This document discusses shear and torsion strength design of beams. It introduces the concepts of shear stress and torsion stress, and how they are related to the internal forces in a beam. The document explains homogeneous and non-homogeneous beam behavior under shear and torsion loading based on classical beam mechanics. It provides equations to calculate maximum shear stresses and strains in homogeneous and non-homogeneous beams. Failure modes such as flexural failure, diagonal tension failure, and shear compression failure are also discussed for beams without diagonal tension reinforcement.
Xi. prestressed concrete circular storage tanks and shell roofChhay Teng
This document discusses the design principles and procedures for prestressed concrete circular storage tanks and shell roofs.
It introduces the history and development of prestressed concrete tanks, which began in the 1920s using tie rods and turnbuckle principles. Internal loads for circular tanks include radial hoop stresses due to liquid pressure. The maximum tensile hoop stress occurs at the base of a freely sliding wall.
For restrained walls, membrane theory is used to calculate the restraining moment and radial shear force at the base due to liquid pressure loading. The maximum flexural stress is determined based on the restraining moment and wall thickness. Design procedures are provided based on mechanics and membrane theory analysis.
Iv.flexural design of prestressed concrete elementsChhay Teng
1. The document introduces flexural design of prestressed concrete elements, including both pretensioned and post-tensioned concrete. It discusses selecting section properties, stress limits at transfer and service loads, and calculation of moments and stresses.
2. Guidelines are provided for selecting homogenous section components and minimum section moduli to satisfy strength requirements. Stress limits are given for transfer and service loads.
3. Formulas are presented for calculating stresses in concrete at transfer and service loads based on prestressing force and section properties. Stresses must satisfy limits for both transfer and service conditions.
Xii.lrfd and stan dard aastho design of concrete bridgeChhay Teng
This document discusses load specifications for bridge design according to the American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) and Standard Specifications. It introduces the AASHTO truck and lane loading models used for design. Key points include:
1) Standard AASHTO and LRFD specifications for truck axle configurations and weights.
2) Provisions for impact, longitudinal forces, and centrifugal forces under the AASHTO Standard (LFD) specifications.
3) Methods for reducing lane load intensity based on number of traffic lanes.
Vii. camber, deflection, and crack controlChhay Teng
This document discusses camber, deflection, and crack control in concrete structures. It introduces the basic assumptions used in deflection calculations, which include elastic behavior, modulus of elasticity, superposition principle, and tendon properties. It then describes the load-deflection relationship in three stages: precracking, postcracking, and postserviceability cracking. Formulas are provided for calculating cracking and serviceability loads based on modulus of rupture and concrete strength. Overall, the document provides an introduction to evaluating and controlling deflection and cracking in concrete members.
X. connections for prestressed concrete elementChhay Teng
This document provides guidance on connections for prestressed concrete elements. It discusses tolerance requirements for connections, introduces composite members formed using situ-cast topping, and describes reinforced concrete bearing in composite members. Specifically, it outlines procedures for calculating the design bearing strength of a reinforced concrete bearing using nominal strength equations. It also presents equations for determining the development length and shear capacity of reinforcing bars at the interface between a concrete bearing and a composite member. The guidance aims to ensure connections have adequate strength and durability while also considering constructability and economics.
Ix. two way prestressed concrete floor systemsChhay Teng
This document provides an overview of two-way prestressed concrete floor systems. It discusses several analysis and design methods, including:
1. The semielastic ACI Code approach, which uses either the direct design method or equivalent frame method.
2. The yield-line method, which is based on classical elasticity but accounts for inelastic behavior and failure mechanisms.
3. Limit analysis theories for plates, which aim to determine lower bound and upper bound solutions for collapse loads.
4. The stripe method, which models the floor system using orthogonal stress fields.
The document emphasizes that two-way slabs and plates exhibit true two-way flexural behavior with bending resistance in both orthogonal
1. This document discusses continuous beams and frames, which are structural elements made of concrete slabs, beams, columns, and footings that are monolithically connected.
2. It describes how to calculate the maximum moment in continuous beams using basic elastic analysis and considering the loading application and moment redistribution. The maximum positive moments within a span and maximum negative moments at supports are also addressed.
3. Formulas are provided to calculate the maximum and minimum positive moments based on the beam's properties and span between supports. The analysis considers both statically determinate and indeterminate continuous beams.
This document discusses the effective length factor (K) used for calculating the effective length of slender columns. It provides three methods for determining K based on the restraint conditions at the column ends:
1. Using alignment charts and restraint factors (ψA and ψB) for the column and bracing members.
2. Equations relating K to ψmin for partially restrained columns.
3. A simplified equation for K if the column is hinged at one end.
Examples are given to calculate K using the alignment chart method for different bracing conditions. The effective length is important for evaluating the strength and stability of slender columns.
Xi. prestressed concrete circular storage tanks and shell roofChhay Teng
This document discusses the design principles and procedures for prestressed concrete circular storage tanks and shell roofs.
It introduces the history and development of prestressed concrete tanks, which began in the 1920s using tie rods and turnbuckle principles. Internal loads for circular tanks include radial hoop stresses due to liquid pressure. The maximum tensile hoop stress occurs at the base of a freely sliding wall.
For restrained walls, membrane theory is used to calculate the restraining moment and radial shear force at the base due to liquid pressure loading. The maximum flexural stress is determined based on the restraining moment and wall thickness. Design procedures are provided based on mechanics and membrane theory analysis.
Iv.flexural design of prestressed concrete elementsChhay Teng
1. The document introduces flexural design of prestressed concrete elements, including both pretensioned and post-tensioned concrete. It discusses selecting section properties, stress limits at transfer and service loads, and calculation of moments and stresses.
2. Guidelines are provided for selecting homogenous section components and minimum section moduli to satisfy strength requirements. Stress limits are given for transfer and service loads.
3. Formulas are presented for calculating stresses in concrete at transfer and service loads based on prestressing force and section properties. Stresses must satisfy limits for both transfer and service conditions.
Xii.lrfd and stan dard aastho design of concrete bridgeChhay Teng
This document discusses load specifications for bridge design according to the American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) and Standard Specifications. It introduces the AASHTO truck and lane loading models used for design. Key points include:
1) Standard AASHTO and LRFD specifications for truck axle configurations and weights.
2) Provisions for impact, longitudinal forces, and centrifugal forces under the AASHTO Standard (LFD) specifications.
3) Methods for reducing lane load intensity based on number of traffic lanes.
Vii. camber, deflection, and crack controlChhay Teng
This document discusses camber, deflection, and crack control in concrete structures. It introduces the basic assumptions used in deflection calculations, which include elastic behavior, modulus of elasticity, superposition principle, and tendon properties. It then describes the load-deflection relationship in three stages: precracking, postcracking, and postserviceability cracking. Formulas are provided for calculating cracking and serviceability loads based on modulus of rupture and concrete strength. Overall, the document provides an introduction to evaluating and controlling deflection and cracking in concrete members.
X. connections for prestressed concrete elementChhay Teng
This document provides guidance on connections for prestressed concrete elements. It discusses tolerance requirements for connections, introduces composite members formed using situ-cast topping, and describes reinforced concrete bearing in composite members. Specifically, it outlines procedures for calculating the design bearing strength of a reinforced concrete bearing using nominal strength equations. It also presents equations for determining the development length and shear capacity of reinforcing bars at the interface between a concrete bearing and a composite member. The guidance aims to ensure connections have adequate strength and durability while also considering constructability and economics.
Ix. two way prestressed concrete floor systemsChhay Teng
This document provides an overview of two-way prestressed concrete floor systems. It discusses several analysis and design methods, including:
1. The semielastic ACI Code approach, which uses either the direct design method or equivalent frame method.
2. The yield-line method, which is based on classical elasticity but accounts for inelastic behavior and failure mechanisms.
3. Limit analysis theories for plates, which aim to determine lower bound and upper bound solutions for collapse loads.
4. The stripe method, which models the floor system using orthogonal stress fields.
The document emphasizes that two-way slabs and plates exhibit true two-way flexural behavior with bending resistance in both orthogonal
1. This document discusses continuous beams and frames, which are structural elements made of concrete slabs, beams, columns, and footings that are monolithically connected.
2. It describes how to calculate the maximum moment in continuous beams using basic elastic analysis and considering the loading application and moment redistribution. The maximum positive moments within a span and maximum negative moments at supports are also addressed.
3. Formulas are provided to calculate the maximum and minimum positive moments based on the beam's properties and span between supports. The analysis considers both statically determinate and indeterminate continuous beams.
This document discusses the effective length factor (K) used for calculating the effective length of slender columns. It provides three methods for determining K based on the restraint conditions at the column ends:
1. Using alignment charts and restraint factors (ψA and ψB) for the column and bracing members.
2. Equations relating K to ψmin for partially restrained columns.
3. A simplified equation for K if the column is hinged at one end.
Examples are given to calculate K using the alignment chart method for different bracing conditions. The effective length is important for evaluating the strength and stability of slender columns.
Appendix b structural steel design based on allowable stressChhay Teng
1) This document discusses allowable stress design (ASD) based on the 1989 AISC specification for structural steel design. It compares ASD to load and resistance factor design (LRFD) and outlines the key differences between the two approaches.
2) Formulas and examples are provided for calculating allowable stresses in tension members based on yielding and fracture, as well as for calculating allowable stresses in compression members based on buckling strength.
3) The document notes that while the AISC Manual still references the older ASD approach, the specification has been updated to the LRFD method, and engineers should follow the specification over the manual.
This document discusses moment amplification in beam-columns. It explains that the actual moment in a beam-column can be higher than the design moment due to the effects of axial load. The moment is amplified due to the nonlinear relationship between moment and axial deformation. Design codes account for this phenomenon using moment magnification factors which relate the actual moment to the design moment based on the level of axial load. The document provides an example calculation to demonstrate moment amplification based on the AISC specification equations.
1. The document discusses torsional moments in beams. It introduces torsion and provides equations to calculate the torsional moment (T) in beams.
2. Formulas are given to calculate T based on the shear force (V) distribution in different beam sections like rectangular and circular. The maximum shear stress (vmax) is calculated from T.
3. For rectangular sections, a modification factor (α) is used to calculate vmax based on the ratio of y/x dimensions. For typical beam sections, α ranges from 0.2 to 0.3.
This document provides an introduction and overview of footings. It discusses the different types of footings, including wall footings, single footings, combined footings, cantilever or strap footings, continuous footings, raft or mat foundations, and pile caps. It also covers the distribution of soil pressure on footings and important design considerations such as footing size, shear strength, bearing capacity, settlement, dowel connections, and differential settlement. Footings are designed to safely transfer structural and soil loads to the ground.
