This document discusses reinforced concrete columns. Columns act as vertical supports that transmit loads to foundations. Columns may fail due to compression failure, buckling, or a combination. Short columns are more prone to compression failure, while slender columns are more likely to buckle. Column sections can be square, circular, or rectangular. The dimensions and bracing affect whether a column is classified as short or slender. Longitudinal reinforcement and links are designed to resist axial loads and moments based on the column's effective height and end conditions. Design charts are used to determine reinforcement for columns with axial and uniaxial bending loads. Examples show how to design column reinforcement.
The document discusses the moment distribution method for analyzing statically indeterminate structures. It begins by outlining the basic principles and definitions of the method, including stiffness factors, carry-over factors, and distribution factors. It then provides an example problem, showing the calculation of fixed end moments, establishment of the distribution table through successive approximations, and determination of shear forces and bending moments. Finally, it discusses extensions of the method to structures with non-prismatic members, including using tables to determine necessary values for analysis.
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.
This document contains information about analyzing portal frames with side sway using the slope deflection method. It provides examples of solving for fixed end moments, developing slope deflection equations, using equilibrium equations, and determining final bending moments. The examples analyze portal frames and continuous beams with various support conditions and loading. Diagrams of the bending moment for each example are included.
The document provides information on column design according to BS 8110-1:1997, including general recommendations, classifications of columns, effective length and minimum eccentricity, design moments, and design. Short columns have a length to height or breadth ratio less than 15 for braced or 10 for unbraced. Braced columns have lateral stability from walls or bracing. Additional moments are considered for slender or unbraced columns based on deflection. Design moments are calculated considering axial load and biaxial bending for different column classifications. Shear design also considers axial load and reinforcement is required if shear exceeds the shear capacity. The interaction diagram is constructed based on equilibrium equations relating stresses on a column cross section to axial load and bending
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.
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.
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 discusses reinforced concrete columns. It begins by defining columns and different column types, including based on shape, reinforcement, loading conditions, and slenderness ratio. Short columns fail due to material strength while slender columns are at risk of buckling. The document covers column design considerations like unsupported length and effective length. It provides examples of single storey building column design and discusses minimum longitudinal reinforcement requirements in columns.
The document discusses the moment distribution method for analyzing statically indeterminate structures. It begins by outlining the basic principles and definitions of the method, including stiffness factors, carry-over factors, and distribution factors. It then provides an example problem, showing the calculation of fixed end moments, establishment of the distribution table through successive approximations, and determination of shear forces and bending moments. Finally, it discusses extensions of the method to structures with non-prismatic members, including using tables to determine necessary values for analysis.
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.
This document contains information about analyzing portal frames with side sway using the slope deflection method. It provides examples of solving for fixed end moments, developing slope deflection equations, using equilibrium equations, and determining final bending moments. The examples analyze portal frames and continuous beams with various support conditions and loading. Diagrams of the bending moment for each example are included.
The document provides information on column design according to BS 8110-1:1997, including general recommendations, classifications of columns, effective length and minimum eccentricity, design moments, and design. Short columns have a length to height or breadth ratio less than 15 for braced or 10 for unbraced. Braced columns have lateral stability from walls or bracing. Additional moments are considered for slender or unbraced columns based on deflection. Design moments are calculated considering axial load and biaxial bending for different column classifications. Shear design also considers axial load and reinforcement is required if shear exceeds the shear capacity. The interaction diagram is constructed based on equilibrium equations relating stresses on a column cross section to axial load and bending
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.
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.
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 discusses reinforced concrete columns. It begins by defining columns and different column types, including based on shape, reinforcement, loading conditions, and slenderness ratio. Short columns fail due to material strength while slender columns are at risk of buckling. The document covers column design considerations like unsupported length and effective length. It provides examples of single storey building column design and discusses minimum longitudinal reinforcement requirements in columns.
The document discusses reinforced concrete columns, including their functions, failure modes, classifications, and design considerations. Columns primarily resist axial compression but may also experience bending moments. They can fail due to compression, buckling, or a combination. Design depends on whether the column is short or slender, braced or unbraced. Reinforcement is designed based on the column's expected loads and dimensions using methods specified in design codes like BS 8110.
