The document discusses statically determinate and indeterminate structures. A determinate structure is one where reactions and internal forces can be determined through static equilibrium equations alone. An indeterminate structure has more unknown reactions or internal forces than equations. The degree of static indeterminacy is the number of redundant unknowns. Continuous beams are internally determinate but can be externally indeterminate. The example beam has a degree of indeterminacy of 1.
Static Indeterminacy and Kinematic IndeterminacyDarshil Vekaria
This ppt is more useful for Civil Engineering students.
I have prepared this ppt during my college days as a part of semester evaluation . Hope this will help to current civil students for their ppt presentations and in many more activities as a part of their semester assessments.
I have prepared this ppt as per the syllabus concerned in the particular topic of the subject, so one can directly use it just by editing their names.
The document provides information about statically determinate and indeterminate structures. It begins with defining a determinate structure as one where the reactions and internal forces can be found using equilibrium equations alone. Simply supported beams are given as an example. An indeterminate structure is then defined as one where the equations of equilibrium are not sufficient to determine all forces. The document further discusses degrees of static indeterminacy and provides examples of determinate and indeterminate structures.
L3 degree of redundancy of plane framesDr. OmPrakash
This document discusses the degree of redundancy in plane frames and grids. It provides equations to calculate the degree of static indeterminacy for rigid and pin-jointed plane frames as well as hybrid frames containing both rigid and pin joints. The degree of static indeterminacy is equal to the number of redundant equations of equilibrium and depends on the number of members (m), joints (j), and external reaction components (R). Examples are given to demonstrate calculating the degree of redundancy for different plane frame and grid structures.
This document discusses the concepts of stability, determinacy, and consistent deformations as they relate to analyzing structures. It defines a stable structure as one that remains stable under any conceivable loading system. Determinacy refers to whether the internal forces in a structure can be fully determined from the available equilibrium equations. A structure is considered statically indeterminate if additional equations are needed beyond equilibrium to solve for all internal forces. The document outlines methods for assessing the external, internal, and total stability and determinacy of structures like trusses and frames through properties such as the number of members, joints, and reactions. Several examples are provided and worked through to demonstrate the application of these analytical methods.
The document discusses statically indeterminate structures, which have more unknown reactive stresses than equations of static equilibrium. This leads to external and internal redundancy. The degree of static indeterminacy (T) is the sum of the external indeterminacy (E), which depends on support conditions, and internal indeterminacy (I), which depends on additional members. A continuous beam has E=3 due to its redundant supports, while a pin-jointed frame can become internally indeterminate if it has more members than required for its geometry.
Lec.2 statically determinate structures & statically indeterminate struct...Muthanna Abbu
The student will learn the determination of internal forces in different structures and the
kind of forces distribution due to external & internal effects .He will also learn about the
structures deformation due to these effects .
determinate and indeterminate structuresvempatishiva
This topic I am uploading here contains some basic topics in structural analysis which includes types of supports, reactions for different support conditions, determinate and indeterminate structures, static and kinematic indeterminacy,external and internal static indeterminacy, kinematic indeterminacy for beams, frames, trusses.
need of finding indeterminacy, different methods available to formulate equations to solve unknowns.
Static Indeterminacy and Kinematic IndeterminacyDarshil Vekaria
This ppt is more useful for Civil Engineering students.
I have prepared this ppt during my college days as a part of semester evaluation . Hope this will help to current civil students for their ppt presentations and in many more activities as a part of their semester assessments.
I have prepared this ppt as per the syllabus concerned in the particular topic of the subject, so one can directly use it just by editing their names.
The document provides information about statically determinate and indeterminate structures. It begins with defining a determinate structure as one where the reactions and internal forces can be found using equilibrium equations alone. Simply supported beams are given as an example. An indeterminate structure is then defined as one where the equations of equilibrium are not sufficient to determine all forces. The document further discusses degrees of static indeterminacy and provides examples of determinate and indeterminate structures.
L3 degree of redundancy of plane framesDr. OmPrakash
This document discusses the degree of redundancy in plane frames and grids. It provides equations to calculate the degree of static indeterminacy for rigid and pin-jointed plane frames as well as hybrid frames containing both rigid and pin joints. The degree of static indeterminacy is equal to the number of redundant equations of equilibrium and depends on the number of members (m), joints (j), and external reaction components (R). Examples are given to demonstrate calculating the degree of redundancy for different plane frame and grid structures.
This document discusses the concepts of stability, determinacy, and consistent deformations as they relate to analyzing structures. It defines a stable structure as one that remains stable under any conceivable loading system. Determinacy refers to whether the internal forces in a structure can be fully determined from the available equilibrium equations. A structure is considered statically indeterminate if additional equations are needed beyond equilibrium to solve for all internal forces. The document outlines methods for assessing the external, internal, and total stability and determinacy of structures like trusses and frames through properties such as the number of members, joints, and reactions. Several examples are provided and worked through to demonstrate the application of these analytical methods.
The document discusses statically indeterminate structures, which have more unknown reactive stresses than equations of static equilibrium. This leads to external and internal redundancy. The degree of static indeterminacy (T) is the sum of the external indeterminacy (E), which depends on support conditions, and internal indeterminacy (I), which depends on additional members. A continuous beam has E=3 due to its redundant supports, while a pin-jointed frame can become internally indeterminate if it has more members than required for its geometry.
