This document discusses the design of two-way floor slab systems. It compares the behavior of one-way and two-way slabs, describing how two-way slabs carry load in two directions versus one direction for one-way slabs. Different two-way slab systems like flat plates, waffle slabs, and ribbed slabs are described. Methods for analyzing two-way slabs include direct design, equivalent frame, elastic, plastic, and nonlinear analysis. Design considerations like minimum slab thickness are discussed along with examples calculating thickness.
Calulation of deflection and crack width according to is 456 2000Vikas Mehta
This document discusses the calculation of crack width in reinforced concrete flexural members. It provides information on:
1) Crack width is calculated to satisfy serviceability limits and is only relevant for Type 3 pre-stressed concrete members that crack under service loads.
2) Crack width depends on factors like amount of pre-stress, tensile stress in bars, concrete cover thickness, bar diameter and spacing, member depth and location of neutral axis, bond strength, and concrete tensile strength.
3) The method of calculation involves determining the shortest distance from the surface to a bar and using equations involving member depth, neutral axis depth, average strain at the surface level. Permissible crack widths are specified depending on exposure
1) The document discusses design considerations for columns according to ACI code, including requirements for different types of columns like tied, spirally reinforced, and composite columns.
2) It provides details on failure modes of tied and spiral columns and code requirements for minimum reinforcement ratios, number of bars, clear spacing, cover, and cross sectional dimensions.
3) Lateral reinforcement requirements are discussed, noting ties help restrain longitudinal bars from buckling while spirals provide additional confinement at ultimate load.
This document discusses the design of an isolated column footing, including:
1) Types of isolated column footings and factors that influence footing size like bearing capacity of soil.
2) Key sections to check for bending moment, shear, and development length.
3) Reinforcement requirements.
4) An example problem where a rectangular isolated sloped footing is designed for a column carrying an axial load of 2000 kN. Design checks are performed for footing size, bending moment, shear, development length, and reinforcement.
The document discusses reinforced concrete columns, including their functions, failure modes, classifications, and design considerations. Columns primarily resist axial compression but may also experience bending moments. They can fail due to compression, buckling, or a combination. Design depends on whether the column is short or slender, braced or unbraced. Reinforcement is designed based on the column's expected loads and dimensions using methods specified in design codes like BS 8110.
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.
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.
Approximate analysis methods make simplifying assumptions to determine preliminary member forces and dimensions for indeterminate structures. Case 1 assumes diagonals cannot carry compression and shares shear between diagonals. Case 2 allows compression in diagonals. Portal and cantilever methods analyze frames by dividing into substructures at assumed hinge locations, solving each sequentially from top to bottom.
This document provides an overview of different seismic analysis methods for reinforced concrete buildings according to Indian code IS 1893-2002, including linear static, nonlinear static, linear dynamic, and nonlinear dynamic analysis. It describes the basic procedures for each analysis type and provides examples of how to calculate design seismic base shear, distribute seismic forces vertically and horizontally, and determine drift and overturning effects. Case studies are presented comparing the results of static and dynamic analysis for regular and irregular multi-storey buildings modeled in SAP2000.
Calulation of deflection and crack width according to is 456 2000Vikas Mehta
This document discusses the calculation of crack width in reinforced concrete flexural members. It provides information on:
1) Crack width is calculated to satisfy serviceability limits and is only relevant for Type 3 pre-stressed concrete members that crack under service loads.
2) Crack width depends on factors like amount of pre-stress, tensile stress in bars, concrete cover thickness, bar diameter and spacing, member depth and location of neutral axis, bond strength, and concrete tensile strength.
3) The method of calculation involves determining the shortest distance from the surface to a bar and using equations involving member depth, neutral axis depth, average strain at the surface level. Permissible crack widths are specified depending on exposure
1) The document discusses design considerations for columns according to ACI code, including requirements for different types of columns like tied, spirally reinforced, and composite columns.
2) It provides details on failure modes of tied and spiral columns and code requirements for minimum reinforcement ratios, number of bars, clear spacing, cover, and cross sectional dimensions.
3) Lateral reinforcement requirements are discussed, noting ties help restrain longitudinal bars from buckling while spirals provide additional confinement at ultimate load.
This document discusses the design of an isolated column footing, including:
1) Types of isolated column footings and factors that influence footing size like bearing capacity of soil.
2) Key sections to check for bending moment, shear, and development length.
3) Reinforcement requirements.
4) An example problem where a rectangular isolated sloped footing is designed for a column carrying an axial load of 2000 kN. Design checks are performed for footing size, bending moment, shear, development length, and reinforcement.
The document discusses reinforced concrete columns, including their functions, failure modes, classifications, and design considerations. Columns primarily resist axial compression but may also experience bending moments. They can fail due to compression, buckling, or a combination. Design depends on whether the column is short or slender, braced or unbraced. Reinforcement is designed based on the column's expected loads and dimensions using methods specified in design codes like BS 8110.
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.
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.
Approximate analysis methods make simplifying assumptions to determine preliminary member forces and dimensions for indeterminate structures. Case 1 assumes diagonals cannot carry compression and shares shear between diagonals. Case 2 allows compression in diagonals. Portal and cantilever methods analyze frames by dividing into substructures at assumed hinge locations, solving each sequentially from top to bottom.
This document provides an overview of different seismic analysis methods for reinforced concrete buildings according to Indian code IS 1893-2002, including linear static, nonlinear static, linear dynamic, and nonlinear dynamic analysis. It describes the basic procedures for each analysis type and provides examples of how to calculate design seismic base shear, distribute seismic forces vertically and horizontally, and determine drift and overturning effects. Case studies are presented comparing the results of static and dynamic analysis for regular and irregular multi-storey buildings modeled in SAP2000.
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.
This document provides information on the structural design of a simply supported reinforced concrete beam. It includes:
- A list of students enrolled in an elementary structural design course.
- Equations and diagrams showing the forces and stresses in a reinforced concrete beam with a singly reinforced bottom section.
- Limits on the maximum depth of the neutral axis according to the grade of steel.
- Examples of analyzing the stresses and determining steel reinforcement for a given beam cross-section.
- A design example calculating the dimensions and steel reinforcement for a rectangular beam with a factored uniform load.
This document summarizes the key aspects of flat slab construction and design according to Indian code IS 456-2000. It defines flat slabs as slabs that are directly supported by columns without beams, and describes four common types based on whether drops and column heads are used. The main topics covered include guidelines for proportioning slabs and drops, methods for determining bending moments and shear forces, requirements for slab reinforcement, and an example problem demonstrating the design of an interior flat slab panel.
Earthquake Load Calculation (base shear method)
The 3-story standard office building is located in Los Angeles situated on stiff soil. The
structure of the building is steel special moment frame. All moment-resisting frames are
located at the perimeter of the building. Determine the earthquake force on each story in
North-South direction.
