses proper detailing of reinforced concrete structures, which is essential for safety and structural performance. It provides guidelines and examples of good and bad detailing practices for common reinforced concrete elements like slabs, beams, columns, and foundations. Proper detailing is important to avoid construction errors and ensure the structural design works as intended under gravity and seismic loads.
Calulation of deflection and crack width according to is 456 2000Vikas Mehta
This document discusses the calculation of crack width in reinforced concrete flexural members. It provides information on:
1) Crack width is calculated to satisfy serviceability limits and is only relevant for Type 3 pre-stressed concrete members that crack under service loads.
2) Crack width depends on factors like amount of pre-stress, tensile stress in bars, concrete cover thickness, bar diameter and spacing, member depth and location of neutral axis, bond strength, and concrete tensile strength.
3) The method of calculation involves determining the shortest distance from the surface to a bar and using equations involving member depth, neutral axis depth, average strain at the surface level. Permissible crack widths are specified depending on exposure
This document provides an overview of the design of steel beams. It discusses various beam types and sections, loads on beams, design considerations for restrained and unrestrained beams. For restrained beams, it covers lateral restraint requirements, section classification, shear capacity, moment capacity under low and high shear, web bearing, buckling, and deflection checks. For unrestrained beams, it discusses lateral torsional buckling, moment and buckling resistance checks. Design procedures and equations for determining effective properties and capacities are also presented.
This document section describes design considerations for precast pretensioned concrete girders. It discusses typical girder sections and common span ranges. The key stages in precast girder design are described as transfer (when prestressing force is transferred to the concrete), service (when self-weight and permanent loads are considered), and ultimate (to resist factored loads). Three stages of stress development are discussed: transfer when prestressing occurs, stage IIA when the girder is erected and before the composite deck is cured, and stage IIB when the composite section develops. Standard precast girder types used in California include I-girders, bulb-tees, bath-tubs, and wide-flange sections,
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 provides information about pile foundations. Piles are long, slender members used to transmit foundation loads through weak soil layers to stronger layers below. They can be made of timber, concrete, steel, or other materials. Factors that influence pile selection include soil conditions, load requirements, availability of materials, and costs. Pile foundations allow buildings and bridges to be supported in places with poor soil by transmitting loads to deeper, stronger layers. The document discusses different types of piles and pile driving methods.
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.
The document provides notes on masonry structures from a course at the University of Illinois. It discusses lateral strength and behavior of unreinforced masonry (URM) shear walls, including design criteria, failure modes, and examples. Key points include allowable stresses for flexure, shear, and axial loading; effects of perforations on stiffness and force distribution; and checking stresses in piers between openings.
The document discusses proper detailing of reinforced concrete structures, which is essential for safety and structural performance. It provides guidelines and examples of good and bad detailing practices for common reinforced concrete elements like slabs, beams, columns, and foundations. Proper detailing is important to avoid construction errors and ensure the structural design works as intended under gravity and seismic loads.
Calulation of deflection and crack width according to is 456 2000Vikas Mehta
This document discusses the calculation of crack width in reinforced concrete flexural members. It provides information on:
1) Crack width is calculated to satisfy serviceability limits and is only relevant for Type 3 pre-stressed concrete members that crack under service loads.
2) Crack width depends on factors like amount of pre-stress, tensile stress in bars, concrete cover thickness, bar diameter and spacing, member depth and location of neutral axis, bond strength, and concrete tensile strength.
3) The method of calculation involves determining the shortest distance from the surface to a bar and using equations involving member depth, neutral axis depth, average strain at the surface level. Permissible crack widths are specified depending on exposure
This document provides an introduction to reinforced concrete, including its key components and purposes. Reinforced concrete is a composite material made of concrete, which resists compression well but has low tensile strength, and steel reinforcing bars, which resist tension well. Together they create an economical and strong structural material. The document outlines structural elements, design considerations for safety, reliability, and economy, and limit state design principles which ensure structures do not fail under expected loads. It also discusses factors that affect concrete durability and different failure modes in reinforced concrete depending on steel reinforcement ratios.
While Designing a High rise Load & Structural Analysis is major factor to consider. Here we analyzed some data and try to describe briefly. We hope that it will help you lot :) Done by Neeti Lamic, Bayezid, Sykot Hasan
Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)Hossam Shafiq II
This document discusses shear in reinforced concrete beams. It covers shear stress and failure modes, shear strength provided by concrete and steel stirrups, design according to code provisions, and critical shear sections. Key points include: transverse loads induce shear stress perpendicular to bending stresses; shear failure is brittle and must be designed to exceed flexural strength; nominal shear strength comes from concrete and steel stirrups according to code equations; design requires checking section adequacy and providing minimum steel area and maximum stirrup spacing. Critical shear sections for design are located a distance d from supports.