Lec.2 statically determinate structures & statically indeterminate struct...Muthanna Abbu
The student will learn the determination of internal forces in different structures and the
kind of forces distribution due to external & internal effects .He will also learn about the
structures deformation due to these effects .
determinate and indeterminate structuresvempatishiva
This topic I am uploading here contains some basic topics in structural analysis which includes types of supports, reactions for different support conditions, determinate and indeterminate structures, static and kinematic indeterminacy,external and internal static indeterminacy, kinematic indeterminacy for beams, frames, trusses.
need of finding indeterminacy, different methods available to formulate equations to solve unknowns.
solving statically indeterminate stucture using stiffnes methodSyed Md Soikot
This document is a presentation on the stiffness method for structural analysis. It was presented by ABU SYED MD. TARIN to the Department of Civil Engineering at Ahsanullah University of Science & Technology on December 4, 2013. The presentation introduces the stiffness method and how it can be used to analyze determinate and indeterminate structures. It also discusses how to apply the stiffness method to analyze trusses, beams, frames and other structural elements.
This document discusses the degree of redundancy for space trusses and space frames. It defines that for a space truss, the degree of static indeterminacy is given by DS = m + R - 3j, where m is the number of members, R is the number of reactions, and j is the number of joints. For a rigid-jointed space frame, the degree of static indeterminacy is DS = 6m + R - 6j. The document also defines kinematic indeterminacy as the number of additional equations needed to determine all independent displacement components at the joints, and provides formulas to calculate kinematic indeterminacy for different types of trusses and frames.
This document discusses statically determinate and indeterminate structures. A statically determinate structure can be analyzed using equilibrium equations alone, while an indeterminate structure has more unknowns than equations. A structure is determinate if the number of reactions r equals 3 times the number of parts n, and indeterminate if r is greater than 3n. Examples are given of determinate and indeterminate structures. Indeterminate structures can be made determinate by removing redundant supports or adding hinges. The advantages of indeterminate structures are that they allow for lighter, more rigid designs with increased safety through redundancy.
This document discusses engineering mechanics and frames/trusses. It defines frames as built structures made of members like angles and channels that resist external loads. Trusses are frames where all members form triangles connected by frictionless pins. Frames are classified as determinate or indeterminate based on whether equilibrium equations can analyze them. Trusses are also classified based on the number of members, including perfect, imperfect deficient and redundant frames. The document also covers support conditions, forces in frames, and methods of analyzing frames and trusses.
The document discusses the degree of redundancy in space trusses and frames. It defines that space trusses have members subjected only to axial forces. The degree of static indeterminacy for space trusses is calculated as the number of members plus the number of independent equations minus three times the number of joints. For rigid-jointed space frames, each member carries six internal forces/moments so the degree of static indeterminacy is six times the number of members plus the number of independent equations minus six times the number of joints. The degree of kinematic indeterminacy, or degrees of freedom, is the number of additional equations needed to determine all independent displacements at the joints. Formulas are provided to calculate k
This document provides an introduction to the moment distribution method for analyzing statically indeterminate structures. It defines key terms like fixed end moments, member stiffness factors, joint stiffness factors, and distribution factors. The method is described as a repetitive process that begins by assuming each joint is fixed, then unlocking and locking joints in succession to distribute moments until joint rotations are balanced. Examples are provided to illustrate how to calculate member stiffness factors based on geometry and applied loads, and how to determine distribution factors by considering a rigid joint connected to members and satisfying equilibrium. The goal of the method is to directly calculate end moments through successive approximations rather than first solving for displacements.
L 2 degree of redundancy of plane trussDr. OmPrakash
This document discusses plane trusses and their degree of redundancy. It defines a truss as a structure composed of links or bars connected by frictionless pins at joints that divide the structure into triangles. A plane truss has all members in one plane, while a space truss exists in three dimensions. The document explains that trusses are statically determinate if the number of members (m) equals 2 times the number of joints (j) minus the number of equilibrium equations (r). It classifies trusses as perfect, deficient, or redundant based on this relationship. Perfect trusses are determinate and stable, while deficient trusses are always unstable and redundant trusses are stable but statically
Solving indeterminate structures by using stiffness method. 10.01.03.130Juwairiyah Jahan
This document discusses solving statically indeterminate structures using the direct stiffness method. It begins with an introduction that defines statically indeterminate structures as those that cannot be analyzed using static equilibrium equations alone, consisting of more members and/or supports than needed for static determinacy.
It then explains that the direct stiffness method is a matrix method that uses member stiffness relations to compute member forces and displacements. It involves adding restraints to make the structure determinate, applying loads to calculate forces, applying displacements one at a time to determine corresponding forces, writing equilibrium equations, and solving the matrix equation to obtain displacements and subsequently other reactions.
The benefits of the direct stiffness method are that it can effectively and
This document discusses the stability and determinacy conditions for frames. It provides the essential formulas: a frame is stable if r < 3n and unstable if r ≥ 3n; a frame is determinate if r = 3n and indeterminate if r > 3n. The degree of indeterminacy I is calculated as r - 3n. Several example frames are then analyzed by calculating n, r, 3n, and determining stability, determinacy, and degree of indeterminacy based on the formulas.
Static and Kinematic Indeterminacy of Structure.Pritesh Parmar
The document discusses static and kinematic indeterminacy of structures. It defines different types of supports for 2D and 3D structures including fixed support, hinged/pinned support, roller support, and their properties. It also discusses internal joints like internal hinge, internal roller, and internal link. The document explains concepts of static indeterminacy, kinematic indeterminacy, and degree of freedom for different types of structures.
This document provides information about the Structural Analysis-I course CEE-311. It includes details about the course instructor, textbook references, evaluation criteria, and topics that will be covered such as truss analysis, influence lines, and structural stability and determinacy. Key concepts that will be discussed are the definitions of what constitutes a structure, and structural analysis which is a detailed evaluation to ensure structural failure will not occur under allowable deformations. Common structural forms such as beams, columns, frames, trusses, plates and shells as well as composite structures will also be examined.
This document provides an overview of structural analysis presented by Hassan Abba Musa. It defines structural analysis as predicting the response of a structure to various loads. Loads are classified as dead loads from the structure's weight and imposed loads like wind and seismic forces. Structural analysis ensures equilibrium, displacement compatibility, and force-displacement relationships. Different structural elements, analysis techniques, and matrix operations are also introduced.
