This document provides a brief history of prestressed concrete, beginning in 1824 with the development of Portland cement. It then outlines several important developments in prestressed concrete technology from the late 19th century through the mid-20th century by innovators from various countries. These include early uses of steel in concrete, prestressing methods like pre-tensioning and post-tensioning, and development of high-strength steel and anchoring systems. It also mentions increased use of prestressed concrete during World War 2 and establishment of professional organizations to support the field.
Post-tensioning is an effective alternative for earthquake-prone regions and dense populations in India. It has advantages over ordinary reinforced concrete like higher seismic resilience, less concrete usage, stiffer foundations, and faster construction. Post-tensioning involves threading steel tendons through ducts and tensioning them after concrete pouring. It provides better crack control, economy, quality, and efficiency. While widely used in other countries, post-tensioning is not yet common in India but has applications in slabs, buildings, and foundations.
Prestressed concrete uses high-strength steel tendons or cables to put concrete members into compression prior to stresses from service loads being applied. This counters the tensile stresses induced by loading and improves the behavior of the concrete. There are two main methods - pretensioning and post-tensioning. Pretensioning involves stressing steel tendons before concrete is cast, while post-tensioning stresses steel tendons after the concrete has hardened. Losses in prestress over time include elastic shortening, anchorage slip, friction, creep, shrinkage, and steel relaxation. Proper material selection and design can minimize these losses and optimize the performance of prestressed concrete.
Prestressed concrete is concrete that is placed under compression using tensioned steel strands, cables, or bars. This is done through either pre-tensioning or post-tensioning. In pre-tensioning, the steel components are tensioned before the concrete is poured, while in post-tensioning, the steel components are tensioned after the concrete has hardened. Prestressed concrete provides benefits over reinforced concrete like lower construction costs, thinner structural elements, and longer spans between supports.
Prestressed concrete is concrete that is placed under compression prior to service loads being applied through tensioning of steel tendons. This counteracts tensile stresses from loads to improve the performance of the concrete. Eugene Freyssinet is considered the father of prestressed concrete, developing techniques like high strength steel wires and conical wedges for post-tensioning in the 1930s-1940s. Prestressing can be through pre-tensioning or post-tensioning, depending on if the steel is tensioned before or after the concrete is cast. Popular post-tensioning systems include Freyssinet, Magnel Blaton, Gifford-Udall, and Lee-McCall methods. Prestressed concrete provides
The document discusses different methods of post-tensioning concrete structures. It describes the Freyssinet system as the first introduced method using steel wires grouped into cables with a helical spring. The Magnel Blaton system stresses wires two at a time using sandwich plates and wedges. The Gifford Udall system uses single wires stressed independently with double-acting jacks and tube or plate anchorages. The Lee McCall system prestresses steel bars using threaded bars tightened with nuts against bearing plates.
Prestressed concrete structures and its applications By Mukesh Singh GhuraiyaMukesh Singh Ghuraiya
1. What is Prestressed??
2. Principle of Prestressed
3. Method of prestressing
4. Prestressed concrete structures
5. Advantages/application of Prestressed concrete
6. Disadvantages of Prestressed concrete
7. Comparison of RCC and Prestressed Concrete Flat Slabs
This document discusses ductile detailing of reinforced concrete (RC) frames according to Indian standards. It explains that detailing involves translating the structural design into the final structure through reinforcement drawings. Good detailing ensures reinforcement and concrete interact efficiently. Key aspects of ductile detailing covered include requirements for beams, columns, and beam-column joints to improve ductility and seismic performance. Specific provisions are presented for longitudinal and shear reinforcement in beams and columns, as well as confining reinforcement and lap splices. The importance of cover and stirrup spacing is also discussed.
Post-tensioning is an effective alternative for earthquake-prone regions and dense populations in India. It has advantages over ordinary reinforced concrete like higher seismic resilience, less concrete usage, stiffer foundations, and faster construction. Post-tensioning involves threading steel tendons through ducts and tensioning them after concrete pouring. It provides better crack control, economy, quality, and efficiency. While widely used in other countries, post-tensioning is not yet common in India but has applications in slabs, buildings, and foundations.
Prestressed concrete uses high-strength steel tendons or cables to put concrete members into compression prior to stresses from service loads being applied. This counters the tensile stresses induced by loading and improves the behavior of the concrete. There are two main methods - pretensioning and post-tensioning. Pretensioning involves stressing steel tendons before concrete is cast, while post-tensioning stresses steel tendons after the concrete has hardened. Losses in prestress over time include elastic shortening, anchorage slip, friction, creep, shrinkage, and steel relaxation. Proper material selection and design can minimize these losses and optimize the performance of prestressed concrete.
Prestressed concrete is concrete that is placed under compression using tensioned steel strands, cables, or bars. This is done through either pre-tensioning or post-tensioning. In pre-tensioning, the steel components are tensioned before the concrete is poured, while in post-tensioning, the steel components are tensioned after the concrete has hardened. Prestressed concrete provides benefits over reinforced concrete like lower construction costs, thinner structural elements, and longer spans between supports.
Prestressed concrete is concrete that is placed under compression prior to service loads being applied through tensioning of steel tendons. This counteracts tensile stresses from loads to improve the performance of the concrete. Eugene Freyssinet is considered the father of prestressed concrete, developing techniques like high strength steel wires and conical wedges for post-tensioning in the 1930s-1940s. Prestressing can be through pre-tensioning or post-tensioning, depending on if the steel is tensioned before or after the concrete is cast. Popular post-tensioning systems include Freyssinet, Magnel Blaton, Gifford-Udall, and Lee-McCall methods. Prestressed concrete provides
The document discusses different methods of post-tensioning concrete structures. It describes the Freyssinet system as the first introduced method using steel wires grouped into cables with a helical spring. The Magnel Blaton system stresses wires two at a time using sandwich plates and wedges. The Gifford Udall system uses single wires stressed independently with double-acting jacks and tube or plate anchorages. The Lee McCall system prestresses steel bars using threaded bars tightened with nuts against bearing plates.
