# Advanced Structural Analysis By Ashok K Jain Pdf Downloadl - Ebook3000

<h1>Introduction</h1>

<p>Structural analysis is the branch of engineering that deals with the determination of the effects of loads on physical structures. It is essential for designing safe and efficient structures that can withstand various types of loading conditions. Structural analysis can be classified into two categories: static analysis and dynamic analysis. Static analysis assumes that the loads are constant or slowly varying, while dynamic analysis considers the effects of time-varying loads such as wind, earthquake, blast, etc.</p>

## Advanced Structural Analysis By Ashok K Jain Pdf Downloadl

<p>Advanced structural analysis is the study of complex and indeterminate structures using advanced methods such as matrix methods, approximate methods, plastic analysis, nonlinear analysis, finite element method, dynamic analysis, etc. These methods are useful for analyzing structures that have complicated geometry, material properties, boundary conditions, loading patterns, etc. Advanced structural analysis can also incorporate the effects of temperature, creep, fatigue, fracture, etc. on the structural behavior.</p>

<p>Ashok K Jain is a professor emeritus of civil engineering at the Indian Institute of Technology (IIT) Kanpur. He has more than 40 years of teaching and research experience in the field of structural engineering. He has authored several books and papers on various topics related to structural analysis, design, mechanics, etc. He has also received many awards and honors for his contributions to the profession.</p>

<p>One of his books is "Advanced Structural Analysis", which was published in 2009 by Nem Chand & Bros. This book covers all the topics mentioned above in a comprehensive and systematic manner. It provides a clear exposition of the theory and applications of advanced structural analysis methods. It also includes numerous solved examples, exercises, diagrams, tables, etc. to illustrate the concepts and techniques. The book is suitable for undergraduate and postgraduate students of civil engineering, as well as practicing engineers and researchers.</p>

<h2>Basic Concepts of Structural Analysis</h2>

<p>Before proceeding to the advanced methods of structural analysis, it is important to review some of the basic concepts and principles that are common to all types of structural analysis. These include:</p>

<ul>

<li><b>Statics and strength of materials:</b> These are the fundamental subjects that deal with the equilibrium of forces and moments, and the stress-strain relationships in solids. They provide the basis for calculating the internal forces and deformations in structures due to external loads.</li>

<li><b>Types of structures and loads:</b> Structures can be classified into different types based on their geometry, support conditions, function, etc. Some common types of structures are beams, trusses, frames, arches, cables, plates, shells, etc. Loads can be classified into different types based on their nature, magnitude, direction, duration, etc. Some common types of loads are dead loads, live loads, wind loads, earthquake loads, thermal loads, etc.</li>

<li><b>Determinacy, stability and indeterminacy:</b> A structure is said to be determinate if the number of unknown reactions is equal to the number of equilibrium equations. In this case, the reactions can be determined by applying the equations of statics. A structure is said to be stable if it does not undergo any rigid body motion when subjected to external loads. A structure is said to be indeterminate if the number of unknown reactions is more than the number of equilibrium equations. In this case, the equations of statics are not sufficient to determine the reactions, and additional equations based on compatibility or energy are required.</li>

<li><b>Methods of analysis for statically determinate structures:</b> These are the methods that can be used to analyze determinate structures by applying the equations of statics. Some common methods are method of joints, method of sections, method of moments, etc. These methods can also be used to calculate the internal forces and deformations in determinate structures.</li>

</ul>

<h3>Analysis of Statically Indeterminate Structures</h3>

<p>Statically indeterminate structures are more complex and realistic than determinate structures. They require more advanced methods of analysis that involve not only the equations of statics, but also the equations of compatibility and energy. These methods can be classified into two categories: force methods and displacement methods. These include:</p>

<ul>

<li><b>Compatibility equations and redundant forces:</b> Compatibility equations are the equations that express the geometric relations between the displacements or deformations of various points or sections in a structure. Redundant forces are the unknown reactions that are removed from a structure to make it determinate. The compatibility equations can be used to express the redundant forces in terms of the displacements or deformations at certain points or sections in a structure.</li>

