1. The document discusses hydraulic flow and provides equations for flow rate, velocity, discharge, and other hydraulic parameters.
2. Charts and equations are presented for calculating flow rate based on cross-sectional area, velocity, hydraulic radius, and other factors.
3. The relationships between flow rate, velocity, height, area, and other variables are explored based on Bernoulli's equation and the conservation of energy principle for hydraulic systems.
1. The document discusses fluid flow and the Bernoulli equation. It presents equations for fluid dynamics including the continuity equation and Bernoulli's equation.
2. Methods for calculating flow velocity, flow rate, water level, and hydraulic radius in open channels are provided. Manning's and Chézy equations for uniform flow are presented.
3. Parameters for flow resistance coefficients for different channel materials are listed, along with typical values for flow depth and hydraulic radius under uniform flow conditions.
1. Fluid statics defines pressure as a force per unit area. Pressure in a static fluid depends on depth and density.
2. Hydrostatic pressure is determined by the fluid density and depth. The pressure is transmitted equally in all directions and increases with depth according to hydrostatic laws.
3. For an incompressible fluid, pressure increases linearly with depth due to the fluid density being constant. For a compressible fluid, pressure increases non-linearly with depth due to changes in density with pressure.
1. The document defines fluid as any substance that can flow and take the shape of its container. It then discusses various fluid properties such as density, specific weight, specific volume, and viscosity.
2. It introduces the basics of fluid mechanics including hydrodynamics, aerodynamics, and different types of fluid flow. The laws of conservation of mass, momentum, and energy as they apply to fluid mechanics are also covered.
3. Various fluid properties are defined including density, specific weight, specific volume, relative density, vapor pressure, and surface tension. Dimensional analysis and units used in fluid mechanics are also introduced.
1. The document discusses hydrostatic forces on plane surfaces and curved surfaces. It describes how to calculate the pressure, force, and center of pressure on rectangular and curved surfaces.
2. Formulas are provided to calculate absolute pressure, resultant force, and the center of pressure on plane surfaces based on factors like depth, density of the fluid, and area of the surface.
3. Graphical methods are described for determining the pressure force and center of pressure on rectangular surfaces. Formulas include summing pressures in x, y, and z directions to calculate total force on curved surfaces.
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.
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.
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.
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.
1. The document discusses fluid flow and the Bernoulli equation. It presents equations for fluid dynamics including the continuity equation and Bernoulli's equation.
2. Methods for calculating flow velocity, flow rate, water level, and hydraulic radius in open channels are provided. Manning's and Chézy equations for uniform flow are presented.
3. Parameters for flow resistance coefficients for different channel materials are listed, along with typical values for flow depth and hydraulic radius under uniform flow conditions.
1. Fluid statics defines pressure as a force per unit area. Pressure in a static fluid depends on depth and density.
2. Hydrostatic pressure is determined by the fluid density and depth. The pressure is transmitted equally in all directions and increases with depth according to hydrostatic laws.
3. For an incompressible fluid, pressure increases linearly with depth due to the fluid density being constant. For a compressible fluid, pressure increases non-linearly with depth due to changes in density with pressure.
1. The document defines fluid as any substance that can flow and take the shape of its container. It then discusses various fluid properties such as density, specific weight, specific volume, and viscosity.
2. It introduces the basics of fluid mechanics including hydrodynamics, aerodynamics, and different types of fluid flow. The laws of conservation of mass, momentum, and energy as they apply to fluid mechanics are also covered.
3. Various fluid properties are defined including density, specific weight, specific volume, relative density, vapor pressure, and surface tension. Dimensional analysis and units used in fluid mechanics are also introduced.
1. The document discusses hydrostatic forces on plane surfaces and curved surfaces. It describes how to calculate the pressure, force, and center of pressure on rectangular and curved surfaces.
2. Formulas are provided to calculate absolute pressure, resultant force, and the center of pressure on plane surfaces based on factors like depth, density of the fluid, and area of the surface.
3. Graphical methods are described for determining the pressure force and center of pressure on rectangular surfaces. Formulas include summing pressures in x, y, and z directions to calculate total force on curved surfaces.
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.
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.
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.
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.
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 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.
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.
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.
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.
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.
[Atlassian meets dev ops and itsm] Building organization and collaboration cu...Open Source Consulting
The document appears to be notes or equations written in an unfamiliar language. It includes mathematical equations like 2H=RT and 23C= mixed with words and abbreviations. References are made to things like heat, temperature, and chemistry concepts. The formatting is inconsistent with text interspersed with symbols and punctuation. Overall it provides an unclear and disorganized collection of technical information that is difficult to interpret without additional context.