1. This document discusses one-way slabs, including their types, design, and analysis according to the ACI Code.
2. The three main types of one-way slabs are: one-way solid slab, one-way joist floor slab (ribbed slab), and one-way floor system (two-way slab).
3. Design and analysis of one-way slabs must consider the slab's moment of inertia, load distribution, and requirements for minimum slab thickness according to the ACI Code.
This document provides details on types of stairs and their components. It discusses:
1) Six common types of stairs including single-flight, double-flight, three or more flight, cantilever, precast flights, and free standing stairs.
2) Stair components like risers, treads, and landings and design considerations for each.
3) Additional stair types like run-riser stairs that have proportional risers and treads.
1. There are several types of retaining walls, including gravity walls, semi-gravity walls, cantilever retaining walls, counterfort retaining walls, and buttressed retaining walls.
2. Forces acting on retaining walls include active and passive soil pressures. Active pressure is exerted by soil pushing on the front face of the retaining wall, while passive pressure acts on the back side of the wall from soil resistance.
3. The magnitude of active and passive soil pressures depends on factors like the soil type, depth of soil, and angle of internal friction of the soil. Formulas developed by Rankine and Coulomb are commonly used to calculate active and passive pressures.
Iii flexural analysis of reinforced concreteChhay Teng
1. This document discusses the flexural analysis of reinforced concrete beams. It includes assumptions made for the analysis, procedures for determining the moment capacity, and calculations for strain conditions in different sections.
2. Methods are described for determining the moment capacity based on the reinforcement ratio and limiting the flexural strain to 0.003. Equations are provided to calculate the strain in the concrete and steel based on the section type (e.g. tension controlled, compression controlled).
3. Procedures for calculating the service load moment capacity using factors for dead and live loads are outlined. Equations are given for calculating the service load bending moment.
1. Structural design involves considering loads and stresses on building elements. Loads are categorized as dead loads and live loads. Dead loads include the self-weight of structural components while live loads represent temporary loads from occupancy and environmental factors.
2. Finite element analysis is used to analyze stresses and deflections in structures under applied loads. Composite structures using combined materials are also analyzed.
3. Fatigue stresses from repetitive or fluctuating live loads over time must also be considered in design.
The document provides an introduction to basic concepts of prestressed concrete. Some key points include:
[1] Prestressed concrete works by applying compressive forces to concrete using tendons before external loads are applied, resulting in improved performance.
[2] The compressive stress in the concrete from the prestressing tendons balances and resists the tensile stresses caused by external loads. This allows prestressed concrete members to carry higher loads.
[3] Economics of prestressed concrete - Prestressed concrete structures typically require 20-35% less concrete material compared to reinforced concrete, reducing costs.
This document discusses the design of two-way slabs. It introduces different types of two-way slabs including slab-on-beam, flat slab, flat plate floor, two-way ribbed slabs, and waffle slab systems. Factors to consider for the economical choice of concrete floor systems such as span, loading, and construction cost are presented. The document emphasizes using design concepts that account for nonlinear behavior and time-dependent effects like creep in the analysis and design of two-way slabs according to the ACI code.
7. approximate analysis of statically indeterminate structuresChhay Teng
This document provides an approximate analysis of statically indeterminate structures. It discusses the use of approximate methods to analyze trusses that are statically indeterminate due to the presence of redundant members. The analysis involves satisfying equilibrium equations at nodes by ignoring compatibility conditions. As an example, it shows the approximate analysis of a plane truss with joints A, B, C, and D. The forces in the members are determined by writing and solving the equations of equilibrium at the joints. Approximate methods provide quick estimates of member forces in statically indeterminate structures for preliminary design.
This document discusses types of structures and loads. It begins with an introduction to structures, which are comprised of elements like beams, columns, trusses, and cables that are designed to support and resist various loads.
Structural elements are then classified, with beams defined as elements that primarily resist bending loads, columns as elements that primarily resist axial loads, and trusses as assemblages of elements that form a rigid body to transfer loads.
Finally, common types of structures are described briefly, including trusses, which use a non-redundant system of elements in tension and compression, as well as cable and arch structures.
1. Deflection and cracking control are important for structural concrete members to ensure serviceability. The ACI Code provides provisions for calculating deflection and cracking.
2. Instantaneous deflection, also called immediate deflection, is the initial deflection of a structural member under load. It is related to the elastic behavior of the member.
3. Cracking moment is the moment at which tensile stresses in concrete first exceed the modulus of rupture, initiating cracking in the member. It can be calculated based on the section properties and concrete strength.
This document discusses simple connections and bolted shear connections. It introduces different types of simple connections using plates and various steel shapes. It then focuses on bolted shear connections, explaining the failure modes of bearing on the bolt or shear of the bolt. Equations for determining the shear capacity of a bolted connection based on bolt diameter and shear area are provided. Examples of single shear and double shear lap joints are shown and how to calculate their shear capacities. Overall, the document provides an overview of simple connections and bolted shear connections, emphasizing proper design to avoid failure.
1) This document discusses composite construction, specifically composite beams. Composite beams are made of concrete cast on top of a steel beam, connecting the two materials and allowing them to act compositely.
2) Shear connectors like headed studs or channels are embedded in the concrete to connect the steel and concrete sections. This allows stresses and forces to be transferred between the two materials, making the beam behave compositely.
3) The elastic stresses in composite beams, including flexural and shear stresses, are analyzed based on the beam behaving as two different materials connected together. Formulas are provided to calculate the stresses based on the transformed area concept, where the steel and concrete sections are converted to an equivalent steel area
1. The document discusses combined stresses, which are stresses from more than one source acting simultaneously on a structural component. It presents methods to analyze combined axial and bending stresses using superposition.
2. Equations are provided to calculate the combined stress from axial stress and bending stress. The maximum combined stress is calculated using superposition for a sample problem involving an I-beam with known loads.
3. A second example calculates the combined stresses in a pipe with an internal pressure and bending moment. The results demonstrate that the combined stress is highest at the extreme fibers where axial and bending stresses act together.
1. This document provides information on the properties of reinforced concrete, including:
2. It discusses the factors that influence concrete strength such as water-cement ratio, aggregate type and size, use of admixtures, compaction and curing time.
3. Details are given on how concrete strength is affected by the size and shape of test specimens such as cylinders, cubes and prisms. Equations are provided relating the strengths obtained from different specimen geometries.
4. Reinforcement ratio and its effect on concrete strength is examined. Formulas for calculating reinforcement ratio based on area are also outlined.
This document provides information on deflection and the elastic curve. It discusses the moment-area method and conjugate beam method for calculating deflection. It also describes using a deflection diagram to represent the elastic curve. The document contains diagrams showing examples of beams with loads and supports, along with the corresponding bending moment and deflection diagrams. Equations for calculating deflection due to bending are also presented.
12. displacement method of analysis moment distributionChhay Teng
1. The displacement method of analysis, also known as moment distribution, is an iterative technique for analyzing indeterminate structures by redistributing internal moments at joints.
2. Key concepts include member stiffness factors (K), which relate the member end moments (M) to angular displacements (θ), joint stiffness factors (KT), which are the sum of the connected member stiffness factors, and distribution factors (DF), which proportion the influence of each member on a joint based on its stiffness factor.
3. The method involves initially assuming end moments, calculating the distribution factors, and using them to calculate new end moments until the values converge within a specified tolerance. This allows determination of the internal forces throughout the structure.
The document appears to be an appendix containing many pages with repetitive headings and references to the Department of Civil Engineering, NPIC, and an appendix number ranging from 831 to 863. It provides essential information but no substantial content beyond the headers and footers.
Appendix b structural steel design based on allowable stressChhay Teng
1) This document discusses allowable stress design (ASD) based on the 1989 AISC specification for structural steel design. It compares ASD to load and resistance factor design (LRFD) and outlines the key differences between the two approaches.
2) Formulas and examples are provided for calculating allowable stresses in tension members based on yielding and fracture, as well as for calculating allowable stresses in compression members based on buckling strength.
3) The document notes that while the AISC Manual still references the older ASD approach, the specification has been updated to the LRFD method, and engineers should follow the specification over the manual.
This document discusses moment amplification in beam-columns. It explains that the actual moment in a beam-column can be higher than the design moment due to the effects of axial load. The moment is amplified due to the nonlinear relationship between moment and axial deformation. Design codes account for this phenomenon using moment magnification factors which relate the actual moment to the design moment based on the level of axial load. The document provides an example calculation to demonstrate moment amplification based on the AISC specification equations.
1. The document discusses torsional moments in beams. It introduces torsion and provides equations to calculate the torsional moment (T) in beams.
2. Formulas are given to calculate T based on the shear force (V) distribution in different beam sections like rectangular and circular. The maximum shear stress (vmax) is calculated from T.
3. For rectangular sections, a modification factor (α) is used to calculate vmax based on the ratio of y/x dimensions. For typical beam sections, α ranges from 0.2 to 0.3.
This document provides an introduction and overview of footings. It discusses the different types of footings, including wall footings, single footings, combined footings, cantilever or strap footings, continuous footings, raft or mat foundations, and pile caps. It also covers the distribution of soil pressure on footings and important design considerations such as footing size, shear strength, bearing capacity, settlement, dowel connections, and differential settlement. Footings are designed to safely transfer structural and soil loads to the ground.
1. This document discusses one-way slabs, including their types, design, and analysis according to the ACI Code.
2. The three main types of one-way slabs are: one-way solid slab, one-way joist floor slab (ribbed slab), and one-way floor system (two-way slab).
3. Design and analysis of one-way slabs must consider the slab's moment of inertia, load distribution, and requirements for minimum slab thickness according to the ACI Code.
This document provides details on types of stairs and their components. It discusses:
1) Six common types of stairs including single-flight, double-flight, three or more flight, cantilever, precast flights, and free standing stairs.
2) Stair components like risers, treads, and landings and design considerations for each.
3) Additional stair types like run-riser stairs that have proportional risers and treads.
1. There are several types of retaining walls, including gravity walls, semi-gravity walls, cantilever retaining walls, counterfort retaining walls, and buttressed retaining walls.
2. Forces acting on retaining walls include active and passive soil pressures. Active pressure is exerted by soil pushing on the front face of the retaining wall, while passive pressure acts on the back side of the wall from soil resistance.
3. The magnitude of active and passive soil pressures depends on factors like the soil type, depth of soil, and angle of internal friction of the soil. Formulas developed by Rankine and Coulomb are commonly used to calculate active and passive pressures.
Iii flexural analysis of reinforced concreteChhay Teng
1. This document discusses the flexural analysis of reinforced concrete beams. It includes assumptions made for the analysis, procedures for determining the moment capacity, and calculations for strain conditions in different sections.
2. Methods are described for determining the moment capacity based on the reinforcement ratio and limiting the flexural strain to 0.003. Equations are provided to calculate the strain in the concrete and steel based on the section type (e.g. tension controlled, compression controlled).