This document discusses the design of beams. It defines different types of beams like floor beams, girders, lintels, purlins, and rafters. It describes how beams are classified based on their support conditions as simply supported, cantilever, fixed, or continuous beams. Commonly used beam sections include universal beams, compound beams, and composite beams. The document also covers plastic analysis of beams, classification of beam sections, and failure modes of beams.
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.
This document discusses types of columns, materials used for columns, design methods, and construction process for columns. It describes short, long, and intermediate columns. Steel is discussed as a column material, noting its advantages of high strength, uniformity, elasticity, and ductility, as well as disadvantages of reduced strength under cyclic loading and potential brittle fracture. Design methods of Allowable Strength Design and Load Resistance Factor Design are covered, along with load combinations. The basic requirements and design formulas are provided.
This document provides an overview of basic equations for the theory of plates and shells. It discusses the state of stress and strain at a point, including defining the six independent stress and strain components. It presents the relationships between strain and displacement, and discusses the equilibrium equations relating stress and body forces. Finally, it provides the equations for both Cartesian and cylindrical coordinate systems. The key concepts covered are the fundamental equations that form the basis of plate and shell theory.
Shear walls are vertical reinforced concrete walls that resist lateral forces like wind and earthquakes. They provide strength and stiffness to control lateral building movement. Shear walls are classified into different types including simple rectangular, coupled, rigid frame, framed with infill, column supported, and core type walls. Design of shear walls involves reviewing the building layout, determining loads, estimating earthquake forces, analyzing the structural system, and designing for flexural and shear strengths with proper reinforcement detailing. The behavior of shear walls under seismic loading depends on their height to width ratio, with squat walls experiencing more shear deformation and slender walls undergoing primarily bending deformation.
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.
This document discusses flitched beams, which are composite beams made of wood beams sandwiched around a steel plate and held together with bolts. It defines beams and types of beams, then explains what composite beams and flitched beams are. It describes the design principle of flitched beams, which combines the properties of wood and steel to provide greater strength than either material alone. Applications of flitched beams include construction of houses and decks where they are stronger than wood but lighter than steel. However, engineered wood has replaced flitched beams due to lower costs and easier installation.
This is a Power Point Presentation discussing briefly about the Slab, Beam & Column of a building construction. It was presented on 6th March, 2014 as part of the Presentations of the subject: DETAILS OF CONSTRUCTION, at Ahsanullah University of Science & Technology (AUST)
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
Retaining walls have the primary function of retaining soils at an angle greater than the soil's natural angle of repose. There are several types of retaining walls including mass retaining walls, cantilever walls, counterfort retaining walls, and precast concrete retaining walls. Design considerations for retaining walls include preventing overturning, forward sliding, using suitable materials, and not overloading the subsoil.
Composite structure of concrete and steel.Suhailkhan204
This document discusses composite structures, which combine steel and concrete materials. The key elements of composite structures are composite deck slabs, beams, and columns, along with shear connectors. Composite structures take advantage of concrete's compressive strength and steel's tensile strength. They provide benefits like increased load capacity, stiffness, fire resistance, and cost savings compared to traditional steel or concrete construction alone. An example project, the Millennium Tower in Vienna, is described. The document analyzes costs and concludes that composite structures are best suited for high-rise buildings due to reduced weight, increased ductility, and savings of around 10% compared to reinforced concrete.
Module 1 Behaviour of RC beams in Shear and TorsionVVIETCIVIL
This document summarizes key concepts related to shear and torsion behavior in reinforced concrete beams. It discusses modes of cracking in shear, shear failure modes, critical sections for shear design, the influence of axial forces and longitudinal reinforcement on shear strength, and shear transfer mechanisms. The key points covered include web shear cracking, flexure-shear cracking, diagonal tension failure, shear-compression and shear-tension failures, and the four mechanisms that contribute to shear transfer: aggregate interlock, dowel action, stirrups, and the interaction between axial compression and shear strength.
This is just an overview about the Reinforced Concrete Deck Girder Bridge
(RCDG Bridge)
the Presentation includes:
Materials for Construction,
Parts of a typical RCDG bridge,
The Forces Acting on the bridge, etc.
The document discusses buckling of columns under axial compression. It describes:
1) Different buckling theories including elastic buckling, inelastic buckling using tangent modulus theory and reduced modulus theory. Shanley's theory accounts for the effect of transverse displacement.
