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.
This document discusses structural analysis methods for statically indeterminate structures. It defines key terms like degree of static indeterminacy, internal and external redundancy, and methods for analyzing indeterminate structures. Specific methods discussed include the flexibility matrix method, consistent deformation method, and unit load method. Examples of statically indeterminate beams and frames are also provided.
This document discusses shear wall analysis and design. It defines shear walls as structural elements used in buildings to resist lateral forces through cantilever action. The document classifies different types of shear walls and discusses their behavior under seismic loading. It outlines the steps for designing shear walls, including reviewing layout, analyzing structural systems, determining design forces, and detailing reinforcement. The document emphasizes the importance of properly locating shear walls in a building to resist seismic loads and minimize torsional effects.
The document discusses the design of staircases. It begins by defining key components of staircases like treads, risers, stringers, etc. It then describes different types of staircases such as straight, doglegged, and spiral. The document outlines considerations for designing staircases like dimensions, loads, and structural behavior. It provides steps for geometric design, load calculations, structural analysis, reinforcement design, and detailing of staircases. Numerical examples are also included to illustrate the design process.
Design of Reinforced Concrete Structure (IS 456:2000)MachenLink
This is the 1st Lecture Series on Design Reinforced Cement Concrete (IS 456 -2000).
In this video, you will learn about the objective of structural designing and then basic properties of concrete and steel.
Concrete properties like...
1. Grade of Concrete
2. Modulus of Elasticity
3. Characteristic Strength
4. Tensile Strength
5. Creep and Shrinkage
6. Durability
Reinforced Steel Properties....
1. Grade and types of steel
2. Yield Strength of Mild Steel and HYSD Bars
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.
Static and Kinematic Indeterminacy of Structure.Pritesh Parmar
The document discusses static and kinematic indeterminacy of structures. It defines different types of supports for 2D and 3D structures including fixed support, hinged/pinned support, roller support, and their properties. It also discusses internal joints like internal hinge, internal roller, and internal link. The document explains concepts of static indeterminacy, kinematic indeterminacy, and degree of freedom for different types of structures.
Footings are structural members that support columns and walls and transmit their loads to the soil. Different types of footings include wall footings, isolated/single footings, combined footings, cantilever/strap footings, continuous footings, rafted/mat foundations, and pile caps. Footings must be designed to safely carry and transmit loads to the soil while meeting code requirements regarding bearing capacity, settlement, reinforcement, and shear strength. A proper footing design involves determining loads, allowable soil pressure, reinforcement requirements, and assessing settlement.
This document discusses structural analysis methods for statically indeterminate structures. It defines key terms like degree of static indeterminacy, internal and external redundancy, and methods for analyzing indeterminate structures. Specific methods discussed include the flexibility matrix method, consistent deformation method, and unit load method. Examples of statically indeterminate beams and frames are also provided.
This document discusses shear wall analysis and design. It defines shear walls as structural elements used in buildings to resist lateral forces through cantilever action. The document classifies different types of shear walls and discusses their behavior under seismic loading. It outlines the steps for designing shear walls, including reviewing layout, analyzing structural systems, determining design forces, and detailing reinforcement. The document emphasizes the importance of properly locating shear walls in a building to resist seismic loads and minimize torsional effects.
The document discusses the design of staircases. It begins by defining key components of staircases like treads, risers, stringers, etc. It then describes different types of staircases such as straight, doglegged, and spiral. The document outlines considerations for designing staircases like dimensions, loads, and structural behavior. It provides steps for geometric design, load calculations, structural analysis, reinforcement design, and detailing of staircases. Numerical examples are also included to illustrate the design process.
Design of Reinforced Concrete Structure (IS 456:2000)MachenLink
This is the 1st Lecture Series on Design Reinforced Cement Concrete (IS 456 -2000).
In this video, you will learn about the objective of structural designing and then basic properties of concrete and steel.
Concrete properties like...
1. Grade of Concrete
2. Modulus of Elasticity
3. Characteristic Strength
4. Tensile Strength
5. Creep and Shrinkage
6. Durability
Reinforced Steel Properties....
1. Grade and types of steel
2. Yield Strength of Mild Steel and HYSD Bars
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.
Static and Kinematic Indeterminacy of Structure.Pritesh Parmar
The document discusses static and kinematic indeterminacy of structures. It defines different types of supports for 2D and 3D structures including fixed support, hinged/pinned support, roller support, and their properties. It also discusses internal joints like internal hinge, internal roller, and internal link. The document explains concepts of static indeterminacy, kinematic indeterminacy, and degree of freedom for different types of structures.
Footings are structural members that support columns and walls and transmit their loads to the soil. Different types of footings include wall footings, isolated/single footings, combined footings, cantilever/strap footings, continuous footings, rafted/mat foundations, and pile caps. Footings must be designed to safely carry and transmit loads to the soil while meeting code requirements regarding bearing capacity, settlement, reinforcement, and shear strength. A proper footing design involves determining loads, allowable soil pressure, reinforcement requirements, and assessing settlement.
The document discusses the design of footings for structures. It begins by explaining that footings are needed to transfer structural loads from members made of materials like steel and concrete to the underlying soil. It then describes different types of shallow and deep foundations, including spread, strap, combined, and raft footings. The document provides details on designing isolated and combined footings to resist vertical loads and moments based on provisions in IS 456. It also discusses wall footings and combined footings that support multiple columns. In summary, the document covers the purpose of footings, various footing types, and design of isolated and combined footings.
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.
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 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.
This document discusses various concepts related to structural analysis of arches:
1. An arch is a curved girder supported at its ends, allowing only vertical and horizontal displacements for arch action.
2. The general cable theorem relates the horizontal tension and vertical distance from any cable point to the cable chord moment.
