This document discusses the computation of parameters for designing reinforced concrete beams and one-way slabs. It outlines six assumptions made in the limit state design approach, including that plane sections remain plane after bending and concrete strain is limited to 0.0035. Three types of beams are described - rectangular, T, and L-beams. Equations of equilibrium are presented, including equations to calculate the total compression and tension forces, C and T. Parameters like the area of tension steel, effective depth, and neutral axis depth are also defined.
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 information on the design of a concrete beam, including:
1) Key principles in beam design such as determining the effective depth ratio and performing deflection checks.
2) Details on flanged beam design including how the location of the neutral axis affects the process.
3) Procedures for continuous beam design including determining load cases, calculating fixed end moments, and using moment distribution.
The document discusses the design of slender columns. It defines a slender column as having a slenderness ratio (length to least lateral dimension) greater than 12. Slender columns experience appreciable lateral deflection even under axial loads alone. The design of slender columns can be done using three methods - the strength reduction coefficient method, additional moment method, or moment magnification method. The document outlines the step-by-step procedure for designing a slender column using the additional moment method, which involves determining the effective length, initial moments, additional moments, total moments accounting for a reduction coefficient, and redesigning the column for combined axial load and bending.
This document discusses reinforcement detailing of common reinforced concrete structural members. It provides guidelines on proper detailing practices and common mistakes to avoid. Key points covered include reinforcement requirements for slabs, beams, columns, and foundations. Specific details are given for elements like continuous beams, cantilever beams, beam-column joints, and seismic detailing. The document emphasizes the importance of reinforcement detailing for structural safety and highlights detailing aspects that are essential for execution and safety of reinforced concrete structures.
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.
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.
Shear, bond bearing,camber & deflection in prestressed concreteMAHFUZUR RAHMAN
This Presentation was presented as a partial fulfillment of Prestressed Concrete Design Lab Course. Behavior & Design of Prestress on above topic is shortly discussed on the presentation. The part "Shear & Shear Design in Prestressed" Concrete was prepared by me. Other topics were prepared by other members of my group. Thanks to all my teachers & friends who helped us in different stages during preparation of the total presentation.
Cofferdams are temporary structures used to allow construction in areas that would otherwise be underwater or difficult to work in. They are enclosures that hold back water and soil to create a dry work area. Various types of cofferdams exist, including braced, earth-type, timber crib, double-walled sheet pile, and cellular designs. Proper construction and safety precautions are vital as workers will be exposed to flooding hazards. Leakage is prevented through measures like cement grouting, clay sealing, and tarpaulins.
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 information on the design of a concrete beam, including:
1) Key principles in beam design such as determining the effective depth ratio and performing deflection checks.
2) Details on flanged beam design including how the location of the neutral axis affects the process.
3) Procedures for continuous beam design including determining load cases, calculating fixed end moments, and using moment distribution.
The document discusses the design of slender columns. It defines a slender column as having a slenderness ratio (length to least lateral dimension) greater than 12. Slender columns experience appreciable lateral deflection even under axial loads alone. The design of slender columns can be done using three methods - the strength reduction coefficient method, additional moment method, or moment magnification method. The document outlines the step-by-step procedure for designing a slender column using the additional moment method, which involves determining the effective length, initial moments, additional moments, total moments accounting for a reduction coefficient, and redesigning the column for combined axial load and bending.
This document discusses reinforcement detailing of common reinforced concrete structural members. It provides guidelines on proper detailing practices and common mistakes to avoid. Key points covered include reinforcement requirements for slabs, beams, columns, and foundations. Specific details are given for elements like continuous beams, cantilever beams, beam-column joints, and seismic detailing. The document emphasizes the importance of reinforcement detailing for structural safety and highlights detailing aspects that are essential for execution and safety of reinforced concrete structures.
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.
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.
Shear, bond bearing,camber & deflection in prestressed concreteMAHFUZUR RAHMAN
This Presentation was presented as a partial fulfillment of Prestressed Concrete Design Lab Course. Behavior & Design of Prestress on above topic is shortly discussed on the presentation. The part "Shear & Shear Design in Prestressed" Concrete was prepared by me. Other topics were prepared by other members of my group. Thanks to all my teachers & friends who helped us in different stages during preparation of the total presentation.
Cofferdams are temporary structures used to allow construction in areas that would otherwise be underwater or difficult to work in. They are enclosures that hold back water and soil to create a dry work area. Various types of cofferdams exist, including braced, earth-type, timber crib, double-walled sheet pile, and cellular designs. Proper construction and safety precautions are vital as workers will be exposed to flooding hazards. Leakage is prevented through measures like cement grouting, clay sealing, and tarpaulins.
Cable Layout, Continuous Beam & Load Balancing MethodMd Tanvir Alam
This document provides information on cable layout and load balancing methods for prestressed concrete beams. It discusses layouts for simple, continuous, and cantilever beams. For simple beams, it describes layouts for pretensioned and post-tensioned beams, including straight, curved, and bent cable configurations. It also compares the load carrying capacities of simple and continuous beams. The document concludes by explaining the load balancing method for design, using examples of how to balance loads in simple, cantilever, and continuous beam configurations.
This document discusses T-beams, which are more suitable than rectangular beams in reinforced concrete. There are two types of T-beams: monolithic and isolated. It provides notations and code recommendations for T-beams from IS: 456. There are three cases for finding the depth of the neutral axis in a T-beam: when it lies in the flange, in the rib, or at the junction. An example problem is worked through to find the moment of resistance for a given T-beam section using the provided concrete and steel properties.
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 provides information on the structural design of bridges and culverts. It discusses the design of solid slab bridges, T-beam bridges, and balanced cantilever bridges. It also covers the distribution of live loads on bridge slabs using methods like Pigeaud's theory and Courbon's method. Finally, it summarizes the design process for box culverts, including determining load cases and calculating bending moments and reinforcement requirements.
The document discusses bolted connections and provides specifications for bolt hole sizes, pitch, and spacing in bolted connections according to IS 800-2007. It covers various types of bolted joints including lap joints, butt joints, and their modes of failure. High strength friction grip bolts are described which provide rigid connections through clamping action and prevent slippage. The advantages of HSFG bolts include their ability to transmit load through friction eliminating stress concentrations in holes, while their drawbacks include higher cost and fabrication efforts compared to normal bolts.
Peer review presentation for the strut and tie method as an analysis and design approach for the mat on piles foundations of the primary separation cell (vessel).