Types of support system,Beam classification,methods for the analysis of indeterminate structures,analysis of indeterminate structures,Formula for Determination of Degree of Static Indeterminacy(DOSI),DOSI,Determine DOSI for the structure.
Chapter 2-analysis of statically determinate structuresISET NABEUL
This chapter discusses the analysis of statically determinate structures. It introduces idealized structures and different types of supports including pin, fixed, and roller supports. Examples are provided to demonstrate determining the reactions of statically determinate beams and trusses by applying the equations of equilibrium. The chapter also discusses the concepts of determinacy, stability, and classifying structures as determinate or indeterminate based on the number of members and unknown forces.
Structural engineering & softwatre application ce406Saqib Imran
The document discusses the matrix method of structural analysis. It introduces matrix algebra and how it can be used to analyze structures. There are two main approaches discussed - the stiffness matrix method and flexibility matrix method. The stiffness matrix method determines displacements at joints by considering member stiffness. The flexibility matrix method determines redundant forces by considering flexibility properties. Several examples are provided to illustrate analyzing beams and trusses using the force method and displacement method within the matrix framework. Formulas are given for defining member and structure stiffness/flexibility matrices and solving for displacements and forces.
Engi6705 structural analysis-classnotes5 (1)humayoun shah
This document discusses analysis of indeterminate structures using the force method. It introduces the force method and method of consistent deformation. For beams, it explains how to make the structure determinate by releasing redundant supports or moments, apply unit loads to determine deformations, and apply compatibility conditions to solve for redundant forces. For trusses and multiple redundancies, it describes a similar process of making the structure determinate, applying unit loads, and setting up compatibility equations. Finally, it notes temperature changes and fabrication errors can be analyzed in the same way.
This document discusses truss structures and their analysis. It defines trusses and describes common types of trusses like simple, compound, and complex trusses. It explains how trusses are modeled as ideal structures where members only experience axial forces. Two methods for analyzing trusses are presented: the method of joints, which uses equilibrium at the joints, and the method of sections, which uses equilibrium of cutting sections. Concepts like determinacy, stability, and redundant members are covered. Truss analysis allows determining member forces and whether a truss is determinate or indeterminate.
This document discusses structural analysis methods for statically indeterminate structures. It defines key terms like degree of static indeterminacy, internal and external redundancy, and methods for analyzing indeterminate structures. Specific methods discussed include the flexibility matrix method, consistent deformation method, and unit load method. Examples of statically indeterminate beams and frames are also provided.
Truss is a framework, typically consisting of rafters, posts, and struts, supporting a roof, bridge, or other structure.
a truss is a structure that "consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object"
This document provides an introduction to the theory of structures course. It defines what a structure is and explains that structures carry loads, transfer loads to other components, and keep the structure in static and dynamic equilibrium. The document distinguishes between statically determinate and indeterminate structures. It provides examples of each and explains how to calculate the degree of static indeterminacy. Key concepts covered include external and internal stability, and how to determine the degree of redundancy for beams.
This document provides information about structural analysis, including:
1. It defines statically determinate and indeterminate structures, and gives examples of each. Determinate structures can be fully analyzed using equilibrium equations alone, while indeterminate structures require additional information.
2. It discusses the degree of static indeterminacy, which is defined as the number of unknown forces exceeding the number of equilibrium equations.
3. It provides formulas to calculate the degree of static indeterminacy for different structural types like beams, trusses, frames, grids, and spatial structures.
4. It also discusses kinematic indeterminacy, or the degree of freedom of a structure, which is the number of
solving statically indeterminate stucture using stiffnes methodSyed Md Soikot
This document is a presentation on the stiffness method for structural analysis. It was presented by ABU SYED MD. TARIN to the Department of Civil Engineering at Ahsanullah University of Science & Technology on December 4, 2013. The presentation introduces the stiffness method and how it can be used to analyze determinate and indeterminate structures. It also discusses how to apply the stiffness method to analyze trusses, beams, frames and other structural elements.
This document discusses the degree of redundancy for space trusses and space frames. It defines that for a space truss, the degree of static indeterminacy is given by DS = m + R - 3j, where m is the number of members, R is the number of reactions, and j is the number of joints. For a rigid-jointed space frame, the degree of static indeterminacy is DS = 6m + R - 6j. The document also defines kinematic indeterminacy as the number of additional equations needed to determine all independent displacement components at the joints, and provides formulas to calculate kinematic indeterminacy for different types of trusses and frames.
This document discusses statically determinate and indeterminate structures. A statically determinate structure can be analyzed using equilibrium equations alone, while an indeterminate structure has more unknowns than equations. A structure is determinate if the number of reactions r equals 3 times the number of parts n, and indeterminate if r is greater than 3n. Examples are given of determinate and indeterminate structures. Indeterminate structures can be made determinate by removing redundant supports or adding hinges. The advantages of indeterminate structures are that they allow for lighter, more rigid designs with increased safety through redundancy.
This document discusses engineering mechanics and frames/trusses. It defines frames as built structures made of members like angles and channels that resist external loads. Trusses are frames where all members form triangles connected by frictionless pins. Frames are classified as determinate or indeterminate based on whether equilibrium equations can analyze them. Trusses are also classified based on the number of members, including perfect, imperfect deficient and redundant frames. The document also covers support conditions, forces in frames, and methods of analyzing frames and trusses.
