This document provides an introduction to singly reinforced concrete beam sections. It discusses the stresses induced in beams due to bending moments, including compression and tension zones. It defines key terms like the neutral axis and neutral surface. The document then covers assumptions made in design, calculation of the moment of resistance considering the forces of compression and tension, and limiting the depth of the neutral axis to prevent brittle failure. It also discusses under-reinforced and over-reinforced beams and their failure modes. Tables provide limiting values for moment capacity, depth of neutral axis, and steel reinforcement percentages for different concrete and steel grades.
The document discusses properties and testing of concrete. It provides information on the constituents of concrete including cement, coarse aggregate, fine aggregate, and water. It also discusses properties of concrete and reinforcements, including their relatively high compressive strength and lower tensile strength. Various tests performed on concrete are mentioned, including tests on workability, compressive strength, flexural strength, and fresh/hardened concrete. Design philosophies for reinforced concrete include the working stress method, ultimate strength method, and limit state method.
The document provides details on the design procedure for beams. It discusses estimating loads, analyzing beams to determine shear forces and bending moments, and designing beams. The design process involves selecting the beam size and shape, calculating the effective span, determining critical moments and shears, selecting reinforcement, and checking requirements such as shear capacity, deflection limits, and development lengths. An example problem demonstrates designing a singly reinforced concrete beam with a span of 5 meters to support a working live load of 25 kN/m.
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.
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 discusses limit state design of reinforced concrete structures. It introduces limit states as conditions where the structure becomes unfit for use, including limit states of strength and serviceability. Limit state design involves characterizing loads and resistances as random variables and using partial safety factors on loads and resistances to achieve a target reliability. The document outlines the general principles of limit state design according to Indian Standard code IS 800, including defining actions, factors governing strength limits, and serviceability limits related to deflection, vibration and durability.
Tension members are structural elements subjected to direct tensile loads. Their strength depends on factors like length of connection, size and spacing of fasteners, cross-sectional area, fabrication type, connection eccentricity, and shear lag. Failure can occur through gross section yielding, net section rupture, or block shear. Design involves selecting a member with sufficient gross area to resist factored loads in yielding, then checking strength considering net section rupture and block shear failure modes.
The document discusses columns, which are structural members that primarily carry axial compressive loads. It defines short columns that do not require consideration of lateral buckling and slender columns that do. It describes uniaxially loaded columns that experience either axial load alone or combined axial and bending load about one axis. It provides examples of column cross-sections and outlines the process for designing uniaxial reinforced concrete columns according to ACI code provisions. This includes calculating load and moment capacities, determining reinforcement ratios from design charts, and checking capacities against demands with safety factors.
The document discusses properties and testing of concrete. It provides information on the constituents of concrete including cement, coarse aggregate, fine aggregate, and water. It also discusses properties of concrete and reinforcements, including their relatively high compressive strength and lower tensile strength. Various tests performed on concrete are mentioned, including tests on workability, compressive strength, flexural strength, and fresh/hardened concrete. Design philosophies for reinforced concrete include the working stress method, ultimate strength method, and limit state method.
The document provides details on the design procedure for beams. It discusses estimating loads, analyzing beams to determine shear forces and bending moments, and designing beams. The design process involves selecting the beam size and shape, calculating the effective span, determining critical moments and shears, selecting reinforcement, and checking requirements such as shear capacity, deflection limits, and development lengths. An example problem demonstrates designing a singly reinforced concrete beam with a span of 5 meters to support a working live load of 25 kN/m.
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.
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 discusses limit state design of reinforced concrete structures. It introduces limit states as conditions where the structure becomes unfit for use, including limit states of strength and serviceability. Limit state design involves characterizing loads and resistances as random variables and using partial safety factors on loads and resistances to achieve a target reliability. The document outlines the general principles of limit state design according to Indian Standard code IS 800, including defining actions, factors governing strength limits, and serviceability limits related to deflection, vibration and durability.
Tension members are structural elements subjected to direct tensile loads. Their strength depends on factors like length of connection, size and spacing of fasteners, cross-sectional area, fabrication type, connection eccentricity, and shear lag. Failure can occur through gross section yielding, net section rupture, or block shear. Design involves selecting a member with sufficient gross area to resist factored loads in yielding, then checking strength considering net section rupture and block shear failure modes.
The document discusses columns, which are structural members that primarily carry axial compressive loads. It defines short columns that do not require consideration of lateral buckling and slender columns that do. It describes uniaxially loaded columns that experience either axial load alone or combined axial and bending load about one axis. It provides examples of column cross-sections and outlines the process for designing uniaxial reinforced concrete columns according to ACI code provisions. This includes calculating load and moment capacities, determining reinforcement ratios from design charts, and checking capacities against demands with safety factors.