The document discusses buckling and its theories. It defines buckling as the failure of a slender structural member subjected to compressive loads. It provides examples of structures that can experience buckling. It explains Euler's theory of buckling which derived an equation for the critical buckling load of a long column based on its bending stress. The assumptions of Euler's theory are listed. Four cases of long column buckling based on end conditions are examined: both ends pinned, both ends fixed, one end fixed and one end pinned, one end fixed and one end free. Effective lengths are defined for each case and the corresponding critical buckling loads given. Limitations of Euler's theory are noted. Rankine's empirical formula for calculating ultimate
this slide will clear all the topics and problem related to singly reinforced beam by limit state method, things are explained with diagrams , easy to understand .
Prestressed concrete is a structural material that allows for predetermined, engineering stresses to be placed in members to counteract the stresses that occur when they are subject to loading.
Lec10 Bond and Development Length (Reinforced Concrete Design I & Prof. Abdel...Hossam Shafiq II
This document discusses bond and development length in reinforced concrete. It defines bond as the adhesion between concrete and steel reinforcement, which is necessary to develop their composite action. Bond is achieved through chemical adhesion, friction from deformed bar ribs, and bearing. Development length refers to the minimum embedment length of a reinforcement bar needed to develop its yield strength by bonding to the surrounding concrete. The development length depends on factors like bar size, concrete strength, bar location, and transverse reinforcement. It also provides equations from design codes to calculate the development length for tension bars, compression bars, bundled bars, and welded wire fabric. Hooked bars can be used when full development length is not available, and the document discusses requirements for standard hook geome
This document discusses the design of beams. It defines different types of beams like floor beams, girders, lintels, purlins, and rafters. It describes how beams are classified based on their support conditions as simply supported, cantilever, fixed, or continuous beams. Commonly used beam sections include universal beams, compound beams, and composite beams. The document also covers plastic analysis of beams, classification of beam sections, and failure modes of beams.
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.
Retaining walls are used to retain earth in a vertical position where there is an abrupt change in ground level. There are several types of retaining walls including gravity, cantilever, counterfort, and buttress walls. Cantilever walls are the most common type for heights up to 8 meters. They consist of a vertical stem and base slab that behave like one-way cantilevers. Counterfort walls include transverse supports called counterforts to reduce bending moments in the stem and slabs. Proper design of the stem, heel slab, toe slab, and foundation depth is required to resist overturning, sliding, soil pressure, and bending failure.
Prestressed concrete combines high-strength concrete and high-strength steel in an active manner by tensioning steel tendons and holding them against the concrete, putting it into compression. This transforms concrete from a brittle to a more elastic material. It allows for optimal use of each material's properties and better behavior under loads. Prestressed concrete was pioneered in the 1930s and its use has expanded, finding applications in bridges and other structures. Common methods are pretensioning and post-tensioning, using various tendon types, with bonded or unbonded configurations. Tensioning is done using mechanical, hydraulic, electrical or chemical devices.
This document summarizes the key aspects of box culvert design and analysis. Box culverts consist of horizontal and vertical slabs built monolithically, and are used for bridges with limited stream flows and high embankments up to spans of 4 meters. They are economical due to their rigidity and do not require separate foundations. Design loads include concentrated wheel loads, uniform loads from embankments and decks, sidewall weights, water pressure when full, earth pressures, and lateral loads. The culvert is analyzed for moments, shears, and thrusts using classical methods to determine force effects from these various loading conditions.
Design of shallow foundation slide sharezameer1979
1. The document discusses various types of shallow foundations including spread footings, combined footings, strap or cantilever footings, and mat or raft foundations.
2. Design of foundations involves determining the safe bearing capacity of soil and proportioning the size, thickness, and reinforcement of footings based on bending moment and shear force calculations.
3. Numerical examples show how to calculate the required width, length, or depth of different footings given soil properties and applied loads using bearing capacity equations.
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 presentation discusses the T-beam design method using the Working Stress Design (WSD) approach for singly and doubly reinforced beams. T-beams have a monolithically cast slab that acts as part of the beam and resists longitudinal compression in positive moment zones. The WSD method designs structures such that all nominal stresses remain in the elastic limit. Singly reinforced beams only have rebar in the tension zone, while doubly reinforced beams require additional rebar in the compression zone to resist the maximum moment. The design procedure for T-beams involves determining the bending moment, section properties, stress limits and distribution, and sizing of reinforcement.
This document provides an example of designing a rectangular reinforced concrete beam. It includes calculating the loads, bending moment, required tension reinforcement, checking shear capacity and deflection. For a simply supported beam with a uniformly distributed load, the document calculates the steel reinforcement area required using formulas and tables. It then checks that the beam satisfies requirements for shear capacity, minimum and maximum steel ratios, and deflection. The document also provides an example of designing a doubly reinforced beam.
Cable Layout, Continuous Beam & Load Balancing MethodMd Tanvir Alam
This document provides information on cable layout and load balancing methods for prestressed concrete beams. It discusses layouts for simple, continuous, and cantilever beams. For simple beams, it describes layouts for pretensioned and post-tensioned beams, including straight, curved, and bent cable configurations. It also compares the load carrying capacities of simple and continuous beams. The document concludes by explaining the load balancing method for design, using examples of how to balance loads in simple, cantilever, and continuous beam configurations.
This document discusses T-beams, which are more suitable than rectangular beams in reinforced concrete. There are two types of T-beams: monolithic and isolated. It provides notations and code recommendations for T-beams from IS: 456. There are three cases for finding the depth of the neutral axis in a T-beam: when it lies in the flange, in the rib, or at the junction. An example problem is worked through to find the moment of resistance for a given T-beam section using the provided concrete and steel properties.
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 provides information on the structural design of bridges and culverts. It discusses the design of solid slab bridges, T-beam bridges, and balanced cantilever bridges. It also covers the distribution of live loads on bridge slabs using methods like Pigeaud's theory and Courbon's method. Finally, it summarizes the design process for box culverts, including determining load cases and calculating bending moments and reinforcement requirements.
The document discusses bolted connections and provides specifications for bolt hole sizes, pitch, and spacing in bolted connections according to IS 800-2007. It covers various types of bolted joints including lap joints, butt joints, and their modes of failure. High strength friction grip bolts are described which provide rigid connections through clamping action and prevent slippage. The advantages of HSFG bolts include their ability to transmit load through friction eliminating stress concentrations in holes, while their drawbacks include higher cost and fabrication efforts compared to normal bolts.
Peer review presentation for the strut and tie method as an analysis and design approach for the mat on piles foundations of the primary separation cell (vessel).
The document discusses buckling and its theories. It defines buckling as the failure of a slender structural member subjected to compressive loads. It provides examples of structures that can experience buckling. It explains Euler's theory of buckling which derived an equation for the critical buckling load of a long column based on its bending stress. The assumptions of Euler's theory are listed. Four cases of long column buckling based on end conditions are examined: both ends pinned, both ends fixed, one end fixed and one end pinned, one end fixed and one end free. Effective lengths are defined for each case and the corresponding critical buckling loads given. Limitations of Euler's theory are noted. Rankine's empirical formula for calculating ultimate
this slide will clear all the topics and problem related to singly reinforced beam by limit state method, things are explained with diagrams , easy to understand .