This document provides 10 examples of problems related to bearing capacity of foundations. The examples calculate bearing capacity using Terzaghi's analysis for different soil and foundation conditions, including cohesionless and cohesive soils, square and strip footings, and considering the water table depth. One example compares results to field plate load tests. The solutions show calculations for determining soil shear strength parameters, factor of safety, and safe bearing capacity.
This document provides an overview of the design of steel beams. It discusses various beam types and sections, loads on beams, design considerations for restrained and unrestrained beams. For restrained beams, it covers lateral restraint requirements, section classification, shear capacity, moment capacity under low and high shear, web bearing, buckling, and deflection checks. For unrestrained beams, it discusses lateral torsional buckling, moment and buckling resistance checks. Design procedures and equations for determining effective properties and capacities are also presented.
The document provides details to design the reinforcement for a basement retaining wall. It includes calculating the required wall thickness, loads on the wall, bending moments, shear forces, and reinforcement requirements. The summary is as follows:
1. The thickness of the basement retaining wall is determined to be 200mm based on the given height and material properties.
2. The loads on the wall, including soil pressure, water pressure, and surcharge loads are calculated.
3. The bending moment and shear force diagrams are drawn, with the maximum bending moment found to be 33.12 kNm and maximum shear force 65.76kN.
4. The required vertical and horizontal reinforcement is calculated for different sections based on
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.
This document provides design calculations for structural elements of a concrete car park structure according to BS-8110, including:
1. A one-way spanning roof slab with a span of 2.8m, designed as simply supported with 10mm main reinforcement bars at 300mm spacing and 8mm secondary bars.
2. A load distribution beam D and non-load bearing beam E, with calculations provided for beam D's dead and imposed loads.
3. Requirements include individual work submission by January 2nd, 2016 and assumptions to be clearly stated.
Footings are structural members that support columns and walls and transmit their loads to the soil. Different types of footings include wall footings, isolated/single footings, combined footings, cantilever/strap footings, continuous footings, rafted/mat foundations, and pile caps. Footings must be designed to safely carry and transmit loads to the soil while meeting code requirements regarding bearing capacity, settlement, reinforcement, and shear strength. A proper footing design involves determining loads, allowable soil pressure, reinforcement requirements, and assessing settlement.
Structural Analysis And Design is a structural analysis and design software. It includes tools for 3D modeling, analysis, and design of structures according to various international codes. The software was originally developed by Research Engineers International and later acquired by Bentley Systems. It allows engineers to generate models using different elements like frames, plates, and solids. Various types of structures like trusses, planes, and spaces can be modeled and analyzed. The software provides tools for assigning properties, loads, boundary conditions, and performing analysis to calculate member forces and deflections. The results can then be used for structural design of elements like beams, columns, slabs, and foundations.
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.
Prestress loss occurs as prestress reduces over time from its initial applied value. There are two types of prestress loss - immediate losses during prestressing/transfer and long-term time-dependent losses. Immediate losses include elastic shortening, anchorage slip, and friction. Long-term losses include creep and shrinkage of concrete and relaxation of prestressing steel. The quantification of losses is based on strain compatibility between concrete and steel. For a pre-tensioned concrete sleeper, the percentage loss due to elastic shortening was calculated to be approximately 2.83% based on the stress in concrete at the level of the tendons.
Tension members can fail due to three modes:
1. Gross section yielding, where the entire cross-section yields
2. Net section yielding, where the reduced cross-section after subtracting holes yields
3. Block shear failure, which also occurs in welded connections along planes of shear and tension
The design strength is the minimum of the strengths from these three failure modes. Block shear is demonstrated using a failed gusset plate connection with failure planes around the weld. The problem determines the tensile strength of a plate connected to a gusset plate, calculating the strength based on gross section yielding, net section yielding, and block shear failure.
This document summarizes the design of a one-way slab for a multi-story building. Key steps include:
1) Determining the effective span is 3.125m based on the room dimensions and support thickness.
2) Calculating the factored bending moment of 5.722 kNm/m based on the loads and effective span.
3) Checking that the provided depth of 150mm is greater than the required depth of 45.53mm.
4) Sizing the main reinforcement as 130mm^2 based on the factored moment and concrete properties.
5) Specifying 10mm diameter bars spaced at 300mm centers along the shorter span.
The document discusses the reinforcement requirements and design process for axially loaded columns. It provides guidelines on the minimum longitudinal and transverse reinforcement, including the pitch and diameter of lateral ties. Examples are given to calculate the ultimate load capacity of rectangular and circular columns based on the grade of concrete and steel. Design assumptions and checks for minimum eccentricity are also outlined.
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.
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.
This document discusses various floor systems for low-rise reinforced concrete buildings. It describes flat plate, flat slab, beam-supported slab, and one-way joist systems. For each system, it covers advantages and disadvantages, span lengths, minimum thickness requirements, reinforcement considerations, and other design details. The primary focus is on optimizing design for economy while meeting strength and serviceability requirements.
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.
This document provides information on the structural design of a simply supported reinforced concrete beam. It includes:
- A list of students enrolled in an elementary structural design course.
- Equations and diagrams showing the forces and stresses in a reinforced concrete beam with a singly reinforced bottom section.
- Limits on the maximum depth of the neutral axis according to the grade of steel.
- Examples of analyzing the stresses and determining steel reinforcement for a given beam cross-section.
- A design example calculating the dimensions and steel reinforcement for a rectangular beam with a factored uniform load.
This document summarizes the key aspects of flat slab construction and design according to Indian code IS 456-2000. It defines flat slabs as slabs that are directly supported by columns without beams, and describes four common types based on whether drops and column heads are used. The main topics covered include guidelines for proportioning slabs and drops, methods for determining bending moments and shear forces, requirements for slab reinforcement, and an example problem demonstrating the design of an interior flat slab panel.
Earthquake Load Calculation (base shear method)
The 3-story standard office building is located in Los Angeles situated on stiff soil. The
structure of the building is steel special moment frame. All moment-resisting frames are
located at the perimeter of the building. Determine the earthquake force on each story in
North-South direction.
This document provides 10 examples of problems related to bearing capacity of foundations. The examples calculate bearing capacity using Terzaghi's analysis for different soil and foundation conditions, including cohesionless and cohesive soils, square and strip footings, and considering the water table depth. One example compares results to field plate load tests. The solutions show calculations for determining soil shear strength parameters, factor of safety, and safe bearing capacity.
This document provides an overview of the design of steel beams. It discusses various beam types and sections, loads on beams, design considerations for restrained and unrestrained beams. For restrained beams, it covers lateral restraint requirements, section classification, shear capacity, moment capacity under low and high shear, web bearing, buckling, and deflection checks. For unrestrained beams, it discusses lateral torsional buckling, moment and buckling resistance checks. Design procedures and equations for determining effective properties and capacities are also presented.
