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1. DEEP BEAM DEFINITION - IS 456
2. DEEP BEAM APPLICATION
3. DEEP BEAM TYPES
4. BEHAVIOUR OF DEEP BEAMS
5. LEVER ARM
6. COMPRESSIVE FORCE PATH CONCEPT
7. ARCH AND TIE ACTION
8. DEEP BEAM BEHAVIOUR AT ULTIMATE LIMIT STATE
9. REBAR DETAILING
10. EXAMPLE 1 – SIMPLY SUPPORTED DEEP BEAM
11. EXAMPLE 2 – SIMPLY SUPPORTED DEEP BEAM; M20, FE415
12. EXAMPLE 3: FIXED ENDS AND CONTINUOUS DEEP BEAM
13. EXAMPLE 4 : FIXED ENDS AND CONTINUOUS DEEP BEAM
- Deep beams are defined as beams with a shear span to depth ratio of less than 2. They behave differently than ordinary beams due to two-dimensional loading and non-linear stress distributions.
- Deep beams transfer significant load through compression forces between the load and supports. Shear deformations are more prominent.
- Design of deep beams requires considering two-dimensional effects, non-linear stress distributions, and large shear deformations. Procedures include checking minimum thickness, designing for flexure and shear, and detailing reinforcement.
The document discusses reinforced concrete columns, including their functions, failure modes, classifications, and design considerations. Columns primarily resist axial compression but may also experience bending moments. They can fail due to compression, buckling, or a combination. Design depends on whether the column is short or slender, braced or unbraced. Reinforcement is designed based on the column's expected loads and dimensions using methods specified in design codes like BS 8110.
information on types of beams, different methods to calculate beam stress, design for shear, analysis for SRB flexure, design for flexure, Design procedure for doubly reinforced beam,
This document 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 the design of footings for structures. It begins by explaining that footings are needed to transfer structural loads from members made of materials like steel and concrete to the underlying soil. It then describes different types of shallow and deep foundations, including spread, strap, combined, and raft footings. The document provides details on designing isolated and combined footings to resist vertical loads and moments based on provisions in IS 456. It also discusses wall footings and combined footings that support multiple columns. In summary, the document covers the purpose of footings, various footing types, and design of isolated and combined footings.
Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)Hossam Shafiq II
This document discusses shear in reinforced concrete beams. It covers shear stress and failure modes, shear strength provided by concrete and steel stirrups, design according to code provisions, and critical shear sections. Key points include: transverse loads induce shear stress perpendicular to bending stresses; shear failure is brittle and must be designed to exceed flexural strength; nominal shear strength comes from concrete and steel stirrups according to code equations; design requires checking section adequacy and providing minimum steel area and maximum stirrup spacing. Critical shear sections for design are located a distance d from supports.
This document discusses the design of compression members subjected to axial load and biaxial bending. It introduces the concept of biaxial eccentricities and explains that columns should be designed considering possible eccentricities in two axes. The document outlines the method suggested by IS 456-2000, which is based on Breslar's load contour approach. It relates the parameter αn to the ratio of Pu/Puz. Finally, it provides a step-by-step process for designing the column section, which involves determining uniaxial moment capacities, computing permissible moment values from charts, and revising the section if needed. It also briefly mentions the simplified method according to BS8110.
This document discusses the design of reinforced concrete deep beams. It defines deep beams as having a span/depth ratio less than 2 or a continuous beam ratio less than 2.5. Deep beams behave differently than elementary beam theory due to non-linear stress distributions. Their behavior depends on loading type and cracking typically occurs between one-third to one-half of the ultimate load. Design considerations include checking for minimum thickness, flexural design, shear design, and anchorage of tension reinforcement.
- Deep beams are defined as beams with a shear span to depth ratio of less than 2. They behave differently than ordinary beams due to two-dimensional loading and non-linear stress distributions.
- Deep beams transfer significant load through compression forces between the load and supports. Shear deformations are more prominent.
- Design of deep beams requires considering two-dimensional effects, non-linear stress distributions, and large shear deformations. Procedures include checking minimum thickness, designing for flexure and shear, and detailing reinforcement.
The document discusses reinforced concrete columns, including their functions, failure modes, classifications, and design considerations. Columns primarily resist axial compression but may also experience bending moments. They can fail due to compression, buckling, or a combination. Design depends on whether the column is short or slender, braced or unbraced. Reinforcement is designed based on the column's expected loads and dimensions using methods specified in design codes like BS 8110.
information on types of beams, different methods to calculate beam stress, design for shear, analysis for SRB flexure, design for flexure, Design procedure for doubly reinforced beam,
This document 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 the design of footings for structures. It begins by explaining that footings are needed to transfer structural loads from members made of materials like steel and concrete to the underlying soil. It then describes different types of shallow and deep foundations, including spread, strap, combined, and raft footings. The document provides details on designing isolated and combined footings to resist vertical loads and moments based on provisions in IS 456. It also discusses wall footings and combined footings that support multiple columns. In summary, the document covers the purpose of footings, various footing types, and design of isolated and combined footings.
Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)Hossam Shafiq II
This document discusses shear in reinforced concrete beams. It covers shear stress and failure modes, shear strength provided by concrete and steel stirrups, design according to code provisions, and critical shear sections. Key points include: transverse loads induce shear stress perpendicular to bending stresses; shear failure is brittle and must be designed to exceed flexural strength; nominal shear strength comes from concrete and steel stirrups according to code equations; design requires checking section adequacy and providing minimum steel area and maximum stirrup spacing. Critical shear sections for design are located a distance d from supports.
This document discusses the design of compression members subjected to axial load and biaxial bending. It introduces the concept of biaxial eccentricities and explains that columns should be designed considering possible eccentricities in two axes. The document outlines the method suggested by IS 456-2000, which is based on Breslar's load contour approach. It relates the parameter αn to the ratio of Pu/Puz. Finally, it provides a step-by-step process for designing the column section, which involves determining uniaxial moment capacities, computing permissible moment values from charts, and revising the section if needed. It also briefly mentions the simplified method according to BS8110.
This document discusses the design of reinforced concrete deep beams. It defines deep beams as having a span/depth ratio less than 2 or a continuous beam ratio less than 2.5. Deep beams behave differently than elementary beam theory due to non-linear stress distributions. Their behavior depends on loading type and cracking typically occurs between one-third to one-half of the ultimate load. Design considerations include checking for minimum thickness, flexural design, shear design, and anchorage of tension reinforcement.
Calulation of deflection and crack width according to is 456 2000Vikas Mehta
This document discusses the calculation of crack width in reinforced concrete flexural members. It provides information on:
1) Crack width is calculated to satisfy serviceability limits and is only relevant for Type 3 pre-stressed concrete members that crack under service loads.