3. Procedures for calculating the service load moment capacity using factors for dead and live loads are outlined. Equations are given for calculating the service load bending moment.
1. Structural design involves considering loads and stresses on building elements. Loads are categorized as dead loads and live loads. Dead loads include the self-weight of structural components while live loads represent temporary loads from occupancy and environmental factors.
2. Finite element analysis is used to analyze stresses and deflections in structures under applied loads. Composite structures using combined materials are also analyzed.
3. Fatigue stresses from repetitive or fluctuating live loads over time must also be considered in design.
The document provides an introduction to basic concepts of prestressed concrete. Some key points include:
[1] Prestressed concrete works by applying compressive forces to concrete using tendons before external loads are applied, resulting in improved performance.
[2] The compressive stress in the concrete from the prestressing tendons balances and resists the tensile stresses caused by external loads. This allows prestressed concrete members to carry higher loads.
[3] Economics of prestressed concrete - Prestressed concrete structures typically require 20-35% less concrete material compared to reinforced concrete, reducing costs.
This document discusses the design of two-way slabs. It introduces different types of two-way slabs including slab-on-beam, flat slab, flat plate floor, two-way ribbed slabs, and waffle slab systems. Factors to consider for the economical choice of concrete floor systems such as span, loading, and construction cost are presented. The document emphasizes using design concepts that account for nonlinear behavior and time-dependent effects like creep in the analysis and design of two-way slabs according to the ACI code.
7. approximate analysis of statically indeterminate structuresChhay Teng
This document provides an approximate analysis of statically indeterminate structures. It discusses the use of approximate methods to analyze trusses that are statically indeterminate due to the presence of redundant members. The analysis involves satisfying equilibrium equations at nodes by ignoring compatibility conditions. As an example, it shows the approximate analysis of a plane truss with joints A, B, C, and D. The forces in the members are determined by writing and solving the equations of equilibrium at the joints. Approximate methods provide quick estimates of member forces in statically indeterminate structures for preliminary design.
This document discusses types of structures and loads. It begins with an introduction to structures, which are comprised of elements like beams, columns, trusses, and cables that are designed to support and resist various loads.
Structural elements are then classified, with beams defined as elements that primarily resist bending loads, columns as elements that primarily resist axial loads, and trusses as assemblages of elements that form a rigid body to transfer loads.
Finally, common types of structures are described briefly, including trusses, which use a non-redundant system of elements in tension and compression, as well as cable and arch structures.
1. Deflection and cracking control are important for structural concrete members to ensure serviceability. The ACI Code provides provisions for calculating deflection and cracking.
2. Instantaneous deflection, also called immediate deflection, is the initial deflection of a structural member under load. It is related to the elastic behavior of the member.
3. Cracking moment is the moment at which tensile stresses in concrete first exceed the modulus of rupture, initiating cracking in the member. It can be calculated based on the section properties and concrete strength.
This document discusses simple connections and bolted shear connections. It introduces different types of simple connections using plates and various steel shapes. It then focuses on bolted shear connections, explaining the failure modes of bearing on the bolt or shear of the bolt. Equations for determining the shear capacity of a bolted connection based on bolt diameter and shear area are provided. Examples of single shear and double shear lap joints are shown and how to calculate their shear capacities. Overall, the document provides an overview of simple connections and bolted shear connections, emphasizing proper design to avoid failure.
1) This document discusses composite construction, specifically composite beams. Composite beams are made of concrete cast on top of a steel beam, connecting the two materials and allowing them to act compositely.
2) Shear connectors like headed studs or channels are embedded in the concrete to connect the steel and concrete sections. This allows stresses and forces to be transferred between the two materials, making the beam behave compositely.
3) The elastic stresses in composite beams, including flexural and shear stresses, are analyzed based on the beam behaving as two different materials connected together. Formulas are provided to calculate the stresses based on the transformed area concept, where the steel and concrete sections are converted to an equivalent steel area
1. The document discusses combined stresses, which are stresses from more than one source acting simultaneously on a structural component. It presents methods to analyze combined axial and bending stresses using superposition.
2. Equations are provided to calculate the combined stress from axial stress and bending stress. The maximum combined stress is calculated using superposition for a sample problem involving an I-beam with known loads.
3. A second example calculates the combined stresses in a pipe with an internal pressure and bending moment. The results demonstrate that the combined stress is highest at the extreme fibers where axial and bending stresses act together.
1. This document provides information on the properties of reinforced concrete, including:
2. It discusses the factors that influence concrete strength such as water-cement ratio, aggregate type and size, use of admixtures, compaction and curing time.
3. Details are given on how concrete strength is affected by the size and shape of test specimens such as cylinders, cubes and prisms. Equations are provided relating the strengths obtained from different specimen geometries.
4. Reinforcement ratio and its effect on concrete strength is examined. Formulas for calculating reinforcement ratio based on area are also outlined.
This document provides information on deflection and the elastic curve. It discusses the moment-area method and conjugate beam method for calculating deflection. It also describes using a deflection diagram to represent the elastic curve. The document contains diagrams showing examples of beams with loads and supports, along with the corresponding bending moment and deflection diagrams. Equations for calculating deflection due to bending are also presented.
12. displacement method of analysis moment distributionChhay Teng
1. The displacement method of analysis, also known as moment distribution, is an iterative technique for analyzing indeterminate structures by redistributing internal moments at joints.
2. Key concepts include member stiffness factors (K), which relate the member end moments (M) to angular displacements (θ), joint stiffness factors (KT), which are the sum of the connected member stiffness factors, and distribution factors (DF), which proportion the influence of each member on a joint based on its stiffness factor.
3. The method involves initially assuming end moments, calculating the distribution factors, and using them to calculate new end moments until the values converge within a specified tolerance. This allows determination of the internal forces throughout the structure.
The document appears to be an appendix containing many pages with repetitive headings and references to the Department of Civil Engineering, NPIC, and an appendix number ranging from 831 to 863. It provides essential information but no substantial content beyond the headers and footers.
This document provides instructions on various AutoCAD commands for 2D drawing and editing, text and hatching, layers, dimensions, blocks, and external references. It consists of 7 chapters that explain tools for drawing lines, circles, arcs, and other objects; editing objects by moving, copying, rotating, mirroring, and arraying; adding text and hatch patterns; managing layers; creating dimensions; inserting blocks; and linking to external drawings. The goal is to teach civil engineering students how to use AutoCAD for 2D drafting.
1. The document outlines the chapters in a civil engineering construction work textbook, including introduction to construction, construction materials, construction equipment, and construction management.
2. Chapter 1 discusses construction introduction, which provides an overview of the construction industry and processes. It explains the roles of various construction professionals and their importance in planning and executing construction projects.
3. Chapter 2 covers construction materials used in civil engineering projects, including their properties, uses, and quality control measures.
14. truss analysis using the stiffness methodChhay Teng
1. The document discusses analyzing truss structures using the stiffness method. It begins by introducing the fundamentals of the stiffness method for truss analysis.
2. It describes how to derive the member stiffness matrix for each truss member, which relates the forces and displacements in the member's local coordinate system.
3. It provides equations to transform between the member's local coordinate system and the global coordinate system of the truss, in order to assemble the overall structure stiffness matrix for the truss.
1) The document discusses column theory and compression members. It introduces the concept of critical buckling load and explains how a column's slenderness ratio affects its buckling strength.
2) The theory of column buckling is explained using Euler buckling formula. The critical buckling load depends on the column's elastic modulus, moment of inertia, and length.
3) Buckling modes are determined by solving the differential equation for the deflection curve of the column. The first buckling mode occurs when the column length is equal to π√(EI/P).
1. This document discusses tension members and their design strength. Tension members are structural elements that are primarily subjected to tensile forces such as those in trusses, suspension bridges, and cable-stayed bridges.
2. The design strength of a tension member is based on either its gross section resisting yielding, or its net section resisting fracture. Allowable stresses are reduced using strength reduction factors to obtain the design strength.
3. Examples are provided to calculate the design strength of given tension members based on their material properties and dimensions. The effective net area is considered to account for things like bolt holes. Combinations of loads are also checked to ensure the design strength is not exceeded.
1. The document discusses member design under compression and bending forces. It provides equations and diagrams for determining the plastic centroid, axial load capacity, moment capacity, and balanced or interaction conditions of members.
2. Safety provisions for member design include minimum reinforcement ratios and load factors that are applied to nominal member strengths based on material properties and cross section details.
3. Diagrams show load-moment interaction curves indicating regions of failure by compression, tension, or balanced flexure for members designed based on provisions in the document.
This document provides instructions on using various commands and tools in Autodesk 3ds Max for geometry creation, modification, and rendering. It covers topics such as viewports, basic geometric shapes like boxes and spheres, splines, mesh editing, modifiers, and lighting/camera settings. Step-by-step explanations are provided for commands to create, manipulate, and render 3D models. The document is intended as a tutorial for learning essential 3ds Max functions.
This document provides guidelines for civil engineering drawing practices in 3 chapters:
1. Structural drawing conventions - Defines scales, views, dimensions, and other structural drawing standards.
2. Drawing components - Details various drawing elements like lines, dimensions, symbols and annotations.
3. CAD drafting - Discusses computer-aided drafting techniques, templates, layers and other digital drafting practices.
The document establishes standards for civil engineering drawings to ensure consistency and clarity across projects. It covers topics like drawing layouts, line weights, dimensioning, modeling and documentation. Adherence to the guidelines will result in structural drawings that effectively communicate engineering design information.
The document appears to be a series of numbers or codes with the name T. Chhay and the letters NPIC repeated at the top. It does not contain enough contextual information to summarize its meaning or purpose in 3 sentences or less.
13 beams and frames having nonprismatic membersChhay Teng
1) The document discusses methods for analyzing non-prismatic structural members, such as tapered or stepped beams and frames, using the slope-deflection and moment distribution methods.
2) It describes calculating the deflection of non-prismatic members through integration, and introduces the concepts of stiffness factor K, carry-over factor COF, and the conjugate beam method for analyzing loading properties.
3) An example problem is presented to demonstrate calculating the fixed-end moment FEM at joints A and B of a tapered beam using the given stiffness factors K and carry-over factors COF from the conjugate beam analysis.
1. The document discusses using the energy method to calculate deflection in beams, trusses, and frames.
2. The energy method equates the external work done by loads to the internal strain energy stored in the deformed structure.
3. Beams, trusses, and frames can be analyzed by calculating the external work done by forces and moments, and equating it to the strain energy due to bending and twisting. Analytical expressions can then be developed relating the loads to deflections.
1) Plastic analysis was performed using the lower-bound theorem and equilibrium method to determine the collapse load of a W30x99 beam with continuous lateral support.