The document provides details to design the reinforcement for a basement retaining wall. It includes calculating the required wall thickness, loads on the wall, bending moments, shear forces, and reinforcement requirements. The summary is as follows:
1. The thickness of the basement retaining wall is determined to be 200mm based on the given height and material properties.
2. The loads on the wall, including soil pressure, water pressure, and surcharge loads are calculated.
3. The bending moment and shear force diagrams are drawn, with the maximum bending moment found to be 33.12 kNm and maximum shear force 65.76kN.
4. The required vertical and horizontal reinforcement is calculated for different sections based on
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.
This document provides design calculations for structural elements of a concrete car park structure according to BS-8110, including:
1. A one-way spanning roof slab with a span of 2.8m, designed as simply supported with 10mm main reinforcement bars at 300mm spacing and 8mm secondary bars.
2. A load distribution beam D and non-load bearing beam E, with calculations provided for beam D's dead and imposed loads.
3. Requirements include individual work submission by January 2nd, 2016 and assumptions to be clearly stated.
Footings are structural members that support columns and walls and transmit their loads to the soil. Different types of footings include wall footings, isolated/single footings, combined footings, cantilever/strap footings, continuous footings, rafted/mat foundations, and pile caps. Footings must be designed to safely carry and transmit loads to the soil while meeting code requirements regarding bearing capacity, settlement, reinforcement, and shear strength. A proper footing design involves determining loads, allowable soil pressure, reinforcement requirements, and assessing settlement.
Structural Analysis And Design is a structural analysis and design software. It includes tools for 3D modeling, analysis, and design of structures according to various international codes. The software was originally developed by Research Engineers International and later acquired by Bentley Systems. It allows engineers to generate models using different elements like frames, plates, and solids. Various types of structures like trusses, planes, and spaces can be modeled and analyzed. The software provides tools for assigning properties, loads, boundary conditions, and performing analysis to calculate member forces and deflections. The results can then be used for structural design of elements like beams, columns, slabs, and foundations.
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.
Prestress loss occurs as prestress reduces over time from its initial applied value. There are two types of prestress loss - immediate losses during prestressing/transfer and long-term time-dependent losses. Immediate losses include elastic shortening, anchorage slip, and friction. Long-term losses include creep and shrinkage of concrete and relaxation of prestressing steel. The quantification of losses is based on strain compatibility between concrete and steel. For a pre-tensioned concrete sleeper, the percentage loss due to elastic shortening was calculated to be approximately 2.83% based on the stress in concrete at the level of the tendons.
Tension members can fail due to three modes:
1. Gross section yielding, where the entire cross-section yields
2. Net section yielding, where the reduced cross-section after subtracting holes yields
3. Block shear failure, which also occurs in welded connections along planes of shear and tension
The design strength is the minimum of the strengths from these three failure modes. Block shear is demonstrated using a failed gusset plate connection with failure planes around the weld. The problem determines the tensile strength of a plate connected to a gusset plate, calculating the strength based on gross section yielding, net section yielding, and block shear failure.
This document summarizes the design of a one-way slab for a multi-story building. Key steps include:
1) Determining the effective span is 3.125m based on the room dimensions and support thickness.
2) Calculating the factored bending moment of 5.722 kNm/m based on the loads and effective span.
3) Checking that the provided depth of 150mm is greater than the required depth of 45.53mm.
4) Sizing the main reinforcement as 130mm^2 based on the factored moment and concrete properties.
5) Specifying 10mm diameter bars spaced at 300mm centers along the shorter span.
The document discusses the reinforcement requirements and design process for axially loaded columns. It provides guidelines on the minimum longitudinal and transverse reinforcement, including the pitch and diameter of lateral ties. Examples are given to calculate the ultimate load capacity of rectangular and circular columns based on the grade of concrete and steel. Design assumptions and checks for minimum eccentricity are also outlined.
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.
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.
This document discusses various floor systems for low-rise reinforced concrete buildings. It describes flat plate, flat slab, beam-supported slab, and one-way joist systems. For each system, it covers advantages and disadvantages, span lengths, minimum thickness requirements, reinforcement considerations, and other design details. The primary focus is on optimizing design for economy while meeting strength and serviceability requirements.
The document summarizes the analysis and design of various foundation types for a seven story building in Nablus city. It describes isolated footings, combined footings, wall footings, mat foundations, and pile foundations. Laboratory test results of soil samples are presented. Loads on each column are calculated. Dimensions, reinforcement details and settlement calculations are provided for each foundation type. Based on the analysis of material quantities, construction costs, and settlement calculations, isolated footings with combined, wall and elevator footings are recommended as the most economical foundation solution.
This document provides the design of a rectangular water tank with a capacity of 2500 cubic meters. It includes:
1) Design of the roof slab as a flat slab with columns spaced 5 meters apart and a thickness of 240mm.
2) Design of columns with a size of 350mm and reinforcement of 6 bars of 16mm diameter.
3) Design of the vertical walls with a thickness of 230mm at the base reducing to 180mm in the middle. Reinforcement of 16mm diameter bars at 125mm centers is provided.
4) Checks for crack width for the columns and walls show the crack width is less than the permissible 0.2mm.
This document provides a work breakdown structure and quantity survey for the construction of a residential villa. It divides the work into sub-structure and super-structure categories. For the sub-structure, it surveys quantities for excavation, footings, tie beams, and columns. For the super-structure, it surveys concrete volumes, reinforcement, and formwork needed for the ground slab, columns, beams, top slab, and staircase. The quantity survey provides detailed calculations of material needs for each building component to develop a bill of quantities for the project.
This document discusses the design of flat slab structures. It begins by defining a flat slab as a type of slab supported directly on columns without beams. It then provides details on the types of flat slabs, their common uses in buildings, and benefits such as flexibility in layout and reduced construction time. The document goes on to discuss key design considerations for flat slabs including thickness, drops, column heads, and methods of analysis. It focuses on the direct design method and provides limitations for its use, such as rectangular panel shapes and span length ratios.
This document discusses the design of flat slab structures. It begins by defining a flat slab as a type of slab supported directly on columns without beams. It then provides details on the types of flat slabs, their common uses in buildings, and benefits such as flexibility in layout and reduced construction time. The document goes on to discuss key design considerations for flat slabs including thickness, drops, column heads, and methods of analysis. It focuses on the direct design method and provides limitations for its use.
1) Two-way slabs are slabs with reinforcement in two directions because bending occurs in both directions when the L/S ratio 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) DDM involves determining the total factored static moment, distributing it to positive and negative moments, then distributing those moments to column and middle strips based on ratios of flexural and torsional stiffness.
Design of concrete structure 2 project-Loay Qabaha &Basel SalameLoay Qabaha
This document provides a design for a two-way ribbed slab system. It begins by defining two-way slab systems and providing structural equations. It then gives the problem definition, including load data. The slab is designed by first assuming a thickness and checking loads and shear. Reinforcement is designed. Frame analysis is done by hand and in SAP2000 to calculate moments, which are within 5% error. Design details like steel areas are attached in an Excel sheet.