Prestressed concrete is a structural material that allows for predetermined, engineering stresses to be placed in members to counteract the stresses that occur when they are subject to loading.
Lec10 Bond and Development Length (Reinforced Concrete Design I & Prof. Abdel...Hossam Shafiq II
This document discusses bond and development length in reinforced concrete. It defines bond as the adhesion between concrete and steel reinforcement, which is necessary to develop their composite action. Bond is achieved through chemical adhesion, friction from deformed bar ribs, and bearing. Development length refers to the minimum embedment length of a reinforcement bar needed to develop its yield strength by bonding to the surrounding concrete. The development length depends on factors like bar size, concrete strength, bar location, and transverse reinforcement. It also provides equations from design codes to calculate the development length for tension bars, compression bars, bundled bars, and welded wire fabric. Hooked bars can be used when full development length is not available, and the document discusses requirements for standard hook geome
This document discusses the design of beams. It defines different types of beams like floor beams, girders, lintels, purlins, and rafters. It describes how beams are classified based on their support conditions as simply supported, cantilever, fixed, or continuous beams. Commonly used beam sections include universal beams, compound beams, and composite beams. The document also covers plastic analysis of beams, classification of beam sections, and failure modes of beams.
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.
Retaining walls are used to retain earth in a vertical position where there is an abrupt change in ground level. There are several types of retaining walls including gravity, cantilever, counterfort, and buttress walls. Cantilever walls are the most common type for heights up to 8 meters. They consist of a vertical stem and base slab that behave like one-way cantilevers. Counterfort walls include transverse supports called counterforts to reduce bending moments in the stem and slabs. Proper design of the stem, heel slab, toe slab, and foundation depth is required to resist overturning, sliding, soil pressure, and bending failure.
Prestressed concrete combines high-strength concrete and high-strength steel in an active manner by tensioning steel tendons and holding them against the concrete, putting it into compression. This transforms concrete from a brittle to a more elastic material. It allows for optimal use of each material's properties and better behavior under loads. Prestressed concrete was pioneered in the 1930s and its use has expanded, finding applications in bridges and other structures. Common methods are pretensioning and post-tensioning, using various tendon types, with bonded or unbonded configurations. Tensioning is done using mechanical, hydraulic, electrical or chemical devices.
This document summarizes the key aspects of box culvert design and analysis. Box culverts consist of horizontal and vertical slabs built monolithically, and are used for bridges with limited stream flows and high embankments up to spans of 4 meters. They are economical due to their rigidity and do not require separate foundations. Design loads include concentrated wheel loads, uniform loads from embankments and decks, sidewall weights, water pressure when full, earth pressures, and lateral loads. The culvert is analyzed for moments, shears, and thrusts using classical methods to determine force effects from these various loading conditions.
Design of shallow foundation slide sharezameer1979
1. The document discusses various types of shallow foundations including spread footings, combined footings, strap or cantilever footings, and mat or raft foundations.
2. Design of foundations involves determining the safe bearing capacity of soil and proportioning the size, thickness, and reinforcement of footings based on bending moment and shear force calculations.
3. Numerical examples show how to calculate the required width, length, or depth of different footings given soil properties and applied loads using bearing capacity equations.
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 presentation discusses the T-beam design method using the Working Stress Design (WSD) approach for singly and doubly reinforced beams. T-beams have a monolithically cast slab that acts as part of the beam and resists longitudinal compression in positive moment zones. The WSD method designs structures such that all nominal stresses remain in the elastic limit. Singly reinforced beams only have rebar in the tension zone, while doubly reinforced beams require additional rebar in the compression zone to resist the maximum moment. The design procedure for T-beams involves determining the bending moment, section properties, stress limits and distribution, and sizing of reinforcement.
This document provides an example of designing a rectangular reinforced concrete beam. It includes calculating the loads, bending moment, required tension reinforcement, checking shear capacity and deflection. For a simply supported beam with a uniformly distributed load, the document calculates the steel reinforcement area required using formulas and tables. It then checks that the beam satisfies requirements for shear capacity, minimum and maximum steel ratios, and deflection. The document also provides an example of designing a doubly reinforced beam.
This document provides an overview of the design of beams and one-way slabs for flexure, shear, and torsion according to IS 456. It discusses key concepts like requirements for flexural reinforcement, minimum and maximum reinforcement limits, clear cover, deflection control, and selection of member sizes. The document also includes a worked example showing the step-by-step design of a rectangular reinforced concrete beam for flexure. Design checks are performed to check for strength and deflection requirements. Modules for the course will cover analysis and design of beams, one-way slabs, and reinforcement detailing in accordance with limit state design principles and code specifications.
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.
The document discusses the analysis of reinforced concrete columns under various loading conditions. It presents 10 cases for analyzing columns, including when axial load is given and eccentricity is less than balanced, when moment is given and steel is yielding, and when depth of neutral axis is given. The key steps shown are setting up the load and moment equations, checking assumptions of steel stress, and iterating to find values of neutral axis depth and steel stresses that satisfy equilibrium. Design procedures are also outlined for short columns under uniaxial bending, with steps to calculate load capacity and check steel strain assumptions.
Doubly reinforced beams have both tension and compression reinforcement, allowing for a shallower beam depth than a singly reinforced beam. There are two cases for the behavior of doubly reinforced beams at ultimate loading:
1) Case I occurs when both tension and compression steel yield. The neutral axis depth can be calculated and the moment capacities from compression steel, concrete, and tension steel determined.
2) Case II occurs when only the tension steel yields, and the compression steel does not yield. The strain in the compression steel must be calculated.
The document discusses the behavior of doubly reinforced beams under ultimate loading conditions for both cases when compression steel does and does not yield. It provides equations to calculate forces, strains, and moment
The document discusses different limit states and design considerations for reinforced concrete structures. It defines limit states as conditions when a structure is no longer acceptable for use. There are three main limit state groups: ultimate, serviceability, and special. Ultimate limit states involve structural collapse. Serviceability limit states refer to disruption of functional use without collapse, such as excessive deflection. Special limit states consider abnormal conditions like earthquakes, floods, or corrosion that can cause damage or failure. Limit state design involves identifying potential failure modes, determining acceptable safety levels, and designing members to resist ultimate states while checking for serviceability.
Prepared by madam rafia firdous. She is a lecturer and instructor in subject of Plain and Reinforcement concrete at University of South Asia LAHORE,PAKISTAN.