Prestressed concrete structures and its applications By Mukesh Singh GhuraiyaMukesh Singh Ghuraiya
1. What is Prestressed??
2. Principle of Prestressed
3. Method of prestressing
4. Prestressed concrete structures
5. Advantages/application of Prestressed concrete
6. Disadvantages of Prestressed concrete
7. Comparison of RCC and Prestressed Concrete Flat Slabs
This document discusses ductile detailing of reinforced concrete (RC) frames according to Indian standards. It explains that detailing involves translating the structural design into the final structure through reinforcement drawings. Good detailing ensures reinforcement and concrete interact efficiently. Key aspects of ductile detailing covered include requirements for beams, columns, and beam-column joints to improve ductility and seismic performance. Specific provisions are presented for longitudinal and shear reinforcement in beams and columns, as well as confining reinforcement and lap splices. The importance of cover and stirrup spacing is also discussed.
Regarding basics of prestressed such as inventor, types of prestressing systems, methods of prestressing, types of grouting, types of cables used for prestressed structure and method of construction etc..
This document defines and describes various types and concepts related to prestressed concrete. It discusses:
1) Definitions of prestressing steel types like wires, strands, tendons, and cables. It also defines bonded and unbonded tendons.
2) Advantages of prestressing like increased strength, reduced cracking, and suitability for precast construction.
3) Limitations include needing skilled technology and higher material costs.
4) Types of prestressing based on force source, location, sequence, member shape, and direction. It provides examples of pre-tensioning and post-tensioning, internal and external prestressing, and linear and circular prestressing.
This document discusses different systems used for prestressing steel, which are grouped into four categories: mechanical, hydraulic, electrical/thermal, and chemical. It provides details on common tensioning devices within each category. Mechanical devices use weights, pulleys, and screw jacks. Hydraulic jacks ranging from 5-600 tonnes are widely used. Electrical/thermal heating of wires before concreting is another option. Chemical devices use expanding cement. The document also describes several popular prestressing systems including Freyssinet, Gifford Udall, Lee-McCall, Magnel Blaton, BBRV, and Baur Leonhardt.
It is the presentation based on pre- stressed concrete construction which includes each and every point and scope which may be useful to civil engineering students
This document summarizes the precast segmental construction method for bridges. It was first used in Western Europe in the 1950s and involves casting concrete segments off-site, transporting them to the construction location, and erecting them using various methods like balanced cantilever, progressive placement, span-by-span, or incremental launching. Machinery like launchers, girders, cranes, and hydraulic jacks are used for erection. Additional steps include external prestressing and grouting. Precast segmental construction allows for longer spans, faster construction times, increased quality control, and is most suitable for long bridges.
this presentation has animations, play it in ms powerpoint as slideshow for better understanding.
this module includes
a) Introduction
b) Advantages and types of
pre-stressing
c) Pre-stressing systems
d) Materials for pre-stressing
E) PREREQUISITE OF SOM
Prestressed concrete is concrete reinforced with tensioned cables to counteract bending forces. There are losses in prestress over time due to various factors including elastic shortening, friction during tensioning, anchorage slip, and shrinkage and creep of the concrete as well as relaxation of the steel cables. These losses are calculated using step-by-step procedures accounting for time-dependent effects like creep and shrinkage to accurately determine the remaining prestress over the lifespan of the structure.
This document discusses losses in prestressed concrete, including short-term and long-term losses. It describes the differences between pre-tensioned and post-tensioned concrete. Losses include elastic shortening, friction, anchorage slip, creep, shrinkage, and relaxation. Total losses can be 15-20% of the initial prestress. Post-tensioned concrete experiences more types of losses but lower overall losses compared to pre-tensioned concrete. Proper design and materials are needed to minimize losses in prestressed concrete.
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.
Prestressing Concept, Materilas and Prestressing SystemLatif Hyder Wadho
The document discusses prestressing concepts and materials used in prestressed concrete. It describes how prestressing applies an initial compressive stress to concrete prior to service loads to improve strength and durability. Common prestressing materials include high-strength steel strands/wires, which are assembled into tendons and anchored internally or externally before or after concrete casting for pre-tensioning or post-tensioning. Grout is also discussed for transmitting stress between steel and concrete.
This document discusses the design and construction of a post-tensioned concrete slab. It begins with objectives to summarize experience with post-tensioning in building construction and discuss design and construction of post-tensioned flat slab structures. It then provides details on prestressed concrete principles, design of the PT slabs including thickness determination and prestress calculations, and execution steps like formwork, concrete pouring, prestressing, and grouting. Post-tensioning offers advantages over reinforced concrete like longer spans, thinner slabs, and improved seismic performance.
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.
This document discusses retrofitting of structures. Retrofitting is required when structures are damaged or do not meet current seismic standards. It summarizes various retrofitting techniques such as adding shear walls, infill walls, steel bracing, wall thickening, wing walls, mass reduction, base isolation, and jacketing structural elements. It provides examples of existing retrofitted structures in Gujarat. Retrofitting increases strength and ductility but can reduce space and increase foundation loads. Materials discussed include steel, fiber reinforced polymer, and reinforced concrete.
This document discusses column jacketing, which is a method of retrofitting and strengthening existing columns. It involves adding reinforced concrete, steel, or fiber-reinforced polymer around the column. The key steps are preparing the column surface, adding shear keys and reinforcement, applying a bonding agent, and casting the new concrete or installing the jacket. Column jacketing increases the strength and seismic capacity of the column. It improves confinement and increases axial, shear, and foundation load capacity without significant weight addition.
This document discusses prefabricated modular structures. Some key points:
1. Prefabricated structures have standardized components that are produced off-site in a controlled environment and then transported for assembly. This allows for faster, more efficient construction.
2. Precast concrete offers advantages like higher quality, less weather dependency, and unlimited design possibilities compared to site-cast construction.
3. There are different precast systems like large panel, frame, and lift-slab. Precast components include walls, floors, beams, and more.
This document compares reinforced concrete (RC) flat slab and post-tensioned (PT) slab systems. It analyzes slabs of varying panel sizes from 9x9m to 12x12m under different loading conditions using software. The PT slabs were found to have higher moment capacity, require less concrete thickness and rebar, and provide better serviceability than RC slabs. Construction photos of completed PT slab projects are also shown. The document concludes that PT slabs are more cost effective for building floor systems compared to RC flat slabs.