The document provides step-by-step instructions for modeling, analyzing, and designing a 10-story reinforced concrete building using ETABS. It defines the material properties, section properties, load cases, and equivalent lateral force parameters. The steps include starting a new model, defining section properties for beams, columns, slabs, and walls, assigning the sections, defining load cases, and specifying the analysis and design procedures.
This document discusses T-beams, which are more suitable than rectangular beams in reinforced concrete. There are two types of T-beams: monolithic and isolated. It provides notations and code recommendations for T-beams from IS: 456. There are three cases for finding the depth of the neutral axis in a T-beam: when it lies in the flange, in the rib, or at the junction. An example problem is worked through to find the moment of resistance for a given T-beam section using the provided concrete and steel properties.
The document discusses the design of slender columns. It defines a slender column as having a slenderness ratio (length to least lateral dimension) greater than 12. Slender columns experience appreciable lateral deflection even under axial loads alone. The design of slender columns can be done using three methods - the strength reduction coefficient method, additional moment method, or moment magnification method. The document outlines the step-by-step procedure for designing a slender column using the additional moment method, which involves determining the effective length, initial moments, additional moments, total moments accounting for a reduction coefficient, and redesigning the column for combined axial load and bending.
The document discusses various types of footings used in building foundations. It defines a footing as the lower part of a foundation constructed below ground level on solid ground. The main purposes of footings are to transfer structural loads to the soil over a large area to prevent soil and building movement, and to resist settlement and lateral loads. Common footing types include isolated, strap, strip/continuous, and combined footings. Key data needed for footing design includes soil bearing capacity, structural loads, and column dimensions. The document outlines general design procedures and considerations for spread, combined, strap, and brick footings.
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 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)
Finite Element analysis -Plate ,shell skew plate S.DHARANI KUMAR
This document provides an overview of plate and shell theory and finite element analysis for plates and shells. It discusses the assumptions and applications of thin plate theory, thick plate theory, and shell theory. It also describes different types of finite elements that can be used to model plates and shells, including plate, shell, solid shell, curved shell, and degenerated shell elements. Additionally, it covers skew plates and different discretization methods that can be used for finite element analysis of skew plates.
This document provides a summary of reinforced concrete columns (RCC columns). It defines a column and describes different types of columns based on reinforcement and length. Short columns are less than 12 times the minimum thickness, while long columns are greater than 12 times the thickness. The document outlines preliminary sizing of columns and the functions of tie/spiral reinforcement. It includes design equations for axially loaded columns in working stress design (WSD) and ultimate stress design (USD). Two sample problems are worked through demonstrating column design using both methods.
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.
OUTLINE:
Introduction
Shoring Process
Effective Beam Flange Width
Shear Transfer
Strength Of Steel Anchors
Partially Composite Beams
Moment Capacity Of Composite Sections
Deflection
Design Of Composite Sections
ETABS is structural analysis software used to analyze and design buildings. It was developed in 1975 by students and later released commercially in 1985 by Computers and Structures Inc. The Burj Khalifa in Dubai was one of the first major projects analyzed using ETABS.
To model a structure in ETABS, materials like concrete and steel must first be defined along with their properties. Frame sections for beams, columns, walls and slabs are then created. The grid is drawn representing the building plan. Beams, columns, walls and slabs can then be drawn by connecting nodes on the grid. Modeling tools allow modifying the structural model by merging joints, aligning elements, and editing frames.
The document discusses the direct analysis method for load and resistance factor design (LRFD) using SAP2000 v20 software. It outlines the general analysis requirements including using second-order analysis, applying notional loads, and reducing member stiffnesses. It provides steps to define loads and combinations in SAP2000 for the design stage. The document notes that using the Tau-b fixed stiffness reduction method may result in incorrect values and recommends either increasing the notional load ratio or changing to the Tau-b variable method to get the correct values.
