This document discusses the equivalent frame method for analyzing two-way slabs. It introduces the equivalent frame method, which transforms a 3D structural system into a 2D system by representing the stiffness of slab and beam members as Ksb, and the modified stiffness of columns as Kec. This allows the 3D behavior to be analyzed using conventional 2D frame analysis methods. The document then covers determining the values of Ksb and Kec to represent the slab and column stiffness in the equivalent frame.
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.
The document discusses the design of a combined footing to support two columns. It first defines what a combined footing is and why it is used. It then describes the types of combined footings and the forces acting on it. The document provides the design steps for a rectangular combined footing, which include determining dimensions, reinforcement requirements, and design checks. As an example, it shows the detailed design of a rectangular combined footing supporting two columns with loads of 450kN and 650kN respectively. The design includes calculating dimensions, reinforcement, development lengths, and design checks.
This document describes the design of a pile cap by a group of civil engineering students. It defines a pile cap as a concrete mat that rests on piles driven into soft ground to provide a stable foundation. It then provides two examples of pile cap design, showing dimensions, load calculations, reinforcement requirements and construction details. The document concludes that a pile cap distributes a building's load to piles to form a stable foundation on unstable soil. It acknowledges the guidance of professors in completing this project.
This document discusses approximate analysis methods for building frames subjected to both vertical and horizontal loads. For vertical loads, assumptions are made that points of zero moment occur at fixed distances from beam supports, reducing each beam to determinacy. The portal method is described for horizontal loads, assuming points of zero moment at midpoints and distributing shear between columns. Example problems demonstrate solving for member forces. The cantilever method also assumes midpoints of zero moment but distributes axial stress in columns by their distance from the storey's centroid.
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 discusses T-beams, which are more suitable than rectangular beams in reinforced concrete. There are two types of T-beams: monolithic and isolated. It provides notations and code recommendations for T-beams from IS: 456. There are three cases for finding the depth of the neutral axis in a T-beam: when it lies in the flange, in the rib, or at the junction. An example problem is worked through to find the moment of resistance for a given T-beam section using the provided concrete and steel properties.
This 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.
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.
The document discusses the design of a combined footing to support two columns. It first defines what a combined footing is and why it is used. It then describes the types of combined footings and the forces acting on it. The document provides the design steps for a rectangular combined footing, which include determining dimensions, reinforcement requirements, and design checks. As an example, it shows the detailed design of a rectangular combined footing supporting two columns with loads of 450kN and 650kN respectively. The design includes calculating dimensions, reinforcement, development lengths, and design checks.
This document describes the design of a pile cap by a group of civil engineering students. It defines a pile cap as a concrete mat that rests on piles driven into soft ground to provide a stable foundation. It then provides two examples of pile cap design, showing dimensions, load calculations, reinforcement requirements and construction details. The document concludes that a pile cap distributes a building's load to piles to form a stable foundation on unstable soil. It acknowledges the guidance of professors in completing this project.
This document discusses approximate analysis methods for building frames subjected to both vertical and horizontal loads. For vertical loads, assumptions are made that points of zero moment occur at fixed distances from beam supports, reducing each beam to determinacy. The portal method is described for horizontal loads, assuming points of zero moment at midpoints and distributing shear between columns. Example problems demonstrate solving for member forces. The cantilever method also assumes midpoints of zero moment but distributes axial stress in columns by their distance from the storey's centroid.
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 discusses T-beams, which are more suitable than rectangular beams in reinforced concrete. There are two types of T-beams: monolithic and isolated. It provides notations and code recommendations for T-beams from IS: 456. There are three cases for finding the depth of the neutral axis in a T-beam: when it lies in the flange, in the rib, or at the junction. An example problem is worked through to find the moment of resistance for a given T-beam section using the provided concrete and steel properties.
This 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.
- 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.
This document presents an example of analysis design of slab using ETABS. This example examines a simple single story building, which is regular in plan and elevation. It is examining and compares the calculated ultimate moment from CSI ETABS & SAFE with hand calculation. Moment coefficients were used to calculate the ultimate moment. However it is good practice that such hand analysis methods are used to verify the output of more sophisticated methods.
Also, this document contains simple procedure (step-by-step) of how to design solid slab according to Eurocode 2.The process of designing elements will not be revolutionised as a result of using Eurocode 2. Due to time constraints and knowledge, I may not be able to address the whole issues.
The document discusses analysis of doubly reinforced concrete beams. It begins by explaining how compression reinforcement allows less concrete to resist tension, moving the neutral axis up. It then provides the equations for analyzing strain compatibility and equilibrium in doubly reinforced sections. The document discusses finding the compression reinforcement strain and stress through iteration. It provides reasons for using compression reinforcement, including reducing deflection and increasing ductility. Finally, it includes an example problem demonstrating the full analysis process.
This document provides an overview of analysis and design methods for concrete slabs, including:
1. Elastic analysis methods like grillage analysis and finite element analysis can be used to determine moments and shear forces in slabs.
2. Yield line theory is an alternative plastic/ultimate limit state approach for determining the ultimate load capacity of ductile concrete slabs. It involves assuming yield line patterns that divide the slab into rigid regions and equating external and internal work.
3. Examples are provided to illustrate yield line analysis for one-way spanning slabs and rectangular two-way slabs. Conventions, assumptions, and calculation procedures are explained.
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.
This document provides an overview of member behavior for beams and columns in seismic design. It discusses the types of moment resisting frames and the principles for designing special moment resisting frames, including strong-column/weak-beam design, avoiding shear failure, and providing ductile details. Beam and column design considerations are covered, such as dimensions, reinforcement, and shear capacity. Beam-column joint design is also summarized, including dimensions, shear determination, and strength.
Seismic Analysis of regular & Irregular RCC frame structuresDaanish Zama
This document discusses seismic analysis of regular and irregular reinforced concrete framed buildings. It analyzes 4 building models - a regular 4-story building, a stiffness irregular building with a soft ground story, and two vertically irregular buildings with setbacks on the 3rd floor and 2nd/3rd floors. Static analysis was performed to compare bending moments, shear forces, story drifts, and joint displacements. Results showed irregular buildings experienced higher seismic demands. The regular building performed best, with the single setback building also performing well. Irregular configurations increase seismic effects and should be minimized in design.
information on types of beams, different methods to calculate beam stress, design for shear, analysis for SRB flexure, design for flexure, Design procedure for doubly reinforced beam,
The document provides details on the design of a reinforced concrete column footing to support a column load of 1100kN from a 400mm square column. It describes the design process which includes determining the footing size, calculating bending moment, reinforcement requirements, checking shear capacity and development length. The design example shows a 3.5m x 3.5m square footing with 12mm diameter bars at 100mm c/c is adequate to support the given load based on the specified material properties and design codes. Reinforcement and footing details are also provided.
