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.
information on types of beams, different methods to calculate beam stress, design for shear, analysis for SRB flexure, design for flexure, Design procedure for doubly reinforced beam,
This document 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 provides details on the design of a reinforced concrete column footing to support a column with a load of 1100kN. It includes calculating the footing size as a 3.5m x 3.5m square to support the load, determining the reinforcement with 12mm diameter bars at 100mm spacing, and checking that the design meets requirements for bending capacity, shear strength, and development length. The step-by-step worked example shows how to analyze and detail the reinforcement of the column footing.
This document describes the design of a pile cap by a group of civil engineering students. It defines a pile cap as a concrete mat that rests on piles driven into soft ground to provide a stable foundation. It then provides two examples of pile cap design, showing dimensions, load calculations, reinforcement requirements and construction details. The document concludes that a pile cap distributes a building's load to piles to form a stable foundation on unstable soil. It acknowledges the guidance of professors in completing this project.
The document 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.
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 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.
information on types of beams, different methods to calculate beam stress, design for shear, analysis for SRB flexure, design for flexure, Design procedure for doubly reinforced beam,
This document 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 provides details on the design of a reinforced concrete column footing to support a column with a load of 1100kN. It includes calculating the footing size as a 3.5m x 3.5m square to support the load, determining the reinforcement with 12mm diameter bars at 100mm spacing, and checking that the design meets requirements for bending capacity, shear strength, and development length. The step-by-step worked example shows how to analyze and detail the reinforcement of the column footing.
This document describes the design of a pile cap by a group of civil engineering students. It defines a pile cap as a concrete mat that rests on piles driven into soft ground to provide a stable foundation. It then provides two examples of pile cap design, showing dimensions, load calculations, reinforcement requirements and construction details. The document concludes that a pile cap distributes a building's load to piles to form a stable foundation on unstable soil. It acknowledges the guidance of professors in completing this project.
The document 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.
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 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 provides details on the design of a reinforced concrete column footing to support a column load of 1100kN from a 400mm square column. It describes the design process which includes determining the footing size, calculating bending moment, reinforcement requirements, checking shear capacity and development length. The design example shows a 3.5m x 3.5m square footing with 12mm diameter bars at 100mm c/c is adequate to support the given load based on the specified material properties and design codes. Reinforcement and footing details are also provided.
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.
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.
This document provides an overview of wind load calculation procedures according to the International Building Code (IBC) 2012 and American Society of Civil Engineers (ASCE) 7-10 standards. It defines important terms related to wind loads and explains changes made in ASCE 7-10 from the previous ASCE 7-05 standard. The major wind load calculation procedures covered are the directional procedure for buildings of all heights, the envelop procedure for low-rise buildings, and the wind tunnel procedure. Steps of the directional procedure are outlined, including determining the risk category, basic wind speed, wind parameters, velocity pressure coefficients, and velocity pressure.
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 is a project report on the design of a shear wall using STAAD Pro software. It includes an introduction to shear walls, which are vertical structural elements that resist lateral loads like wind and earthquakes. The report discusses the purpose, applications, advantages, and disadvantages of shear walls. It also describes the different types of shear walls and their behavior under loads. The design procedure for shear walls in STAAD Pro and as per reference codes is explained. The conclusion summarizes that shear walls provide strength and stiffness to resist lateral loads in buildings.
Ring or circular rafts can be used for cylindrical structures such as chimneys, silos, storage tanks, TV-towers and other structures. In this case, ring or circular raft is the best suitable foundation to the natural geometry of such structures. The design of circular rafts is quite similar to that of other rafts.
This document discusses the design of two-way slabs. It defines a two-way slab as having a ratio of long to short spans of less than 2. The main types of two-way slabs described are flat slabs with drop panels, two-way slabs with beams, flat plates, and waffle slabs. The basic steps of two-way slab design are outlined, including choosing the slab type and thickness, the design method, calculating moments, determining reinforcement, and checking shear strength. Two common design methods are described: the direct design method which uses coefficients, and the equivalent frame method which analyzes frames cut between columns.
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.
This presentation summarizes the key aspects of one-way slab design:
1) One-way slabs have an aspect ratio of 2:1 or greater, where bending occurs primarily along the long axis. They can be solid, hollow, or ribbed.
2) Design and analysis treats a unit strip of the slab as a rectangular beam of unit width and the slab thickness as the depth.
3) The ACI code specifies minimum slab thickness, concrete cover, span length, bar spacing, reinforcement ratios, and other design requirements.
4) An example problem demonstrates the design process, calculating loads, moments, minimum reinforcement, and checking the proposed slab thickness.
5) One-
Shear walls are preferred in seismic regions because they are very effective at resisting lateral forces during earthquakes. Shear walls are vertical structural elements designed to transfer seismic forces throughout the height of the building. They provide large strength, high stiffness, and ductility. Shear wall buildings have performed much better during past earthquakes compared to reinforced concrete frame buildings. Some key advantages of shear walls include good earthquake resistance when designed properly, easy construction, reduced construction costs, and minimized damage to structural and non-structural elements during seismic events.
This document summarizes the key aspects of flat slab construction and design according to Indian code IS 456-2000. It defines flat slabs as slabs that are directly supported by columns without beams, and describes four common types based on whether drops and column heads are used. The main topics covered include guidelines for proportioning slabs and drops, methods for determining bending moments and shear forces, requirements for slab reinforcement, and an example problem demonstrating the design of an interior flat slab panel.
This document discusses prying action in bolted steel connections. Prying action occurs when the deformation of connected elements under tension increases the tensile force in bolts. It is affected by the strength and stiffness of the connection. The document outlines how to design for prying action by ensuring sufficient bolt diameter, fitting thickness, and distance between bolts. It provides examples calculating the required thickness to prevent prying action. It concludes that prying forces should be considered in design and sufficient rigidity of connected elements is most important.
This document provides an overview of reinforced concrete design principles for civil engineers and construction managers. It discusses the aim of structural design according to BS 8110, describes the properties and composite action of reinforced concrete, explains limit state design methodology, and summarizes key elements like slabs, beams, columns, walls, and foundations. The document also covers material properties, stress-strain curves, failure modes, and general procedures for slab sizing and design.