The document discusses the use of computer programs like STAAD Pro for structural design and analysis. It explains how earlier structural designs were done manually using slide rules and calculators but computers now allow for more accurate analysis of frames, beams and modeling of entire buildings in 3D. STAAD Pro is highlighted as a powerful program that can be used for 3D modeling and analysis of multi-storied buildings, offering various analysis types and design capabilities for steel, concrete and other materials according to different codes.
The document discusses reinforced concrete columns, including their functions, failure modes, classifications, and design considerations. Columns primarily resist axial compression but may also experience bending moments. They can fail due to compression, buckling, or a combination. Design depends on whether the column is short or slender, braced or unbraced. Reinforcement is determined based on the loads applied, including axial load only, symmetrical beam loading, or loading in one or two bending directions. Links are included to prevent bar buckling. Examples show how to design column longitudinal reinforcement and links for different load cases.
Structural Mechanics: Shear stress in Beams (1st-Year)Alessandro Palmeri
- The document discusses shear stress in beams, specifically focusing on Jourawski's formula for calculating shear stress.
- Jourawski's formula provides an approximate solution for the shear stress distribution over a beam cross-section using simple equilibrium considerations.
- The formula can be applied to solid rectangular sections, giving a parabolic shear stress distribution, but provides inaccurate results for T-section and I-section flanges.
- For T-sections and I-sections, the formula can be applied to the web, where it accurately models the shear stress as parabolic. The maximum shear stress occurs at the neutral axis.
Trusses Analysis Of Statically DeterminateAmr Hamed
The document discusses the analysis of statically determinate trusses. It describes the characteristics of determinate trusses, including their slender members, pinned/bolted/welded joints, and loads acting at joints with members in tension or compression. It also discusses terminology and selection criteria for different types of trusses used in roofs and bridges. The document outlines the assumptions and methods for analyzing trusses, including the method of joints and method of sections.
This document provides information on the design of reinforced concrete columns, including:
- Columns transmit loads vertically to foundations and may resist both compression and bending. Common cross-sections are square, circular and rectangular.
- Columns are classified as braced or unbraced depending on lateral stability, and short or slender based on buckling resistance. Short column design considers axial load capacity while slender column design accounts for second-order effects.
- Reinforcement details include minimum longitudinal bar size and spacing and design of lateral ties. Slender column design determines loadings and calculates moments from stiffness, deflection and biaxial bending effects. Design charts are used to select reinforcement for columns under axial and uniaxial
The document discusses bar bending schedules (BBS), which provide essential information for bending and placing reinforcement bars during construction. A BBS includes the location, type, size, length, number, and bending details of each bar. It allows bars to be pre-bent in a factory and transported to the construction site, reducing time. A BBS also improves quality control and provides better estimates of steel requirements.
The document discusses reinforced concrete columns, including their functions, failure modes, classifications, and design considerations. Columns primarily resist axial compression but may also experience bending moments. They can fail due to compression, buckling, or a combination. Design depends on whether the column is short or slender, braced or unbraced. Reinforcement is designed based on the column's expected loads and dimensions using methods specified in design codes like BS 8110.
The document provides step-by-step instructions for modeling, analyzing, and designing a 10-story reinforced concrete building using ETABS. It defines the material properties, section properties, load cases, and equivalent lateral force parameters. The steps include starting a new model, defining section properties for beams, columns, slabs, and walls, assigning the sections, defining load cases, and specifying the analysis and design procedures.
This document discusses T-beams, which are more suitable than rectangular beams in reinforced concrete. There are two types of T-beams: monolithic and isolated. It provides notations and code recommendations for T-beams from IS: 456. There are three cases for finding the depth of the neutral axis in a T-beam: when it lies in the flange, in the rib, or at the junction. An example problem is worked through to find the moment of resistance for a given T-beam section using the provided concrete and steel properties.
The document discusses the design of slender columns. It defines a slender column as having a slenderness ratio (length to least lateral dimension) greater than 12. Slender columns experience appreciable lateral deflection even under axial loads alone. The design of slender columns can be done using three methods - the strength reduction coefficient method, additional moment method, or moment magnification method. The document outlines the step-by-step procedure for designing a slender column using the additional moment method, which involves determining the effective length, initial moments, additional moments, total moments accounting for a reduction coefficient, and redesigning the column for combined axial load and bending.