The document discusses the degree of redundancy in space trusses and frames. It defines that space trusses have members subjected only to axial forces. The degree of static indeterminacy for space trusses is calculated as the number of members plus the number of independent equations minus three times the number of joints. For rigid-jointed space frames, each member carries six internal forces/moments so the degree of static indeterminacy is six times the number of members plus the number of independent equations minus six times the number of joints. The degree of kinematic indeterminacy, or degrees of freedom, is the number of additional equations needed to determine all independent displacements at the joints. Formulas are provided to calculate k
This document provides an introduction to the moment distribution method for analyzing statically indeterminate structures. It defines key terms like fixed end moments, member stiffness factors, joint stiffness factors, and distribution factors. The method is described as a repetitive process that begins by assuming each joint is fixed, then unlocking and locking joints in succession to distribute moments until joint rotations are balanced. Examples are provided to illustrate how to calculate member stiffness factors based on geometry and applied loads, and how to determine distribution factors by considering a rigid joint connected to members and satisfying equilibrium. The goal of the method is to directly calculate end moments through successive approximations rather than first solving for displacements.
L 2 degree of redundancy of plane trussDr. OmPrakash
This document discusses plane trusses and their degree of redundancy. It defines a truss as a structure composed of links or bars connected by frictionless pins at joints that divide the structure into triangles. A plane truss has all members in one plane, while a space truss exists in three dimensions. The document explains that trusses are statically determinate if the number of members (m) equals 2 times the number of joints (j) minus the number of equilibrium equations (r). It classifies trusses as perfect, deficient, or redundant based on this relationship. Perfect trusses are determinate and stable, while deficient trusses are always unstable and redundant trusses are stable but statically
Solving indeterminate structures by using stiffness method. 10.01.03.130Juwairiyah Jahan
This document discusses solving statically indeterminate structures using the direct stiffness method. It begins with an introduction that defines statically indeterminate structures as those that cannot be analyzed using static equilibrium equations alone, consisting of more members and/or supports than needed for static determinacy.
It then explains that the direct stiffness method is a matrix method that uses member stiffness relations to compute member forces and displacements. It involves adding restraints to make the structure determinate, applying loads to calculate forces, applying displacements one at a time to determine corresponding forces, writing equilibrium equations, and solving the matrix equation to obtain displacements and subsequently other reactions.
The benefits of the direct stiffness method are that it can effectively and
This document discusses the stability and determinacy conditions for frames. It provides the essential formulas: a frame is stable if r < 3n and unstable if r ≥ 3n; a frame is determinate if r = 3n and indeterminate if r > 3n. The degree of indeterminacy I is calculated as r - 3n. Several example frames are then analyzed by calculating n, r, 3n, and determining stability, determinacy, and degree of indeterminacy based on the formulas.
Static and Kinematic Indeterminacy of Structure.Pritesh Parmar
The document discusses static and kinematic indeterminacy of structures. It defines different types of supports for 2D and 3D structures including fixed support, hinged/pinned support, roller support, and their properties. It also discusses internal joints like internal hinge, internal roller, and internal link. The document explains concepts of static indeterminacy, kinematic indeterminacy, and degree of freedom for different types of structures.
This document provides information about the Structural Analysis-I course CEE-311. It includes details about the course instructor, textbook references, evaluation criteria, and topics that will be covered such as truss analysis, influence lines, and structural stability and determinacy. Key concepts that will be discussed are the definitions of what constitutes a structure, and structural analysis which is a detailed evaluation to ensure structural failure will not occur under allowable deformations. Common structural forms such as beams, columns, frames, trusses, plates and shells as well as composite structures will also be examined.
This document provides an overview of structural analysis presented by Hassan Abba Musa. It defines structural analysis as predicting the response of a structure to various loads. Loads are classified as dead loads from the structure's weight and imposed loads like wind and seismic forces. Structural analysis ensures equilibrium, displacement compatibility, and force-displacement relationships. Different structural elements, analysis techniques, and matrix operations are also introduced.
Types of support system,Beam classification,methods for the analysis of indeterminate structures,analysis of indeterminate structures,Formula for Determination of Degree of Static Indeterminacy(DOSI),DOSI,Determine DOSI for the structure.
Chapter 2-analysis of statically determinate structuresISET NABEUL
This chapter discusses the analysis of statically determinate structures. It introduces idealized structures and different types of supports including pin, fixed, and roller supports. Examples are provided to demonstrate determining the reactions of statically determinate beams and trusses by applying the equations of equilibrium. The chapter also discusses the concepts of determinacy, stability, and classifying structures as determinate or indeterminate based on the number of members and unknown forces.
Structural engineering & softwatre application ce406Saqib Imran
The document discusses the matrix method of structural analysis. It introduces matrix algebra and how it can be used to analyze structures. There are two main approaches discussed - the stiffness matrix method and flexibility matrix method. The stiffness matrix method determines displacements at joints by considering member stiffness. The flexibility matrix method determines redundant forces by considering flexibility properties. Several examples are provided to illustrate analyzing beams and trusses using the force method and displacement method within the matrix framework. Formulas are given for defining member and structure stiffness/flexibility matrices and solving for displacements and forces.
Engi6705 structural analysis-classnotes5 (1)humayoun shah
This document discusses analysis of indeterminate structures using the force method. It introduces the force method and method of consistent deformation. For beams, it explains how to make the structure determinate by releasing redundant supports or moments, apply unit loads to determine deformations, and apply compatibility conditions to solve for redundant forces. For trusses and multiple redundancies, it describes a similar process of making the structure determinate, applying unit loads, and setting up compatibility equations. Finally, it notes temperature changes and fabrication errors can be analyzed in the same way.
This document discusses truss structures and their analysis. It defines trusses and describes common types of trusses like simple, compound, and complex trusses. It explains how trusses are modeled as ideal structures where members only experience axial forces. Two methods for analyzing trusses are presented: the method of joints, which uses equilibrium at the joints, and the method of sections, which uses equilibrium of cutting sections. Concepts like determinacy, stability, and redundant members are covered. Truss analysis allows determining member forces and whether a truss is determinate or indeterminate.