This document discusses prestressed concrete and provides details on:
- The definition and principle of prestressing concrete by applying compression prior to external loads
- Common prestressing methods like hydraulic, mechanical, electrical, and chemical prestressing
- Tests conducted on prestressed concrete components like post-tensioned splices and cast-in-place splices
- Advantages of prestressed concrete like reduced materials and increased strength
- Applications in bridges, buildings, water tanks, and more
- A case study on widening the Harrods Creek Arch Bridge using prestressed concrete
This document discusses different methods of prestressing concrete, including pretensioning and post-tensioning. Pretensioning involves stressing steel tendons before placing concrete around them, while post-tensioning involves stressing tendons after the concrete has cured using hydraulic jacks. Post-tensioning allows for longer spans, thinner slabs, and more architectural freedom compared to conventional reinforced concrete or pretensioned concrete. Common applications of post-tensioning include parking structures, bridges, and building floors and roofs.
Prestressed concrete is concrete in which internal stresses are introduced to counteract external loads. Tendons are stretched elements that impart prestress, and anchorage devices enable the tendons to impart and maintain prestress. There are two main methods - pretensioning, where tendons are tensioned before concrete is cast, and post-tensioning, where tendons are tensioned against hardened concrete. Prestressed concrete uses high-strength materials like cement, concrete, and steel tendons or strands to achieve its compressive strength and durability advantages over reinforced concrete.
Pre stressed concrete- modular construction technologyAnjith Augustine
This document provides an overview of pre-stressed concrete, including its history, types (pre-tensioning and post-tensioning), materials, applications, advantages, and tensioning devices. Some key points include: pre-stressed concrete was developed in the 1930s-1940s and the first pre-stressed concrete bridge was built in India in 1948; it uses high-strength steel tendons to put concrete under compression and improve its tensile strength; common applications include bridges, buildings, and other structures; and advantages are increased strength, reduced cracking, and lighter/thinner designs.
Regarding basics of prestressed such as inventor, types of prestressing systems, methods of prestressing, types of grouting, types of cables used for prestressed structure and method of construction etc..
This document defines and describes various types and concepts related to prestressed concrete. It discusses:
1) Definitions of prestressing steel types like wires, strands, tendons, and cables. It also defines bonded and unbonded tendons.
2) Advantages of prestressing like increased strength, reduced cracking, and suitability for precast construction.
3) Limitations include needing skilled technology and higher material costs.
4) Types of prestressing based on force source, location, sequence, member shape, and direction. It provides examples of pre-tensioning and post-tensioning, internal and external prestressing, and linear and circular prestressing.
This document discusses different systems used for prestressing steel, which are grouped into four categories: mechanical, hydraulic, electrical/thermal, and chemical. It provides details on common tensioning devices within each category. Mechanical devices use weights, pulleys, and screw jacks. Hydraulic jacks ranging from 5-600 tonnes are widely used. Electrical/thermal heating of wires before concreting is another option. Chemical devices use expanding cement. The document also describes several popular prestressing systems including Freyssinet, Gifford Udall, Lee-McCall, Magnel Blaton, BBRV, and Baur Leonhardt.
It is the presentation based on pre- stressed concrete construction which includes each and every point and scope which may be useful to civil engineering students
This document summarizes the precast segmental construction method for bridges. It was first used in Western Europe in the 1950s and involves casting concrete segments off-site, transporting them to the construction location, and erecting them using various methods like balanced cantilever, progressive placement, span-by-span, or incremental launching. Machinery like launchers, girders, cranes, and hydraulic jacks are used for erection. Additional steps include external prestressing and grouting. Precast segmental construction allows for longer spans, faster construction times, increased quality control, and is most suitable for long bridges.
this presentation has animations, play it in ms powerpoint as slideshow for better understanding.
this module includes
a) Introduction
b) Advantages and types of
pre-stressing
c) Pre-stressing systems
d) Materials for pre-stressing
E) PREREQUISITE OF SOM
Prestressed concrete is concrete reinforced with tensioned cables to counteract bending forces. There are losses in prestress over time due to various factors including elastic shortening, friction during tensioning, anchorage slip, and shrinkage and creep of the concrete as well as relaxation of the steel cables. These losses are calculated using step-by-step procedures accounting for time-dependent effects like creep and shrinkage to accurately determine the remaining prestress over the lifespan of the structure.
This document discusses losses in prestressed concrete, including short-term and long-term losses. It describes the differences between pre-tensioned and post-tensioned concrete. Losses include elastic shortening, friction, anchorage slip, creep, shrinkage, and relaxation. Total losses can be 15-20% of the initial prestress. Post-tensioned concrete experiences more types of losses but lower overall losses compared to pre-tensioned concrete. Proper design and materials are needed to minimize losses in prestressed concrete.
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.
Prestressing Concept, Materilas and Prestressing SystemLatif Hyder Wadho
The document discusses prestressing concepts and materials used in prestressed concrete. It describes how prestressing applies an initial compressive stress to concrete prior to service loads to improve strength and durability. Common prestressing materials include high-strength steel strands/wires, which are assembled into tendons and anchored internally or externally before or after concrete casting for pre-tensioning or post-tensioning. Grout is also discussed for transmitting stress between steel and concrete.
This document discusses the design and construction of a post-tensioned concrete slab. It begins with objectives to summarize experience with post-tensioning in building construction and discuss design and construction of post-tensioned flat slab structures. It then provides details on prestressed concrete principles, design of the PT slabs including thickness determination and prestress calculations, and execution steps like formwork, concrete pouring, prestressing, and grouting. Post-tensioning offers advantages over reinforced concrete like longer spans, thinner slabs, and improved seismic performance.
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.
This document discusses retrofitting of structures. Retrofitting is required when structures are damaged or do not meet current seismic standards. It summarizes various retrofitting techniques such as adding shear walls, infill walls, steel bracing, wall thickening, wing walls, mass reduction, base isolation, and jacketing structural elements. It provides examples of existing retrofitted structures in Gujarat. Retrofitting increases strength and ductility but can reduce space and increase foundation loads. Materials discussed include steel, fiber reinforced polymer, and reinforced concrete.