2) Factors affecting buckling strength including end conditions, initial crookedness, and residual stresses. Effective length accounts for end restraint.
3) Local buckling of thin plate elements can reduce the column's strength before its calculated buckling strength is reached. Flange and web buckling must be prevented.
information on types of beams, different methods to calculate beam stress, design for shear, analysis for SRB flexure, design for flexure, Design procedure for doubly reinforced beam,
This document provides an introduction to reinforced concrete, including its key components and purposes. Reinforced concrete is a composite material made of concrete, which resists compression well but has low tensile strength, and steel reinforcing bars, which resist tension well. Together they create an economical and strong structural material. The document outlines structural elements, design considerations for safety, reliability, and economy, and limit state design principles which ensure structures do not fail under expected loads. It also discusses factors that affect concrete durability and different failure modes in reinforced concrete depending on steel reinforcement ratios.
While Designing a High rise Load & Structural Analysis is major factor to consider. Here we analyzed some data and try to describe briefly. We hope that it will help you lot :) Done by Neeti Lamic, Bayezid, Sykot Hasan
Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)Hossam Shafiq II
This document discusses shear in reinforced concrete beams. It covers shear stress and failure modes, shear strength provided by concrete and steel stirrups, design according to code provisions, and critical shear sections. Key points include: transverse loads induce shear stress perpendicular to bending stresses; shear failure is brittle and must be designed to exceed flexural strength; nominal shear strength comes from concrete and steel stirrups according to code equations; design requires checking section adequacy and providing minimum steel area and maximum stirrup spacing. Critical shear sections for design are located a distance d from supports.
This document discusses the design of beams. It defines different types of beams like floor beams, girders, lintels, purlins, and rafters. It describes how beams are classified based on their support conditions as simply supported, cantilever, fixed, or continuous beams. Commonly used beam sections include universal beams, compound beams, and composite beams. The document also covers plastic analysis of beams, classification of beam sections, and failure modes of beams.
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.
This document discusses types of columns, materials used for columns, design methods, and construction process for columns. It describes short, long, and intermediate columns. Steel is discussed as a column material, noting its advantages of high strength, uniformity, elasticity, and ductility, as well as disadvantages of reduced strength under cyclic loading and potential brittle fracture. Design methods of Allowable Strength Design and Load Resistance Factor Design are covered, along with load combinations. The basic requirements and design formulas are provided.
This document provides an overview of basic equations for the theory of plates and shells. It discusses the state of stress and strain at a point, including defining the six independent stress and strain components. It presents the relationships between strain and displacement, and discusses the equilibrium equations relating stress and body forces. Finally, it provides the equations for both Cartesian and cylindrical coordinate systems. The key concepts covered are the fundamental equations that form the basis of plate and shell theory.
Shear walls are vertical reinforced concrete walls that resist lateral forces like wind and earthquakes. They provide strength and stiffness to control lateral building movement. Shear walls are classified into different types including simple rectangular, coupled, rigid frame, framed with infill, column supported, and core type walls. Design of shear walls involves reviewing the building layout, determining loads, estimating earthquake forces, analyzing the structural system, and designing for flexural and shear strengths with proper reinforcement detailing. The behavior of shear walls under seismic loading depends on their height to width ratio, with squat walls experiencing more shear deformation and slender walls undergoing primarily bending deformation.
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.
This document discusses flitched beams, which are composite beams made of wood beams sandwiched around a steel plate and held together with bolts. It defines beams and types of beams, then explains what composite beams and flitched beams are. It describes the design principle of flitched beams, which combines the properties of wood and steel to provide greater strength than either material alone. Applications of flitched beams include construction of houses and decks where they are stronger than wood but lighter than steel. However, engineered wood has replaced flitched beams due to lower costs and easier installation.
This is a Power Point Presentation discussing briefly about the Slab, Beam & Column of a building construction. It was presented on 6th March, 2014 as part of the Presentations of the subject: DETAILS OF CONSTRUCTION, at Ahsanullah University of Science & Technology (AUST)
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
Retaining walls have the primary function of retaining soils at an angle greater than the soil's natural angle of repose. There are several types of retaining walls including mass retaining walls, cantilever walls, counterfort retaining walls, and precast concrete retaining walls. Design considerations for retaining walls include preventing overturning, forward sliding, using suitable materials, and not overloading the subsoil.