Shear Force And Bending Moment Diagram For FramesAmr Hamed
This document discusses analyzing shear and moment diagrams for frames. It provides procedures for determining reactions, axial forces, shear forces, and moments at member ends. Examples are given of drawing shear and moment diagrams for simple frames with different joint conditions, including pin and roller supports. Diagrams for a three-pin frame example are shown.
This document provides a summary of IS 800:2007, the Indian Standard Code of Practice for general construction in steel. Some key points:
- IS 800 covers general steel construction using hot rolled sections joined by riveting, bolting or welding. It provides guidance on loads, analysis methods, design requirements, fabrication and erection.
- The standard has been revised to update it based on the latest developments in steel construction technology and allow use of new varieties of structural steel produced in India.
- The revision was carried out by the Indian Institute of Technology Madras with support from the Institute of Steel Development and Growth. It references other Indian and international standards.
- Key changes in the revision include expanding
A raft foundation is a large concrete slab that interfaces columns with the base soil. It can support storage tanks, equipment, or tower structures. There are different types including flat plate, plate with thickened columns, and waffle slab. The structural design uses conventional rigid or flexible methods. It involves determining soil pressures, load eccentricities, moment and shear diagrams for strips, punching shear sections, steel reinforcement, and checking stresses. A beam-slab raft foundation design follows the same process as an inverted beam-slab roof.
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.
ANALYSIS AND DESIGN OF G+4 RESIDENTIAL BUILDING contentsila vamsi krishna
This document outlines the process and methods used to analyze and design a multi-story residential building using STAAD Pro software. It includes chapters on software used, literature review of analysis methods, load calculations, design of building elements like beams, columns, slabs and footings. Load combinations are defined according to Indian standards. Material properties and design assumptions are provided. The document then describes the analysis and design of each building element and provides sample output diagrams from STAAD Pro.
The document discusses reinforcement detailing requirements according to Eurocode 2 (EC2). It covers general rules on bar spacing, minimum bend diameters, and anchorage and lapping of bars. For anchorage, it explains how to calculate the basic and design anchorage lengths according to EC2 equations and factors. A worked example calculates the design anchorage length for straight and bent H16 bars in concrete C25/30 with 25mm cover.
Design of short columns using helical reinforcementshivam gautam
Helical reinforcement, also known as spiral reinforcement, is used in circular concrete columns. It consists of longitudinal bars enclosed within a continuously wound spiral reinforcement. Helical reinforcement is sometimes designed instead of normal links for columns because it provides increased strength and ductility. The spiral reinforcement acts compositely with the concrete core and allows the column to sustain higher loads than those with normal links. It also minimizes the risk of stirrups opening during seismic events. The document then provides details on the design of helical reinforcement for short concrete columns, including governing equations and an example problem.
The document provides details on the design of a reinforced concrete column footing to support a column load of 1100kN from a 400mm square column. It describes the design process which includes determining the footing size, calculating bending moment, reinforcement requirements, checking shear capacity and development length. The design example shows a 3.5m x 3.5m square footing with 12mm diameter bars at 100mm c/c is adequate to support the given load based on the specified material properties and design codes. Reinforcement and footing details are also provided.
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.
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.
This document provides an overview of wind load calculation procedures according to the International Building Code (IBC) 2012 and American Society of Civil Engineers (ASCE) 7-10 standards. It defines important terms related to wind loads and explains changes made in ASCE 7-10 from the previous ASCE 7-05 standard. The major wind load calculation procedures covered are the directional procedure for buildings of all heights, the envelop procedure for low-rise buildings, and the wind tunnel procedure. Steps of the directional procedure are outlined, including determining the risk category, basic wind speed, wind parameters, velocity pressure coefficients, and velocity pressure.
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 is a project report on the design of a shear wall using STAAD Pro software. It includes an introduction to shear walls, which are vertical structural elements that resist lateral loads like wind and earthquakes. The report discusses the purpose, applications, advantages, and disadvantages of shear walls. It also describes the different types of shear walls and their behavior under loads. The design procedure for shear walls in STAAD Pro and as per reference codes is explained. The conclusion summarizes that shear walls provide strength and stiffness to resist lateral loads in buildings.
Ring or circular rafts can be used for cylindrical structures such as chimneys, silos, storage tanks, TV-towers and other structures. In this case, ring or circular raft is the best suitable foundation to the natural geometry of such structures. The design of circular rafts is quite similar to that of other rafts.
This document discusses the design of two-way slabs. It defines a two-way slab as having a ratio of long to short spans of less than 2. The main types of two-way slabs described are flat slabs with drop panels, two-way slabs with beams, flat plates, and waffle slabs. The basic steps of two-way slab design are outlined, including choosing the slab type and thickness, the design method, calculating moments, determining reinforcement, and checking shear strength. Two common design methods are described: the direct design method which uses coefficients, and the equivalent frame method which analyzes frames cut between columns.
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.
This presentation summarizes the key aspects of one-way slab design:
1) One-way slabs have an aspect ratio of 2:1 or greater, where bending occurs primarily along the long axis. They can be solid, hollow, or ribbed.
2) Design and analysis treats a unit strip of the slab as a rectangular beam of unit width and the slab thickness as the depth.
3) The ACI code specifies minimum slab thickness, concrete cover, span length, bar spacing, reinforcement ratios, and other design requirements.
4) An example problem demonstrates the design process, calculating loads, moments, minimum reinforcement, and checking the proposed slab thickness.
5) One-
Shear walls are preferred in seismic regions because they are very effective at resisting lateral forces during earthquakes. Shear walls are vertical structural elements designed to transfer seismic forces throughout the height of the building. They provide large strength, high stiffness, and ductility. Shear wall buildings have performed much better during past earthquakes compared to reinforced concrete frame buildings. Some key advantages of shear walls include good earthquake resistance when designed properly, easy construction, reduced construction costs, and minimized damage to structural and non-structural elements during seismic events.
