Civil Engineering. Structural Analysis. Comprehensive Theory with Solved Examples and Practice Questions. Publications

Size: px
Start display at page:

Download "Civil Engineering. Structural Analysis. Comprehensive Theory with Solved Examples and Practice Questions. Publications"

Transcription

1 Civil Engineering Structural Analysis Comprehensive Theory with Solved Examples and Practice Questions Publications

2 Publications MADE EASY Publications Corporate Office: 44-A/4, Kalu Sarai (Near Hauz Khas Metro Station), New Delhi Contact: , Visit us at: Structural Analysis Copyright, by MADE EASY Publications. All rights are reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted in any form or by any means (electronic, mechanical, photo-copying, recording or otherwise), without the prior written permission of the above mentioned publisher of this book. First Edition: 2015 Second Edition (Revised and Updated): 2016 All rights reserved by MADE EASY PUBLICATIONS. No part of this book may be reproduced or utilized in any form without the written permission from the publisher.

3 Preface This book was motivated by the desire to further the evolution of a concise book on Structural Analysis. Keeping in focus the importance of this subject in GATE and ESE, we have done a proper study and thereafter developed the content of the book accordingly. This edition has an expanded discussion of all relevant topics in the subject. Initially, we compiled the perceptions of our students on their problems in GATE and ESE while dealing with the questions from this subject. We identified their various problems like- lack of fundamentals of the subject, difficulty in solving simple solutions, shortage of a complete study package, etc. These strengthened our determination to present a complete edition of Structural Analysis textbook. The book addresses all the requirements of the students, i.e. comprehensive coverage of theory, fundamental concepts, objective type problems and conventional problems, articulated in a lucid language. The concise presentation will help the readers grasp the concepts with clarity and apply them with ease to solve problems quickly. The books not only covers the entire syllabus of GATE and ESE, but also addresses the need of many other competitive examinations. Topics like Stability and Indeterminacy, Influence Line Diagram and Rolling Loads, Trusses, Arches, External Equilibrium of Structures, Methods of Indeterminate Analysis : Basic Methods, Energy Methods of Analysis, Moment Distribution Method of Analysis, Slope Deflection Method of Analysis, Matrix Methods of Analysis are given full coverage in line with our research on their importance in competitive examinations. We have put in our sincere efforts to present elaborate solutions for various problems, different problem solving methodology, some useful quick techniques to save time while attempting MCQs without compromising the accuracy of answers. A summary of important points to remember is added at the end of each topic. For the convenience of readers, points to remember are specifically highlighted in the form of a note- both in theory as well as solved examples. At the end of each chapter, sets of practice question are given with their keys, that will allow the readers to evaluate their understanding of the topics and sharpen their problem solving skills. Our team has made their best efforts to remove all possible errors of any kind. Nonetheless, we would highly appreciate and acknowledge if you find and share with us any printing, calculation and conceptual error. It is impossible to thank all the individuals who helped us, but we would like to sincerely thank all the co-authors, editors and reviewers for putting in their efforts to publish this book. We also express our thanks to MADE EASY publications for completing and publishing the book on time. With Best Wishes B. Singh CMD, MADE EASY

4 Contents Structural Analysis Chapter 1 Stability and Indeterminacy Support System D Supports D Internal Joints D Supports Structure Elements of Structure Types of Structures Types of Loading Stability of Structures External Stability Internal Stability Overall Stability Statically Determinate and Indeterminate Structures Statically Determinate Structures Statically Indeterminate Structures Degree of Indeterminacy Static Indeterminacy Degree of Kinematic Indeterminacy...24 Chapter 2 Objective Brain Teasers...29 Influence Line Diagram and Rolling Loads Introduction Influence Line Diagram Influence Line for Determinate Structure Muller Breslau s Principle Application of ILD Effect of Rolling Loads Single Point Load Uniformly Distributed Load Longer than the Span Uniformly Distributed Load Smaller than the Span Series of Point Load Influence Line Diagram for Statically Indeterminate Beams...70 Objective Brain Teasers...79 Conventional Practice Questions...83 Chapter 3 Trusses Introduction Classification of Trusses Stability of Trusses Determinate and Indeterminate Trusses Methods of Analysis of Determinate Truss Method of Joints Method of Sections Methods of Analysis of Indeterminate Truss Unit Load Method Stiffness Method Deflection of Truss Joints Maxwell s Method/Unit Load Method Influence Line Diagram for Trusses Objective Brain Teasers Conventional Practice Questions (v)