Composite structure of concrete and steel.Suhailkhan204
This document discusses composite structures, which combine steel and concrete materials. The key elements of composite structures are composite deck slabs, beams, and columns, along with shear connectors. Composite structures take advantage of concrete's compressive strength and steel's tensile strength. They provide benefits like increased load capacity, stiffness, fire resistance, and cost savings compared to traditional steel or concrete construction alone. An example project, the Millennium Tower in Vienna, is described. The document analyzes costs and concludes that composite structures are best suited for high-rise buildings due to reduced weight, increased ductility, and savings of around 10% compared to reinforced concrete.
Module 1 Behaviour of RC beams in Shear and TorsionVVIETCIVIL
This document summarizes key concepts related to shear and torsion behavior in reinforced concrete beams. It discusses modes of cracking in shear, shear failure modes, critical sections for shear design, the influence of axial forces and longitudinal reinforcement on shear strength, and shear transfer mechanisms. The key points covered include web shear cracking, flexure-shear cracking, diagonal tension failure, shear-compression and shear-tension failures, and the four mechanisms that contribute to shear transfer: aggregate interlock, dowel action, stirrups, and the interaction between axial compression and shear strength.
This is just an overview about the Reinforced Concrete Deck Girder Bridge
(RCDG Bridge)
the Presentation includes:
Materials for Construction,
Parts of a typical RCDG bridge,
The Forces Acting on the bridge, etc.
The document discusses buckling of columns under axial compression. It describes:
1) Different buckling theories including elastic buckling, inelastic buckling using tangent modulus theory and reduced modulus theory. Shanley's theory accounts for the effect of transverse displacement.
2) Factors affecting buckling strength including end conditions, initial crookedness, and residual stresses. Effective length accounts for end restraint.
3) Local buckling of thin plate elements can reduce the column's strength before its calculated buckling strength is reached. Flange and web buckling must be prevented.
information on types of beams, different methods to calculate beam stress, design for shear, analysis for SRB flexure, design for flexure, Design procedure for doubly reinforced beam,
The document discusses different methods of designing concrete structures, focusing on the limit state method. It describes the limit state method's goal of achieving an acceptable probability that a structure will not become unsuitable for its intended use during its lifetime. The document then discusses stress-strain curves for concrete and steel. It covers stress block parameters and equations for calculating the depth of the neutral axis and moment of resistance for singly reinforced concrete beams. The document concludes by providing examples of analyzing an existing beam section and designing a new beam section.
This document provides information on reinforced concrete design including:
- Concrete and steel properties such as modulus of elasticity and grades/strengths of reinforcing bars.
- Minimum concrete cover requirements for reinforcement.
- Load factors and combinations for ultimate strength design.
- Flexural design procedures for reinforced concrete beams including assumptions, stress/strain diagrams, and analysis for cases where steel yields or does not yield.
- Requirements for reinforcement spacing, minimum member thicknesses, and ductility.
This document provides information on analysis and design of reinforced concrete beams. It discusses key concepts such as modular ratio, neutral axis, stress diagrams, and types of reinforcement. It also defines under-reinforced, balanced, and over-reinforced beam sections. Several examples are provided to illustrate determination of neutral axis depth, moment of resistance, steel percentage, and stresses in concrete and steel reinforcement. Design aspects like maximum load capacity are also explained through examples.
The document discusses different methods of concrete design including working stress method, limit state method, ultimate load method, and probabilistic method. It then focuses on explaining the limit state method. Key points include:
- The limit state method aims to achieve an acceptable probability that a structure will not reach an unsafe limit state during its lifetime.
- Structures must withstand all reliably expected loads over lifetime and satisfy serviceability requirements like deflection and cracking limits.
- Important limit states to consider in design are flexure, compression, shear, and torsion failure modes.
- Examples are given of analyzing and designing reinforced concrete beam sections using the limit state method. Design calculations for moment of resistance are shown.
The document summarizes the analysis of reinforced concrete beam cross sections to determine their moment of resistance at the ultimate limit state. It outlines the key assumptions of the strength design method and describes the behavior of beams under small, moderate and ultimate loads. It also discusses balanced, under-reinforced and over-reinforced beam sections, and introduces the concept of the equivalent stress block to simplify calculations. Worked examples are provided to demonstrate how to determine the depth of the neutral axis and moment of resistance for various beam cross sections.