<li><b>Methods of consistent deformations and slope-deflection:</b> These are the force methods that can be used to analyze indeterminate structures by using the compatibility equations and redundant forces. The method of consistent deformations involves calculating the displacements or deformations at certain points or sections in a structure due to external loads and redundant forces separately, and then equating them using the compatibility equations. The slope-deflection method involves calculating the rotations or slopes at certain points or sections in a structure due to external loads and redundant forces separately, and then equating them using the compatibility equations.</li>

<li><b>Moment distribution method and Kani's method:</b> These are the displacement methods that can be used to analyze indeterminate structures by using the stiffness properties and equilibrium conditions. The moment distribution method involves distributing the unbalanced moments at each joint in a structure iteratively until equilibrium is achieved. The Kani's method involves calculating the rotations or slopes at each joint in a structure by using a recursive formula based on the stiffness coefficients and fixed-end moments.</li>

<li><b>Influence lines for indeterminate structures:</b> Influence lines are graphical representations of the variation of a certain response quantity (such as reaction, shear force, bending moment, deflection, etc.) in a structure due to a unit load moving along a certain path. Influence lines can be used to analyze indeterminate structures for various types of moving loads by using superposition principle. Influence lines can be constructed by using either force methods or displacement methods.</li>

</ul>

<h4>Matrix Methods of Structural Analysis</h4>

<p>Matrix methods of structural analysis are the methods that use matrix algebra and notation to simplify and systematize the analysis of complex and indeterminate structures. Matrix methods can be applied to both force methods and displacement methods. Matrix methods have several advantages over conventional methods, such as compactness, generality, automation, accuracy, etc. Matrix methods include:</p>

<ul>

<h4>Matrix Methods of Structural Analysis</h4>

<p>Matrix methods of structural analysis are the methods that use matrix algebra and notation to simplify and systematize the analysis of complex and indeterminate structures. Matrix methods can be applied to both force methods and displacement methods. Matrix methods have several advantages over conventional methods, such as compactness, generality, automation, accuracy, etc. Matrix methods include:</p>

<ul>

<li><b>Stiffness matrix and flexibility matrix methods:</b> These are the matrix versions of displacement methods and force methods, respectively. The stiffness matrix method is based on the relation between the nodal displacements and the nodal forces, while the flexibility matrix method is based on the relation between the nodal forces and the nodal displacements. The stiffness matrix method is more commonly used than the flexibility matrix method, because it is easier to formulate and solve.</li>

<li><b>Transformation matrices and coordinate systems:</b> These are the tools that are used to transform the stiffness matrices, load vectors and displacement vectors from one coordinate system to another. Transformation matrices are square matrices that contain the direction cosines or trigonometric functions of the angles between the coordinate axes. Coordinate systems can be classified into global and local systems. The global system is fixed and common to all the elements in a structure, while the local system is attached to each element and aligned with its geometry.</li>

<li><b>Bandwidth minimization and sparse matrix techniques:</b> These are the techniques that are used to reduce the computational effort and storage requirements for solving large matrix equations. Bandwidth minimization is the process of rearranging the order of nodes or equations to reduce the number of nonzero entries outside the main diagonal band of a matrix. Sparse matrix techniques are the methods of storing and manipulating only the nonzero entries of a matrix, using special data structures and algorithms.</li>

</ul>

<h5>Approximate Methods of Structural Analysis</h5>

<p>Approximate methods of structural analysis are the methods that use simplifying assumptions and approximations to obtain approximate solutions for complex and indeterminate structures. Approximate methods are useful for obtaining quick and rough estimates of structural behavior, or for checking the validity of more rigorous methods. Approximate methods include:</p>

<ul>

<li><b>Portal method and cantilever method for frames:</b> These are the approximate methods that can be used to analyze indeterminate frames for vertical loads by assuming a certain distribution of bending moments along the height of the frame. The portal method assumes that the bending moments at each joint are proportional to the shear forces at that joint, while the cantilever method assumes that the bending moments at each joint are proportional to the distance from that joint to the nearest support.</li>

