# How to Use NDT Techniques for Masonry Structures Based on Dayaratnam's Work

## Introduction

Structural analysis is the branch of engineering that deals with determining the effects of loads on physical structures such as buildings, bridges, dams, etc. Structural analysis is essential for designing safe, efficient and economical structures that can withstand various types of loads such as gravity, wind, earthquake, etc.

## Advanced Structural Analysis By Dayaratnam.pdf

Advanced structural analysis is a term that refers to the application of more sophisticated methods and techniques of structural analysis that go beyond the basic or classical methods. Advanced structural analysis can handle complex structures with nonlinear behavior, large deformations, material nonlinearity, dynamic loading, etc. Advanced structural analysis can also provide more accurate and realistic results than basic structural analysis.

Dayaratnam Pasala was a renowned Indian civil engineer who specialized in structural engineering. He was a professor at Andhra University and later at IIT Madras. He authored several books on structural engineering, including "Advanced Structural Analysis", which was published in 1980 by Oxford & IBH Publishing Co. The book is considered as one of the classic texts on advanced structural analysis that covers a wide range of topics with clarity and rigor.

## Overview of Dayaratnam's book "Advanced Structural Analysis"

The book "Advanced Structural Analysis" by Dayaratnam was written with the aim of providing a comprehensive treatment of advanced structural analysis for undergraduate and postgraduate students as well as practicing engineers. The book covers four major topics: matrix methods of structural analysis, plastic analysis of structures, finite element method of analysis, and structural stability. The book also includes a chapter on dynamic analysis of structures as an introduction to the subject.

The book has the following features:

It presents the theoretical concepts and principles of advanced structural analysis in a logical and systematic manner.

It provides numerous examples and exercises to illustrate the application of the methods and techniques of advanced structural analysis.

It includes solved problems from various examinations and competitive tests to help the students prepare for them.

It uses SI units throughout the book for consistency and convenience.

The book is organized into six chapters as follows:

ChapterTitlePages

1Matrix Methods of Structural Analysis1-120

2Plastic Analysis of Structures121-212

3Finite Element Method of Analysis213-332

4Structural Stability333-436

5Dynamic Analysis of Structures437-516

6Solved Problems from Various Examinations and Competitive Tests517-608

### Chapter-wise summary of the book

#### Chapter 1: Matrix Methods of Structural Analysis

This chapter introduces the matrix methods of structural analysis, which are based on the use of matrices and vectors to represent the structural system and its behavior. The matrix methods have several advantages over the classical methods, such as simplicity, generality, accuracy, efficiency, etc. The chapter covers the following topics:

The basic concepts and terminology of matrix methods, such as degrees of freedom, displacement vector, force vector, stiffness matrix, flexibility matrix, equilibrium equations, compatibility equations, etc.

The stiffness and flexibility methods for analyzing trusses, beams and frames. The stiffness method is based on the relation between displacements and forces, while the flexibility method is based on the relation between forces and displacements. The chapter explains how to formulate the stiffness and flexibility matrices for different types of structural elements and how to solve the equilibrium and compatibility equations using matrix operations.

The examples and exercises that demonstrate the application of the matrix methods to various problems of trusses, beams and frames. The examples include both determinate and indeterminate structures with different types of loading and boundary conditions. The exercises provide additional problems for practice and self-assessment.

#### Chapter 2: Plastic Analysis of Structures

This chapter introduces the plastic analysis of structures, which is based on the assumption that the material of the structure behaves in a perfectly plastic manner, i.e., it can undergo large deformations without any increase in stress beyond a certain limit called the yield stress. The plastic analysis has several applications, such as designing structures for ultimate load capacity, estimating collapse loads, optimizing structural weight, etc. The chapter covers the following topics:

The basic concepts and assumptions of plastic analysis, such as plastic moment, plastic hinge, plastic zone, fully plastic section, partially plastic section, etc.

The plastic hinge concept and collapse mechanisms. The plastic hinge is a point where a structural member reaches its plastic moment and rotates freely without any increase in moment. The collapse mechanism is a configuration of plastic hinges that causes the structure to collapse under a given load. The chapter explains how to identify the location and number of plastic hinges in a structure and how to determine the collapse load using virtual work principle.