2) Crack width depends on factors like amount of pre-stress, tensile stress in bars, concrete cover thickness, bar diameter and spacing, member depth and location of neutral axis, bond strength, and concrete tensile strength.
3) The method of calculation involves determining the shortest distance from the surface to a bar and using equations involving member depth, neutral axis depth, average strain at the surface level. Permissible crack widths are specified depending on exposure
Design of Reinforced Concrete Structure (IS 456:2000)MachenLink
This is the 1st Lecture Series on Design Reinforced Cement Concrete (IS 456 -2000).
In this video, you will learn about the objective of structural designing and then basic properties of concrete and steel.
Concrete properties like...
1. Grade of Concrete
2. Modulus of Elasticity
3. Characteristic Strength
4. Tensile Strength
5. Creep and Shrinkage
6. Durability
Reinforced Steel Properties....
1. Grade and types of steel
2. Yield Strength of Mild Steel and HYSD Bars
1) Two-way slabs are slabs that require reinforcement in two directions because bending occurs in both the longitudinal and transverse directions when the ratio of longest span to shortest span is less than 2.
2) The document discusses various types of two-way slabs and design methods, focusing on the direct design method (DDM).
3) Using the DDM, the total factored load is first calculated, then the total factored moment is distributed to positive and negative moments. The moments are further distributed to column and middle strips using factors that consider the slab and beam properties.
This document discusses various concepts related to structural analysis of arches:
1. An arch is a curved girder supported at its ends, allowing only vertical and horizontal displacements for arch action.
2. The general cable theorem relates the horizontal tension and vertical distance from any cable point to the cable chord moment.
3. Arches are classified based on support conditions (3, 2, or 1 hinged) or shape (curved, parabolic, elliptical, polygonal).
4. Horizontal thrust in arches reduces the bending moment and is calculated differently for various arch types (e.g. parabolic) and loading (e.g. UDL).
The document provides information on constructing interaction diagrams for reinforced concrete columns. It defines an interaction diagram as a graph showing the relationship between axial load (Pu) and bending moment (Mu) for different failure modes of a column section. The document outlines the design procedure for constructing interaction diagrams, including considering pure axial load, axial load with uniaxial bending, and axial load with biaxial bending. An example is provided to demonstrate constructing the interaction diagram for a given reinforced concrete column cross-section.
A continuous beam has more than one span carried by multiple supports. It is commonly used in bridge construction since simple beams cannot support large spans without requiring greater strength and stiffness. Continuous prestressed concrete beams provide adequate strength and stiffness while allowing for redistribution of moments, resulting in higher load capacity, reduced deflections, and more evenly distributed bending moments compared to equivalent simple beams. Analysis of continuous beams requires determining primary moments from prestressing, secondary moments induced by support reactions, and the combined resultant moments.
This document provides an overview of design in reinforced concrete according to BS 8110. It discusses the basic materials used - concrete and steel reinforcement - and their properties. It describes two limit states for design: ultimate limit state considering failure, and serviceability limit state considering deflection and cracking. Key aspects of beam design are summarized, including types of beams, design for bending and shear resistance, and limiting deflection. Reinforcement detailing rules are also briefly covered.
This document discusses bolted connections used in structural engineering. It begins by explaining why connection failures should be avoided, as they can lead to catastrophic structural failures. It then classifies bolted connections based on their method of fastening, rigidity, joint resistance, fabrication location, joint location, connection geometry, and type of force transferred. It describes different types of bolts and bolt tightening techniques used for friction grip connections. It discusses advantages and drawbacks of bolted connections compared to riveted or welded connections. The document provides detailed information on design and behavior of various bolted connections.
The document discusses composite construction using precast prestressed concrete beams and cast-in-situ concrete. It describes how the two elements act compositely after the in-situ concrete hardens. Composite beams can be constructed as either propped or unpropped. Propped construction involves supporting the precast beam during casting to relieve it of the wet concrete weight, while unpropped construction allows stresses to develop under self-weight. Design and analysis of composite beams involves calculating stresses and deflections considering composite action. Differential shrinkage between precast and in-situ concrete also induces stresses.
Prestress loss occurs as prestress reduces over time from its initial applied value. There are two types of prestress loss - immediate losses during prestressing/transfer and long-term time-dependent losses. Immediate losses include elastic shortening, anchorage slip, and friction. Long-term losses include creep and shrinkage of concrete and relaxation of prestressing steel. The quantification of losses is based on strain compatibility between concrete and steel. For a pre-tensioned concrete sleeper, the percentage loss due to elastic shortening was calculated to be approximately 2.83% based on the stress in concrete at the level of the tendons.
Static and Kinematic Indeterminacy of Structure.Pritesh Parmar
The document discusses static and kinematic indeterminacy of structures. It defines different types of supports for 2D and 3D structures including fixed support, hinged/pinned support, roller support, and their properties. It also discusses internal joints like internal hinge, internal roller, and internal link. The document explains concepts of static indeterminacy, kinematic indeterminacy, and degree of freedom for different types of structures.
Design of steel structure as per is 800(2007)ahsanrabbani
It does not offer resistance against rotation and also termed as a hinged or pinned connections.
It transfers only axial or shear forces and it is not designed for moment
It is generally connected by single bolt/rivet and therefore full rotation is allowed
This document discusses the design of compression members under uniaxial bending. It notes that columns are rarely under pure axial compression due to eccentricities from rigid frame action or accidental loading. Columns can experience uniaxial or biaxial bending based on the loading. The behavior depends on the relative magnitudes of the bending moment and axial load, which determine the position of the neutral axis. Methods for designing eccentrically loaded short columns include using equations that calculate the neutral axis position and failure mode, or using interaction diagrams that graphically show the safe ranges of moment and axial load.
This document provides information on the structural design of a simply supported reinforced concrete beam. It includes:
- A list of students enrolled in an elementary structural design course.
- Equations and diagrams showing the forces and stresses in a reinforced concrete beam with a singly reinforced bottom section.
- Limits on the maximum depth of the neutral axis according to the grade of steel.
- Examples of analyzing the stresses and determining steel reinforcement for a given beam cross-section.
- A design example calculating the dimensions and steel reinforcement for a rectangular beam with a factored uniform load.
This document discusses the design of column braces for structures. It defines braced and unbraced columns, with braced columns having zero sway and stability provided by walls or bracing, while unbraced columns are subjected to sway with stability only from other columns. It describes different types of internal and external bracing patterns and factors to consider in brace analysis, including displacement, base shear, wind loads, maximum shear and bending moments. The document provides guidelines for designing braces based on column moments and explains how bracing type affects seismic resistance parameters through a parametric study.