This document discusses the limit state method for designing reinforced concrete beams. It describes key concepts like limit states, stress-strain curves for concrete and steel, and the parameters used to calculate the depth of the neutral axis and moment of resistance. There are three main types of reinforced concrete beams discussed: singly reinforced, doubly reinforced, and singly or doubly reinforced flanged beams. The document focuses on the design and analysis of singly reinforced beams, providing examples of determining the moment of resistance of a given cross-section, as well as designing a beam to resist a specific bending moment.
rectangular and section analysis in bending and shearqueripan
The document discusses the design of reinforced concrete beams for bending and shear. It covers the analysis of singly and doubly reinforced rectangular beam sections. Key points covered include the concept of neutral axis, under-reinforced and over-reinforced sections, design of bending reinforcement, design of shear reinforcement including link spacing, and deflection criteria. Worked examples are provided to demonstrate the design of bending and shear reinforcement for rectangular beams.
The document discusses guidelines for detailing reinforcement in concrete structures. It begins by defining detailing as the preparation of working drawings showing the size and location of reinforcement. Good detailing ensures reinforcement and concrete interact efficiently. The document then discusses sources of tension in concrete structures from various loading conditions like bending, shear, and connections. It provides equations from AS3600-2009 for calculating minimum development lengths for reinforcing bars to develop their yield strength based on bar size, concrete strength, and transverse reinforcement. It also discusses lap splice requirements. In summary, the document provides best practice guidelines for detailing reinforcement to efficiently resist loads and control cracking in concrete structures.
This document provides an overview of the design of rectangular reinforced concrete beams that are singly or doubly reinforced. It defines key assumptions in the design process including plane sections remaining plane after bending. It also covers evaluation of design parameters such as moment factors, strength reduction factors, and balanced reinforcement ratios. The design procedures for singly and doubly reinforced beams are described including checking crack width for singly reinforced beams. Figures are also provided to illustrate concepts such as stress distributions and the components of a doubly reinforced beam.
This document provides an overview of structural steel design and connections. It discusses the benefits of steel structures, common lateral load resisting systems like braced and rigid frames, and types of bracing configurations. It also examines different types of steel frame connections including simple, moment, and eccentric braced connections. Design considerations and capacity equations for moment connections are presented.
The document discusses column buckling and spar buckling in aircraft structures. It provides introductions and reminders on column buckling theory including buckling of columns with various boundary conditions. It discusses buckling of spar webs and the concept of complete diagonal tension in spar webs. Examples are provided on calculating buckling loads of columns and stresses in spars.
This document discusses the load carrying capacity and design of reinforced concrete beams. It provides information on:
1. The loads carried by different types of beams supporting one-way or two-way slabs. Equations are given for calculating equivalent uniform distributed loads.
2. Slab load per unit area calculations for different floor types, including dead loads from self-weight, finishes, and live loads.
3. The process for designing singly reinforced concrete beams using the strength method, including selecting dimensions and reinforcement ratios to satisfy strength and serviceability limits.
4. Details on reinforcement schedules, bar types, hook lengths, and calculating rebar quantities.
Lec 13-14-15-flexural analysis and design of beams-2007-rCivil Zone
This document discusses the load carrying capacity and design of reinforced concrete beams. It provides information on:
1. The loads carried by different types of beams supporting one-way or two-way slabs. Equations are given for calculating equivalent uniform distributed loads.
2. Slab load per unit area calculations for different floor types, including dead loads from self-weight, finishes, and live loads.
3. The process for designing singly reinforced concrete beams using the strength method, including selecting dimensions and reinforcement ratios to satisfy strength and serviceability limits.
4. Details on reinforcement schedules, bar types, hook lengths, and calculating rebar quantities.
Deflections in PT elements pt structure for all pt slabs in civil industry.pdfvijayvijay327286
The document discusses factors that influence deflections in prestressed concrete members and methods for predicting deflections. It covers:
- Short term deflections of unracked members which can be estimated using Mohr's theorem.
- How the tendon profile affects deflections, providing formulas for straight, trapezoidal, parabolic, and other tendon types.
- Downward deflections due to self-weight and imposed loads that can be calculated using formulas provided.
- Estimation of long-term deflections accounting for creep and shrinkage effects, discussing various methods like those of Busemann, McHenry, and Neville.
This document summarizes key concepts related to shear stresses and flexural design in prestressed concrete beams.
It discusses how prestressing increases the shear resistance of concrete sections by providing compression. The design ultimate shear resistance is calculated for both uncracked and cracked sections using equations that consider factors like prestressing steel stress and effective depth.
A three-case design procedure is outlined for providing shear reinforcement if needed. The document also covers flexural design basics like assuming a triangular stress distribution, calculating resistance moment using prestressing steel properties and depth parameters, and working through examples to determine moment capacity.