2) The working load was first determined by calculating the yield moment My. Once yielding occurred, the plastic moment capacity Mp was used.
3) Equilibrium of internal and external moments was satisfied at the collapse mechanism to determine the ultimate load. The uniqueness theorem confirmed this was the collapse load.
This document provides instructions for plastering and mortar work. It includes a list of tools needed for the job such as trowels, buckets, and brooms. It also provides details on mixing mortar, applying plaster, and techniques for smoothing and finishing walls. The document specifies mortar ratios and curing times. It aims to clearly explain the steps for plastering and mortaring work.
4.internal loading developed in structural membersChhay Teng
1. The document describes analyzing internal loading developed in structural members.
2. It provides procedures for determining support reactions, drawing free-body diagrams, establishing equilibrium equations, and calculating shear forces and bending moments at points of interest.
3. Examples are included to demonstrate solving for unknown shear forces and bending moments at specific points on beams and cantilevers.
1. Cables and arches are important structural elements that are commonly used in bridges and buildings to support concentrated and distributed loads.
2. Cables can support significant loads and transfer forces over large distances when subjected to tension. The behavior of cables depends on their ability to carry only tensile forces and flexibility.
3. When cables are subjected to concentrated loads, their sag or deflection can be determined through equilibrium equations. The forces in the cables can then be solved for each connection.
2.analysis of statically determinate structureChhay Teng
The document provides an overview of statically determinate structures and their analysis. It defines idealized structures and discusses different types of supports including pinned supports, roller supports, fixed supports, pin-connected joints and fixed-connected joints. It also presents examples of idealized structures showing various supports and loads, and determines reactions and internal forces through structural analysis. The summary highlights key points about idealized structures, different support types, and analyzing structures to determine unknown reactions and internal forces.
1. The document discusses bending behavior and plastic moment capacity of beams. When a beam yields, plastic hinges form which allow unstable collapse mechanisms to develop.
2. Bending stress is calculated based on the elastic bending formula. As the stress increases, the beam first yields at the outer fibers where the maximum bending stress reaches the yield strength.
3. After initial yielding, the stress can redistribute until the plastic neutral axis forms. The plastic moment capacity is then reached and is calculated based on the plastic section modulus.
1. Shear and diagonal tension are two failure modes of reinforced concrete beams. Shear failure occurs when the shear stresses exceed the shear capacity of the beam. Diagonal tension failure occurs due to cracking along a diagonal plane.
2. Shear stresses can be calculated using equilibrium equations that relate applied shear, shear capacity, and section properties. The shear capacity is generally limited to less than 1.5 times the square root of the concrete compressive strength.
3. Shear reinforcement such as stirrups or bent bars is used to improve the ductility and increase the shear capacity of beams subjected to high shear stresses. Codes specify minimum shear reinforcement ratios to prevent brittle shear failures.
1. The document discusses the design of reinforced concrete columns under axial load.
2. It provides guidelines on column dimension, reinforcement ratio, and confining reinforcement according to ACI code.
3. Formulas for calculating the nominal axial load capacity of a column based on its cross-sectional area and steel reinforcement are presented.
11e.deflection of beam the energy methode10Chhay Teng
1. The deflection of a beam can be determined using either the energy method (equating external work to internal potential energy) or the virtual work method.
2. In the energy method, the external work done by the load is set equal to the change in the potential energy of the beam.
3. In the virtual work method, the structure is subjected to a small virtual displacement and the external virtual work is set equal to the internal virtual work to determine the displacement. This method is applicable to both trusses and beams.
1. The resultant of two concurrent forces acting on a particle is calculated. The forces are F1 = 100 N at 30° and F2 = 140 N at 45°.
2. Using the law of cosines, the resultant is found to be 192 N at an angle of 44.8° from F1.
3. The method of components is used to analyze the coplanar force system, resolving the forces into horizontal (X) and vertical (Y) components. The resultant is verified to be 214 N at an angle of 35.9° from the X-axis.
This document discusses various types of stresses and strains that can occur in materials. It defines axial stresses as normal stresses along an axis, and shear stresses as stresses that cause or induce sliding or twisting in the material. It also discusses tensile and compressive strains that occur due to stretching or compressing of materials. Other concepts covered include Poisson's ratio, which is the ratio of transverse to axial strain; shear strain; and stress-strain diagrams, which graphically show the relationship between stress and strain in a material.
Similar to V. shear and torsional strength design (11)
This document provides an introduction and overview of Corus Advance structural sections for use in steel construction. It includes the following key points:
- Corus is a major UK and global steel producer and manufacturer of structural steel sections.
- Steel construction offers benefits like speed of construction, economy, flexibility, sustainability, and recyclability.
- The document contains selection of structural section property tables from the Corus Advance range to assist students in steel structure design.
- For the full listing of Advance section properties and capacities, the online "Blue Book" can be downloaded from the Corus website.
2009 ncdd-csf-technical-manual-vol-i-study-design-guidelinesChhay Teng
This document provides guidelines for the study and design of small-scale infrastructure projects funded by the Commune/Sangkat Fund in Cambodia. It introduces the technical forms and template designs used for roads, irrigation systems, water supply, education, health and sanitation projects. Guidelines are given on how to read and use the template drawings, which conform to the standards of relevant line ministries. The manual aims to support good quality project design and construction supervision that can be implemented with locally available skills and resources. Field visits by technical support officers are recommended to verify project needs and objectives.
The document provides an overview of concrete basics, including the materials used to make concrete, properties of concrete in different states, common concrete tests to measure workability and strength, and factors that affect the strength and durability of hardened concrete. Concrete is made by mixing cement, water, coarse and fine aggregates, and sometimes admixtures, and its workability and strength can be tested using slump and compression tests.
Rebar arrangement and construction carryoutChhay Teng
The document discusses rebar arrangement and construction procedures. It begins by emphasizing the importance of thoroughly understanding construction drawings before beginning work. It then provides details on different types of drawings used for construction, including plans, elevations, sections, and structural drawings. Finally, it discusses rebar characteristics, production processes, and standard symbols and terminology used in construction drawings.
1 dimension and properties table of w shapesChhay Teng
This document provides dimension and properties data for various W-shape steel beams, including their area, depth, web and flange dimensions, elastic properties, plastic modulus, and warping properties. Metrics such as the nominal weight, compact section criteria, moment of inertia, plastic section modulus, and warping constant are given for each beam designation. Over 30 different W-shape beams ranging in size from W1120x4.89 to W910x12.37 are listed with their respective dimension and mechanical properties.
2 dimension and properties table of s shapeChhay Teng
This table provides dimensional and mechanical properties for various S-shape steel beams. It includes properties like cross-sectional area, depth, wall thickness, elastic modulus, plastic modulus, shear center location, and weight. Properties are listed for beam designations ranging from S610x1.77 down to S80x0.08. The data allows comparison of key metrics across different standardized beam sizes.
3 dimension and properties table of hp shapeChhay Teng
This table provides dimensional properties and elastic properties for various HP-shape steel beams. It includes measurements like area, depth, web thickness, flange width and thickness, moment of inertia, plastic modulus, and polar moment of inertia. The data is sourced from an online structural drafting resource and specifies properties for beams with designations like HP360x1.71, HP300x1.23, and HP360x0.53.
4 dimension and properties table c shapeChhay Teng
This document provides dimensional and mechanical properties for various C-shaped cross section profiles. It lists nominal dimensions such as depth, web thickness, flange width and thickness, along with mechanical properties including section area, elastic modulus, plastic modulus, shear center location, polar moment of inertia, and warping constant. C-shapes ranging from 380x0.73mm to 80x0.073mm are specified. Key dimensional and mechanical properties are given to characterize each cross sectional geometry.
6 dimension and properties table of ipe shapeChhay Teng
This document provides dimensional properties for various IPE steel beam shapes. It includes dimensions, cross-sectional area, weight, section properties such as moments of inertia, and minimum dimensions for connections. The table lists data for IPE beams ranging from 80 mm to 600 mm, including their height, width, wall thicknesses, and other geometric properties.
This document provides dimensional properties and specifications for different profiles of IPN-shaped steel beams, ranging from IPN 80 to IPN 600. For each profile, it lists dimensions, cross-sectional area, weight, dimensional properties for detailing, and mechanical properties along the strong and weak axes. A total of 24 IPN profiles are defined in the table with increasing dimensions, areas, and load-bearing capacities from smaller to larger sizes.
8 dimension and properties table of equal leg angleChhay Teng
This document provides dimensional properties and specifications for equal leg angle steel beams of various sizes. It includes dimensions, cross-sectional area, weight, position of axes, surface area, and other mechanical properties. Sizes range from 20x20mm to 120x120mm beams with wall thicknesses of 3mm to 13mm.
The document provides dimensional properties for various UPE-shaped steel beams, including their height, width, wall thickness, flange thickness, area, weight, moments of inertia, and other specifications. Dimensions are given in millimeters and kilograms per meter. Beams range in size from a UPE 80 with a height of 80mm up to a UPE 400 with a height of 400mm.
This document provides dimensional properties for various UPN steel beam shapes. It includes dimensions for the height, width, thicknesses, radii, slopes, cross-sectional areas, weights, and other geometric properties. The table lists these specifications for UPN beams ranging in size from 80x45x6 mm to 400x110x14 mm.
2. NPIC
TajEkg (tensile normal stress) ft nigkugRtaMgkat; v CatMélenAkñúgFatu A1 enAelIkat;bøg; a − a
Rtg;cMgay y BIG½kSNWt.