The document discusses various types of footings used in building foundations. It defines a footing as the lower part of a foundation constructed below ground level on solid ground. The main purposes of footings are to transfer structural loads to the soil over a large area to prevent soil and building movement, and to resist settlement and lateral loads. Common footing types include isolated, strap, strip/continuous, and combined footings. Key data needed for footing design includes soil bearing capacity, structural loads, and column dimensions. The document outlines general design procedures and considerations for spread, combined, strap, and brick footings.
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 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)
Finite Element analysis -Plate ,shell skew plate S.DHARANI KUMAR
This document provides an overview of plate and shell theory and finite element analysis for plates and shells. It discusses the assumptions and applications of thin plate theory, thick plate theory, and shell theory. It also describes different types of finite elements that can be used to model plates and shells, including plate, shell, solid shell, curved shell, and degenerated shell elements. Additionally, it covers skew plates and different discretization methods that can be used for finite element analysis of skew plates.
This document provides a summary of reinforced concrete columns (RCC columns). It defines a column and describes different types of columns based on reinforcement and length. Short columns are less than 12 times the minimum thickness, while long columns are greater than 12 times the thickness. The document outlines preliminary sizing of columns and the functions of tie/spiral reinforcement. It includes design equations for axially loaded columns in working stress design (WSD) and ultimate stress design (USD). Two sample problems are worked through demonstrating column design using both methods.
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.
OUTLINE:
Introduction
Shoring Process
Effective Beam Flange Width
Shear Transfer
Strength Of Steel Anchors
Partially Composite Beams
Moment Capacity Of Composite Sections
Deflection
Design Of Composite Sections
ETABS is structural analysis software used to analyze and design buildings. It was developed in 1975 by students and later released commercially in 1985 by Computers and Structures Inc. The Burj Khalifa in Dubai was one of the first major projects analyzed using ETABS.
To model a structure in ETABS, materials like concrete and steel must first be defined along with their properties. Frame sections for beams, columns, walls and slabs are then created. The grid is drawn representing the building plan. Beams, columns, walls and slabs can then be drawn by connecting nodes on the grid. Modeling tools allow modifying the structural model by merging joints, aligning elements, and editing frames.
The document discusses the direct analysis method for load and resistance factor design (LRFD) using SAP2000 v20 software. It outlines the general analysis requirements including using second-order analysis, applying notional loads, and reducing member stiffnesses. It provides steps to define loads and combinations in SAP2000 for the design stage. The document notes that using the Tau-b fixed stiffness reduction method may result in incorrect values and recommends either increasing the notional load ratio or changing to the Tau-b variable method to get the correct values.
The document discusses the use of computer programs like STAAD Pro for structural design and analysis. It explains how earlier structural designs were done manually using slide rules and calculators but computers now allow for more accurate analysis of frames, beams and modeling of entire buildings in 3D. STAAD Pro is highlighted as a powerful program that can be used for 3D modeling and analysis of multi-storied buildings, offering various analysis types and design capabilities for steel, concrete and other materials according to different codes.
The document discusses reinforced concrete columns, including their functions, failure modes, classifications, and design considerations. Columns primarily resist axial compression but may also experience bending moments. They can fail due to compression, buckling, or a combination. Design depends on whether the column is short or slender, braced or unbraced. Reinforcement is determined based on the loads applied, including axial load only, symmetrical beam loading, or loading in one or two bending directions. Links are included to prevent bar buckling. Examples show how to design column longitudinal reinforcement and links for different load cases.
Structural Mechanics: Shear stress in Beams (1st-Year)Alessandro Palmeri
- The document discusses shear stress in beams, specifically focusing on Jourawski's formula for calculating shear stress.
- Jourawski's formula provides an approximate solution for the shear stress distribution over a beam cross-section using simple equilibrium considerations.
- The formula can be applied to solid rectangular sections, giving a parabolic shear stress distribution, but provides inaccurate results for T-section and I-section flanges.