This document discusses column jacketing, which is a method of retrofitting and strengthening existing columns. It involves adding reinforced concrete, steel, or fiber-reinforced polymer around the column. The key steps are preparing the column surface, adding shear keys and reinforcement, applying a bonding agent, and casting the new concrete or installing the jacket. Column jacketing increases the strength and seismic capacity of the column. It improves confinement and increases axial, shear, and foundation load capacity without significant weight addition.
This document discusses prefabricated modular structures. Some key points:
1. Prefabricated structures have standardized components that are produced off-site in a controlled environment and then transported for assembly. This allows for faster, more efficient construction.
2. Precast concrete offers advantages like higher quality, less weather dependency, and unlimited design possibilities compared to site-cast construction.
3. There are different precast systems like large panel, frame, and lift-slab. Precast components include walls, floors, beams, and more.
This document compares reinforced concrete (RC) flat slab and post-tensioned (PT) slab systems. It analyzes slabs of varying panel sizes from 9x9m to 12x12m under different loading conditions using software. The PT slabs were found to have higher moment capacity, require less concrete thickness and rebar, and provide better serviceability than RC slabs. Construction photos of completed PT slab projects are also shown. The document concludes that PT slabs are more cost effective for building floor systems compared to RC flat slabs.
This document discusses prestressed concrete and provides details on:
- The definition and principle of prestressing concrete by applying compression prior to external loads
- Common prestressing methods like hydraulic, mechanical, electrical, and chemical prestressing
- Tests conducted on prestressed concrete components like post-tensioned splices and cast-in-place splices
- Advantages of prestressed concrete like reduced materials and increased strength
- Applications in bridges, buildings, water tanks, and more
- A case study on widening the Harrods Creek Arch Bridge using prestressed concrete
This document discusses different methods of prestressing concrete, including pretensioning and post-tensioning. Pretensioning involves stressing steel tendons before placing concrete around them, while post-tensioning involves stressing tendons after the concrete has cured using hydraulic jacks. Post-tensioning allows for longer spans, thinner slabs, and more architectural freedom compared to conventional reinforced concrete or pretensioned concrete. Common applications of post-tensioning include parking structures, bridges, and building floors and roofs.
Prestressed concrete is concrete in which internal stresses are introduced to counteract external loads. Tendons are stretched elements that impart prestress, and anchorage devices enable the tendons to impart and maintain prestress. There are two main methods - pretensioning, where tendons are tensioned before concrete is cast, and post-tensioning, where tendons are tensioned against hardened concrete. Prestressed concrete uses high-strength materials like cement, concrete, and steel tendons or strands to achieve its compressive strength and durability advantages over reinforced concrete.
Pre stressed concrete- modular construction technologyAnjith Augustine
This document provides an overview of pre-stressed concrete, including its history, types (pre-tensioning and post-tensioning), materials, applications, advantages, and tensioning devices. Some key points include: pre-stressed concrete was developed in the 1930s-1940s and the first pre-stressed concrete bridge was built in India in 1948; it uses high-strength steel tendons to put concrete under compression and improve its tensile strength; common applications include bridges, buildings, and other structures; and advantages are increased strength, reduced cracking, and lighter/thinner designs.
The document discusses the history and development of pre-stressed concrete. It notes that Eugene Freyssinet is often referred to as the Father of Pre-stressed concrete and developed techniques like high-strength steel wires and conical wedges in the late 1930s. It provides examples of early pre-stressed concrete structures like the Pamban Road Bridge in India. It also discusses the basic concepts of pre-stressing including the materials used and different types of pre-stressing.
The document provides an overview of prestressed concrete structures including:
- Definitions of prestressing where internal stresses counteract external loads.
- The key terminology used including tendons, anchorage, pretensioning vs post-tensioning.
- The materials used including cement, concrete, and steel types.
- The stages of loading and advantages of prestressing over reinforced concrete.
- Details of pretensioning and post-tensioning systems including equipment, processes, and differences between the two methods.
Prestressing is a technique where tension is applied to concrete before hardening to improve its performance. There are two main types - pre-tensioning and post-tensioning. Pre-tensioning involves tensioning steel tendons before casting concrete, while post-tensioning tensions tendons after casting. There are losses in prestress over time from factors like elastic shortening, shrinkage, creep, and steel relaxation. Proper materials and design are needed to account for these losses and ensure structures perform as intended.
This document provides an overview of pre-stressed and precast concrete. It discusses basic concepts like pre-stressing, uses of pre-stressed concrete, materials used including high-strength concrete and steel, and methods of prestressing like pre-tensioning and post-tensioning. It also covers topics like tendon profiles, advantages and disadvantages of pre-stressed concrete, losses in prestressing, types of prestressing steel, properties of prestressing steel, and use of non-prestressed reinforcement. The document is submitted by 5 students and contains 15 chapters with information on concepts, introduction, early introduction, uses, the basic idea, methods, profiles, advantages, disadvantages, losses, materials, types of
Reinforced cement concrete (RCC) is a composite material made of cement concrete reinforced with steel bars. Some key points:
- François Coignet built the first reinforced concrete structure, a four story house in Paris in 1853.
- RCC is used in the construction of columns, beams, footings, slabs, dams, water tanks, tunnels, bridges, walls and towers due to its high strength and durability.
- The steel reinforcement provides tensile strength, while the concrete primarily resists compressive forces and protects the steel from corrosion. Together they form a very strong, stable structural material.
These presentations were created during the 2016–2021 B.Arch programme.
Please refer to the references column at the end of each presentation for the information within.
This document discusses prestressed concrete, including:
- The basic concepts of prestressing including using metal bands, pre-tensioned spokes, and introducing stresses to counteract external loads.
- Design concepts like losses in prestressing structures from elastic shortening, creep, shrinkage, relaxation, friction, and anchorage slip.
- Provisions for prestressing in the Indian Road Congress Bridge Code and Indian Standard Code.
- Construction aspects like casting of girders, post-tensioning work, and load testing of structures.
