The document presents closed-form expressions for determining the bending moments in two directions of a rectangular two-way slab under a concentrated load uniformly distributed over a defined area. Equations (16) and (17) provide the bending moment expressions for the short and long directions, respectively, as functions of the span ratio, load area dimensions ratios, and other geometric properties. Comparisons are made between results from the proposed analysis method, Egyptian code approximate method, Pigweed's theory, and finite element analysis, showing better accuracy of the proposed method and Pigweed's theory over the Egyptian code method.
Estimation of Damping Derivative of a Delta Wing with Half Sine Wave Curved L...IOSR Journals
1) The document analyzes the effect of angle of attack on the damping derivative of a delta wing with a half sine wave curved leading edge for attached shock cases in supersonic flow.
2) A strip theory combined with Ghosh's piston theory is used to relate pressure on the wing surface to equivalent piston Mach number, allowing calculation of stability derivatives.
3) Results show the damping derivative increases linearly with angle of attack up to a Mach-dependent limit, and decreases with increasing Mach number and with the pivot position moving aft.
Analysis of Stress Distribution in a Curved Structure Using Photoelastic and ...IOSR Journals
1) The document analyzes stress distribution in a curved structure subjected to uniaxial tension using photoelastic and finite element methods.
2) Photoelasticity is used to experimentally determine stress distribution in models of the curved structure with and without circular and elliptical stress relievers. Finite element analysis is then used to validate the experimental photoelastic results.
3) The study found that an elliptical stress reliever with its major axis normal to the load more effectively reduced stress concentration at the inner boundary of the curved structure compared to a circular stress reliever.
Closed-Form Expressions for Moments of Two-Way Slabs under Concentrated LoadsIOSR Journals
The document presents closed-form expressions for determining the bending moments in two directions of a rectangular two-way slab under a concentrated load uniformly distributed over a defined area. Two expressions are derived based on elastic analysis and Navier's method. The expressions relate the bending moments to factors that influence them, including the span ratio, the dimensions ratio of the loaded area, and the ratio of the short span to the parallel length of the loaded area. Comparisons are made between results from the new expressions, an approximate method in the Egyptian code ECCS 203-2007, Pigweed's theory, and finite element analysis. Significant differences are found between the code's method and finite element results, while Pigweed's theory agrees well with finite element
Fluid and structural modeling of cavitating propeller flowsPhuong Dx
This document summarizes previous research on modeling cavitating propeller flows and hydroelastic effects. It presents the objective to develop a coupled boundary element-finite element model to predict cavitation patterns and hydroelastic response of propellers. An overview is given of the boundary element formulation used, including the assumptions of potential, incompressible, and cavitating sheet flow. Boundary conditions at wetted surfaces and cavities are described. Validation with experiments is discussed.
Three primary aspects of strength of materials problem solving are analyzing equilibrium of forces, relating applied forces to structural deformation, and determining compatibility of deformations with structural integrity. Members under axial loads will deform linearly between stress and strain initially, then strain may greatly increase beyond the yield point with partial unloading. Stress is the ratio of load to original area under load, and strain is the ratio of deformation to original length. Combined stresses must consider each stress type independently.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Axial force, shear force, torque and bending moment diagramDooanh79
This document introduces shear force, bending moment, and torque diagrams. It discusses:
1. The purpose of these diagrams is to visualize the internal forces along a member under loading conditions.
2. Two methods are presented for constructing these diagrams - the basic method uses equilibrium equations, while the graphical method uses relationships between loading, shear, and bending.
3. Examples are provided to demonstrate the application of both methods to calculate shear force and bending moment diagrams for beams under different load scenarios.
Fe investigation of semi circular curved beam subjected to out-of-plane loadeSAT Journals
Abstract Curved beams are used as machine or structural members in many applications. Based on application of load they can be classified into two categories. Curved beams subjected to In-Plane loads are more familiar and are used for crane hooks, C-clamps etc. The other categories of curved beams are the ones that are subjected to out-of-plane loads. They find applications in automobile universal joints, raider arms and many civil structures etc.The results of this research on semicircular curved beam subjected to out-of-plane loads have revealed some interesting results. For semicircular curved beams subjected to out-of-plane loads, it is shown that every section is subjected to a combination of transverse shear force, bending moment and twisting moment. By using ANSYS tool it is shown that Maximum principal stress occurs at section 120 degrees from the section containing the loading line. Moreover it is observed that fixed end of this curved beam is subjected to a state of pure shear. Key Words: Semi circular curved beam, Stress in curved beam, Out-of-plane load, FE analysis.
Estimation of Damping Derivative of a Delta Wing with Half Sine Wave Curved L...IOSR Journals
1) The document analyzes the effect of angle of attack on the damping derivative of a delta wing with a half sine wave curved leading edge for attached shock cases in supersonic flow.
2) A strip theory combined with Ghosh's piston theory is used to relate pressure on the wing surface to equivalent piston Mach number, allowing calculation of stability derivatives.
3) Results show the damping derivative increases linearly with angle of attack up to a Mach-dependent limit, and decreases with increasing Mach number and with the pivot position moving aft.
Analysis of Stress Distribution in a Curved Structure Using Photoelastic and ...IOSR Journals
1) The document analyzes stress distribution in a curved structure subjected to uniaxial tension using photoelastic and finite element methods.
2) Photoelasticity is used to experimentally determine stress distribution in models of the curved structure with and without circular and elliptical stress relievers. Finite element analysis is then used to validate the experimental photoelastic results.
3) The study found that an elliptical stress reliever with its major axis normal to the load more effectively reduced stress concentration at the inner boundary of the curved structure compared to a circular stress reliever.
Closed-Form Expressions for Moments of Two-Way Slabs under Concentrated LoadsIOSR Journals
The document presents closed-form expressions for determining the bending moments in two directions of a rectangular two-way slab under a concentrated load uniformly distributed over a defined area. Two expressions are derived based on elastic analysis and Navier's method. The expressions relate the bending moments to factors that influence them, including the span ratio, the dimensions ratio of the loaded area, and the ratio of the short span to the parallel length of the loaded area. Comparisons are made between results from the new expressions, an approximate method in the Egyptian code ECCS 203-2007, Pigweed's theory, and finite element analysis. Significant differences are found between the code's method and finite element results, while Pigweed's theory agrees well with finite element
Fluid and structural modeling of cavitating propeller flowsPhuong Dx
This document summarizes previous research on modeling cavitating propeller flows and hydroelastic effects. It presents the objective to develop a coupled boundary element-finite element model to predict cavitation patterns and hydroelastic response of propellers. An overview is given of the boundary element formulation used, including the assumptions of potential, incompressible, and cavitating sheet flow. Boundary conditions at wetted surfaces and cavities are described. Validation with experiments is discussed.
Three primary aspects of strength of materials problem solving are analyzing equilibrium of forces, relating applied forces to structural deformation, and determining compatibility of deformations with structural integrity. Members under axial loads will deform linearly between stress and strain initially, then strain may greatly increase beyond the yield point with partial unloading. Stress is the ratio of load to original area under load, and strain is the ratio of deformation to original length. Combined stresses must consider each stress type independently.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Axial force, shear force, torque and bending moment diagramDooanh79
This document introduces shear force, bending moment, and torque diagrams. It discusses:
1. The purpose of these diagrams is to visualize the internal forces along a member under loading conditions.
2. Two methods are presented for constructing these diagrams - the basic method uses equilibrium equations, while the graphical method uses relationships between loading, shear, and bending.
3. Examples are provided to demonstrate the application of both methods to calculate shear force and bending moment diagrams for beams under different load scenarios.
Fe investigation of semi circular curved beam subjected to out-of-plane loadeSAT Journals
Abstract Curved beams are used as machine or structural members in many applications. Based on application of load they can be classified into two categories. Curved beams subjected to In-Plane loads are more familiar and are used for crane hooks, C-clamps etc. The other categories of curved beams are the ones that are subjected to out-of-plane loads. They find applications in automobile universal joints, raider arms and many civil structures etc.The results of this research on semicircular curved beam subjected to out-of-plane loads have revealed some interesting results. For semicircular curved beams subjected to out-of-plane loads, it is shown that every section is subjected to a combination of transverse shear force, bending moment and twisting moment. By using ANSYS tool it is shown that Maximum principal stress occurs at section 120 degrees from the section containing the loading line. Moreover it is observed that fixed end of this curved beam is subjected to a state of pure shear. Key Words: Semi circular curved beam, Stress in curved beam, Out-of-plane load, FE analysis.
IRJET- Design of Girder using Thin Beam Walled Theory with Influence of S...IRJET Journal
This document presents a study on the design of U-shaped girder bridges using a thin beam walled theory that accounts for the influence of shear forces. It introduces a new analytical method to calculate displacements and stresses in thin-walled beams with cross-sections having one or two axes of symmetry. The method considers shear deformations using shear factors. Several examples are analyzed and show good agreement with finite element results. The theory provides a way to simplify the analysis and design of U-girder bridges.
This document discusses curved beams and provides equations for calculating stresses in curved beams. It begins by stating that beam theory can be applied to curved beams to determine stresses in shapes like crane hooks. It provides symbols for variables used in the equations. The main differences between straight and curved beams are that the neutral axis and centroid axis do not coincide for curved beams. Equations are provided to calculate strain and stress at different radii along the curved beam based on the eccentricity between the neutral and centroid axes. An example calculation for a crane hook is also shown.
Finite Element analysis -Plate ,shell skew plate S.DHARANI KUMAR
This document provides an overview of plate and shell theory and finite element analysis for plates and shells. It discusses the assumptions and applications of thin plate theory, thick plate theory, and shell theory. It also describes different types of finite elements that can be used to model plates and shells, including plate, shell, solid shell, curved shell, and degenerated shell elements. Additionally, it covers skew plates and different discretization methods that can be used for finite element analysis of skew plates.