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.
Approximate analysis methods make simplifying assumptions to determine preliminary member forces and dimensions for indeterminate structures. Case 1 assumes diagonals cannot carry compression and shares shear between diagonals. Case 2 allows compression in diagonals. Portal and cantilever methods analyze frames by dividing into substructures at assumed hinge locations, solving each sequentially from top to bottom.
This document provides details on the design of staircases, including:
1. It describes the typical components of a staircase like flights, landings, risers, treads, nosings, waist slabs, and soffits.
2. It discusses different types of staircases like straight, quarter turn, dog-legged, open well, spiral and helicoidal.
3. It classifies staircases structurally into those with stair slabs spanning transversely or longitudinally and provides examples of each type.
4. It provides an example calculation for the design of a waist slab spanning longitudinally, including loading, bending moment calculation, reinforcement design and checks.
This document discusses several special concreting techniques:
- Pumped concrete is concrete that can be pushed through a pipeline and must have a design that prevents blockages.
- Shortcrete or gunite is a mortar or fine concrete pneumatically projected at high velocity, used for thin sections with less formwork.
- Underwater concrete requires special mixes placed via bagging, buckets, tremie pipes, or grouted aggregates to prevent water intrusion.
- Other techniques include pre-packed concrete placed underwater and special considerations for hot/cold weather concreting. Proper mix design and placement methods are essential for successful implementation of special concreting applications.
Deep beams are structural elements where a significant portion of the load is carried to the supports by compression forces combining the load and reaction. As a result, the strain distribution is nonlinear and shear deformations are significant compared to pure flexure. Examples include floor slabs under horizontal loads, short span beams carrying heavy loads, and transfer girders. The behavior of deep beams is two-dimensional rather than one-dimensional, and plane sections may not remain plane. Analysis requires a two-dimensional stress approach.
This document discusses various types of beam and column connections used in steel structures. It describes rigid, pinned, and semi-rigid connections. It also discusses different beam to beam connections like web cleat angle, clip and seat angle, and web and seat angle connections. Beam to column connections including web angle, clip and seat angle stiffened and unstiffened are explained. Finally, it covers moment resistant connections like eccentrically loaded, light moment and heavy moment connections and provides examples of designing some typical connections.
Calulation of deflection and crack width according to is 456 2000Vikas Mehta
This document discusses the calculation of crack width in reinforced concrete flexural members. It provides information on:
1) Crack width is calculated to satisfy serviceability limits and is only relevant for Type 3 pre-stressed concrete members that crack under service loads.
2) Crack width depends on factors like amount of pre-stress, tensile stress in bars, concrete cover thickness, bar diameter and spacing, member depth and location of neutral axis, bond strength, and concrete tensile strength.
3) The method of calculation involves determining the shortest distance from the surface to a bar and using equations involving member depth, neutral axis depth, average strain at the surface level. Permissible crack widths are specified depending on exposure
Design of Reinforced Concrete Structure (IS 456:2000)MachenLink
This is the 1st Lecture Series on Design Reinforced Cement Concrete (IS 456 -2000).
In this video, you will learn about the objective of structural designing and then basic properties of concrete and steel.
Concrete properties like...
1. Grade of Concrete
2. Modulus of Elasticity
3. Characteristic Strength
4. Tensile Strength
5. Creep and Shrinkage
6. Durability
Reinforced Steel Properties....
1. Grade and types of steel
2. Yield Strength of Mild Steel and HYSD Bars
1) Two-way slabs are slabs that require reinforcement in two directions because bending occurs in both the longitudinal and transverse directions when the ratio of longest span to shortest span is less than 2.
2) The document discusses various types of two-way slabs and design methods, focusing on the direct design method (DDM).
3) Using the DDM, the total factored load is first calculated, then the total factored moment is distributed to positive and negative moments. The moments are further distributed to column and middle strips using factors that consider the slab and beam properties.
This document discusses various concepts related to structural analysis of arches:
1. An arch is a curved girder supported at its ends, allowing only vertical and horizontal displacements for arch action.
2. The general cable theorem relates the horizontal tension and vertical distance from any cable point to the cable chord moment.
3. Arches are classified based on support conditions (3, 2, or 1 hinged) or shape (curved, parabolic, elliptical, polygonal).
4. Horizontal thrust in arches reduces the bending moment and is calculated differently for various arch types (e.g. parabolic) and loading (e.g. UDL).
The document provides information on constructing interaction diagrams for reinforced concrete columns. It defines an interaction diagram as a graph showing the relationship between axial load (Pu) and bending moment (Mu) for different failure modes of a column section. The document outlines the design procedure for constructing interaction diagrams, including considering pure axial load, axial load with uniaxial bending, and axial load with biaxial bending. An example is provided to demonstrate constructing the interaction diagram for a given reinforced concrete column cross-section.
A continuous beam has more than one span carried by multiple supports. It is commonly used in bridge construction since simple beams cannot support large spans without requiring greater strength and stiffness. Continuous prestressed concrete beams provide adequate strength and stiffness while allowing for redistribution of moments, resulting in higher load capacity, reduced deflections, and more evenly distributed bending moments compared to equivalent simple beams. Analysis of continuous beams requires determining primary moments from prestressing, secondary moments induced by support reactions, and the combined resultant moments.
This document provides an overview of design in reinforced concrete according to BS 8110. It discusses the basic materials used - concrete and steel reinforcement - and their properties. It describes two limit states for design: ultimate limit state considering failure, and serviceability limit state considering deflection and cracking. Key aspects of beam design are summarized, including types of beams, design for bending and shear resistance, and limiting deflection. Reinforcement detailing rules are also briefly covered.
This document discusses bolted connections used in structural engineering. It begins by explaining why connection failures should be avoided, as they can lead to catastrophic structural failures. It then classifies bolted connections based on their method of fastening, rigidity, joint resistance, fabrication location, joint location, connection geometry, and type of force transferred. It describes different types of bolts and bolt tightening techniques used for friction grip connections. It discusses advantages and drawbacks of bolted connections compared to riveted or welded connections. The document provides detailed information on design and behavior of various bolted connections.
The document discusses composite construction using precast prestressed concrete beams and cast-in-situ concrete. It describes how the two elements act compositely after the in-situ concrete hardens. Composite beams can be constructed as either propped or unpropped. Propped construction involves supporting the precast beam during casting to relieve it of the wet concrete weight, while unpropped construction allows stresses to develop under self-weight. Design and analysis of composite beams involves calculating stresses and deflections considering composite action. Differential shrinkage between precast and in-situ concrete also induces stresses.