The theorems of plastic analysis and their applications. The chapter presents three important theorems of plastic analysis: the lower bound theorem, which states that any statically admissible distribution of moments is lower than or equal to the collapse load; the upper bound theorem, which states that any kinematically admissible collapse mechanism is greater than or equal to the collapse load; and the uniqueness theorem, which states that if a distribution of moments satisfies both statical and kinematical admissibility, then it is equal to the collapse load. The chapter shows how to use these theorems to analyze various types of structures such as beams, frames, arches, etc.

The examples and exercises that demonstrate the application of the plastic analysis to various problems of beams, frames, arches, etc. The examples include both statically determinate and indeterminate structures with different types of loading and boundary conditions. The exercises provide additional problems for practice and self-assessment.

#### Chapter 3: Finite Element Method of Analysis

This chapter introduces the finite element method of analysis, which is a numerical technique that divides the structure into smaller and simpler parts called finite elements. The finite element method can handle complex geometries, material properties, loading conditions, etc. The chapter covers the following topics:

The basic concepts and steps of finite element method, such as domain discretization, element formulation, assembly, boundary conditions, solution and post-processing. The chapter explains how to derive the element stiffness matrix and load vector for different types of elements using variational or weighted residual methods.

The finite element formulation for one-dimensional problems, such as bars, beams and trusses. The chapter shows how to apply the finite element method to solve problems involving axial forces, bending moments, shear forces and torsion.

The finite element formulation for two-dimensional problems, such as plane stress, plane strain and axisymmetric problems. The chapter introduces different types of elements for two-dimensional problems, such as triangular, quadrilateral and isoparametric elements. The chapter also discusses how to deal with special issues such as singularities, stress concentrations and mesh refinement.

The finite element formulation for three-dimensional problems, such as solid mechanics and plate bending problems. The chapter presents different types of elements for three-dimensional problems, such as tetrahedral, hexahedral and shell elements. The chapter also explains how to incorporate various effects such as transverse shear deformation, large deformation and nonlinear material behavior.

The examples and exercises that demonstrate the application of the finite element method to various problems of one-dimensional, two-dimensional and three-dimensional structures. The examples include both static and dynamic problems with different types of loading and boundary conditions. The exercises provide additional problems for practice and self-assessment.

#### Chapter 4: Structural Stability

This chapter introduces the structural stability, which is the ability of a structure to maintain its equilibrium state under small perturbations or disturbances. Structural stability is important for ensuring the safety and reliability of structures that are subjected to compressive forces or moments that can cause buckling or instability. The chapter covers the following topics:

The basic concepts and definitions of stability, such as equilibrium state, stable equilibrium, unstable equilibrium, neutral equilibrium, bifurcation point, critical load, buckling mode, etc.

The stability criteria and methods of analysis for columns, beams and frames. The chapter explains how to use the energy method and the differential equation method to determine the critical load and buckling mode of various types of columns, beams and frames. The chapter also discusses how to account for different factors affecting stability, such as initial imperfections, slenderness ratio, end conditions, eccentric loading, etc.

The buckling modes and factors affecting stability. The chapter describes different types of buckling modes that can occur in structures, such as Euler buckling, lateral-torsional buckling, local buckling and interactive buckling. The chapter also identifies different factors that can influence the stability behavior of structures, such as material properties, geometric properties, loading conditions, boundary conditions, etc.

The examples and exercises that demonstrate the application of the structural stability analysis to various problems of columns, beams and frames. The examples include both elastic and inelastic buckling problems with different types of loading and boundary conditions. The exercises provide additional problems for practice and self-assessment.

#### Chapter 5: Dynamic Analysis of Structures

This chapter introduces the dynamic analysis of structures, which is concerned with the response of structures to time-varying loads such as wind, earthquake, blast, etc. Dynamic analysis is important for evaluating the performance and safety of structures under dynamic loading conditions. The chapter covers the following topics:

The basic concepts and equations of motion for dynamic systems, such as mass, damping, stiffness, natural frequency, mode shape, damping ratio, etc. The chapter explains how to derive the equations of motion for single-degree-of-freedom and multi-degree-of-freedom systems using Newton's second law or energy methods.