The document discusses the analysis and design of different types of slabs in reinforced concrete structures. It describes one-way slabs, which act as a series of parallel beams, and two-way slabs, which are supported on all four edges. Two-way slabs can be edge-supported by beams or columns. The minimum thickness, reinforcement requirements, and design procedures are provided for one-way and two-way slabs according to code specifications. Various examples are also presented to illustrate how to analyze and design one-way and two-way slabs.
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
The document contains three practice exam questions related to civil engineering board exams. The first question provides information about a three-hinged arch and asks for the vertical reaction, total reaction at a hinge, and total reaction at point B. The second question provides information about reinforced concrete beams and asks for properties related to analyzing the beams as T-beams. The third question provides information about a steel column and asks for computed axial stress, allowable axial stress, and maximum moment the column can carry.
The document summarizes the design procedures for slab systems according to the ACI 318 Code, including:
1) The direct design method and equivalent frame method for determining moments at critical sections.
2) Distributing the total design moment between positive and negative moments.
3) Distributing moments laterally between column strips, middle strips, and beams.
4) A 5-step basic design procedure involving determining moments, distributing moments, sizing reinforcement, and designing beams if present.
Determination of load transfer in reinforced concrete solid slabs by finite e...IOSR Journals
This document analyzes load transfer in reinforced concrete solid slabs using finite element analysis. It models two types of slabs in SAP2000: 1) slabs with pin supports on all four edges and 2) slabs with pin supports at corners and beams along edges. For type 1, stresses are higher in the short direction but still significant in the long direction, showing load is transferred two-way. For type 2, stresses in the short direction increase with stiffer beams while stresses in the long direction decrease. The analysis concludes all concrete solid slabs behave as two-way slabs, transferring load in both directions regardless of dimensions or support conditions.
This document provides a summary of reinforced concrete columns (RCC columns). It defines a column and describes different types of columns based on reinforcement and length. Short columns are less than 12 times the minimum thickness, while long columns are greater than 12 times the thickness. The document outlines preliminary sizing of columns and the functions of tie/spiral reinforcement. It includes design equations for axially loaded columns in working stress design (WSD) and ultimate stress design (USD). Two sample problems are worked through demonstrating column design using both methods.
This document discusses the design and analysis of flat slab structures. It begins with an introduction to flat slabs and their uses of column heads and drop panels. The benefits of flat slabs are then outlined, including flexibility in layout, reduced building height, and ease of M&E installation. Design considerations are presented such as structural stiffness, deflection limits, and shear reinforcement. The document analyzes flat slab design methodology including finite element analysis, simplified methods, and equivalent frame analysis. Moment distribution, punching shear, deflection, and detailing of reinforcement mesh are also summarized.
This report compares design codes for hollow block and ribbed slabs. It includes:
- A comparison of limitations between Egyptian, British, Euro and American codes on rib spacing, slab thickness, and other parameters.
- Solved examples for one-way and two-way slabs according to different codes, finding the Egyptian code most economical.
- Analysis of using one or two cross-ribs, determining one rib at midspan is sufficient.
- Different modeling methods for the slabs in structural analysis software, with minor differences in results.
- Case studies presented for one-way, cantilever, two-way hollow block slabs, and ribbed slabs using
Ch4 Bridge Floors (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...Hossam Shafiq II
This chapter discusses bridge floors for roadway and railway bridges. It describes three main types of structural systems for roadway bridge floors: slab, beam-slab, and orthotropic plate. For railway bridges, the two main types are open timber floors and ballasted floors. The chapter then covers design considerations for allowable stresses, stringer and cross girder cross sections, and provides an example design for the floor of a roadway bridge with I-beam stringers and cross girders.
The document summarizes the analysis and design of troughed floors according to Eurocode. It introduces troughed floors as slabs that combine the advantages of ribbed floors and flat slabs, providing efficient long-span floors up to 12m. It describes the components of troughed floors and provides equations to size the elements and estimate self-weight. The analysis is carried out using coefficients for one-way slabs and beams. The design considers flexure and shear of the ribs and beams according to Eurocode 2. A worked example is included to demonstrate the complete design of a troughed slab and supporting beam.
There are three main steps to designing a column splice:
1. Determine loads on the splice from axial, bending and shear forces. For axial loads, splices are designed to carry 50% of the load for machined ends or 100% for non-machined ends.
2. Design the splice plates to resist the loads using the yield stress as the design strength. Plate size is calculated based on load and stress.
3. Determine the number and size of bolts required based on the plate load capacity and bolt strengths in shear or bearing. Splice widths match the column and minimum plate thickness is 6mm.
Spot speed studies involve measuring the speeds of individual vehicles passing a specific location on a roadway. This provides speed distribution data that can be used for traffic planning and safety purposes. There are both manual and automatic methods for collecting spot speed data. Manual methods involve using a stopwatch to time vehicles over a short known distance. Automatic methods include using road detectors, radar guns, or cameras to directly measure vehicle speeds. The collected speed data is typically presented through tables and graphs showing the frequency distribution and cumulative frequency of observed speeds. This allows calculations of speed percentiles and other metrics.
The document summarizes key concepts in fluid mechanics including:
1) Types of fluid flow such as steady, unsteady, uniform, and non-uniform flow. It also discusses the continuity, Bernoulli, and momentum equations used to solve fluid problems.
2) Applications of Bernoulli's equation such as flow over weirs, through orifices and pipes, and venturi meters. It also discusses concepts like total energy, hydraulic grade line, and more.
3) Examples are provided calculating velocity, pressure, flow rates, and more at different points in pipe systems using the governing equations.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
This document provides instructions on creating simple formulas in Excel 2003. It discusses using formulas to perform calculations with cell references and mathematical operators. Common functions like SUM, AVERAGE, MAX and MIN are explained. It also covers using the AutoSum button to easily insert formulas, and editing existing formulas by dragging range borders to modify the cell references. The document is intended to teach basic formula creation and functions to new Excel users.
This document provides instructions for using Excel to calculate cash flow projections using a data list. It explains how to create a data list, add and delete rows, and use the OFFSET function to calculate a running balance that does not break when rows are deleted. The OFFSET function references cells indirectly, allowing the formula to still work correctly when the worksheet structure changes from deleted rows.
This document contains 10 examples of calculating seepage and pore water pressure using flow nets. It provides the key steps and calculations for:
1) Determining flow rate, factor of safety against piping, and effective stress at a point.
2) Calculating uplift pressures at multiple points, seepage loss under a dam, and factor of safety against boiling.
3) Estimating how high water would rise in piezometers and seepage loss for a dam.
1. The document provides examples of calculating consolidation parameters such as void ratio, coefficient of consolidation, and primary consolidation settlement from given soil testing data.
2. Parameters like initial void ratio, applied pressure, and thickness of soil layers are used to determine the change in stress and void ratio to then calculate settlement.