This document discusses structural analysis methods for statically indeterminate structures. It defines key terms like degree of static indeterminacy, internal and external redundancy, and methods for analyzing indeterminate structures. Specific methods discussed include the flexibility matrix method, consistent deformation method, and unit load method. Examples of statically indeterminate beams and frames are also provided.
Truss is a framework, typically consisting of rafters, posts, and struts, supporting a roof, bridge, or other structure.
a truss is a structure that "consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object"
This document provides an introduction to the theory of structures course. It defines what a structure is and explains that structures carry loads, transfer loads to other components, and keep the structure in static and dynamic equilibrium. The document distinguishes between statically determinate and indeterminate structures. It provides examples of each and explains how to calculate the degree of static indeterminacy. Key concepts covered include external and internal stability, and how to determine the degree of redundancy for beams.
This document provides information about structural analysis, including:
1. It defines statically determinate and indeterminate structures, and gives examples of each. Determinate structures can be fully analyzed using equilibrium equations alone, while indeterminate structures require additional information.
2. It discusses the degree of static indeterminacy, which is defined as the number of unknown forces exceeding the number of equilibrium equations.
3. It provides formulas to calculate the degree of static indeterminacy for different structural types like beams, trusses, frames, grids, and spatial structures.
4. It also discusses kinematic indeterminacy, or the degree of freedom of a structure, which is the number of
1. There are two types of structures: mass structures which resist loads through their weight, and framed structures which resist loads through their geometry.
2. Framed structures are made of basic elements like rods, beams, columns, plates, and slabs. Plane frames have all members in one plane, while space frames have members in three dimensions.
3. Structures are designed to resist bending moments, shear forces, deflections, torsional stresses, and axial stresses which are evaluated at critical sections through structural analysis. Member dimensions are then determined through design based on these stresses.
01 - Introduction to Statically Indeterminate Structures.pptxJoshuaBuluran1
The support reactions and internal forces of statically determinate structures can be determined from the equations of equilibrium.
the equilibrium equations alone are not sufficient for determining the reactions and internal forces of such structures and must be supplemented by additional relationships based on the geometry of deformation of structures.
Compatibility conditions, ensure that the continuity of the displacements is maintained throughout the structure and that the structure’s various parts fit together.
Regardless of whether a structure is statically determinate or indeterminate, its complete analysis requires the use of three types of relationships:
Equilibrium Equations
Compatibility Conditions
Member force-deformation relations
In the analysis of indeterminate structures, it is necessary to solve the equilibrium equations in conjunction with the compatibility conditions of the structure to determine its response.
The resulting system of equations containing only one type of unknowns is then solved for the unknown forces or displacements, which are then substituted into the fundamental relationships to determine the remaining response of the structure
Force and displacement methods are exact because they satisfy the equilibrium and compatibility of the structure.
The preliminary designs of indeterminate structures are often based on the result of the approximate analysis.
Internal forces are estimated by making certain assumptions about the deformations or the distribution of forces
Statically indeterminate structures have more supports or members than required for static stability
The excess reactions and internal forces of indeterminate structure are referred as Redundants.
The number of redundants is termed as degree of indeterminacy.
The support reactions and internal forces of statically determinate structures can be determined from the equations of equilibrium.
the equilibrium equations alone are not sufficient for determining the reactions and internal forces of such structures and must be supplemented by additional relationships based on the geometry of deformation of structures.
Compatibility conditions, ensure that the continuity of the displacements is maintained throughout the structure and that the structure’s various parts fit together.
Regardless of whether a structure is statically determinate or indeterminate, its complete analysis requires the use of three types of relationships:
Equilibrium Equations
Compatibility Conditions
Member force-deformation relations
In the analysis of indeterminate structures, it is necessary to solve the equilibrium equations in conjunction with the compatibility conditions of the structure to determine its response.
The resulting system of equations containing only one type of unknowns is then solved for the unknown forces or displacements, which are then substituted into the fundamental relationships to determine the remaining response of the structure
Force and displace
2_Introduction Classification of Structure.pptxDr. Nitin Naik
The document discusses different types of structures including discrete systems made of line elements like beams and columns, continuum systems with surface or volume elements like plates and shells, and hybrid systems combining different element types. It also defines structure as any construction consisting of members, joints, supports that can resist loads, and describes skeletal structures as framed structures idealized as theoretical models with point joints.
This document provides an overview of the Theory and Design of Structures module. It outlines the lecture hours, units covered, and aim of the module. The main topics covered include statically determinate and indeterminate structures, types of loads acting on structures, stress, strain, bending stress, moment of inertia, and section modulus. The document also defines key terms related to structural analysis and design.
Static-Determinacy-Stability (Theory of Structures).pdfshienellajacildo
The document discusses different types of forces and stability in structures. It defines internal forces as those within a structure and external forces as outside actions on the structure. A structure is internally stable if it maintains its shape when detached from supports, and externally stable if there are enough support reactions to prevent rigid body movement. Overall stability requires both internal and external stability. Structures can be statically determinate, where forces can be calculated from equilibrium equations alone, or indeterminate otherwise. Trusses are structures of slender members joined at endpoints, and their stability and determinacy are also discussed.
This document discusses methods for analyzing the internal forces in different types of structures. It focuses on plane trusses, which are frameworks composed of members joined at their ends to form a rigid structure. The two main methods discussed for analyzing truss forces are the method of joints, which satisfies equilibrium conditions at each joint, and the method of sections, which analyzes equilibrium across a cut section. Key assumptions made in truss analysis are that members only experience two internal forces and connections act as pin joints.
I am a passionate and driven academic who is committed to multidisciplinary working (health/clinical). I strive to ensure that the interrelationship between research informed teaching and enterprise informed teaching is maintained to enhance the delivery of undergraduate and postgraduate curriculums. I have a particular interest in the role of spinal biomechanics & spinal orthotics.