<h5>Approximate Methods of Structural Analysis</h5>

<p>Approximate methods of structural analysis are the methods that use simplifying assumptions and approximations to obtain approximate solutions for complex and indeterminate structures. Approximate methods are useful for obtaining quick and rough estimates of structural behavior, or for checking the validity of more rigorous methods. Approximate methods include:</p>

<ul>

<li><b>Portal method and cantilever method for frames:</b> These are the approximate methods that can be used to analyze indeterminate frames for vertical loads by assuming a certain distribution of bending moments along the height of the frame. The portal method assumes that the bending moments at each joint are proportional to the shear forces at that joint, while the cantilever method assumes that the bending moments at each joint are proportional to the distance from that joint to the nearest support.</li>

<li><b>Substitute frame method and portal frame method for buildings:</b> These are the approximate methods that can be used to analyze indeterminate buildings for vertical loads by simplifying the geometry and loading of the structure. The substitute frame method assumes that the moment in the beams of any floor is influenced by loading on that floor alone, and divides the multi-storeyed structure into smaller frames called substitute frames. The portal frame method assumes that each storey of the building behaves like a portal frame, and calculates the bending moments at each joint by using a moment coefficient table.</li>

<li><b>Column analogy method and area-moment method for beams:</b> These are the approximate methods that can be used to analyze indeterminate beams for bending by using analogies or relations between different quantities. The column analogy method assumes that a beam subjected to bending is analogous to a column subjected to axial load, and uses the concept of strain energy to derive the compatibility equations. The area-moment method assumes that there is a relation between the area of the bending moment diagram and the slope or deflection of the beam, and uses integration to obtain the displacement equations.</li>

</ul>

<h6>Plastic Analysis of Structures</h6>

<p>Plastic analysis of structures is the analysis that considers the plastic behavior of materials beyond their elastic limit. Plastic analysis is useful for designing structures that can undergo large deformations without failure, such as steel frames, bridges, pressure vessels, etc. Plastic analysis can also provide a more realistic estimate of the ultimate load capacity and collapse mechanism of structures. Plastic analysis involves:</p>

<ul>

<li><b>Introduction to plasticity theory and plastic hinges:</b> Plasticity theory is the branch of mechanics that deals with the permanent deformation and flow of materials under stress. Plastic hinges are the regions in a structure where plastic deformation occurs due to bending. Plastic hinges can form when a certain critical value of bending moment, called plastic moment, is reached.</li>

<h6>Plastic Analysis of Structures</h6>

<p>Plastic analysis of structures is the analysis that considers the plastic behavior of materials beyond their elastic limit. Plastic analysis is useful for designing structures that can undergo large deformations without failure, such as steel frames, bridges, pressure vessels, etc. Plastic analysis can also provide a more realistic estimate of the ultimate load capacity and collapse mechanism of structures. Plastic analysis involves:</p>

<ul>

<li><b>Introduction to plasticity theory and plastic hinges:</b> Plasticity theory is the branch of mechanics that deals with the permanent deformation and flow of materials under stress. Plastic hinges are the regions in a structure where plastic deformation occurs due to bending. Plastic hinges can form when a certain critical value of bending moment, called plastic moment, is reached.</li>

<li><b>Collapse load and mechanism methods for frames:</b> Collapse load is the maximum load that a structure can sustain before it collapses due to formation of a mechanism. A mechanism is a system of plastic hinges that makes the structure lose its stability and undergo uncontrolled displacement. Collapse load and mechanism methods are the methods that can be used to determine the collapse load and mechanism of indeterminate frames by using either upper bound or lower bound theorems. The upper bound theorem states that any mechanism that satisfies equilibrium provides an upper bound for the collapse load, while the lower bound theorem states that any stress distribution that satisfies equilibrium and yield criterion provides a lower bound for the collapse load.</li>

<li><b>Upper bound and lower bound theorems for plates:</b> These are the extensions of the collapse load and mechanism methods for frames to two-dimensional plate structures. The upper bound theorem states that any kinematically admissible velocity field that satisfies compatibility provides an upper bound for the collapse load, while the lower bound theorem states that any statically admissible stress field that satisfies equilibrium and yield criterion provides a lower bound for the collapse load.</li>