This document summarizes a master's thesis presentation on modeling deep girders supporting shear walls. The presentation introduces various analysis techniques for deep beams, including the strut-and-tie method, finite element analysis using VecTor2, and two parameter kinematic theory. Seven test beams with varying sizes, loading eccentricities are described to compare the predictions of failure load between VecTor2 and the other methods. The results show that VecTor2 predictions match well but the other methods are unconservative. Adjusting parameters in the two parameter kinematic theory improves predictions. Size effects are demonstrated through a scaled model analysis.
Chapter 6: Pure Bending and Bending with Axial ForcesMonark Sutariya
This summary provides the key points about pure bending and bending with axial forces from the document:
1. Pure bending occurs when a beam segment is in equilibrium under bending moments alone, with examples being a cantilever loaded at the end or a beam segment between concentrated forces.
2. For beams with symmetric cross-sections, plane sections remain plane after bending according to the fundamental flexure theory. The elastic flexure formula gives the normal stress as proportional to the bending moment and the distance from the neutral axis.
3. The second moment of area, or moment of inertia, represents the beam's resistance to bending and is used to calculate maximum bending stresses. The elastic section modulus is a ratio of the moment
Estimation of Damping Derivative in Pitch of a Supersonic Delta Wing with Cur...iosrjce
In the Present paper effect of angle of incidence on Damping derivative of a delta wing with Curved
leading edges for attached shock case in Supersonic Flow has been studied. A Strip theory is used in which
strips at different span wise location are independent of each other. This combines with similitude to give a
piston theory which gives closed form solutions for damping derivatives at low to high supersonic Mach
numbers. From the results it is seen that with the increase in the Mach number, there is a progressive decrease
in the magnitude of damping derivatives for all the Mach numbers of the present studies; however, the decrease
in the magnitude is variable at different inertia level. It is seen that with the increase in the angle of attack the
damping derivative increases linearly, nevertheless, this linear behavior limit themselves for different Mach
numbers. For Mach number M = 2, this limiting value of validity is fifteen degrees, for Mach 2.5 & 3, it is
twenty five degrees, whereas, for Mach 3.5 & 4 it becomes thirty five degrees, when these stability derivatives
were considered at various pivot positions; namely at h = 0.0, 0.4, 0.6, and 1.0. After scanning the results it is
observed that with the shift of the pivot position from the leading edge to the trailing edge, the magnitude of the
damping derivatives continue to decrease throughout. Results have been obtained for supersonic flow of perfect
gases over a wide range of angle of attack and Mach number. The effect of real gas, leading edge bluntness of
the wing, shock motion, and secondary wave reflections are neglected.
Solution of Chapter- 05 - stresses in beam - Strength of Materials by SingerAshiqur Rahman Ziad
This document discusses stresses in beams, including flexural and shearing stresses. It provides formulas for calculating flexural stress based on the beam's moment of inertia, bending moment, and distance from the neutral axis. Several example problems are worked through applying these formulas. The document also discusses using economic beam sections that optimize the use of material by placing more area on the outer fibers where stresses are highest.
This document provides information about shear force and shear force diagrams. It defines shear force as the sum of vertical forces acting to the left or right of a beam section. A shear force diagram graphically represents the variation of shear force along the length of a beam, with ordinates showing shear force values and abscissas showing section positions. Shear force diagrams are useful analytical tools for structural design, allowing designers to determine required member sizes and materials to support loads without failure. The document also discusses sign conventions, methods for drawing shear force diagrams, practical applications, and examples of shear force diagrams for different beam types and load configurations.
This document discusses bending moments and shear forces in beams. It defines different types of beams such as simply supported beams, cantilever beams, and beams with overhangs. It also defines types of loads like concentrated loads, distributed loads, and couples. It explains how to calculate the shear force and bending moment at any cross-section of a beam and discusses relationships between loads, shear forces and bending moments. It provides examples of drawing shear force and bending moment diagrams. Finally, it discusses bending stresses in beams and bending of beams made of two materials.
Chapter 11: Stability of Equilibrium: ColumnsMonark Sutariya
1) The document discusses various buckling modes of columns including flexural, torsional-flexural, and torsional buckling. It provides examples of buckling in thin-walled tubes and prismatic members.
2) Euler buckling formulas are presented for columns with different end conditions, such as both ends pinned, one end fixed and one end pinned. The critical buckling load depends on the effective length which accounts for the end conditions.
3) Limitations of the Euler formulas and generalized formulas are discussed. The tangent modulus formula extends the elastic analysis to the inelastic range by using the tangent modulus.
PRESENTATION OF AXIAL FORCE DIAGRAM by 10.01.03.132Enamul Nasir
This presentation discusses axial force diagrams (AFDs). It defines axial force as a load applied through the center of gravity of a cross-section, producing compression or tension. An AFD graphically represents the axial loads along structural members, with tension plotted above and compression below a reference line. The presentation covers how to draw an AFD by taking cuts, making free body diagrams, and using equilibrium equations to calculate forces. It also discusses the characteristics, mathematical representation, and importance of AFDs, noting they help visualize stresses and inform structural design and modification.
Dynamic analysis of a reinforced concrete horizontal curved beam using softwareeSAT Journals
Abstract
Dynamic analysis of a reinforced concrete beam bridge, horizontally curved in plan is done using a finite element software. The
support conditions considered are simple supports. Dynamic loading in the form of moving vehicular load is taken into account
for the purpose of analysis. IRC Class AA type of vehicle is simulated on two lanes on the beam of span 31m, having a box type
cross-section. A parametric study is done varying the radius of curvature of the beam from 50 m to 250 m with the interval of 50
m to check the behavior of the beam. Various responses of the beam like bending moment, shear force, torsional moment and
deflection are calculated. The influence of a non-dimensional parameter L/R i.e. ratio of length of the beam to radius of curvature
of the beam is verified for the responses of the beam. From the results, it has been found that the responses i.e. the bending
moment, shear force, torsional moment and deflection of the beam decrease as the radius of curvature of the beam in increased.
Also, the responses of the beam increase as the L/R ratio is increased.
Keywords: Dynamic analysis, horizontally curved beam, finite element, moving vehicular moving load, Simply
Supported, Box type, parametric study, L/R ratio
The document discusses axial force and axial force diagrams (AFDs). It defines axial force as any force that directly acts on the center axis of an object, typically stretching or compression forces. An AFD is a graphical representation of the axial loads acting at each section of a structural member, plotted proportionately with signs indicating tension or compression. The document provides examples of drawing AFDs for simply supported beams, cantilever beams, and frames under different loading conditions. It also lists some common structural analysis software that can be used to draw AFDs, such as ETABS, STAAD-Pro, and SAP-2000.
The aim of the experiment is to find the flexural rigidity (EI) of a beam and compare it to the theoretical value. A beam with overhangs is loaded at the free ends and the central deflection is measured for different loads. The flexural rigidity is calculated using the measured deflection and load values and beam properties. This calculated EI is then compared to the theoretical EI calculated using the beam's cross-section dimensions and modulus of elasticity. Observing the beam's deflection under various loads allows determining its flexural rigidity and verifying beam theory calculations.
The document discusses the strut-and-tie model approach for analyzing and designing concrete structures. It provides an overview of the strut-and-tie model methodology, including key concepts such as struts, ties, nodes, and modeling techniques. Examples are given to illustrate strut-and-tie models for different structural elements like beams, slabs, corbels, and joints. Design considerations such as limiting stresses and reinforcement details are also covered.
In this section the concept of stress will be introduced, and this will be applied to components that are in a state of tension, compression, and shear. Strain measurement methods will also be briefly discussed.
This document provides an overview of basic equations for the theory of plates and shells. It discusses the state of stress and strain at a point, including defining the six independent stress and strain components. It presents the relationships between strain and displacement, and discusses the equilibrium equations relating stress and body forces. Finally, it provides the equations for both Cartesian and cylindrical coordinate systems. The key concepts covered are the fundamental equations that form the basis of plate and shell theory.
This document describes the development of an algorithm for a 16-bit Wallace tree multiplier (WTM). It begins with background on binary multipliers and discusses methods like ripple carry array and Wallace trees. The Wallace tree approach is analyzed in more detail, outlining its three main steps: partial product generation, reduction stages using adders, and final addition. The document then proposes improvements to the partial product generation step to reduce complexity from O(n2) to O(n). It also presents a scheme for clearly representing signals in the different reduction stages. Finally, the design is synthesized for an FPGA and simulation results are shown comparing the WTM to other multipliers in terms of delay, area, power-delay product,
An Unmanned Rotorcraft System with Embedded DesignIOSR Journals
This document describes the design and implementation of an embedded control system for an unmanned rotorcraft. It uses a backstepping control law with state estimation provided by an extended Kalman filter using data from a marker-based vision system and inertial measurement unit. A self-organizing map is used to select local operating regimes for modeling the nonlinear dynamics. The control algorithm was tested in a hardware-in-the-loop simulation and able to track spiral paths in 3D space with the embedded controller implemented on a Freescale MPC555 processor.
IRJET- Design of Girder using Thin Beam Walled Theory with Influence of S...IRJET Journal
This document presents a study on the design of U-shaped girder bridges using a thin beam walled theory that accounts for the influence of shear forces. It introduces a new analytical method to calculate displacements and stresses in thin-walled beams with cross-sections having one or two axes of symmetry. The method considers shear deformations using shear factors. Several examples are analyzed and show good agreement with finite element results. The theory provides a way to simplify the analysis and design of U-girder bridges.
This document discusses curved beams and provides equations for calculating stresses in curved beams. It begins by stating that beam theory can be applied to curved beams to determine stresses in shapes like crane hooks. It provides symbols for variables used in the equations. The main differences between straight and curved beams are that the neutral axis and centroid axis do not coincide for curved beams. Equations are provided to calculate strain and stress at different radii along the curved beam based on the eccentricity between the neutral and centroid axes. An example calculation for a crane hook is also shown.