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 mat foundations. It discusses common types of mat foundations including flat plate, flat plate thickened under columns, beams and slab, and slab with basement walls. It describes how to calculate the bearing capacity of mat foundations and differential settlement. Methods for structural design of mat foundations are presented, including the conventional rigid method and approximate flexible method. Examples are provided to illustrate how to design combined footings, calculate bearing capacity, and structurally design mat foundations.
This document discusses shear wall analysis and design. It defines shear walls as structural elements used in buildings to resist lateral forces through cantilever action. The document classifies different types of shear walls and discusses their behavior under seismic loading. It outlines the steps for designing shear walls, including reviewing layout, analyzing structural systems, determining design forces, and detailing reinforcement. The document emphasizes the importance of properly locating shear walls in a building to resist seismic loads and minimize torsional effects.
Compression members are structural members subjected to axial compression or compressive forces. Their design is governed by strength and buckling capacity. Columns can fail due to local buckling, squashing, overall flexural buckling, or torsional buckling. Built-up columns use components like lacings, battens, and cover plates to help distribute stress more evenly and increase buckling resistance compared to a single member. Buckling occurs when a straight compression member becomes unstable and bends under a critical load.
This document provides details on the design of a rectangular water tank resting on ground. It discusses the analysis done to determine bending moments and tensile forces in the walls. It then shows the step-by-step design of the walls and base slab of a 5m x 4m rectangular tank with 3m depth, reinforced with Fe415 steel bars in M20 concrete. Reinforcement details are calculated and sketched to resist vertical and horizontal bending moments at the wall corners and edges.
Because of torsion, the beam fails in diagonal tension forming the spiral cracks around the beam. Warping of the section does not allow a plane section to remain as plane after twisting. Clause 41 of IS 456:2000 provides the provisions for
the design of torsional reinforcements. The design rules for torsion are based on the equivalent moment.
This document provides information about the design of strap footings. It begins with an overview of strap footings, noting they are used to connect an eccentrically loaded column footing to an interior column. The strap transmits moment caused by eccentricity to the interior footing to generate uniform soil pressure beneath both footings.
It then outlines the basic considerations for strap footing design: 1) the strap must be rigid, 2) footings should have equal soil pressures to avoid differential settlement, and 3) the strap should be out of contact with soil to avoid soil reactions. Finally, it provides the step-by-step process for designing a strap footing, including proportioning footing dimensions, evaluating soil pressures, designing reinforcement,
Lec11 Continuous Beams and One Way Slabs(1) (Reinforced Concrete Design I & P...Hossam Shafiq II
The document discusses reinforced concrete continuity and analysis methods for continuous beams and one-way slabs. It describes how steel reinforcement must extend through members to provide structural continuity. The ACI/SBC coefficient method of analysis is summarized, which uses coefficient tables to determine maximum shear forces and bending moments for continuous beams and one-way slabs under various loading conditions in a simplified manner compared to elastic analysis. Requirements for applying the coefficient method include having multiple spans with ratios less than 1.2, prismatic member sections, and live loads less than 3 times dead loads.
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.
Design of flat plate slab and its Punching Shear Reinf.MD.MAHBUB UL ALAM
This document provides design considerations and an example problem for designing a flat plate slab using the Direct Design Method (DDM). It discusses slab thickness, load calculations, moment distribution, and reinforcement design for a sample four-story building with 16'x20' panels supported by 12" square columns. The design of panel S-4 is shown in detail, calculating loads, moments, and reinforcement requirements for the column and middle strips in both the long and short directions.
The document provides details on the design of a reinforced concrete column footing to support a column with a load of 1100kN. It includes calculating the footing size as a 3.5m x 3.5m square to support the load, determining the reinforcement with 12mm diameter bars at 100mm spacing, and checking that the design meets requirements for bending capacity, shear strength, and development length. The step-by-step worked example shows how to analyze and detail the reinforcement of the column footing.
This document describes research using neural networks to predict the propagation path of plastic hinges in moment resisting frames under seismic loading. Pushover analyses were conducted on various frame configurations to create a database for training a neural network. The neural network takes frame element stiffness values as input and outputs the plastic hinge condition at different nodes. Training results showed the network could accurately predict plastic hinge distribution and collapse mechanisms. Validation on additional frames found reasonable correlation between predicted and actual plastic hinge statuses. The research demonstrates neural networks may provide a useful tool for assessing frame post-elastic behavior and collapse mechanisms at the design stage.
“REVIEW ON EXPERIMENTAL ANALYSIS ON STRENGTH CHARACTERISTICS OF FIBER MODIFIE...IRJET Journal
This document reviews literature on using natural and synthetic fibers to modify the strength properties of concrete. It summarizes several studies that tested how bamboo, fiberglass, carbon fiber, and basalt fiber reinforcements impacted the bending strength, tensile strength, and deformation of concrete beams compared to steel-reinforced beams. The review found that fiber reinforcements can improve concrete strength characteristics but noted gaps in research on using fiber-reinforced polymer composites as the main reinforcement and on reinforcing hollow concrete columns.
- 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.
This document presents an example of analysis design of slab using ETABS. This example examines a simple single story building, which is regular in plan and elevation. It is examining and compares the calculated ultimate moment from CSI ETABS & SAFE with hand calculation. Moment coefficients were used to calculate the ultimate moment. However it is good practice that such hand analysis methods are used to verify the output of more sophisticated methods.
Also, this document contains simple procedure (step-by-step) of how to design solid slab according to Eurocode 2.The process of designing elements will not be revolutionised as a result of using Eurocode 2. Due to time constraints and knowledge, I may not be able to address the whole issues.
The document discusses analysis of doubly reinforced concrete beams. It begins by explaining how compression reinforcement allows less concrete to resist tension, moving the neutral axis up. It then provides the equations for analyzing strain compatibility and equilibrium in doubly reinforced sections. The document discusses finding the compression reinforcement strain and stress through iteration. It provides reasons for using compression reinforcement, including reducing deflection and increasing ductility. Finally, it includes an example problem demonstrating the full analysis process.
This document provides an overview of analysis and design methods for concrete slabs, including:
1. Elastic analysis methods like grillage analysis and finite element analysis can be used to determine moments and shear forces in slabs.
2. Yield line theory is an alternative plastic/ultimate limit state approach for determining the ultimate load capacity of ductile concrete slabs. It involves assuming yield line patterns that divide the slab into rigid regions and equating external and internal work.
3. Examples are provided to illustrate yield line analysis for one-way spanning slabs and rectangular two-way slabs. Conventions, assumptions, and calculation procedures are explained.
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.