This presentation introduces plastic analysis concepts. It discusses stress-strain curves and the difference between elastic and plastic analysis. Key assumptions of plastic analysis are that plane sections remain plane and the stress-strain relationship is identical in compression and tension. Plastic hinges form where the moment equals the plastic moment. Shape factors determine the plastic modulus for different cross-sections. Methods of plastic analysis include static and kinematic approaches. Failure mechanisms involve forming plastic hinges until collapse. Beam examples and problems are provided to demonstrate plastic analysis methods.
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 discusses the working stress method for designing reinforced concrete structures. It defines key terms like neutral axis, lever arm, and moment of resistance. It describes the assumptions and steps of the working stress method, including designing for under-reinforced, balanced, and over-reinforced beam sections. The document also discusses limitations of the working stress method and introduces the limit state method as a more modern approach.
This document provides an overview of the design of steel beams. It discusses various beam types and sections, loads on beams, design considerations for restrained and unrestrained beams. For restrained beams, it covers lateral restraint requirements, section classification, shear capacity, moment capacity under low and high shear, web bearing, buckling, and deflection checks. For unrestrained beams, it discusses lateral torsional buckling, moment and buckling resistance checks. Design procedures and equations for determining effective properties and capacities are also presented.
This document 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.
Slope and Deflection Method ,The Moment Distribution Method ,Strain Energy Me...Aayushi5
This document provides information about the Design of Structure I course taught to 5th semester civil engineering students. It discusses the course objectives, outcomes, syllabus, and various structural analysis methods taught - Slope Deflection Method, Moment Distribution Method, and Strain Energy Method. The document focuses on the Slope Deflection Method, providing the theory, procedure, an example numerical problem, and derivation of slope-deflection equations for a continuous beam with 4 degrees of indeterminacy. It summarizes the steps to analyze a structure using the slope-deflection approach.
There are several types of retaining structures, including gravity, sheet pile, cantilever, and anchored earth/ mechanically stabilized earth (reinforced earth) walls and slopes. Gravity retaining walls use their weight to resist earth pressures.
This document summarizes key concepts related to structural analysis including:
1) The effects of axial and eccentric loading on columns including direct stress, bending stress, and maximum/minimum stresses.
2) Maximum and minimum pressures at the base of dams and retaining walls including calculations of total water/earth pressure, eccentricity, and stability conditions.
3) Forces and stresses on chimneys and walls due to wind pressure including calculations of direct stress from self-weight, wind force, induced bending moment, and maximum/minimum stresses.
This document provides instructions for analyzing and designing a G+4 multistory building using ETABS. It includes steps to model the building with beams, columns, slabs and walls. Materials are defined for concrete, rebar and masonry. Section properties are created for beams, columns and slabs. The building grid is laid out and elements are drawn. Supports are assigned and loads including dead, live, wind and earthquake are applied. Load combinations are defined and an analysis is run to obtain shear and moment diagrams and joint reactions.
This document discusses wind loading and its effects on structures. It provides key points about wind loads and how they are typically converted to constant pressure for design. It describes the effects of wind on a structure, including areas of positive and negative pressure. It discusses how to obtain design wind speeds based on location factors and how to calculate wind forces on a structure using pressure coefficients and surface area. Three examples are provided to demonstrate calculating wind forces on a wall, chimney, and towers.
The document provides steps for designing different structural elements:
1. Design of a beam subjected to torsion including calculation of torsional and bending moments, determination of steel requirements, and detailing.
2. Design of continuous beams involving calculation of bending moments and shears, reinforcement sizing, shear design, deflection check, and detailing including curtailment.
3. Design of circular water tanks with both flexible base and rigid base using approximate and IS code methods. This includes sizing hoop and vertical tension reinforcement, sizing wall thickness, designing cantilever sections and base slabs, and providing detailing diagrams.
This document discusses the classification of steel cross sections according to Indian Standard IS 800:2007. It explains that cross sections are classified into four classes - plastic, compact, semi-compact, and slender - based on their width-thickness ratio and ability to develop plastic hinges and plastic moment capacity. Formulas and limiting ratios for each class are provided. Three example cross sections are then classified - a ISHB 400 section is compact, a ISMC 300 section is plastic, and a ISA 150X150X12 angle section is semi-compact.
Static Indeterminacy and Kinematic IndeterminacyDarshil Vekaria
This ppt is more useful for Civil Engineering students.
I have prepared this ppt during my college days as a part of semester evaluation . Hope this will help to current civil students for their ppt presentations and in many more activities as a part of their semester assessments.
I have prepared this ppt as per the syllabus concerned in the particular topic of the subject, so one can directly use it just by editing their names.
This document discusses the analysis and design of reinforced concrete footings. It describes different types of footings including isolated, combined, continuous, and raft foundations. It also covers design considerations such as minimum thickness, concrete cover, reinforcement sizes and spacing, and critical sections. An example is provided to demonstrate the step-by-step design of an isolated square footing, calculating loads, sizing the footing, checking effective depth, determining steel requirements, and verifying hook and dowel bar needs.
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.
The document discusses different methods of designing reinforced concrete elements:
1. Modular ratio (working stress) method, which assumes elastic behavior and uses factors of safety. It was the first accepted method but has limitations.