Finite Element analysis -Plate ,shell skew plate S.DHARANI KUMAR
This document provides an overview of plate and shell theory and finite element analysis for plates and shells. It discusses the assumptions and applications of thin plate theory, thick plate theory, and shell theory. It also describes different types of finite elements that can be used to model plates and shells, including plate, shell, solid shell, curved shell, and degenerated shell elements. Additionally, it covers skew plates and different discretization methods that can be used for finite element analysis of skew plates.
This document summarizes a master's thesis presentation on modeling deep girders supporting shear walls. The presentation introduces various analysis techniques for deep beams, including the strut-and-tie method, finite element analysis using VecTor2, and two parameter kinematic theory. Seven test beams with varying sizes, loading eccentricities are described to compare the predictions of failure load between VecTor2 and the other methods. The results show that VecTor2 predictions match well but the other methods are unconservative. Adjusting parameters in the two parameter kinematic theory improves predictions. Size effects are demonstrated through a scaled model analysis.
Chapter 6: Pure Bending and Bending with Axial ForcesMonark Sutariya
This summary provides the key points about pure bending and bending with axial forces from the document:
1. Pure bending occurs when a beam segment is in equilibrium under bending moments alone, with examples being a cantilever loaded at the end or a beam segment between concentrated forces.
2. For beams with symmetric cross-sections, plane sections remain plane after bending according to the fundamental flexure theory. The elastic flexure formula gives the normal stress as proportional to the bending moment and the distance from the neutral axis.
3. The second moment of area, or moment of inertia, represents the beam's resistance to bending and is used to calculate maximum bending stresses. The elastic section modulus is a ratio of the moment
Estimation of Damping Derivative in Pitch of a Supersonic Delta Wing with Cur...iosrjce
In the Present paper effect of angle of incidence on Damping derivative of a delta wing with Curved
leading edges for attached shock case in Supersonic Flow has been studied. A Strip theory is used in which
strips at different span wise location are independent of each other. This combines with similitude to give a
piston theory which gives closed form solutions for damping derivatives at low to high supersonic Mach
numbers. From the results it is seen that with the increase in the Mach number, there is a progressive decrease
in the magnitude of damping derivatives for all the Mach numbers of the present studies; however, the decrease
in the magnitude is variable at different inertia level. It is seen that with the increase in the angle of attack the
damping derivative increases linearly, nevertheless, this linear behavior limit themselves for different Mach
numbers. For Mach number M = 2, this limiting value of validity is fifteen degrees, for Mach 2.5 & 3, it is
twenty five degrees, whereas, for Mach 3.5 & 4 it becomes thirty five degrees, when these stability derivatives
were considered at various pivot positions; namely at h = 0.0, 0.4, 0.6, and 1.0. After scanning the results it is
observed that with the shift of the pivot position from the leading edge to the trailing edge, the magnitude of the
damping derivatives continue to decrease throughout. Results have been obtained for supersonic flow of perfect
gases over a wide range of angle of attack and Mach number. The effect of real gas, leading edge bluntness of
the wing, shock motion, and secondary wave reflections are neglected.
Solution of Chapter- 05 - stresses in beam - Strength of Materials by SingerAshiqur Rahman Ziad
This document discusses stresses in beams, including flexural and shearing stresses. It provides formulas for calculating flexural stress based on the beam's moment of inertia, bending moment, and distance from the neutral axis. Several example problems are worked through applying these formulas. The document also discusses using economic beam sections that optimize the use of material by placing more area on the outer fibers where stresses are highest.
This document provides information about shear force and shear force diagrams. It defines shear force as the sum of vertical forces acting to the left or right of a beam section. A shear force diagram graphically represents the variation of shear force along the length of a beam, with ordinates showing shear force values and abscissas showing section positions. Shear force diagrams are useful analytical tools for structural design, allowing designers to determine required member sizes and materials to support loads without failure. The document also discusses sign conventions, methods for drawing shear force diagrams, practical applications, and examples of shear force diagrams for different beam types and load configurations.
This document discusses bending moments and shear forces in beams. It defines different types of beams such as simply supported beams, cantilever beams, and beams with overhangs. It also defines types of loads like concentrated loads, distributed loads, and couples. It explains how to calculate the shear force and bending moment at any cross-section of a beam and discusses relationships between loads, shear forces and bending moments. It provides examples of drawing shear force and bending moment diagrams. Finally, it discusses bending stresses in beams and bending of beams made of two materials.
Chapter 11: Stability of Equilibrium: ColumnsMonark Sutariya
1) The document discusses various buckling modes of columns including flexural, torsional-flexural, and torsional buckling. It provides examples of buckling in thin-walled tubes and prismatic members.
2) Euler buckling formulas are presented for columns with different end conditions, such as both ends pinned, one end fixed and one end pinned. The critical buckling load depends on the effective length which accounts for the end conditions.
3) Limitations of the Euler formulas and generalized formulas are discussed. The tangent modulus formula extends the elastic analysis to the inelastic range by using the tangent modulus.
PRESENTATION OF AXIAL FORCE DIAGRAM by 10.01.03.132Enamul Nasir
This presentation discusses axial force diagrams (AFDs). It defines axial force as a load applied through the center of gravity of a cross-section, producing compression or tension. An AFD graphically represents the axial loads along structural members, with tension plotted above and compression below a reference line. The presentation covers how to draw an AFD by taking cuts, making free body diagrams, and using equilibrium equations to calculate forces. It also discusses the characteristics, mathematical representation, and importance of AFDs, noting they help visualize stresses and inform structural design and modification.
Dynamic analysis of a reinforced concrete horizontal curved beam using softwareeSAT Journals
Abstract
Dynamic analysis of a reinforced concrete beam bridge, horizontally curved in plan is done using a finite element software. The
support conditions considered are simple supports. Dynamic loading in the form of moving vehicular load is taken into account
for the purpose of analysis. IRC Class AA type of vehicle is simulated on two lanes on the beam of span 31m, having a box type
cross-section. A parametric study is done varying the radius of curvature of the beam from 50 m to 250 m with the interval of 50
m to check the behavior of the beam. Various responses of the beam like bending moment, shear force, torsional moment and
deflection are calculated. The influence of a non-dimensional parameter L/R i.e. ratio of length of the beam to radius of curvature
of the beam is verified for the responses of the beam. From the results, it has been found that the responses i.e. the bending
moment, shear force, torsional moment and deflection of the beam decrease as the radius of curvature of the beam in increased.
Also, the responses of the beam increase as the L/R ratio is increased.
Keywords: Dynamic analysis, horizontally curved beam, finite element, moving vehicular moving load, Simply
Supported, Box type, parametric study, L/R ratio
The document discusses axial force and axial force diagrams (AFDs). It defines axial force as any force that directly acts on the center axis of an object, typically stretching or compression forces. An AFD is a graphical representation of the axial loads acting at each section of a structural member, plotted proportionately with signs indicating tension or compression. The document provides examples of drawing AFDs for simply supported beams, cantilever beams, and frames under different loading conditions. It also lists some common structural analysis software that can be used to draw AFDs, such as ETABS, STAAD-Pro, and SAP-2000.
The aim of the experiment is to find the flexural rigidity (EI) of a beam and compare it to the theoretical value. A beam with overhangs is loaded at the free ends and the central deflection is measured for different loads. The flexural rigidity is calculated using the measured deflection and load values and beam properties. This calculated EI is then compared to the theoretical EI calculated using the beam's cross-section dimensions and modulus of elasticity. Observing the beam's deflection under various loads allows determining its flexural rigidity and verifying beam theory calculations.
The document discusses the strut-and-tie model approach for analyzing and designing concrete structures. It provides an overview of the strut-and-tie model methodology, including key concepts such as struts, ties, nodes, and modeling techniques. Examples are given to illustrate strut-and-tie models for different structural elements like beams, slabs, corbels, and joints. Design considerations such as limiting stresses and reinforcement details are also covered.
In this section the concept of stress will be introduced, and this will be applied to components that are in a state of tension, compression, and shear. Strain measurement methods will also be briefly discussed.
This document provides an overview of basic equations for the theory of plates and shells. It discusses the state of stress and strain at a point, including defining the six independent stress and strain components. It presents the relationships between strain and displacement, and discusses the equilibrium equations relating stress and body forces. Finally, it provides the equations for both Cartesian and cylindrical coordinate systems. The key concepts covered are the fundamental equations that form the basis of plate and shell theory.
This document describes the development of an algorithm for a 16-bit Wallace tree multiplier (WTM). It begins with background on binary multipliers and discusses methods like ripple carry array and Wallace trees. The Wallace tree approach is analyzed in more detail, outlining its three main steps: partial product generation, reduction stages using adders, and final addition. The document then proposes improvements to the partial product generation step to reduce complexity from O(n2) to O(n). It also presents a scheme for clearly representing signals in the different reduction stages. Finally, the design is synthesized for an FPGA and simulation results are shown comparing the WTM to other multipliers in terms of delay, area, power-delay product,
An Unmanned Rotorcraft System with Embedded DesignIOSR Journals
This document describes the design and implementation of an embedded control system for an unmanned rotorcraft. It uses a backstepping control law with state estimation provided by an extended Kalman filter using data from a marker-based vision system and inertial measurement unit. A self-organizing map is used to select local operating regimes for modeling the nonlinear dynamics. The control algorithm was tested in a hardware-in-the-loop simulation and able to track spiral paths in 3D space with the embedded controller implemented on a Freescale MPC555 processor.
PageRank algorithm and its variations: A Survey reportIOSR Journals
This document provides an overview and comparison of PageRank algorithms. It begins with a brief history of PageRank, developed by Larry Page and Sergey Brin as part of the Google search engine. It then discusses variants like Weighted PageRank and PageRank based on Visits of Links (VOL), which incorporate additional factors like link popularity and user visit data. The document also gives a basic introduction to web mining concepts and categorizes web mining into content, structure, and usage types. It concludes with a comparison of the original PageRank algorithm and its variations.