This document provides an overview of member behavior for beams and columns in seismic design. It discusses the types of moment resisting frames and the principles for designing special moment resisting frames, including strong-column/weak-beam design, avoiding shear failure, and providing ductile details. Beam and column design considerations are covered, such as dimensions, reinforcement, and shear capacity. Beam-column joint design is also summarized, including dimensions, shear determination, and strength.
Seismic Analysis of regular & Irregular RCC frame structuresDaanish Zama
This document discusses seismic analysis of regular and irregular reinforced concrete framed buildings. It analyzes 4 building models - a regular 4-story building, a stiffness irregular building with a soft ground story, and two vertically irregular buildings with setbacks on the 3rd floor and 2nd/3rd floors. Static analysis was performed to compare bending moments, shear forces, story drifts, and joint displacements. Results showed irregular buildings experienced higher seismic demands. The regular building performed best, with the single setback building also performing well. Irregular configurations increase seismic effects and should be minimized in design.
information on types of beams, different methods to calculate beam stress, design for shear, analysis for SRB flexure, design for flexure, Design procedure for doubly reinforced beam,
The document provides details on the design of a reinforced concrete column footing to support a column load of 1100kN from a 400mm square column. It describes the design process which includes determining the footing size, calculating bending moment, reinforcement requirements, checking shear capacity and development length. The design example shows a 3.5m x 3.5m square footing with 12mm diameter bars at 100mm c/c is adequate to support the given load based on the specified material properties and design codes. Reinforcement and footing details are also provided.
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 mat foundations. It discusses common types of mat foundations including flat plate, flat plate thickened under columns, beams and slab, and slab with basement walls. It describes how to calculate the bearing capacity of mat foundations and differential settlement. Methods for structural design of mat foundations are presented, including the conventional rigid method and approximate flexible method. Examples are provided to illustrate how to design combined footings, calculate bearing capacity, and structurally design mat foundations.
This document discusses shear wall analysis and design. It defines shear walls as structural elements used in buildings to resist lateral forces through cantilever action. The document classifies different types of shear walls and discusses their behavior under seismic loading. It outlines the steps for designing shear walls, including reviewing layout, analyzing structural systems, determining design forces, and detailing reinforcement. The document emphasizes the importance of properly locating shear walls in a building to resist seismic loads and minimize torsional effects.
Compression members are structural members subjected to axial compression or compressive forces. Their design is governed by strength and buckling capacity. Columns can fail due to local buckling, squashing, overall flexural buckling, or torsional buckling. Built-up columns use components like lacings, battens, and cover plates to help distribute stress more evenly and increase buckling resistance compared to a single member. Buckling occurs when a straight compression member becomes unstable and bends under a critical load.
This document provides details on the design of a rectangular water tank resting on ground. It discusses the analysis done to determine bending moments and tensile forces in the walls. It then shows the step-by-step design of the walls and base slab of a 5m x 4m rectangular tank with 3m depth, reinforced with Fe415 steel bars in M20 concrete. Reinforcement details are calculated and sketched to resist vertical and horizontal bending moments at the wall corners and edges.
Because of torsion, the beam fails in diagonal tension forming the spiral cracks around the beam. Warping of the section does not allow a plane section to remain as plane after twisting. Clause 41 of IS 456:2000 provides the provisions for
the design of torsional reinforcements. The design rules for torsion are based on the equivalent moment.
This document provides information about the design of strap footings. It begins with an overview of strap footings, noting they are used to connect an eccentrically loaded column footing to an interior column. The strap transmits moment caused by eccentricity to the interior footing to generate uniform soil pressure beneath both footings.
It then outlines the basic considerations for strap footing design: 1) the strap must be rigid, 2) footings should have equal soil pressures to avoid differential settlement, and 3) the strap should be out of contact with soil to avoid soil reactions. Finally, it provides the step-by-step process for designing a strap footing, including proportioning footing dimensions, evaluating soil pressures, designing reinforcement,
Lec11 Continuous Beams and One Way Slabs(1) (Reinforced Concrete Design I & P...Hossam Shafiq II
The document discusses reinforced concrete continuity and analysis methods for continuous beams and one-way slabs. It describes how steel reinforcement must extend through members to provide structural continuity. The ACI/SBC coefficient method of analysis is summarized, which uses coefficient tables to determine maximum shear forces and bending moments for continuous beams and one-way slabs under various loading conditions in a simplified manner compared to elastic analysis. Requirements for applying the coefficient method include having multiple spans with ratios less than 1.2, prismatic member sections, and live loads less than 3 times dead loads.
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.
Design of flat plate slab and its Punching Shear Reinf.MD.MAHBUB UL ALAM
This document provides design considerations and an example problem for designing a flat plate slab using the Direct Design Method (DDM). It discusses slab thickness, load calculations, moment distribution, and reinforcement design for a sample four-story building with 16'x20' panels supported by 12" square columns. The design of panel S-4 is shown in detail, calculating loads, moments, and reinforcement requirements for the column and middle strips in both the long and short directions.
The document provides details on the design of a reinforced concrete column footing to support a column with a load of 1100kN. It includes calculating the footing size as a 3.5m x 3.5m square to support the load, determining the reinforcement with 12mm diameter bars at 100mm spacing, and checking that the design meets requirements for bending capacity, shear strength, and development length. The step-by-step worked example shows how to analyze and detail the reinforcement of the column footing.
This document describes research using neural networks to predict the propagation path of plastic hinges in moment resisting frames under seismic loading. Pushover analyses were conducted on various frame configurations to create a database for training a neural network. The neural network takes frame element stiffness values as input and outputs the plastic hinge condition at different nodes. Training results showed the network could accurately predict plastic hinge distribution and collapse mechanisms. Validation on additional frames found reasonable correlation between predicted and actual plastic hinge statuses. The research demonstrates neural networks may provide a useful tool for assessing frame post-elastic behavior and collapse mechanisms at the design stage.
“REVIEW ON EXPERIMENTAL ANALYSIS ON STRENGTH CHARACTERISTICS OF FIBER MODIFIE...IRJET Journal
This document reviews literature on using natural and synthetic fibers to modify the strength properties of concrete. It summarizes several studies that tested how bamboo, fiberglass, carbon fiber, and basalt fiber reinforcements impacted the bending strength, tensile strength, and deformation of concrete beams compared to steel-reinforced beams. The review found that fiber reinforcements can improve concrete strength characteristics but noted gaps in research on using fiber-reinforced polymer composites as the main reinforcement and on reinforcing hollow concrete columns.