3. Arches are classified based on support conditions (3, 2, or 1 hinged) or shape (curved, parabolic, elliptical, polygonal).
4. Horizontal thrust in arches reduces the bending moment and is calculated differently for various arch types (e.g. parabolic) and loading (e.g. UDL).
Steel structures involve structural steel members designed to carry loads and provide rigidity. Some famous steel structures include the Walt Disney Concert Hall, Tyne Bridge, and Howrah Bridge. Steel structures have advantages like high strength, ductility, elasticity, and ease of fabrication and erection. The Howrah Bridge is a steel cantilever bridge that connects Howrah and Kolkata. When built, it was the 3rd longest cantilever bridge in the world. It uses steel components like I-beams, rivets, and expansion joints and was constructed between 1936-1942.
This document provides an overview of different seismic analysis methods for reinforced concrete buildings according to Indian code IS 1893-2002, including linear static, nonlinear static, linear dynamic, and nonlinear dynamic analysis. It describes the basic procedures for each analysis type and provides examples of how to calculate design seismic base shear, distribute seismic forces vertically and horizontally, and determine drift and overturning effects. Case studies are presented comparing the results of static and dynamic analysis for regular and irregular multi-storey buildings modeled in SAP2000.
The document discusses properties and testing of concrete. It provides information on the constituents of concrete including cement, coarse aggregate, fine aggregate, and water. It also discusses properties of concrete and reinforcements, including their relatively high compressive strength and lower tensile strength. Various tests performed on concrete are mentioned, including tests on workability, compressive strength, flexural strength, and fresh/hardened concrete. Design philosophies for reinforced concrete include the working stress method, ultimate strength method, and limit state method.
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.
Design of steel structure as per is 800(2007)ahsanrabbani
It does not offer resistance against rotation and also termed as a hinged or pinned connections.
It transfers only axial or shear forces and it is not designed for moment
It is generally connected by single bolt/rivet and therefore full rotation is allowed
This document provides 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.
The document provides details on the design procedure for beams. It discusses estimating loads, analyzing beams to determine shear forces and bending moments, and designing beams. The design process involves selecting the beam size and shape, calculating the effective span, determining critical moments and shears, selecting reinforcement, and checking requirements such as shear capacity, deflection limits, and development lengths. An example problem demonstrates designing a singly reinforced concrete beam with a span of 5 meters to support a working live load of 25 kN/m.
The document discusses the design of steel structures according to BS 5950. It provides definitions for key terms related to steel structural elements and their design. These include beams, columns, connections, buckling resistance, capacity, and more. It then discusses the design process and different types of structural forms like tension members, compression members, beams, trusses, and frames. The properties of structural steel and stress-strain behavior are also covered. Methods for designing tension members, including consideration of cross-sectional area and end connections, are outlined.
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.
Columns are structural members that experience compression loads. They can buckle if loaded beyond their buckling (or critical) load. Short columns fail through crushing, while long columns fail through lateral buckling. The Euler formula calculates the buckling load of a long column based on its properties and end conditions. The Rankine-Gordon formula provides a more accurate calculation of buckling load that applies to all column types by accounting for both buckling and crushing. Proper design of columns involves ensuring they are loaded below their safe loads, which incorporate factors of safety applied to the theoretical buckling loads.
This document provides information on the structural design of a simply supported reinforced concrete beam. It includes:
- A list of students enrolled in an elementary structural design course.
- Equations and diagrams showing the forces and stresses in a reinforced concrete beam with a singly reinforced bottom section.
- Limits on the maximum depth of the neutral axis according to the grade of steel.
- Examples of analyzing the stresses and determining steel reinforcement for a given beam cross-section.
- A design example calculating the dimensions and steel reinforcement for a rectangular beam with a factored uniform load.
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.
Compression members are structural members subjected to axial compression or compressive forces. Their design is governed by strength and buckling capacity. Columns can fail due to local buckling, squashing, overall flexural buckling, or torsional buckling. Built-up columns use components like lacings, battens, and cover plates to help distribute stress more evenly and increase buckling resistance compared to a single member. Buckling occurs when a straight compression member becomes unstable and bends under a critical load.
1) Two-way slabs are slabs that require reinforcement in two directions because bending occurs in both the longitudinal and transverse directions when the ratio of longest span to shortest span is less than 2.
2) The document discusses various types of two-way slabs and design methods, focusing on the direct design method (DDM).
3) Using the DDM, the total factored load is first calculated, then the total factored moment is distributed to positive and negative moments. The moments are further distributed to column and middle strips using factors that consider the slab and beam properties.
This document 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 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.
The document discusses the design of footings for structures. It begins by explaining that footings are needed to transfer structural loads from members made of materials like steel and concrete to the underlying soil. It then describes different types of shallow and deep foundations, including spread, strap, combined, and raft footings. The document provides details on designing isolated and combined footings to resist vertical loads and moments based on provisions in IS 456. It also discusses wall footings and combined footings that support multiple columns. In summary, the document covers the purpose of footings, various footing types, and design of isolated and combined footings.
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.
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 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.
This document discusses various concepts related to structural analysis of arches:
1. An arch is a curved girder supported at its ends, allowing only vertical and horizontal displacements for arch action.
2. The general cable theorem relates the horizontal tension and vertical distance from any cable point to the cable chord moment.
3. Arches are classified based on support conditions (3, 2, or 1 hinged) or shape (curved, parabolic, elliptical, polygonal).
4. Horizontal thrust in arches reduces the bending moment and is calculated differently for various arch types (e.g. parabolic) and loading (e.g. UDL).