IOSR Journal of Humanities and Social Science is an International Journal edited by International Organization of Scientific Research (IOSR).The Journal provides a common forum where all aspects of humanities and social sciences are presented. IOSR-JHSS publishes original papers, review papers, conceptual framework, analytical and simulation models, case studies, empirical research, technical notes etc.
VHDL Implementation of DSDV Ad-Hoc Routing ProtocolIOSR Journals
Abstract: An Ad-Hoc network deals with the collection of mobile nodes without any centralized structure. This
can be well suited for environment where changes are frequent and establishment of infrastructure is not very
cost effective. In short it can turn the dream of ‘anytime anywhere’ into reality[1]. Here we deal with the VHDL
implementation of DSDV(destination sequenced distance vector) routing protocol to fulfill these requirements of
Ad-hoc network more effectively.
Keywords: Adhoc, DSDV,FPGA,VHDL,Routing
Design Issues for Search Engines and Web Crawlers: A ReviewIOSR Journals
This document provides a review of design issues for search engines and web crawlers. It discusses how search engines use web crawlers to collect web documents for storage and indexing from the growing World Wide Web. The three main parts of a search engine are the crawler, indexer, and query engine. Crawler-based search engines create listings automatically using algorithms while human-powered directories rely on human organization. Designing efficient search engines and crawlers faces challenges from the diversity of web documents and changing user behaviors. Web crawlers prioritize URLs to download pages and extract new links to update search engine databases.
Analysis of Interfacial Microsstructure of Post Weld Heat Treated Dissimilar ...IOSR Journals
This document analyzes the interfacial microstructure of a post weld heat treated dissimilar metal weld between type 316LN austenitic stainless steel and C-steel. Single V-groove butt joints were welded using Inconel 182 welding consumables. The joints were post weld heat treated at temperatures between 898K to 973K for 1 hour. Microstructural analysis found that in the as-welded condition, the weld/C-steel interface consisted mostly of martensite or ferrite and carbides. Post weld heat treatment resulted in the precipitation of carbides at the interface. Heat treating at 973K led to recrystallized grains in the C-
This document discusses developing an inventory model for India's public distribution system (PDS) using binary particle swarm optimization (BPSO) to minimize costs. The PDS involves procuring rice from mills and distributing it through multiple levels - from central warehouses run by the Food Corporation of India (FCI) to district warehouses (MLSPs) and then to local fair price shops (FPSs). The current system has high costs for procurement, inventory, reordering and transportation. The proposed model uses BPSO to optimize procurement quantities at each level and estimate costs, with the aim of reducing total variable costs by around 2 crore rupees compared to the existing system.
A Public-Key Cryptosystem Based On Discrete Logarithm Problem over Finite Fie...IOSR Journals
This document presents a public-key cryptosystem based on the discrete logarithm problem over finite fields. The security of the system relies on the difficulty of finding discrete logarithms in the function field Fp^n. The system uses a primitive polynomial f(x) of degree n over the finite field Fp as the base polynomial. The public key consists of f(x) and another primitive polynomial fk(x) with a root that is the kth power of the root of f(x), where k is the secret key. Encryption involves multiplying the message polynomial by a term related to fk(x) or f(x) depending on the secret key. Decryption uses the secret key to recover the message
Scale-Free Networks to Search in Unstructured Peer-To-Peer NetworksIOSR Journals
This document discusses using scale-free networks to improve search efficiency in unstructured peer-to-peer networks. It proposes the EQUATOR architecture, which creates an overlay network topology based on the scale-free Barabasi-Albert model. Simulation results show that EQUATOR achieves good lookup performance comparable to the ideal Barabasi-Albert network, with low message overhead even under node churn. The scale-free topology allows random walks to efficiently locate resources by directing searches to high-degree "hub" nodes with greater knowledge of the network.
Corporate Policy Governance in Secure MD5 Data Changes and Multi Hand Adminis...IOSR Journals
1) The document discusses a proposed approach for collaborative policy administration to securely manage changes to data and allow for multi-user administration.
2) It involves generating public and private keys using multi-user administration, where one member generates a public key and administrators generate private keys. These keys are used to verify and authorize any major data definition language changes.
3) If an intruder tries to modify content, an alert message is sent to administrators via SMTP. This approach aims to prevent malicious modifications while allowing flexible multi-user administration of database systems and applications.
Periodic Table Gets Crowded In Year 2011.IOSR Journals
Abstract: Year 2011, has been specially important for teachers and students of chemistry, as after a gap of about 14 years at least five new elements were named and included in the periodic table. All these elements are synthetic and radioactive and some were actually made in 1999, but got their name and status by IUPAC, in July 2011. The total number of elements now in periodic table is 112, and scientists are trying their best to prepare elements with atomic numbers 118, 119 and 120 as well.
On The Origin of Electromagnetic Waves from Lightning DischargesIOSR Journals
Interaction of up going ion beam forming current flow in the pre-ionized stepped leader plasma and
the way, how the kinetic energy of the beam particles is converted into electromagnetic energy have been
discussed. The ion beam interaction with the plasma wave modes in the stepped leader channel produces
perturbations in the return stroke current flow and changes its uniformity and becomes non-uniform. In the
present study, the return current is taken to be deeply modulated at a given modulation frequency, and
considered that it behaves like an antenna for electromagnetic radiation. In this paper the total amount of
energy associated with return stroke is given to electromagnetic waves is estimated.
This document discusses bio-CNG (compressed biogas) as a transportation fuel alternative to fossil fuels. It begins by introducing the problems of increasing fossil fuel usage and outlines biogas production methods from waste sources. The main processes for cleaning biogas - including water scrubbing, pressure swing adsorption, amine adsorption and membrane permeation - are then summarized. The paper also covers converting cleaned biogas into bio-CNG and its storage. Key advantages of bio-CNG are highlighted such as reduced greenhouse gas emissions compared to diesel and potential cost savings versus petrol and diesel. The conclusion promotes bio-CNG as a viable replacement for fossil fuels that could support more sustainable living.
This document discusses characterization of countably normed nuclear spaces. It begins by defining countably normed spaces and providing an example using Kothe sequence spaces. It then proves that a nuclear Frechet space is countably normed if and only if it is isomorphic to a subspace of a nuclear Kothe space with a continuous norm. This nuclear Kothe space can be chosen to be a quotient of the space (s). The proof constructs a Kothe space K(a) and shows that the original space can be continuously embedded as a subspace of K(a).
Performance Analysis of Positive Output Super-Lift Re-Lift Luo Converter With...IOSR Journals
This document presents a simulation study comparing PI and neural network (neuro) controllers for regulating the output voltage of a positive output super-lift re-lift Luo converter. The converter circuit and operating principles are described. Simulation results using MATLAB show the performance of each controller under startup conditions and in response to changes in input voltage and load. The neuro controller provided faster response times, while the PI controller produced less overshoot. Tables compare the performance of the PI controller under different operating conditions.
Design and Implementation of New Encryption algorithm to Enhance Performance...IOSR Journals
This document summarizes a research paper that proposes a new encryption algorithm to improve performance parameters. The algorithm is divided into two phases. Phase 1 involves reversing, swapping, circularly shifting bits of the plaintext and XORing with the key. Phase 2 divides the output into blocks, then recombines the left bits of each block. The paper analyzes avalanche effect and execution time of the proposed algorithm compared to existing algorithms to evaluate its performance. The results show better performance than existing algorithms.
This document summarizes a study on traffic noise pollution in the city of Anand, India. The study found that the main sources of noise pollution are loudhailers and vehicles. However, religious noises affect the female population more than the male population. Effects of noise pollution include psychological impacts like depression and sleep disturbance, as well as physiological impacts like hearing loss. Most respondents complain to authorities to stop noise, though few contact the police. Public education campaigns are seen as the best approach to control noise pollution by respondents. Government and non-governmental organizations can play an important role in addressing this issue.
IOSR Journal of Humanities and Social Science is an International Journal edited by International Organization of Scientific Research (IOSR).The Journal provides a common forum where all aspects of humanities and social sciences are presented. IOSR-JHSS publishes original papers, review papers, conceptual framework, analytical and simulation models, case studies, empirical research, technical notes etc.
Determination of load transfer in reinforced concrete solid slabs by finite e...IOSR Journals
This document analyzes load transfer in reinforced concrete solid slabs using finite element analysis. It models two types of slabs in SAP2000: 1) slabs with pin supports on all four edges and 2) slabs with pin supports at corners and beams along edges. For type 1, stresses are higher in the short direction but still significant in the long direction, showing load is transferred two-way. For type 2, stresses in the short direction increase with stiffer beams while stresses in the long direction decrease. The analysis concludes all concrete solid slabs behave as two-way slabs, transferring load in both directions regardless of dimensions or support conditions.
This document presents an analysis of orthotropic reinforced concrete slabs with long side openings using the affine theorem and yield line method. Ten possible yield line failure patterns are considered for slabs with continuous, simply supported, two long sides continuous, and two short sides continuous edge conditions. Virtual work equations are formulated for each failure pattern. Numerical examples are provided to illustrate the governing failure patterns for different slab geometries and support conditions. The affine theorem is used to transform orthotropic slab properties into equivalent isotropic properties to simplify the analysis.