11. displacement method of analysis slope deflection equationsChhay Teng
1. The document discusses the displacement method of analysis known as the slope-deflection method. This method analyzes the deformations of structures using slope-deflection equations.
2. General procedures for the displacement method are described, including determining degrees of freedom and establishing slope-deflection equations for each member.
3. Slope-deflection equations relate the displacements (rotations and translations) of joints to member end actions (moments and shears). These equations allow determining member forces based on known joint displacements.
15. beam analysis using the stiffness methodChhay Teng
1. The document discusses analyzing beams using the stiffness method. It introduces node coordinates and degrees of freedom, and defines member stiffness matrices for individual beam elements.
2. It provides examples of applying the method to simple structures like trusses and slider mechanisms by assembling the element stiffness matrices into a global stiffness matrix.
3. The method relates displacements at nodes to applied forces using the member stiffness matrices. This allows solving for unknown displacements given known forces or vice versa.
A.matrix algebra for structural analysisdocChhay Teng
The document provides definitions and examples of different types of matrices including matrix algebra, matrix operations, and properties of matrix operations. It defines matrices, matrix types (square, identity, symmetric, triangular), and matrix operations including addition, subtraction, scalar multiplication, and matrix multiplication. Matrix multiplication involves multiplying the rows of the first matrix with the columns of the second matrix. The properties discussed are that matrix multiplication is noncommutative, distribution over addition holds, and distribution over matrix multiplication holds.
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. 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.
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.
The document appears to be about roof tile production and installation. It includes sections on:
1. Measuring and preparing the roof surface.
2. Selecting and installing the tiles, including laying underlayment and setting tiles at the appropriate angle.
3. Installing battens, ridges and other roof elements.
The document provides diagrams and specifications for tile sizes, roof measurements, angles and spacing for a proper roof installation. Proper preparation and installation techniques are emphasized.
This document discusses different types of reactors used to model environmental systems, including batch reactors and completely mixed reactors (CFSTRs). It provides the mass balance equations for batch and completely mixed reactors under steady-state and transient-state conditions. It also defines hydraulic retention time and explains how to determine effluent concentrations for a completely mixed reactor under steady-state conditions using the retention time and reaction rate constant. Examples are provided of tracer and reactant concentration profiles over time in a completely mixed reactor.
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.
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 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. 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.
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.
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.
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. 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 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.
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.
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.
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.
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.
[Atlassian meets dev ops and itsm] Building organization and collaboration cu...Open Source Consulting
The document appears to be notes or equations written in an unfamiliar language. It includes mathematical equations like 2H=RT and 23C= mixed with words and abbreviations. References are made to things like heat, temperature, and chemistry concepts. The formatting is inconsistent with text interspersed with symbols and punctuation. Overall it provides an unclear and disorganized collection of technical information that is difficult to interpret without additional context.
11. displacement method of analysis slope deflection equationsChhay Teng
1. The document discusses the displacement method of analysis known as the slope-deflection method. This method analyzes the deformations of structures using slope-deflection equations.
2. General procedures for the displacement method are described, including determining degrees of freedom and establishing slope-deflection equations for each member.
3. Slope-deflection equations relate the displacements (rotations and translations) of joints to member end actions (moments and shears). These equations allow determining member forces based on known joint displacements.
15. beam analysis using the stiffness methodChhay Teng
1. The document discusses analyzing beams using the stiffness method. It introduces node coordinates and degrees of freedom, and defines member stiffness matrices for individual beam elements.
2. It provides examples of applying the method to simple structures like trusses and slider mechanisms by assembling the element stiffness matrices into a global stiffness matrix.
3. The method relates displacements at nodes to applied forces using the member stiffness matrices. This allows solving for unknown displacements given known forces or vice versa.
A.matrix algebra for structural analysisdocChhay Teng
The document provides definitions and examples of different types of matrices including matrix algebra, matrix operations, and properties of matrix operations. It defines matrices, matrix types (square, identity, symmetric, triangular), and matrix operations including addition, subtraction, scalar multiplication, and matrix multiplication. Matrix multiplication involves multiplying the rows of the first matrix with the columns of the second matrix. The properties discussed are that matrix multiplication is noncommutative, distribution over addition holds, and distribution over matrix multiplication holds.
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. 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.
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.
The document appears to be about roof tile production and installation. It includes sections on:
1. Measuring and preparing the roof surface.
2. Selecting and installing the tiles, including laying underlayment and setting tiles at the appropriate angle.
3. Installing battens, ridges and other roof elements.
The document provides diagrams and specifications for tile sizes, roof measurements, angles and spacing for a proper roof installation. Proper preparation and installation techniques are emphasized.