This document summarizes the key aspects of flat slab construction and design according to Indian code IS 456-2000. It defines flat slabs as slabs that are directly supported by columns without beams, and describes four common types based on whether drops and column heads are used. The main topics covered include guidelines for proportioning slabs and drops, methods for determining bending moments and shear forces, requirements for slab reinforcement, and an example problem demonstrating the design of an interior flat slab panel.
This document discusses prying action in bolted steel connections. Prying action occurs when the deformation of connected elements under tension increases the tensile force in bolts. It is affected by the strength and stiffness of the connection. The document outlines how to design for prying action by ensuring sufficient bolt diameter, fitting thickness, and distance between bolts. It provides examples calculating the required thickness to prevent prying action. It concludes that prying forces should be considered in design and sufficient rigidity of connected elements is most important.
This document provides an overview of reinforced concrete design principles for civil engineers and construction managers. It discusses the aim of structural design according to BS 8110, describes the properties and composite action of reinforced concrete, explains limit state design methodology, and summarizes key elements like slabs, beams, columns, walls, and foundations. The document also covers material properties, stress-strain curves, failure modes, and general procedures for slab sizing and design.
Shear Force And Bending Moment Diagram For FramesAmr Hamed
This document discusses analyzing shear and moment diagrams for frames. It provides procedures for determining reactions, axial forces, shear forces, and moments at member ends. Examples are given of drawing shear and moment diagrams for simple frames with different joint conditions, including pin and roller supports. Diagrams for a three-pin frame example are shown.
This document provides a summary of IS 800:2007, the Indian Standard Code of Practice for general construction in steel. Some key points:
- IS 800 covers general steel construction using hot rolled sections joined by riveting, bolting or welding. It provides guidance on loads, analysis methods, design requirements, fabrication and erection.
- The standard has been revised to update it based on the latest developments in steel construction technology and allow use of new varieties of structural steel produced in India.
- The revision was carried out by the Indian Institute of Technology Madras with support from the Institute of Steel Development and Growth. It references other Indian and international standards.
- Key changes in the revision include expanding
A raft foundation is a large concrete slab that interfaces columns with the base soil. It can support storage tanks, equipment, or tower structures. There are different types including flat plate, plate with thickened columns, and waffle slab. The structural design uses conventional rigid or flexible methods. It involves determining soil pressures, load eccentricities, moment and shear diagrams for strips, punching shear sections, steel reinforcement, and checking stresses. A beam-slab raft foundation design follows the same process as an inverted beam-slab roof.
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.
ANALYSIS AND DESIGN OF G+4 RESIDENTIAL BUILDING contentsila vamsi krishna
This document outlines the process and methods used to analyze and design a multi-story residential building using STAAD Pro software. It includes chapters on software used, literature review of analysis methods, load calculations, design of building elements like beams, columns, slabs and footings. Load combinations are defined according to Indian standards. Material properties and design assumptions are provided. The document then describes the analysis and design of each building element and provides sample output diagrams from STAAD Pro.
The document discusses reinforcement detailing requirements according to Eurocode 2 (EC2). It covers general rules on bar spacing, minimum bend diameters, and anchorage and lapping of bars. For anchorage, it explains how to calculate the basic and design anchorage lengths according to EC2 equations and factors. A worked example calculates the design anchorage length for straight and bent H16 bars in concrete C25/30 with 25mm cover.
Design of short columns using helical reinforcementshivam gautam
Helical reinforcement, also known as spiral reinforcement, is used in circular concrete columns. It consists of longitudinal bars enclosed within a continuously wound spiral reinforcement. Helical reinforcement is sometimes designed instead of normal links for columns because it provides increased strength and ductility. The spiral reinforcement acts compositely with the concrete core and allows the column to sustain higher loads than those with normal links. It also minimizes the risk of stirrups opening during seismic events. The document then provides details on the design of helical reinforcement for short concrete columns, including governing equations and an example problem.
The document discusses guidelines for detailing reinforcement in concrete structures. It begins by defining detailing as the preparation of working drawings showing the size and location of reinforcement. Good detailing ensures reinforcement and concrete interact efficiently. The document then discusses sources of tension in concrete structures from various loading conditions like bending, shear, and connections. It provides equations from AS3600-2009 for calculating minimum development lengths for reinforcing bars to develop their yield strength based on bar size, concrete strength, and transverse reinforcement. It also discusses lap splice requirements. In summary, the document provides best practice guidelines for detailing reinforcement to efficiently resist loads and control cracking in concrete structures.
The document discusses the design requirements for lacing, battening, and column bases according to IS 800-2007. It provides details on:
- Two types of lacing systems - single and double
- Design requirements for lacing including angle of inclination, slenderness ratio, effective lacing length, bar width and thickness
- Design of battening including number of battens, spacing, thickness, effective depth, and transverse shear
- Minimum thickness requirements for rectangular slab column bases
It also provides an example problem demonstrating the design of a slab base foundation for a column.
The document discusses buckling of columns under axial compression. It describes:
1) Different buckling theories including elastic buckling, inelastic buckling using tangent modulus theory and reduced modulus theory. Shanley's theory accounts for the effect of transverse displacement.
2) Factors affecting buckling strength including end conditions, initial crookedness, and residual stresses. Effective length accounts for end restraint.
3) Local buckling of thin plate elements can reduce the column's strength before its calculated buckling strength is reached. Flange and web buckling must be prevented.
A column is a vertical structural member subjected to compression and bending forces. Short columns fail through crushing or splitting, while slender columns fail through buckling. The document provides examples of calculating required reinforcement area and diameter for a short reinforced concrete column. It also provides examples of calculating the critical buckling load of a rod and determining a suitable universal column section for a given load based on its effective length and slenderness ratio.
This document provides the design of a rectangular water tank with a capacity of 2500 cubic meters. It includes:
1) Design of the roof slab as a flat slab with columns spaced 5 meters apart and a thickness of 240mm.
2) Design of columns with a size of 350mm and reinforcement of 6 bars of 16mm diameter.
3) Design of the vertical walls with a thickness of 230mm at the base reducing to 180mm in the middle. Reinforcement of 16mm diameter bars at 125mm centers is provided.
4) Checks for crack width for the columns and walls show the crack width is less than the permissible 0.2mm.