BIeKalkarN_ classical emkanic eKGacsresrkugRtaMgEkg (normal stress) f nigkugRtaMg
kat; v sMrab;Fatu A1 dUcxageRkam³
My
f = (5.1)
I
nig v=
VA y VQ
Ib
=
Ib
(5.2)
Edl M nig V = m:Um:g;Bt; nigkMlaMgkat;enARtg;muxkat; a − a
A = RkLaépÞrbs;muxkat;enARtg;bøg;Edlkat;tamTIRbCMuTMgn;rbs;Fatu A1
y = cMgayBIFatuGnnþtUceTAG½kSNWt
y = cMgayBITIRbCMuTMgn;rbs; A eTAG½kSNWt
karKNnaersIusþg;kMlaMgkat; nigersIusþg;kMlaMgrmYl 215
3. T.Chhay
m:Um:g;niclPaBrbs;muxkat;
I=
Q = m:Um:g;sþaTicrbs;RkLaépÞmuxkat;EdlenABIxagelI b¤BIxageRkamG½kSNWt
b = TTwgrbs;Fñwm
rUbTI 5>2 bgðajBIkugRtaMgxagkñúgEdlmanGMeBIelIFatuGnnþtUc A1 nig A2 . edayeRbIrgVg;m:
(Mohr’s cicle) enAkñúgrUbTI 5>2(b) kugRtaMgemsMrab;Fatu A1 enAkñúgtMbn;TajxageRkamG½kSNWtkøayCa
2
⎛f ⎞
f t (max)
f
= t + ⎜ t ⎟ + v2
2 ⎝2⎠
kugRtaMgTajem (5.3a)
2
⎛f ⎞
f c (max ) =
ft
2
− ⎜ t ⎟ + v2
⎝2⎠
kugRtaMgsgát;em (5.3b)
nig tan 2θ max =
v
ft / 2
Shear and Torsion Strength Design 216
6. NPIC
enAkñúgFñwmeRbkugRtaMg muxkat;esÞIrEtrgkugRtaMgsgát;TaMgGs;eRkamGMeBIbnÞúkeFVIkar (service
load). BIrUbTI 5>2 (c) nig (d) kugRtaMgemsMrab;Fatu A2 KW
f t (max ) = − c + ( f c / 2)2 + v 2
f
2
kugRtaMgTajem (5.4a)
f c (max ) = − c − ( f c / 2)2 + v 2
f
2
kugRtaMgsgát;em (5.4b)
nig tan 2θ max =
v
f /2 c
k> KMrU)ak;rbs;FñwmEdlKμanEdkTajGgát;RTUg
Modes of Failure of Beams without Diagonal Tension Reinforcement
pleFobElVgkat;elIkMBs; (slenderness ratio) rbs;FñwmkMNt;nUvKMrU)ak;rbs;Fñwm. rUbTI 5>5
bgðajBIkar)ak;sMrab;EdnkMNt;én slenderness ratio epSg². RbEvgElVgkMlaMgkat; (shear span) a
sMrab;bnÞúkcMcMnucCacMgayrvagcMnucénkarGnuvtþbnÞúk nigépÞénTMr. sMrab;bnÞúkBRgay shear span lc Ca
clear beam span. CaeKalkarN_ KMrUénkar)ak;manbIEbbKW kar)ak;edaykarbegáag (flexural failure),
kar)ak;edaykMlaMgTajGgát;RTUg (diagonal tension failure) nigkar)ak;edaybnSMkarkat; nigkarsgát;
(shear compression failure or web shear). Fñwmkan;EtRsav kareFVIkarrbs;vakan;EtxiteTArklkçN³
begáagdUckarerobrab;xageRkam.
karKNnaersIusþg;kMlaMgkat; nigersIusþg;kMlaMgrmYl 219
11. T.Chhay
BIsmIkar 5.2 kugRtaMgkat;ÉktþasuT§ v enARtg;kMBs;Nak¾edayrbs;muxkat;KW
Vc Q
vc = (5.6)
Ib
karEbgEckkugRtaMgsréssgát; fc EdlbNþalBIm:Um:g;Bt;xageRkAKW
Pe Pe ec M T c
fc = − ± m (5.7)
Ac Ic Ic
ehIyBIsmIkar 5.4a kugRtaMgTajemKW
f 't = ( f c / 2)2 + vc2 − fc
(5.8)
2
k> Flexural-Shear Strength
edIm,IsikSaKNnasMrab;kMlaMgkat; eKcaM)ac;kMNt;faetI flexural shear b¤ web shear lubedIm,I
eFVIkareRCIserIsersIusþg;kat; Vc rbs;ebtug. sñameRbHeRTtEdlmanlMnwg (inclined stabilized crack)
enAcMgay d / 2 BI flexural crack EdlekItmanenAeBlrg first cracking load enAkñúgkrNI flexure
shear RtUv)anbgðajenAkñúgrUbTI 5>8. RbsinebI kMBs;RbsiT§PaBCa d p ¬kMBs;BIsréssgát;eTATIRbCMu
TMgn;rbs;EdkeRbkugRtaMgbeNþay¦ bMErbMrYlm:Um:g;rvagmuxkat; @ nig # KW
Vd p
M − M cr ≅ (5.9a)
2
b¤ V=
M cr
M /V − d p / 2
(5.9b)
Shear and Torsion Strength Design 224
12. NPIC
Edl V CakMlaMgkat;enARtg;muxkat;EdlBicarNa. lT§plénkarBiesFCaeRcInbgðajfaeKRtUvkar
kMlaMgkat;bBaÄrbEnßmEdlmanTMhM 0.6bwd p f 'c sMrab;xñat US nig bwd p f 'c / 20 sMrab;xñat SI
edIm,IeFVIeGaymansñameRbHeRTtenAkñúgrUbTI 5>8 eBjelj. dUcenH kMlaMgkat;bBaÄrsrubEdleFVIGMeBI
enARtg;bøg;elx @ rbs;rUbTI 5>8 KW
Vci =
M cr
M /V − d / 2
+ 0.6bw d p f 'c + Vd ¬xñat US¦ (5.10)
p
Vci =
M cr
M /V − d p / 2
+
bw d p f 'c
20
+ Vd ¬xñat SI¦
karKNnaersIusþg;kMlaMgkat; nigersIusþg;kMlaMgrmYl 225
14. NPIC
Edl ersIusþg;sgát;rbs;ebtugEdlbNþalBIeRbkugRtaMgRbsiT§PaBeRkaykMhatbg;enARtg;
f ce =
srésxageRkAbMputrbs;muxkat;EdlkugRtaMgTajRtUv)anbgáeLIgedaybnÞúkxageRkA.
enARtg;TIRbCMuTMgn; fce = f c .
f d = kugRtaMgEdlbNþalBIbnÞúkGefrKμanemKuNenARtg;srésxageRkAbMputrbs;muxkat;Edl
bNþalEtBIbnÞúkpÞal;EdlkugRtaMgTajRtUv)anbgáedaybnÞúkxageRkA.
yt = cMgayBIG½kSTIRbCMuTMgn;eTAsrésrgkarTajxageRkA
ehIy M cr = EpñkxøHrbs;m:Um:g;énbnÞúkxageRkAEdlbgáeGaymansñameRbH. CakarsMrYl eKGacCMnYs
Sb CMnYseGay I c / yt .
rUbTI 5>9 bgðajBIdüaRkamrbs;smIkar 5.10 CamYynwgTinñn½yénkarBiesaF.
cMNaMfa eKeRbIkarsikSaKNnadUcKñaEdlGnuvtþsMrab;muxkat;cak;Rsab; sMrab;karsikSaKNna
kMlaMgkat;énmuxkat;smas. BIeRBaHkarsikSaKNnasMrab;kMlaMgkat;KWQrelIsßanPaBkMNt;edA
eBl)ak;eRkamGMeBIbnÞúkemKuN. eTaHbICa muxkat;TaMgmUlrbs;muxkat;smasTb;Tl;nwgkMlaMgkat;
smasdUcmuxkat;Edlcak;kñúgeBlEtmYy (monolithic section) k¾eday k¾karKNnaersIusþg;kMlaMg
karKNnaersIusþg;kMlaMgkat; nigersIusþg;kMlaMgrmYl 227
15. T.Chhay
kat; Vc KYrQrelIlkçN³rbs;muxkat;cak;Rsab; edaysarersIusþg;kMlaMgkat;PaKeRcInpþl;eGayeday
RTnugrbs;muxkat;cak;Rsab;. dUcenH fce nig f d enAkñúgsmIkar 5.12 RtUv)anKNnaedayeRbIragFrNI
maRtrbs;muxkat;cak;Rsab;.
x> ersIusþg;kMlaMgkat;RTnug Web-Shear Strength
sñameRbHkMlaMgkat;RTnug (web-shear crack) enAkñúgFñwmeRbkugRtaMgekIteLIgedaysarkugRtaMg
EdlminGackMNt;)an (indeterminate stress) EdlCakarRbesIreKKYrKNnavaedaykugRtaMgTajemenA
Rtg;bøg;eRKaHfñak;BIsmIkar 5.8. eKGaccat;TukkugRtaMgkat; vc CakugRtaMgkat;RTnug vcw nigmantMél
GtibrmaenAEk,rTIRbCMuTMgn; cgc énmuxkat;EdlsñameRbHGgát;RTUgCak;EsþgekItman dUckarBiesaFeTA
dl;kar)ak;CaeRcIn)anbgðaj. RbsinebIeKCMnYs vc sMrab; vcw nig fc sMrab; f c ¬EdlCakugRtaMgeb-
tug fc EdlbNþalBIeRbkugRtaMgRbsiT§PaBenARtg;nIv:U cgc¦ enAkñúgsmIkar smIkarEdleGaykugRtaMg
TajemenAkñúgebtugesμInwgersIusþg;TajpÞal; (direct tensile strength) køayCa
( f c / 2) + vcw − f2c
f 't = 2
(5.13)
Edl vcw = Vcw / (bwd p ) CakugRtaMgkat;enAkñúgebtugEdlbNþalBIbnÞúkTaMgGs;EdleFVIeGayman
ersIusþg;kMlaMgkat;bBaÄrFmμta Vcw enAkñúgRTnug. edaHRsayrk vcw enAkñúgsmIkar 5.13
vcw = f 't 1 + f c / f 't (5.14a)
edayeRbI f 't = 3.5 f 'c psi(0.3 f 'c MPa) CatMéld¾smrmüsMrab;kugRtaMgTajedayQrelIlT§pl
énkarBiesaFCaeRcIn smIkar 5.14(a) køayCa
vcw = 3.5 f 'c ⎛ 1 + f c / 3.5 f 'c ⎞
⎜
⎝
⎟
⎠
¬xñat US¦ (5.14b)
vcw = 0.3 f 'c ⎛ 1 + f c / 0.3 f 'c ⎞
⎜
⎝
⎟
⎠
¬xñat SI¦
EdleyIgGacsMrYl)andUcxageRkam
vcw = 3.5 f 'c + 0.3 f c ¬xñat US¦ (5.14c)
vcw = 0.3( f 'c + f c ) ¬xñat SI¦
enAkñúg ACI Code eKeRbI f pc CMnYseGay f c . nimitþsBaØaEdleRbIenATIenHKWcg;bBa¢ak;favaCakugRtaMg
enAkñúgebtugminEmnenAkñúgEdkeRbkugRtaMgeT. ersIusþg;kMlaMgkat;Fmμta Vcw EdleGayedayebtugenA
eBlsñameRbHGgát;RTUgekItBIkugRtaMgTajemd¾FMenAkñúgRTnugkøayCa
Vcw = (3.5λ f 'c + 0.3 f c )bw d p + V p ¬xñat US¦ (5.15)
Shear and Torsion Strength Design 228
16. NPIC
( )
Vcw = 0.3 λ f 'c + f c bw d p + V p ¬xñat SI¦
Edl V p = bgÁúMbBaÄrénkMlaMgeRbkugRtaMgRbsiT§PaBenARtg;muxkat;BiessEdlcUlrYmnwgersIusþg;
FmμtabEnßm
λ = 1.0 sMrab;ebtugTMgn;Fmμta nigmantMéltUcCagenHsMrab;ebtugTMgn;Rsal
d p = cMgayBIsréssgát;xageRkAeTATMRbCMuTMng;rbs;EdkeRbkugRtaMg b¤ 0.8h edayykmYy
NaEdlFMCag
ACI Code yktMél f c CakugRtaMgsgát;pÁÜbrbs;ebtugenARt;gTIRbCMuTMgn;rbs;muxkat; b¤Rtg;
kEnøgEdlkat;KñarvagRTnug nigsøabenAeBlEdlTIRbCMuTMgn;sßitenAkñúgsøab. enAkñúgkrNImuxkat;smas
eKKNna f c edayQrelIkugRtaMgEdlekIteLIgedaykMlaMgeRbkugRtaMg nigm:Um:g;EdlTb;Tl;eday
Ggát;cak;Rsab;EdleFVIkarEtÉg. düaRkaménTMnak;TMngrvagkugRtaMgkat;RTnugFmμta (nominal web
shear stress) vcw nigkugRtaMgsgát;rbs;ebtugRtg;TIRbCMuTMgn;RtUv)aneGayenAkñúgrUbTI 5>10. cMNaMfa
PaBdUcKñarvagExSekagénsmIkar 5.14b nig c bgðajfasmIkar 5.14c RtUv)anEktMrUvBIsmIkar 5.14b
edIm,IeGaymanlkçN³bnÞat;. Code GnuBaØateGayeRbIemKuN 1.0 CMnYseGayemKuN 0.3 sMrab;tYTIBIr
énsmIkar 5.15.