This document discusses different types of reactors used to model environmental systems, including batch reactors and completely mixed reactors (CFSTRs). It provides the mass balance equations for batch and completely mixed reactors under steady-state and transient-state conditions. It also defines hydraulic retention time and explains how to determine effluent concentrations for a completely mixed reactor under steady-state conditions using the retention time and reaction rate constant. Examples are provided of tracer and reactant concentration profiles over time in a completely mixed reactor.
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.
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 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. 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.
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.
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.
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 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).
6. influence lines for statically determinate structuresChhay Teng
1) The document discusses influence lines for statically determinate structures like beams, trusses, and floor girders. It describes how to calculate and graph influence lines for reactions, shearing forces, and bending moments.
2) The procedures involve tabulating load positions and magnitudes, determining the maximum and minimum values from the influence lines, and deriving the mathematical expressions for the influence lines.
3) Several examples are provided to demonstrate calculating and graphing influence lines for reactions, shearing forces, and bending moments of beams and trusses.
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.
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.
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.
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.
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.
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.
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. 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) 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) 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.
1. The document discusses the history of Cambodia from 1960 to 1999, focusing on the rule of Prime Minister Lon Nol from 1973 to 1975 and Pol Pot's Khmer Rouge regime from 1975 to 1979.
2. It describes how the Khmer Rouge forcibly evacuated Phnom Penh and other cities, sending people to work in agricultural communes where they endured forced labor, starvation, and executions.
3. The era ended in 1979 when Vietnam invaded Cambodia and overthrew the Khmer Rouge, but the country continued to suffer from the impacts of the regime for many years through civil war and instability.
This document provides an overview of MATLAB commands organized into categories such as general purpose commands, input/output commands, vector and matrix commands, plotting commands, programming commands, mathematical functions, numerical methods, and symbolic math toolbox functions. It summarizes the purpose and usage of many common MATLAB functions and operators.
This document provides an introduction to MATLAB for engineering students. It covers basic MATLAB functionality like performing calculations, plotting graphs, generating matrices, and programming with M-files. The document is divided into multiple chapters that teach essential MATLAB skills such as its interface, basic commands, mathematical functions, plotting, matrix operations, solving equations, programming constructs, debugging scripts, and more. It serves as a tutorial for new MATLAB users to learn its main features.
1) The document discusses the stability of floating bodies, including neutral stability and partially submerged bodies.
2) For a floating body to be stable, the metacenter height (r) must be greater than the distance between the center of buoyancy and center of gravity (δ). Bodies are unstable if r is less than δ.
3) The stability of partially submerged bodies depends on factors like the angle of submergence (α), metacenter height (r), center of buoyancy, center of gravity, and the relationship between r and eccentricity (б). Bodies are stable if r/б is greater than 1.
1. This chapter provides an introduction to quality management systems. It discusses total quality management (TQM), the importance of customer focus and satisfaction, and continuous improvement.
2. Quality management systems aim to ensure consistency and improve processes. Organizations implement quality management standards like ISO 9000 to formalize processes and get certified.
3. The chapter emphasizes the role of documentation in quality systems. Documents provide records of activities and ensure requirements are met. Maintaining accurate documentation is important for quality assurance and improvement.
1) Samdech Hun Sen was born on April 5, 1952 in Kampong Chhnang province. He studied law in Phnom Penh and became involved in politics in the 1960s.
2) In 1977, he became a member of the Central Committee of the Kampuchean (Cambodian) People's Revolutionary Party. From 1979-1993, he held various senior positions in the government and helped negotiate peace agreements.
3) From 1979-1981 and 1985-1991, he served as Prime Minister of the People's Republic of Kampuchea and led Cambodia's government during the 1980s.
The document summarizes a student's visit to the Phnom Penh Water Supply Authority (PPWSA). It discusses the background and operations of PPWSA, including the locations and capacities of their four water treatment plants. The objectives of the visit were to understand Phnom Penh's water supply process, water quality control, and maintenance of equipment. Students toured the facilities and learned about the treatment process involving chemicals, sedimentation tanks, and chlorine disinfection. The visit provided students with practical knowledge to supplement their academic studies and strengthen collaboration between their university and PPWSA.
The document provides instructions for various commands in AutoCAD 2D, including how to draw lines, erase objects, use construction lines, copy, mirror and offset objects, create multilines, polylines, polygons, and arrays. For each command, 3-4 examples are given with the specific steps to use the command and its options, such as drawing a line 10000mm long, creating a rectangular or polar array, or offsetting an object by 700mm.
This document provides details on the design of an irrigation canal system for an area in Kampong Thom Province, Cambodia. It discusses the background of the study area, objectives to increase agricultural productivity and reduce poverty. It outlines the methodology, which includes collecting climate and soil data, establishing a water management committee, and determining irrigation water needs using the Blaney-Criddle formula. Design considerations are provided for the main and sub-canals, including calculating required discharge and designing the hydraulic sections. Finally, cost estimates are presented for constructing the main and sub-canals as well as system foundations.