Steel structures involve structural steel members designed to carry loads and provide rigidity. Some famous steel structures include the Walt Disney Concert Hall, Tyne Bridge, and Howrah Bridge. Steel structures have advantages like high strength, ductility, elasticity, and ease of fabrication and erection. The Howrah Bridge is a steel cantilever bridge that connects Howrah and Kolkata. When built, it was the 3rd longest cantilever bridge in the world. It uses steel components like I-beams, rivets, and expansion joints and was constructed between 1936-1942.
This document provides an overview of different seismic analysis methods for reinforced concrete buildings according to Indian code IS 1893-2002, including linear static, nonlinear static, linear dynamic, and nonlinear dynamic analysis. It describes the basic procedures for each analysis type and provides examples of how to calculate design seismic base shear, distribute seismic forces vertically and horizontally, and determine drift and overturning effects. Case studies are presented comparing the results of static and dynamic analysis for regular and irregular multi-storey buildings modeled in SAP2000.
The document discusses properties and testing of concrete. It provides information on the constituents of concrete including cement, coarse aggregate, fine aggregate, and water. It also discusses properties of concrete and reinforcements, including their relatively high compressive strength and lower tensile strength. Various tests performed on concrete are mentioned, including tests on workability, compressive strength, flexural strength, and fresh/hardened concrete. Design philosophies for reinforced concrete include the working stress method, ultimate strength method, and limit state method.
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.
Design of steel structure as per is 800(2007)ahsanrabbani
It does not offer resistance against rotation and also termed as a hinged or pinned connections.
It transfers only axial or shear forces and it is not designed for moment
It is generally connected by single bolt/rivet and therefore full rotation is allowed
This document provides 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.
The document provides details on the design procedure for beams. It discusses estimating loads, analyzing beams to determine shear forces and bending moments, and designing beams. The design process involves selecting the beam size and shape, calculating the effective span, determining critical moments and shears, selecting reinforcement, and checking requirements such as shear capacity, deflection limits, and development lengths. An example problem demonstrates designing a singly reinforced concrete beam with a span of 5 meters to support a working live load of 25 kN/m.
The document discusses the design of steel structures according to BS 5950. It provides definitions for key terms related to steel structural elements and their design. These include beams, columns, connections, buckling resistance, capacity, and more. It then discusses the design process and different types of structural forms like tension members, compression members, beams, trusses, and frames. The properties of structural steel and stress-strain behavior are also covered. Methods for designing tension members, including consideration of cross-sectional area and end connections, are outlined.
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.
Columns are structural members that experience compression loads. They can buckle if loaded beyond their buckling (or critical) load. Short columns fail through crushing, while long columns fail through lateral buckling. The Euler formula calculates the buckling load of a long column based on its properties and end conditions. The Rankine-Gordon formula provides a more accurate calculation of buckling load that applies to all column types by accounting for both buckling and crushing. Proper design of columns involves ensuring they are loaded below their safe loads, which incorporate factors of safety applied to the theoretical buckling loads.
This document provides information on the structural design of a simply supported reinforced concrete beam. It includes:
- A list of students enrolled in an elementary structural design course.
- Equations and diagrams showing the forces and stresses in a reinforced concrete beam with a singly reinforced bottom section.
- Limits on the maximum depth of the neutral axis according to the grade of steel.
- Examples of analyzing the stresses and determining steel reinforcement for a given beam cross-section.
- A design example calculating the dimensions and steel reinforcement for a rectangular beam with a factored uniform load.
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.
Compression members are structural members subjected to axial compression or compressive forces. Their design is governed by strength and buckling capacity. Columns can fail due to local buckling, squashing, overall flexural buckling, or torsional buckling. Built-up columns use components like lacings, battens, and cover plates to help distribute stress more evenly and increase buckling resistance compared to a single member. Buckling occurs when a straight compression member becomes unstable and bends under a critical load.
1) Two-way slabs are slabs that require reinforcement in two directions because bending occurs in both the longitudinal and transverse directions when the ratio of longest span to shortest span is less than 2.
2) The document discusses various types of two-way slabs and design methods, focusing on the direct design method (DDM).
3) Using the DDM, the total factored load is first calculated, then the total factored moment is distributed to positive and negative moments. The moments are further distributed to column and middle strips using factors that consider the slab and beam properties.
This document 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 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.
The document discusses the design of columns and footings in concrete structures. It covers various topics related to column design including classification of columns based on type of reinforcement, loading, and slenderness ratios. Short columns subjected to axial loads with or without eccentricity are analyzed. Design aspects such as effective length, minimum reinforcement requirements, cover and transverse tie spacing are described based on code specifications. Equations for equilibrium of uniformly loaded short columns are also presented.
Analysis and Design of Rectangular and L-Shaped Columns Subjected to Axial Lo...Nitin Dahiya
Next to rectangular and circular columns, L-shaped columns may be the most frequently encountered reinforced concrete columns, since they can be used as a corner column in framed structures. The behaviour of irregular shaped reinforced concrete columns has been a constant concern for a structural engineer, to design a safe and economic structure in modern buildings and bridge piers. L-shaped reinforced concrete column subjected to biaxial bending and axial compression is a common design problem. Axial load capacity and Moment capacity of rectangular and L-shaped reinforced concrete columns have been done in this work. A computer program has been developed to obtain the axial load capacity and moment capacity of reinforced concrete columns of rectangular and L-shaped.
This document discusses two-way slabs, which deform in two orthogonal directions and require reinforcement in both directions. It describes different types of two-way slabs and analyzes one-way versus two-way slab action. Methods of analysis including Westergaard's theory and Rankine-Grashoff method are covered. Design procedures are provided for reinforced concrete two-way slabs based on Indian code IS 456, including equations to calculate bending moments and requirements for reinforcement.