2-Flexural Analysis and Design of Beams.pdfHammadAmjad14
This document discusses the flexural behavior of reinforced concrete beams under service loads. It provides assumptions and equations used to analyze beams in their elastic range when both concrete and steel are within their proportional limits. The key points are:
1) Plane sections remain plane after bending. Strains in steel and concrete are equal due to bond.
2) Cracks form when tension stresses exceed concrete's tensile strength, but steel reinforcement carries load.
3) Compression stresses are limited to 0.85 times concrete's compressive strength. Strain diagrams and equations for moment capacity are derived.
Deep beams are structural elements where a significant portion of the load is carried to the supports by compression forces combining the load and reaction. As a result, the strain distribution is nonlinear and shear deformations are significant compared to pure flexure. Examples include floor slabs under horizontal loads, short span beams carrying heavy loads, and transfer girders. The behavior of deep beams is two-dimensional rather than one-dimensional, and plane sections may not remain plane. Analysis requires a two-dimensional stress approach.
This is an overview of my current metallic design and engineering knowledge base built up over my professional career and two MSc degrees : - MSc in Advanced Manufacturing Technology University of Portsmouth graduated 1st May 1998, and MSc in Aircraft Engineering Cranfield University graduated 8th June 2007.
Better Builder Magazine brings together premium product manufactures and leading builders to create better differentiated homes and buildings that use less energy, save water and reduce our impact on the environment. The magazine is published four times a year.
An In-Depth Exploration of Natural Language Processing: Evolution, Applicatio...DharmaBanothu
Natural language processing (NLP) has
recently garnered significant interest for the
computational representation and analysis of human
language. Its applications span multiple domains such
as machine translation, email spam detection,
information extraction, summarization, healthcare,
and question answering. This paper first delineates
four phases by examining various levels of NLP and
components of Natural Language Generation,
followed by a review of the history and progression of
NLP. Subsequently, we delve into the current state of
the art by presenting diverse NLP applications,
contemporary trends, and challenges. Finally, we
discuss some available datasets, models, and
evaluation metrics in NLP.
Online train ticket booking system project.pdfKamal Acharya
Rail transport is one of the important modes of transport in India. Now a days we
see that there are railways that are present for the long as well as short distance
travelling which makes the life of the people easier. When compared to other
means of transport, a railway is the cheapest means of transport. The maintenance
of the railway database also plays a major role in the smooth running of this
system. The Online Train Ticket Management System will help in reserving the
tickets of the railways to travel from a particular source to the destination.
Covid Management System Project Report.pdfKamal Acharya
CoVID-19 sprang up in Wuhan China in November 2019 and was declared a pandemic by the in January 2020 World Health Organization (WHO). Like the Spanish flu of 1918 that claimed millions of lives, the COVID-19 has caused the demise of thousands with China, Italy, Spain, USA and India having the highest statistics on infection and mortality rates. Regardless of existing sophisticated technologies and medical science, the spread has continued to surge high. With this COVID-19 Management System, organizations can respond virtually to the COVID-19 pandemic and protect, educate and care for citizens in the community in a quick and effective manner. This comprehensive solution not only helps in containing the virus but also proactively empowers both citizens and care providers to minimize the spread of the virus through targeted strategies and education.
7. 7
Introduction to Beams
• A beam is a horizontal
structural member used
to support loads
• Beams are used to
support the roof and
floors in buildings
8. 8
Beam Theory
• Consider a simply supported beam of length,
L. The cross section is rectangular, with width,
b, and depth, h.
L
b
h
9. 9
Beam Theory
• An area has a centroid, which is similar to a center of gravity of
a solid body.
• The centroid of a symmetric cross section can be easily found
by inspection. X and Y axes intersect at the centroid of a
symmetric cross section, as shown on the rectangular cross
section.
h/2
h/2
b/2 b/2
X - Axis
Y - Axis
10. 10
Beam Theory
• An important variable in beam design is the moment of
inertia of the cross section, denoted by I.
• Inertia is a measure of a body’s ability to resist rotation.
• Moment of inertia is a measure of the stiffness of the beam
with respect to the cross section and the ability of the beam
to resist bending.
• As I increases, bending and deflection will decrease.
• Units are (LENGTH)4, e.g. in4, ft4, cm4
11. 11
Beam Theory
• I can be derived for any common area using calculus.
However, moment of inertia equations for common cross
sections (e.g., rectangular, circular, triangular) are readily
available in math and engineering textbooks.
• For a rectangular cross section,
• b is the dimension parallel to the bending axis. h is the
dimension perpendicular to the bending axis.