1. The document describes how to determine the proportions of different soil types (A, B, C) needed to achieve a desired soil mixture. It provides an example where 30.4% of material A, 45.6% of material B, and 24% of material C are needed.
2. To achieve at least 95% maximum dry density (MDD), between 16.66 and 120.78 liters of water per cubic meter of soil is required, depending on the water content between 9% and 15.25%.
3. The total volume of the dam to be compacted to 95% MDD is calculated to be 160,103 cubic meters based on cross-sectional area calculations for 15
Watershed models simulate natural processes like water flow, sediment movement, and nutrient cycling within watersheds. They also quantify the impacts of human activities on these processes. Watershed models come in different forms with varying complexity and computational requirements. They are used to address a wide range of environmental and water resource issues like flooding, erosion, pollution, and more. Watershed models can be classified based on how they acquire and treat data, and whether they take a lumped or distributed approach. The key steps in developing and applying a watershed model include establishing objectives, model design, calibration, validation, application, and accounting for uncertainty.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
Batteries -Introduction – Types of Batteries – discharging and charging of battery - characteristics of battery –battery rating- various tests on battery- – Primary battery: silver button cell- Secondary battery :Ni-Cd battery-modern battery: lithium ion battery-maintenance of batteries-choices of batteries for electric vehicle applications.
Fuel Cells: Introduction- importance and classification of fuel cells - description, principle, components, applications of fuel cells: H2-O2 fuel cell, alkaline fuel cell, molten carbonate fuel cell and direct methanol fuel cells.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
2. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 2
a kMBs;TVaTwkebIk ,m
cth kMBs;Twks,Wt ,m
cth'' kMBs;Twks¶b;xageRkay ,m
cth =ε'×a
1
ct
j
a x
=
+å
emKuNel,Ón
0.95 0.97j =
a
H
0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75
ε' 0.615 0.618 0.620 0.625 0.628 0.628 0.638 0.638 0.645 0.650 0.650 0.650 0.690 0.705
2
0
α2J
H = H + , m
2g
rUbTI1
cth cth''
H
0H
0J
cth
TVVVVVVVVVaTwk
xagmux
H
rUbTI2
taragbgðajGMBIε'
cth
H
0H
0J
a 2h
2J
2
2 g
a J
rlkTwkxageRkay
h av
3. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 3
B rgVHTwk ,m rUbmnþ
b )atRbLay ,m
m eCIget
H kMBs;Twk , m
N PaBeRKImrbs;TMr ,mm
DkMBs;bMrug ,m
rUbmnþTUeTA
edIm,IeGaymuxkat;RbLaymanlk<N³smRsbeKeRbIrUbmnþ
3
0 ct
mQ = φ × ε' × a × b × 2g(H -h ) ,
s
a kMBs;TVaTwkEdlebIk , m
b TTwgTVaTwk , m
ε' emKuNénpleFobkarebIkTVaTwk
H0 kMBs;Twkxagmux ,m
Hct kMBs;TwkxageRkayTVa
x Gab;sIuelanPaBkkit
n n
B
b
H
m h a´ ´ D
2
2
2
1 21
6 32
2 1
3
3 2
ω = bh + mh = (b+mh)h
P = b + 2h 1+m