This document provides a design example for a reinforced concrete T-beam bridge girder. It includes the design of the deck slab, longitudinal girders, and cross girders. The design uses Courbon's method to calculate live load bending moments and shear forces. Details are given for the design of an interior deck slab panel including reinforcement sizing. Design of the longitudinal girders includes calculating reaction factors and sizing reinforcement to resist bending moments and shear forces from dead and live loads.
DESIGN OF DECK SLAB AND GIRDERS- BRIDGE ENGINEERINGLiyaWilson4
This document provides a design example for a reinforced concrete T-beam bridge girder. It includes the design of the deck slab, longitudinal girders, and cross girders. The design uses Courbon's method to calculate live load bending moments and shear forces. Details are given for the design of an interior deck slab panel including reinforcement sizing. Design of the longitudinal girders includes calculating reaction factors and sizing reinforcement to resist bending moments and shear forces from dead and live loads.
This document provides an overview of torsion in thin-walled beams. It discusses how torsional loads are generated in wing structures from factors like engine placement. Methods are presented for calculating shear stress and twist angle due to torsion in closed and open section beams, as well as multicellular wing sections. Examples are worked through to demonstrate calculating shear flow distribution, shear stress, and twist angle for beams with various cross-sectional geometries under applied torques.
This document contains a question paper for an examination on the design of machine elements. It includes the following:
1) Part A contains 10 short answer questions covering topics like stresses in components, failure theories, types of joints, springs, flywheels, and bearings.
2) Part B contains 5 long answer questions involving calculations for shafts, couplings, bolts, springs, and bearings. Design problems include determining sizes based on strength, load capacity, and stress.
3) Part C contains 2 design problems - determining dimensions and stresses for a flywheel and connecting rod based on given load and stress criteria.
This document provides instructions and questions for a structural design exam. It consists of 4 questions. Students must answer question 1 and any other two questions. Question 1 involves calculating bending moments, designing reinforcement, and determining shear capacity for concrete beams. Question 2 involves checking the adequacy of steel sections and designing a bolt connection. Question 3 uses force methods to determine reactions and draws shear and bending moment diagrams. Question 4 analyzes a frame under vertical and lateral loads to determine reactions and internal forces at specific points. The document also includes relevant design formulas and appendices on load combinations, bending moment coefficients, and steel design strengths.
The document contains 38 questions related to machine design. The questions cover topics such as standardization of sizes, tolerances, fits, design of joints, shafts, levers, frames and other machine elements. Design calculations are required to determine dimensions that satisfy given loading and stress criteria. Materials, their properties and appropriate factors of safety are provided. References for solutions and examples are given from standard machine design textbooks.
This document discusses the design of flat slab structures with and without slab drops. It begins with an introduction to flat slabs and their components. It then outlines the design methodology and considerations. The main body compares the bending moments and steel requirements for interior and exterior panels of flat slabs without drops and with drops, for slab sizes of 20x20m, 40x40m, and 60x60m. The key findings are that flat slabs without drops require less steel in the middle strips compared to flat slabs with drops, but flat slabs with drops have lower bending moments and steel requirements in the column strips.
This document summarizes the key components and design process of flat slab construction without slab drops. It provides examples of designing interior and exterior panels of sizes 5x5m, 10x10m, and 15x15m for a 20x20m flat slab without drops. The design process involves determining slab depth, load calculations, moment distribution, and reinforcement sizing. Tables are included that show bending moments and steel areas for column strips and middle strips of the example panels. Interior panels have negative and positive moments in both directions while exterior panels only have negative moments in the column strip and positive moments in the middle strip.
This document provides a summary of the design and verification of anchor bolts and a shear lug for a column base connection. It includes the geometry, loads, materials, and design calculations for the base plate, anchor bolts, and shear lug plate. The calculations show the base plate and anchor bolts satisfy strength requirements for bearing, tension, and shear. The shear lug plate is designed to resist the portion of shear load not resisted by friction, and calculations verify it satisfies strength requirements for bearing and shear.
This document contains information about an examination for the sixth semester of a Bachelor of Engineering degree in Computer Engineering. It includes the course code, title (Integrated Manufacturing), maximum marks, duration, and parts of the exam. Part A includes questions on automation strategies, transfer mechanisms, automated flow line analysis, and line balancing. Part B includes questions on product design for assembly, parts delivery systems, automated guided vehicle systems, computer-aided design systems, material requirement planning, computer numerical control systems, robot configurations, and programming. The document provides context, guidelines, and potential exam questions for students to prepare.
Iron ore is mined all over the world and must contain at least 20% iron to be economically viable. Magnetite and hematite ores have high iron content. Approximately 2 billion tons of iron ore are mined annually, with China, Australia and Brazil dominating production. Steel is produced via smelting iron ore in blast furnaces or electric arc furnaces. Rebar, structural sections and nuts/bolts are common steel products. Steel is strong and has properties well-suited for reinforcing concrete. The steelmaking process involves melting scrap, adjusting chemistry, continuous casting and rolling billets. Rebar is tested to ensure it meets specifications for strength, elongation and bending.
The document provides an overview of concrete, including its composition, properties, and factors that affect its performance. Concrete is made by mixing water, cement, fine aggregate (sand), and coarse aggregate (gravel) in specific proportions. Its key properties include strength in compression but weakness in tension. Strength increases with curing time. Workability, permeability, durability, and elasticity are also addressed. Factors like water-cement ratio, compaction, aggregate size and quality influence concrete properties.
Lecture 4, constituents of concrete-coarse aggregateDr. H.M.A. Mahzuz
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Column math
1. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 1
RCC Column
What is Column?
Column may be defined as a vertical structural member that carry loads chiefly in compression. It can carry moment
as well, about one or both axes of the cross section. Bending action may produce tensile forces over a part of the
cross-section. Even in such case columns are referred as compression members because compression force
dominates its behavior. Its ratio of height to least lateral dimension is
t
L
3.
Types of Column:
A) Based on reinforcement column can be divided into the following was:
1) Column reinforced with longitudinal bar and lateral ties.
2) Column reinforced with longitudinal bar and continuous spirals.
3) Composite compression members reinforced longitudinal with structural steel shapes,pipe or tubing.