Prestress loss occurs as prestress reduces over time from its initial applied value. There are two types of prestress loss - immediate losses during prestressing/transfer and long-term time-dependent losses. Immediate losses include elastic shortening, anchorage slip, and friction. Long-term losses include creep and shrinkage of concrete and relaxation of prestressing steel. The quantification of losses is based on strain compatibility between concrete and steel. For a pre-tensioned concrete sleeper, the percentage loss due to elastic shortening was calculated to be approximately 2.83% based on the stress in concrete at the level of the tendons.
Static and Kinematic Indeterminacy of Structure.Pritesh Parmar
The document discusses static and kinematic indeterminacy of structures. It defines different types of supports for 2D and 3D structures including fixed support, hinged/pinned support, roller support, and their properties. It also discusses internal joints like internal hinge, internal roller, and internal link. The document explains concepts of static indeterminacy, kinematic indeterminacy, and degree of freedom for different types of structures.
Design of steel structure as per is 800(2007)ahsanrabbani
It does not offer resistance against rotation and also termed as a hinged or pinned connections.
It transfers only axial or shear forces and it is not designed for moment
It is generally connected by single bolt/rivet and therefore full rotation is allowed
This document discusses the design of compression members under uniaxial bending. It notes that columns are rarely under pure axial compression due to eccentricities from rigid frame action or accidental loading. Columns can experience uniaxial or biaxial bending based on the loading. The behavior depends on the relative magnitudes of the bending moment and axial load, which determine the position of the neutral axis. Methods for designing eccentrically loaded short columns include using equations that calculate the neutral axis position and failure mode, or using interaction diagrams that graphically show the safe ranges of moment and axial load.
This document provides information on the structural design of a simply supported reinforced concrete beam. It includes:
- A list of students enrolled in an elementary structural design course.
- Equations and diagrams showing the forces and stresses in a reinforced concrete beam with a singly reinforced bottom section.
- Limits on the maximum depth of the neutral axis according to the grade of steel.
- Examples of analyzing the stresses and determining steel reinforcement for a given beam cross-section.
- A design example calculating the dimensions and steel reinforcement for a rectangular beam with a factored uniform load.
This document discusses the design of column braces for structures. It defines braced and unbraced columns, with braced columns having zero sway and stability provided by walls or bracing, while unbraced columns are subjected to sway with stability only from other columns. It describes different types of internal and external bracing patterns and factors to consider in brace analysis, including displacement, base shear, wind loads, maximum shear and bending moments. The document provides guidelines for designing braces based on column moments and explains how bracing type affects seismic resistance parameters through a parametric study.
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.
Approximate analysis methods make simplifying assumptions to determine preliminary member forces and dimensions for indeterminate structures. Case 1 assumes diagonals cannot carry compression and shares shear between diagonals. Case 2 allows compression in diagonals. Portal and cantilever methods analyze frames by dividing into substructures at assumed hinge locations, solving each sequentially from top to bottom.
This document provides details on the design of staircases, including:
1. It describes the typical components of a staircase like flights, landings, risers, treads, nosings, waist slabs, and soffits.
2. It discusses different types of staircases like straight, quarter turn, dog-legged, open well, spiral and helicoidal.
3. It classifies staircases structurally into those with stair slabs spanning transversely or longitudinally and provides examples of each type.
4. It provides an example calculation for the design of a waist slab spanning longitudinally, including loading, bending moment calculation, reinforcement design and checks.
This document discusses several special concreting techniques:
- Pumped concrete is concrete that can be pushed through a pipeline and must have a design that prevents blockages.
- Shortcrete or gunite is a mortar or fine concrete pneumatically projected at high velocity, used for thin sections with less formwork.
- Underwater concrete requires special mixes placed via bagging, buckets, tremie pipes, or grouted aggregates to prevent water intrusion.
- Other techniques include pre-packed concrete placed underwater and special considerations for hot/cold weather concreting. Proper mix design and placement methods are essential for successful implementation of special concreting applications.
Deep beams are structural elements where a significant portion of the load is carried to the supports by compression forces combining the load and reaction. As a result, the strain distribution is nonlinear and shear deformations are significant compared to pure flexure. Examples include floor slabs under horizontal loads, short span beams carrying heavy loads, and transfer girders. The behavior of deep beams is two-dimensional rather than one-dimensional, and plane sections may not remain plane. Analysis requires a two-dimensional stress approach.
This document discusses various types of beam and column connections used in steel structures. It describes rigid, pinned, and semi-rigid connections. It also discusses different beam to beam connections like web cleat angle, clip and seat angle, and web and seat angle connections. Beam to column connections including web angle, clip and seat angle stiffened and unstiffened are explained. Finally, it covers moment resistant connections like eccentrically loaded, light moment and heavy moment connections and provides examples of designing some typical connections.
The document describes the design of a stepped footing to support a column with an unfactored load of 800 kN. A square footing with dimensions of 2.1m x 2.1m is designed with two 300mm steps. Reinforcement of #12 bars at 150mm c/c is provided. Checks are performed for bending moment, one-way shear, two-way shear, and development length which all meet code requirements. Therefore, the stepped footing design is adequate to support the given column load.
This document discusses shear and diagonal tension in beams. It begins with an introduction to shear forces and shear failure, known as diagonal tension. It then discusses direct shear stresses in beams, shear failure mechanisms, and when shear effects need to be considered in design. The document covers theoretical background on shear stresses and principal stresses. It focuses on diagonal tension failure, including the orientation of principal planes and reinforcement requirements to prevent diagonal cracking. It discusses ACI code provisions for the design of shear reinforcement, including requirements for minimum shear reinforcement.
This document discusses shear failure in reinforced concrete beams. It begins by explaining that beams require shear reinforcement to prevent dangerous shear failure before flexural failure under overloading. Shear failure is difficult to predict due to diagonal tension cracks forming within the beam. The document then examines shear stresses and diagonal tension stresses in homogeneous beams and how flexural cracks and diagonal cracks form in reinforced concrete beams without shear reinforcement. It notes that shear reinforcement in the form of stirrups is required to control diagonal cracking and prevent diagonal tension failure.
- Beam-column joints are the weakest points in reinforced concrete frames during earthquakes due to stresses that cause cracking and failure. There are two main types of failure: shear and anchorage.
- Proper design of beam-column joints including use of closed loop ties, intermediate bars, wider columns, and straight beam bars inserted into the column improves earthquake resistance by resisting distortion and improving concrete confinement.
- Innovative techniques for strengthening joints include fiber reinforced concrete and FRP wrapping to prevent cracking and increase strength. Well designed joints are crucial to avoiding damage during seismic activity.
This resource material is exclusively for the purpose of knowledge dissemination for the use of Civil engineering Fraternity, professionals & students.