The document discusses stress ribbon bridges. It begins by explaining that a stress ribbon bridge is a tension structure similar to a suspension bridge, with suspension cables embedded in the deck which follows a catenary arc. Unlike simple suspension bridges, the ribbon is stressed in compression which adds stiffness. Supports provide upward thrusting arcs to change the grade between spans. Stress ribbon bridges are typically reinforced concrete with steel tensioning cables to prevent excessive flexing from vehicle traffic. Fewer than 50 have been built worldwide due to their rare design.
This document provides an introduction to prestressed concrete, including:
- Prestressing concrete involves applying an initial compressive load to counteract tensile stresses during use. Ancient examples include metal bands on wood.
- Prestressing provides advantages over reinforced concrete like reduced cracking, increased strength and stiffness, and suitability for precast construction.
- It describes prestressing materials, common systems like pre-tensioning and post-tensioning, and concepts in the analysis and design of prestressed concrete like stress conditions and load balancing.
Tall Structures
Usually structure or building having height more than 80m is considered as a tall structure.
Generally tall structure may be defined as one that because of its height it is affected by lateral.
Classification: 1. Multi storeyedresidential building.
2. Multi storeyedcommercial building.
3. Tall chimneys.
4. Transmission Towers
5. Cooling towers
Prestressed Concrete
•Prestressis defined as a method of applying pre-compression to control the stresses resulting due to external loads below the neutral axis of the beam tension developed due to external load which is more than the permissible limits of the plain concrete.
Demolition
•The action or process of destroying(demolishing)the building or other structures.
•In congested area, in particular, the quality of demolition technique becomes an essential element which determines the success of revitalization of city.
•In addition to efficiency in demolition, strategies must be adopted to avoid noise, vibration and dust which affect the surrounding environment and there must be efficient disposal of waste products
This document discusses prestressed concrete, which uses tensioned steel cables or bars to put concrete members into compression and increase their strength. It describes three main methods: pre-tensioned concrete where the steel is tensioned before the concrete is cast; bonded post-tensioned concrete where steel is tensioned after casting to compress the concrete; and unbonded post-tensioned concrete where greased steel is used to allow individual adjustment. Applications include buildings, bridges, nuclear reactors and earthquake resistant structures. Advantages are lower costs, thinner members, and increased spans.
The document provides information on methods of prestressing in concrete, including pretensioning and post-tensioning. It discusses:
- Pretensioning involves stressing steel tendons before the concrete is cast around them.
- Post-tensioning involves stressing steel tendons after the concrete has cured using jacks, then grouting the voids.
- Both methods put the concrete in compression and increase its strength and durability compared to conventional reinforced concrete.
The document provides information on methods of prestressing concrete, including pretensioning and post-tensioning. It discusses:
- Pretensioning involves stressing steel tendons before the concrete is cast around them.
- Post-tensioning involves stressing steel tendons after the concrete has cured using jacks, then grouting the voids.
- Both methods put the concrete in compression and increase its strength and durability compared to conventional reinforced concrete.
Reinforced concrete columns and beams are important structural elements that carry compressive and bending loads respectively. Columns can be categorized as short or long based on their height-width ratio and as spiral or tied columns based on their shape. Beams are classified based on their supports as simply supported, fixed, continuous, or cantilever beams. The construction of RCC columns and beams involves laying reinforcement, forming the structure, and pouring concrete to create these load-bearing elements.
This document provides information on a syllabus for a course on prestressed concrete. It outlines the course objectives which are to understand the principles, necessity, techniques, losses, and analysis and design of prestressed concrete members. The course outcomes are for students to acquire knowledge on the evolution of prestressing, prestressing techniques, and skills in analyzing and designing prestressed structural elements per code provisions. The syllabus then outlines 5 units that will be covered which include introduction, methods and systems, losses of prestress, flexure, shear, transfer of prestress, composite beams, and deflections. Relevant textbooks and codes are also listed.
This document provides information on prestressed concrete and the Freyssinet prestressing system. It discusses the principles of prestressing, including pre-tensioning and post-tensioning methods. It also describes the key components of the Freyssinet post-tensioning system, including prestressing steels, anchorages, ducts, supports, and couplers. The anchorages can be mono-strand or multi-strand and are designed to transfer prestressing forces to the concrete structure.
The document provides an introduction to the Finite Element Method (FEM). It discusses the history and development of FEM from the 1950s to the present. It outlines the basic concepts of FEM including discretization of the domain into finite elements connected at nodes, and the approximation of displacements within each element. The document also discusses minimum potential energy theory, which is the variational principle that FEM is based on. Example problems and a tutorial are mentioned. Advantages of FEM include its ability to model complex geometries and loading, while disadvantages include increased computational time and memory requirements compared to other methods.
This document outlines 25 topics related to the finite element method (FEM) including:
1) The historical development and general steps of FEM
2) The advantages and disadvantages of FEM and common engineering applications
3) Methods for deriving element stiffness matrices and equations
4) Concepts like discretization, shape functions, element types, and node positioning
5) Specific shape functions and required nodes for linear and triangular elements
6) The theorem of stationary potential energy and Raleigh-Ritz approximation method
7) Developing differential equations of equilibrium for 2D and 3D stress systems
8) Developing strain-displacement and stress-strain relationships for elastic bodies
9) Distinguishing between plane
The document outlines the questions for a finite element method exam, with the deadline being July 28, 2016. It includes 7 questions assessing various concepts in finite element analysis, such as the steps in FEM, simplex and complex elements, the theorem of stationary potential energy, differential equations of equilibrium, strain-displacement relationships, and plane stress/strain problems. It also includes a problem to determine displacements and reactions for a system under the principle of minimum potential energy.
A system of prestressing involves tensioning tendons and securing them firmly to concrete. There are two main types: pre-tensioning and post-tensioning. Pre-tensioning involves pulling tendons tight between anchored abutments before concrete is poured. The Hoyer or long-line pre-tensioning system uses bulkheads to stretch wires over which molds are placed for concrete pouring. The Freyssinet system was the first post-tensioning method, using a cable of high-strength wires grouted into a duct within the concrete beam. Wires are anchored using conical plugs pushed into holes in concrete cylinders after jacking. The Magnel Blaton system tensions wires in pairs using sandwich plates
The document discusses different systems of prestressing including the Magnel Blaton System and the Gifford Udall System. It mentions these systems and notes there is continued information about each one.