B) Based on length:
1. Short column: Short columns those whose ratio of effective length to the minimum thickness is less then 12
(i.e. 12 ). Material strength is the main factor for its failure.
2. Long Column: Short columns those whose ratio of effective length to the minimum thickness is greater
then 12 ( 12). Material strength and buckling are the main factors for its failure.
C) Depending on position at a building or loading pattern:
1) Axially loaded column
2) Uni-axial column
3) Bi-axial column.
Preliminary size of column:
The initial stage in column design involves estimating the required of the column. There is no simple rule to do this
as the axial load capacity of a given cross-section varies depending on the moment acting on the section.The
approximate relation between axial load and gross area for tied column is,
)(45.0 ',
gyc
U
trialg
ff
P
A
The approximate relation between axial load and gross area for tied column is,
)(55.0 ',
gyc
U
trialg
ff
P
A
Depending on span length an initial approximation for gross area of column can also be made. For columns
supporting heavily loaded floors minimum overall dimensions of one-fifteenth the average span of the panel is
considered satisfactory.Roof columns may be somewhat lighter; one-eighteenth the average span is specified by
some codes as a minimum diameter.
Function of Tie/ spiral/ Transverse reinforcement:
1. To hold longitudinal bars in position in forms while the concrete is being placed. For this purpose both of
them are wired togetherto form a cage of reinforcement.
2. To prevent the highly stressed slenderlongitudinal bars from buckling outward bursting the thin concrete
cover.
2. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 2
Fig: Tied column Fig: Spiral column
Serial No. Contents Tied Spiral
a) Least Dimension Minm 10 in, in EQ regions 12 in. Minm 12 in
b) Least area -- ---------
c) Steel ratio, min,g 1% 1%
d) Steel ratio, max,g 8% 8%
e) Minm No. of longitudinal bar 4 6
f) Minm longitudinal bar size #5 bar #5 bar
g) Minm No. of tie bar #3 (for bundle bars or longitudinal
bar size>#10 use #4 bar as tie)
#3
h) Minm Clear cover 1.5 in 1.5 in
Note: Generally max,g is preferable between 1%- 4% to avoid steel congestion.
Guideline for Tie/ spiral reinforcement:
1) All bars of tied columns shall be enclosed by lateral ties, at least No. 3 in size for longitudinal bars up to No. 10,
and at least No. 4 in size for Nos. 11, 14, and 18 and bundled longitudinal bars.
2) The spacing of the ties shall not exceed 16 diameters of longitudinal bars (16D), 48 diameters of tie bars
(48d), nor the least dimension (tmin) of the column.
3) No bar shall be farther than 6 in. clear on either side from such a laterally supported bar.
4) The ties shall be so arranged that every corner and alternate longitudinal bar shall have lateral support pro -
vided by the corner of a tie having an included angle of not more than 135°.
5) Spirals shall be continuous bar of not less than #3. The c lear spacing between turns of the spiral must not
exceed 3 inch (but not less than 1 inch).
Design of axially loaded column:
WSD:
3. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 3
For concentrically loaded spirally reinforced column Code provides the following formula for maximum allowable
load:
)25.0( '
gscg ffAP
For concentrically loaded tied reinforced column Code provides the following formula for maximum allowable load:
)25.0(85.0 '
gscg ffAP
Ag = Gross concrete area,
g
s
g
A
A
.
USD:
Let us consider an axially loaded column where the load is taken by both concrete and steel. Therefore,
sycc AfAfP '
. But full strength of
'
cf is not used rather 0.85
'
cf . So we can say:
sycc AfAfP '
85.0 . Rearranging the equation we get,
g
g
s
ysgc A
A
A
fAAfP )(85.0 '
})1(85.0{ '
gygcg ffAP
For concentrically loaded tied reinforced column Code provides the following formula for maximum allowable
load:
})1(85.0{ '
gygcg ffAP
85.0 and 75.0 for spiral column
80.0 and 70.0 for tied column
Recommendation for tie:
Fig: Minimum details for frames in regions of moderate risk
4. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 4
Problem 1:
Design a tied column for load 500 kip both in WSD and USD.
Suggestedsolution:
WSD
Considering, 02.0g
)25.0(85.0 '
gscg ffAP
)02.0604.0325.0(85.0500 gA
2
24.478 inAg [ "87.2124.4782
hh ]
Therefore select a square section 22''22''.
As = gg A = 0.022222 = 9.68 in2. So provide 10 No. # 9 bar as main bar.
Tie reinforcement:
1) 16D= 16 18
8
9
'' 2) 48d= 18
8
3
48 '' 3) tmin= 22'', So provide #3 @18''c/c as tie reinforcement.
USD
})1(85.0{ '
gygcg ffAP
As 80.0 and 70.0 for tied column. Considering, 01.0g
)01.060)01.01(385.0(70.08.0500 gA
2
76.285 inAg [ "7.1676.2852
hh ]
Select a square section 18''18''.
As = gg A = 0.011818 = 3.2420.28 in2
So provide 6 No. # 6 bar as main bar.
Tie reinforcement:
1) 16D= 16 12
8
6
'' 2) 48d= 18
8
3
48 '' 3) tmin= 18'', So provide #3 @12''c/c as tie reinforcement.
Note: This problem is done assuming an arbitrary g value. If anyone does this problem assuming an arbitrary gA
then this way is also ok but remember that the g value must have to be greater than 0.01.
Problem 2:
A plan showing the beams and columns of a 10 storied market building is shown in Fig: 1(a). Here brick walls are
used only for partition. Design the Column A for Ground floor and 4th floor in both WSD and USD having the
following information:
a) Slab thickness = 6.5'',
b) Beam cross-section = 18''12''
c) Live load on the floor = 100 psf
d) Live load in the roof = 60 psf.
e) Brick wall thickness = 5''.
5. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 5
f) Story clear height = 10'
g)
'
cf =3 ksi, and yf = 60 ksi
SuggestedSolution:
WSD
Item No Item Calculation Load
1. Slab self load calculation =
10)
12
5.6
2
1720
2
2225
(15.0
353.3 kip
2. Beam weight =
10)
1212
2218
2
17202225
(15.0
173.25
3. Wall weight =
10)10
12
5
2
17202225
(12.0
210 kip
4. Floor Live load =
0.1
9)
2
1720
2
2225
(
391.3 kip
5. Roof Live load =
0.06
1)
2
1720
2
2225
(
26.1 kip
1153.95 kip
Trial gross area of column,
)(45.0 ',
gyc
trialg
ff
P
A
, considering, 03.0g
2
, 24.534
)03.0603(45.0
95.1153
inA trialg
[ "11.2324.5342
hh ]
Select a square section = 24''24''.
Self load of column = 0.15' 60100
12
24
12
24
kip
Total load = 1153.95 + 60 = 1214 kip
For concentrically loaded tied reinforced column Code provides the following formula for maximum allowable load:
)25.0(85.0 '
gscg ffAP
6. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 6
)03.0604.0325.0(85.012.1032 gA
2
03.826 inAg [ "74.2803.8262
hh ]
Select a square section = 30''30''.
Self load of column = 0.15' 100
12
30
12
30
93.8 kip
Total load = 981.7+93.8=1075.45 kip
)25.0(85.0 '
gscg ffAP
)03.0604.0325.0(85.045.1075 gA
2
7.860 inAg [ "34.297.8602
hh ]
Therefore the selected square section 30''30'' is ok!!!!
As = gg A = 0.033030 = 27 in2, So provide 28 No. # 9 bar as main bar.
Note: Sometimes extra bar has to be used to make the section symmetric.
Tie reinforcement:
1) 16D= 16 18
8
9
'' 2) 48d= 18
8
3
48 '' 3) tmin= 30'', So provide #3 @18''c/c as tie reinforcement.
USD
Item No Item Calculation Load
6. Slab self load calculation =
4.110)
12
5.6
2
1720
2
2225
(15.0
494.62 kip
7. Beam weight =
4.110)10
12
5
2
17202225
(12.0
294 kip
8. Floor Live load =
0.1
7.19)
2
1720
2
2225
(
665.21
9. Roof Live load =
0.06
7.11)
2
1720
2
2225
(
44.37 kip
1498.2 kip
7. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 7
Trial gross area of column,
)(45.0 ',
gyc
trialg
ff
P
A
, considering, 03.0g
2
, 96.1046
)03.0603(45.0
2.1498
inA trialg
[ "36.3296.10462
hh ]
Select a square section = 33''33''.
Self load of column = 0.15' 4.1100
12
33
12
33
158.82 kip
Total load = 1498.2+158.82=1657.1 kip
For concentrically loaded tied reinforced column Code provides the following formula for maximum allowable load:
})1(85.0{ '
gygcg ffAP
80.0 and 70.0 for tied column
)03.060)03.01(385.0(70.08.01.1657 gA
2
43.692 inAg [ "31.2643.6932
hh ]
Select a square section = 27''27''.
Self load of column = 0.15' 4.1100
12
27
12
27
106.31 kip
Total load = 1498.2+106.31=1604.6 kip
})1(85.0{ '
gygcg ffAP
as 80.0 and 70.0 for tied column
)03.060)03.01(385.0(70.08.06.1604 gA
2
5.670 inAg [ "89.255.6702
hh ]
Select a square section 26''26''.
As = gg A = 0.032626 = 20.28 in2. So provide 26 No. # 8 bar as main bar.
Note: Sometimes extra bar has to be used to make the section symmetric.
Tie reinforcement:
1) 16D= 16 16
8
8
'' 2) 48d= "18
8
3
48 3) tmin= 26'', So provide #3 @16''c/c as tie reinforcement.
Short column: Its strength is governed by strength of materials (i.e. concrete and steel) nd geometry of
cross-section.
𝜌𝑠 can be selected by the equation, 𝜌𝑠 = 0.45(
𝐴 𝑔
𝐴 𝑐
− 1)
𝑓𝑐
′
𝑓𝑦
Problem :3 Design a column for 474 kip load.
Answer:
Assume the missing data, 𝒇 𝒄
′ = 4 𝑘𝑠𝑖, 𝒇 𝒚 = 60 𝑘𝑠𝑖, 𝐴 𝑔= 15x15 in2
.
8. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 8
})1(85.0{ '
gygcgn ffAPP
80.0 and 70.0 for tied column, 85.0 and 75.0 for spiral column,
})1(85.0{ '
gygcg ffAP
)60)1(485.0(151570.08.0474 gg
01.00064.0 g , use 01.0min
2
25.2151501.0 inbhA gs
Problem :4 Design a column for 700 kip load.
Answer:
Assume the missing data, 𝒇 𝒄
′ = 4 𝑘𝑠𝑖, 𝒇 𝒚 = 60 𝑘𝑠𝑖, 𝐴 𝑔= 15x15 in2
.
})1(85.0{ '
gygcgn ffAPP
80.0 and 70.0 for tied column, 85.0 and 75.0 for spiral column,
})1(85.0{ '
gygcg ffAP
)60)1(485.0(151570.08.0700 gg
00381.0 g
2
57.815150381.0 inbhA gs
Problem :5 Design a column for 1200 kip load.
Answer:
Assume the missing data, 𝒇 𝒄
′ = 4 𝑘𝑠𝑖, 𝒇 𝒚 = 60 𝑘𝑠𝑖, 𝐴 𝑔= 15x15 in2
.
})1(85.0{ '
gygcgn ffAPP
80.0 and 70.0 for tied column, 85.0 and 75.0 for spiral column,
})1(85.0{ '
gygcg ffAP
)60)1(485.0(151570.08.01200 gg
08.011.0 g
Change the material property/ section/ both and redesign
Assume the missing data, 𝒇 𝒄
′ = 4 𝑘𝑠𝑖, 𝒇 𝒚 = 60 𝑘𝑠𝑖, 𝐴 𝑔= 24x18 in2
.