Time history analysis of braced and unbraced steel StructuresSoumitra Das
This document summarizes a study that analyzed the behavior of braced and unbraced steel structures under earthquake loading through time history analysis. A 10-story steel building was designed and analyzed with no bracing, concentric bracing, and eccentric bracing. Earthquake records from Imperial Valley of varying magnitudes were applied. Results showed that the cross-braced structure experienced the highest bending moments and shear forces at the base of corner columns compared to other bracing types. While the concentric braced structure was found to be safer with smaller displacements, the eccentric braced structure was determined to be the most economical option.
1) The document discusses the design of compression members and buckling behavior. It covers topics like Euler buckling analysis, factors that affect column strength, and modern design using column curves.
2) Key aspects reviewed include elastic buckling of pin-ended columns, the influence of imperfections and eccentric loading on column strength, and classification of sections based on their buckling behavior.
3) Design approaches like effective length, slenderness ratio, and determining the design compressive stress are summarized. Both elastic and inelastic buckling modes are addressed.
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 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 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.
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
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
Braced steel frames are commonly used to resist lateral loads from earthquakes. There are two main types of bracing configurations: concentric and eccentric. Cross bracing provides the highest lateral stiffness compared to diagonal bracing or unbraced frames. Analysis of a sample braced steel frame model found that cross bracing reduced story drift by 87% and column shear and bending moments compared to an unbraced frame. However, axial forces in the columns increased with the addition of bracing. Response spectrum analysis accounted for multiple vibration modes while time history analysis used specific earthquake acceleration records over time. Cross bracing consistently performed best at reducing lateral deformation and forces in the frame.
Special moment frames are reinforced concrete frames designed to resist earthquakes through flexural, axial, and shearing actions. They have additional proportioning and detailing requirements compared to intermediate or ordinary moment frames to improve seismic resistance. This includes the strong column weak beam design where the sum of the flexural strengths of the columns at a joint must exceed 120% of the sum of the flexural strengths of the beams to ensure plastic hinges form in the beams before the columns. Proper hinge reinforcement is also required to allow hinges to undergo large rotations without losing strength.
1. The document discusses steel structures and compression members. Compression members include columns that support axial loads through their centroid and are found as vertical supports in buildings.
2. Compression members are more complex than tension members as they can buckle in various modes. They must satisfy limit state requirements regarding their nominal section capacity and member capacity in compression.
3. Long columns are more prone to buckling out of the plane of loading compared to short columns that crush under pure compression. Euler's formula defines the critical load for a pin-ended column to buckle based on its properties and dimensions.
This presentation summarizes the design of uniaxial columns. It defines uniaxial columns as those that rotate about a single axis due to eccentric loading. It discusses how bending moments occur in columns due to unbalanced loads, lateral loads from wind/earthquake, and construction inaccuracies. The presentation covers different column types based on loading and dimensions, and the design of short columns using the interaction curve and working stress design methods. It also briefly discusses slender column design and the additional moment method for analyzing column moments and deflections.
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mechanical and civil engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mechanical and civil engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Beam and column and its types in detailBilal Rahman
The document discusses different types of beams and columns. It describes beams based on their end support (simply supported, continuous, overhanging, cantilevered, fixed), cross-section shape (I-beam, T-beam, C-beam), and equilibrium condition (statically determinate, statically indeterminate). It also describes columns based on their shape (rectangular, L-shaped), type of reinforcement, loading conditions, and slenderness ratio. Columns can also serve decorative purposes by carrying sculpture or commemorating events.
Similar to Design of columns as per IS 456-2000 (20)
This document discusses the design of compression members under uniaxial bending. It notes that columns are rarely under pure axial compression due to eccentricities from rigid frame action or accidental loading. Columns can experience uniaxial or biaxial bending based on the loading. The behavior depends on the relative magnitudes of the bending moment and axial load, which determine the position of the neutral axis. Methods for designing eccentrically loaded short columns include using equations that calculate the neutral axis position and failure mode, or using interaction diagrams that graphically show the safe ranges of moment and axial load.
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.
A column is a vertical structural element that transmits loads from above to the foundation below. Columns are designed to support both axial loads (compression or tension) as well as bending moments. The design of columns involves consideration of factors like cross-sectional dimensions, length, end conditions, and material strength to ensure it can safely support the loads applied to the structure.
A continuous beam has more than one span carried by multiple supports. It is commonly used in bridge construction since simple beams cannot support large spans without requiring greater strength and stiffness. Continuous prestressed concrete beams provide adequate strength and stiffness while allowing for redistribution of moments, resulting in higher load capacity, reduced deflections, and more evenly distributed bending moments compared to equivalent simple beams. Analysis of continuous beams requires determining primary moments from prestressing, secondary moments induced by support reactions, and the combined resultant moments.
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Prestressed concrete uses tensioned steel to put concrete in compression and improve its performance. Circular structures like pipes, tanks and poles are well-suited for circular prestressing using hoop tension to counteract internal fluid pressure. Pipes can be made through monolithic, two-stage or precast construction. Design considerations include stresses from handling, support conditions, working pressure and cracking. Tanks come in different shapes and are analyzed as shells. Poles are designed for various loads as vertical cantilevers with tapering cross-sections.
Prestressed concrete combines high-strength concrete and high-strength steel in an active manner by tensioning steel tendons and holding them against the concrete, putting it into compression. This transforms concrete from a brittle to a more elastic material. It allows for optimal use of each material's properties and better behavior under loads. Prestressed concrete was pioneered in the 1930s and its use has expanded, finding applications in bridges and other structures. Common methods are pretensioning and post-tensioning, using various tendon types, with bonded or unbonded configurations. Tensioning is done using mechanical, hydraulic, electrical or chemical devices.
We have designed & manufacture the Lubi Valves LBF series type of Butterfly Valves for General Utility Water applications as well as for HVAC applications.
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Data Communication and Computer Networks Management System Project Report.pdfKamal Acharya
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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.