2. Load factor method, which avoids modular ratio and uses load factors to account for ultimate loads. However, it does not consider serviceability.
3. Limit state method, adopted in modern codes, which considers both ultimate and serviceability limit states using partial safety factors applied to loads and material strengths. It provides a comprehensive solution for safety and serviceability.
This document discusses the calculation of wind loads for structural design. It provides background on wind loads and defines key terms. It outlines wind speed areas in Tanzania and the design procedure, which involves determining the site wind speed, characteristic wind pressure, external and internal pressures on the structure, and the net pressure. Examples are provided to demonstrate calculating wind loads. Load factors of safety and load combinations are also defined.
Because of torsion, the beam fails in diagonal tension forming the spiral cracks around the beam. Warping of the section does not allow a plane section to remain as plane after twisting. Clause 41 of IS 456:2000 provides the provisions for
the design of torsional reinforcements. The design rules for torsion are based on the equivalent moment.
The document summarizes the analysis of reinforced concrete beam cross sections to determine their moment of resistance at the ultimate limit state. It outlines the key assumptions of the strength design method and describes the behavior of beams under small, moderate and ultimate loads. It also discusses balanced, under-reinforced and over-reinforced beam sections, and introduces the concept of the equivalent stress block to simplify calculations. Worked examples are provided to demonstrate how to determine the depth of the neutral axis and moment of resistance for various beam cross sections.
This document provides information on reinforced concrete design including:
- Concrete and steel properties such as modulus of elasticity and grades/strengths of reinforcing bars.
- Minimum concrete cover requirements for reinforcement.
- Load factors and combinations for ultimate strength design.
- Flexural design procedures for reinforced concrete beams including assumptions, stress/strain diagrams, and analysis for cases where steel yields or does not yield.
- Requirements for reinforcement spacing, minimum member thicknesses, and ductility.
This presentation introduces plastic analysis concepts. It discusses stress-strain curves and the difference between elastic and plastic analysis. Key assumptions of plastic analysis are that plane sections remain plane and the stress-strain relationship is identical in compression and tension. Plastic hinges form where the moment equals the plastic moment. Shape factors determine the plastic modulus for different cross-sections. Methods of plastic analysis include static and kinematic approaches. Failure mechanisms involve forming plastic hinges until collapse. Beam examples and problems are provided to demonstrate plastic analysis methods.
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 discusses the working stress method for designing reinforced concrete structures. It defines key terms like neutral axis, lever arm, and moment of resistance. It describes the assumptions and steps of the working stress method, including designing for under-reinforced, balanced, and over-reinforced beam sections. The document also discusses limitations of the working stress method and introduces the limit state method as a more modern approach.
This document provides an overview of the design of steel beams. It discusses various beam types and sections, loads on beams, design considerations for restrained and unrestrained beams. For restrained beams, it covers lateral restraint requirements, section classification, shear capacity, moment capacity under low and high shear, web bearing, buckling, and deflection checks. For unrestrained beams, it discusses lateral torsional buckling, moment and buckling resistance checks. Design procedures and equations for determining effective properties and capacities are also presented.
This document 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.
Slope and Deflection Method ,The Moment Distribution Method ,Strain Energy Me...Aayushi5
This document provides information about the Design of Structure I course taught to 5th semester civil engineering students. It discusses the course objectives, outcomes, syllabus, and various structural analysis methods taught - Slope Deflection Method, Moment Distribution Method, and Strain Energy Method. The document focuses on the Slope Deflection Method, providing the theory, procedure, an example numerical problem, and derivation of slope-deflection equations for a continuous beam with 4 degrees of indeterminacy. It summarizes the steps to analyze a structure using the slope-deflection approach.
There are several types of retaining structures, including gravity, sheet pile, cantilever, and anchored earth/ mechanically stabilized earth (reinforced earth) walls and slopes. Gravity retaining walls use their weight to resist earth pressures.
This document summarizes key concepts related to structural analysis including:
1) The effects of axial and eccentric loading on columns including direct stress, bending stress, and maximum/minimum stresses.
2) Maximum and minimum pressures at the base of dams and retaining walls including calculations of total water/earth pressure, eccentricity, and stability conditions.
3) Forces and stresses on chimneys and walls due to wind pressure including calculations of direct stress from self-weight, wind force, induced bending moment, and maximum/minimum stresses.
This document provides instructions for analyzing and designing a G+4 multistory building using ETABS. It includes steps to model the building with beams, columns, slabs and walls. Materials are defined for concrete, rebar and masonry. Section properties are created for beams, columns and slabs. The building grid is laid out and elements are drawn. Supports are assigned and loads including dead, live, wind and earthquake are applied. Load combinations are defined and an analysis is run to obtain shear and moment diagrams and joint reactions.