karKNnaersIusþg;kMlaMgkat; nigersIusþg;kMlaMgrmYl 229
17. T.Chhay
K> karRtYtBinitütMélrbs;V nigV sMrab;KNnaersIusþg;ebtugRTnugV
ci cw c
Controlling Values of Vci and Vcw for the Determination of the
Web Concrete Strength Vc
ACI Code mansmIkarbEnßmsMrab;kMNt;Vci nig Vcw edIm,IeRCIserIstMél Vc EdlRtUvkarenA
kñúgkarKNna³
(a) enAkñúgGgát;eRbkugRtaMgEdlmuxkat;enAcMgay h / 2 BIépÞénTMrenAEk,rcugénGgát;CagRbEvgepÞr
rbs;EdkeRbkugRtaMg enaHeKRtUvBicarNatMéleRbkugRtaMgkat;bnßyenAeBlKNna Vcw . tMél
Vcw enHRtUv)anKitCaEdlGtibrmarbs; Vc enAkñúgsmIkar
⎛ Vu d p ⎞
Vcw = ⎜ 0.6λ f 'c + 700
⎜ ⎟bw d p ≥ 2λ f 'c bw d p
⎝ Mu ⎟ ⎠
≤ 5λ f 'c bw d p ¬xñat US¦ (5.16)
⎛ Vu d p ⎞
Vcw = ⎜ 0.05λ f 'c + 5
⎜ ⎟bw d p ≥ 0.2λ f 'c bw d p
⎝ Mu ⎟ ⎠
≤ 0.4λ f 'c bw d p ¬xñat SI¦
tMél Vu d p / M u minGacFMCag 1.0 eT.
(b) enAkñúgGgát;eRbkugRtaMgEdl bonding rbs; tendon xøHmin)anBnøÚtdl;cugrbs;Ggát; enaHeKRtUv
KiteRbkugRtaMgkat;bnßyenAeBlkMNt; Vc edayeRbIsmIkar 5.16 b¤eRbItMéltUcCageKkñúg
cMeNamtMél Vc EdlTTYl)anBIsmIkar 5.11 nigBIsmIkar 5.15. dUcKña tMélrbs; Vcw Edl
KNnaedayeRbIeRbkugRtaMgkat;bnßyRtUvyktMélGtibrmaénsmIkar 5.16.
(c) eKGaceRbIsmIkar 5.16 kñúgkarkMNt; Vc sMrab;Ggát;EdlkMlaMgeRbkugRtaMgRbsiT§PaBmintUc
Cag 40% énersIusþg;Tajrbs;EdkrgkarBt; (flexural reinforcement) ebImindUcenaHeT luH
RtaEteKGnuvtþkarviPaKlMGitedayeRbIsmIkar 5.11 sMrab; Vci nigsmIkar 5.15 sMrab; Vcw
ehIyedayeRCIserIsyktMéltUcCageKéntMélTaMgBIrCatMélkMNt; Vc edIm,IeRbICaersIusþg;
rbs;RTnugkñúgkarKNnaEdkRTnug.
(d) bøg;dMbUgsMrab;ersuIsþg;kat;FmμtaEdlRtUvkarsrub (total required nominal shear strength)
Vn = Vu / φ EdlRtUv)aneRbIsMrab;KNnaEdkRTnugk¾sßitenARtg;cMgay h / 2 BIépÞrbs;TMr.
Shear and Torsion Strength Design 230
21. T.Chhay
Ts Ts V 1
= = s (5.18c)
s1 ns sin α d (cos α + cos β )
RbsinebIeKmanEdkkgeRTtcMnYn n Edlman analoguos truss chord RbEvg s1 ehIyRbsin
ebI Av CaRkLaépÞénEdkkgeRTtmYy enaH
Ts = nAv f y (5.19a)
dUcenH nAv =
Vs ns
d sin α (cot β + cot α ) f y
(5.19b)
b:uEnþGacsnμt;fa enAkñúgkrNI)ak;edaykMlaMgTajGgát;RTUg (diagonal tension failure) Ggát;RTUgrgkar
sgát;manmMu β = 45o dUcenHsmIkar 5.19b nwgkøayCa
Av f y d
Vs = [sin α (1 + cot α )]
s
Av f y d
b¤ Vs =
s
(sin α + cos α ) (5.20a)
edaHRsayrk s edayeRbI Vs = Vu − Vc
Av f y d
s= (sin α + cos α ) (5.20b)
Vu − Vc
RbsinebIEdkRTnugeRTtpÁúMeLIgedayEdkeTal b¤RkuménEdkeTalEdlEdkTaMgenARtUv)anBt; nigRtUv)an
dak;enAcMgaydUcKñaBIépÞénTMr enaH
Vs = Av f y sin α ≤ 3.0 f 'c bw d ¬xñat US¦
Vs = Av f y sin α ≤ 0.25 f 'c bw d ¬xñat SI¦
RbsinebIeKeRbIEdkkgbBaÄr mMu α nwgesμInwg 90o enaHeK)an
Av f y d
Vs = (5.21a)
s
Av f y dAvφf y d
b¤ s= =
(Vu / φ ) − Vc Vu − φVc
(5.21b)
enAkñúgsmIkar 5.21a nig b/ d p CacMgayBIsréssgát;xageRkAbMputeTAkan;TIRbCMuTMgn;rbs;EdkeRbkug
RtaMg ehIy d CacMgayBIsréssgát;xageRkAbMputeTATIRbCMuTMgn;rbs;EdkFmμta. tMélrbs; d p min
RtUvtUcCag 0.80h eT.
Shear and Torsion Strength Design 234
22. NPIC
K> EdlkMNt;énTMhM nigKMlatrbs;Edkkg
Limitation on Size and Spacing of Stirrups
smIkar 5.20 nig 5.21 eGaynUvTMnak;TMngRcasKñarvagKMlatEdkkg nigkMlaMgkat; b¤kugRtaMg
kat;EdlvaRtUvTb;Tl;. enAeBlEdl s fycuH (Vu − Vc ) nwgekIneLIg. edIm,IeGayEdkkgbBaÄrTb;Tl;
sñameRbHGgát;RTUg dUcbgðajenAkñúgrUbTI 5>11 (c) eKRtUvGnuvtþEdnkMNt;KMlatGtibrmasMrab;Edkkg
bBaÄrdUcxageRkam³
(a) smax ≤ 3 h ≤ 24in.(60cm) Edl h CakMBs;srubrbs;muxkat;
4
(b) RbsinebI Vs > 4λ f 'c bw d p ¬xñat US¦ Vs > λ f 'c bw d p / 3 ¬xñat SI¦ eKRtUvkat;
bnßyKMlatGtibrmarbs; (a) Bak;kNþal ¬ smax ≤ 83 h ≤ 12in.(30cm)
(c) RbsinebI Vs > 8λ f 'c bw d p ¬xñat US¦ Vs > 2λ f 'c bw d p / 3 ¬xñat SI¦
eKRtUvBRgIkmuxkat;.
(d) RbsinebI Vu = φVn > φVc / 2 / eKRtUvdak;EdkkMlaMgkat;Gb,brma. eKKNnaRkLaépÞ
EdkGb,brmaenHedaysmIkar
Av = 0.75 f 'c w
b s
f
b¤ Av = 50fbws edayykmYyNaEdlFMCag
y y
RbsinebIkMlaMgeRbkugRtaMgRbsiT§PaB Pe FMCag b¤esμInwg 40% énersIusþg;Tajrbs;EdkBt;
(flexural reinforcement) enaH
A ps f pu s dp
Av = (5.22b)
80 f y d bw
Edlvapþl;nUv Av Gb,brmaRtUvkartUcCag ehIyEdleKGaceRbIvaCMnYs)an.