Limit States Solution to CSCS Orthotropic Thin Rectangular Plate Carrying Tra...ijtsrd
The analysis of thin rectangular orthotropic plate with two opposite edges clamped and the other two opposite edges simply supported CSCS , carrying transverse loads was investigated in this study. The Ritz total potential energy functional was used. The minimization of the total potential energy functional produces the expression for the coefficient of deflection. The coefficient of deflection was used to obtain equation for the maximum lateral load of an orthotropic thin rectangular plate based on allowable deflection. Also, equation for the maximum lateral load of an orthotropic thin rectangular plate based on allowable stress was developed.Developed stiffness coefficients were substituted in the lateral load equations to obtain the maximum lateral load values for a CSCS plate. Numerical examples using permissible deflection of 10mm and yield strength of 250MPa, plate thickness varying from 5mm to 12.5 mm with 0.5mm intervals were done to determine the maximum lateral loads corresponding to an orthotropic thin rectangular CSCS plate carrying transverse loads when n1 = Ey Ex = 0.7 and n2 = G Ex = 0.41 for aspect ratios b a of 1.0, 1.25 and 1.50. Bertram D. I. | Okere C. E. | Ibearugbulem O. M. | Nwokorobia G. C. "Limit States Solution to CSCS Orthotropic Thin Rectangular Plate Carrying Transverse Loads" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-6 , October 2021, URL: https://www.ijtsrd.com/papers/ijtsrd47566.pdf Paper URL : https://www.ijtsrd.com/engineering/civil-engineering/47566/limit-states-solution-to-cscs-orthotropic-thin-rectangular-plate-carrying-transverse-loads/bertram-d-i
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
Chapter 5 strip.pptx STRIP METHOD FOR SLABtekalign24
The strip method is a plastic analysis method for reinforced concrete slabs where the slab is divided into strips. Equilibrium equations are used to determine moment distributions within the strips that satisfy boundary conditions. Reinforcement is then designed for each strip's moment. Several examples are provided of dividing a slab into strips and determining moment distributions, including for slabs with different support conditions. Discontinuity lines are used to define the strip regions and load distributions between strips can be adjusted to achieve more realistic moment variations.
This document summarizes a lecture on flat slab design and analysis. It discusses key topics such as:
1. Definitions of flat slabs and their components like column strips and middle strips.
2. Methods of analyzing flat slabs including numerical methods and manual methods like the method of substitutive beams.
3. Design considerations for flat slabs including steel distribution above columns, welded mesh reinforcement, loading schemes, and punching shear design.
4. Different types of shear reinforcement that can be used at column heads like links, cages, and bent-up bars.
The document summarizes the design procedures for slab systems according to the ACI 318 Code, including:
1) The direct design method and equivalent frame method for determining moments at critical sections.
2) Distributing the total design moment between positive and negative moments.
3) Distributing moments laterally between column strips, middle strips, and beams.
4) A 5-step basic design procedure involving determining moments, distributing moments, sizing reinforcement, and designing beams if present.
A Closed-Form Elastic Solution For Stresses And Displacements Around TunnelsAndrea Porter
This document presents a closed-form elastic solution for stresses and displacements around tunnels using complex potential functions and conformal mapping. The solution models a homogeneous, isotropic, linear elastic geomaterial with an initially homogeneous stress state that is disturbed by the excavation of a tunnel. The tunnel can have a variety of cross-sectional shapes like semi-circular or double-arch. The analytical solution provides stress and displacement distributions that compare well with numerical modeling, providing insight into variable influences for preliminary tunnel design assessments.
Deflections in PT elements pt structure for all pt slabs in civil industry.pdfvijayvijay327286
The document discusses factors that influence deflections in prestressed concrete members and methods for predicting deflections. It covers:
- Short term deflections of unracked members which can be estimated using Mohr's theorem.
- How the tendon profile affects deflections, providing formulas for straight, trapezoidal, parabolic, and other tendon types.
- Downward deflections due to self-weight and imposed loads that can be calculated using formulas provided.
- Estimation of long-term deflections accounting for creep and shrinkage effects, discussing various methods like those of Busemann, McHenry, and Neville.
Analysis and Design of Rectangular and L-Shaped Columns Subjected to Axial Lo...Nitin Dahiya
Next to rectangular and circular columns, L-shaped columns may be the most frequently encountered reinforced concrete columns, since they can be used as a corner column in framed structures. The behaviour of irregular shaped reinforced concrete columns has been a constant concern for a structural engineer, to design a safe and economic structure in modern buildings and bridge piers. L-shaped reinforced concrete column subjected to biaxial bending and axial compression is a common design problem. Axial load capacity and Moment capacity of rectangular and L-shaped reinforced concrete columns have been done in this work. A computer program has been developed to obtain the axial load capacity and moment capacity of reinforced concrete columns of rectangular and L-shaped.
This document summarizes a study that uses modal pushover analysis (MPA) to estimate the inelastic seismic response of a multi-span concrete bridge. MPA involves performing separate pushover analyses for each vibration mode of the bridge using its mass-weighted modal shape as the lateral load pattern. The peak responses from each mode are then combined using the square root of the sum of squares method to estimate the total seismic demand on the bridge. The study models a 13-span concrete bridge in the SAP2000 nonlinear analysis program and applies MPA to investigate its performance under lateral seismic forces.
A Modal Pushover Analysis on Multi-Span Bridge to Estimate Inelastic Seismic ...IOSR Journals
This document summarizes a study that evaluates the use of modal pushover analysis (MPA) to estimate the inelastic seismic response of a multi-span concrete bridge. MPA accounts for higher mode effects by performing separate pushover analyses for each mode using its respective modal load pattern. Peak modal responses are then combined using the square root of the sum of squares method. The study models a 13-span bridge and applies MPA and nonlinear time history analysis to compare responses. MPA is found to provide a good estimate of deck displacements and plastic hinge rotations, with differences generally within 10% compared to time history analysis results. MPA is concluded to improve accuracy over conventional pushover analysis for estimating seismic demands on long-
This document discusses bending and constructing shear and moment diagrams for beams. It defines beams as long, straight members that support loads applied perpendicular to their axis. Beams can be simply supported, cantilevered, or overhanging. Shear and moment diagrams show the variation of shear and bending moment along a beam under applied loads. The document establishes sign conventions and provides examples of drawing shear and moment diagrams for various loaded beams through a graphical method.
A COMPARATIVE STUDY OF VARIOUS METHODS TO EVALUATE IMPEDANCE FUNCTION FOR SHA...Samirsinh Parmar
Impedance function, Foundation Vibration, dynamic soil-structure interaction, Barkan, Dominguez, Dobry and Gazetas for evaluation of impedance functions for various modes of vibration of shallow foundation
ANALYTICAL BENDING ANALYSIS OF A CIRCULAR SANDWICH PLATE UNDER DISTRIBUTED LOADijmech
In this paper, bending analysis of a circular sandwich plate under distributed load with simply supported and clamped boundary conditions is investigated. First, the governing equations of the circular sandwich plate are obtained and they are solved using the Bessel functions. Then in order to validate the correctness of analytical results, numerical finite element method is used and its results are presented in the forms of
contours and graphs. The results indicate that under distributed load, maximum deflection happens at 0.3
of outside radius, away from centre, and minimum deflection occurs at the outer edge of the circular sandwich plate. The results from analytical and numerical methods are compared and it shows that analytical method provides an acceptable accuracy.
This document discusses foundation design and soil-structure interaction. It begins by introducing elastic foundation theory and its applications. It then discusses the governing equations for beams and plates on elastic foundations, including the Winkler and two-parameter elastic foundation models. It evaluates the spring constant in Winkler's soil model using plate load tests and discusses Poisson's ratio of soil.
This document discusses foundation design and soil-structure interaction. It begins by introducing elastic foundation models, which represent the soil as springs or elastic layers. These include the Winkler, Filonenko-Borodich, Hetenyi, and Pasternak models. The document then presents the governing equations for beams and plates on elastic foundations. It discusses determining soil reaction and evaluating the spring constant using plate load tests. The spring constant, or modulus of subgrade reaction, represents the soil's elastic properties.
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This document provides a technical review of secure banking using RSA and AES encryption methodologies. It discusses how RSA and AES are commonly used encryption standards for secure data transmission between ATMs and bank servers. The document first provides background on ATM security measures and risks of attacks. It then reviews related work analyzing encryption techniques. The document proposes using a one-time password in addition to a PIN for ATM authentication. It concludes that implementing encryption standards like RSA and AES can make transactions more secure and build trust in online banking.
This document analyzes the performance of various modulation schemes for achieving energy efficient communication over fading channels in wireless sensor networks. It finds that for long transmission distances, low-order modulations like BPSK are optimal due to their lower SNR requirements. However, as transmission distance decreases, higher-order modulations like 16-QAM and 64-QAM become more optimal since they can transmit more bits per symbol, outweighing their higher SNR needs. Simulations show lifetime extensions up to 550% are possible in short-range networks by using higher-order modulations instead of just BPSK. The optimal modulation depends on transmission distance and balancing the energy used by electronic components versus power amplifiers.
This document provides a review of mobility management techniques in vehicular ad hoc networks (VANETs). It discusses three modes of communication in VANETs: vehicle-to-infrastructure (V2I), vehicle-to-vehicle (V2V), and hybrid vehicle (HV) communication. For each communication mode, different mobility management schemes are required due to their unique characteristics. The document also discusses mobility management challenges in VANETs and outlines some open research issues in improving mobility management for seamless communication in these dynamic networks.
This document provides a review of different techniques for segmenting brain MRI images to detect tumors. It compares the K-means and Fuzzy C-means clustering algorithms. K-means is an exclusive clustering algorithm that groups data points into distinct clusters, while Fuzzy C-means is an overlapping clustering algorithm that allows data points to belong to multiple clusters. The document finds that Fuzzy C-means requires more time for brain tumor detection compared to other methods like hierarchical clustering or K-means. It also reviews related work applying these clustering algorithms to segment brain MRI images.
1) The document simulates and compares the performance of AODV and DSDV routing protocols in a mobile ad hoc network under three conditions: when users are fixed, when users move towards the base station, and when users move away from the base station.
2) The results show that both protocols have higher packet delivery and lower packet loss when users are either fixed or moving towards the base station, since signal strength is better in those scenarios. Performance degrades when users move away from the base station due to weaker signals.
3) AODV generally has better performance than DSDV, with higher throughput and packet delivery rates observed across the different user mobility conditions.