Covid Management System Project Report.pdfKamal Acharya
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2. 2
► Dr. H.J. Shah,Dr. H.J. Shah, “Reinforced Concrete Vol-1”“Reinforced Concrete Vol-1”, 8, 8thth
Edition, 2009.Edition, 2009.
► Dr. H.J. Shah,Dr. H.J. Shah, “Reinforced Concrete Vol-2”“Reinforced Concrete Vol-2”, 6, 6thth
Edition, 2012.Edition, 2012.
► S. Unnikrishna Pillai and Devadas Menon,S. Unnikrishna Pillai and Devadas Menon, “Reinforced Concrete Design”“Reinforced Concrete Design”,,
33rdrd
Edition, 2009Edition, 2009
► P.C.Varghese,P.C.Varghese, “Limit State Design of Reinforced Concrete”“Limit State Design of Reinforced Concrete”, PHI, 2, PHI, 2ndnd
edition, 2009edition, 2009
► Ashok K Jain,Ashok K Jain, “Reinforced Concrete, Limit State Design“Reinforced Concrete, Limit State Design”, Nem Chand and”, Nem Chand and
Bros, 7Bros, 7thth
Edition, 2012Edition, 2012
► M.L.Gambhir, “M.L.Gambhir, “Design of Reinforced Concrete StructuresDesign of Reinforced Concrete Structures”, PHI, 2008”, PHI, 2008
Reference booksReference books
3. 3
► Dr. B.C. Punmia et al,Dr. B.C. Punmia et al, “Limit State Design of Reinforced concrete”“Limit State Design of Reinforced concrete”, Laxmi,, Laxmi,
2007.2007.
► J.N. Bandyopadhyay,J.N. Bandyopadhyay, “Design of Concrete Structures”“Design of Concrete Structures”, PHI, 2008., PHI, 2008.
► N.Krishna Raju,N.Krishna Raju, “Structural Design and Drawing, Reinforced concrete and“Structural Design and Drawing, Reinforced concrete and
steel”steel”, Universities Press, 1992, Universities Press, 1992
► M.R. Dheerencdra Babu,M.R. Dheerencdra Babu, “Structural Engineering Drawing”“Structural Engineering Drawing”, Falcon, 2011, Falcon, 2011
► Bureau of Indian Standards,Bureau of Indian Standards, IS456-2000, IS875-1987, SP16, SP34IS456-2000, IS875-1987, SP16, SP34
4. IntroductionIntroduction
► A column is an important components of R.C. Structures.
► A column, in general, may be defined as a member carrying direct axial
load which causes compressive stresses of such magnitude that these
stresses largely control its design.
► A column or strut is a compression member, the effective length of
which exceeds three times the least lateral dimension.(Cl. 25.1.1)(Cl. 25.1.1)
► When a member carrying mainly axial load is vertical, it is termed as
column ,while if it is inclined or horizontal, it is termed as a strut.
► Columns may be of various shape such as circular, rectangular,
square, hexagonal etc.
► ‘‘Pedestal’ is a vertical compression member whose ‘effective length’ isPedestal’ is a vertical compression member whose ‘effective length’ is
less than three times its least lateral dimension [Cl. 26.5.3.1(h)].less than three times its least lateral dimension [Cl. 26.5.3.1(h)].
4
11. Classification of columnsClassification of columns
11
Based on Type of Reinforcement
a) Tied Columns-where the main
longitudinal bars are enclosed within
closely spaced lateral ties( all cross
sectional shapes)
b) Spiral columns-where the main
longitudinal bars are enclosed within
closely spaced and continuously wound
spiral reinforcement (Circular, square,
octagonal sections)
c) Composite Columns-where the
reinforcement is in the form of structural
steel sections or pipes, with or without
longitudinal bars
12. Based on Type of Loading
a) Columns with axial loading (applied concentrically)
b) Columns with uniaxial eccentric loading
c) Columns with biaxial eccentric loading
12
15. ► The occurrence of ‘pure’ axial compression in a column (due to
concentric loads) is relatively rare.
► Generally, flexure accompanies axial compression — due to ‘rigid
frame’ action, lateral loading and/or actual(or even,
unintended/accidental) eccentricities in loading.
► The combination of axial compression (P) with bending moment (M) at
any column section is statically equivalent to a system consisting of the
load P applied with an eccentricity e = M/P with respect to the
longitudinal centroidal axis of the column section.
► In a more general loading situation, bending moments (Mx and My) are
applied simultaneously on the axially loaded column in two
perpendicular directions — about the major axis (XX) and minor axis
(YY) of the column section. This results in biaxial eccentricities ex=
Mx/P and ey= My/P, as shown in [Fig.(c)]. 15
16. ► Columns in reinforced concrete framed buildings, in general, fall into
the third category, viz. columns with biaxial eccentricities.
► The biaxial eccentricities are particularly significant in the case of the
columns located in the building corners.
► In the case of columns located in the interior of symmetrical, simple
buildings, these eccentricities under gravity loads are generally of a
low order (in comparison with the lateral dimensions of the column),
and hence are sometimes neglected in design calculations.
► In such cases, the columns are assumed to fall in the first category,
viz. columns with axial loading.
► The Code, however, ensures that the design of such columns is
sufficiently conservative to enable them to be capable of resisting
nominal eccentricities in loading
16
17. Based on Slenderness Ratio (Cl. 25.1.2)(Cl. 25.1.2)
Columns (i.e., compression members) may be classified into the following
two types, depending on whether slenderness effects are considered
insignificant or significant:
1. Short columns
2. Slender (or long) columns.
‘Slenderness’ is a geometrical property of a compression member
which is related to the ratio of its ‘effective length’ to its lateral
dimension. This ratio, called slenderness ratio, also provides a
measure of the vulnerability to failure of the column by elastic
instability (buckling) — in the plane in which the slenderness ratio is
computed.. 17
19. Columns with low slenderness ratios, i.e., relatively short and stocky
columns, invariably fail under ultimate loads with the material
(concrete, steel) reaching its ultimate strength, and not by buckling.