ω ( b + mh )
R = =
P b+2h 1+m
1
tgθ =
m
a
m = Cotg =
h
Q = ω × J = ω × c R
1 1
= R × R × = × R × × ω
n n
1 mQ = × R × ,
sn
i
i i
i
b
β =
h
4. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 4
cMNaM
J > 0.5 eTA 0.6 m/s rt;kñúgRbLaykñúgkrNIEdlel,Ónrt;kñúgmanbBaðaBIrKW
J eRcaHdac; = KQ0.1
kkpk;
mmA = 0.33 , ω < 1.5
mmA = 0.44 , ω = 1.5 35
s
mmA = 0.55 , ω > 3.5
s
s
K emKuNeRcaHdac;
Q brimaNFaTwkkúñgRbLay m3
/s
W el,ÓnFøak;cuHRKab;dI mm/s
lkçx½NÐ
rMhUrqøgkat;rgVHragRtIekaN
J = AQ0.2
J kkPk < J < J eRcaHdac; ( el,Ónrt;kñúgRbLay)
Q h
P
B
b
z
32.5 mQ = 1.14h ,
s
6. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 6
eRbIsMrabépÞFM eRbIsMrabépÞtUc
3
mQ =
s
m emKuNbrimaNFaTwk
ωmuxkat;épÞTwk m2
H0 kMBs;TwklMeHogedayEpñk ,m
g = 9.81m/s2
rUbmnþ
1 rMhUrvtßúravqøgkCBa¢aMgesþIgEdlmankMBs;Twkefr
tamsmIkar Bernoulli BI AA eTA CC
2 2
o 0 0 c
P.C
P α J αJ tP
H + + = 0 + + + h
g 2g 2g 2gr
P0 sm<aFxageRkARtg; AA
P sm<aFxagkñúgRtg; CC
0J el,ÓnTwkrt;BIépÞb:HxagelImkrnrnæ ,m/s
ctJ el,Ónecjrnæ m/s
P.Ch kMhatbg; ,m
e m.p
e
R 100 0.6
R > 100000 μ = 0.60 0.62
ε = 0.62 0.64
φ = 0.97
x£ =
2
0 0 0
0H H + +
2
P P
g g
a J
r
-
=
2
ct
0H ( )
2g
J
a x= +S
0
3
Ω
H H Ω 4ω < 15%
ω
= 1% 5ω
mQ = μω 2gh ,
s
³
W W ³
snμt; 1
=j
a x+S
ct 0= 2gHJ j
0Q = μω 2gH Q = μω 2gH
c
c
atm 0P = P
H
A A
o
0H ctω
ctJ
7. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 7
kñúgkrNIEdl
0 atm
2
0 0
0
0
0
P = P = P
α
H = H+
2g
H = H
Q
=
J
J
W
W muxkat;rbs;épÞTwkénGag
2
0
2 2
2
0
μω 2ghα Q
Q = μω 2g(H+ ) or Q =
2gΩ ω
1-μ α
Ω
cMeBaH
0
3
Ω
H H Ω 4ω < 15%
ω
= 1% 5ω
mQ = μω 2gh ,
s
³
W W ³
eKdwgfaemKuNénkarkkitRtg;Rckecj
ε , φ Gnuvtþn_tamlkçN³
e
2gh
R , = 2ghJ
n
=
dUcenH
e m.p
e
R 100 0.6
R > 100000 μ = 0.60 0.62
ε = 0.62 0.64
x£ =
(emKuNrbs;el,ÓnTwk )
8. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 8
rUbmnþ
cth = ε' × a
a kMBs;ebIkTVaTwk ,m
ε' emKuNkkitrvagTwkCamYyTVaTwk
cth kMBs;TwkEdles,WtRtg;cMnucEdlTabCageK ,m
rMhUrqøgkat;TVaTwk
H
haJ
a
0J
a
cth
2
0
2g
aJatmP
ah J
Up Down
haJ kMBs;Twks¶b;xageRkayTVaTwk , m
a kMBs;ebIkTVaTwk , m
0J el,ÓnTwkxagmuxTVaTwk ,m
H kMBs;TwkxagmuxTVaTwk ,m
0H kMBs;TwklMeGogedayEPñk ,m
cth kMBs;TwkkkitenARtg;Rckecj,m
hz
kMBs;TwkenAEk,rTVaTwk ,m
2J el,ÓnTwkenAeRkayTVaTwk m/s
H 0H
a
ctJ
zh
2J
0J
zh haJ=
2
21
1
b
cth
9. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 9
cMeBaHel,ÓnTwkrt;xageRkamTVaTwk
ct 0 ctφ 2g(H -h )J =
nigbrimaNFaTwk
ct ct 0 ctQ = ω = ε'×a×b×φ 2g(H -h )ctJ´
sMKal;
b TTwgTVaTwk , m
dUcenH
3
ct 0 ct
mQ = φ × ε' × a × b 2g(H -h ) ,
s
2
0
0
ct
1
H = H ,m , φ =
2 α +Σξg
aJ
+ emKuNrbs;el,Ón
cMeBaH φ = 0.95 eTA 0.97 bRgYmmkvijeKGacsresr
ε' × φ = μ emKuNrbs;brimaNFarTwkhUreRkamTVaTwk
3
ct 0 ct
mQ = μ × a × b × 2h(H -h ) ,
s lkçN³edNUey (mincal;)
3
ct 0 ct
mQ = μ × a × b × 2h(H -h ) ,
s lkçN³NUey (mincal;eRkay)
a
H
0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75
ε' 0.615 0.618 0.620 0.622 0.625 0.628 0.630 0.638 0.645 0.650 0.660 0.675 0.690 0.705
ctha
rUbPaBebIkTVaTwk