This document describes the design and implementation of 4-bit QPSK and 256-bit QAM modulation techniques using MATLAB. It compares the two techniques based on SNR, BER, and efficiency. The key steps of implementing each technique in MATLAB are outlined, including generating random bits, modulation, adding noise, and measuring BER. Simulation results show scatter plots and eye diagrams of the modulated signals. A table compares the results, showing that 256-bit QAM provides better performance than 4-bit QPSK. The document concludes that QAM modulation is more effective for digital transmission systems.
The document proposes a hybrid technique using Anisotropic Scale Invariant Feature Transform (A-SIFT) and Robust Ensemble Support Vector Machine (RESVM) to accurately identify faces in images. A-SIFT improves upon traditional SIFT by applying anisotropic scaling to extract richer directional keypoints. Keypoints are processed with RESVM and hypothesis testing to increase accuracy above 95% by repeatedly reprocessing images until the threshold is met. The technique was tested on similar and different facial images and achieved better results than SIFT in retrieval time and reduced keypoints.
This document studies the effects of dielectric superstrate thickness on microstrip patch antenna parameters. Three types of probes-fed patch antennas (rectangular, circular, and square) were designed to operate at 2.4 GHz using Arlondiclad 880 substrate. The antennas were tested with and without an Arlondiclad 880 superstrate of varying thicknesses. It was found that adding a superstrate slightly degraded performance by lowering the resonant frequency and increasing return loss and VSWR, while decreasing bandwidth and gain. Specifically, increasing the superstrate thickness or dielectric constant resulted in greater changes to the antenna parameters.
This document describes a wireless environment monitoring system that utilizes soil energy as a sustainable power source for wireless sensors. The system uses a microbial fuel cell to generate electricity from the microbial activity in soil. Two microbial fuel cells were created using different soil types and various additives to produce different current and voltage outputs. An electronic circuit was designed on a printed circuit board with components like a microcontroller and ZigBee transceiver. Sensors for temperature and humidity were connected to the circuit to monitor the environment wirelessly. The system provides a low-cost way to power remote sensors without needing battery replacement and avoids the high costs of wiring a power source.
1) The document proposes a model for a frequency tunable inverted-F antenna that uses ferrite material.
2) The resonant frequency of the antenna can be significantly shifted from 2.41GHz to 3.15GHz, a 31% shift, by increasing the static magnetic field placed on the ferrite material.
3) Altering the permeability of the ferrite allows tuning of the antenna's resonant frequency without changing the physical dimensions, providing flexibility to operate over a wide frequency range.
This document summarizes a research paper that presents a speech enhancement method using stationary wavelet transform. The method first classifies speech into voiced, unvoiced, and silence regions based on short-time energy. It then applies different thresholding techniques to the wavelet coefficients of each region - modified hard thresholding for voiced speech, semi-soft thresholding for unvoiced speech, and setting coefficients to zero for silence. Experimental results using speech from the TIMIT database corrupted with white Gaussian noise at various SNR levels show improved performance over other popular denoising methods.
This document reviews the design of an energy-optimized wireless sensor node that encrypts data for transmission. It discusses how sensing schemes that group nodes into clusters and transmit aggregated data can reduce energy consumption compared to individual node transmissions. The proposed node design calculates the minimum transmission power needed based on received signal strength and uses a periodic sleep/wake cycle to optimize energy when not sensing or transmitting. It aims to encrypt data at both the node and network level to further optimize energy usage for wireless communication.
This document discusses group consumption modes. It analyzes factors that impact group consumption, including external environmental factors like technological developments enabling new forms of online and offline interactions, as well as internal motivational factors at both the group and individual level. The document then proposes that group consumption modes can be divided into four types based on two dimensions: vertical (group relationship intensity) and horizontal (consumption action period). These four types are instrument-oriented, information-oriented, enjoyment-oriented, and relationship-oriented consumption modes. Finally, the document notes that consumption modes are dynamic and can evolve over time.
The document summarizes a study of different microstrip patch antenna configurations with slotted ground planes. Three antenna designs were proposed and their performance evaluated through simulation: a conventional square patch, an elliptical patch, and a star-shaped patch. All antennas were mounted on an FR4 substrate. The effects of adding different slot patterns to the ground plane on resonance frequency, bandwidth, gain and efficiency were analyzed parametrically. Key findings were that reshaping the patch and adding slots increased bandwidth and shifted resonance frequency. The elliptical and star patches in particular performed better than the conventional design. Three antenna configurations were selected for fabrication and measurement based on the simulations: a conventional patch with a slot under the patch, an elliptical patch with slots
1) The document describes a study conducted to improve call drop rates in a GSM network through RF optimization.
2) Drive testing was performed before and after optimization using TEMS software to record network parameters like RxLevel, RxQuality, and events.
3) Analysis found call drops were occurring due to issues like handover failures between sectors, interference from adjacent channels, and overshooting due to antenna tilt.
4) Corrective actions taken included defining neighbors between sectors, adjusting frequencies to reduce interference, and lowering the mechanical tilt of an antenna.
5) Post-optimization drive testing showed improvements in RxLevel, RxQuality, and a reduction in dropped calls.
This document describes the design of an intelligent autonomous wheeled robot that uses RF transmission for communication. The robot has two modes - automatic mode where it can make its own decisions, and user control mode where a user can control it remotely. It is designed using a microcontroller and can perform tasks like object recognition using computer vision and color detection in MATLAB, as well as wall painting using pneumatic systems. The robot's movement is controlled by DC motors and it uses sensors like ultrasonic sensors and gas sensors to navigate autonomously. RF transmission allows communication between the robot and a remote control unit. The overall aim is to develop a low-cost robotic system for industrial applications like material handling.
This document reviews cryptography techniques to secure the Ad-hoc On-Demand Distance Vector (AODV) routing protocol in mobile ad-hoc networks. It discusses various types of attacks on AODV like impersonation, denial of service, eavesdropping, black hole attacks, wormhole attacks, and Sybil attacks. It then proposes using the RC6 cryptography algorithm to secure AODV by encrypting data packets and detecting and removing malicious nodes launching black hole attacks. Simulation results show that after applying RC6, the packet delivery ratio and throughput of AODV increase while delay decreases, improving the security and performance of the network under attack.
The document describes a proposed modification to the conventional Booth multiplier that aims to increase its speed by applying concepts from Vedic mathematics. Specifically, it utilizes the Urdhva Tiryakbhyam formula to generate all partial products concurrently rather than sequentially. The proposed 8x8 bit multiplier was coded in VHDL, simulated, and found to have a path delay 44.35% lower than a conventional Booth multiplier, demonstrating its potential for higher speed.
This document discusses image deblurring techniques. It begins by introducing image restoration and focusing on image deblurring. It then discusses challenges with image deblurring being an ill-posed problem. It reviews existing approaches to screen image deconvolution including estimating point spread functions and iteratively estimating blur kernels and sharp images. The document also discusses handling spatially variant blur and summarizes the relationship between the proposed method and previous work for different blur types. It proposes using color filters in the aperture to exploit parallax cues for segmentation and blur estimation. Finally, it proposes moving the image sensor circularly during exposure to prevent high frequency attenuation from motion blur.
This document describes modeling an adaptive controller for an aircraft roll control system using PID, fuzzy-PID, and genetic algorithm. It begins by introducing the aircraft roll control system and motivation for developing an adaptive controller to minimize errors from noisy analog sensor signals. It then provides the mathematical model of aircraft roll dynamics and describes modeling the real-time flight control system in MATLAB/Simulink. The document evaluates PID, fuzzy-PID, and PID-GA (genetic algorithm) controllers for aircraft roll control and finds that the PID-GA controller delivers the best performance.
AI 101: An Introduction to the Basics and Impact of Artificial IntelligenceIndexBug
Imagine a world where machines not only perform tasks but also learn, adapt, and make decisions. This is the promise of Artificial Intelligence (AI), a technology that's not just enhancing our lives but revolutionizing entire industries.
5th LF Energy Power Grid Model Meet-up SlidesDanBrown980551
5th Power Grid Model Meet-up
It is with great pleasure that we extend to you an invitation to the 5th Power Grid Model Meet-up, scheduled for 6th June 2024. This event will adopt a hybrid format, allowing participants to join us either through an online Mircosoft Teams session or in person at TU/e located at Den Dolech 2, Eindhoven, Netherlands. The meet-up will be hosted by Eindhoven University of Technology (TU/e), a research university specializing in engineering science & technology.
Power Grid Model
The global energy transition is placing new and unprecedented demands on Distribution System Operators (DSOs). Alongside upgrades to grid capacity, processes such as digitization, capacity optimization, and congestion management are becoming vital for delivering reliable services.
Power Grid Model is an open source project from Linux Foundation Energy and provides a calculation engine that is increasingly essential for DSOs. It offers a standards-based foundation enabling real-time power systems analysis, simulations of electrical power grids, and sophisticated what-if analysis. In addition, it enables in-depth studies and analysis of the electrical power grid’s behavior and performance. This comprehensive model incorporates essential factors such as power generation capacity, electrical losses, voltage levels, power flows, and system stability.
Power Grid Model is currently being applied in a wide variety of use cases, including grid planning, expansion, reliability, and congestion studies. It can also help in analyzing the impact of renewable energy integration, assessing the effects of disturbances or faults, and developing strategies for grid control and optimization.
What to expect
For the upcoming meetup we are organizing, we have an exciting lineup of activities planned:
-Insightful presentations covering two practical applications of the Power Grid Model.
-An update on the latest advancements in Power Grid -Model technology during the first and second quarters of 2024.
-An interactive brainstorming session to discuss and propose new feature requests.
-An opportunity to connect with fellow Power Grid Model enthusiasts and users.
Fueling AI with Great Data with Airbyte WebinarZilliz
This talk will focus on how to collect data from a variety of sources, leveraging this data for RAG and other GenAI use cases, and finally charting your course to productionalization.
Webinar: Designing a schema for a Data WarehouseFederico Razzoli
Are you new to data warehouses (DWH)? Do you need to check whether your data warehouse follows the best practices for a good design? In both cases, this webinar is for you.