3. Several methods are presented to calculate the average effective stress and stress change at different points to then determine the consolidation settlement under different boundary conditions, stress histories, and soil properties.
Three point loads and a uniform contact pressure on a circular foundation are used to calculate the vertical stress increase at various points below the foundations. The solutions involve determining shape factors from charts and formulas to calculate the stress contribution from each loading area. The stress increases are then summed to find the total vertical stress increase at the point of interest, which ranges from 0-186 kN/m^2 depending on the example.
The document provides 8 examples of calculating total stress, effective stress, and pore water pressure at different depths for various soil profiles. The examples solve for the stresses and pressures at specific points or depths by considering the layer thicknesses, soil unit weights, depth of water table, and degree of saturation. The effective stress is calculated by subtracting the pore water pressure from the total stress at each point.
The document provides examples of classifying soils using the AASHTO and USCS soil classification systems. Key steps include determining the particle size distribution, plasticity characteristics (liquid limit, plastic limit, plasticity index), and using this data on classification charts to identify the appropriate soil type symbols. Soils are classified as sand, silt, clay or combinations based on their grain size and plasticity properties.
The document provides calculations to design the reinforcement for a beam cross-section under maximum positive and negative moments. For the maximum positive moment case, the required reinforcement is calculated as 8 #35 bars and 2 #32 bars. For the maximum negative moment case, the required reinforcement is calculated as 3 #35 bars. Sketches of the reinforced cross-sections are requested to show bar sizes, arrangements, and spacing.
4 pages from matlab an introduction with app.-2Malika khalil
This document discusses several methods for solving systems of linear equations and algebraic eigenvalue problems, including Gauss elimination, LU decomposition, Cholesky decomposition, Gauss-Seidel, Gauss-Jordan, and Jacobi methods. It provides the mathematical formulations and iterative procedures for each method. Numerical examples using MATLAB are provided to illustrate how to apply the procedures.
Design of column trail and error exampleMalika khalil
This document presents the solution to a multi-step word problem involving geometry, algebra, and calculations with percentages. Key details include side lengths of 500 units for a square field with dimensions reduced by fences on all sides, calculations to determine the area inside the fences and percentage of the field remaining, and checking if the results satisfy given constraints.
This document defines key terms used in soil phase relations, including water content, void ratio, porosity, degree of saturation, bulk density, saturated density, dry density, and specific gravity. It presents the relationships between these terms using a phase diagram and mass-volume equations. The key relationship highlighted is that for a given soil fraction, the sum of the volumes of soil grains, air, and water equals the total volume.
This document discusses different types of solids found in environmental samples and their measurement. It defines total solids, total suspended solids, total dissolved solids, volatile solids, and fixed solids. Key points include: total solids are all solids in a sample, total suspended solids are filterable, total dissolved solids pass through a filter, and volatile solids are lost during ignition while fixed solids remain. The document provides methods for measuring total suspended solids, including filtration, drying, ignition, and calculations. It also discusses the environmental significance of different solids measurements.
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.
Menus are ubiquitous in websites and applications of all types. They are critical to accessing the information and actions that users need, yet they can be very frustrating to use. In our UX consulting practice, many clients have come to us for help solving problems with menus, such as scaling to handle long lists of options, and overcoming usability issues with hover and flyout menus. In this presentation we’ll review what we have learned about best practices for designing mega menus, context menus, hamburger menus, full page menus and other types, and share case studies of menu redesigns we have worked on for enterprise applications, mobile apps, and information-rich websites.
Design Thinking is a problem-solving framework that emphasizes a user-centered approach to innovation and design. It involves understanding user needs, challenging assumptions, redefining problems, and creating innovative solutions through iterative testing and refinement. The process is typically divided into five stages:
Empathize: Understand the users and their needs through observation, interviews, and user research. This stage focuses on gaining a deep insight into the user's experiences and emotions.
Define: Clearly articulate the problem or challenge based on the insights gathered during the empathize stage. This involves synthesizing the information to define the core issues that need to be addressed.
Ideate: Generate a wide range of creative ideas and potential solutions. This stage encourages brainstorming and thinking outside the box to explore different possibilities.
Prototype: Create tangible representations of selected ideas. Prototypes can be simple sketches, models, or interactive simulations that allow designers to explore and test their concepts.
Test: Evaluate the prototypes with real users to gather feedback and insights. This stage involves refining and improving the solutions based on user interactions and responses.
Design Thinking is iterative, meaning that the stages are revisited as needed to refine the solution. It promotes collaboration, creativity, and a deep understanding of the user, leading to more effective and innovative outcomes. This approach is widely used in various fields, including product design, service design, business strategy, and social innovation.
UI (User Interface) and UX (User Experience) design are critical components of creating effective, user-friendly digital products.
UI Design focuses on the visual aspects of a product. It involves designing the layout, buttons, icons, and other interactive elements that users interact with. A good UI design ensures that the product is visually appealing, consistent, and intuitive, making it easy for users to navigate and complete their tasks.
UX Design, on the other hand, is about the overall experience a user has with a product. It encompasses the entire user journey, from the initial discovery of the product to its continued use. UX designers conduct user research, create user personas, and develop wireframes and prototypes to ensure that the product meets the users' needs effectively. A strong UX design makes the product accessible, enjoyable, and valuable to the user.
Together, UI and UX design aim to create products that are not only functional and easy to use but also delightful and engaging. While UI design is concerned with the product’s aesthetics and interactive components, UX design focuses on the user’s overall journey and satisfaction. Combining both fields leads to a cohesive, effective, and user-centered product design.
UI/UX design is an essential discipline in the digital world, focusing on creating user-friendly and visually app
This is Stage one of my Future Deep Strike Aircraft project to develop a replacement for the FB-111 / F-111F / F-15E and B-1B. This stage covers requirements and threats. Stage 2 will cover Design Studies, and the CCA Wingman.
7. The two-way ribbed slab and waffled slab system:
General thickness of the slab is 2 to 4 in.
8. Comparison of One-way and Two-
way slab behavior Economic
Choices
Flat Plate suitable span 20 to 25 ft with LL= 60 -100 psf
Advantages
Low cost formwork
Exposed flat ceilings
Fast
Disadvantages
Low shear capacity
Low Stiffness (notable deflection)
9. Flat Slab suitable span 20 to 30 ft with LL= 80 -150 psf
Advantages
Low cost formwork
Exposed flat ceilings
Fast
Disadvantages
Need more formwork for capital and panels
10. Waffle Slab suitable span 30 to 48 ft with LL= 80 -
150 psf
Advantages
Carries heavy loads
Attractive exposed ceilings
Fast
Disadvantages
Formwork with panels is expensive
11. One-way Slab on beams suitable span 10 to 20 ft with
LL= 60-100 psf
Can be used for larger spans with relatively higher
cost and higher deflections
One-way joist floor system is suitable span 20 to 30 ft
with LL= 80-120 psf
Deep ribs, the concrete and steel quantities are
relative low
Expensive formwork expected.