Prepared by madam rafia firdous. She is a lecturer and instructor in subject of Plain and Reinforcement concrete at University of South Asia LAHORE,PAKISTAN.
Design of reinforced concrete as per aci 318Jose Fabricio
Reinforced concrete design to American code,
This Code provides minimum requirements
for design and construction of structural concrete
members of any structure erected under requirements
of the legally adopted general building code of which
this Code forms a part. In areas without a legally
adopted building code, this Code defines minimum
acceptable standards for materials, design, and
construction practice. This Code also covers the
strength evaluation of existing concrete structures.
Lecture is in support of:
• Building Support Structures, Analysis and Design with SAP2000 Software, 2nd ed., eBook by Wolfgang Schueller, 2015. The SAP2000V15 Examples and Problems SDB files are available on the Computers & Structures, Inc. (CSI) website: http://www.csiamerica.com/go/schueller
• The Design of Building Structures (Vol.1, Vol. 2), rev. ed., PDF eBook by Wolfgang Schueller, 2016, published originally by Prentice Hall, 1996, 868 pages
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.
The document discusses building maintenance, common defects, and remedial methods for RCC structures. It describes three main common defects: foundations, walls, and concrete/RCC frames. For foundations, common issues include differential settlement, uplift of shrinkage soil, and dampness. For walls, issues include cracking, dampness penetration, and failure during cyclones. For concrete frames, common problems discussed are seepage/leakage, spalling of concrete, and corrosion of steel reinforcement. The document provides detailed remedial methods for addressing each of these defects.
The document provides an overview of the Ministry of Education in Pakistan including its constitution, functions, organizations, departments, and wings. Key points include:
- The Ministry is responsible for developing education policies, plans, curricula, and overseeing federal educational institutions.
- It has several wings that handle functions like policy and planning, projects, training, curriculum development, administration, and monitoring and evaluation.
- Attached departments include the Federal Directorate of Education and Department of Libraries. Autonomous bodies include examination boards and educational foundations.
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.
This document discusses short compression members under axial load with uniaxial bending. It describes the behavior of such columns and their three modes of failure: balanced failure, compression failure, and tension failure. Balanced failure occurs when the outermost longitudinal steel yields simultaneously with maximum concrete compression. Compression failure happens with a neutral axis outside the section. Tension failure occurs when the neutral axis is inside the section, developing tensile strains. An interaction diagram plots load versus moment pairs that cause failure. The behavior and failure modes depend on the neutral axis location and load eccentricity.
This document defines key terms related to compression members, classifies columns based on reinforcement type, loadings, and slenderness ratio, and outlines design assumptions. It defines effective length, pedestal, column, and wall. It classifies columns as tied, helically reinforced, or composite. Columns are classified by loadings as subjected to axial load only, axial with uniaxial bending, or axial with bi-axial bending. Columns are classified as short or slender based on slenderness ratios. Design assumes minimum eccentricity and considers different failure modes.
This document provides instruction on analyzing three-hinged arches. It defines a three-hinged arch as a statically determinate structure with three hinges: two at the supports and one at the crown. The document describes how to determine the reactions of a three-hinged arch under a concentrated load using equations of static equilibrium. It presents an example problem showing how bending moment is reduced in a three-hinged arch compared to a simply supported beam carrying the same load.
Analysis of Multi-storey Building Frames Subjected to Gravity and Seismic Loa...Pralhad Kore
This document summarizes the results of analyzing 3-bay, 5-bay, and 7-bay 9-story reinforced concrete frames with varying geometric properties under gravity and seismic loads. The response of frames was studied when incorporating idealized T-beams between points of contraflexure in beams and providing haunches of varying widths at beam-column joints. Results found that axial forces in columns increased linearly from top to bottom, while bending moments decreased with larger beam-column stiffness ratios. Lateral displacements under seismic loads were reduced by incorporating T-beams and haunches, demonstrating their beneficial effects on structural response.
Analysis of multi storey building frames subjected to gravity and seismic loa...Pralhad Kore
This document summarizes a study on the seismic response of reinforced concrete frames with varying numbers of bays and storeys. Three frame configurations - 3 bay, 5 bay, and 7 bay with 9 stories each - were modeled and analyzed under gravity and seismic loads. Both prismatic frames and frames with non-prismatic elements like stepped beams and haunches at beam-column joints were considered. The effects of variables like haunch size, beam inertia, and live load patterns on internal forces and storey drift were examined. Key results showed that non-prismatic elements can reduce bending moments and axial forces compared to conventional prismatic frames.
base plate in bending and anchor bolts in tensionabdul latief
This document describes analytical models for predicting the behavior of base plate connections under bending and anchor bolts in tension. It presents models for the stiffness and resistance of the "T-stub" component, which includes the base plate and anchor bolts. The models account for whether contact occurs between the base plate and concrete. The analytical models are verified by tests and finite element analysis. Key factors influencing behavior are the relative stiffness of the base plate and bolts, and the effective length of the T-stub.
This document contains 15 problems related to determining stresses in beams undergoing bending and shearing. The problems involve calculating stresses in beams with various cross-sectional shapes under different loading conditions. The beams are made of materials like steel, wood, and brass. Parameters like moment of inertia, shear force, beam dimensions, and material properties are provided to calculate stresses.
This document contains a 50 question multiple choice exam on engineering mechanics topics like stress-strain behavior, bending of beams, torsion, columns, thermal stresses, and failure theories. The questions cover definitions, theories, and calculations related to properties of materials, stresses and strains, bending, shear, and combined stresses.
This document discusses two approximate methods for analyzing building frames subjected to loads: the portal method and cantilever method. The portal method assumes inflection points at midpoints of beams and mid-heights of columns, and that interior columns carry twice the shear of exterior columns. The cantilever method assumes inflection points at beam midpoints and column mid-heights, and that column axial stresses are proportional to their distance from the storey's centroid. Examples demonstrate applying each method to determine member forces in frames.
Analysis and Design of Reinforced Concrete Beamsc4ppuc1n0
The document discusses the behavior of reinforced concrete beams under flexure. It covers the basic assumptions in flexure theory including plane sections remaining plane, equal strains in concrete and steel, and modeling the concrete stress-strain relationship. It also discusses the stress block model used to calculate flexural strength and provides examples of calculating the centroid and moment of inertia for uncracked and cracked beam sections. The examples show how cracking causes the centroid to shift upward and the moment of inertia to decrease significantly.
This document discusses the preparation of design charts for compression members. It defines design charts and their purpose in simplifying the column design process by avoiding lengthy calculations. It identifies the key design parameters for columns as the cross section dimensions, longitudinal reinforcement, concrete and steel grades, and transverse reinforcement. It derives the governing equations for columns under different loading conditions in non-dimensional form using parameters like Pu/fckbD and Mu/fckbD^2. Finally, it explains the step-by-step process for preparing design charts by determining the values of these non-dimensional parameters for different locations of the neutral axis.