A data warehouse is a central relational database that contains all measurements about a business or an organisation. This data comes from a variety of heterogeneous data sources, which includes databases of any type that back the applications used by the company, data files exported by some applications, or APIs provided by internal or external services.
But designing a data warehouse correctly is a hard task, which requires gathering information about the business processes that need to be analysed in the first place. These processes must be translated into so-called star schemas, which means, denormalised databases where each table represents a dimension or facts.
We will discuss these topics:
- How to gather information about a business;
- Understanding dictionaries and how to identify business entities;
- Dimensions and facts;
- Setting a table granularity;
- Types of facts;
- Types of dimensions;
- Snowflakes and how to avoid them;
- Expanding existing dimensions and facts.
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?Speck&Tech
ABSTRACT: A prima vista, un mattoncino Lego e la backdoor XZ potrebbero avere in comune il fatto di essere entrambi blocchi di costruzione, o dipendenze di progetti creativi e software. La realtà è che un mattoncino Lego e il caso della backdoor XZ hanno molto di più di tutto ciò in comune.
Partecipate alla presentazione per immergervi in una storia di interoperabilità, standard e formati aperti, per poi discutere del ruolo importante che i contributori hanno in una comunità open source sostenibile.
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HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-und-domino-lizenzkostenreduzierung-in-der-welt-von-dlau/
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1. IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE)
e-ISSN: 2278-1684,p-ISSN: 2320-334X, Volume 12, Issue 1 Ver. III (Jan- Feb. 2015), PP 106-111
www.iosrjournals.org
DOI: 10.9790/1684-1213106111 www.iosrjournals.org 106 | Page
Closed-Form Expressions for Moments of Two-Way Slabs under
Concentrated Loads
Magdy Israel Salama1
1
(Civil Engineering Dept., Faculty of Engineering, Kafrelsheikh University, Egypt)
Abstract: The analysis of rectangular two-way slabs subjected to concentrated load uniformly distributed over
defined area after dispersion down in the two directions to the reinforcement is a practically important case. As
presented by Egyptian code for design and construction of concrete structures ECCS 203-2007, the analysis of
this problem can be performed by using the elastic analysis or by using an approximate method which depends
on the distribution of the concentrated load in the two directions by the ratio of the long length and short length
of the rectangular slab. Significant differences between the results of these methods must take our attention. An
alternative approximate method for determining the bending moments of the slab under study in the two
directions is investigated in this paper based on the elastic analysis. Two closed-form expressions were obtained
which describe the relation between the bending moments and all factors that affect it (the span ratio, the
dimensions ratio of the loaded area and the ratio between the short span to the parallel length of the loaded
area). Comparisons between the straining actions in the two directions resulting from the present analysis and
these from the existing approximate method of the ECCS 203-2007 with those obtained by Pigweed’s theory and
those obtained by finite element method are given also in this paper.
Keywords: Slab, two ways, concentrated load, bending moment, elastic analysis.
I. Introduction
When a slab is supported other than on two opposite sides only, the precise amount and distribution of
the load taken by each support, and consequently the magnitude of the bending moments on the slab, are not
easily calculated if assumptions resembling practical conditions are made. Therefore approximate analyses are
generally used. The method applicable in any particular case depends on the shape of the panel of slab, the
condition of restraint at supports, and the type of load.
Two basic methods [1-3] are commonly used to analyse slabs spanning in two directions. These are the
theory of plates which is based on elastic analysis under service loads, and yield-line theory in which the
behaviour of the slab as collapse approaches is considered. A less well-known alternative to the latter is
Hillerborg’s strips method [2], [4].
For rectangular panel carrying uniform load simply supported along all four edges and which no
provision is made at the corners to prevent them lifting or to resist torsion, the Grashof and Rankine method [4]
is applicable. When the corners of the slab are prevented from lifting and torsional restraint is provided, the
simple Grashof and Rankine method is inappropriate. A more exact elastic analysis, assuming a value of
Poisson’s ratio, is performed and the resulting service bending moments at mid-span is given in tables for
simplicity as used in most international codes [5-6].
When a slab carries a load concentrated on a part only of the slab, such as a wheel load on the deck of a
bridge, the contact area of the load is first extended by dispersion through the thickness of the slab and the
flooring (if any). If the slab supported on two opposite sides only, the width of slab carrying the load may be
assumed and the total concentrated load is then divided by this width to give the load carried on a unit width of
slab for purpose of calculating the bending moments. For slabs spanning in two directions carrying a load
uniformly distributed over a defined area on a part only of the slab, Pigweed’s theory [4] gives the bending
moments on simply supported panel along all four sides with restrained corners by curves but the Egyptian code
ECCS 203-2007 [7] presents an approximate method which depends on the distribution of the load in the two
directions.
In this paper, our attention is, firstly, focussed to the significant differences between the results of these
methods and the comparison between these results and the finite element method. The results obtained from
Pigweed’s theory agreed with the results obtained by finite element method with good accuracy while the
difference between the results of the ECCS 203-2007 and the finite element method is not acceptable.
Also in this paper, closed-form expressions are obtained using a theoretical analysis based on the
theory of plates to determine the bending moments in the two directions directly as a function of the variables. A
comparison of the results with finite element method [8] is given in this thesis.
2. Closed-form expressions for moments of two-way slabs under concentrated loads
DOI: 10.9790/1684-1213106111 www.iosrjournals.org 107 | Page
II. Model and Assumptions
Consider a rectangular plate simply supported along all four edges as shown in Fig. 1, carrying a
concentrated load (P) uniformly distributed over a defined area with the following assumptions
- There is no deformation in the middle plane of the plate. This plane remains neutral during bending.
- The corners of the slab are prevented from lifting and torsional restraint is provided.
b
a
y
x
b/2b/2
v
u
Fig. 1: Simply Supported Rectangular Slab Subjected to a Concentrated Load Uniformly Distributed
Over a Defined Area
III. Review Of Egyptian Code (ECCS 203-2007) And Pigweed’s Theory
Egyptian Code (ECCS 203-2007)
As introduced in clause (6-2-1-5) of the Egyptian code for design and construction of concrete
structures ECCS 203-2007, the concentrated load is considered to disperse down to a rectangular area with sides
u and v which is determined from
tctutctv 22 21 and (1)
Where t1 and t2 are the contact area of the concentrated load in directions perpendicular to and parallel
to the main reinforcement, c is the flooring thickness and t is the slab thickness.
The concentrated load is distributed by an inverse ratio of the slab lengths according to these relations
ba
a
PP
ba
b
PP ba
and
(2)
To calculate the bending moment in direction (a), Pa is considered distributed on a length A of the
effective span a and in a breadth B in the direction perpendicular to direction )a(. in the contrary, the bending
moment in direction, Pb is considered distributed on a length B of the effective span b and in a breadth A in the
direction perpendicular to direction )b(, where,
]2[4.04.0 baavBauA and (3)
Pigweed’s theory
The concentrated load is considered to disperse down to a rectangular area with sides u and v which are
determined from
dctudctv 2222 21 and
(4)
The positive bending moments on unit width of slab are given by these expressions
)(and)( 4444 xyyyxx PMPM
(5)
Where values of x4 and y4 obtained by curves for the appropriate value of the spans ratio (r = b/a)
corresponding to the ratios u/a and v/b.
IV. Method Of Analysis And Theoretical Equations
The bending moments of the slab spanning in two directions carrying concentrated load uniformly
distributed over a rectangular area is obtained in [1] using Navier’s method by the following expressions:
)1)(()1(
sin4
ln2
8
a
a
P
Mx (6)
3. Closed-form expressions for moments of two-way slabs under concentrated loads
DOI: 10.9790/1684-1213106111 www.iosrjournals.org 108 | Page
)1)(()1(
sin4
ln2
8
a
a
P
M y
(7)
In which,
,,sin
cosh
12
1,sin
cosh
43 2
1
2
2
1
a
bm
a
m
a
b
a
me
m
m mm m
m
221111
,tan
11
tan,tan
11
tan vu
u
v
kk
kk
kk
kk
k
and
In order to derive simple expressions to determine bending moments, we let ( = a/2 ) where
the maximum
bending moments and by some arrangements, the bending moment in the short direction Mx can be put in the
following form
)()()()()1(
1
4
ln2
8 2
1
k
kP
Mx (8)
Where uak 1
Putting,
2where
2
1
cosh
mm
m
e (9)
And using the known series
1
1
1
x
m
mx
e
e (10)
The terms and can be expressed as
1
1
8383
1
/
r
m
abm
e
e
(11)
1
1
8181
1
/
r
m
abm
e
rer
(12)
The terms and are wholly independent of dimensions of u and v of loaded area where these are
function in spans ratio r only. In the contrary, the values of factors and are depending only on the ratio v/u.
Substituting Eqs. (11-12) into Eq. (6), the terms (), (, (), and () can be put in simple
expressions as
),1(
1
8
2)(),1(
1
8
4)( r
e
r
e rr
k
kk
k 11
tan
2
)(
1
tan2)(
and (13)
Substituting Eq. (13) into Eq. (8), and assuming Poisson’s ratio =0.20 which is recommended by ECCS 203-
2007 and other international codes as BS 8110 [6], the bending moment Mx can be expressed as
k
kk
ke
r
kk
P
M rx
1
tan4.0tan
2
1
4.66.9
4.4
1
4
ln4.2
8
11
2
1
(14)
4. Closed-form expressions for moments of two-way slabs under concentrated loads
DOI: 10.9790/1684-1213106111 www.iosrjournals.org 109 | Page
Putting, )tan2/(
1
tan 11
k
k
(15)
Eq. (14) can be expressed in simple expression as follows
5
tan)
2
4.0(
1
4.66.9
4.4
1
4
ln4.2
8
1
2
1
k
k
k
k
e
r
k
kP
M rx (16)
In a similar manner, we get the bending moment in the long direction My as follows
kk
k
k
e
r
k
kP
M ry
1
2
1
tan)
4.0
2(
1
4.66.9
8.2
1
4
ln4.2
8
(17)
If t1 = t2 (i.e. u=v), k=1
Eqs. (16), (17) can be expressed in the simple forms
r
x ekPM 64.2
1 75.009.0ln*1.0
(18)
r
y ekPM 0.2
1 145.0026.0ln*1.0
(19)
V. Illustrative Examples
To describe the problem considered in this paper and to clarify applying of the obtained equations in
the present work, three numerical examples are given which are solved by the approximate method introduced
in ECCS 203-2007, Pigweed’s theory and the present work. Also, the three examples are solved by Finite
element method [8] to check the accuracy of each one of the previous methods,
Example 1: A square slab of 3.0 m side simply supported on all four sides, subjected to a concentrated load 200
kN symmetrically placed at the centre of the panel. Contact area being 75 mm by 600 mm. the slab thickness is
200 mm (d=175 mm) and the flooring is 50 mm thickness.