This document discusses structural analysis and beam analysis. It covers topics such as support reactions, shear force and bending moment diagrams, equilibrium of forces in structures, and determinacy. Key points include:
1. To design structures, it is necessary to know bending moments, torsion moments, shear forces, and axial forces in each member.
2. Equilibrium requires that the downward forces from gravity have equal and opposite upward reaction forces.
3. Shear force and bending moment diagrams show the variation of these internal forces along a beam under different loading conditions.
This document provides an introduction to mechanics of materials, which deals with analyzing how solid objects deform under stress. It discusses key topics like stress and strain analysis, mechanical properties of materials, and static equilibrium as it relates to determining internal forces in loaded structures. The document provides examples of using free body diagrams and equilibrium equations to calculate reactions, shear forces, bending moments, and other internal forces in beams, pipes, and other loaded bodies.
The document discusses different types of structures and structural concepts. It describes compression structures like columns and arches, shear structures like reinforced concrete walls, and bending structures like beams and slabs. It also defines trusses, rigid and hinged connections, dead and live loads, impact, earthquake loading, equilibrium, internal and external forces, stability, and static determinacy.
The document discusses the objectives and syllabus for the course AR7202 Mechanics of Structures I. It aims to make students aware of how structural resolutions are important in architectural design and teach basic properties of solids and sections. The syllabus covers principles of statics including types of forces, force systems, and equilibrium. It also addresses analysis of plane trusses, properties of cross-sections, elastic properties of solids, and elastic constants. The course aims to teach students to apply equilibrium concepts and understand material behavior under forces.
This document discusses structural analysis and determining the degree of static indeterminacy for different structural elements including beams, frames, and trusses. It defines determinate and indeterminate structures, and explains how to calculate the external static indeterminacy, internal static indeterminacy, and total degree of static indeterminacy. Several examples are provided to demonstrate calculating the degree of static indeterminacy for beams, 2D and 3D frames, and trusses.
This document discusses the concepts of structural equilibrium and determinacy. It defines equilibrium as a state where internal and external forces balance such that no net forces or couples act on the structure. A structure is in static equilibrium if it remains stationary under applied forces. Determinacy refers to the ability to calculate all reactions from the equilibrium equations; a structure is determinate if it has exactly three reactions and indeterminate if more than three reactions exist. The document provides examples of determinate, indeterminate, and unstable structures and discusses the conditions required for stability.
Mechanical properties of dental materialsalka shukla
The document provides an overview of mechanical properties of dental materials. It defines key terms like stress, strain, elastic modulus, strength properties, and more. Stress is the force per unit area acting on materials and is expressed as force over area. Strain is the change in length under stress. Elastic modulus describes stiffness and is the ratio of stress to strain within the elastic region. Strength properties include elastic limit, yield strength, tensile strength, and flexural strength. The document discusses these properties for different dental materials like enamel, dentin, gold, and ceramics.
This document discusses the analysis of multi-story buildings. It begins by introducing structural analysis and the different load types buildings must withstand. It then describes five common structural systems for multi-story buildings: (1) load bearing wall systems, (2) buildings with flexural systems, (3) moment resisting frame systems, (4) dual frame systems, and (5) tube systems. For each system, it provides details on how the system resists gravity and lateral loads.
1) When a load is applied suddenly to a structural member, the maximum instantaneous stress can be calculated as the stress equal to twice the applied load divided by the cross-sectional area.
2) The strain energy due to shock or sudden loading is equal to the stress squared times the cross-sectional area times the length, divided by two times the Young's modulus.
3) The strain energy due to shear loading is given by tau (the shear stress) squared times the volume, divided by two times the shear modulus.
This document discusses the conjugate beam method for analyzing deflections in structures. It provides examples of using the conjugate beam method to calculate deflections and rotations at various points on beams. The conjugate beam method involves setting up double integrals of the bending moment with respect to the beam's flexural rigidity and length. For example, one problem calculates the maximum deflection of a beam using the conjugate beam method by integrating the bending moment diagram squared over the beam's length, divided by the beam's flexural rigidity.
L24 Numerical on Moment of Distribution MethodDr. OmPrakash
This document provides an example of analyzing an indeterminate beam ABCD using the moment distribution method. It presents a continuous beam problem to analyze using slope deflection and then draw the bending moment diagram. The example is from lecture 24 of the Theory of Structures course presented by Dr. Omprakash Netula, Professor and Head of the Department of Civil Engineering at Gandhinagar Institute of Technology.
L23 overview of slope deflection methodDr. OmPrakash
This document provides an overview of the slope deflection method for analyzing indeterminate beams. It was developed in 1914 by Axel Bendixen. The method solves for unknown joint rotations expressed in terms of applied loads and bending moments. Assumptions include rigid joints and neglecting distortion from axial/shear stresses. Applications include continuous beams and frames with or without side sway. The procedure involves determining fixed end moments, expressing end moments in terms of rotations using slope-deflection equations, solving simultaneous equations for joint rotations, then computing end moments, reactions, and drawing diagrams.
This document discusses the analysis of indeterminate beams using the moment distribution method. It provides the modified stiffness factor equation when the end of the beam is simply supported. It then gives an example problem and shows the step-by-step solution using the moment distribution method, including calculating the distribution factors, compiling the moment distribution table through multiple cycles, and determining the shear forces and bending moments. Finally, it briefly mentions analyzing nonprismatic members and using design tables with the moment distribution method.
L18 analysis of indeterminate beams by moment distribution methodDr. OmPrakash
The document discusses the moment distribution method for analyzing indeterminate beams. It begins with an overview of the method and some basic definitions. It then describes the step-by-step process, which involves (1) computing fixed end moments by assuming locked joints, (2) releasing joints causing unbalanced moments, (3) distributing unbalanced moments according to member stiffnesses, (4) carrying moments over to other joints, and (5) repeating until moments converge. Key terms discussed include stiffness factors, carry-over factors, and distribution factors.