This document discusses wind loading and its effects on structures. It provides key points about wind loads and how they are typically converted to constant pressure for design. It describes the effects of wind on a structure, including areas of positive and negative pressure. It discusses how to obtain design wind speeds based on location factors and how to calculate wind forces on a structure using pressure coefficients and surface area. Three examples are provided to demonstrate calculating wind forces on a wall, chimney, and towers.
The document provides steps for designing different structural elements:
1. Design of a beam subjected to torsion including calculation of torsional and bending moments, determination of steel requirements, and detailing.
2. Design of continuous beams involving calculation of bending moments and shears, reinforcement sizing, shear design, deflection check, and detailing including curtailment.
3. Design of circular water tanks with both flexible base and rigid base using approximate and IS code methods. This includes sizing hoop and vertical tension reinforcement, sizing wall thickness, designing cantilever sections and base slabs, and providing detailing diagrams.
This document discusses the classification of steel cross sections according to Indian Standard IS 800:2007. It explains that cross sections are classified into four classes - plastic, compact, semi-compact, and slender - based on their width-thickness ratio and ability to develop plastic hinges and plastic moment capacity. Formulas and limiting ratios for each class are provided. Three example cross sections are then classified - a ISHB 400 section is compact, a ISMC 300 section is plastic, and a ISA 150X150X12 angle section is semi-compact.
Static Indeterminacy and Kinematic IndeterminacyDarshil Vekaria
This ppt is more useful for Civil Engineering students.
I have prepared this ppt during my college days as a part of semester evaluation . Hope this will help to current civil students for their ppt presentations and in many more activities as a part of their semester assessments.
I have prepared this ppt as per the syllabus concerned in the particular topic of the subject, so one can directly use it just by editing their names.
This document discusses the analysis and design of reinforced concrete footings. It describes different types of footings including isolated, combined, continuous, and raft foundations. It also covers design considerations such as minimum thickness, concrete cover, reinforcement sizes and spacing, and critical sections. An example is provided to demonstrate the step-by-step design of an isolated square footing, calculating loads, sizing the footing, checking effective depth, determining steel requirements, and verifying hook and dowel bar needs.
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.
The document discusses different methods of designing reinforced concrete elements:
1. Modular ratio (working stress) method, which assumes elastic behavior and uses factors of safety. It was the first accepted method but has limitations.
2. Load factor method, which avoids modular ratio and uses load factors to account for ultimate loads. However, it does not consider serviceability.
3. Limit state method, adopted in modern codes, which considers both ultimate and serviceability limit states using partial safety factors applied to loads and material strengths. It provides a comprehensive solution for safety and serviceability.
This document discusses the calculation of wind loads for structural design. It provides background on wind loads and defines key terms. It outlines wind speed areas in Tanzania and the design procedure, which involves determining the site wind speed, characteristic wind pressure, external and internal pressures on the structure, and the net pressure. Examples are provided to demonstrate calculating wind loads. Load factors of safety and load combinations are also defined.
Because of torsion, the beam fails in diagonal tension forming the spiral cracks around the beam. Warping of the section does not allow a plane section to remain as plane after twisting. Clause 41 of IS 456:2000 provides the provisions for
the design of torsional reinforcements. The design rules for torsion are based on the equivalent moment.
The document summarizes the analysis of reinforced concrete beam cross sections to determine their moment of resistance at the ultimate limit state. It outlines the key assumptions of the strength design method and describes the behavior of beams under small, moderate and ultimate loads. It also discusses balanced, under-reinforced and over-reinforced beam sections, and introduces the concept of the equivalent stress block to simplify calculations. Worked examples are provided to demonstrate how to determine the depth of the neutral axis and moment of resistance for various beam cross sections.
This document provides information on reinforced concrete design including:
- Concrete and steel properties such as modulus of elasticity and grades/strengths of reinforcing bars.
- Minimum concrete cover requirements for reinforcement.
- Load factors and combinations for ultimate strength design.
- Flexural design procedures for reinforced concrete beams including assumptions, stress/strain diagrams, and analysis for cases where steel yields or does not yield.
- Requirements for reinforcement spacing, minimum member thicknesses, and ductility.
This document discusses the flexural analysis of prestressed concrete using the strain compatibility method. It provides details on:
1) The iterative process used to calculate the ultimate flexural strength, which involves assuming a steel stress value and recalculating until strains match.
2) Applying the method to calculate the ultimate moment capacity of an I-beam example, with given concrete strength, steel properties, and effective prestress force.
3) Noting that while the equivalent stress block depth exceeds the flange thickness, the approximation has little effect on the results in this case due to the average flange thickness.
Reinforced concrete II Hand out Chapter 5_PPT_Torsion.pdfObsiNaanJedhani
This document discusses torsion in reinforced concrete beams. It describes:
- How torsional stresses develop and are distributed in circular, rectangular, and thin-walled hollow members. The maximum stress occurs at the surface.
- Cracking and failure occur due to principal tensile stresses at 45 degrees, forming spirals. Torsion reinforcement controls cracking.
- An equivalent space truss model is used to design for torsion, with stirrups resisting shear across cracks like tension members and longitudinal bars as chords.