<li><b>Plastic analysis of continuous beams and slabs:</b> These are the applications of plastic analysis to one-dimensional and two-dimensional flexural members. Plastic analysis of continuous beams and slabs involves finding the plastic moment capacity, plastic hinge locations, collapse load and mechanism, and redistribution of moments.</li>

</ul>

<h7>Nonlinear Analysis of Structures</h7>

<p>Nonlinear analysis of structures is the analysis that accounts for the nonlinear behavior of materials, geometry, or boundary conditions. Nonlinear analysis is essential for capturing the realistic response of structures under large deformations, material nonlinearities, contact problems, etc. Nonlinear analysis can also provide more accurate estimates of stress, strain, displacement, buckling, fracture, etc. Nonlinear analysis involves:</p>

<ul>

<li><b>Introduction to nonlinear behavior and sources of nonlinearity:</b> Nonlinear behavior is the behavior that does not follow a linear relation between input and output variables. Sources of nonlinearity can be classified into three categories: material nonlinearity, geometric nonlinearity, and boundary nonlinearity. Material nonlinearity refers to the nonlinear stress-strain relationship of materials due to plasticity, damage, viscoelasticity, etc. Geometric nonlinearity refers to the nonlinear deformation of structures due to large displacements, rotations, or strains. Boundary nonlinearity refers to the nonlinear boundary conditions or constraints due to contact, friction, gaps, etc.</li>

<h7>Nonlinear Analysis of Structures</h7>

<p>Nonlinear analysis of structures is the analysis that accounts for the nonlinear behavior of materials, geometry, or boundary conditions. Nonlinear analysis is essential for capturing the realistic response of structures under large deformations, material nonlinearities, contact problems, etc. Nonlinear analysis can also provide more accurate estimates of stress, strain, displacement, buckling, fracture, etc. Nonlinear analysis involves:</p>

<ul>

<li><b>Introduction to nonlinear behavior and sources of nonlinearity:</b> Nonlinear behavior is the behavior that does not follow a linear relation between input and output variables. Sources of nonlinearity can be classified into three categories: material nonlinearity, geometric nonlinearity, and boundary nonlinearity. Material nonlinearity refers to the nonlinear stress-strain relationship of materials due to plasticity, damage, viscoelasticity, etc. Geometric nonlinearity refers to the nonlinear deformation of structures due to large displacements, rotations, or strains. Boundary nonlinearity refers to the nonlinear boundary conditions or constraints due to contact, friction, gaps, etc.</li>

<li><b>Material nonlinearity and constitutive models:</b> Material nonlinearity is the nonlinearity that arises from the material properties and behavior. Constitutive models are the mathematical models that describe the material responses to different mechanical and/or thermal loading conditions, which provide the stress-strain relations to formulate the governing equations. Constitutive models can be classified into different types based on their complexity and assumptions, such as elastic, plastic, viscoelastic, damage, fracture, etc.</li>

<li><b>Geometric nonlinearity and large deformations:</b> Geometric nonlinearity is the nonlinearity that arises from the geometry and kinematics of structures. Large deformations are the deformations that are so large that they affect the geometry and stiffness of structures. Geometric nonlinearity and large deformations require the use of nonlinear strain measures and nonlinear equilibrium equations. Geometric nonlinearity and large deformations can cause various phenomena such as buckling, snap-through, post-buckling, etc.</li>

<li><b>Solution methods and algorithms for nonlinear problems:</b> Solution methods and algorithms are the numerical techniques that are used to solve nonlinear problems. Nonlinear problems are usually solved by iterative methods that involve linearization and convergence criteria. Some common solution methods and algorithms for nonlinear problems are Newton-Raphson method, modified Newton-Raphson method, arc-length method, load-control method, displacement-control method, etc.</li>

</ul>

<h8>Finite Element Method of Structural Analysis</h8>

<p>Finite element method (FEM) of structural ana