ANALYSIS AND DESIGN OF THREE STOREY FRAMED BUILDINGJoshua Gorinson
This document discusses the history of structural analysis methods. It explains that statically indeterminate structures require analysis to ensure they have sufficient strength and rigidity. Two fundamental methods are described: force methods, which satisfy compatibility equations; and displacement methods, which satisfy equilibrium equations. Specific displacement methods discussed include the slope deflection method, which considers bending deformations, and the moment distribution method introduced by Hardy Cross, which is an iterative method for analyzing frames.
Effect of Moment Capacity Ratio at Beam-Column Joint of RC Framed building: A...IRJET Journal
This document reviews research on the effect of moment capacity ratio (MCR) at beam-column joints in reinforced concrete framed buildings. It summarizes several studies that investigated how increasing the MCR, defined as the ratio of column moment capacity to beam moment capacity, improves structural performance during seismic events. A higher MCR promotes a strong-column weak-beam design that increases ductility and lateral strength while reducing structural damage and failure probability. Most codes recommend a minimum MCR of 1.0-2.0, but the ideal ratio may vary based on building design, geometry, and seismic zone. Nonlinear analysis shows higher MCR generally enhances displacement capacity and reduces fragility, helping structures better withstand earthquake forces.
This document summarizes a lecture on the design of reinforced concrete beams for shear. It addresses topics like shear stresses in beams, diagonal tension cracking, types of cracks, shear strength of concrete, web reinforcement requirements, and ACI code provisions for shear design. An example is also presented on calculating the required area of web reinforcement based on the code equations. The document provides information needed to understand and apply the design of beams for shear stresses.
IRJET- Seismic Analysis of Steel Frame Building using Bracing in ETAB SoftwareIRJET Journal
This paper compares the seismic analysis of a G+11 square building and L-shaped building using time history analysis in ETAB 17.01 software. Different types of bracing systems are used, including X, V, inverted V, and diagonal bracing. The response of the buildings is compared in terms of displacement, base shear, and pseudo acceleration to determine which type of building and bracing system provides the minimum response. The L-shaped building with X bracing is found to have the minimum displacement, while the square building with X bracing has the minimum base shear and pseudo acceleration.
Today, retrofitting of the old structures is important. For this purpose, determination of capacities for these buildings, which mostly are non-ductile, is a very useful tool. In this context, non-ductile RC joint in concrete structures, as one of the most important elements in these buildings are considered, and the shear capacity, especially for retrofitting goals can be very beneficial. In this paper, three famous soft computing methods including artificial neural networks (ANN), adaptive neuro-fuzzy inference system (ANFIS) and also group method of data handling (GMDH) were used to estimating the shear capacity for this type of RC joints. A set of experimental data which were a failure in joint are collected, and first, the effective parameters were identified. Based on these parameters, predictive models are presented in detail and compare with each other. The results showed that the considered soft computing techniques are very good capabilities to determine the shear capacity.
This document summarizes a study on using frequency response methods to identify structural damage in layered composite materials. It proposes a new vibration-based technique that uses changes in the frequency response functions (FRFs) of an undamaged structure compared to a damaged one. Most reported works are based on changes in modal parameters, but this new method detects damage through existence, localization and extent using frequency response function curvature. It aims to establish an online damage identification method for laminated composites to address needs for health monitoring of composite structures, as damage alters their dynamic characteristics.
This document summarizes an experimental study on the flexural strengthening of continuous two-span unbonded post-tensioned concrete beams with end-anchored CFRP laminates. Five full-scale beams were tested: one control beam and four beams strengthened with CFRP laminates of varying widths and end anchorage configurations. The study found that CFRP strengthening increased the service load capacity more than the ultimate capacity. Proper end anchorage and installation of the CFRP laminates was important to achieve effective load transfer and prevent premature debonding failures. The strengthened beams exhibited higher stiffness and load capacity compared to the control beam.
1) The document presents the results of a linear and non-linear analysis of reinforced concrete frames with members of varying inertia (non-prismatic beams) for buildings ranging from G+2 to G+10 storeys.
2) Both bare frames and frames with infill walls were analyzed considering different beam cross-sections - prismatic, linear haunch, parabolic haunch, and stepped haunch.
3) The linear analysis was performed using ETABS and considered parameters like fundamental time period, base shear, and top storey displacement. The non-linear analysis used pushover analysis in SAP2000 to determine effective time period, effective stiffness, and hinge formation patterns.
Performance based plastic design method for steel concentric bracedEr Sharma
This document presents a performance-based plastic design (PBPD) methodology for designing steel concentric braced frames. The design begins by selecting a target drift and intended yield mechanism. The design base shear is then determined by equating the energy required to push the structure to the target drift with the demanded energy from an equivalent single-degree-of-freedom system. P-Δ effects are considered to determine member strengths. Braces are designed to yield according to plastic design, while beams and columns remain elastic. Three baseline frames are also designed and analyzed to validate the PBPD methodology.
DESIGN AND ANALYSIS OF BRIDGE WITH TWO ENDS FIXED ON VERTICAL WALL USING FIN...IAEME Publication
The Finite element analyses are conducted to model the tensile capacity of steel fiber-reinforced concrete (SFRC). For this purpose bridge with two ends fixed one specimen are casted and tested under direct and uni-axial tension. Two types of aggregates (brick and stone) are used to cast the SFRC and plain concrete. The fiber volume ratio is maintained 1.5 %. Total 8 numbers of dog-bone specimens are made and tested in a 1000-kN capacity digital universal testing machine (UTM). The strain data are gathered employing digital image correlation technique from high-definition images and high-speed video clips. Then, the strain data are synthesized with the load data obtained from the load cell of the UTM.
The lecture coveres the actuall problem of being the engineer. It conciders the transformation of the minds of professionals from the classical and well-established technics of engineering matter design into the creative art of design corresponded the demands of the XXIst century.
Similar to Lecture 12 equivalent frame method (13)
In human communication, explanations serve to increase understanding, overcome communication barriers, and build trust. They are, in most cases, dialogues. In computer science, AI explanations (“XAI”) map how an AI system expresses underlying logic, algorithmic processing, and data sources that make up its outputs. One-way communication.
How do we craft designs that "explain" concepts and respond to users’ intent? Can AI identify, elicit and apply relevant user contexts, to help us understand AI outputs? How do explanations become two-way?
We must create experiences with systems that will be required to respect user needs and dynamically explain logic and seek understanding. This is a significant challenge that, at its heart, needs UX leadership. The safety, trust, and understandability of systems we design hinge on the way we craft models for explanation.
World trade center in kerala proposal- AR. DEEKSHITH MAROLI 724519251008 REPORTdeekshithmaroli666
World trade center live proposal in kerala.
Future of our nation is looking towards kerala..?