This lecture discusses analysis of indeterminate beams. It begins with an introduction to structures, including what structures are, what they do, and how their performance is assessed. Structures must carry and transfer loads safely while maintaining equilibrium. The degree of indeterminacy, or whether a structure has enough equations to solve for its unknown forces, is then introduced. The document provides equations to assess the degree of indeterminacy in two-dimensional and three-dimensional truss and framed structures based on the number of members, joints, and external constraints. Various examples of determinate and indeterminate structures are shown.
L16 : Slope Deflection Method for Analysis of Indeterminate Beams Dr. OmPrakash
1. This document provides an example of analyzing an indeterminate beam using the slope deflection method. It gives the steps to determine internal moments at each joint of a frame.
2. The steps include determining fixed end moments, calculating joint moments using slope deflection equations, and applying equilibrium conditions to solve for unknown slope values.
3. The values obtained are then substituted into the joint moment equations to find the internal moments at each joint of the frame.
L15: Analysis of Indeterminate Beams by Slope Deflection Method Dr. OmPrakash
1) The document discusses analyzing indeterminate beams using the slope deflection method. It provides an example of determining moments at each joint of a frame.
2) Equilibrium equations are set up and solved simultaneously to find the slopes at specific joints.
3) The bending moment diagram is drawn based on the calculated slopes, with anticlockwise and clockwise moments indicated at each joint.
This document discusses the slope deflection method of structural analysis. It begins with an introduction that describes slope deflection as a displacement method where slopes and displacements are unknowns used to find end moments. It then lists the assumptions of rigid joints and negligible distortion. Sign conventions for rotations are defined. The derivation of slope deflection equations is outlined. An example problem is presented to calculate support moments in a continuous beam due to a vertical settlement, with the solution shown.
1. The document discusses the slope deflection method of structural analysis, which uses displacements as unknowns rather than forces.
2. The method is based on assumptions that joints are rigid and axial/shear distortions are negligible.
3. Derivation of the slope deflection equations involves determining fixed end moments and correcting for end rotations and member rotation from applied loads.
4. An example problem is presented to calculate support moments in a continuous beam due to vertical settlement of one support, by setting up and solving slope deflection equations.
1) The conjugate beam method uses mathematical analogies between slope-deflection equations of actual beams and load-shear-moment equations of imaginary conjugate beams.
2) The method establishes mathematical equivalence between the behavior of actual beams and their conjugate beams, allowing values like shear (V) and moment (M) to be obtained for actual beams using deflections (w) of corresponding conjugate beams.
3) Conjugate beams are imaginary beams used for mathematical convenience without consideration of their physical stability; their deflections allow determining shear and moment in actual beams using simple equations.
The document discusses the conjugate-beam method for analyzing indeterminate beams. It states that the conjugate-beam method uses a mathematical analogy between the slope-deflection equations of the actual beam and the load-shear-moment equations of an imaginary conjugate beam. It notes that the conjugate beam has the same deflected shape and internal forces as the actual beam, allowing the internal forces in the actual beam to be determined. The document provides equations showing the mathematical equivalence between the actual beam and conjugate beam and illustrates determining the internal forces at different points along the beams.
This document discusses the moment area method for determining slopes of beams. It presents the first and second moment area theorems which relate the bending moment to the area under the moment-curvature diagram. These theorems are used to calculate the slopes at two points on a beam given the modulus of elasticity, second moment of area, and bending moment values. An example problem demonstrates applying the theorems to find the slopes at points B and C of a beam.
This document discusses the moment-area method for analyzing beams. It presents the first and second moment-area theorems, which relate the bending moment, slope, and shear of a beam to the area under the moment diagram. The document also gives an example problem that applies the theorems to determine the slope at two points on a beam given the bending moment diagram.
This document discusses the degree of indeterminacy of space trusses. It provides formulas to calculate the degree of kinematic indeterminacy (Dkand) for different structural systems, including plane and space trusses and frames. For a space truss example provided, the number of members is 10, the number of reactions is 6, and the number of joints is 9. Using the formula for space trusses, Dkand is calculated as 11. The document also briefly introduces the principle of superposition, which allows separating loads to analyze individual load effects that can then be summed.
This document discusses the degree of indeterminacy of space trusses. It provides formulas to calculate the degree of kinematic indeterminacy (Dkand) for different structural systems like plane trusses, space trusses, plane frames, and space frames. It also includes an example calculation for a space truss where R is the number of reactions, m is the number of members, and j is the number of joints. The resulting Dkand is the degree of redundancy. Additionally, it briefly introduces the principle of superposition, which allows separating loads to analyze individual load effects that can then be summed.
L15 analysis of indeterminate beams by moment distribution methodDr. OmPrakash
This document discusses the moment distribution method for analyzing indeterminate beams. It begins with an overview and introduction to the method, which was developed by Prof. Hardy Cross in 1932. It then describes the basic principles through a 5 step process: 1) joints are locked to determine fixed end moments, 2) joints are released allowing rotation, 3) unbalanced moments modify joint moments based on stiffness, 4) moments are distributed and modify other joints, 5) steps 3-4 repeat until moments converge. Key terms like stiffness and carry-over factors are also defined.
L10 slope deflection method for the analysis of indeterminateDr. OmPrakash
The slope deflection method is used to analyze indeterminate structures. It uses the principle of superposition to consider the moments developed at each support of a continuous beam due to applied loads and displacements. The method establishes load-displacement relationships and develops slope-deflection equations to solve for member forces and displacements. Key steps include assuming fixed ends to determine initial end moments, releasing one end to calculate its moment-rotation relationship, and developing equations relating member end moments to nodal displacements.