(e) edIm,IRbsiT§PaB EdkRTnugRtUvEtmanRbEvgbgáb; (development lengt) RtUvkareBjelj.
enHmann½yfaEdkkgRtUvBnøÚtcUleTAkñúgEpñkrgkarsgát; nigEpñkrgkarTajrbs;muxkat;/
RtUvkarkMras;ebtugkarBarEdk (clear concrete cover) tUc nigeKGaceRbITMBk; 90o b¤
135o enAkñúgtMbn;sgát;.
rUbTI 5>13 bgðajBIdüaRkaménkardak;EdkkgRTnugeTAtamtMbn;énRbEvgElVgrbs;FñwmeRbkug
RtaMgEdlrgGMeBIénbnÞúkBRgayesμI. épÞqUtCakMlaMgkat;elIs Vs EdlRtUvkarEdkRTnug.
karKNnaersIusþg;kMlaMgkat; nigersIusþg;kMlaMgrmYl 235
23. T.Chhay
7> ersIusþg;kMlaMgkat;edkenAkñúgeRKOgbgÁúMsmas
Horizontal Shear Strength in Composite Construction
snμt;fakMlaMgkat;tamTisedkepÞreBjeljRtg;épÞb:HénkEnøgEdlCYbKña.
k> eRkamGMeBIbnÞúkeFVIkar Service-Load Level
eKGackMNt;kugRtaMgkat;tamTisedkGtibrma vh BIeKalkarN_mUldæanrbs;emkanic
VQ
vh = (5.23)
I c bv
Edl V= kugRtaMgkat;KNnaKμanemKuN (unfactored design vertical shear) EdleFVIGMeBIelImux
kat;smas
Q = m:Um:g;RkLaépÞeFob cgc énkMNt;muxkat;EdlenABIxagelI b¤BIxageRkam cgc
I c = m:Um:g;niclPaBénmuxkat;smasTaMgmUl
bv = TTwgRtg;kEnøgb:Hrbs;muxkat;RTnugénGgát;cak;Rsab; b¤TTwgénmuxkat;EdleKKNna
kMlaMgkat;edk
Shear and Torsion Strength Design 236
24. NPIC
eKGacsMrYlsmIkar 5.23 dUcxageRkam
V
vh = (5.24)
bv d pc
Edl d pc CakMBs;RbsiT§PaBBIsréssgát;xageRkAénmuxkat;smaseTATIRbCMuTMgn; cgc rbs;EdkeRbkug
RtaMg.
x> Ultimate-Load Level
Direct Method: sMrab;kar)ak;enAkñúgsßanPaBkMNt; eKGacEkERbsmIkar 5.24 edayCMnYs V
eday Vu dUcenHeyIgTTYl)an
Vu
vuh = (5.25a)
bv d pc
b¤ sMrab;ersIusþg;kMlaMgkat;bBaÄrFmμta Vn
Vu / φ V
vnh = = n (5.25b)
bv d pc bv d pc
Edl φ = 0.75 / RbsinebI Vnh CaersIusþg;kMlaMgkat;edkFmμta enaH Vu ≤ Vnh ehIyersIusþg;kMlaMgkat;
FmμtasrubKW
Vnh = vnhbv d pc (5.25c)
ACI Code kMNt; vnh Rtwm 80 psi(0.55MPa ) RbsinebIeKmineRbIEdkEdkrgcaM (dowel) b¤EdkkgbBaÄr
ehIyépÞ b:HmanlkçN³eRKIm b¤RbsinebIeKeRbIEdkkgbBaÄrGb,brma b:uEnþépÞb:HminmanlkçN³eRKIm.
vnh GaceTAdl; 500 psi (3.45MPa ) EteKRtUveRbI friction theory CamYynwgkarsnμt;xageRkam
(a) enAeBlEdlminmanEdkkgbBaÄr b:uEnþépÞb:HénGgát;cak;Rsab;manlkçN³eRKIm
enaHeKeRbI
Vnh ≤ 80 Ac ≤ 80bv d pc (5.26a)
Edl Ac CaRkLaépÞrbs;ebtugEdlTb;Tl;kMlaMgkat; = bv d pc
(b) enAeBlEdleKeRbIEdkkgGb,brma Edl Ac = 50(bws ) / f y b:uEnþépÞb:Hrbs;Ggát;cak;
Rsab;minmanlkçN³eRKIm
vnh ≤ 80bv d pc
(c) RbsinebIépÞb:Hrbs;Ggát;cak;Rsab;manlkçN³eRKImEdlmankMBs; 1 / 4in.(6mm) ehIy
EdkbBaÄrGb,brmaenAkñúg (b) RtUv)andak; enaHeKeRbI
Vnh ≤ 500bv d pc (5.26b)
karKNnaersIusþg;kMlaMgkat; nigersIusþg;kMlaMgrmYl 237
25. T.Chhay
(d) RbsinebIkMlaMgkat;emKuN Vu > φ (500bv d pc )/ eKGaceRbI shear friction theory edIm,I
KNnaEdk dowel. enAkñúgkrNIenH kMlaMgkat;edkTaMgGs;RtUv)anKitedaybøg;EkgEdl
Vnh = μAvf f y (5.27)
Edl Avf = RkLaépÞén shear-friction reinforcement/ in.2
f y = design yield strength/ minRtUvelIs 60,000 psi (414 MPa )
μ = emKuNkkit
= 1.0λ sMrab;ebtugEdlcak;elIépÞebtugEdlmaneRKIm
= 0.6λ sMrab;ebtugEdlcak;elIépÞebtugEdlminmaneRKIm
λ = emKuNsMrab;RbePTebtug
enAkñúgkrNITaMgGs; ersIusþg;kat;Fmμta Vn ≤ 0.20 f 'c Acc ≤ 800 Acc Edl Acc CaRkLaépÞb:Hrbs;
ebtugEdlTb;Tl;nwgkMlaMgkat;epÞr (shear transfer). cMNaMfa enAkñúgkrNICaeRcIn kugRtaMgkat; vuh
EdlTTYl)anBIkMlaMgkat;emKuNGt;FMCag 500 psi(3.45MPa ) eT. dUcenH eKmincaM)ac;RtUvkareRbIEt
shear friction theory kñúgkarKNnaEdkrgcaM (dowel) sMrab;skmμPaBsmas (composite action)
enaHeT.
KMlatGnuBaØatGtibrmaénEdkrgcaM (dowel) b¤ tie sMrab;kMlaMgkat;edkKWtMéltUcCageKkñúg
cMeNam 4 dgénTMhMtUcCageKénmuxkat;TMr nig 24in.(60cm) .
Basic Method: ACI Code GnuBaØateGayeRbIviFIepSgeTotEdlkMlaMgkat;edkRtUv)anGegát
edayKNnabMErbMrYlCak;EsþgénkMlaMgsgát; b¤kMlaMgTajenAkñúgbøg;NamYy nigedayepþrkMlaMgkat;edk
enaHeTAGgát;EdlCaTMr. eKCMnYsRkLaépÞb:H Acc sMrab; bv d pc enAkñúgsmIkar 5.25b nig c enaHeK
TTYl)an
Vnh = vnh Acc (5.28)
Edl Vnh ≥ Fh / kMlaMgkat;edk ehIyy:agehacNas;vaRtUvesμInwgkMlaMgsgát; C b¤kMlaMgTaj T enA
kñúgrUbTI 5>14. ¬emIlsmIkar 5.30 sMrab;tMélrbs; Fh ¦
eKGackMNt;RkLaépÞb:H Acc dUcxageRkam
Acc = bv lvh (5.29)
Edl lvh CaRbEvgkMlaMgkat;edk (horizontal shear length) EdlkMNt;enAkñúgrUbTI 5.15(a) nig (b)
sMrab;Ggát;TMrsamBaØ nigsMrab;Ggát;TMrCab; erogKña.
Shear and Torsion Strength Design 238
27. T.Chhay
K> karKNnaEdkrgcaMskmμsmas
Design of Composite-Action Dowel Reinforcement
Edk tie sMrab;kMlaMgkat;edkGacpSMeLIgBIr)arEdkeTal (single bars or wires)/ BIEdkkgeCIg
eRcIn (multiple leg stirrup) b¤BI vertical legs of welded wire fabric. KMlatrbs;vaminGacFMCagbYn
dgénTMhMEdltUcCageKénGgát;TMr b¤ 24in.(60cm) edayykmYyNaEdltUcCageK. RbsinebI μ Ca
emKuNkMlaMgkkit enaHeKGackMNt;kMlaMgkat;edkFmμta Fh enAkñúgrUbTI 5>14 dUcxageRkam
Fh = μAvf f y ≤ Vnh (5.30)
tMél ACI rbs; μ KWQrelIersIusþg;kkit-kMlaMgkat;kMNt; (limit shear-friction strength) 800 psi
(5.5MPa ) ¬vaCatMélEdlmanlkçN³suvtßiPaBbnþicEdlbgðajedaykarBiesaF¦. viTüasßanebtugeRb
kugRtaMg (Prestressed Concrete Institute) ENnaM μe = 2.9 CMnYseGay μ = 1.0λ sMrab;ebtug
Edlcak;elIépÞebtugeRKIm ehIykMlaMgkat;KNnaGtibrma (maximum design shear force)
Vu ≤ 0.25λ2 f 'c Ac ≤ 1,000λ2 Acc (5.31a)
CamYynwgRkLaépÞcM)ac;rbs;Edkkkit-kMlaMgkat; (shear-friction steel)
Vuh
Avf = (5.31b)
φf y μ e
b¤ Avh =
Vnh F
= h
μe f y μe f y
(5.31c)
edayeRbItMél PCI EdlminsUvsuvtßiPaB smIkar 5.31c køayCa
Fh ≤ μ e Avf f y ≤ Vnh (5.32)
λ 2
CamYynwg μe = 1,000F bv I vh ≤ 2.9
h
Edl bvlvh = Acc / EdkGb,brmaKW
50bv s 50bv lvh
Av = = (5.33)
fy fy
8> CMhanKNnaEdkRTnugsMrab;kMlaMgkat;
Web Reinforcement Design Procedure for Shear
xageRkamCakarsegçbBICMhanénkarKNnaEdkRTnugsMrab;kMlaMgkat;³
!> kMNt;tMélersIusþg;kMlaMgkat;FmμtaEdlRtUvkar Vn = Vu / φ enARtg;cMgay h / 2 BIépÞénTMr Edl
φ = 0.75 .
Shear and Torsion Strength Design 240
28. NPIC
@> KNnaersIusþg;kMlaMgkat;Fmμta (nominal shear strength) Vc EdlRTnugmanedayeRbIviFImYy
kñúgcMeNamviFIBIrxageRkam³
(a) ACI conservative method RbsinebI f pe > 0.40 f pu
⎛ 700Vu d p ⎞
Vc = ⎜ 0.60λ f 'c +
⎜ ⎟bw d p ¬xñat US¦
⎟
⎝ M u ⎠
⎛ λ f 'c V d⎞
Vc = ⎜
⎜ 20
+ 5 u ⎟bw d p
Mu ⎟
¬xñat SI¦
⎝ ⎠
Edl 2λ f 'c bw d p ≤ Vc ≤ 5λ f 'c bw d p sMrab;xñat US
λ f 'c bw d p / 5 ≤ Vc ≤ 0.4λ f 'c bw d p sMrab;xñat SI
Vu d p
≤ 1.0
Mu
ehIyeKKNna Vu enARtg;muxkat;dUcKñasMrab;karKNna M u .
RbsinebIersIusþg;eRcokTajmFüm (average tensile splitting strength) fct sMrab;
ebtugTMgn;Rsal enaH λ = fct / 6.7 f 'c sMrab;xñat US b¤ λ = fct / 0.556 f 'c
sMrab;xñat SI CamYynwg f 'c Gt;FMCag 100 psi(0.67MPa ) .