12
bh3
x
I
b
h
X-axis (passing
through centroid)
12. Beam Formula
• Shear and moment diagrams
• Simple beam (uniformly distributed load)
– Reaction force formula
– Maximum moment formula
• Simple beam (concentrated load at center)
– Reaction force formula
– Maximum moment formula
13. Beam Formulas
• Similar loading conditions = similar shear and
moment diagrams
• Standard formula can represent the magnitude of
shear and moment based on loading condition
• Magnitude of shear and bending moment
depend on
– Span length of beam
– Magnitude of applied load
– Location of applied load
14. Shear and Moment Diagrams
Simple Beams (Uniformly Distributed Load)
Uniform load = 1000 lb/ft
L = 20 ft
Uniform load = 1200 lb/ft
L = 35 ft
19. Beam Formula
Simple Beam (Uniformly Distributed Load)
L
Beam Diagram
A B
w
(at center)
(at center)
20. Simple Beam
(Concentrate Load at Center)
Find a formula for the end reaction forces and
for the maximum moment for a simply
supported beam with a single concentrated
load, P, applied at center span.
P
L
35. Distance of center of gravity of compression force
from top fiber,
k . x u = b A . 3 x u . 1 + B ( 3 x u + 3 . 4 x u )
C 7 2 7 8 7
= 0.416 x u ie k = 0.416
0.36fck. x u b = 0.87 . f y . As from which,
ku = x u / d = 2 .417 fy (p) where p = As / bd
fck
Ultimate Moment
Mu = C (d - k x u)
Total compression = Total tension
= 0.36 fck . x u.b( d – 0.416 x u)
= Q . bd 2
36. where Q = 0.36 k u fck ( 1 – 0.416 k u)
Solving earlier equation for x u gives ,
___________________
k u = x u / d = 1.2 1 - 1 - 4.62 Mu / fck bd 2
41. The shear force V is resisted by
Vc , from the un-cracked concrete compression zone,
Vd, from the dowel action of longitudinal reinforcement.
Va, from vertical component of the force due to aggregate interlock or interface
shear transfer.
V = Vc + Vd + Va
42. d
s
d
d – d’
d’ = cover + / 2
Shear resisted by stirrups
Vu = stress (area of stirrup)(number of stirrups in
length ‘d’) = 0.87fy x Av x d / s
SHEAR CONCEPTS
Compression diagonal Compression chord
Tension diagonal Tension chord
43. 10 mm dia
stirrups
5 Nos 22 mm
dia bars
1 No 20 mm
dia bent bar
SHEAR CONCEPTS
Shear resisted bent up bars
0.87 fy As Sin 45
44. Location of Maximum Shear for Beam
Design
Compression fan carries load
directly to support
d
45. CLASSIFICATION OF LIMIT STATES
1 COLLAPSE
Compression
Tension
Shear
Bending
Torsion
2 STABILITY
Sliding
Overturning
Buckling
Sinking
3 SERVICEABILITY
Deflection
Cracking
Vibration
4 DURABILITY
Fire damage
Environmental
attack
50. FLANGE WIDTH FOR T BEAMS
x1 x1 x2 x2
bf bf
bw bw
(a) For T beams
bf = lo/6 +bw + 6 Df and bf = bw + x1 + x2 ; whichever
is less
(b) For isolated T beams
bf = 0.5 lo / (lo/b +4) + bw and bf = b; whichever is less
bf = effective width of flange bw = breadth of web
b = actual width of flange
lo = distance between points of zero moment in a beam ;
(for continuous beams lo = 0.7 Le)
Df = thickness of slab / flange
x1 , x2 are half of clear distance between adjacent beams
51. Ld
T = 0.87 fy .As
R = fb . Ld .
= 0.87 fy 2
4
T
fb . Ld . = 0.87 fy 2
4
Ld = 0.87 fy / 4 fb
BAR ANCHORAGE
R = T
52. BAR ANCHOR LENGTH
fy
N / mm2
Anchor length for conc. grade of :
M20 M25 M30
250 45.3 38.8 36.3
415 47.0 40.3 37.6
500 56.6 48.6 45.3
fy
N/mm2
Anchor length for conc. grade of :
M20 M25 M30
250 45 40 40
415 50 40 40
500 57 50 45
53. Slope
1 in 6
Cover
Outer face
of concrete
Lap
length
LAPPING OF REBARS
54. PRESTRESSED CONCRETE
• WHAT IS WEAKNESS OF RCC?