12. Comparison of One-way and
Two-way slab behavior
ws =load taken by short direction
wl = load taken by long direction
dA = dB
Rule of Thumb: For B/A > 2,
design as one-way slab
EI
Bw
EI
Aw
384
5
384
5 4
l
4
s
ls
4
4
l
s
162ABFor ww
A
B
w
w
13. Two-Way Slab Design
Static Equilibrium of Two-Way Slabs
Analogy of two-way slab to plank and beam floor
Section A-A:
Moment per ft width in planks
Total Moment
ft/ft-k
8
2
1wl
M
ft-k
8
2
1
2f
l
wlM
14. Static Equilibrium of Two-Way Slabs
Analogy of two-way slab to plank and beam floor
Uniform load on each beam
Moment in one beam (Sec: B-B) ft-k
82
2
21
lb
lwl
M
k/ft
2
1wl
15. Static Equilibrium of Two-Way Slabs
Total Moment in both beams
Full load was transferred east-west by the planks and then was
transferred north-south by the beams;
The same is true for a two-way slab or any other floor system.
ft-k
8
2
2
1
l
wlM
16. General Design Concepts
(1) Direct Design Method (DDM)
Limited to slab systems to uniformly distributed
loads and supported on equally spaced columns.
Method uses a set of coefficients to determine the
design moment at critical sections. Two-way slab
system that do not meet the limitations of the ACI
Code 13.6.1 must be analyzed more accurate
procedures
17. (2) Equivalent Frame Method (EFM)
A three-dimensional building is divided into a
series of two-dimensional equivalent frames by
cutting the building along lines midway between
columns. The resulting frames are considered
separately in the longitudinal and transverse
directions of the building and treated floor by
floor.
20. Method of Analysis
(1) Elastic Analysis
Concrete slab may be treated as an elastic
plate. Use Timoshenko’s method of analyzing
the structure. Finite element analysis
21. (2) Plastic Analysis
The yield method used to determine the limit state
of slab by considering the yield lines that occur in
the slab as a collapse mechanism.
The strip method, where slab is divided into strips
and the load on the slab is distributed in two
orthogonal directions and the strips are analyzed as
beams.
The optimal analysis presents methods for
minimizing the reinforcement based on plastic
analysis
22. (3) Nonlinear analysis
Simulates the true load-deformation characteristics
of a reinforced concrete slab with finite-element
method takes into consideration of nonlinearities of
the stress-strain relationship of the individual
members.
23. Column and Middle Strips
The slab is broken
up into column
and middle strips
for analysis
24. Minimum Slab Thickness for
Two-way Construction
The ACI Code 9.5.3 specifies a minimum slab thickness
to control deflection. There are three empirical
limitations for calculating the slab thickness (h), which
are based on experimental research. If these limitations
are not met, it will be necessary to compute deflection.
25. 22.0 m (a) For
2.0536
200,000
8.0
m
y
n
f
l
h
fy in psi. But not less than 5 in.
28. Slabs without interior
beams spanning
between supports and
ratio of long span to
short span < 2
See section 9.5.3.3
For slabs with beams
spanning between
supports on all sides.
29. The definitions of the terms are:
h = Minimum slab thickness without interior beams
ln =
m=
Clear span in the long direction measured face to
face of column
the ratio of the long to short clear span
The average value of for all beams on the sides
of the panel.
30. Definition of Beam-to-Slab Stiffness
Ratio,
Accounts for stiffness effect of beams located along
slab edge reduces deflections of panel
adjacent to beams.
slabofstiffnessflexural
beamofstiffnessflexural
31. With width bounded laterally by centerline of
adjacent panels on each side of the beam.
scs
bcb
scs
bcb
E
E
/4E
/4E
I
I
lI
lI
slabuncrackedofinertiaofMomentI
beamuncrackedofinertiaofMomentI
concreteslabofelasticityofModulusE
concretebeamofelasticityofModulusE
s
b
sb
cb
35. Minimum Slab Thickness for
Two-way Construction
Slabs without drop panels meeting 13.3.7.1 and 13.3.7.2,
tmin = 5 in
Slabs with drop panels meeting 13.3.7.1 and 13.3.7.2,
tmin = 4 in
36. Example - Slab
A flat plate floor system with
panels 24 by 20 ft is supported on
20 in. square columns.
Determine the minimum slab
thickness required for the interior
and corner panels. Use fc = 4 ksi
and fy = 60 ksi
37. Slab thickness, from table 9.5(c) for fy = 60 ksi
and no edge beams
n
min
n
min
30
20 in. 1 ft.
24 ft. 2 22.33 ft.
2 12 in.
12 in.
22.33 ft.
1 ft.
8.93 in. 9 in.
30
l
h
l
h
38. Example - Slab
Slab thickness, from table 9.5(c) for fy = 60 ksi
and no edge beams for = m = 0 (no beams)
n
min
min
33
12 in.
22.33 ft.
1 ft.
8.12 in. 8.5 in.
33
l
h
h
39. – Calculations
The floor system consists of
solid slabs and beams in two
directions supported on 20-in.
square columns. Determine the
minimum slab thickness, h,
required for the floor system.
Use fc = 4 ksi and fy = 60 ksi
41. To find h, we need to find m therefore Ib, Islab and
for each beam and slab in long short direction.
Assume slab thickness h = 7 in. so that x = y < 4 tf
f22 in. 7 in. 15 in. 4 4 7 in. 28 in.t
e 16 in. 2 15 in. 46 in.b
42. Compute the moment of inertia and centroid
b h Ai (in2
) yi (in) yiAi (in3
) I (in4
) d (in) d2
A (in4
)
Flange 7 46 322 3.5 1127 1314.833 -4.69751 7105.442
Beam 15 16 240 14.5 3480 4500 6.302491 9533.135
562 4607 5814.833 16638.58
ybar = 8.197509 in
I = 22453.41 in4
4
beam
33
slab
4
22453 in
1 1 12 in.
20 ft 7 in.
12 12 1 ft.
6860 in
I
I bh
43. Compute the coefficient for the long direction
Short side of the moment of inertia
4
beam
long 4
slab
22453 in
6860 in
3.27
EI
EI
33
slab
4
1 1 12 in.
24 ft 7 in.
12 12 1 ft.
8232 in
I bh
44. Compute the coefficient for short direction
The average m for an interior panel is
4
beam
short 4
slab
22453 in
8232 in
2.73
EI
EI
long short
avg
2 2 2 3.27 2 2.73
4 4
3.0
45. Compute the coefficient
Compute the thickness for m > 2
Use slab thickness, 6.5 in. or 7 in.
long
short
20 in. 1 ft.
24 ft. 2
2 12 in.
1.22
20 in. 1 ft.