This file contains state of art techniques adopted & practiced as per IS456 code provisions for analysis design & detailing of flat slab structural systems.
The presentation aims to provide clear,concise, technical details of flat slabs design.
The presentation deals with structural actions & behavior of flat slabs with visual representations obtained through finite element analysis.
The knowledge gained can be used for designing building structures frequently encountered in construction.
The presentation covers an important feature of slab systems supported on rigid & flexible support & clearly demarcates the minimum beam dimensions required to consider the supports to be either rigid or flexible.
The presentation alsoincludes clear technical drawings to highlight the importance of detailing w.r.t. rebar lay out - positioning & curtailment. Typical section drawing through middle & column strips are also included for visualizing rebar patterns in 3 -d views.
This presentation is an outcome of series of lectures for undergrad & grad students studying in civil engineering.
My next presentation would be on Analysis & design of deep beams.
Kindly mail me ( vvietcivil@gmail.com) your questions & valuable feedback.
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.
This document discusses ductile detailing of reinforced concrete (RC) frames according to Indian standards. It explains that detailing involves translating the structural design into the final structure through reinforcement drawings. Good detailing ensures reinforcement and concrete interact efficiently. Key aspects of ductile detailing covered include requirements for beams, columns, and beam-column joints to improve ductility and seismic performance. Specific provisions are presented for longitudinal and shear reinforcement in beams and columns, as well as confining reinforcement and lap splices. The importance of cover and stirrup spacing is also discussed.
This document discusses the design of columns subjected to axial compression. It covers various buckling failure modes including flexural, local, and torsional buckling. It provides definitions of critical load and slenderness ratio, which are important parameters for column design. Design approaches are discussed including selecting a trial section based on slenderness ratio, calculating the design compressive stress, and checking if the design strength exceeds the factored load. Details are also provided on built-up column design using lacing, battens, and back-to-back members.
The document discusses the behavior and analysis of reinforced concrete beams. It describes the three stages a beam undergoes when loaded: uncracked, cracked-elastic, and ultimate strength. The transformed area method is presented for calculating stresses in cracked beams. An example problem demonstrates using this method to find bending stresses in a beam section. The allowable resisting moment is also determined based on specified material stresses.
1) The document discusses the design of compression members and buckling behavior. It covers topics like Euler buckling analysis, factors that affect column strength, and modern design using column curves.
2) Key aspects reviewed include elastic buckling of pin-ended columns, the influence of imperfections and eccentric loading on column strength, and classification of sections based on their buckling behavior.
3) Design approaches like effective length, slenderness ratio, and determining the design compressive stress are summarized. Both elastic and inelastic buckling modes are addressed.
Lec03 Flexural Behavior of RC Beams (Reinforced Concrete Design I & Prof. Abd...Hossam Shafiq II
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This is a great way to be more productive but a few things to
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Design and Detailing of RC Deep beams as per IS 456-2000
1. Module 3
Design of Reinforced Concrete Deep Beams
Introduction – Minimum thickness -Steps of Designing Deep beams – design by IS 456 - Detailing of Deep beams.
Two Span Continuous
Deep Beam with Two
Point Loading
2. 1. Deep Beam Definition - IS 456
RC deep beams have useful applications in
• tall buildings,
• offshore structures and foundations
2. Deep Beam Application
A deep beam is having a depth comparable to the span
TRANSFER GIRDER
RIBBED MAT FOUNDATION
3. Deep Beam – Types
• Simply Supported or Continuous
• Rectangular or Flanged Beams
• Top or Bottom or Side Loaded
• with or without openings
3. 4. Behaviour of Deep Beams
• The elementary theory of bending for simple beams may not be applicable to deep beams even
under the linear elastic assumption.
• A deep beam is in fact a vertical plate subjected to loading in its own plane. The strain or stress
distribution across the depth is no longer a straight line, and the variation is mainly dependent on
the aspect ratio of the beam.
• The analysis of a deep beam should therefore be treated as a two dimensional plane stress
problem, and two-dimensional stress analysis methods should be used in order to obtain a realistic
stress distribution in deep beams even for a linear elastic solution.
5. L/D 2
L/D < 1
• Following approximations are suggested for design
purposes to compute the lever arm Z
Z
Z
6. 5. Compressive force path concept
• The load-carrying capacity of an RC structural member is
associated with the strength of concrete in the region of the
paths along which compressive forces are transmitted to the
supports.
• The path of a compressive force may be visualized as a flow
of compressive stresses with varying sections perpendicular
to the path direction and with the compressive force,
representing the stress resultant at each section.
7. • Failure is considered to be related to the development of
tensile stresses in the region of the path that may develop
due to a number of causes, the main ones being ;
• Changes in the path direction
• Varying intensity of compressive stress field along
path Stress increase at the tip of inclined cracks
• Bond failure
8. 6. Arch and tie action
• Mode of failure is not associated with beam
action.
• The variation in bending moment along the
beam span is mainly effected by a change of
the lever arm rather than the magnitude of the
internal horizontal actions.
• Such behaviour has been found to result from
the fact that the force sustained by the tension
reinforcement of a deep beam at its ultimate
limit state is constant throughout the beam
span.
• RC deep beam at its ultimate limit state cannot
rely on beam action to sustain the shear
forces, it would have to behave as a tied arch.
10. 7. Deep beam behaviour at ultimate limit state
Behaviour of a deep RC beam with a rectangular cross section and without shear
reinforcement may be divided into two types of behaviour depending on
• either a/d, for beams subjected to two-point loading,
• or L/d, for beams under UDL
• The Figure indicates that the mode of failure is
characterized by a deep inclined crack which
appears to have formed within the shear span
independently of the flexural cracks.
• The inclined crack initiates at the bottom face of the
beam close to the support, extends towards the top
face of the beam in the region of the load point.
Case 1:Deep beam without web reinforcement subjected to two-point loading with a / d=1.5
• Eventually causes failure of the compressive zone in the middle zone of the beam.
• The causes of failure should therefore be sought within the middle, rather than the shear
span of such beams
11. • Failure is associated with a large reduction of the size of the compressive
zone of the cross-section coinciding with the tip of the main inclined crack.
• This type of failure may be prevented either by providing transverse
reinforcement that would sustain the tensile stresses that cannot be
sustained by concrete alone, or by reducing the compressive stresses.
• Transverse reinforcement only within the shear span can be equally effective.
• Such reinforcement reduces the compressive stresses that develop in the
cross-section which coincides with the tip of the inclined crack, as it sustains
a portion of the bending moment developing in that section.
• However, the presence of transverse reinforcement beyond the critical
section is essential, as with stirrups only to the critical section does not
safeguard against brittle failure.