- For T-sections and I-sections, the formula can be applied to the web, where it accurately models the shear stress as parabolic. The maximum shear stress occurs at the neutral axis.
Trusses Analysis Of Statically DeterminateAmr Hamed
The document discusses the analysis of statically determinate trusses. It describes the characteristics of determinate trusses, including their slender members, pinned/bolted/welded joints, and loads acting at joints with members in tension or compression. It also discusses terminology and selection criteria for different types of trusses used in roofs and bridges. The document outlines the assumptions and methods for analyzing trusses, including the method of joints and method of sections.
This document provides information on the design of reinforced concrete columns, including:
- Columns transmit loads vertically to foundations and may resist both compression and bending. Common cross-sections are square, circular and rectangular.
- Columns are classified as braced or unbraced depending on lateral stability, and short or slender based on buckling resistance. Short column design considers axial load capacity while slender column design accounts for second-order effects.
- Reinforcement details include minimum longitudinal bar size and spacing and design of lateral ties. Slender column design determines loadings and calculates moments from stiffness, deflection and biaxial bending effects. Design charts are used to select reinforcement for columns under axial and uniaxial
The document discusses bar bending schedules (BBS), which provide essential information for bending and placing reinforcement bars during construction. A BBS includes the location, type, size, length, number, and bending details of each bar. It allows bars to be pre-bent in a factory and transported to the construction site, reducing time. A BBS also improves quality control and provides better estimates of steel requirements.
The document discusses various types of compression members including columns, pedestals, walls, and struts. It describes design considerations for compression members including strength and buckling resistance. It defines effective length as the vertical distance between points of inflection when the member buckles. Various classifications of columns are discussed based on loadings, slenderness ratio, and reinforcement type. Code requirements for longitudinal and transverse reinforcement as well as detailing are provided. Two examples of column design are included, one with axial load only and one with spiral reinforcement.
This document defines key terms related to compression members, classifies columns based on reinforcement type, loadings, and slenderness ratio, and outlines design assumptions. It defines effective length, pedestal, column, and wall. It classifies columns as tied, helically reinforced, or composite. Columns are classified by loadings as subjected to axial load only, axial with uniaxial bending, or axial with bi-axial bending. Columns are classified as short or slender based on slenderness ratios. Design assumes minimum eccentricity and considers different failure modes.
This document summarizes how beams and columns in reinforced concrete (RC) buildings resist earthquakes. It discusses the reinforcement and design strategies for beams and columns.
For beams, it describes the longitudinal bars and stirrups that provide flexural strength and resist shear cracks. The design focuses on placement of steel to resist stretching on both faces. Columns use longitudinal bars and transverse ties to resist axial and shear stresses. The design aims to prevent shear failure through close spacing of ties. Reinforcement details like hook ends and lap lengths are specified to improve ductility.
This document discusses ductile detailing of reinforced concrete (RC) frames according to Indian standards. It explains that detailing involves translating the structural design into the final structure through reinforcement drawings. Good detailing ensures reinforcement and concrete interact efficiently. Key aspects of ductile detailing covered include requirements for beams, columns, and beam-column joints to improve ductility and seismic performance. Specific provisions are presented for longitudinal and shear reinforcement in beams and columns, as well as confining reinforcement and lap splices. The importance of cover and stirrup spacing is also discussed.
This document contains lecture notes on the design of concrete columns. It defines key terms like effective length, pedestal, column, and discusses the classification of columns based on type of reinforcement, loadings, and slenderness ratio. It describes the functions of bracing in columns and design requirements for longitudinal and transverse reinforcement. The document states assumptions in limit state design of columns and the need to consider minimum eccentricity in design. It concludes with sample exercises related to column design.
Ch8 Truss Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...Hossam Shafiq II
This chapter discusses truss bridges. It begins by defining a truss as a triangulated assembly of straight members that can be used to replace girders. The main advantages of truss bridges are that primary member forces are axial loads and the open web system allows for greater depth.
The chapter then describes the typical components of a through truss bridge and the most common truss forms including Pratt, Warren, curved chord, subdivided, and K-trusses. Design considerations like truss depth, economic spans, cross section shapes, and wind bracing are covered. The chapter concludes with sections on determining member forces, design principles, and specific design procedures.