On the other hand, columns with very high slenderness ratios are in
danger of buckling (accompanied with large lateral deflection) under
relatively low compressive loads, and thereby failing suddenly.
19
20. Braced columns & unbraced column
In most of the cases, columns are also subjected to horizontal loads like
wind, earthquake etc. If lateral supports are provided at the ends of the
column, the lateral loads are borne entirely by the lateral supports.
Such columns are known as braced columns.(When relative
transverse displacement between the upper and lower ends of a
column is prevented, the frame is said to be braced (against sideway)).
Other columns, where the lateral loads have to be resisted by them, in
addition to axial loads and end moments, are considered as unbraced
columns. (When relative transverse displacement between the upper
and lower ends of a column is not prevented, the frame is said to be
unbraced (against sideway).
20
28. Design of single storey public buildingDesign of single storey public building
29.
30.
31.
32.
33.
34.
35.
36. Unsupported Length
Code (Cl. 25.1.3) defines the ‘unsupported length’ l of a column
explicitly for various types of constructions.
Effective length of a column
The effective length of a column in a given plane is defined as the
distance between the points of inflection in the buckled configuration of
the column in that plane.
The effective length depends on the unsupported length l and the
boundary conditions at the column ends
36
38. Code recommendations for idealised boundary conditions
(Cl. E–1)-Use of Code Charts
Charts are given in Fig. 26 and Fig. 27 of the Code for determining theCharts are given in Fig. 26 and Fig. 27 of the Code for determining the
effective length ratios of braced columns and unbraced columnseffective length ratios of braced columns and unbraced columns
respectively in terms of coefficientsrespectively in terms of coefficients 1 and 2 which represent theβ β1 and 2 which represent theβ β
degrees of rotational freedom at the top and bottom ends of thedegrees of rotational freedom at the top and bottom ends of the
column.column.
38
41. Recommended effective length ratios for normal usage (Table 28,
Page 94)
1. columns braced against sideway:
a) both ends ‘fixed’ rotationally : 0.65
b) one end ‘fixed’ and the other ‘pinned : 0.80
c) both ends ‘free’ rotationally (‘pinned’) : 1.00
2. columns unbraced against sideway:
a) both ends ‘fixed’ rotationally : 1.20
b) one end ‘fixed’ and the other ‘partially fixed’ : 1.50
c) one end ‘fixed’ and the other free : 2.00
41
42. Reinforcement in columnReinforcement in column
► Concrete is strong in compression.Concrete is strong in compression.
► However, longitudinal steel rods are always provided to assist inHowever, longitudinal steel rods are always provided to assist in
carrying the direct loads.carrying the direct loads.
► A minimum area of longitudinal steel is provided in the column, whetherA minimum area of longitudinal steel is provided in the column, whether
it is required from load point of view or not.it is required from load point of view or not.
► This is done to resist tensile stresses caused by some eccentricity ofThis is done to resist tensile stresses caused by some eccentricity of
the vertical loads.the vertical loads.
► There is also an upper limit of amount of reinforcement in RC columns,There is also an upper limit of amount of reinforcement in RC columns,
because higher percentage of steel may cause difficulties in placingbecause higher percentage of steel may cause difficulties in placing
and compacting the concrete.and compacting the concrete.
► Longitudinal reinforcing bars are “tied” laterally by “ties” or “stirrups”Longitudinal reinforcing bars are “tied” laterally by “ties” or “stirrups”
at suitable interval so that the bars do not buckleat suitable interval so that the bars do not buckle
42
49. Functions of longitudinal reinforcementFunctions of longitudinal reinforcement
► To share the vertical compressive load, thereby reducing the overall
size of the column.
► To resist tensile stresses caused in the column due to (i) eccentric
load (ii) Moment (iii) Transverse load.
► To prevent sudden brittle failure of the column.
► To impart certain ductility to the column.
► To reduce the effects of creep and shrinkage due to sustained loading..
49
53. Functions of Transverse reinforcementFunctions of Transverse reinforcement
► To prevent longitudinal buckling of longitudinal reinforcement.
► To resist diagonal tension caused due to transverse shear due to
moment/transverse load.
► To hold the longitudinal reinforcement in position at the time of
concreting.
► To confine the concrete, thereby preventing its longitudinal splitting.
► To impart ductility to the column.
► To prevent sudden brittle failure of the columns.
53
54. 54
Clause 26.5.3.2 Page No:49–IS 456-2000
Cover to reinforcementCover to reinforcement
For a longitudinal reinforcing bar in a column, the nominal cover shall not
be less than 40mm, nor less than the diameter of such bar.
In the case of columns of minimum dimension of 200mm or under, whose
reinforcing bars does not exceed 12mm, a cover of 25mm may be used.
Clause 26.4.2.1 Page No:49–IS 456-2000
71. Based on Type of Loading
a) Columns with axial loading (applied concentrically)
b) Columns with uniaxial eccentric loading
c) Columns with biaxial eccentric loading
71
72. Column under axial compression and Uni-axialColumn under axial compression and Uni-axial
BendingBending
► Let us now take a case of a column which is subjected to combinedLet us now take a case of a column which is subjected to combined
action of axial load (Paction of axial load (Puu) and Uni-axial Bending moment (M) and Uni-axial Bending moment (Muu).).
► This case of loading can be reduced to a single resultant load PThis case of loading can be reduced to a single resultant load Puu actingacting
at an eccentricity e such that e= Mat an eccentricity e such that e= Muu / P/ Puu ..