• This type of failure may be prevented by extending the transverse
reinforcement beyond the critical section to a distance approximately equal
to the depth of the compressive zone.
12. Case 2 ; Deep beam, without shear reinforcement, under two point loading with a/d = 1.0
• This mode of failure is characterized by a deep inclined
crack which appears to have formed within the shear
span independently of the flexural cracks.
• Inclined crack almost coincides with the line joining
the load point and the support.
• It usually starts within the beam web, almost half way
between the loading and support points, at a load
level significantly lower than the beam load-carrying
capacity, and propagates simultaneously towards
these points with increasing load.
• Eventually, collapse of the beam occurs owing to a
sudden extension of the inclined crack towards the top
and bottom face of the beam in the regions of the load
point and support, respectively, within the shear span.
• Such a mode of failure is usually referred to as
‘diagonal- splitting’
Diagonal Splitting
13. • Due to the large compressive forces carried by deep beams, it is unlikely
that, the presence of conventional web reinforcement in the form of
vertical stirrups considerably improves load-carrying capacity.
• Such reinforcement may delay the cracking process but may give only a
small increase in load-carrying capacity.
• Web reinforcement is provided in order to prevent splitting of the
inclined portion of the compressive force path (diagonal splitting).
18. C. Web Reinforcement in Deep Beams
CASE 1: TOP LOADED DEEP BEAMS
• Load is resisted by ARCH action as it is stiffer than
Truss action
• Stirrups are not necessary as they do not cross the
cracks
• A minimum reinforcement placed in both vertical
and horizontal directions as in RC walls is adequate.
Failure
Pattern in
TOP LOADED
DEEP BEAMS
19. • In continuous beams half
the flexural reinforcement
(horizontal) provided over
the supports may be part
of this
• Near the supports,
additional bars of the
same size used for web
reinforcement should be
introduced as shown
20. CASE 2: BOTTOM LOADED DEEP BEAMS
Failure
Pattern in
BOTTOM
LOADED
DEEP BEAMS
• Load is resisted mainly by vertical or inclined tension
towards the supports
• To enable the compression arch to develop, the whole
of the suspended load must be transferred by means
of vertical reinforcement into the compression zone of
the beam.
• Suspender Stirrups should completely surround the
bottom flexural reinforcement and extend into the
compression zone of the beam.
• Spacing should not exceed 150 mm
21. Example 1 – Simply Supported Deep Beam
A transfer girder 5.25 m length supports two columns located at 1.75 m from each end.
Column loads = 3750 kN . Total depth of the beam = 4.2m and width of support = 520mm.
Concrete Grade = M40, Fe 415 steel.
Design and Detail the girder.
Leff
1. C/C distance between supports
2. 1.15 x clear span whichever is less
22. Step 1: Check for bearing capacity at support
• Let B = Beam width
• Allowable stress = 0.45 x 40 = 18MPa
• Support width = 520 mm
• Effective width of support = 0.2x Clear Span
= 0.2x(5250 - 2x520) = 842 mm
• Adopt 520 mm
• 18 = 1.5 x 3750 x 103 / (520 x B); B = 600 mm
• Leff = 5250 - 520 = 4730 mm or 1.15 x (5250 – 2 x520) = 4841 mm ; Leff = 4730 mm CL 29.2
• D/b < 25 or L/b < 50 : 4200/600 = 7 ; 4730/600 = 7.88
• L/D = 4730/4200 = 1.13 > 1 and < 2 ; Deep Beam category CL 29.1
23. Step 2 : Factored Moments, Ast
• Mu = 1. 5 x ( 3750 x 1.49) = 8382 kNm
• Lever arm Z = 0.2 (Leff + 2D) = 0.2 x (4730 + 2 x 4200) = 2626mm CL 29.2 (a)
• Ast = Mu/(0.87fy Z) = 8382 x106 /(0.87 x 415 x 2626) = 8841 mm2
• Ast min = 0.85 x b x D /415 = 0.85 x 600 x 4200 /415 = 5161 mm2 cl 26.5.1.1
• Adopt 18 - #25 , Ast = 8836 mm2
Step 3: Detailing of Rebars
CL 29.3.1
• Tension Zone Depth = 0.25 D – 0.05Leff = 0.25 x 4200 –
0.05 x 4730 = 814 mm
Assume Clear bottom and side cover = 40 mm
• Arrange bars in 6 rows in a depth = 814 mm
814
39
155
600
24. Step 4: Detailing of Vertical Rebars: CL 32.5
• Ast min / m length = 0.0012 x 600 x 1000 = 720 mm2/m
• Provide on each face : 360 mm2/m
• Spacing of #12 rebars = 1000 x 113/360= 313 mm < 450 mm
• Adopt #12@300 mm c/c
Step 5: Detailing of Horizontal Rebars
29.3.4 Side Face Reinforcement
Side face reinforcement shall comply with requirements of minimum
reinforcement of walls
• Ast min / m length = 0.002 x 600 x 1000 = 1200 mm2/m
• Provide on each face : 600 mm2/m
• Spacing of #16 rebars = 1000 x 201/600 = 335 mm < 450 mm
• Adopt #16@300 mm c/c
25. Dia 50 Dia
Anchorage value
Ld 0.8Ld
With 900 Bend
8dia*
With 1800 Hook
16 dia** * ** * **
25 1250 -200 -400 1050 850 840 680
16 800 -128 -256 672 544 540 435
End Anchorage as per CL 29.3.1(b)
40
520
355
5dia
(125)
485
• For #25 - middle bars Corner bars
ELEVATION
40
520
3555dia