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Drought is an extended period of below average precipitation that can cause water shortages and impact ecosystems, agriculture, and local economies. It is defined as rainfall 20% or more below normal levels for a region. Drought leads to economic impacts like agricultural losses, higher costs for irrigation and fuel, and reduced business from industries tied to farming. It also causes environmental impacts such as loss of wildlife habitat and food sources, increased wildfires, and erosion. Socially, drought can negatively impact public health and safety, as well as cause conflicts over limited water resources. Major droughts in India have historically led to severe famines that caused millions of deaths from starvation and hunger.
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1) Natural disasters have been increasing since 1960 due to better recording, monitoring and global communication.
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The document discusses different types of natural and man-made disasters. It categorizes natural disasters as meteorological, topographical/geological, and environmental. Man-made disasters are categorized as technological, industrial, and warfare. Specific natural disasters discussed include floods, cyclones, earthquakes, tsunamis, volcanoes, landslides, and more. Man-made disasters include accidents, pollution, industrial accidents, and wars. The document also provides details on the causes and impacts of various disasters like earthquakes, floods, oil spills, and epidemics. Classification schemes for different types of disasters are presented.
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This document describes an experiment to determine total dissolved and suspended solids in a water sample. The procedure involves filtering a water sample and evaporating the filtrate to determine total dissolved solids based on residue weight. Total suspended solids are determined by filtering a sample through a weighed filter and calculating residue weight. The results are used to classify water quality and evaluate treatment effectiveness.
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Information and Communication Technology in EducationMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 2)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐈𝐂𝐓 𝐢𝐧 𝐞𝐝𝐮𝐜𝐚𝐭𝐢𝐨𝐧:
Students will be able to explain the role and impact of Information and Communication Technology (ICT) in education. They will understand how ICT tools, such as computers, the internet, and educational software, enhance learning and teaching processes. By exploring various ICT applications, students will recognize how these technologies facilitate access to information, improve communication, support collaboration, and enable personalized learning experiences.
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐫𝐞𝐥𝐢𝐚𝐛𝐥𝐞 𝐬𝐨𝐮𝐫𝐜𝐞𝐬 𝐨𝐧 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐫𝐧𝐞𝐭:
-Students will be able to discuss what constitutes reliable sources on the internet. They will learn to identify key characteristics of trustworthy information, such as credibility, accuracy, and authority. By examining different types of online sources, students will develop skills to evaluate the reliability of websites and content, ensuring they can distinguish between reputable information and misinformation.
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7. 1.1.3 Brief History
1824 Aspdin, J., (England)
Obtained a patent for the manufacture of Portland
cement.
1857 Monier, J., (France)
Introduced steel wires in concrete to make flower
pots, pipes, arches and slabs.
1886 Jackson, P. H., (USA)
Introduced the concept of tightening steel tie rods
in artificial stone and concrete arches.
8. • 1888 Doehring, C. E. W., (Germany)
Manufactured concrete slabs and small beams
with embedded tensioned steel.
• 1908 Stainer, C. R., (USA)
Recognised losses due to shrinkage and creep,
and suggested retightening the rods to recover
lost prestress.
• 1923 Emperger, F., (Austria)
Developed a method of winding and pre-
tensioning high tensile steel wires around
concrete pipes.
9. • 1924 Hewett, W. H., (USA)
Introduced hoop-stressed horizontal
reinforcement around walls of concrete tanks
through the use of turnbuckles.
• 1925 Dill, R. H., (USA)
Used high strength unbonded steel rods. The
rods were tensioned and anchored after
hardening of the concrete.
10. • 1926 Eugene Freyssinet (France)
Used high tensile steel wires, with ultimate
strength as high as 1725 MPa and yield stress
over 1240 MPa. In 1939, he developed conical
wedges for end anchorages for post-tensioning
and developed double-acting jacks. He is often
referred to as the Father of Prestressed concrete.
• 1938 Hoyer, E., (Germany)
Developed ‘long line’ pre-tensioning method.
• 1940 Magnel, G., (Belgium)
Developed an anchoring system for post-
tensioning, using flat wedges.
11. • During the Second World War, applications of
prestressed and precast concrete increased
rapidly
• Guyon, Y., (France) built numerous prestressed
concrete bridges in western and central
Europe. Abeles, P. W., (England) introduced
the concept of partial prestressing. Leonhardt,
F., (Germany), Mikhailor, V., (Russia) and Lin, T.
Y., (USA) are famous in the field of prestressed
concrete.
12. • The International Federation for Prestressing
(FIP), a professional organisation in Europe was
established in 1952. The Precast/Prestressed
Concrete Institute (PCI) was established in USA in
1954.
• In India, the applications of prestressed concrete
diversified over the years. The first prestressed
concrete bridge was built in 1948 under the
Assam Rail Link Project. Among bridges, the
Pamban Road Bridge at Rameshwaram,
Tamilnadu, remains a classic example of the use
of prestressed concrete girders.
19. Definitions
The terms commonly used in prestressed concrete are
explained. The terms are placed in groups as per usage.
Forms of Prestressing Steel
• Wires : Prestressing wire is a single unit made of steel.
• Strands: Two, three or seven wires are wound to form a
prestressing strand.
• Tendon: A group of strands or wires are wound to form
a prestressing tendon.
• Cable : A group of tendons form a prestressing cable.
• Bars : A cable can be made up of a single steel bar. The
diameter of a bar is much larger than that of a wire.
20. Nature of Concrete-Steel Interface
Bonded tendon
When there is adequate bond between the
prestressing tendon and concrete, it is called a
bonded tendon. Pre-tensioned and grouted post-
tensioned tendons are bonded tendons.
Unbonded tendon
When there is no bond between the prestressing
tendon and concrete, it is called unbonded
tendon. When grout is not applied after post-
tensioning, the tendon is an unbonded tendon.
21. Stages of Loading
The analysis of prestressed members can be different for
the different stages of loading. The stages of loading
are as follows.
1) Initial : It can be subdivided into two stages.
a) During tensioning of steel
b) At transfer of prestress to concrete.
2) Intermediate : This includes the loads during
transportation of the prestressed members.