kñúgkarGnuvtþn_ε' = 0.64
taragbgðajGMBItMél
10. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 10
CMBUkTI 2
rMhUrÉksNæanenAkñúgépÞTwkcMh
α
a
2
1α
2g
J
1P
gr
1Z i
h = const
2
2α
2g
J
2P
gr
2Z
pc lh = h
L
'L
sMKal;
p lI = I CMralrbs;épÞTwk
i CMral)atRbLay
2
α
2g
J
famBlsIuenTic ,m
1 2P P
,
g gr r
famBlsMBaF ,m
1 2Z , Z famBlbU:tgEsül ,m
h kMBs;Twkefr,m
'a mMulMgak
L RbevgbeNþayRbLay
L' RbevgbeNþayRbLay ,m
p lh = h kMhatbg;tambeNþayRbLay,m
12. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 12
D
B
b
m=1.5
H
0H
BMnuHkat;AA
sMKal;
b )atRbLay ,m
B rgVHmat;RbLay ,m
D kMBs;suvtßiPaB , m (0.2 eTA 2m )
GaRs½yFaTwk 3
mQ =
s
m= 1.5 nig m=1 CaCMraleCIgeTrkñúgnigeRkAénRbLay
h kMBs;TwkkñúgRbLayRtg;muxkat;NamYy ,m
H = h + Δ ,m
A
A
m=1
m=1.5
13. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 13
II rUbmnþsMrab;KNnaemKuN Chezy nigemKuNénPaBeRKImrbs;RbLay
0.5y1 mC = R , (Pavlovski)
sn
n PaBeRKImrbs;RbLay
R kaMGIuRdUlik,m
y s½VyKuN
y = 2.5 n - 0.13 - 0.75 R( n-0.10)
y = 1.5 n cMeBaH R < 1m
y = 1.3 n cMeBaH R > 1m
kúñgkrNI n = 0.009 eTA 0.040 R=0.1 eTA 3m
c = 4 2g (k+lgR)
0.51 mc = + 17.72lgR ,
sn
0.51/61 m** c = R , Manning
sn
(enAelITIpSareKniymeRbICaCnCatiGg;eKøs)
2/3 1/21 m= R × i ,
sn
J
emKuNénPaBeRKImeRcInRbePT
( )
1/2N
2
i i
1
equiralent 1/2
x n
n =
x
é ù
ê ú
ê úë û
å
sMKal;
xi kMras;énPaBeRKImnimYy ,m
ni RKab;dInimYYy² ,m
rUbmnþenHbgðajGMBImuxkarRbLayragctuekaNBañaynig)ar:abUlik
Agroskine
14. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 14
h H
D
B
a
θ
b
sMKal;
b TTwg)atRbLay ,m
m. eCIgeTxagkñúgRbLay,m
h kMBs;TwkkñúgRbLay,m
D kMBs;suvtßiPaB,m
w RkLaépÞRbLay,m
2
ω = bh + mh = (b+mh)h
P brimaRtrbs;RbLay,m
B rgVHTwkxagelI,m
H = h´DkMBs;Twksurb,m
θ mMulMgak;rbs;RbLay a
m = cotgθ = ,m=0
h
2
2
P = b+2h 1+m or P=b+m'h
m' = 2 1+m
R kaMGIuRdUlik ,m
2
ω bh+mh
R = =
P b+m'h
edUm,IeGayrUbragRbLayctuekaNBañaymanlkçN³l¥RbesIrKWeKRtUvGnuvtþrUbm
nþ
0
2
0
m hb
β = and δ =
h b+mh
m = m' - m = 2 1+m - m
B = b + 2mh
rUbmnþ)ar:abUlik
15. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 15
muxkat;
Q = k i
RbEvgbrimaRtesIm
x = P 2τ(1+2τ)+ln( 2τ+ 1+2τ)
ω 2Bh
R = =
x 2PN
é ù
ê úë û
EdltMél N man
N = 2τ(1+2τ) + ln( 2τ+ 1+2τ)
kúñgkrNI
B h³
eK)an
x B
rUbmnþbgðajmuxkat;RbLayragctuekaNBñay nig)ar:abUlik
B
D
H
b
P
2 θ
h
H
A
B
x
y
rUbmnþ
x2
=2Py
P)ar:Em:Rtrbs;)ar:abUlik
H CMerATwk ,m
H = h+D ,m
B rgVHmat;elI ,m
D kMBs;bMrug ,m
h
τ-
P
CMerATwkR)akd
1
m-
2τ
CMerArbs;épÞTwk
2
ω = B×h ,m B = b ,m
P = B ,m
ω B×h
R = = = h ,m
P B
16. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 16
taragbgðajGMBIemKuNeCIgeTr
RbePTdI ,m m
dIdæ 1 eTA 1.25
dIl,aydIdæ 1.25 eTA 1.50
dIl,ayxSac; 1.50 eTA 1.75
dIxSac;suTæ 1.70 eTA 2.25
cMNaM
muxkat;)atRbLay b = 0.4m CatMélGb,brima ( Minivaum ) eKGacKNnatamviFImü:ageTot rbs;
RbLayeRsacRsBtamlkçx½NÐrbs;elak Ghirshkan
cMeBaHtMélDvijKWRtUvGnuvtþtamsþg;darUsSI
3
mQ
s ,mD
<1 0.25
1 eTA 10 0.4
10 eTA 30 0.5
>30 0.6
sikSaGMBIlkçx½NÐénel,ÓnTwk m,
s
J mankrNI2y:agKW J eRcaHdac; nig J kkPk; .