This document provides an overview of the design of compression members (columns) in reinforced concrete structures. It discusses various types of columns based on reinforcement, loading conditions, and slenderness ratio. It describes the classification of columns as short or slender. The document also covers effective length, braced vs unbraced columns, codal provisions for reinforcement, and functions of longitudinal and transverse reinforcement. Key points include types of column reinforcement, minimum reinforcement requirements, cover requirements, and assumptions for the limit state of collapse under compression.
The document summarizes the design procedures for slab systems according to the ACI 318 Code, including:
1) The direct design method and equivalent frame method for determining moments at critical sections.
2) Distributing the total design moment between positive and negative moments.
3) Distributing moments laterally between column strips, middle strips, and beams.
4) A 5-step basic design procedure involving determining moments, distributing moments, sizing reinforcement, and designing beams if present.
This document provides an overview of member behavior for beams and columns in seismic design. It discusses the types of moment resisting frames and the principles for designing special moment resisting frames, including strong-column/weak-beam design, avoiding shear failure, and providing ductile details. Beam and column design considerations are covered, such as dimensions, reinforcement, and shear capacity. Beam-column joint design is also summarized, including dimensions, shear determination, and strength.
This document provides an overview of column design and analysis. It defines columns and discusses their common uses in structures like buildings and bridges. Short columns fail through crushing, while long columns fail through buckling. Euler developed the first equation to analyze buckling in columns. The document discusses factors that influence a column's buckling capacity, like its effective length which depends on end support conditions. It presents design equations and factors for different column types (short, long, intermediate) and materials (steel). Safety factors are larger for columns than other members due to their importance for structural stability.
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 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.
- Beam-column joints are the weakest points in reinforced concrete frames during earthquakes due to stresses that cause cracking and failure. There are two main types of failure: shear and anchorage.
- Proper design of beam-column joints including use of closed loop ties, intermediate bars, wider columns, and straight beam bars inserted into the column improves earthquake resistance by resisting distortion and improving concrete confinement.
- Innovative techniques for strengthening joints include fiber reinforced concrete and FRP wrapping to prevent cracking and increase strength. Well designed joints are crucial to avoiding damage during seismic activity.
Ch4 Bridge Floors (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...Hossam Shafiq II
This chapter discusses bridge floors for roadway and railway bridges. It describes three main types of structural systems for roadway bridge floors: slab, beam-slab, and orthotropic plate. For railway bridges, the two main types are open timber floors and ballasted floors. The chapter then covers design considerations for allowable stresses, stringer and cross girder cross sections, and provides an example design for the floor of a roadway bridge with I-beam stringers and cross girders.
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.
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.
Cricket management system ptoject report.pdfKamal Acharya
The aim of this project is to provide the complete information of the National and
International statistics. The information is available country wise and player wise. By
entering the data of eachmatch, we can get all type of reports instantly, which will be
useful to call back history of each player. Also the team performance in each match can
be obtained. We can get a report on number of matches, wins and lost.
Particle Swarm Optimization–Long Short-Term Memory based Channel Estimation w...IJCNCJournal
Paper Title
Particle Swarm Optimization–Long Short-Term Memory based Channel Estimation with Hybrid Beam Forming Power Transfer in WSN-IoT Applications
Authors
Reginald Jude Sixtus J and Tamilarasi Muthu, Puducherry Technological University, India
Abstract
Non-Orthogonal Multiple Access (NOMA) helps to overcome various difficulties in future technology wireless communications. NOMA, when utilized with millimeter wave multiple-input multiple-output (MIMO) systems, channel estimation becomes extremely difficult. For reaping the benefits of the NOMA and mm-Wave combination, effective channel estimation is required. In this paper, we propose an enhanced particle swarm optimization based long short-term memory estimator network (PSOLSTMEstNet), which is a neural network model that can be employed to forecast the bandwidth required in the mm-Wave MIMO network. The prime advantage of the LSTM is that it has the capability of dynamically adapting to the functioning pattern of fluctuating channel state. The LSTM stage with adaptive coding and modulation enhances the BER.PSO algorithm is employed to optimize input weights of LSTM network. The modified algorithm splits the power by channel condition of every single user. Participants will be first sorted into distinct groups depending upon respective channel conditions, using a hybrid beamforming approach. The network characteristics are fine-estimated using PSO-LSTMEstNet after a rough approximation of channels parameters derived from the received data.