Yes, because the biggest sludge less port is going to open in kerala soon and also about the hidden massing growth of tourism, it , business sector
My Fashion PPT is my presentation on fashion and TrendssMedhaRana1
This Presentation is in one way a guide to master the classic trends and become a timeless beauty. This will help the beginners who are out with the motto to excel and become a Pro Fashionista, this Presentation will provide them with easy but really useful ten ways to master the art of styles. Hope This Helps.
1. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Lecture 13
Lecture-13
Equivalent Frame Method
By: Prof Dr. Qaisar Ali
Civil Engineering Department
NWFP UET Peshawar
drqaisarali@nwfpuet.edu.pk
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures 1
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Topics Addressed
Introduction
Stiffness of Slab-Beam Member
Stiffness of Equivalent Column
Stiffness of Column
Stiffness of Torsional Member
Examples
Prof. Dr. Qaisar Ali 2
1
2. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Topics Addressed
Moment Distribution Method
Arrangement of Live Loads
Critical Sections for Factored Moments
Moment Redistribution
Factored Moments in Column and Middle Strips
Summary
Prof. Dr. Qaisar Ali 3
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (ACI 13.7)
Introduction
Consider a 3D structure shown in figure. It is intended to transform this 3D
system into 2D system for facilitating analysis. This can be done by using
the transformation technique of Equivalent Frame Analysis (ACI 13.7).
Prof. Dr. Qaisar Ali 4
2
3. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (ACI 13.7)
Introduction
First, a frame is detached from the 3D structure. In the given figure, an
interior frame is detached.
The width of the frame is same as mentioned in DDM. The length of the
frame extends up to full length of 3D system and the frame extends the full
height of the building.
Prof. Dr. Qaisar Ali 5
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Introduction
Interior 3D frame detached from 3D structure.
Prof. Dr. Qaisar Ali 6
3
4. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Introduction
This 3D frame is converted to a 2D frame by taking effect of stiffness of
laterally present members (slabs and beams).
Prof. Dr. Qaisar Ali 7
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Introduction
This 3D frame is converted to a 2D frame by taking effect of stiffness of
laterally present members (slabs and beams).
Prof. Dr. Qaisar Ali 8
4
5. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Introduction
This 3D frame is converted to a 2D frame by taking effect of stiffness of
laterally present members (slabs and beams).
Prof. Dr. Qaisar Ali 9
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Introduction
Ksb represents the combined stiffness of slab and longitudinal beam (if any).
Kec represents the modified column stiffness. The modification depends on lateral
members (slab, beams etc) and presence of column in the storey above.
Ksb Ksb Ksb Ksb Ksb
Kec Kec Kec Kec Kec Kec
Ksb Ksb Ksb Ksb Ksb
Kec Kec Kec Kec Kec Kec
Ksb Ksb Ksb Ksb Ksb
Kec Kec Kec Kec Kec Kec
Ksb Ksb Ksb Ksb Ksb
Kec Kec Kec Kec Kec Kec
Prof. Dr. Qaisar Ali 10
5
6. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Introduction
Therefore, the effect of 3D behavior of a frame is transformed into a 2D frame in terms of
these stiffness i.e., Ksb and Kec.
Once a 2D frame is obtained, the analysis can be done by any method of 2D frame analysis.
Ksb Ksb Ksb Ksb Ksb
Kec Kec Kec Kec Kec Kec
Ksb Ksb Ksb Ksb Ksb
Kec Kec Kec Kec Kec Kec
Ksb Ksb Ksb Ksb Ksb
Kec Kec Kec Kec Kec Kec
Ksb Ksb Ksb Ksb Ksb
Kec Kec Kec Kec Kec Kec
Prof. Dr. Qaisar Ali 11
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Introduction
Next the procedures for determination of Ksb and Kec are presented.
Ksb Ksb Ksb Ksb Ksb
Kec Kec Kec Kec Kec Kec
Ksb Ksb Ksb Ksb Ksb
Kec Kec Kec Kec Kec Kec
Ksb Ksb Ksb Ksb Ksb
Kec Kec Kec Kec Kec Kec
Ksb Ksb Ksb Ksb Ksb
Kec Kec Kec Kec Kec Kec
Prof. Dr. Qaisar Ali 12
6
7. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Stiffness of Slab Beam member (Ksb):
( )
The stiffness of slab beam (Ksb = kEIsb/l) consists of combined stiffness of
slab and any longitudinal beam present within.
For a span, the k factor is a direct function of ratios c1/l1 and c2/l2
Tables are available in literature (Nilson and MacGregor) for determination
of k for various conditions of slab systems.
c1
l2 c2
l1
Prof. Dr. Qaisar Ali 13
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Stiffness of Slab Beam member (Ksb):
( )
Determination of k
Prof. Dr. Qaisar Ali 14
7
8. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Stiffness of Slab Beam member (Ksb):
( )
Isb determination
Prof. Dr. Qaisar Ali 15
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Stiffness of Slab Beam member (Ksb): Values of k for usual
( )
cases of structural systems.
Column l1 l2 c1/l1 c2/l1 k
dimension
12 × 12 10 10 0.10 0.10 4.182 As evident from the
15 15 0.07 0.07 4.05 table, the value of k for
20 20 0.05 0.05 4.07 usual cases of structures
15 × 15 10 10 0.13 0.13 4.30 is 4.
15 15 0.08 0.08 4.06
20 20 0.06 0.06 4.04
18 × 18 10 10 0.15 0.15 4.403
15 15 0.10 0.10 4.182
20 20 0.08 0.08 4.06
Prof. Dr. Qaisar Ali 16
8
9. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Stiffness of Equivalent Column (Kec):
q ( )
Stiffness of equivalent column consists of stiffness of actual columns
{above (if any) and below slab-beam} plus stiffness of torsional members.
Mathematically,
nKc × mKt
1/Kec = 1/nKc + 1/mKt OR Kec =
nKc + mKt
Where,
n = 2 for interior storey (for flat plates only)
= 1 for top storey (for flat plates only)
m = 1 for exterior frames (half frame)
= 2 for interior frames (full frame)
Note: n will be replaced by ∑ for columns having different stiffness
Prof. Dr. Qaisar Ali 17
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Stiffness of Column (Kc):
( )
General formula of flexural stiffness is given by K = kEI/l
Design aids are available from which value of k can be readily obtained for
different values of (ta/tb) and (lu/lc).
These design aids can be used if moment distribution method is used as
method of analysis.
Prof. Dr. Qaisar Ali 18
9
10. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Stiffness of Column (Kc):
( )
Prof. Dr. Qaisar Ali 19
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Stiffness of Column (Kc):
( )
Determination of k
Prof. Dr. Qaisar Ali 20
10
11. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Stiffness of Column (Kc):
( )
Determination of k: Values of k for usual cases of structural
systems.
ta tb ta/tb lc lu lc/lu k
As evident from the
table, the value of k for
3 3 1.00 10 9.5 1.05 4.52
usual cases of structures
4 3 1.33 10 9.4
94 1.06 4.56
is 5.5.