rUbmnþtamlkçx½NÐ
afJ J£ el,ÓneRcaHdac;
J el,ÓnFmμtarbs;TwkkñúgRbLay ,m/s
0.1
af = kQJ
K emKuNénel,ÓneRcaHdac;
3
4
h = (0.7 1.0) Q
β = 3 Q - m
B = ( 3 5 ) Q
17. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 17
rUbmnþbgðajGMBImuxkat;RbLayragctuekaNBñay nig)ar:abUlik
RbePTdI K
dIdæ 0.75
dIdæsuTæ 0.85
dIl,ayxSac; 0.53
dImemak 0.57 eTA 0.68
rUbmnþrbs;el,ÓnkkPk;
0.2
an = AQ ,m sJJ
A emKuNénel,ÓnmFümRKab;dIEdlFøak;cuHeTAkñúg)atRbLay
mmA = 0.33 w < 1.5
s
mmA = 0.44 w = 3.5
s
mmA = 0.55 w >3.5
s
WrYm = ( Σw tamEpñkP)/100
Q
× k = = α
τ
´k
wS el,ÓnRKab;dIepSg²Føak;cuHmm/s
Pi PaKryénRKab;epSg²
Q = k i
18. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 18
V < gh
1rF <
r
V > gh
F 1>
cariklkçN³rbs;RbLaycMhman 4FM²
1 Stationary
V = 0
Fr ( froud ) = 0
2 Subcritical
3 Studding ware flout
4 Super critical
Critical Flow
19. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 19
- Vc Velocity critical ,m/s
- H Hydraulic depth ,m
- G 9.81 m/s2
- Fr Froude umber
rMhUrminÉksNæan
eKGacniyayfarMhUrclnavtßúravkñúgRbLaycMhminÉksNæanKW
- CMral)at I i¹ CMralrbs;épÞTwk
- H CakMlBs;TwkERbRbYlenAkñúgRbLay
- CMerAekIneLIgtamTisedAénclnavtßúrav
- CMerAfycuHtamTisedApÞúyénclnavtßúrav
Vc
Fr = = 1
gh
begÁa
h
0i >
ExSekagrWm:U (l,akTwkekInrYcFøakcuH)
ExSekagedRKuy ( l,ak;TwkFøak )
a
0i >
a) TwsedATwkRsktamCMral)at
b) i=0 TwsedATwkRsbtamCMral)at
a
0i <
c) TwsedATwkpÞúyBICMral
20. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 20
rUbmnþEdlRtUveRbIKW
0 0 0 0 0 0Q = ω c R i = k i
sMKal;
0 0 0 0ω , c , i , R CatMélEdlRtUv h = h0
sMrab;
1) i0 = i TisedARsb
2) i0 = i TisedARsbtMélviC¢man
3) i0 < i TisedApÞúy( KitkñúgtMéldac;xat)
eKeRbIkMNt;brimaNFaTwkQ’ tamclnaTisedATwki0 > 0 .
bB¢ak; ³ Q’CabrimaNFaTwkRtg;cMNucNamYyEdleyIgRtUvsÁal;beNþayRbLayeQñaH ( edb‘IhVicTis ) .