- Equations are provided to calculate required torsional reinforcement and the maximum torque before crushing of the concrete.
information on types of beams, different methods to calculate beam stress, design for shear, analysis for SRB flexure, design for flexure, Design procedure for doubly reinforced beam,
The document discusses concepts of stress, including:
1. Stress is defined as the force per unit area acting on a surface or section. There are two main types: normal stress and shear stress.
2. To determine if a structure can safely support a load, both the internal forces and the material properties must be considered.
3. Allowable stress values lower than the actual failure stress are used in design, with factors of safety typically between 1-3 depending on the application. This ensures the structure does not fail under expected loading conditions.
presentation on rectangular beam design singly or doubly (wsd)raihan mannan
This document discusses the design of rectangular beams. It describes singly reinforced beams which have steel reinforcement only in the tensile zone below the neutral axis. It also describes doubly reinforced beams which have steel reinforcement in both the tensile and compressive zones. The key steps in the design of rectangular beams using the working stress method are described, including determining the stress distribution, calculating moments, and sizing the reinforcement. Design considerations like clear cover and bar spacing are also outlined.
This document discusses different types of stresses including normal stress, shear stress, bearing stress, and stresses in thin-walled pressure vessels. It provides definitions and formulas for calculating normal stress, shear stress, and bearing stress. For thin-walled pressure vessels, it explains that the tangential stress is twice the longitudinal stress and provides the formulas for calculating each. It also includes example problems calculating stresses in cylindrical and spherical pressure vessels.
This document discusses various types of losses in prestressing force that occur in pre-tensioned and post-tensioned concrete members. It defines key terms like prestressing force, pre-tensioning and post-tensioning. It explains different types of losses - elastic shortening, anchorage slip, friction, creep, shrinkage and relaxation. Methods to calculate losses in prestressing force due to elastic shortening are presented for different member types like axial and bending members. Friction loss occurring uniquely in post-tensioning is also explained.
Strengthofmaterialsbyskmondal 130102103545-phpapp02Priyabrata Behera
This document contains a table of contents for a book on strength of materials with 16 chapters covering topics like stress and strain, bending, torsion, columns, and failure theories. It also contains introductory material on stress, strain, Hooke's law, true stress and strain, volumetric strain, Young's modulus, shear modulus, and bulk modulus. Key definitions provided include normal stress, shear stress, tensile strain, compressive strain, engineering stress and strain, true stress and strain, Hooke's law, and the relationships between elastic constants.
- Stress is defined as the internal force per unit area within a material. It can be tensile or compressive. Common types include normal stress and shear stress.
- Strain is a measure of deformation in a material under stress. Normal strain measures changes in length while shear strain measures changes in shape.
- The allowable stress for a material is less than its failure stress to ensure safety under loads. Factor of safety is defined as the ratio of failure stress to allowable stress.
This document discusses bending moment stress, including uniaxial and biaxial bending stress. It defines bending as causing deflection from a straight line, and bending moment as a measure of bending force applied at a distance from a beam's neutral axis. Bending moment stress induces tension or compression in a bent body. Examples show calculations for uniaxial 3-point and 4-point bending stresses, as well as an example of biaxial bending stress distribution and the line of zero stress in a loaded block.
This document discusses concepts related to the design of concrete beams including:
1. It introduces concepts like bending, shear, tension and compression as they relate to beam design.
2. It provides formulas for calculating reactions, shear forces, and bending moments in simply supported beams under different loading conditions.
3. It explains concepts like the neutral axis, stress blocks, and strain diagrams that are important to beam design.
4. It discusses factors that influence the strength of beams like the moment of inertia and reinforcement ratio.
5. It compares working stress and limit state methods of design.
This document discusses the design of beams for torsion. It defines important terminology related to torsional design. It explains how torsion occurs in structures like bridges and buildings. It discusses threshold torsion and moment redistribution. It also covers torsional stresses, the torsional moment strength, and the torsional reinforcement required to resist torsional forces.
Chapter-1 Concept of Stress and Strain.pdfBereketAdugna
The document discusses concepts of stress and strain in materials. It defines stress as an internal force per unit area within a material. Stress can be normal (perpendicular to the surface) or shear (parallel to the surface). Normal stress can be tensile or compressive. Strain is a measure of deformation in response to stress. Hooke's law states that stress is proportional to strain in the elastic region. Poisson's ratio describes the contraction that occurs perpendicular to an applied tensile load. Stress-strain diagrams are used to analyze a material's behavior under different loads. The document also discusses volumetric strain, shear stress and strain, bearing stress, and provides examples of stress and strain calculations.
1) The document discusses torsional stress and analysis of circular shafts subjected to twisting moments. It defines torsional stress and provides formulas to calculate maximum shear stress and angle of twist.
2) Key assumptions in the analysis are that the shaft has a uniform cross-section, plane sections remain plane after torque is applied, and shear strain varies linearly with radius.