5 3 1.67 10 9.3 1.07 4.60
6 3 2.00 10 9.3 1.08 5.20
7 3 2.33 10 9.2 1.09 5.39
8 3 2.67 10 9.1 1.10 5.42
9 3 3.00 10 9.0 1.11 5.46
10 3 3.33 10 8.9 1.12 5.5
Prof. Dr. Qaisar Ali 21
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Stiffness of Torsional Member (Kt):
( )
Torsional members (transverse members) provide moment transfer
between the slab-beams and the columns.
Assumed to have constant cross-section throughout their length.
Two conditions of torsional members (given next).
Prof. Dr. Qaisar Ali 22
11
12. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Stiffness of Torsional Member (Kt):
( )
Condition (a) – No transverse beams framing into columns
Prof. Dr. Qaisar Ali 23
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Stiffness of Torsional member (Kt):
( )
Condition (b) – Transverse beams framing into columns
Prof. Dr. Qaisar Ali 24
12
13. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Stiffness of Torsional member (Kt):
( )
Stiffness Determination: The torsional stiffness Kt of the torsional member is
given as:
If beams frame into the support in the direction of analysis the torsional
analysis,
stiffness Kt needs to be increased.
Ecs = modulus of elasticity of slab concrete; Isb = I of slab with beam; Is = I of slab without beam
Prof. Dr. Qaisar Ali 25
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Stiffness of Torsional member (Kt):
( )
Cross sectional constant, C:
Prof. Dr. Qaisar Ali 26
13
14. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Equivalent Frame
q
Finally using the flexural stiffness values of the slab-beam
and equivalent columns, a 3D frame can be converted to 2D
frame.
Ksb Ksb Ksb
Kec Kec Kec Kec
Ksb Ksb Ksb
Kec Kec Kec Kec
Ksb Ksb Ksb
Kec Kec Kec Kec
Prof. Dr. Qaisar Ali 27
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Example: Find the equivalent 2D frame for 1st storey of the E-W interior
frame of fl t plate structure shown b l
f f flat l t t t h below. Th slab i 10″ thi k and LL i
The l b is thick d is
144 psf so that ultimate load on slab is 0.3804 ksf. All columns are 14″
square. Take fc′ = 4 ksi and fy = 60 ksi. Storey height = 10′ (from floor
top to slab top)
Data:
l1 = 25′ (ln = 23.83′)
l2 = 20′
Column strip width = 20/4 = 5′
Prof. Dr. Qaisar Ali 28
14
15. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 01: 3D frame selection.
20′
Prof. Dr. Qaisar Ali 29
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 01: 3D frame extraction.
20′
10′
10′
25′
25′
10′
25′
Prof. Dr. Qaisar Ali 25′ 30
15
16. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 02: Extraction of single storey from 3D frame for separate analysis.
20′
25′
25′
10′
25′
25′
Prof. Dr. Qaisar Ali 31
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 03a: Slab-beam Stiffness calculation.
Table: Slab beam stiffness (Ksb).
l1 and l2 and k
Spa
Span c1/l1 c2/l2 I =l h 3/12
l / Ksb=kEIs/l
c1 c2 ( bl A-20) s 2 f
(table A 20)
25' & 20' and
A2-B2 0.05 0.06 4.047 20000 270E
14" 14"
The remaining spans will have the same values as the geometry is same.
Prof. Dr. Qaisar Ali 32
16
17. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Prof. Dr. Qaisar Ali 33
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 03b: Equivalent column stiffness calculation
(1/Kec = 1/∑Kc +1/Kt)
Calculation of torsional member stiffness (Kt)
Table: Kt calculation.
Column
l2 c2 C = ∑ (1 – 0 63x/y)x3y/3 (i 4)
0.63x/y)x (in Kt = ∑ 9EcsC/ {l2(1 – c2/l2)3}
location
A2 20′ 14" {1 – 0.63 × 10/ 14} × 103 × 14/3 = 2567 2 × [9Ecs×2567/ {20×12 (1–14/ (20×12))3}]=231Ecs
Note 01: Kt term is multiplied with 2 because two similar torsional members meet at column A2.
Note 02: Kt values for all other columns will be same as A2 because of similar column
dimensions.
Prof. Dr. Qaisar Ali 34
17
18. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM): A
lu
Solution:
B
Step 03b: Equivalent column stiffness calculation
(1/Kec = 1/∑Kc +1/Kt)
Calculation of column stiffness (Kc)
Table: ∑Kc calculation.
kAB CAB
Ic (in4)
Column (from (from
lc lu = (lc – hf) lc / lu for 14″ × 14″ ta/tb ΣKc = 2 × kEIc/lc
location table table
column
A23) A23)
10′ 120/110 = 14 × 143/12 = 2×(5.09Ecc×3201/ 120)
A2 110″ 5/5 = 1 5.09 0.57
(120″) 1.10 3201 = 272Ecc
Note: For flat plates, ∑Kc term is multiplied with 2 for interior storey with similar columns
above and below. For top storey, the ∑Kc term will be a single value (multiplied by 1)
Prof. Dr. Qaisar Ali 35
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Prof. Dr. Qaisar Ali 36
18
19. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 03b: Equivalent column stiffness calculation
(1/Kec = 1/∑Kc +1/Kt)
Calculation of column stiffness (Kc)
Equivalent column stiffness calculation (1/Kec = 1/∑Kc +1/Kt)
1/Kec = 1/∑Kc +1/Kt = 1/272Ecc + 1/231Ecs
Because the slab and the columns have the same strength
concrete, Ecc = Ecs = Ec.
Therefore, Kec = 124.91Ec
As all columns have similar dimensions and geometric
conditions, the Kec value for all columns will be 124.91Ec
Prof. Dr. Qaisar Ali 37
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: Equivalent Frame; can be analyzed using any method of analysis
Prof. Dr. Qaisar Ali 38
19
20. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: To analyze the frame in SAP, the stiffness values are multiplied by
lengths.
Ksblsb = 270×25×12=81000E
Keclec = 124.91×10×12=14989E
10′
Prof. Dr. Qaisar Ali 39
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Load on frame:
Solution: As the horizontal frame element
Step 04: SAP results (moment at center). represents slab beam, load is
computed by multiplying slab load
with width of frame
wul2 = 0.3804 × 20 = 7.608 kip/ft
Prof. Dr. Qaisar Ali 40
20
21. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: SAP results (moment at center).
Prof. Dr. Qaisar Ali 41
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: SAP results (moment at faces).