KMnUsbMRBYjrbs;épÞdIeRsacRsB
* muxkat; ED = F1 ,ha
* muxkat; DC = F1+F2 ,ha
* muxkat; CB = F1+F2 + F3 ,ha
* muxkat; BA = F1+F2 + F3+ F4 ,ha
RbPBTwk
4F
3F
2F
1F
D
B
C
E
2h
2h
3h
BMnuHkat;beNþaysMng;Farasa®sþ
22. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 22
P CMerArbs;r)aMgxageRkay ,m
haJ kMBs;Twks¶b;xageRkaysMNg;begðór ,m
Z kMBs;eFobrvagnIvUTwkxageRkaysMNg;,m
b rgVHTwkhUr ,m
B muxkat;RbLayxagelI ,m
CMBUkTI3
rMhUrqøgkat;sMNg;begðór
sMKal;
P1 kMBs;r)aMgrbs;sMNg;begðór ,m
l’ 3 eTA 5 dgén H
0J el,ÓnTwkhUrxagmuxsMNg;begðór , m/s
S kMBs;rbs;r)aMg,m
1 cMNat;fñak;rbs;sMNgbegðór
sMNg;begðórmanEckCaeRcIny:agKW
a. sMNg;begðórmanCBa¢aMgesþIg
P
Z
h a J
1P
0J
H
Q
V H S
l
D ow ntream
BMnuHkat;beNþaysMNg;begðór
23. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 23
H0H e
1P
0V
S
xül; P
avh
2
0
2
v
g
a
l = 3 5m for H
lkçx½NÐ
-S < 0.5H
-
2
0
0
αr
H = H + ,
2g
m
b. sMNg;begðórr)aMgRkas;
C. sMNg;begðórsßitkñúglkçN³Fmμta
0H H 0J
J
P
h
haJ
her
l S
2H < S < 10H
haJ
P
1P
H0H
l S
2
0
2g
aJ
2
0
2g
aJ
P
0H H
haJ
1P
Sl
0.5H < S < 2H
24. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 24
ctuekaNEkg ctuekaNBñay
RtIekaN rgVg;
H
P
0J
0J
d. rgVHrMHUrrbs;sMNg;begðór
e. sMNg;begðórragekag
f. rgVHsMNg;begðórRtg;
g. rgVHsMng;begðórbBaäit
H
P
P
H
H
P
0J
0H 1P
P
r
0
2g
aJ
cthl S
rlkTwkxμÜlsμaj;
r kaMrgVg;
26. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 26
mankarkkittic
B=b
mankarkkitxøaMg
B > b
2 cMNat;fñak; énsMNg;begðór
EdlrMhUrmanlkçN³ceg¥ót niglkçN³TUlay
3 RbePTrMhUrrbs;Twk
rUbmnþ
3/2
0Q = mb 2gH sMrab;rMhUredNUey
m emKuNbrimaNFaTwk
b rgVHsMng;begðór ,m
2
0
0
α
H = H + ,m
2g
J
TwkxagmuxsMNg;begðór ,m
33/2
n
mQ = σ mb 2gH ,
s
( sMrab;NUey )
nσ < 1
0J B b
0J
B
b
P1P
H0H
haJ
rMhUredNUey
2
0
2g
aJ
P1P
H0H
haJ
rMhUrNUey
2
0
2g
aJ
27. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 27
4.sMNg;begðórragctuekaNEkgRtg;lkçN³edNUeyEdlmanCBa¢aMesIþg
5. sMNg;begðórEdlmanCBa¢aMgesþIgedayragctuekaNEkg
a
b
xül;
c
0.27H
3H 0.67H
0.112H
0.22H0.15H0.003H
H
a
a
H
P
h
A
θ 1θ
b
P
H
a
B
sMrab;RtIekaN
2 3
5 mQ = 1.14H
s
sMrab;ctuekaNBañy
3 3
5 mQ = 1.86bH
s
eday b> 3H
28. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 28
0H H
1P
P
erh h
Sl
b
b
Bil
TVaTwk
6. sMNg;begðórEdlmanCBa¢aMgRkas;
3
0
mQ = ω × = φ × b × h 2g(H -h) ,
s
J
0
2
h= H
3
or
3
3
2 mQ = mb 2gH ,
s
( edNUey )
m = 0.35 eTA0.36
cMeBaHsMNg;begðórkñúglkçN³NUey
3
2 3
n 0
n
mQ = σ mb 2gH ,
s
b <1
7. sMNg;begðórEdlmanragCaekagCaExSekag
3
2
0Q = mb 2gH
m = 0.48 0.49
8. sMNg;BIlEdlfitenAsMNg;begðór
29. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 29
P
2h
2h
1Q
2Q
2h
rUbmnþ
3
2 3
0
0
0
mQ = ε m b 2gH ,
s
H
ε =1 - a
b+H
a emKuNrbs;rUbragBil
9 sMNg;begðórLaetral;
QLaetral; = mLaetral; x b x
3
2
02gH
3
m,
s
mLaetral; = 0.25 + 0.167( 2
1
2
H
-
H
cinP )
2
2
2
cin
2
P
gh
J
=
10>sMNg;begðóreFμjrNa
A=0.20
r=0.5t
A=0.11 A=0.11 A=0.06
t t t
1b
2b
b
B
n n n
B
h
31. sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 31
CMBUkTI 4
rlkTwkeRkaysMNg;begðór
I rUbPaBénsMNg;Farasa®sþ
rMhUrmanBIry:ag
- cr cinh < h and P > 1
rUr:gEsül ( Twktic )
- cr cinh > h and P < 1
PøúyrIy:al; ( TwkCn )
0J
0H H
cth
haJ
1P P
Upstream Down stream
0J0H H
cth
haJ
1P
P
Q