})1(85.0{ '
gygcgn ffAPP
80.0 and 70.0 for tied column, 85.0 and 75.0 for spiral column,
})1(85.0{ '
gygcg ffAP
)60)1(485.0(182470.08.01200 gg
01.00276.0 g
2
91.1118240276.0 inbhA gs
Spacing of transverse reinforcement should be not less
then (NON-EQ zone)
𝑠 = (
16 diameter of Longitudinal steel (16D)
48 diameter of transverse steel (48d)
Least dimension of column (tmin)
)
Spacing of transverse reinforcement should be not less
then (EQ zone)
𝑠 = (
8 diameter of Longitudinal steel (8D)
24 diameter of transverse steel (24d)
1
2
of least dimension of column
)
9. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 9
and 2s
Problem :6 Design a square column at middle for a DL=1 kip/ft and LL= 0.7 kip/ft. Consider that the
building 10 storied. Also Consider, 𝒇 𝒄
′ = 3 𝑘𝑠𝑖, 𝒇 𝒚 = 60 𝑘𝑠𝑖,
11. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 11
+(0.15 ×
15
12
×
15
12
× 10) × 3} = 111.37 + 52.25 = 1166 kip
Considering, 𝜌𝑔 = 0.03,
𝑃 = 𝜑𝑃𝑛 = 𝛼𝜑𝐴 𝑔(0.85𝑓𝑐
′(1 − 𝜌𝑔 ) + 𝑓𝑦 𝜌𝑔)
=> 1166 = 0.8 × 0.7𝐴 𝑔(0.85 × 3 × (1 − 0.03) + 60 × 0.03)
=> 𝐴 𝑔 = 487.2 𝑖𝑛2 = 22.07 × 22.07 < 24×24(ok)
So, 𝑃6 = 111.37 × 6 = 668.2 kip
Considering, 𝜌𝑔 = 0.02,
𝑃 = 𝜑𝑃𝑛 = 𝛼𝜑𝐴 𝑔(0.85𝑓𝑐
′(1 − 𝜌𝑔 ) + 𝑓𝑦 𝜌𝑔)
=> 668.2 = 0.8 × 0.7𝐴 𝑔(0.85 × 3 × (1 − 0.02) + 60 × 0.02)
=> 𝐴 𝑔 = 322.6 𝑖𝑛2 = 17.96 × 17.96, take − 18" × 18"
𝐴 𝑠 = 0.02 × 18" × 18" = 6.48 𝑖𝑛2 = 16 #6
Provide this column at 5th
, 6th
and 7th
story.
So, 𝑃3 = 111.37 × 3 = 334.11 kip
Considering, 𝜌𝑔 = 0.01,
𝑃 = 𝜑𝑃𝑛 = 𝛼𝜑𝐴 𝑔(0.85𝑓𝑐
′(1 − 𝜌𝑔 ) + 𝑓𝑦 𝜌𝑔)
=> 334.11 = 0.8 × 0.7𝐴 𝑔(0.85 × 3 × (1 − 0.01) + 60 × 0.01)
=> 𝐴 𝑔 = 190.95 𝑖𝑛2 = 13.82 × 13.82, take − 15" × 15"
𝐴 𝑠 = 0.01 × 15" × 15" = 2.25 𝑖𝑛2 = 8 #5
Provide this column at 8th
, 9th
and 10th
story.
Interaction Diagram (ID):
For a column subjected to concentrated load or the loading condition where 10.
h
e the following equations are
the dominating equations for design.
)25.0(85.0 '
gscg ffAP (WSD) , })1(85.0{ '
gygcg ffAP (USD)
But if 10.
h
e then it is an easy practice to take the help of Interaction Diagram.
Interaction diagram is the graphical presentation of the different safe combinations
of load (P) and moment (M). The following equations are necessary this diagram.
sssscn fAfAabfP '''
85.0
)
2
()'
2
()
22
(85.0 ''' h
dfAd
h
fA
ah
abfM sssscn
These equations will be able to give us the Nominal strength curve only. To make
that usable an ACI design strength curve has to be made. Depending on column
geometry, tie/ spiral values of and are important for that. The shaded portion
12. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 12
is the final ID for a typical column. By the help of ID any type of column even shear walls can be designed.
Design of column subjected to Uni-axial moment:
Problem: 7
In a two storied structure an exterior column is to be designed for a service dead load of 142 kips, maximum live
load of 213 kips, dead load moment of 83 kip-ft, live load moment of 124 kip-ft. The minimum live load compatible
with the full the full live load moment is 106 kips, obtained when no live load is placed on the roof but a full live
load is placed on the 2nd floor. Consider column dimension b = 16 in, and h = 20 in.
'
cf =4 ksi, and yf = 60 ksi
(a) Find the column RF for the full live load condition.
(b) Check to ensure that the column is adequate for the condition of no live load on the roof.
Answer:
(a)
kipPu 5612137.11424.1
ftkipMu 3271247.1834.1
Now, ksi
A
P
g
u
75.1
320
561
and
ksi
hA
M
g
u
61.0
20320
12327
. With a cover 2.5 in
75.0
20
520
Having these main information from the graph
039.0g
Therefore,
2
48.122016039.0 inbhA gs
Select 10 No.10 bars.
(b)
kipPu 3791067.11424.1
ftkipMu 327 (as before)
Now, ksi
A
P
g
u
18.1
320
379
and ksi
hA
M
g
u
61.0
20320
12327
. With a cover 2.5 in 75.0
20
520
Having these main information from the graph 032.0g
13. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 13
Therefore,
2
24.102016032.0 inbhA gs
< the result of case (a). So no modification is required.
Problem: 8
A column carries a factored load 518 kip and factored
moment 530 kip-ft. Design the column.
Answer:
As no other information are given so let us assume
03.0g , h = 24 inch and a concrete cover 3 inch
75.0
24
624
.
Now, eccentricity, inch
P
M
e
u
u
3.12
518
12530
,
51.0
24
3.12
h
e
. Using g and e from graph
ksi
A
P
g
u
35.1
2
52.11241603.0 inbhA gs
Select 8 No.11 bars.
What will happen if interaction diagram is not given?????????
Design of column subjected to Bi-axial moment:
Problem: 9
The column shown below has to carry a factored load 275 kips. The is acting with eccentricities "3ye and
"6xe . The material strength
'
cf = 4 ksi, and yf = 60 ksi. Check the adequacy of the trial section.