► The behavior of such column depends upon the relative magnitudes ofThe behavior of such column depends upon the relative magnitudes of
MMuu and Pand Puu , or indirectly on the value of eccentricity e., or indirectly on the value of eccentricity e.
► For a column subjected to load PFor a column subjected to load Puu at an eccentricity e, the location ofat an eccentricity e, the location of
neutral axis (NA) will depend upon the value of eccentricity e.neutral axis (NA) will depend upon the value of eccentricity e.
► Depending upon the value of eccentricity and the resulting position (XDepending upon the value of eccentricity and the resulting position (Xuu))
of NA., We will consider the following cases.of NA., We will consider the following cases.
72
73. Case ICase I :: Concentric loading: Zero Eccentricity or nominalConcentric loading: Zero Eccentricity or nominal
eccentricity (Xeccentricity (Xuu =∞)=∞)
Case IICase II :: Moderate eccentricity (XModerate eccentricity (Xuu > D)> D)
Case IIICase III :: Moderate eccentricity (XModerate eccentricity (Xuu = D)= D)
Case IVCase IV :: Moderate eccentricity (XModerate eccentricity (Xuu < D)< D)
Case I (e=0 and e<eCase I (e=0 and e<eminmin ))
73
74. 74
Case II (Neutral axis outside the sectionCase II (Neutral axis outside the section)
76. 76
Case IV (Neutral Axis lying within the section)Case IV (Neutral Axis lying within the section)
77. Modes of Failure in Eccentric CompressionModes of Failure in Eccentric Compression
► The mode of failure depends upon the relative magnitudes ofThe mode of failure depends upon the relative magnitudes of
eccentricity e. (e = Meccentricity e. (e = Muu / P/ Puu ))
77
Eccentricity Range Behavior Failure
e = Mu / Pu
Small Compression Compression
e = Mu / Pu
Large Flexural Tension
e = Mu / Pu
In between
two
Combination Balanced
78. Column Interaction DiagramColumn Interaction Diagram
► A column subjected to varying magnitudes of P and M will act with itsA column subjected to varying magnitudes of P and M will act with its
neutral axis at varying points.neutral axis at varying points.
78
79. Method of Design of Eccentrically loaded short columnMethod of Design of Eccentrically loaded short column
79
The design of eccentrically loaded short column can be done by two
methods
I) Design of column using equations
II) Design of column using Interaction charts
80. Design of column using equationsDesign of column using equations
80
86. IntroductionIntroduction
► A column with axial load and biaxial bending is commonly found inA column with axial load and biaxial bending is commonly found in
structures because of two major reasons:structures because of two major reasons:
Axial load may have natural eccentricities, though small, withAxial load may have natural eccentricities, though small, with
respect to both the axes.respect to both the axes.
Corner columns of a building may be subjected to bendingCorner columns of a building may be subjected to bending
moments in both the directions along with axial loadmoments in both the directions along with axial load
ExamplesExamples
1)1) External façade columns under combined vertical and horizontalExternal façade columns under combined vertical and horizontal
loadload
2)2) Beams supporting helical or free-standing stairs or oscillating andBeams supporting helical or free-standing stairs or oscillating and
rotary machinery are subjected to biaxial bending with or withoutrotary machinery are subjected to biaxial bending with or without
axial load of either compressive or tensile stress.axial load of either compressive or tensile stress.
86
87. Biaxial EccentricitiesBiaxial Eccentricities
►Every column should be treated as beingEvery column should be treated as being
subjected to axial compression along withsubjected to axial compression along with
biaxial bending by considering possiblebiaxial bending by considering possible
eccentricities of the axial load with respecteccentricities of the axial load with respect
to both the major axis(xx-axis) as well asto both the major axis(xx-axis) as well as
minor axis (yy-axis).minor axis (yy-axis).
►These eccentricities, designated as eThese eccentricities, designated as exx andand
eeyy with respect of x and y axes, may bewith respect of x and y axes, may be
atleast eatleast eminmin though in majority of cases ofthough in majority of cases of
biaxial bending, these may be much morebiaxial bending, these may be much more
then ethen emin.min.
87
89. Method Suggested by IS 456-2000Method Suggested by IS 456-2000
►The method set out in clause 39.6 of the code is based on anThe method set out in clause 39.6 of the code is based on an
assumed failure surface that extends the axial load-momentassumed failure surface that extends the axial load-moment
diagram (Pdiagram (Puu-M-Muu) for single axis bending in three dimensions.) for single axis bending in three dimensions.
Such an approach is also known as Breslar’s Load contourSuch an approach is also known as Breslar’s Load contour
method.method.
►According to the code, the left hand side of the equationAccording to the code, the left hand side of the equation
89
90. Shall not exceed 1. Thus we haveShall not exceed 1. Thus we have
The code further relatesThe code further relates ααnn to the ratio of Pto the ratio of Puu/P/Puzuz
as under:as under:
For intermediate values, linear interpolationFor intermediate values, linear interpolation
may be done from figure.may be done from figure.
Load PLoad Puzuz is given byis given by
Load PLoad Puzuz may be evaluated from chart 63 of ISImay be evaluated from chart 63 of ISI
Handbook(SP-16-2000)Handbook(SP-16-2000)
90
Pu/Puz Between 0.2 and 0.8
91. Design of ColumnDesign of Column
Step-1Step-1-Assume the cross-section of the column and the area of-Assume the cross-section of the column and the area of
reinforcement along with its distribution, based on moment Mreinforcement along with its distribution, based on moment Muu
given by equationgiven by equation
where a may vary between 1.10 to 1.20- lower of awhere a may vary between 1.10 to 1.20- lower of a
for higher axial loading (Pfor higher axial loading (Puu/P/Puzuz))
Step-2Step-2- Compute P- Compute Puzuz either using Equation or chart. Find ratio ofeither using Equation or chart. Find ratio of
PPuu/P/Puz.uz.