Online train ticket booking system project.pdfKamal Acharya
Rail transport is one of the important modes of transport in India. Now a days we
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Sachpazis_Consolidation Settlement Calculation Program-The Python Code and th...Dr.Costas Sachpazis
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Covid Management System Project Report.pdfKamal Acharya
CoVID-19 sprang up in Wuhan China in November 2019 and was declared a pandemic by the in January 2020 World Health Organization (WHO). Like the Spanish flu of 1918 that claimed millions of lives, the COVID-19 has caused the demise of thousands with China, Italy, Spain, USA and India having the highest statistics on infection and mortality rates. Regardless of existing sophisticated technologies and medical science, the spread has continued to surge high. With this COVID-19 Management System, organizations can respond virtually to the COVID-19 pandemic and protect, educate and care for citizens in the community in a quick and effective manner. This comprehensive solution not only helps in containing the virus but also proactively empowers both citizens and care providers to minimize the spread of the virus through targeted strategies and education.
2. INTRODUCTION
• What is a structure?
General Types: Based on deformation and type of primary load
carried [Axial (tensile, compressive), flexure, shear and torsion
What does a structure do? –
Carries the load - Loads acting on the structure: Dead & Live (people,
equipment, wind, wave, seismic)-
Superposition Principle - Keeps the structure in static and dynamic
equilibrium - Transfers the load to contiguous structural components
- Transfers the load safely - Transfers the loads to the foundation
]..
3. Statically Determinate structure
• The structure for which the reactions at the supports & internal forces in the
members can be found out by the conditions of static equilibrium, is called a
statically determinate structure.
• Example of determinate structures are: simply supported beams, cantilever beams, single
and double overhanging beams, three hinged arches, etc.
• There are three basic conditions of static equilibrium:
ΣH = 0
ΣV = 0
ΣM = 0
4. Statically indeterminate structure
• The structure for which the reactions at the supports & the internal forces in the members can not be
found out by the conditions of static equilibrium, is called statically indeterminate structure.
• Examples of indeterminate structures are: fixed beams, continuous beams, fixed arches, two hinged
arches, portals, multistoried frames, etc.
• If equations of static equilibrium are not sufficient to determine all the unknown reactions (vertical,
horizontal & moment reactions) acting on the structure, it is called externally indeterminate structure or
externally redundant structure.
• If equations of static equilibrium are not sufficient to determine all the internal forces and moments in the
member of the structure, even though all the external forces acting on the structure are known, is called
internally indeterminate structure or internally redundant structure.
5. DEGREE OF STATIC INDETERMINCY(DS):
• The degree of static indeterminacy of the structure may be defined as the number of
unknown forces in excess of equations of statics.
It is also known as degree of redundancy.
Therefore,
degree of static indeterminacy
= Total no. of unknown forces – Number of equations of static available
• Redundants may be support reactions or internal forces in the members.
• If redundants are removed from the structure, it becomes determinate.
• Thus, the degree of indetermincy is equal to the number of releases necessary make the
structure determinate.
DS = DSE + DSI
6. S. No. Determinate Structures Indeterminate Structures
1 Equilibrium conditions are fully
adequate to analyse the structure.
Conditions of equilibrium are
not adequate to fully analyze
the structure.
2 Bending moment or shear force at
any section is independent of the
material property of the structure.
Bending moment or shear force
at any section depends upon
the material property.
3 The bending moment or shear
force at any section is
independent of the cross-section
or moment of inertia.
The bending moment or shear
force at any section depends
upon the cross-section or
moment of inertia.
4 Temperature variations do not
cause stresses.
Temperature variations cause
stresses.
5 No stresses are caused due to
lack of fit.
Stresses are caused due to lack
of fit.
6 Extra conditions like compatibility
of displacements are not required
to analyze the structure.
Extra conditions like
compatibility of displacements
are required to analyze the
structure along with the
equilibrium equations.
7. External stability:
• The support system shown in fig. (a) are
unstable, because it can provide only
parallel reaction components. It cannot,
therefore, resist a force perpendicular to
the direction of the reactive forces.
• The support system shown in fig. (b) are
also unstable, because the reactive
forces are concurrent. Hence, the
support system is incapable of resisting a
couple about the point “o”.
8. Internal stability:
• A structural system is internally stable if it can preserve its geometry under the action of all kinds of
forces tending to deform it. Significant internal forces are produced in the members of a structural
system as a result of even small changes in geometry.
• On the other hand, the geometry of unstable system, known as MECHANISMS, can change substantially
without generating appreciable internal forces.
• For pin-jointed plane & space structures, if the number of members is less than the minimum
requirement, an unstable system, known as mechanism is obtained.
• If number of members is more than the minimum required, an overstiff statically indeterminate system
is obtained.
• If the number of members is equal to the minimum required, a stable & determinate system is
obtained.
• A rigid-jointed frame is internally stable & statically determinate if it has an open configuration.
9. DEGREE OF REDUNDANCY OF BEAMS:
• In case of continuous beams, the shear & moment at any point in the beam are readily
known once the reaction components are determined. Thus these beams are statically
determinate internally.
• Therefore,
For beams, DSi = 0
The degree of indetermincy of a beam is therefore equal to its external redundancy.
DS = DSe
• As stated earlier,
DS = DSe = R – r
Where, R = total no. of reaction components
r = total no. of condition equations available
10. Example for beam:
• DS = R – r
Where, R = No. of reaction components.
r = no. of condition equation available.
• DS = (3+1+3) – 6
= 1
• Therefore, beam is indeterminate to first
degree.
• Internal roller act as a link & provide two
extra conditions.
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![INTRODUCTION
• What is a structure?
General Types: Based on deformation and type of primary load
carried [Axial (tensile, compressive), flexure, shear and torsion
What does a structure do? –
Carries the load - Loads acting on the structure: Dead & Live (people,
equipment, wind, wave, seismic)-
Superposition Principle - Keeps the structure in static and dynamic
equilibrium - Transfers the load to contiguous structural components
- Transfers the load safely - Transfers the loads to the foundation
]..](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)