Prof. Dr. Qaisar Ali 42
21
22. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: Comparison with SAP 3D model results.
Load on model = 144 psf (LL)
Slab thickness = 10″
Columns = 14″× 14″
Prof. Dr. Qaisar Ali 43
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: Comparison of SAP 3D model with EFM.
Prof. Dr. Qaisar Ali 44
22
23. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Example: Find the equivalent 2D frame for 1st storey of the E-W interior
frame of b
f f beam supported f
t d frame structure shown b l
t t h below. Th slab i 7″
The l b is
thick with LL of 144 psf so that ultimate load on slab is 0.336 ksf. All
columns are 14″ square. Take fc′ = 4 ksi and fy = 60 ksi. Storey height =
10′ (from floor top to slab top)
Data:
l1 = 25′ (ln = 23.83′)
l2 = 20′
Column strip width = 20/4 = 5′
Prof. Dr. Qaisar Ali 45
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 01: 3D frame selection.
20′
Prof. Dr. Qaisar Ali 46
23
24. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 01: 3D frame extraction.
20′
10′
10′
25′
25′
10′
25′
Prof. Dr. Qaisar Ali 25′ 47
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 02: Extraction of single storey from 3D frame for separate analysis.
20′
25′
25′
10′
25′
25′
Prof. Dr. Qaisar Ali 48
24
25. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 03a: Slab-beam Stiffness calculation.
Table: Slab beam stiffness (Ksb).
l1 and l2 and k
Span c1/l1 c2/l2 Isb Ksb=kEIs/l1
c1 c2 (table A 20)
A-20)
25' & 20' and
A2-B2 0.0467 0.058 4.051 25844 349E
14" 14"
The remaining spans will have the same values as the geometry is same.
Prof. Dr. Qaisar Ali 49
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 03b: Equivalent column stiffness calculation
(1/Kec = 1/∑Kc +1/Kt)
Calculation of torsional member stiffness (Kt)
Table: Kt calculation.
Column
l2 c2 C = ∑ (1 – 0 63x/y)x3y/3 (i 4)
0.63x/y)x (in Kt = ∑ 9EcsC/ {l2(1 – c2/l2)3}
location
A2 20′ 14" 11208 3792.63Ecs
B2 20′ 14" 12694 4295.98Ecs
Prof. Dr. Qaisar Ali 50
25
26. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM): A
lu
Solution:
B
Step 03b: Equivalent column stiffness calculation
(1/Kec = 1/∑Kc +1/Kt)
Calculation of column stiffness (Kc)
Table: ∑Kc calculation.
Ic (in4)
kAB (from
Column location lc lu lc / lu for 14″ × 14″
14 14 ta/tb Kc
table A23)
column
10′ 120/100 = 14 × 143/12 = 16.5/3.5 =
A2 (bottom) 100″ 7.57 201.9Ecc
(120″) 1.20 3201 4.71
10′ 120/100 = 14 × 143/12 = 3.5/16.5=
A2 (top) 100″ 5.3 141.39Ecc
(120″) 1.20 3201 0.21
∑Kc = 202Ecc + 141Ecc = 343Ecc
Prof. Dr. Qaisar Ali 51
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM): A
lu
Solution:
B
Step 03b: Equivalent column stiffness calculation
(1/Kec = 1/∑Kc +1/Kt)
Calculation of column stiffness (Kc)
Table: ∑Kc calculation.
Ic (in4)
kAB (from
Column location lc lu lc / lu for 14″ × 14″
14 14 ta/tb Kc
table A23)
column
10′ 120/100 = 14 × 143/12 = 16.5/3.5 =
B2 (bottom) 100″ 7.57 201.9Ecc
(120″) 1.20 3201 4.71
10′ 120/100 = 14 × 143/12 = 3.5/16.5=
B2 (top) 100″ 5.3 141.39Ecc
(120″) 1.20 3201 0.21
∑Kc = 202Ecc + 141Ecc = 343Ecc
Prof. Dr. Qaisar Ali 52
26
27. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 03b: Equivalent column stiffness calculation (Column A2)
(1/Kec = 1/∑Kc +1/Kt)
Calculation of column stiffness (Kc)
Equivalent column stiffness calculation (1/Kec = 1/∑Kc +1/Kt)
1/Kec = 1/∑Kc +1/Kt = 1/343Ecc + 1/3792.63Ecs
Because the slab and the columns have the same strength
concrete, Ecc = Ecs = Ec.
Therefore, Kec = 315Ec
Prof. Dr. Qaisar Ali 53
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 03b: Equivalent column stiffness calculation (Column B2)
(1/Kec = 1/∑Kc +1/Kt)
Calculation of column stiffness (Kc)
Equivalent column stiffness calculation (1/Kec = 1/∑Kc +1/Kt)
1/Kec = 1/∑Kc +1/Kt = 1/343Ecc + 1/4295.98Ecs
Because the slab and the columns have the same strength
concrete, Ecc = Ecs = Ec.
Therefore, Kec = 318Ec
Prof. Dr. Qaisar Ali 54
27
28. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: Equivalent Frame; can be analyzed using any method of analysis
Prof. Dr. Qaisar Ali 55
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: To analyze the frame in SAP, the stiffness values are multiplied by
lengths. Ksblsb = 349×25×12=104700E
Keclec = 315×10×12=37800E
Keclec = 318×10×12=38160E
Prof. Dr. Qaisar Ali 56
28
29. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Load on frame:
Solution: As the horizontal frame element
Step 04: SAP results (moment at center). represents slab beam, load is
computed by multiplying slab load
with width of frame
wul2 = 0.336 × 20 = 6.72 kip/ft
Prof. Dr. Qaisar Ali 57
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: SAP results (moment at center).
Prof. Dr. Qaisar Ali 58
29
30. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: SAP results (moment at faces).
Prof. Dr. Qaisar Ali 59
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: Comparison with SAP 3D model results.
Load on model = 144 psf (LL)
Slab thickness = 7″
Columns = 14″× 14″
Beams = 14″× 20″
Prof. Dr. Qaisar Ali 60
30
31. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: Comparison of beam moments of SAP 3D model with beam
moments of EFM by SAP 2D analysis.
Prof. Dr. Qaisar Ali 61
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Moment Distribution Method:
The original derivation of EFM assumed that moment distribution would be
the procedure used to analyze the slabs, and some of the concepts in the
method are awkward to adapt to other methods of analysis.
In lieu of computer software, moment distribution is a convenient hand
calculation method for analyzing partial frames in the Equivalent Frame
Method.
Once stiffnesses are obtained from EFM, the distribution factors are
conveniently calculated.