Using ECCS 203-2007: the sides of the loaded area after the load disperses down to the reinforcement (u, v)
are:
u = 75+2x50+200=375 mm, and v = 600+2x50+200 = 900 mm
The loads distributed in each direction are:
Pa=200x3/(3+3)=100 kN, and Pb=100 kN
Pa is distributed on a length A of the effective span a and in a breadth B in the direction perpendicular to
direction a where,
A = 0.375+0.4x3.00 = 1.575 m, and B = 0.9+0.4x3[2-3/3] =2.10 m
Thus, the service bending moments per metre width are:
Mx = 26.34 kN.m/m
My = 30.95 kN.m/m
Using Pigweed’s theory:
The sides of the loaded area (u, v) are
u = 75+2x50+2x175 = 525 mm, and v = 600+2x50+2x175 = 1050 mm
r =3.0/3.0 =1.0
From the appropriate curve (r =1.0) and corresponding to u/a = 0.525/3.0 = 0.175, and v/b =1.05/3=0.35 the
coefficient x4 and y4 are obtained as
x4 = 0.16 and y4 = 0.13
Thus,
Mx = 200(0.16+0.2x0.13) = 37.20 kN.m/m,
My = 200(0.16x0.2+0.13) = 32.40 kN.m/m
Using present work:
The sides of the loaded area (u, v) are:
u = 75+2x50+2x175 = 525 mm, and v = 600+2x50+2x175 = 1050 mm
r =3.0/3.0 =1.0, k = v/u =1.05/.525 = 2.0, and k1= a/u = 3.0/0.525 = 5.714
Substituting in Eqs. (16), (17)
5. Closed-form expressions for moments of two-way slabs under concentrated loads
DOI: 10.9790/1684-1213106111 www.iosrjournals.org 110 | Page
5
)2(
)2(tan)
)2(
2
)2(4.0(
1
)1(4.66.9
4.4
)2(1
)714.5(4
ln4.2
8
)200( 1
)1(2
e
M x = 35.11 kN.m/m
)2()2(tan)
)2(
4.0
)2(2(
1
)1(4.66.9
8.2
)2(1
)714.5(4
ln4.2
8
)200( 1
)1(2 e
M y = 32.07 kN.m/m
Using F.E.M.:
Mx = 36.64 kN.m/m,
My =32.22 kN.m/m
Example 2: Consider a rectangular slab which is 3.75 m long by 3.0 m wide simply supported on all four sides, subjected to
the same load and assuming the same assumptions given in the previous example.
Using ECCS 203-2007:
u = 75+2x50+200=375 mm, and v = 600+2x50+200 = 900 mm
Pa= 200x3.75/(3+3.75) =111.11 kN, and Pb = 88.89 kN
A = 0.375+0.4x3.00 = 1.575 m, and B = 0.9+0.4x3[2-3/3.75] =2.34 m
Thus,
Mx = 26.26 kN.m/m
My = 25.82 kN.m/m
Using Pigweed’s theory:
u = 75+2x50+2x175=525 mm, v =600+2x50+2x175=1050 mm and r =3.75/3.0 =1.25
From the appropriate curve (r =1.25) and corresponding to u/a=0.525/3.0 = 0.175, and v/b =1.05/3 = 0.35, the coefficient x4
and y4 are obtained as x4= 0.19 and y4=0.12
Thus,
Mx = 200(0.19+0.2x0.12) = 42.80 kN.m/m,
My = 200(0.19x0.2+0.12) = 31.60 kN.m/m
Using present work:
r = 3.75/3.0 =1.25, k = v/u = 1.05/.525=2.0, and k1= a/u =3.0/0.525 = 5.714
Substituting in Eqs.(16-17)
Mx = 40.23 kN.m/m,
My = 30.78 kN.m/m
Using F.E.M.:
Mx = 40.74 kN.m/m,
My = 31.48 kN.m/m
Example 3: Consider a rectangular slab which is 5.64 m long by 4.0 m wide simply supported on all four sides, subjected to
the concentrated load 200 kN symmetrically placed at the centre of the panel. Contact area being 300 mm by 300 mm. the
slab thickness is 200 mm (d=175 mm) and the flooring is 50 mm thickness.
.
Using ECCS 203-2007:
u = v = 300+2x50+200=600 mm,
Pa= 200x5.64/(4+5.64) =117 kN, and Pb = 83 kN
A = 0.6+0.4x4.00 = 2.2 m, and B = 0.6+0.4x4[2-4/5.64] =2.665 m
Thus,
Mx = 31.83 kN.m/m
My = 40.63 kN.m/m
Using Pigweed’s theory:
u = v = 300+2x50+2x175=750 mm, and r =5.64/4.0 =1.41
From the appropriate curve (r =1.41) and corresponding to u/a=0.75/4.0 = 0.188, and v/b =0.75/5.64 = 0.133, the coefficient
x4 and y4 are obtained as x4= 0.21 and y4=0.155
Thus,
Mx = 200(0.21+0.2x0.155) = 48.20 kN.m/m,
My = 200(0.21x0.2+0.155) = 39.40 kN.m/m
Using present work:
r = 5.64/4.0 =1.41, k = v/u =1.0, and k1= a/u =4.0/0.75 = 5.33
Substituting in Eqs.(18-19)
41.1*64.2
75.009.033.5ln*1.0
ePMx = 47.85 kN.m/m
6. Closed-form expressions for moments of two-way slabs under concentrated loads
DOI: 10.9790/1684-1213106111 www.iosrjournals.org 111 | Page
41.1*0.2
145.0026.033.5ln*1.0
ePM y = 40.40 kN.m/m
Using F.E.M.:
Mx = 46.72 kN.m/m,
My = 39.87 kN.m/m
VI. Comparison Of The Results
From the results of the previous three examples, table 1 shows the comparison of the bending moments obtained
by Eqs. (16-17) of the present work (P.W.), the approximate method given in clause (6-2-1-5) of the ECCS 203-2007 and
Pigweed’s theory with the results obtained by elastic analysis as programmed by finite element method [8].
Table1. Comparison of Mx and My obtained by P. W., ECCS 203-2007 and Pigweed’s theory with
F.E.M.[8]
Example F.E.M P.W. % Diff. ECCS. 203 % Diff.
Pigweed’s
theory
% Diff.
Example 1
Mx 36.640 35.110 -4.18% 26.340 -28.11% 37.200 +1.53%
b=3.00 m
a=3.00 m
My 32.220 32.070 -0.47% 30.950 -3.94% 32.400 +0.56%
P=200 kN
Example 2
Mx 40.740 40.230 -1.25% 26.260 -35.54% 42.800 +5.06%
b=3.75 m
a=3.00 m
My 31.480 30.780 -2.22% 25.820 -17.98% 31.600 +0.38%
P=200 kN
Example 3
Mx 46.720 47.850 +2.42% 31.830 -31.87% 48.200 +3.17%
b=5.64 m
a=4.00 m
My 39.870 40.400 +1.33% 40.630 +1.90% 39.400 -1.18%
P=200 kN
It can be noticed that although the present equations are simple, it gave more accurate results when compared
with the solution by finite element method. Then, the present equations can be rather used by the designer
engineers.
VII. Conclusion
In this paper, a theoretical analysis based on the elastic analysis is developed to determine the service bending
moments of the slab spanning in two directions carrying a concentrated load uniformly distributed over a defined area on a
part only of the slab. From results and examples carried out in this paper, the following conclusions are drawn
1. Significant differences between the results of the approximate method introduced in clause (6-2-1-5) of the Egyptian
code for design and construction of concrete structures ECCS 203-2007 and the elastic solution e.g. by finite element
method. Also, significant differences between the results of ECCS 203-2007 and that obtained by other methods as the
Pigweed’s theory. These differences are large enough to consider the approximate method introduced in ECCS 203-
2007 to be unsafe.
2. The present analysis describes the relation between the bending moments and all the factors that affect it which are the
span ratio, the dimensions ratio of the loaded area and the ratio between the short span to the parallel length of the
loaded area (represented by factors r, k and k1 respectively).
The great advantage of the present analysis is the determination of the bending moments by using hand
calculations only (without the use of curves or tables). Three numerical examples demonstrated the use of the obtained
equations for slabs under study and comparing the results with Pigweed’s theory [4,6] as well as the finite element method,
as programmed in SAP2000 [8].
Finally, the present analysis provides relatively simple two expressions from which the bending moments for slabs under
study can be easily calculated. These equations can be of great help for design purposes. The comparison of the results with
the finite element method confirms the accuracy of such equations.
References
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Sons, Inc, Hoboken, New Jersey.
[3]. Richard, J.Y. And Shanmugan, N.E. (2005), “Handbook Of Structural Engineering”, CRC Press.
[4]. Reynolds, C.E., Steedman, J.C. And Threlfall, A. J. (2008), “Reynolds's Reinforced Concrete Designer's Handbook”, Taylor &
Francis Group, London And New York, Eleventh Edition.
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95)” American Code Institute, Farmington Hills, Michigan.
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