(125)
Support Face
PLAN
40
40
600(BeamWidth)
325
1
1
2
2
26. 814
Tension Zone
CL 29.3.1
Compression Zone
3386 mm
5250
520
#12@300 ; cl 32.5 (a)
Vertical Stirrups
#16@300;cl32.5(c) 18-#25 in
6 Rows
#12@300
Vertical additional rebars
near support CL 32.5 (a)
#16@300 additional rebars near support (horizontal)
adequately anchored as per CL 32.5(c)
1260
2100
TYP
27. Example 2 – Simply Supported Deep Beam ; M20, Fe415
Step 1: Check for bearing capacity at support
• Allowable stress = 0.45 x 20 = 9MPa
• Support width = 500 mm
• Effective width of support = 0.2x Clear Span
= 0.2 x 5000 = 1000 mm
• Adopt 500 mm
• Total Load W = 0.25 x 3.5 x 6 x 25 + 200 x 6 = 1332 kN
• Reaction at each support = W/2 =666 kN
• Bearing Pressure = 1.5 x 666 x 103 / (500 x 250) = 8 MPa < 9 MPa OK
• Leff = 5500 mm or 1.15 x 5000 = 5750 mm ; Leff = 5500 mm CL 29.2
• D/b = 14 ; < 25 or L/b=22; < 50
• L/D = 5500/3500 = 1.57 > 1 and < 2 ; Deep Beam category CL 29.1
28. Step 2 : Factored Moments, Ast
• w(kN/m) = 1332/6 = 222 kN/m
• Mu = 1. 5 x 222 x 5.52/8 = 1260 kNm
• Lever arm Z = 0.2 (Leff+ 2D) = 0.2 x (5500 + 2 x 3500) = 2500mm CL 29.2 (a)
• Ast = Mu/(0.87fy Z) = 1260 x 106 /(0.87 x 415 x 2500) = 1396 mm2
• Ast min = 0.85 x b x D /415 = 0.85 x 250 x 3500 /415 = 1792 mm2 CL 26.5.1.1
• Adopt 10 - #16 , Ast = 2010 mm2
Step 3: Detailing of Rebars
CL 29.3.1
• Tension Zone Depth = 0.25 D – 0.05Leff = 0.25 x 3500 – 0.05 x 5500 = 600 mm
• Assume Clear bottom and side cover = 40 mm
• Arrange bars in 5 rows in a depth = 600 mm
600
40
140
140
140
250
140
29. Step 4: Detailing of Vertical Rebars: CL 32.5
• Ast min / m length = 0.0012 x 250 x 1000 = 300 mm2/m
• Provide on each face : 150 mm2/m
• Spacing of #10 rebars = 1000 x 78.5/150= 523 mm > 450 mm
• Adopt #10@450 mm c/c
Step 5: Detailing of Horizontal Rebars
29.3.4 Side Face Reinforcement
Side face reinforcement shall comply with requirements of minimum
reinforcement of walls
• Ast min / m length = 0.002 x 250 x 1000 = 500 mm2/m
• Provide on each face : 250 mm2/m
• Spacing of #12 rebars = 1000 x 113/250 = 452 mm > 450 mm
• Adopt #12@450 mm c/c
30. Dia 50 Dia
With 1800 Bend
Anchorage
value = 16dia
Ld 0.8Ld
12 600 -192 408 326
16 800 -256 544 435
End Anchorage as per CL 29.3.1(b)
• For #16 in all rows
40
500
3805dia
(80)
Support Face
PLAN
40
40
250(BeamWidth)
64 (min = 4dia)
1
1
2
2
Rebars are embedded into the support by extending it to
a maximum possible length and then providing 1800
hook which project along the width of the beam
31. 600
Tension Zone
CL 29.2.1
Compression Zone
2900 mm
6000
500
#10@450 ; cl 32.5 (a)
Vertical Stirrups
#12@450
cl32.5(c)
10 -#16 in
5 Rows
#10@450
Vertical additional rebars
near support CL 32.5 (a)
#12@450 additional rebars near support (horizontal)
adequately anchored as per CL 32.5(c)
1050
1750
TYP
1050
32. Example 3 : Fixed ends and continuous Deep Beam
Step 1: Check for bearing capacity at support
• Concrete Grade = M35
• Allowable stress = 0.45 x 35 = 15.75 MPa CL 34.4
• Support width = 500 mm
• Effective width of support = 0.2x Clear Span
= 0.2 x 5000 = 1000 mm
• Adopt 500 mm
• Total Load W = 0.25 x 3 x 11.5 x 25 + 200 x11.5 = 2515.625 kN
• Reaction at Interior support = W = 2515.625/2 =1257.81 kN
• Bearing Pressure = 1.5 x 1257.81 x 103 / (500 x 250)
= 15 MPa < 15.75 MPa OK
• Leff = 5500 mm or 1.15 x 5000 = 5750 mm
• Adopt Leff = 5500 mm CL 29.2
• D/b = 12 < 25 or L/b=22; < 50
• L/D = 5500/3000 = 1.83 > 1 and < 2.5
• Deep Beam category CL 29.1
33. Step 2 : Factored Moments, Ast
w(kN/m) = 2515.625 /11.5 = 218.75 kN/m
Span Moment
• Mu = 1. 5 x 218.75 x 5.52/24 = 413.6 kNm
• Lever arm Z = 0.2 (Leff + 1.5D) = 0.2 x (5500 + 1.5 x 3000) = 2000mm CL 29.2 (b)
• Ast = Mu/(0.87fy Z) = 413.6 x 106 /(0.87 x 415 x 2000) = 573 mm2
• Ast min = 0.85 x b x D /415 = 0.85 x 250 x 3000 /415 = 1536 mm2 CL 26.5.1.1
• Adopt 8 - #16 , Ast = 1608 mm2
Support Moment
• Mu = 1. 5 x 218.75 x 5.52/12 = 827 kNm
• Lever arm Z = 0.2 (Leff + 1.5D) = 0.2 x (5500 + 1.5 x 3000) = 2000mm CL 29.2 (b)
• Ast = Mu/(0.87fy Z) = 827 x 106 /(0.87 x 415 x 2000) = 1145 mm2
• Ast min = 0.85 x b x D /415 = 0.85 x 250 x 3000 /415 = 1536 mm2 CL 26.5.1.1
• Adopt Ast = 1536 mm2
34. Step 3: Detailing of Rebars in Span region
CL 29.3.1
• Tension Zone Depth = 0.25 D – 0.05Leff = 0.25 x 3000 – 0.05 x 5500 = 475 mm
• Assume Clear bottom and side cover = 40 mm
• Arrange bars in 4 rows in a depth = 475 mm 475
40
145
145
145
250
35. Step 4: Detailing of Rebars in Support region CL 29.3.2
• Clear Span / D = 5000 / 3000 = 1.67 > 1 and < 2.5
• Rebars are placed in two zones CL 29.3.2 (b)
• Ast = 1536 mm2
• Zone1
• Depth = 0.2D = 0.2 x 3000 = 600 mm
• Ast1 = 1536 x 0.5 x (1.67 – 0.5) = 900 mm2
• Adopt 6 - #16 – 1206 mm2 in three rows
• Zone2
• Depth = 0.3D = 0.3 x 3000 = 900 mm on both sides of mid depth
• Ast1 = (1536 – 900) = 636 mm2
• Adopt 6 - #12 – 678 mm2 in three rows