Step-3Step-3- Determine Uniaxial Moment Capacities M- Determine Uniaxial Moment Capacities Mux1ux1 and Mand Muy1uy1
combined with axial load Pcombined with axial load Puu , using Appropriate Interaction, using Appropriate Interaction
curves(Design charts) for case of column subjected to axialcurves(Design charts) for case of column subjected to axial
load (Pload (Puu ) and Uniaxial Moment.) and Uniaxial Moment.
91
92. Step-4Step-4-Compute the values of M-Compute the values of Muxux/M/Mux1ux1 and Mand Muyuy/M/Muy1uy1 from chart 64 offrom chart 64 of
SP-16, Find the permissible value of MSP-16, Find the permissible value of Muxux/M/Mux1ux1 corresponding topcorresponding top
the above values of Mthe above values of Muyuy/M/Muy1uy1 and Pand Puu/P/Puzuz .If actual value of M.If actual value of Muxux/M/Mux1ux1
is more than the above value found from chart 64 of SP 16, theis more than the above value found from chart 64 of SP 16, the
assumed section is unsafe and needs revision. Even if theassumed section is unsafe and needs revision. Even if the
assumed value is over safe, it needs revision for the sake ofassumed value is over safe, it needs revision for the sake of
economy.economy.
92
99. IntroductionIntroduction
► A Compression member may be considered as slender or long whenA Compression member may be considered as slender or long when
the slenderness ratio lthe slenderness ratio lexex/D and l/D and leyey/b are more than 12./b are more than 12.
► Thus, if lThus, if lexex/D > 12, the column is considered to be slender for bending/D > 12, the column is considered to be slender for bending
about x-x axis, while if labout x-x axis, while if leyey/b > 12, the column is considered to be slender/b > 12, the column is considered to be slender
for bending about y-y axis.for bending about y-y axis.
► When a short column is loaded even with an axial load, the lateralWhen a short column is loaded even with an axial load, the lateral
deflection is either zero or very small.deflection is either zero or very small.
► Similarly when a slender column is loaded even with axial load, theSimilarly when a slender column is loaded even with axial load, the
lateral deflection ∆, measured from the original centre line along itslateral deflection ∆, measured from the original centre line along its
length, becomes appreciable.length, becomes appreciable.
99
100. The design of a slender column can be carried out by followingThe design of a slender column can be carried out by following
simplified methodssimplified methods
1) The Strength Reduction Coefficient method1) The Strength Reduction Coefficient method
2) The Additional moment Method2) The Additional moment Method
3) The Moment Magnification Method3) The Moment Magnification Method
The reduction coefficient method, given by IS 456-2000 isThe reduction coefficient method, given by IS 456-2000 is
recommended for working stress design for service load and is basedrecommended for working stress design for service load and is based
on allowable stresses in steel and concrete.on allowable stresses in steel and concrete.
The additional moment method is recommended by Indian and BritishThe additional moment method is recommended by Indian and British
codes.codes.
The ACI Code recommends the use of moment magnification method.The ACI Code recommends the use of moment magnification method.
100
Methods of Design of Slender ColumnsMethods of Design of Slender Columns
104. Bending of columns in framesBending of columns in frames
104
(a) Braced (b) unbraced
105. Procedure for Design of Slender ColumnProcedure for Design of Slender Column
Step-1-Step-1- Determine the Effective Length and Slenderness Ratio in eachDetermine the Effective Length and Slenderness Ratio in each
directiondirection
Step-2-Step-2- (a) Determine Initial Moment (M(a) Determine Initial Moment (Muiui) from given primary end) from given primary end
moments Mmoments Mu1u1 and Mand Mu2u2 in each direction.in each direction.
(b) Calculate e(b) Calculate eminmin and Mand Mu,minu,min in each direction.in each direction.
(c) Compare moments computed in steps (a) and (b) above and take the(c) Compare moments computed in steps (a) and (b) above and take the
greater one of the two as initial moment Mgreater one of the two as initial moment Muiui ,in each direction.,in each direction.
Step-3-Step-3- (a) Compute additional moment (M(a) Compute additional moment (Maa) in each direction, using) in each direction, using
equationequation
105
106. (b) Compute total moment (M(b) Compute total moment (Mutut ) in each direction from using equation) in each direction from using equation
without considering reduction factor (kwithout considering reduction factor (kaa))
(c) Make Preliminary design for P(c) Make Preliminary design for Puu and Mand Mutut and find area of steel. Thus p isand find area of steel. Thus p is
known.known.
Step-4-Step-4- (a) Obtain P(a) Obtain Puzuz. Also obtain P. Also obtain Pbb in each direction, for reinforcementin each direction, for reinforcement
ration p determined above.ration p determined above.
(b) Determine the value of k(b) Determine the value of kaa in each direction.in each direction.
(c) Determine the Modified design value of moment in each direction(c) Determine the Modified design value of moment in each direction
MMutut = M= Muiui + k+ kaa MMaa
106
107. Step-5-Step-5- Redesign the column for PRedesign the column for Puu and Mand Mutut . If the column is slender about. If the column is slender about
both the axes, design the column for biaxial bending, for (Pboth the axes, design the column for biaxial bending, for (Puu , M, Muxtuxt) about) about
x-axis and (Px-axis and (Puu , M, Muytuyt) about y-axis.) about y-axis.
Note-When external moments are absent, bending moment due toNote-When external moments are absent, bending moment due to
minimum eccentricity should be added to additional moment about theminimum eccentricity should be added to additional moment about the
corresponding axes.corresponding axes.
107