Prof. Dr. Qaisar Ali 62
31
32. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Moment Distribution Method:
Distribution Factors:
Kct
Ksb1
1 Kt
2 Ksb2 lc
l1 Kt
Kec
l1 3
Kcb
K = kEI/l lc
Prof. Dr. Qaisar Ali 63
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Moment Distribution Method:
Distribution Factors:
Slab Beam Distribution Factors:
Ksb1
DF (span 2-1) =
Ksb1 + Ksb2 + Kec
Ksb2
DF (span 2-3) =
Ksb1 + Ksb2 + Kec
Prof. Dr. Qaisar Ali 64
32
33. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Moment Distribution Method:
Distribution Factors:
Equivalent Column Distribution factors:
Kec
DF =
Ksb1 + Ksb2 + Kec
Prof. Dr. Qaisar Ali 65
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Moment Distribution Method:
Distribution Factors:
These distribution factors are used in analysis.
The equivalent frame of example 02 shall now be analyzed using
moment distribution method.
The comparison with SAP 3D model result for beam moments is also
done.
done
Prof. Dr. Qaisar Ali 66
33
34. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: Comparison of SAP 3D model with EFM done by Moment
distribution method.
Joint A B C D E
CarryOver 0.5034 0.5034 0.5034 0.5034
DF 0.000 0.301 0.699 0.412 0.177 0.412 0.412 0.177 0.412 0.412 0.177 0.412 0.699 0.301 0.000
Slab Column Slab Slab Column Slab Slab Column Slab Slab Column Slab Slab Column Slab
FEM 0.000 0.000 399.103 ‐399.103 0.000 399.103 ‐399.103 0.000 399.103 ‐399.103 0.000 399.103 ‐399.103 0.000 0.000
Bal 0.000 ‐119.955 ‐279.148 0.000
119.955 279.148 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 279.148 119.955 0.000
Carry over 0.000 ‐140.529 0.000 0.000 0.000 0.000 140.529 0.000
Bal 0.000 0.000 0.000 57.838 24.854 57.838 0.000 0.000 0.000 ‐57.838 ‐24.854 ‐57.838 0.000 0.000 0.000
Carry over 29.117 0.000 0.000 29.117 ‐29.117 0.000 0.000 ‐29.117
Bal 0.000 ‐8.751 ‐20.365 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 20.365 8.751 0.000
Carry over 0.000 ‐10.252 0.000 0.000 0.000 0.000 10.252 0.000
Bal 0.000 0.000 0.000 4.220 1.813 4.220 0.000 0.000 0.000 ‐4.220 ‐1.813 ‐4.220 0.000 0.000 0.000
Total 0.000‐129.395 129.395 ‐488.302 26.810 461.492‐367.695 0.000 367.695‐461.492‐26.810488.302‐129.395129.395 0.000
Prof. Dr. Qaisar Ali 67
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: Comparison of SAP 3D model with EFM.
Prof. Dr. Qaisar Ali 68
34
35. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution of example 02 by Moment Distribution Method:
p y
Step 04: Analysis using Moment distribution method.
Joint A B C D E
CarryOver 0.5034 0.5034 0.5034 0.5034
DF 0.000 0.474 0.526 0.344 0.313 0.344 0.344 0.313 0.344 0.344 0.313 0.344 0.526 0.474 0.000
Slab Column Slab Slab Column Slab Slab Column Slab Slab Column Slab Slab Column Slab
FEM 0.000 0.000 351.891 ‐351.891 0.000 351.891‐351.891 0.000 351.891‐351.891 0.000 351.891‐351.891 0.000 0.000
Bal 0.00 ‐166.90 ‐185.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 185.00 166.90 0.00
Carry over 0.00 ‐93.13 0.00 0.00 0.00 0.00 93.13 0.00
Bal 0.00 0.00 0.00 31.99 29.15 31.99 0.00 0.00 0.00 ‐31.99 ‐29.15 ‐31.99 0.00 0.00 0.00
Carry over 16.11 0.00 0.00 16.11 ‐16.11 0.00 0.00 ‐16.11
Bal 0.00 ‐7.64 ‐8.47 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 8.47 7.64 0.00
Carry over 0.00 ‐4.26 0.00 0.00 0.00 0.00 4.26 0.00
Bal 0.00 0.00 0.00 1.46 1.33 1.46 0.00 0.00 0.00 ‐1.46 ‐1.33 ‐1.46 0.00 0.00 0.00
Total 0. ‐174.900 174.900 ‐415.961 30.544 385.417‐335.012 0.000 335.012‐385.417‐30.544415.961‐174.900174.900 0.000
Prof. Dr. Qaisar Ali 69
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM):
Solution:
Step 04: Comparison of beam moments of SAP 3D model with EFM analysis
results obtained by moment distribution method.
Prof. Dr. Qaisar Ali 70
35
36. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Arrangement of Live loads (ACI 13.7.6):
g ( )
When LL ≤ 0.75DL
Maximum factored moment when Full factored LL on all spans
Other cases
Pattern live loading using 0.75(Factored LL) to determine maximum
factored moment
Prof. Dr. Qaisar Ali 71
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Prof. Dr. Qaisar Ali 72
36
37. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Critical section for factored moments (ACI 13.7.7):
( )
Interior supports
Critical section at face of rectilinear support but ≤ 0.175l1 from center of
the support
Exterior supports
At exterior supports with brackets or capitals, the critical section < ½ the
pp p ,
projection of bracket or capital beyond face of supporting element.
Prof. Dr. Qaisar Ali 73
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Prof. Dr. Qaisar Ali 74
37
38. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Moment Redistribution (ACI 13.7.7.4):
( )
Mu2
Mu1
Mo
Mu3
ln
c1/2 c1/2
l1
Prof. Dr. Qaisar Ali 75
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Factored moments in column strips and middle strips:
p p
Same as in the Direct Design Method
Prof. Dr. Qaisar Ali 76
38
39. Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
Two Way Slab
Equivalent Frame Method (EFM)
Summary of Steps required for analysis using EFM
y p q y g
Extract the 3D frame from the 3D structure.
Extract a storey from 3D frame for gravity load analysis.
Identify EF members i.e., slab beam, torsional member and columns.
Find stiffness (kEI/l) of each EF member using tables.
Assign stiffnesses of each EF member to its corresponding 2D frame member.
Analyze the obtained 2D frame using any method of analysis to get longitudinal moments
based on center to center span.
Distribute slab-beam longitudinal moment laterally using lateral distribution procedures of
DDM.
Prof. Dr. Qaisar Ali 77
Department of Civil Engineering, N-W.F.P. University of Engineering and Technology Peshawar
The End
Prof. Dr. Qaisar Ali 78
39
雅虎竞拍
煤炉代买
paypay商城
乐天二手
日本亚马逊
乐天新品
ZOZOTOWN