3) The maximum shear stress formula is derived using Hooke's law, assumptions of linear elasticity, and integrating shear stress over the cross-sectional area which equals the applied torque.
The document discusses stress concentration and fatigue failure in machine elements. It defines stress concentration as irregular stress distribution caused by abrupt changes in cross-section shape. Stress concentration factors are introduced to quantify the maximum stress compared to nominal stress. The document also discusses endurance limit and fatigue strength testing methods. Factors that affect fatigue strength like material properties, surface finish, size and temperature are summarized. Methods to evaluate and reduce stress concentration in designs are provided.
This document discusses bending moment stress, which is the internal stress caused by bending moments in a beam. It defines bending moment stress and provides the formula to calculate it based on the moment acting, distance from the neutral axis, and moment of inertia. It also discusses uniaxial bending stress, which acts in one direction, and biaxial bending stress, which acts in two directions. Examples of each type are provided to illustrate stress distribution under different loading conditions.
This document discusses bending moment stress, which is the internal stress caused by bending moments in a beam. It defines bending moment stress and provides the formula to calculate it based on the moment acting, distance from the neutral axis, and moment of inertia. It also discusses uniaxial bending stress, which acts in one direction, and biaxial bending stress, which acts in two directions. Examples of each type are provided to illustrate stress distribution under different loading conditions.
This document discusses bending moment stress, which is the internal stress caused by bending moments in a beam. It defines bending moment stress and provides the formula to calculate it based on the moment acting, distance from the neutral axis, and moment of inertia. It also discusses uniaxial bending stress, which acts in one direction, and biaxial bending stress, which acts in two directions. Examples of each type are provided to illustrate stress distribution under different loading conditions.
Similar to 1-Singly Reinforced Sections - Beams - AUDIO.pptx (20)
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
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His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
2. INTRODUCTION
The beam when subjected to vertical loads causing moments which tends to
bend the beam in a vertical plane as shown in the following Figure.
Such moments which are applied in a vertical plane containing the longitudinal
axis of the beam bends it in the same plane are termed as In-plane Moments.
Such a situation stresses the fibres of the beam.
It can be clearly visualised that the beam fibres in the upper portion are
compressed i.e. they are in a state of compression and those in the lower
portion are elongated i.e. they are in a state of tension.
Hence the cross-section of the beam is subjected to compressive stresses in the
upper zone and to the tensile stresses in the lower portion.
But there is a transition zone where compression changes to tension.
Such a surface where the fibres of the beam are not at all stressed i.e. they are
not subjected to either tensile or compressive stresses is termed as Neutral
Surface of the beam.
Its intersection with the transverse section or plane through the beam is termed
Neutral Axis of the beam.
2
4. SINGLY REINFORCED SECTIONS - [ BEAMS ]
4
A
A
NA
Tension
Compression
Clear Span
b
D d
A Reinforced Concrete Flexure Member should be able to resist the following
stresses induced due to Imposed Loads :
Tensile Stress
Compressive Stress
Shear Stress
Concrete :-
Fairly Strong in Compression
Weak in Tension
Tensile Strength taken as Zero
Steel:-
Very Strong in Tension
Steel takes up Tension in the Tensile Zone of the Flexural Member.
5. While Designing a Reinforced Concrete Section, the Loading, Span, Grade of
Concrete, Grade of Steel and Width of Section are usually known in advance.
The Section Dimensions and Area of Steel Bars [Reinforcing Steel] are to be
determined.
There can be no unique section for a given set of forces. There are many
possible combinations.
Thus the cost will decide the final design
5
6. ASSUMPTIONS
Design for the Limit State of Collapse in Flexure shall be based on the assumptions
as per IS 456 – 2000; Clause 38.1, p 69
Plane Sections Normal to the Axis remain Plane after Bending
The Maximum Strain in Concrete at the outermost Compression Fibre is taken as
0.0035 in Bending
The Relationship between Stress-Strain distribution in Concrete is Parabolic upto
a Strain of 0.002 and then constant upto a Strain of 0.0035 at which the concrete is
said to have failed [IS 456 – 2000, Fig 21, pp. 69]
For Design purpose the Compressive Strength of Concrete is taken as 0.67 times
the Characteristic Strength of Concrete. A Partial Safety Factor m = 1.5 shall be
applied in addition to this.
The Tensile Strength of Concrete is ignored
The Stress in the Reinforcement is derived from the representative Stress-Strain
Curve for the type of Steel used. The typical Curves are given in Fig 23 of IS 456 –
2000; pp. 70
For Design Purposes the Partial Safety Factor of m = 1.15 shall be applied to the
Characteristic Strength of Steel
6
7. The Maximum Strain in Tension Reinforcement in the Section at Failure should
not be less than the following i.e.
Bending of Beams
We know that
OR
fcr = 0.7fCK
7
8. MOMENT OF RESISTANCE
Neutral Axis
Fig 8: Stress Block Parameters
Consider a Simply Supported Beam subjected to Bending under factored loads.