20 ft. 2
2 12 in.
l
l
y
n
12 in. 600000.8 22.33 ft. 0.8
200000 1 ft. 200000
36 9 36 9 1.22
6.28 in.
f
l
h
46. Compute the moment of inertia and centroid for the
L-beam
b h Ai (in2
) yi (in) yiAi (in3
) I (in4
) d (in) d2
A (in4
)
Flange 7 27 189 3.5 661.5 771.75 -5.36585 5441.761
Beam 15 12 180 14.5 2610 3375 5.634146 5713.849
369 3271.5 4146.75 11155.61
ybar = 8.865854 in
I = 15302.36 in4
4
L-beam
33
slab
4
15302 in
1 1 12 in.
10 ft 7 in.
12 12 1 ft.
3430 in
I
I bh
47. Compute the m coefficient for long direction
Short side of the moment of inertia
4
L-beam
long 4
slab
15302 in
3430 in
4.46
EI
EI
33
slab
4
1 1 12 in.
12 ft 7 in.
12 12 1 ft.
4116 in
I bh
48. Compute the m coefficient for the short direction
4
L-beam
short 4
slab
15302 in
4116 in
3.72
EI
EI
49. Compute the m coefficient for the edges and corner
m
4.46 2.73 3.27 2.73
4
3.30
m
3.72 3.27 2.73 3.27
4
3.25
50. Compute the m coefficient for the edges and corner
m
3.72 4.46 2.73 3.27
4
3.55
51. Compute the largest length ln of the slab/beam, edge to
first interior column.
n
20 in. 1 ft. 12 in. 1 ft.
24 ft.
2 12 in. 2 12 in.
22.67 ft.
l
52. Compute the thickness of the slab with m > 2
The overall depth of the slab is 7 in.
Use slab thickness, 6.5 in. or 7 in.
y
n
12 in. 600000.8 22.67 ft. 0.8
200000 1 ft. 200000
36 9 36 9 1.22
6.37 in.
f
l
h
53. Shear Strength of Slabs
In two-way floor systems, the slab must have adequate
thickness to resist both bending moments and shear
forces at critical section. There are three cases to look at
for shear.
Two-way Slabs supported on beams
Two-Way Slabs without beams
Shear Reinforcement in two-way slabs
without beams.
1.
2.
3.
54. Two-way slabs supported on beams
The critical location is found at d distance from the
column, where
The supporting beams are stiff and are capable of
transmitting floor loads to the columns.
bdfV 2 cc
55. The shear force is calculated using the triangular and
trapezoidal areas. If no shear reinforcement is provided,
the shear force at a distance d from the beam must equal
where,
bdfVV 2 ccud
d
l
wV
2
2
uud
56. There are two types of shear that need to be addressed
Two-Way Slabs without beams
One-way shear or beam shear at distance d
from the column
Two-way or punch out shear which occurs
along a truncated cone.
1.
2.
57. One-way shear or beam shear at distance d from
the column
Two-way or punch out shear which occurs along a
truncated cone.
1.
2.
58. One-way shear considers critical section a distance d
from the column and the slab is considered as a wide
beam spanning between supports.
bdfVV 2 ccud
59. Two-way shear fails along a a truncated cone or pyramid
around the column. The critical section is located d/2 from
the column face, column capital, or drop panel.
60. If shear reinforcement is not provided, the shear strength
of concrete is the smaller of:
perimeter of the critical section
ratio of long side of column to short side
bo =
c =
dbfdbfV ococ
c
c 4
4
2
61. If shear reinforcement is not provided, the shear
strength of concrete is the smaller of:
s is 40 for interior columns, 30 for edge
columns, and 20 for corner columns.
dbf
b
d
V oc
o
s
c 2
62. Shear Reinforcement in two-way slabs without
beams.
For plates and flat slabs, which do not meet the condition
for shear, one can either
- Increase slab thickness
- Add reinforcement
Reinforcement can be done by shearheads, anchor bars,
conventional stirrup cages and studded steel strips.
63. Shearhead consists of steel I-beams or channel welded
into four cross arms to be placed in slab above
a column. Does not apply to external columns
due to lateral loads and torsion.
67. The reinforced slab follows section 11.12.4 in the
ACI Code, where Vn can not
The spacing, s, can not exceed d/2.
If a shearhead reinforcement is provided
dbfVVV ocscn 6
s
dfA
V
dbfV
yv
s
occ 4
dbfV ocn 7
68. Example Problem
Determine the shear
reinforcement required for an
interior flat panel considering
the following: Vu= 195k, slab
thickness = 9 in., d = 7.5 in.,
fc = 3 ksi, fy= 60 ksi, and
column is 20 x 20 in.
69. Compute the shear terms find b0 for
c c 04V f b d
0
column
4 4 20 in. 7.5 in.
width
110 in.
b d
70. Compute the maximum allowable shear
Vu =195 k > 135.6 k Shear reinforcement is need!
c c 04
1 k
0.75 4 3000 110 in. 7.5 in.
1000 lbs
135.6 k
V f b d
71. Compute the maximum allowable shear
So Vn >Vu Can use shear reinforcement
c c 06
1 k
0.75 6 3000 110 in. 7.5 in.
1000 lbs
203.3 k
V f b d
72. Use a shear head or studs as
in inexpensive spacing.
Determine the a for
c c 02V f b d
0
column
4 2
width
b a
73. Determine the a for
The depth = a+d
= 41.8 in. +7.5 in. = 49.3 in. 50 in.
u c 02
19500 lb 0.75 2 3000 4 20 in. 2 7.5 in.
41.8 in.
V f b d
a
a
75. Determine shear reinforcement
Use a #3 stirrup Av = 2(0.11 in2) = 0.22 in2
s
14.85 k
19.8 k
0.75
V
v y v y
s
s
A f d A f d
V s
s V
76. Determine shear reinforcement spacing
Maximum allowable spacing is
7.5 in.
3.75 in.
2 2
d
2
v y
s
0.22 in 60 ksi 7.5 in.
19.8 k
5.0 in.
A f d
s
V
77. Use s = 3.5 in.
The total distance is 15(3.5 in.)= 52.5 in.
50 in.
# of stirrups 14.3 Use 15 stirrups
3.5 in.
78. The final result:
15 stirrups at total distance of
52.5 in. So that a = 45 in. and
c = 20 in.
79. Direct Design Method for Two-
way Slab
Minimum of 3 continuous spans in each direction.
(3 x 3 panel)
Rectangular panels with long span/short span 2
Method of dividing total static moment Mo into
positive and negative moments.
Limitations on use of Direct Design method
1.
2.
80. Limitations on use of Direct Design method
Successive span in each direction shall not differ by
more than 1/3 the longer span.
3.
4. Columns may be offset from
the basic rectangular grid of
the building by up to 0.1
times the span parallel to the
offset.
81. Limitations on use of Direct Design method
All loads must be due to gravity only (N/A to
unbraced laterally loaded frames, from mats or
pre-stressed slabs)
Service (unfactored) live load 2 service dead
load
5.