Keywords
Signal to Noise Ratio (SNR), Bit Error Rate (BER), mm-Wave, MIMO, NOMA, deep learning, optimization.
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2. Introduction to column
• Columns act as vertical supports to beams and
slabs, and to transmit the loads to the
foundations.
• Columns are primarily compression members,
although they may also have to resist bending
moment transmitted by beams.
• Columns may be classified as short or slender,
braced or unbraced depending on various
dimensional and structural factors.
3. Column sections
• Common column cross sections are: (a)
square, (b) circular and (c) rectangular section.
• The greatest dimension should not exceed
four times its smaller dimension. (h≤4b).
• For h>4b, the member should be regarded as
a wall for design purpose.
4. Failure modes of columns
• Columns may fail in one of three mechanisms:
1. Compression failure of the concrete or steel
reinforcement;
2. Buckling
3. Combination of buckling and compression
failure.
• Compression failure is likely to occur with
columns which are short and stocky.
• Buckling is probable with columns which are long
and slender.
6. Short and slender columns
(Clause
3.8.1.3, BS 8110)
• A braced column is classified as being short if :
7. Braced and unbraced columns
(clause
3.8.1.5, BS 8110)
• A column may be considered braced in a given
plane if lateral stability to the structure as a
whole is provided by wall or bracing or
buttressing designed to resist all lateral forces
in that plane. It should otherwise be
considered as unbraced.
10. Effective height of column (clause
3.8.1.6, BS 8110)
• The effective height, le of a column in a given
plane may be obtained from the following
equation:
Where is a coefficient depending on the fixity
at the column ends and lo is the height of the
columns.
• Effective height for a column in two plane
directions may be different.
11. Effective height of column
(clause
3.8.1.6, BS 8110)
• for braced column can be obtained from
Table 3.19.
• End condition 1 signifies that the column end is fully
restrained.
• End condition 2 signifies that the column end is partially
restrained .
• End condition 3 signifies that the column is nominally
restrained.
12. End conditions (clause 3.8.1.6.2, BS 8110)
• End condition 1 – the end of the column is
connected monolithically to beams on either side
which are at least as deep as the overall dimension
of the column in the plane considered. Where the
column is connected to foundation, it should be
designed to carry moment.
13. • End condition 2 – the end of column is connected
monolithically to beams or slabs on either side which
are shallower than the overall dimension of the
column in the plane considered.
End conditions (clause 3.8.1.6.2, BS 8110)
14. • End condition 3 – the end of the column is
connected to members which, while not specifically
designed to provide restraint to rotation of the
column will nevertheless, provide some nominal
restraint.
End conditions (clause 3.8.1.6.2, BS 8110)
17. Short column design
• The short column are divided into three
categories:
1. Columns resisting axial load only,
2. Columns supporting an approximately
symmetrical arrangement of beams,
3. Columns resisting axial loads and uniaxial or
biaxial bending
18. • B2 will resist an axial load only, as it supports beams
equal in length and symmetrically arranged.
19. • C2 supports a symmetrical arrangement of beams
but which are unequal in length. If (a) the loadings
on the beam are uniformly distributed, (2)the beam
spans do not differ by more than 15 percent, the
column C2 belongs to category 2.
• If the column does not meet criteria (a) and (b), then
the column belongs to category 3.
20. Theoretical strength of reinforced concrete
column
The equation is derived on the assumption that the axial load is
applied perfectly at the centre of the column.
21. Clause 3.8.4.3 Nominal eccentricity of short columns
resisting moments and axial force
• Toallow for nominal eccentricity, BS 8110
reduce the theoretical axial load capacity by
about 10%.