This document discusses the preparation of design charts for compression members. It defines design charts and their purpose in simplifying the column design process by avoiding lengthy calculations. It identifies the key design parameters for columns and explains how to derive non-dimensional equations of equilibrium for different locations of the neutral axis. These equations are then used to determine the non-dimensional parameters (Pu/fckbD) and (Mu/fckbD2) for different points, generating the design chart. The process involves deriving equations for when the neutral axis is at infinity, outside the section, within the section, and when the column behaves like a steel beam.
The document discusses composite beams, which combine steel beams with concrete slabs to act compositely. It provides examples and discusses the advantages of composite beams over normal steel beams. The performance of composite beams is similar to reinforced concrete beams, but differs in that the steel beam's properties cannot be ignored and shear connection is needed between the steel and concrete. Design of composite beams follows reinforced concrete design methods with modifications. An example problem is provided to demonstrate the design process for a composite beam, including checking the beam properties, shear connectors, and deflection.
Deflections in PT elements pt structure for all pt slabs in civil industry.pdfvijayvijay327286
The document discusses factors that influence deflections in prestressed concrete members and methods for predicting deflections. It covers:
- Short term deflections of unracked members which can be estimated using Mohr's theorem.
- How the tendon profile affects deflections, providing formulas for straight, trapezoidal, parabolic, and other tendon types.
- Downward deflections due to self-weight and imposed loads that can be calculated using formulas provided.
- Estimation of long-term deflections accounting for creep and shrinkage effects, discussing various methods like those of Busemann, McHenry, and Neville.
1. The document contains multiple choice and numerical problems related to the design of reinforced concrete structures and their behavior under earthquake loading.
2. It covers topics such as seismic design coefficients, equivalent lateral forces, bending moment and shear force diagrams, design of beams and ductility.
3. The problems involve calculating quantities like base shear, lateral forces, moment capacities, rebar arrangements, and load capacities of beams.
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.
IRJET- Developing of an Equivalent Rectanuglar Column for an L-Shaped RC Colu...IRJET Journal
This document discusses developing an equivalent rectangular column for an L-shaped reinforced concrete column with similar ultimate load and moment characteristics. It describes analyzing the behavior of L-shaped columns through interaction diagrams. Values of ultimate load and moment resisting capacity are calculated for varying neutral axis positions within and outside the section of both L-shaped and equivalent rectangular columns. Interaction curves are generated and compared for the L-shaped column and rectangular columns of different breadth-to-depth ratios, keeping the area of steel and concrete the same. The study aims to obtain an equivalent rectangular section for the L-shaped column with matching load-moment behavior.
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.
1. The author proposes modifications to the roof bar (girder) design used for strata control in underground mines extracting thick seams via the blasting gallery method.
2. The existing roof bar design fails prematurely due to bending stresses, as support resistance from props is transferred to the roof bar rather than the roof.
3. The author's modified design places lagging directly above props to transfer support resistance to the roof, eliminating bending of the roof bar. The web thickness and dimensions are also increased to strengthen the roof bar against failure.
This document discusses energy conservation and the various sources of energy. It begins by explaining that the sun is the primary source of most natural energy in the world. Fossil fuels like coal and oil get their energy from the sun over millions of years. It then classifies sources of energy as either renewable (sun, wind, water, geothermal) or non-renewable (fossil fuels, nuclear fuels). Conservation of energy is important because demand is exceeding supply as populations and industries grow. Every unit of energy saved can be used elsewhere, and non-renewable fuel sources will eventually be depleted. The document provides tips for conserving energy at home through more efficient use of appliances, lighting and cooking fuels.
Energy conservation involves using less energy to achieve the same results. It is important for several reasons:
1) Demand for energy exceeds supply due to increasing population and development. By reducing demand through conservation and wise use of energy, we can help close the gap between supply and demand.
2) Energy that is saved is like money saved in a bank - it can be "withdrawn" and used later when needed. The more energy each person conserves, the less need there is to produce additional energy. Saved energy can also be used elsewhere to prevent power cuts.
3) Non-renewable sources of energy like fossil fuels are limited. Conserving these sources helps ensure availability for future generations.
This thesis aims to design a modular and climate-adaptive facade system for existing office buildings. The facade system uses prefabricated modules that can be adapted to different climate conditions in Sweden and Spain. The goal is to reduce environmental impacts, lower costs, and improve occupant comfort through an interdisciplinary design approach. An iterative process is used to optimize the facade design based on life cycle assessment, daylighting/glare simulations, and life cycle cost analysis. The final design consists of different module combinations that provide climate-specific shading and daylighting solutions while minimizing material usage and energy consumption over the lifespan of the building.
This report evaluates 5 algorithms for estimating solar irradiance on vertical surfaces based on measurements of global horizontal and direct normal irradiance. High-resolution measurements of irradiance were collected at multiple orientations at the Solar Energy Research Institute's Solar Radiation Research Laboratory between July-September 1984. The algorithms make different assumptions about the diffuse sky irradiance and ground-reflected irradiance components, ranging from isotropic to anisotropic models. Evaluation of the algorithms found they generally overestimated irradiance on north-facing surfaces by 18-46.5% compared to measurements. South-facing surfaces showed better agreement within measurement accuracy. Estimates for east- and west-facing surfaces ranged from underpredicting by 3% to
This document provides an overview of cooling and heating load calculations and solar radiation modeling. It defines key terms related to solar geometry like latitude, declination, hour angles, and derived angles. It also describes the ASHRAE solar radiation model for calculating direct, diffuse and reflected radiation on surfaces. The objectives are to introduce cooling/heating load calculations, explain the importance of solar radiation, define relevant solar angles, and describe estimating radiation using ASHRAE models.
This document discusses inventory control models and techniques for determining optimal order quantities and reorder points. The Economic Order Quantity (EOQ) model is introduced as a method to determine how much of an item to order to minimize total inventory costs. The EOQ model balances ordering costs and carrying costs. It assumes demand is known and constant. The Economic Production Quantity (EPQ) model extends the EOQ model to situations where inventory is produced rather than ordered. Safety stock models account for uncertain demand by holding extra inventory to prevent stockouts. ABC analysis classifies inventory items into important and less important groups.
Comparative analysis between traditional aquaponics and reconstructed aquapon...bijceesjournal
The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.
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### How TDM Works
1. **Time Slots Allocation**: The core principle of TDM is to assign distinct time slots to each signal. During each time slot, the respective signal is transmitted, and then the process repeats cyclically. For example, if there are four signals to be transmitted, the TDM cycle will divide time into four slots, each assigned to one signal.