6.
82. For panels with beams between supports on all
sides, relative stiffness of the beams in the 2
perpendicular directions.
Shall not be less than 0.2 nor greater than 5.0
Limitations on use of Direct Design method
7.
2
12
2
21
l
l
83. Definition of Beam-to-Slab Stiffness
Ratio,
Accounts for stiffness effect of beams located along
slab edge reduces deflections of panel
adjacent to beams.
slabofstiffnessflexural
beamofstiffnessflexural
84. Definition of Beam-to-Slab Stiffness
Ratio,
With width bounded laterally by centerline of adjacent
panels on each side of the beam.
scs
bcb
scs
bcb
4E
4E
/4E
/4E
I
I
lI
lI
slabuncrackedofinertiaofMomentI
beamuncrackedofinertiaofMomentI
concreteslabofelasticityofModulusE
concretebeamofelasticityofModulusE
s
b
sb
cb
85. Static Equilibrium of Two-Way Slabs
Analogy of two-way slab to plank and beam floor
Section A-A:
Moment per ft width in planks
Total Moment
ft/ft-k
8
2
1wl
M
ft-k
8
2
1
2f
l
wlM
86. Static Equilibrium of Two-Way Slabs
Analogy of two-way slab to plank and beam floor
Uniform load on each beam
Moment in one beam (Sec: B-B) ft-k
82
2
21
lb
lwl
M
k/ft
2
1wl
87. Static Equilibrium of Two-Way Slabs
Total Moment in both beams
Full load was transferred east-west by the planks and then was
transferred north-south by the beams;
The same is true for a two-way slab or any other floor system.
ft-k
8
2
2
1
l
wlM
88. Basic Steps in Two-way Slab
Design
Choose layout and type of slab.
Choose slab thickness to control deflection. Also,
check if thickness is adequate for shear.
Choose Design method
Equivalent Frame Method- use elastic frame
analysis to compute positive and negative
moments
Direct Design Method - uses coefficients to
compute positive and negative slab moments
1.
2.
3.
89. Calculate positive and negative moments in the slab.
Determine distribution of moments across the width of
the slab. - Based on geometry and beam stiffness.
Assign a portion of moment to beams, if present.
Design reinforcement for moments from steps 5 and 6.
Check shear strengths at the columns
4.
5.
6.
7.
8.
90. Minimum Slab Thickness for
two-way construction
Maximum Spacing of Reinforcement
At points of max. +/- M:
Min Reinforcement Requirements
7.12.3ACIin.18and
13.3.2ACI2
s
ts
s min s T&S
from ACI 7.12 ACI 13.3.1A A
93. Total static Moment, Mo
3-13ACI
8
2
n2u
0
llw
M
cn
n
2
u
0.886dhusingcalc.columns,circularfor
columnsbetweenspanclear
striptheofwidthetransvers
areaunitperloadfactored
l
l
l
wwhere
94. Column Strips and Middle
Strips
Moments vary across width of slab panel
Design moments are averaged over
the width of column strips over the
columns & middle strips between
column strips.
95. Column strips Design
w/width on either side of
a column centerline equal
to smaller of
1
2
25.0
25.0
l
l
l1= length of span in
direction moments are
being determined.
l2= length of span
transverse to l1
99. M0 is divided into + M and -M Rules given in ACI
sec. 13.6.3
8
2
n2u
0avguu
llw
MMM
100. Longitudinal Distribution
of Moments in Slabs
For a typical interior panel, the total static moment is
divided into positive moment 0.35 Mo and negative
moment of 0.65 Mo.
For an exterior panel, the total static moment is
dependent on the type of reinforcement at the outside
edge.
103. Transverse Distribution of
Moments
The longitudinal moment values mentioned are for the
entire width of the equivalent building frame. The
width of two half column strips and two half-middle
stripes of adjacent panels.
104. Transverse distribution
of the longitudinal
moments to middle and
column strips is a
function of the ratio of
length l2/l1,1, and t.
105. Transverse Distribution of
Moments
Transverse distribution of the longitudinal moments to
middle and column strips is a function of the ratio of
length l2/l1,1, and t.
torsional constant
3
63.0
1
2
3
scs
cb
t
scs
bcb
1
yx
y
x
C
IE
CE
IE
IE
106. Distribution of M0
ACI Sec 13.6.3.4
For spans framing into a common support negative
moment sections shall be designed to resist the larger
of the 2 interior Mu’s
ACI Sec. 13.6.3.5
Edge beams or edges of slab shall be proportioned to
resist in torsion their share of exterior negative
factored moments
107. Factored Moment in
Column Strip
Ratio of flexural stiffness of beam to stiffness of
slab in direction l1.
Ratio of torsional stiffness of edge beam to
flexural stiffness of slab(width= to beam length)
t
1
111. Factored Moment in
Column Strip
Ratio of flexural stiffness of beam to stiffness of
slab in direction l1.
Ratio of torsional stiffness of edge beam to
flexural stiffness of slab(width= to beam length)
t
1
112. Factored Moment in Column
Strip
Ratio of flexural stiffness of beam to stiffness of
slab in direction l1.
Ratio of torsional stiffness of edge beam to
flexural stiffness of slab(width= to beam length)
t
1
113. Ratio of flexural stiffness of beam to stiffness of
slab in direction l1.
Ratio of torsional stiffness of edge beam to
flexural stiffness of slab(width= to beam length)
t
1
114. Factored Moments
Factored Moments in beams (ACI Sec. 13.6.3)
Resist a percentage of column strip moment plus
moments due to loads applied directly to beams.
115. Factored Moments
Factored Moments in Middle strips (ACI Sec. 13.6.3)
The portion of the + Mu and - Mu not resisted
by column strips shall be proportionately
assigned to corresponding half middle strips.
Each middle strip shall be proportioned to
resist the sum of the moments assigned to its 2
half middle strips.
116. ACI Provisions for Effects of
Pattern Loads
The maximum and minimum bending moments at
the critical sections are obtained by placing the live
load in specific patterns to produce the extreme
values. Placing the live load on all spans will not
produce either the maximum positive or negative
bending moments.
117. The ratio of live to dead load. A high ratio will
increase the effect of pattern loadings.
The ratio of column to beam stiffness. A low ratio
will increase the effect of pattern loadings.
Pattern loadings. Maximum positive moments
within the spans are less affected by pattern loadings.
1.
2.
3.
118. Reinforcement Details Loads
After all percentages of the static moments in the
column and middle strip are determined, the steel
reinforcement can be calculated for negative and
positive moments in each strip.
2
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2
bdR
a
dfAM
119. Calculate Ru and determine the steel ratio r, where
=0.9. As = rbd. Calculate the minimum As from
ACI codes. Figure 13.3.8 is used to determine the
minimum development length of the bars.
c
y
u
ucuu 59.01
f
f
w
wfwR
r