36. Step 5: Detailing of Vertical Rebars: CL 32.5
• Ast min / m length = 0.0012 x 250 x 1000 = 300 mm2/m
• Provide on each face : 150 mm2/m
• Spacing of #10 rebars = 1000 x 78.5/150= 523 mm > 450 mm
• Adopt #10@450 mm c/c (stirrups)
Step 6: Detailing of Horizontal Rebars
29.3.4 Side Face Reinforcement
Side face reinforcement shall comply with requirements of minimum
reinforcement of walls
• Ast min / m length = 0.002 x 250 x 1000 = 500 mm2/m
• Provide on each face : 250 mm2/m
• Spacing of #12 rebars = 1000 x 113/250 = 452 mm > 450 mm
• Adopt #12@450 mm c/c
37. Dia 50 Dia
With 1800 Bend
Anchorage
value = 16dia
Ld 0.8Ld
12 600 -192 408 326
16 800 -256 544 435
End Anchorage as per CL 29.3.1(b)
• For #16 in all rows
40
500
3805dia
(80)
Support Face
PLAN
40
40
250(BeamWidth)
64 (min = 4dia)
1
1
2
2
Rebars are embedded into the support by extending it to
a maximum possible length and then providing 1800
hook which project along the width of the beam
38. 900 900 0.3D
900
900
(0.5D)
1500
8 - #16 in
4 Rows
475
(0.2D) 600
(0.6D)
1800
6 - #16 in 3 Rows (Zone 1)
1500* 1500*1500* 1500*
#10@450 ; cl 32.5 (a)
Vertical Stirrups
6 - #12 in
3 Rows
(Zone2)
5500 5500
3000
* Curtailment position measured
from support face
Additional Rebars in Support
Regions (A,B,C) on both faces
#10@450 (vertical)
+
#12 @450 (Horizontal)
A
B C
#12 @450
CL 32.5 (c)
250
8 - #16 in
4 Rows
6 - #12 in
3 Rows (Zone2)
6 - #16 in
3 Rows (Zone 1)
#10@450
39. Example 4 : Fixed ends and continuous Deep Beam
A reinforced girder 4.5 m deep is continuous over two spans 9 m c/c, resting on column supports 900 mm
width is to be designed to support a total load of 200 kN/m including its own weight. M20 and Fe415
Step 1: Check for bearing capacity at support
• Concrete Grade = M20; Allowable stress = 0.45 x 20 = 9 MPa CL 34.4
• Support width = 900 mm; Effective width of support = 0.2x Clear Span = 0.2 x 8100 = 1620 mm
• Adopt 900 mm
• Total Load W = 200 x 18.9 = 3780 kN
• Reaction at Interior support = W = 3780/2 =1890 kN
• 1.5 x 1890 x 103 / (900 x B) = 9 ; B = 350 mm
• Leff = 9000 mm or 1.15 x 8100 = 9315 mm
• Adopt Leff = 9000 mm CL 29.2
• D/b = 12.8 < 25 or L/b=25.7 < 50
• L/D = 9000/4500 = 2 > 1 and < 2.5
• Deep Beam category CL 29.1
40. Step 2 : Factored Moments, Ast
Span Moment
• Mu = 1. 5 x 200 x 92/24 = 1012.5 kNm
• Lever arm Z = 0.2 (Leff + 1.5D) = 0.2 x (9000 + 1.5 x 4500) = 3150mm CL 29.2 (b)
• Ast = Mu/(0.87fy Z) = 1012.5 x 106 /(0.87 x 415 x 3150) = 890 mm2
• Ast min = 0.85 x b x D /415 = 0.85 x 350 x 4500 /415 = 3226 mm2 CL 26.5.1.1
• Adopt 8 - #25 in 4 rows
Support Moment
• Mu = 1. 5 x 200 x 92/12 = 2025 kNm
• Ast = Mu/(0.87fy Z) = 2025 x 106 /(0.87 x 415 x 3150) = 1780 mm2
• Ast min = 3226 mm2 CL 26.5.1.1
• Adopt Ast = 3226 mm2
41. Step 3: Detailing of Rebars in Span region
CL 29.3.1
• Tension Zone Depth = 0.25 D – 0.05Leff = 0.25 x 4500 – 0.05 x 9000 = 675 mm
• Assume Clear bottom and side cover = 40 mm
• Arrange bars in 4 rows in a depth = 675 mm 675
45
210
210
210
350
42. Step 4: Detailing of Rebars in Support region CL 29.3.2
• Clear Span / D = 8100/ 4500 = 1.8 > 1 and < 2.5
• Rebars are placed in two zones CL 29.3.2 (b)
• Ast = 3226 mm2
• Zone1
• Depth = 0.2D = 0.2 x 4500 = 900 mm
• Ast1 = 3226 x 0.5 x (1.8 – 0.5) = 2097 mm2
• Adopt 8 - #20 – 2512 mm2 in Four rows
• Zone2
• Depth = 0.3D = 0.3 x 4500 = 1350 mm on both sides of mid depth
• Ast1 = (3226 – 2097) = 1129 mm2
• Adopt 6 - #16 – 1206 mm2 in three rows
43. Step 4: Detailing of Vertical Rebars: CL 32.5
• Ast min / m length = 0.0012 x 350 x 1000 = 420 mm2/m
• Provide on each face : 210 mm2/m
• Spacing of #10 rebars = 1000 x 78.5/210= 373 mm < 450 mm
• Adopt #10@300 mm c/c (stirrups)
Step 5: Detailing of Horizontal Rebars
29.3.4 Side Face Reinforcement
Side face reinforcement shall comply with requirements of minimum
reinforcement of walls
• Ast min / m length = 0.002 x 350 x 1000 = 700 mm2/m
• Provide on each face : 350 mm2/m
• Spacing of #12 rebars = 1000 x 113/350 = 322 mm < 450 mm
• Adopt #12@300 mm c/c
44. Dia 50 Dia
With 1800 hook
Anchorage
value = 16 dia
Ld 0.8Ld
12 600 -192 408 326
16 800 -256 544 435
20 1000 -320 680 544
25 1250 -400 850 680
End Anchorage as per CL 29.3.1(b)
40
900
7355dia
(125)
Support Face
PLAN
40
40
350(BeamWidth)
100 (min = 4dia)
1
1
2
2 Rebars are embedded into the support by extending it to
a maximum possible length and then providing 1800
hook which project along the width of the beam
For # 25 bars
45. 1350 1350 0.3D
1350
1350
(0.5D)
2250
8 - #25 in
4 Rows
675
(0.2D) 900
(0.6D)
2700
8 - #20 in 4 Rows (Zone 1)
2250* 2250*2250* 2250*
#10@300 ; cl 32.5 (a)
Vertical Stirrups
6 - #16 in
3 Rows
(Zone2)
9000 9000
4500
*0.5D - Curtailment position
measured from support face
Additional Rebars in Support
Regions (A,B,C) on both faces
#10@300 (vertical)
+
#12 @300 (Horizontal)
A B C
#12 @300
CL 32.5 (c)