The free and forced vibrations of single-degree-of-freedom systems. The chapter shows how to solve the free vibration problem for undamped and damped systems using analytical or numerical methods. The chapter also shows how to solve the forced vibration problem for harmonic, periodic and non-periodic excitations using superposition principle or frequency response functions.

The response spectrum method for multi-degree-of-freedom systems. The chapter introduces the concept of response spectrum, which is a plot of the maximum response of a single-degree-of-freedom system as a function of its natural frequency and damping ratio for a given ground motion. The chapter explains how to use the response spectrum method to estimate the maximum response of a multi-degree-of-freedom system by combining the modal responses using modal analysis or mode superposition techniques.

The examples and exercises that demonstrate the application of the dynamic analysis to various problems of single-degree-of-freedom and multi-degree-of-freedom systems. The examples include both linear and nonlinear systems with different types of damping and loading conditions. The exercises provide additional problems for practice and self-assessment.

## Benefits and limitations of the book

The book "Advanced Structural Analysis" by Dayaratnam has several benefits and limitations that can be summarized as follows:

### Benefits

The book provides a comprehensive coverage of advanced structural analysis topics that are relevant for engineering students and practitioners.

The book presents the theoretical concepts and principles of advanced structural analysis in a logical and systematic manner that facilitates understanding and learning.

The book provides numerous examples and exercises that illustrate the application of advanced structural analysis methods and techniques to various problems of practical interest.

The book includes solved problems from various examinations and competitive tests that help the students prepare for them.

The book uses SI units throughout the book for consistency and convenience.

### Limitations

The book is relatively old (published in 1980) and may not reflect the latest developments and advances in advanced structural analysis.

The book is mainly focused on structural mechanics problems and does not cover other aspects of structural engineering such as design, optimization, reliability, etc.

The book is written in a formal and academic style that may not appeal to some readers who prefer a more informal and conversational style.

The book does not provide any software or code for implementing the advanced structural analysis methods and techniques.

The book does not include any color illustrations or figures that could enhance the visual appeal and clarity of the presentation.

## Conclusion

## In conclusion, the book "Advanced Structural Analysis" by Dayaratnam is a classic text on advanced structural analysis that covers a wide range of topics with clarity and rigor. The book is suitable for undergraduate and postgraduate students as well as practicing engineers who want to learn advanced structural analysis methods and techniques. The book has several benefits such as comprehensive coverage, logical presentation, numerous examples and exercises, solved problems from examinations and tests, and consistent use of SI units. However, the book also has some limitations such as being old, being focused on mechanics only, being formal and academic in style, not providing any software or code, and not including any color illustrations or figures. Therefore, the book can be recommended as a useful reference for advanced structural analysis, but it may need to be supplemented by other sources that address its limitations. FAQs

Here are some frequently asked questions and answers related to the topic of advanced structural analysis by Dayaratnam:

What is the difference between basic and advanced structural analysis?

Basic structural analysis is the application of simple methods and techniques of structural analysis that can handle simple structures with linear behavior, small deformations, material linearity, static loading, etc. Advanced structural analysis is the application of more sophisticated methods and techniques of structural analysis that can handle complex structures with nonlinear behavior, large deformations, material nonlinearity, dynamic loading, etc.

What are the advantages of matrix methods of structural analysis?

Matrix methods of structural analysis are based on the use of matrices and vectors to represent the structural system and its behavior. The matrix methods have several advantages over the classical methods, such as simplicity, generality, accuracy, efficiency, etc.

What are the applications of plastic analysis of structures?

Plastic analysis of structures is based on the assumption that the material of the structure behaves in a perfectly plastic manner, i.e., it can undergo large deformations without any increase in stress beyond a certain limit called the yield stress. The plastic analysis has several applications, such as designing structures for ultimate load capacity, estimating collapse loads, optimizing structural weight, etc.

What are the benefits of finite element method of analysis?

Finite element method of analysis is a numerical technique that divides the structure into smaller and simpler parts called finite elements. The finite element method can handle complex geometries, material properties, loading conditions, etc. The finite element method can also provide more accurate and realistic results than other methods.

What are the factors affecting structural stability?

Structural stability is the ability of a structure to maintain its equilibrium state under small perturbations or disturbances. Structural stability is affected by various factors such as material properties, geometric properties, loading conditions, boundary conditions, etc.

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