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### Types of TDM
1. **Synchronous TDM**: In synchronous TDM, time slots are pre-assigned to each signal, regardless of whether the signal has data to transmit or not. This can lead to inefficiencies if some time slots remain empty due to the absence of data.
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### Applications of TDM
- **Telecommunications**: TDM is extensively used in telecommunication systems, such as in T1 and E1 lines, where multiple telephone calls are transmitted over a single line by assigning each call to a specific time slot.
- **Digital Audio and Video Broadcasting**: TDM is used in broadcasting systems to transmit multiple audio or video streams over a single channel, ensuring efficient use of bandwidth.
- **Computer Networks**: TDM is used in network protocols and systems to manage the transmission of data from multiple sources over a single network medium.
### Advantages of TDM
- **Efficient Use of Bandwidth**: TDM all
International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
International Conference on NLP, Artificial Intelligence, Machine Learning and Applications (NLAIM 2024) offers a premier global platform for exchanging insights and findings in the theory, methodology, and applications of NLP, Artificial Intelligence, Machine Learning, and their applications. The conference seeks substantial contributions across all key domains of NLP, Artificial Intelligence, Machine Learning, and their practical applications, aiming to foster both theoretical advancements and real-world implementations. With a focus on facilitating collaboration between researchers and practitioners from academia and industry, the conference serves as a nexus for sharing the latest developments in the field.
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Batteries -Introduction – Types of Batteries – discharging and charging of battery - characteristics of battery –battery rating- various tests on battery- – Primary battery: silver button cell- Secondary battery :Ni-Cd battery-modern battery: lithium ion battery-maintenance of batteries-choices of batteries for electric vehicle applications.
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Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
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This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
3. Instructional Objectives:
At the end of this lesson, the student should be able to:
• identify the primary load carrying mechanisms of reinforced concrete beams
and slabs,
• name three different types of reinforced concrete beam with their specific
applications,
• identify the parameters influencing the effective widths of T and L-beams,
• differentiate between one-way and two-way slabs,
• state and explain the significance of six assumptions of the design,
• draw the stress-strain diagrams across the depth of a cross-section of
rectangular beam,
• write the three equations of equilibrium,
• write and derive the expressions of total compression and tension forces C
and T, respectively.
3.4.1 Introduction
Version 2 CE IIT, Kharagpur
4. Reinforced concrete beams and slabs carry loads primarily by bending
(Figs. 3.4.1 to 3). They are, therefore, designed on the basis of limit state of
collapse in flexure. The beams are also to be checked for other limit states of
shear and torsion. Slabs under normal design loadings (except in bridge decks
etc.) need not be provided with shear reinforcement. However, adequate
torsional reinforcement must be provided wherever needed.
Version 2 CE IIT, Kharagpur
6. This lesson explains the basic governing equations and the computation of
parameters required for the design of beams and one-way slabs employing limit
state of collapse in flexure. There are three types of reinforced concrete beams:
(i) Singly or doubly reinforced rectangular beams (Figs. 3.4.4 to 7)
(ii) Singly or doubly reinforced T-beams (Figs. 3.4.8 to 11)
(iii) Singly or doubly reinforced L-beams (Figs. 3.4.12 to 15)
Version 2 CE IIT, Kharagpur
7. During construction of reinforced concrete structures, concrete slabs and beams
are cast monolithic making the beams a part of the floor deck system. While
bending under positive moments near midspan, bending compression stresses at
the top are taken by the rectangular section of the beams above the neutral axis
and the slabs, if present in T or L-beams (Figs. 3.4.4, 5, 8, 9, 12 and 13).
However, under the negative moment over the support or elsewhere, the bending
compression stresses are at the bottom and the rectangular sections of
rectangular, T and L-beams below the neutral axis only resist that compression
(Figs. 3.4.6, 7, 10, 11, 14 and 15). Thus, in a slab-beam system the beam will be
Version 2 CE IIT, Kharagpur
8. considered as rectangular for the negative moment and T for the positive
moment. While for the intermediate spans of slabs the beam under positive
moment is considered as T, the end span edge beam is considered as L-beam if
the slab is not projected on both the sides of the beam. It is worth mentioning that
the effective width of flange of these T or L-beams is to be determined which
depends on:
Version 2 CE IIT, Kharagpur
10. (a) if it is an isolated or continuous beam
(b) the distance between points of zero moments in the beam
(c) the width of the web
(d) the thickness of the flange
Reinforced concrete slabs are classified as one-way or two-way
depending on if they are spanning in one or two directions (Figs. 3.4.16 and 17).
As a guideline, slabs whose ratio of longer span (ly) to the shorter span (lx) is
more than two are considered as one-way slabs. One-way slabs also can be
designed following the procedure of the design of beams of rectangular cross-
section. Again, slabs may be isolated or continuous also.
Version 2 CE IIT, Kharagpur
12. The following are the assumptions of the design of flexural members (Figs.
3.4.18 to 20) employing limit state of collapse:
(i) Plane sections normal to the axis remain plane after bending.
This assumption ensures that the cross-section of the member does not
warp due to the loads applied. It further means that the strain at any point on the
cross-section is directly proportional to its distance from the neutral axis.
(ii) The maximum strain in concrete at the outer most compression fibre is
taken as 0.0035 in bending (Figs. 3.4.19 and 20).
This is a clearly defined limiting strain of concrete in bending compression
beyond which the concrete will be taken as reaching the state of collapse. It is
very clear that the specified limiting strain of 0.0035 does not depend on the
strength of concrete.
(iii) The acceptable stress-strain curve of concrete is assumed to be parabolic
as shown in Fig. 1.2.1 of Lesson 2.
The maximum compressive stress-strain curve in the structure is obtained
by reducing the values of the top parabolic curve (Figs. 21 of IS 456:2000) in two
stages. First, dividing by 1.5 due to size effect and secondly, again dividing by
1.5 considering the partial safety factor of the material. The middle and bottom
curves (Fig. 21 of IS 456:2000) represent these stages. Thus, the maximum
compressive stress in bending is limited to the constant value of 0.446 fck for the
strain ranging from 0.002 to 0.0035 (Figs. 3.4.19 and 20, Figs. 21 and 22 of IS
456:2000).
Version 2 CE IIT, Kharagpur
13. (iv) The tensile strength of concrete is ignored.
Concrete has some tensile strength (very small but not zero). Yet, this
tensile strength is ignored and the steel reinforcement is assumed to resist the
tensile stress. However, the tensile strength of concrete is taken into account to
check the deflection and crack widths in the limit state of serviceability.
(v) The design stresses of the reinforcement are derived from the
representative stress-strain curves as shown in Figs. 1.2.3 and 4 of Lesson 2 and
Figs. 23A and B of IS 456:2000, for the type of steel used using the partial safety
factor γm as 1.15.