3) Final : It can be subdivided into two stages.
a) At service, during operation.
b) At ultimate, during extreme events.
22. Advantages of Prestressing
The prestressing of concrete has several
advantages as compared to traditional
reinforced concrete (RC) without prestressing.
A fully prestressed concrete member is usually
subjected to compression during service life.
This rectifies several deficiencies of concrete.
23. Advantages of Prestressing
1) Section remains uncracked under service loads
• Reduction of steel corrosion
– Increase in durability.
• Full section is utilised
– Higher moment of inertia (higher stiffness)
– Less deformations (improved serviceability).
• Suitable for use in pressure vessels, liquid retaining
structures.
• Increases the shear capacity.
• Improved performance (resilience) under dynamic and
fatigue loading.
24. 2) High span-to-depth ratios
• Larger spans possible with prestressing (bridges,
buildings with large column-free spaces)
• Typical values of span-to-depth ratios in slabs are given
below.
Non-prestressed slab 28:1
Prestressed slab 45:1
For the same span, less depth compared to RC member.
• Reduction in self weight
• More aesthetic appeal due to slender sections
• More economical sections.
25. 3) Suitable for precast construction The advantages of
precast construction are as follows.
• Rapid construction
• Better quality control
• Reduced maintenance
• Suitable for repetitive construction
• Multiple use of formwork
⇒ Reduction of formwork
• Availability of standard shapes.
27. Limitations of Prestressing
• Prestressing needs skilled technology. Hence,
it is not as common as reinforced concrete.
• The use of high strength materials is costly.
• There is additional cost in auxiliary
equipments.
• There is need for quality control and
inspection.
28. Types of Prestressing
Source of prestressing force
This classification is based on the method
by which the prestressing force is generated.
There are four sources of prestressing force:
Mechanical, hydraulic, electrical & Chemical.
29. External or internal prestressing
This classification is based on the location
of the prestressing tendon with respect to the
concrete section.
30. Pre-tensioning or post-tensioning
This is the most important classification
and is based on the sequence of casting the
concrete and applying tension to the tendons.
31. Linear or circular prestressing
This classification is based on the shape of
the member prestressed.
Full, limited or partial prestressing
Based on the amount of prestressing force,
three types of prestressing are defined.
32. Uniaxial, biaxial or multi-axial prestressing
As the names suggest, the classification is
based on the directions of prestressing a
member.
33. Stages of Pre-tensioning
• In pre-tensioning system, the high-strength
steel tendons are pulled between two end
abutments (also called bulkheads) prior to the
casting of concrete. The abutments are fixed
at the ends of a prestressing bed.
• Once the concrete attains the desired strength
for prestressing, the tendons are cut loose
from the abutments.
34. The prestress is transferred to the concrete from the tendons,
due to the bond between them. During the transfer of prestress,
the member undergoes elastic shortening. If the tendons are
located eccentrically, the member is likely to bend and deflect
(camber).
The various stages of the pre-tensioning operation are
summarised as follows.
1) Anchoring of tendons against the end abutments
2) Placing of jacks
3) Applying tension to the tendons
4) Casting of concrete
5) Cutting of the tendons.
35.
36. Advantages of Pre-tensioning
The relative advantages of pre-tensioning as
compared to post-tensioning are as follows.
• Pre-tensioning is suitable for precast members
produced in bulk.
• In pre-tensioning large anchorage device is not
present.
37. Disadvantages of Pre-tensioning
The relative disadvantages are as follows.
• A prestressing bed is required for the pre-
tensioning operation.
• There is a waiting period in the prestressing
bed, before the concrete attains sufficient
strength.
• There should be good bond between concrete
and steel over the transmission length.
38. Devices
The essential devices for pre-tensioning are as
follows.
• Prestressing bed
• End abutments
• Shuttering / mould
• Jack
• Anchoring device
• Harping device (optional)
39. Jacks
The jacks are used to apply tension to the
tendons. Hydraulic jacks are commonly used.
These jacks work on oil pressure generated by
a pump. The principle behind the design of
jacks is Pascal’s law. The load applied by a jack
is measured by the pressure reading from a
gauge attached to the oil inflow or by a
separate load cell.
40.
41. Anchoring Devices
Anchoring devices are often made on the
wedge and friction principle. In pre-tensioned
members, the tendons are to be held in
tension during the casting and hardening of
concrete. Here simple and cheap quick-release
grips are generally adopted
42.
43. Harping Devices
The tendons are frequently bent, except in
cases of slabs-on-grade, poles, piles etc. The
tendons are bent (harped) in between the
supports with a shallow sag as shown below.
44.
45. Stages of Post-tensioning
In post-tensioning systems, the ducts for the
tendons (or strands) are placed along with the
reinforcement before the casting of concrete. The
tendons are placed in the ducts after the casting
of concrete. The duct prevents contact between
concrete and the tendons during the tensioning
operation.
Unlike pre-tensioning, the tendons are pulled
with the reaction acting against the hardened
concrete.
46.
47.
48. The various stages of the post-tensioning
operation are summarised as follows :
1) Casting of concrete.
2) Placement of the tendons.
3) Placement of the anchorage block and jack.
4) Applying tension to the tendons.
5) Seating of the wedges.
6) Cutting of the tendons.
49.
50. Advantages of Post-tensioning
The relative advantages of post-tensioning as
compared to pre-tensioning are as follows:
• Post-tensioning is suitable for heavy cast-in-
place members.
• The waiting period in the casting bed is less.
• The transfer of prestress is independent of
transmission length.
51. Disadvantage of Post-tensioning
The relative disadvantage of post-
tensioning as compared to pre-tensioning is
the requirement of anchorage device and
grouting equipment.
52. Devices
The essential devices for post-tensioning are as
follows.
1) Casting bed
2) Mould/Shuttering
3) Ducts
4) Anchoring devices
5) Jacks
6) Couplers (optional)
7) Grouting equipment (optional).
53.
54. Anchoring Devices
In post-tensioned members the anchoring
devices transfer the prestress to the concrete.
The devices are based on the following
principles of anchoring the tendons.