(b) Detailed analysis Edl Vc CatMéltUcCageKkñúgcMeNam Vci nig Vcw
¬xñat US¦ 1.7λ f 'c bw d p ≤ Vci = 0.60λ f 'c bw d p + Vd +
Vi
M max
(M cr ) ≤ 5.0λ f 'c bwd p
λ f 'c bw d p λ f 'c bw d p
¬xñat SI¦ 7
≤ Vci =
20
+ Vd +
Vi
M max
(M cr ) ≤ 0.4λ f 'c bwd p
¬xñat US¦ ( )
Vcw = 3.5λ f 'c + 0.3 f c bw d p + V p
¬xñat SI¦ ( )
Vcw = 0.3 λ f 'c + f c bw d p + V p
edayeRbItMélNaEdlFMCageKkñúgcMeNam d p nig 0.8h
Edl M cr = (I c / yt )(6λ f 'c + fce − f d ) ¬xñat US¦
M cr = (I c / yt )(0.5λ f 'c + f ce − f d ) ¬xñat SI¦
b¤ M cr = Sb (6λ f 'c + fce − f d ) ¬xñat US¦
M cr = Sb (0.5λ f 'c + f ce − f d ) ¬xñat SI¦
Vi = kMlaMgkat;emKuNEdlbNþalBIbnÞúkGnuvtþn_BIxageRkAEdlekItmankñúg
eBldMNalKñaCamYynwg M max
karKNnaersIusþg;kMlaMgkat; nigersIusþg;kMlaMgrmYl 241
29. T.Chhay
kugRtaMgsgát;enAkñúgebtugeRkayekItmankMhatbg;TaMgGs;enARtg;
f ce =
srésxageRkArbs;muxkat;EdlbnÞúkxageRkAbgáeGaymankugRtaMgTaj.
f ce køayCa f c sMrab;kugRtaMgenARtg;TIRbCMuTMgn;rbs;muxkat;.
#> RbsinebI Vu / φ ≤ Vc / 2 vaminRtUvkarEdkRTnugeT. RbsinebI Vc / 2 < Vu / φ < Vc vaRtUvkar
EdkGb,brma. RbsinebI Vu / φ > Vc nig
RbsinebI Vs = Vu / φ − Vc ≤ 8λ f 'c bw d p ¬xñat US¦
Vs = Vu / φ − Vc ≤ 2λ f 'c bw d p / 3 ¬xñat SI¦
eKRtUvKNnaEdkRTnug.
RbsinebI Vs = Vu / φ − Vc > 8λ f 'c bw d p b¤ Vs > φ (Vc + 8λ f 'c bw d p ) ¬xñat US¦
Vs = Vu / φ − Vc > 2λ f 'c bw d p / 3 ¬xñat SI¦
eKRtUvtMeLIgmuxkat;.
$> KNnaEdkRTnugGb,brmaEdlRtUvkar. KMlatKW s ≤ 0.75h b¤ 24in.(60cm) edayykmYyNa
EdltUcCageK.
Av min = 0.75 f 'c w b¤ Av min = ¬US¦ edayykmYyNaEdlFMCag
b s 50bw s
f y f y
Av min = f 'c
bw s
16 f y
b¤ Av min = 50fbws ¬SI¦ edayykmYyNaEdlFMCag
y
RbsinebI /
f pe ≥ 0.40 f pu Av min EdlmanlkçN³suvtßiPaBticCagCatMéltUcCageKkñúg
cMeNam
A ps f pu s dp
Av =
80 f y d p bw
Edl d p ≥ 0.80h
CamYynwg Av min = 0.75 f 'c
bw s
fy
b¤ Av min = 50fbws ¬US¦
y
Av min = f 'c
bw s
16 f y
b¤ Av min = 50fbws ¬SI¦
y
%> KNnaTMhM nigKMlatEdkRTnugEdlRtUvkar. RbsinebI
¬xñat US¦
Vs = (Vu / φ − Vc ) ≤ 4λ f 'c bw d p
Vs = Vu / φ − Vc ≤ λ f 'c bw d p / 3 ¬xñat SI¦
enaHKMlatEdkkg s EdlRtUvkarKWesμInwgtMélEdlKNnaedaysmIkarEdleGayenAkñúgCMhan ^.
Shear and Torsion Strength Design 242
30. NPIC
EtRbsinebI
¬xñat US¦
Vs = (Vu / φ − Vc ) > 4λ f 'c bw d p
Vs = Vu / φ − Vc > λ f 'c bw d p / 3 ¬xñat SI¦
enaHKMlatEdkkg s EdlRtUvkarKWesμInwgBak;kNþaléntMélEdlKNnaedaysmIkarEdleGay
enAkñúgCMhan ^.
^> s = (VAvφf)y− V = VAv −yφdVp ≤ 0.75h ≤ 24in.(60cm) ≥ s Gb,brmaEdl)anBICMhan $
dp f
u c u c
&> sg; shear envelope enAelIElVgFñwm nigKUsbBa¢ak;tMbn;EdlRtUvkarEdkRTnug
*> KUrBRgayEdkRTnugtambeNþayElVgedayeRbIEdkkgTMhM #3 b¤ #4 tamEdlcUlcitþ b:uEnþEdk
kgminRtUvmanTMhMFMCag #6 eT.
(> KNnaEdkrgcaM (dowel reinforcement) bBaÄrkñúgkrNImuxkat;smas
(a) Vnh ≤ 80bv d pc sMrab;TaMgépÞb:HeRKImedayKμanEdkrgcaM b¤Edk tie bBaÄr nigsMrab;TaMgépÞb:H
EdlmineRKImb:uEnþeRbIEdk tie bBaÄrGb,brma. eRbI
50bw s 50bv I vh
Av = =
fy fy
(b) Vnh ≤ 500bw d pcsMrab;épÞeRKImEdlmanecjk,alfμkMBs; 1 / 4in.(6mm)
(c) sMrab;krNIEdl Vnh > 500bw d pc / KNnaEdk tie bBaÄrsMrab; Vnh = Avf f y μ
Edl Avf = RkLaépÞrbs;EdkrgcaMEdlmanlkçN³kkit (frictional steel dowel)
μ = emKuNkkit = 1.0λ sMrab;épÞEdlmanlkçN³eRKIm Edl λ = 1.0 sMrab;
ebtugTMgn;Fmμta. sMrab;RKb;krNITaMgGs; Vn ≤ Vnh ≤ 0.2 f 'c Acc
≤ 800 Acc Edl Acc = bv lvh .
viFIepSgeToténkarKNnaRkLaépÞEdkrgcaM Avf KWedayKNnakMlaMgedk Fh enARtg;épÞkkit
rbs;ebtugEdl
Fh ≤ μ e Avf f y ≤ Vnh
1,000λ2bv lvh
Edl μe =
Fh
≤ 2.9
rUbTI 5>16 bgðajBICMhanKNnaEdl)anerobrab;xagelICaTMrg; flowchart.
karKNnaersIusþg;kMlaMgkat; nigersIusþg;kMlaMgrmYl 243
39. T.Chhay
bw = 6in.(15cm )
ec = 15in.(38cm )
ee = 12.5in.(32cm )
(
I c = 70,700in.4 18.09 × 106 cm 4 )
(
Ac = 377in.2 2,432cm 2 )
(
r 2 = 187.5in.2 1,210cm 2 )
cb = 18.84in.(48cm )
ct = 21.16in.(54cm )
Pe = 308,255lb(1.371kN )
bnÞúkemKuN Wu = 1.2D + 1.6L
= 1.2(100 + 393) + 1.6 × 1,100 = 2,352 plf
kMlaMgkat;enARtg;épÞTMr Vu = Wu L / 2
= (2,352 × 65) / 2 = 76,440lb
Vn tMrUvkar = Vu / φ = 76,440 / 0.75 = 101,920lb enARtg;TMr
bøg;enARtg; 12 d p BIépÞénTMr
!> ersIusþg;kMlaMgkat;Fmμta (nominal shear strength) Vc rbs;RTnug ¬CMhanTI2 nigTI3¦
1 36.16
dp = ≅ 1.5 ft
2 2 × 12
Vn = 101,920 ×
[(65 / 2) − 1.5] = 97,216lb
65 / 2
Vu enARtg;1
2
d p = 0.75 × 97,216 = 72,912lb
f pe = 155,000 psi
0.40 f pu = 0.40 × 270,000 = 108,000 psi (745MPa )
< f pe = 155,000 psi (1,069 MPa )
eRbI ACI alternate method
edaysar d p > 0.8h / eRbI d p = 36.16in. edaysnμt;faEdkeRbkugRtaMgxøHRtg;rhUtdl;TMr.
BIsmIkar 5.16
Shear and Torsion Strength Design 252
40. NPIC
⎛ Vu d p ⎞
Vc = ⎜ 0.60λ f 'c + 700
⎜ ⎟bw d p ≥ 2λ f 'c bw d p ≤ 5λ f 'c bw d p
⎝ Mu ⎟ ⎠
λ = 1 .0sMrab;ebtugTMgn;Rsal
Wu (1.5)2
M u enARtg; d / 2 BIépÞ = Rbtikmμ × 1.5 −
2
2,352(1.5)2
= 76,440 × 1.5 − = 112,014 ft − lb
2
= 1,344,168in. − lb
Vu d p 72,912 × 36.16
= = 1.96 > 1.0
Mu 1,344,168
dUcenHeRbI Vu d p / M u = 1.0 enaH
Vc Gb,brma = 2λ f 'c bw d p = 2 × 1.0 5,000 × 6 × 36.16 = 30,683lb
Vc Gtibrma = 5λ f 'c bw d p = 76,707lb(341kN )
Vc = (0.60 × 1.0 5,000 + 700 × 1.0 )6 × 36.16
= 161,077lb > Vc Gtibrma = 76,707lb
bnÞab;mk Vc = 76,707lb / lub. dUcKña Vu / φ > Vc / 2 dUcenH eKRtUvkarEdkRTnug.
Vu
Vs = − Vc = 97,216 − 76,707 = 20,509lb
φ
8λ f 'c bw d p = 8 × 1.0 5,000 × 6 × 36.16 = 122,713lb(546kN )
> Vs = 20,509lb
dUcenHkMBs;rbs;muxkat;RKb;RKan;.
@> EdkRTnugGb,brma ¬CMhanTI4¦
BIsmIkar 5.22b
Av
s
Gb,brma = 80psf fdpu d p
A
b y p w
1.99 × 270,000 36.16
= = 0.0076in.2 / in.
80 × 60,000 × 36.16 6
#> EdkRTnugtMrUvkar ¬CMhanTI5 nigTI6¦
BIsmIkar 5.21b
Av f y d p
s= ≤ 0.75h ≤ 24in.
Vu / φ − Vc
b¤ Av
s
V
= s =
20,509
f y d p 60,000 × 36.16
= 0.0095in.2 / in.
karKNnaersIusþg;kMlaMgkat; nigersIusþg;kMlaMgrmYl 253