In the reinforced concrete structures, two types of steel are used: one with
definite yield point (mild steel, Figs. 1.2.3 of Lesson 2 and Figs. 23B of IS
456:2000) and the other where the yield points are not definite (cold work
deformed bars). The representative stress-strain diagram (Fig. 1.2.4 of Lesson 2
and Fig. 23A of IS 456:2000) defines the points between 0.8 fy and 1.0 fy in case
of cold work deformed bars where the curve is inelastic.
(vi) The maximum strain in the tension reinforcement in the section at failure
shall not be less than fy/(1.15 Es) + 0.002, where fy is the characteristic strength
of steel and Es = modulus of elasticity of steel (Figs. 3.4.19 and 20).
This assumption ensures ductile failure in which the tensile reinforcement
undergoes a certain degree of inelastic deformation before concrete fails in
compression.
3.4.3 Singly Reinforce Rectangular Beams
Figure 3.4.18 shows the singly reinforced rectangular beam in flexure. The
following notations are used (Figs. 3.4.19 and 20):
Ast = area of tension steel
b = width of the beam
C = total compressive force of concrete
d = effective depth of the beam
L = centre to centre distance between supports
P = two constant loads acting at a distance of L/3 from the two supports
of the beam
T = total tensile force of steel
xu = depth of neutral axis from the top compression fibre
3.4.4 Equations of Equilibrium
The cross-sections of the beam under the applied loads as shown in Fig.
3.4.18 has three types of combinations of shear forces and bending moments: (i)
Version 2 CE IIT, Kharagpur
14. only shear force is there at the support and bending moment is zero, (ii) both
bending moment (increasing gradually) and shear force (constant = P) are there
between the support and the loading point and (iii) a constant moment (= PL/3) is
there in the middle third zone i.e. between the two loads where the shear force is
zero (Fig. 1.1.1 of Lesson 1). Since the beam is in static equilibrium, any cross-
section of the beam is also in static equilibrium. Considering the cross-section in
the middle zone (Fig. 3.4.18) the three equations of equilibrium are the following
(Figs. 3.4.19 and 20):
(i) Equilibrium of horizontal forces: Σ H = 0 gives T = C
(3.1)
(ii) Equilibrium of vertical shear forces: Σ V = 0
(3.2)
This equation gives an identity 0 = 0 as there is no shear in the middle
third zone of the beam.
(iii) Equilibrium of moments: Σ M = 0,
(3.3)
This equation shows that the applied moment at the section is fully resisted by
moment of the resisting couple T a = C a , where a is the operating lever arm
between T and C (Figs. 3.4.19 and 20).
3.4.5 Computations of C and T
Version 2 CE IIT, Kharagpur
15. Figures 3.4.21a and b present the enlarged view of the compressive part
of the strain and stress diagrams. The convex parabolic part of the stress block of
Fig. 3.4.21b is made rectangular by dotted lines to facilitate the calculations
adding another concave parabolic stress zone which is really non-existent as
marked by hatch in Fig. 3.4.21b.
The different compressive forces C, C1, C2 and C3 and distances x1 to x5
and xu as marked in Fig. 3.4.21b are explained in the following:
C = Total compressive force of concrete = C1 + C2
C1 = Compressive force of concrete due to the constant stress of 0.446
fck and up to a depth of x3 from the top fibre
C2 = Compressive force of concrete due to the convex parabolic stress
block of values ranging from zero at the neutral axis to 0.446 fck at a
distance of x3 from the top fibre
C3 = Compressive force of concrete due to the concave parabolic stress
block (actually non-existent) of values ranging from 0.446 fck at the
neutral axis to zero at a distance of x3 from the top fibre
x1 = Distance of the line of action of C1 from the top compressive fibre
x2 = Distance of the line of action of C (= C1 + C2) from the top
compressive fibre
x3 = Distance of the fibre from the top compressive fibre, where the strain
= 0.002 and stress = 0.446 fck
x4 = Distance of the line of action of C2 from the top compressive fibre
x5 = Distance of the line of action of C3 from the top compressive fibre
xu = Distance of the neutral axis from the top compressive fibre.
From the strain triangle of Fig. 3.4.21a, we have
570
7
4
00350
00203 .
.
.
x
xx
u
u ===
−
, giving
x3 = 0.43 xu
(3.4)
Since C1 is due to the constant stress acting from the top to a distance of x3, the
distance x1 of the line of action of C1 is:
Version 2 CE IIT, Kharagpur
16. x1 = 0.5 x3 = 0.215 xu
(3.5)
From Fig. 3.4.21a:
x5 = x3 +
4
3
(xu - x3) = 0.43 xu + 0.75(0.57 xu)
or x5 = 0.86 xu
(3.6)
The compressive force C1 due to the rectangular stress block is:
C1 = b x3(0.446 fck) = 0.191 b xu fck
(3.7)
The compressive force C2 due to parabolic stress block is:
C2 = b (xu - x3)
3
2
(0.446 fck) = 0.17 b xu fck
(3.8)
Adding C1 and C2, we have
C = C1 + C2 = 0.361 b xu fck = 0.36 b xu fck (say)
(3.9)
The non-existent compressive force C3 due to parabolic (concave) stress block
is:
C3 = b (xu - x3)
3
1
(0.446 fck) = 0.085 b xu fck
(3.10)
Now, we can get x4 by taking moment of C2 and C3 about the top fibre as follows:
C2(x4) + C3 (x5) = (C2 + C3) (x3 +
2
3xxu −
)
which gives x4 = 0.64 xu
(3.11)
Similarly, x2 is obtained by taking moment of C1 and C2 about the top fibre as
follows:
C1(x1) + C2(x4) = C(x2)
which gives x2 = 0.4153 xu
Version 2 CE IIT, Kharagpur
17. or x2 = 0.42 xu (say).
(3.12)
Thus, the required parameters of the stress block (Fig. 3.4.19) are
C = 0.36 b xu fck (3.9)
x2 = 0.42 xu (3.12)
and lever arm = (d - x2) = (d - 0.42 xu)
(3.13)
The tensile force T is obtained by multiplying the design stress of steel with the
area of steel. Thus,
T = styst
y
Af.A)
.
f
( 870
151
=
(3.14)
3.4.6 Practice Questions and Problems with Answers
Q.1: How do the beams and slabs primarily carry the transverse loads ?
A.1: The beams and slabs carry the transverse loads primarily by bending.
Q.2: Name three different types of reinforced concrete beams and their specific
applications.
A.2: They are:
(i) Singly reinforced and doubly reinforced rectangular beams - used in
resisting negative moments in intermediate spans of continuous
beams over the supports or elsewhere in slab-beam monolithic
constructions, and positive moments in midspan of isolated or
intermediate spans of beams with inverted slab (monolithic)
constructions and lintels.