– IN CONCRETE, COMPRESSIVE STRENGTH IS HIGH
– IN TENSION ZONE CONCRETE CRACKS AND IS
INEFFECTIVE
• CAN WE DO SOMETHING?
– DON’T ALLOW TENSION
You may have noticed that some patterns emerged in the shear and bending moment diagrams during the last Activity (3.2.3). In fact, two beams that are loaded in a similar way will have shear and bending moment diagrams that exhibit the same shape, even though the beam span length and load magnitude are different.
For instance, both of these beams are simply supported and loaded with a uniformly distributed load along the entire span of the beam. The left beam is 20 feet long and is loaded with a 1000 lb/ft uniform load. The right beam carries a 1200 lb/ft load and is 35 feet long.
Notice that the shape of the shear diagrams are the same for the two beams. The shape of the bending moment diagrams are also the same for the two beams. In fact, every simply supported beam with a uniformly distributed load will exhibit the same shape of shear and moment diagrams.
Although the diagram shapes are the same, the magnitude of the shear and bending moments differ. This is because the beam spans and the magnitude of the applied loads are different.
Remember from your earlier beam analysis that you used the equations of equilibrium to calculate the end reaction forces. The calculations always followed the same procedure for every beam. The only difference in calculations for two similarly loaded beams is the magnitude of the load and the span length of the beam. We can find a formula to represent the magnitude of the reaction forces that is true for every simply supported beam with a uniform load. The formula will use variables to represent the span length and the magnitude of the applied load since these will change from beam to beam.
Because the shear and bending moment diagrams are dependent on the reaction forces and the length of the beam, we can also derive a formula to provide the maximum bending moment experienced by a beam. Again, the span length and magnitude of the applied load will be variable. If all simply supported beams that carry a uniform load exhibit similar shear and bending moment diagrams, it stands to reason that we should be able to find mathematical formulas to represent the shear and moment magnitudes. The beam span length and the magnitude of the load will be variables because they will change.
Find the beam formulas for a simply supported beam with a uniform load across the entire span.
First, we will find formulas for the end reactions. One or both of the end reactions will typically be equal to the maximum shear.
Then we can use the algebraic representations for the end reactions to find the formula for the maximum moment.
Find formulas for the end reactions of a uniformly distributed load on a simple beam. Remember, we can neglect the horizontal reaction force at the pinned connection (A) since there are no horizontally applied loads.
Use the equations of equilibrium. First sum the moments about a point. One of the end points will be most efficient, but it doesn’t matter which point. Let’s choose point A.
The reaction force at point A for a simple supported beam with a uniform load will always be wL/2.
Next sum the vertical forces.
Both RA and RB are equal to wL/2.
In fact, whenever the beam loading is symmetrical, the end reaction forces will be equal.
NOTE: Click the mouse to display the shaded area and Mmax = shaded area. Then click again to show each line of the derivation.
Because RA is wL/2, the magnitude of the shear at point A will be wL/2 as well. The shear will decrease at a rate equal to the magnitude of the applied uniform load (w) resulting in the shear diagram shown. The point of zero shear is at mid-span. In fact, the point of zero shear will be at mid span for all symmetrically loaded beams.
To find the maximum moment, (click the mouse) find the area of the shear diagram to the left of the point of zero shear (mid-span) which is shaded in the diagram.
The area of a triangle is A = .5 b h (Click the mouse).
Therefore, the maximum moment for every simple beam loaded with a uniform load is wL^2/8 (Click the mouse).
The resulting formulas are often presented in tables with a beam diagram showing the loading condition.
A similar but more complicated derivation can be performed for the deflection of a beam. The deflection formula for a simple beam with a uniformly distributed load along the entire beam is also shown. We will look at deflection more closely later in the lesson.
Use the equations of equilibrium to find the end reactions for the beam.
NOTE: Let students attempt to find the formula for the end reactions before clicking the mouse to display the derivation.
Summation of moments results in RA = P/2
Summation of vertical forces results in RB = P/2
Note: Let students attempt to find the Mmax before clicking the mouse to display the derivation.
The shear diagram will show the magnitude of RA at the left (P/2) which will remain unchanged until mid-span where the concentrated load is applied. The concentrated load causes a vertical drop of P at mid span. Therefore, the right half of the beam must carry a shear of –P/2.
The moment diagram will display two linear segments with slopes equal to the shear values.
The maximum moment can be calculated by finding the area under the shear diagram to the left of the point of zero shear (which is shaded).
雅虎竞拍
煤炉代买
paypay商城
乐天二手
日本亚马逊
乐天新品
ZOZOTOWN