• Design maximum axial load capacity of short
column is:
22. Clause 3.8.4.4 Short braced columns supporting an
approximately symmetrical arrangement of beam
• The column is subjected to axial and small
moment when it supports approximately
symmetrical arrangement of beams:
•
• The design axial load capacity:
23. Column resisting an axial load and
uniaxial bending
• For column resisting axial load and bending moment
at one direction, the area of longitudinal
reinforcement is calculated using design charts in
Part 3 BS 8110.
• The design charts are available for columns having a
rectangular cross section and symmetrical
arrangement of reinforcement.
24. Column resisting an axial load and
uniaxial bending
• Design charts are derived based on yield stress of
460 N/mm2 for reinforcement steel. They are
applicable for reinforcement with yield stress of
500 N/mm2, but the area of reinforcement
obtained will be approximately 10% greater than
required.
• Design charts are available for concrete grades –
25, 30, 35, 40, 45 and 50.
• The d/h ratios are in the range of 0.75 to 0.95 in
0.05 increment.
25. Design chart for column resisting an axial load and
uniaxial bending moment, (Part 3, BS 8110)
26. Column resisting an axial load and
biaxial bending
• The columns are subjected to an
axial and bending moment in both x
and y directions.
• The columns with biaxial moments
are simplified into the columns with
uniaxial momentby increasing the
moment about one of the axes then
design the reinforcement according
the increased moment.
27. Column resisting an axial load and biaxial
bending (clause 3.8.4.5, BS 8110)
28. Reinforcement details: longitudinal
reinforcement (clause 3.12.5, BS 8110)
1. Size and minimum number of bars – bar size should not be
less than 12 mm in diameter. Rectangular column should
reinforced with minimum 4 bars; circular column should
reinforced with minimum 6 bars.
2. The area of longitudinal reinforcement should lie in the
limits:
3. Spacing of reinforcement – the minimum distance between
adjacent bars should not be less than the diameter of the
bar or hagg + 5 mm.
29. Reinforcement details – links (clause 3.12.7, BS 8110)
• The axial loading on the column may cause buckling
of the longitudinal reinforcement and subsequent
cracking and spalling of concrete cover.
• Links are passing round the bars to prevent buckling.
30. Reinforcement details – links (clause 3.12.7, BS 8110)
1. Size and spacing of links – the diameter of
the link should be at least one quarter of the
largest longitudinal bar size or minimum 8
mm. The maximum spacing is 12 times of the
smallest longitudinal bar.
2. Arrangement of links
31. Example 3.20 axially loaded column (Arya, 2009)
• Design the longitudinal and links for a 350mm square, short
braced column based on following information.
33. Example 3.21 Column supporting an approximately
symmetrical arrangement of beam ( Arya, 2009)
• An internal column in a braced two-storey building supporting
an approximately symmetrical arrangement of beams
(350mm wide x 600 mm deep) results in characteristic dead
and imposed loads each of 1100 kN being applied to the
column. The column is 350 mm square and has a clear height
of 4.5 m. Design the longitudinal reinforcement and links.
34. Example 3.21 Column supporting an approximately
symmetrical arrangement of beam ( Arya, 2009)
35. Example 3.21 Column supporting an approximately
symmetrical arrangement of beam ( Arya, 2009)
36. Example 3.21 Column supporting an approximately
symmetrical arrangement of beam ( Arya, 2009)
• Links
• link = diameter of largest longitudinal bar/4
• = 32/4 = 8 mm (equal to minimum bar size
of 8 mm)
• The spacing of the links
• = the lesser of (12 smallest longitudinal bar or
the smallest cross sectional dimension of
column)
• = the lesser of (12x25 = 300 mm or 350 mm)
• = 300 mm
37. Example 3.22 Columns resisting an
axial load and bending moment
• Design the longitudinal and shear reinforcement for
a 275 mm square, short braced column which
supports either
(a) An ultimate axial load of 1280 kN and a moment of
62.5 kNm about the x-x axis
(b) An ultimate axial load of 1280 kN and bending
moment of 35 kNm about the x-x axis and 25 kNm
about the y-y axis
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