Answer:
Let us follow the Reciprocal load method.
Considering bending about the Y-axis Considering bending about the Y-axis
;
75.0
20
520
3.0
20
6
h
e
033.0
2012
8
g
s
A
A
;
58.0
12
512
(say = 0.6)
25.0
12
6
h
e
033.0
2012
8
g
s
A
A
inchb
P
bhA u
g
1698.15
2435.1
518
35.1
14. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 14
From Graph A.7
kipPksi
A
P
yOu
g
yOu
40875.1 ,
,
kipPksi
A
P
o
g
o
87665.3
From Graph A.7
kipPksi
A
P
xOu
g
xOu
43282.1 ,
,
kipPksi
A
P
o
g
o
87665.3
Known,
OyOnxOnn PPPP
1111
,,
876
1
408
1
432
11
nP
92.275 un PP kip> the design load (275 kip). Therefore the selection of column section is ok!!
Design for long/slender column:
Problem: 10
A 22X14 inch2 (trial section)column carries an axial load Pd = 125 Md = 105 k-ft, Pl=112 kip, and Ml =96 kip-ft
due to live load. The column is part of a frame that is braced against side-sway ant bent in single curvature about its
major axis. The unsupported column length is lu = 19 ft. The moments at both ends of the column are equal. Design
the column. The material strength
'
cf = 4 ksi, and yf = 60 ksi.
Answer:
15. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 15
kipPu 4.3651127.11254.1
ftkipMu 2.310967.11054.1
Now, ksi
A
P
g
u
2.1
1422
4.365
and ksi
hA
M
g
u
55.0
221422
122.310
. Considering 75.0 from graph
026.0g
Now let us check whether it is slender or not……
)5.34
223.0
12191
(
r
klu
)2211234(1234
2
1
M
M
Therefore it is a slender column.
478.0
4.365
1254.1
7.14.1
4.1
LD
D
d
2
12119435
478.01
1242236054.0
1
4.0
inkip
IE
EI
d
gc
kip
kl
EI
P
u
c 3313
)( 2
2
)(4.014.06.0
4.0
6.0
2
1
ok
M
M
Cm
Moment magnifier 17.1
331375.0
4.365
1
1
75.0
1
c
u
m
nx
P
P
C
Design ftkipMM unsc 3632.31017.1
Again,
Now, ksi
A
P
g
u
2.1
1422
4.365
and ksi
hA
M
g
u
65.0
221422
12363
.
From the same graph 036.0g
2
1.111422036.0 inbhA gs Provide 12 No. 9 bars
16. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 16
Construction of interaction diagram:
Basic equations Manipulation:
s
s
y
E
f
yu
u
b dc
ca 85.0 (At balanced condition bcc )
ysus f
c
cd
Ef
ysus f
c
dc
Ef
''
sssscn fAfAabfP '''
85.0
)
2
()'
2
()
22
(85.0 ''' h
dfAd
h
fA
ah
abfM sssscn
s
s
u
u
b
E
f
dc
ysus f
c
cd
Ef
ysus f
c
dc
Ef
''
sssscn fAfAcbf.P '''2
850
)
2
()'
2
()
2
85.0
(85.0 '''2 h
dfAd
h
fA
ch
bfM sssscn
Problem: 11
a. Construct an interaction diagram of the column section shown at right.
b. Construct an ACI design strength diagram for the same section.
c. Is the column is good choice for a load 540 kips applied at an eccentricity e = 4.44''?
Answer:
At first let us simplify the process:
ssn
ssn
sssscnn
ffccM
ff
c
cM
h
dfAd
h
fA
ch
cbfePM
5.225.22)425.08(8.57
)
2
16
13(25.22)3
2
16
(25.22)
2
85.016
(16585.0
)
2
()'
2
()
2
85.0
(85.0
'
'2
'''2
ssn
ssn
sssscn
ffcP
ffcP
fAfAcbf.P
5.45.480.57
25.2225.2216585.0
850
'
'2
'''2
17. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 17
Table for Interaction diagram:
Condition
c
sf '
s
f ssn ffcP 5.45.480.57 '
ssn ffccM 5.225.22)425.08(8.57 '
B 7.69'' 53.06 413.52 4647.03
T 6.69 47.99 332.64 4423.8
T 5.69 41.13 243.97 4111.16
T 4.69 31.35 142.16 3683.7
T 3.69 16.27 16.5 3087.85
C 9 38.67 616.19 4391.91
C 11 15.82 834.61 3819.99
C 13 0.00 1021.4 3209.72
C 15 -11.60 1189.2 2497.88
Note: The more the pointscan be plotted the better the shape of ID will be.
Interaction diagram and ACI design strength diagram
If the column is subjected to a load 540 kips applied at an eccentricity e = 4.44'' then the corresponding moment is
inchkip 23764.4540 . Form the figure it is seen that the point lies in the ACI recommended safe zone.
There it can be said that the column is a good choice for a load 540 kips applied at an eccentricity e = 4.44''
Column Interaction Diagram0; 1628
2497.88; 1189.2
3209.72; 1021.4
3819.99; 834.61
4391.91; 616.19
4674.03; 413.52
4423.8; 332.64
4111.16; 243.97
3683.7; 142.16
3087.85; 16.5
0; 1139.6
2246.804; 832.44
2673.993; 584.227
3074.337; 431.333
3271.821; 289.464
3096.66; 232.848
2877.812; 170.779
2578.59; 99.512
2161.495; 11.55
2376; 540
1748.516; 832.44
0; 911.68
0
200
400
600
800
1000
1200
1400
1600
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Moment (Kip-inch)
Load(Kip)
18. Lecture note of Dr.H.M.A.Mahzuz on RCC Column
Page- 18
Few questions:
Why is lower for column?
What is the significance of distributed and un-symmetric reinforcement on column?
Lecture Summery for column:
1) Introduction.
2) Several considerations in design of column.
3) Short column:
i) Concentrically loaded column.
ii) Eccentrically loaded column:
a) Uni-axial
b) Bi-axial
4) Long column.
5) Construction of Strength Interaction Diagram.
The End