(ii) Singly reinforced and doubly reinforced T-beams - used in resisting
positive moments in isolated or intermediate spans (midspan) in
slab-beam monolithic constructions and negative moments over the
support for continuous spans with inverted slab (monolithic)
constructions.
Version 2 CE IIT, Kharagpur
18. (iii) Singly reinforced and doubly reinforced L-beams - Same as (ii)
above except that these are for end spans instead of intermediate
spans.
Q.3: Name four parameters which determine the effective widths of T and L-
beams.
A.3: The four parameters are:
(i) isolated or continuous beams,
(ii) the distance between points of zero moments in the beam,
(iii) the breadth of the web,
(iv) the thickness of the flange.
Q.4: Differentiate between one-way and two-way slabs.
A.4: One-way slab spans in one direction and two-way slab spans in both the
directions. Slabs whose ratio of longer span (ly) to shorter span (lx) is more
than 2 are called one-way. Slabs of this ratio up to 2 are called two-way
slabs.
Q.5: State and explain the significance of the six assumptions of design of
flexural members employing limit state of collapse.
A.5: Sec. 3.4.2 gives the full answer.
Q.6: Draw a cross-section of singly reinforced rectangular beam and show the
strain and stress diagrams.
A.6: Fig. 3.4.19.
Q.7: Write the three equations of equilibrium needed to design the reinforced
concrete beams.
A.7: Vide sec. 3.4.4 and Eqs. 3.1 to 3.
Q.8: Write the final expression of the total compressive force C and tensile
force T for a rectangular reinforced concrete beam in terms of the
designing parameters.
A.8: Eq. 3.9 for C and Eq. 3.14 for T.
Version 2 CE IIT, Kharagpur
19. 3.4.7 References
1. Reinforced Concrete Limit State Design, 6th
Edition, by Ashok K. Jain,
Nem Chand & Bros, Roorkee, 2002.
2. Limit State Design of Reinforced Concrete, 2nd
Edition, by P.C.Varghese,
Prentice-Hall of India Pvt. Ltd., New Delhi, 2002.
3. Advanced Reinforced Concrete Design, by P.C.Varghese, Prentice-Hall of
India Pvt. Ltd., New Delhi, 2001.
4. Reinforced Concrete Design, 2nd
Edition, by S.Unnikrishna Pillai and
Devdas Menon, Tata McGraw-Hill Publishing Company Limited, New
Delhi, 2003.
5. Limit State Design of Reinforced Concrete Structures, by P.Dayaratnam,
Oxford & I.B.H. Publishing Company Pvt. Ltd., New Delhi, 2004.
6. Reinforced Concrete Design, 1st
Revised Edition, by S.N.Sinha, Tata
McGraw-Hill Publishing Company. New Delhi, 1990.
7. Reinforced Concrete, 6th
Edition, by S.K.Mallick and A.P.Gupta, Oxford &
IBH Publishing Co. Pvt. Ltd. New Delhi, 1996.
8. Behaviour, Analysis & Design of Reinforced Concrete Structural Elements,
by I.C.Syal and R.K.Ummat, A.H.Wheeler & Co. Ltd., Allahabad, 1989.
9. Reinforced Concrete Structures, 3rd
Edition, by I.C.Syal and A.K.Goel,
A.H.Wheeler & Co. Ltd., Allahabad, 1992.
10.Textbook of R.C.C, by G.S.Birdie and J.S.Birdie, Wiley Eastern Limited,
New Delhi, 1993.
11.Design of Concrete Structures, 13th
Edition, by Arthur H. Nilson, David
Darwin and Charles W. Dolan, Tata McGraw-Hill Publishing Company
Limited, New Delhi, 2004.
12.Concrete Technology, by A.M.Neville and J.J.Brooks, ELBS with
Longman, 1994.
13.Properties of Concrete, 4th
Edition, 1st
Indian reprint, by A.M.Neville,
Longman, 2000.
14.Reinforced Concrete Designer’s Handbook, 10th
Edition, by C.E.Reynolds
and J.C.Steedman, E & FN SPON, London, 1997.
15.Indian Standard Plain and Reinforced Concrete – Code of Practice (4th
Revision), IS 456: 2000, BIS, New Delhi.
16.Design Aids for Reinforced Concrete to IS: 456 – 1978, BIS, New Delhi.
3.4.8 Test 4 with Solutions
Maximum Marks = 50, Maximum Time = 30 minutes
Answer all questions.
TQ.1: Tick the correct answer: (4 x 5 = 20
marks)
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20. (i) Beams and slabs carry the transverse loads primarily by
(a) truss action
(b) balance of shear action
(c) bending
(d) slab-beam interaction
A.TQ.1: (i): (c)
(ii) The ratio of longer span (ly) to shorter span (lx) of a two-way slab is
(a) up to 2
(b) more than 2
(c) equal to 1
(d) more than 1
A.TQ.1: (ii): (a)
(iii) An inverted T-beam is considered as a rectangular beam for the design
(a) over the intermediate support of a continuous beam where the bending
moment is negative
(b) at the midspan of a continuous beam where the bending moment is
positive
(c) at the point of zero bending moment
(d) over the support of a simply supported beam
A.TQ.1: (iii): (b)
(iv) The maximum strain in the tension reinforcement in the section at failure
shall be
(a) more than fy /(1.15 Es) + 0.002
(b) equal to 0.0035
(c) more than fy /Es + 0.002
(d) less than fy /(1.15 Es) + 0.002
A.TQ.1: (iv): (d)
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21. TQ.2: Draw a cross-section of singly reinforced rectangular beam and show the
strain and stress diagrams.
(10)
A.TQ.2: Fig. 3.4.19
TQ.3: Name four parameters which determine the effective widths of T and L-
beams. (6)
A.TQ.3: The four parameters are:
(i) isolated or continuous beams,
(ii) the distance between points of zero moments in the beam,
(iii) the breadth of the web,
(iv) the thickness of the flange.
TQ.4: Derive the final expressions of the total compressive force C and tensile
force T for a rectangular reinforced concrete beam in terms of the
designing parameters.
(10 +
4 = 14)
A.TQ.4: Section 3.4.5 is the full answer.
3.4.9 Summary of this Lesson
Lesson 4 illustrates the primary load carrying principle in a slab-beam
structural system subjected to transverse loadings. It also mentions three
different types of singly and doubly reinforced beams normally used in
construction. Various assumptions made in the design of these beams employing
limit state of collapse are explained. The stress and strain diagrams of a singly
reinforced rectangular beam are explained to write down the three equations of
equilibrium. Finally, the computations of the total compressive and tensile forces
are illustrated.
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