For Equilibrium total force of Compression must be equal to the total force of
Tension i.e.
C = T
The applied Bending Moment at Collapse i.e. Factored Bending Moment is equal to
the Resisting Moment of the Section provided by the Internal Stresses.
This called the Ultimate Moment of Resistance.
8
9. Now
Force = C = C1 + C2
C = Stress x Area
And
MR = Force x Lever Arm
The portion above the Neutral Axis is in Compression and the Strain is
proportional to distance from Neutral Axis (NA) to the Extreme Compression
Fibre i.e. Zero at the NA to a Maximum at the Extreme fibre.
The cross section below the NA is in Tension and hence the Concrete is
assumed to have Cracked.
All the Tensile Stresses are supposed to be borne by steel bars and stresses in
all the steel bars are equal.
The resultant Tensile Force thus acts at the Centroid of the Reinforcing Bars.
The distance from the Extreme Compression Fibre to the centroid of the
Reinforcing Bars i.e. line of action of Tensile Force is called the Effective Depth
'd'.
Now,
Maximum Compressive Stress in Concrete without Safety Factor
= 0.67 fCK [Assumption 4]
9
10. Let,
X1 : Depth of Parabolic Portion
X2 : Depth of Rectangular Portion
From,
Similar Triangles of Strain Diagram,
Depth of Parabolic Portion is
Or,
Depth of Rectangular Portion
X2 = XU - X1
=
OR
10
11. Force of Compression
Parabolic Block :-
C1 = Stress x Area
= (0.67 fCK ) × (2/3 X1 . b)
= (0.67 fCK ) × (2/3 . XU . b)
C1 = 0.255 fCK .b . XU
•
Rectangular Block:-
C2 = Stress x Area
= (0.67 fCK ) × ( X2 . b)
= (0.67 fCK ) × ( 3/7 . XU . b)
C2 = 0.287 fCK .b . XU
•
Hence Total Force of Compression without Partial Safety Factor
CO = C1 + C2
= 0.255 fCK .b . XU + 0.287 fCK .b . XU
CO = 0.542 fCK b XU {Without Partial Safety Factor}
11
12. Now Applying Partial Safety Factor of 1.5 the Design Force of Compression is:-
C = 0.36 fCK b XU
Now,
Moment of Resistance = Force × Lever Arm
Lever Arm = Z = d ˗ a
Where,
'a' is the distance of line of action of force of compression from the extreme top
fibre.
To determine 'a' take moment of all the forces about top extreme fibre. i.e.
12
13. CO × a = 0.225 fCK .b . XU
2
a = 0.42 XU
Where,
XU : Depth of Neutral Axis from Top Fibre
B : Width of the Section
DEPTH OF NEUTRAL AXIS
Depth of NA can be obtained by considering the equilibrium of normal force i.e.
Force of Compression = Force of Tension
Resultant Force of Compression
C = Average Stress × Area
13
14. C = 0.36 fCK b XU
Resultant Force of Tension
T = 0.87 fY At
Now
C = T
0.36 fCK b XU = 0.87 fY At
OR,
Where,
At = Area of Tension Steel
14
15. LEVER ARM
The forces of Compression and Tension forms a Couple.
The distance between the lines of action of these two forces is called the Lever
Arm and is denoted by 'Z'.
The equation of equilibrium Σ M = 0 is satisfied by equating the factored
Bending Moment to the Moment of Resistance offered by either Force of
Compression or Force of Tension.
Lever Arm Z = d ˗ a
OR
Z = d ˗ 0.42 XU
Now,
Moment of Resistance
15
16. Now,
Moment of Resistance w. r. t. Concrete
MRC = Compressive Force × Lever Arm
MRC = 0.36 fCK b XU . Z
Moment of Resistance w. r. t. Steel
MRt = Compressive Force × Lever Arm
MRt = 0.87 fY At . Z
16
17. MODES OF FAILURE
Balanced Section :-
If the ratio of Steel to Concrete in a beam is such that the maximum strain in
concrete and steel reach simultaneously, a sudden failure would occur with less
alarming deflections.
Such a beam is referred to as a Balanced Reinforced Beam.
Under Reinforced Beam :-
When the amount of steel is kept less than that in the Balanced Section, the NA
moves upwards so as to reduce the area under compression to maintain the
Equilibrium Condition i.e.
Force of Compression is equal to the Force of Tension. [This is because the Force
of tension becomes less than the Force of Compression and hence the Force of
Compression has to be reduced]
In this process the Centre of Gravity of compressive forces also shifts upwards.
Under increasing Bending Moments Steel is strained beyond Yield Point and the
Maximum Strain in concrete remains less than 0.35% i.e. 0.0035.
If the beam is further loaded, the strain in the section increases. Once the steel has
yielded it does not take any additional stresses for the additional strain and the
total force of tension remains constant.
However compressive stresses in concrete increases with the additional strain.
17
18. Thus the NA and Centre of Gravity of Compressive Forces further shifts upwards
to maintain Equilibrium.