1) Wedge action
2) Direct bearing
3) Looping the wires
59. Couplers
The couplers are used to connect strands
or bars. They are located at the junction of the
members, for example at or near columns in
post-tensioned slabs, on piers in post-
tensioned bridge decks
60.
61. Grouting
Grouting can be defined as the filling of duct,
with a material that provides an anti-corrosive
alkaline environment to the prestressing steel
and also a strong bond between the tendon and
the surrounding grout.
The major part of grout comprises of water
and cement, with a water-to-cement ratio of
about 0.5, together with some water-reducing
admixtures, expansion agent and pozzolans.
70. Concrete
Constituents of Concrete:
Concrete is a composite material composed of
gravels or crushed stones (coarse aggregate),
sand (fine aggregate) and hydrated cement
(binder).
71.
72. Aggregate
The coarse aggregate are granular materials
obtained from rocks and crushed stones. They
may be also obtained from synthetic material
like slag, shale, fly ash and clay for use in light-
weight concrete.
The sand obtained from river beds or quarries
is used as fine aggregate. The fine aggregate
along with the hydrated cement paste fill the
space between the coarse aggregate.
73. The important properties of aggregate are as
follows:
1) Shape and texture
2) Size gradation
3) Moisture content
4) Specific gravity
5) Unit weight
6) Durability and absence of deleterious materials
74. The requirements of aggregate is covered in Section
4.2 of IS:1343 - 1980.
The nominal maximum coarse aggregate size is
limited by the lowest of the following quantities.
1) 1/4 times the minimum thickness of the member
2) Spacing between the tendons/strands minus 5
mm
3) 40 mm.
75. The deleterious substances that should be
limited in aggregate are clay lumps, wood,
coal, chert, silt, rock dust (material finer than
75 microns), organic material, unsound and
friable particles.
76. Cement
In present day concrete, cement is a mixture of lime stone and
clay heated in a kiln to 1400 - 1600ºC. The types of cement
permitted by IS:1343 - 1980 (Clause 4.1) for prestressed
applications are the following.
The information is revised as per IS:456 - 2000, Plain and
Reinforced – Concrete Code of Practice.
1) Ordinary Portland cement confirming to IS:269 - 1989,
Ordinary Portland Cement, 33 Grade – Specification.
2) Portland slag cement confirming to IS:455 - 1989, Portland
Slag Cement – Specification, but with not more than 50%
slag content.
3) Rapid-hardening Portland cement confirming to IS:8041 -
1990, Rapid Hardening Portland Cement – Specification.
77. Water
The water should satisfy the requirements of
Section 5.4 of IS:456 - 2000.
“Water used for mixing and curing shall be clean
and free from injurious amounts of oils, acids,
alkalis, salts, sugar, organic materials or other
substances that may be deleterious to
concrete and steel”.
78. Admixtures
IS:1343 - 1980 allows to use admixtures that conform
to IS:9103 - 1999, Concrete Admixtures – Specification. The
admixtures can be broadly divided into two types:
chemical admixtures and mineral admixtures. The
common chemical admixtures are as follows.
1) Air-entraining admixtures
2) Water reducing admixtures
3) Set retarding admixtures
4) Set accelerating admixtures
5) Water reducing and set retarding admixtures
6) Water reducing and set accelerating admixtures.
79. The common mineral admixtures are as follows.
1) Fly ash
2) Ground granulated blast-furnace slag
3) Silica fumes
4) Rice husk ash
5) Metakoline
These are cementitious and pozzolanic materials.
80. Properties of Hardened Concrete
The concrete in prestressed applications has to be
of good quality. It requires the following
attributes.
1) High strength with low water-to-cement ratio
2) Durability with low permeability, minimum
cement content and proper mixing, compaction
and curing
3) Minimum shrinkage and creep by limiting the
cement content.
81. 1) Strength of concrete
2) Stiffness of concrete
3) Durability of concrete
4) High performance concrete
5) Allowable stresses in concrete
82. Strength of Concrete
Compressive Strength
The compressive strength of concrete is
given in terms of the characteristic
compressive strength of 150 mm size cubes
tested at 28 days (fck). The characteristic
strength is defined as the strength of the
concrete below which not more than 5% of
the test results are expected to fall.
83. The following sections describe the properties with
reference to IS:1343 - 1980. The strength of concrete
is required to calculate the strength of the members.
For prestressed concrete applications, high strength
concrete is required for the following reasons.
1) To sustain the high stresses at anchorage regions.
2) To have higher resistance in compression, tension,
shear and bond.
3) To have higher stiffness for reduced deflection.
4) To have reduced shrinkage cracks.
84. The sampling and strength test of concrete
are as per Section 15 of IS:1343 - 1980. The
grades of concrete are explained in Table 1 of
the Code.
The minimum grades of concrete for prestressed
applications are as follows.
• 30 MPa for post-tensioned members
• 40 MPa for pre-tensioned members.
The maximum grade of concrete is 60 MPa.
85. Since at the time of publication of IS:1343
in 1980, the properties of higher strength
concrete were not adequately documented, a
limit was imposed on the maximum strength.
It is expected that higher strength concrete
may be used after proper testing.
86. The increase in strength with age as given
in IS:1343 - 1980, is not observed in present
day concrete that gains substantial strength
in 28 days. Hence, the age factor given in
Clause 5.2.1 should not be used. It has been
removed from IS:456 - 2000.
87. Tensile Strength
The tensile strength of concrete can be expressed
as follows.
1) Flexural tensile strength: It is measured by
testing beams under 2 point loading (also called 4
point loading including the reactions).
2) Splitting tensile strength: It is measured by
testing cylinders under diametral compression.
3) Direct tensile strength: It is measured by testing
rectangular specimens under direct tension.
88. Stiffness of Concrete
The stiffness of concrete is required to estimate
the deflection of members. The stiffness is given by the
modulus of elasticity. For a non-linear stress (fc) versus
strain (εc) behaviour of concrete the modulus can be
initial, tangential or secant modulus.
IS:1343 - 1980 recommends a secant modulus at a
stress level of about 0.3fck. The modulus is expressed
in terms of the characteristic compressive strength
and not the design compressive strength. The
following figure shows the secant modulus in the
compressive stress-strain curve for concrete.