This results in an increase in the Moment of Resistance of the Beam. This process of
shift in the NA continues until maximum strain reaches its Ultimate Value i.e.
0.35% and the Concrete Crushes.
Such a beam is referred to as "Under Reinforced Beam".
The Failure is called Tension Failure because Yielding of Steel was responsible for
higher strains in concrete resulting in its failure.
Over Reinforced Beam :-
When the amount of steel is kept more than that in the Balanced Section, the NA
tends to move downwards and the Strain in Steel remains in Elastic Region.
If the beam is further loaded the stresses in steel keeps on increasing and so the
force of tension.
Here the force of tension is more than that of compression, and hence to maintain
the equilibrium of tensile and compressive forces the area of concrete resisting
compression has to increase so as to increase the force of compression.
In this process the NA further shifts downwards until maximum strain in concrete
reaches its ultimate value of 0.35% and concrete crushes. The Steel is well within
Elastic Limits.
Such a beam is referred to as an "Over Reinforced Beam" and the failure as
Compression Failure
18
19. MAXIMUM DEPTH OF NEUTRAL AXIS
A compression failure in a Over Reinforced Beam is a Brittle Failure.
The Maximum Depth of NA is therefore limited to ensure that the Steel will
reach its Yield Point before Concrete fails in Compression, so that a brittle
Failure is avoided.
Let the Limiting Value of the depth of NA be XU Lim.
When,
XU = XU Lim [ Balanced Section ]
XU < XU Lim [ Under Reinforced Section ]
XU > XU Lim [ Over Reinforced Section ]
19
20. The Limiting Value of Depth of NA XU Lim. for different grades of steel can be
obtained from Strain Diagram as shown in Fig 8.
From Similar Triangles
or
or
Where
E = 2 × 105 N/mm2
The Limiting values of Depth of NA for different grades of steel are given in Table 1
20
From Fig 8
0.0035
0.002
X1
X2
XU Lim
d
21. Grade of Steel fY
(N/mm2)
XU Lim
250 0.53 d
415 0.48 d
500 0.46 d
550 0.44 d
Table 1 Maximum Depth of Neutral Axis
LIMITING VALUES OF TENSION STEELAND MOMENT OF RESISTANCE
Since the maximum depth of NA is limited the maximum value of moment of resistance
is also limited i.e.
MU Lim w. r. t Concrete = 0.36 fCK b XU . Z
MU Lim = 0.36 fCK b XU Lim (d ˗ 0.42 XU Lim ) {Balanced Section}
MU Lim w. r. t Steel = 0.87 fY At . Z
MU Lim = 0.87 fY At (d ˗ 0.42 XU Lim ) { Balanced Section}
21
22. For a given Rectangular Beam Section, the Limiting Values of MU Lim depends on
the Grade of Concrete and the Grade of Steel.
The Values of Limiting Moment of Resistance with respect to different Grades of
Concrete and Steel are given in Table 2.
Grade of
Concrete
Fe 250 Fe 415 Fe 500 Fe 550
General 0.148fCK b d2 0.138fCK b d2 0.133fCK b d2 0.130fCK b d2
M 20 2.96 b d2 2.76 b d2 2.66 b d2 2.60 b d2
M 25 3.70 b d2 3.45 b d2 3.33 b d2 3.25 b d2
M 30 4.4 b d2 4.14 b d2 3.99 b d2 3.90 b d2
Table 2: Limiting Moment of Resistance (N-mm)
The percentage of Tensile Reinforcement Corresponding to Limiting Moment of
Resistance is obtained by equating the forces of tension and compression
0.87 fY At = 0.36 fCK b XU Lim
22
23. Let,
The limiting values of tensile reinforcement percentage corresponding to different
grades of steel and concrete in a Singly Reinforced Beam are given in Table 3.
Grade of
Concrete
Percentage of Tensile Steel
fCK (N/mm2) Fe 250 N/mm2 Fe 415 N/mm2 Fe 500 N/mm2 Fe 550 N/mm2
M 20 1.76 0.96 0.76 0.66
M 25 2.20 1.19 0.94 0.83
M 30 2.64 1.43 1.13 1.00
Table 3: Limiting Tensile Steel in Rectangular Section (%)
23
24. Minimum and Maximum Tension Reinforcement
Minimum Reinforcement : [ As per Clause 26.5.1.1; pp. 46; of IS 456 - 2000 ]
The minimum area of tension reinforcement should not be less than that given
by the following :
Where,
AS = Minimum Area of Tension Reinforcement
b = Breadth of Beam or breadth of Web of T-Beam
d = Effective depth of Beam
fY = Characteristic Strength of Steel Reinforcement in N/mm2
Maximum Reinforcement :
• The maximum area of tension reinforcement should not exceed 4% of the
Gross Cross-Sectional area of beam to avoid difficulty in placing and
compacting concrete properly in the formwork i.e.
ASM > 0.04 b D
24