5 Chapter 4 Arches Introduction Comparison between Cable and Arch Comparison between the behaviour of Arch and Beam Advantages of Arch over Beam Disadvantages of Arch over Beam Analysis of Three-Hinged Arches Three Hinge Parabolic Arch Subjected to UDL over Entire Span Three Hinge Semi-circular Arch Subjected to UDL over Entire Span Three Hinge Semi-circular Arch Subjected to Concentrated Load at Crown Three Hinged Parabolic Arch with Abutments at Different Heights Subjected to UDL over Entire Span Temperature Effect on Three Hinged Arches Two Hinges Arches Two Hinged Semi-circular Arch Subjected to Concentrated Load at Crown Two Hinged Semi-circular Arch Subjected to UDL over Entire Span Two Hinge Parabolic Arch Subjected to UDL over Entire Span Two Hinged Parabolic Arch Subjected to Concentrated Load at Crown Temperature Effect on Two Hinged Arches Reaction Locus for a Two Hinged Arch The Linear Arch or Theoretical Arch Influence Line Diagrams for Three Hinged Arches ILD for Horizontal Thrust ILD for Bending Moment ILD for Radial Shear ILD for Normal Thrust Influence for Two Hinged Arches ILD for Horizontal Thrust ILD for Bending Moment ILD for Radial Shear ILD for Normal Thrust Chapter 5 Objective Brain Teasers Conventional Practice Questions External Equilibrium of Structures Equations of Equilibrium Free Body Diagram Objective Brain Teasers Chapter 6 Methods of Indeterminate Analysis : Basic Methods Introduction Castigliano s Theorem Castigliano s First Theorem Castigliano s Second Theorem Principle of Minimum Potential Energy Betti s Law Maxwell s Reciprocal Theorem Principal of Virtual Work Principle of Superposition Consistent Deformation of Method Procedure of Analysis by Consistent Deformation Method Three Moment Equation Application of Three Moment Equation to Continuous Beams with Fixed Ends Application of Three Moment Equation to Continuous Chapter 7 Beam with Support at Different Level Objective Brain Teasers Conventional Practice Questions Energy Methods of Analysis Application of Minimum Potential Energy Algorithm for Analysis (vi)

6 7.3 Unit Load Method Algorithm to Find Slope/Deflection Chapter 8 Objective Brain Teasers Conventional Practice Questions Moment Distribution Method of Analysis Introduction Stiffness Carry over Factors Distribution Theorem Distribution Factor Fixed End Moments Standard Results of Fixed End Moments Bending Moment Diagram Using Stiffness Approach Procedure of Analysis by Moment Distribution Method Sway Analysis Frames without Sway Frames with Sway Beam Sway (Joint Displacement) Procedure of Sway Analysis Sway Analysis of Non-prismatic Beams Sway of Skew Frames Chapter 9 Objective Brain Teasers Conventional Practice Questions Slope Deflection Method of Analysis Introduction Sign Convention Derivation of Slope Deflection Equations Procedure of Analysis Analysis of Frames without Sway Analysis of Frames with Sway Beam Sway (Joint Displacement) Objective Brain Teasers Conventional Practice Questions Chapter 10 Matrix Methods of Analysis Algebra of Matrices Types of Matrices Matrices Operations Standard Results of Slope and Deflection Flexibility and Stiffness Flexibility Matrix Properties Procedure to Develop Flexibility Matrix Stiffness Matrix Properties Procedure to Develop Stiffness Matrix Standard Results for Stiffness Analysis of Beam and Frame Using Flexibility Matrix Method Degree of Static Indeterminacy Basic Released Structure Analysis of Beam and Frame Using Stiffness Matrix Method Objective Brain Teasers Conventional Practice Questions (vii)

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

Engineering. Mathematics. GATE 2019 and ESE 2019 Prelims. For. Comprehensive Theory with Solved Examples

Engineering. Mathematics. GATE 2019 and ESE 2019 Prelims. For. Comprehensive Theory with Solved Examples Thoroughly Revised and Updated Engineering Mathematics For GATE 2019 and ESE 2019 Prelims Comprehensive Theory with Solved Examples Including Previous Solved Questions of GATE (2003-2018) and ESE-Prelims

More information

Engineering Mathematics

Engineering Mathematics Thoroughly Revised and Updated Engineering Mathematics For GATE 2017 and ESE 2017 Prelims Note: ESE Mains Electrical Engineering also covered Publications Publications MADE EASY Publications Corporate

More information

Structural Analysis. For. Civil Engineering.

Structural Analysis. For. Civil Engineering. Structural Analysis For Civil Engineering By www.thegateacademy.com ` Syllabus for Structural Analysis Syllabus Statically Determinate and Indeterminate Structures by Force/ Energy Methods; Method of Superposition;

More information

Theory of Structures

Theory of Structures SAMPLE STUDY MATERIAL Postal Correspondence Course GATE, IES & PSUs Civil Engineering Theory of Structures C O N T E N T 1. ARCES... 3-14. ROLLING LOADS AND INFLUENCE LINES. 15-9 3. DETERMINACY AND INDETERMINACY..

More information

techie-touch.blogspot.com DEPARTMENT OF CIVIL ENGINEERING ANNA UNIVERSITY QUESTION BANK CE 2302 STRUCTURAL ANALYSIS-I TWO MARK QUESTIONS UNIT I DEFLECTION OF DETERMINATE STRUCTURES 1. Write any two important

More information

Methods of Analysis. Force or Flexibility Method

Methods of Analysis. Force or Flexibility Method INTRODUCTION: The structural analysis is a mathematical process by which the response of a structure to specified loads is determined. This response is measured by determining the internal forces or stresses

More information

6/6/2008. Qualitative Influence Lines for Statically Indeterminate Structures: Muller-Breslau s Principle

6/6/2008. Qualitative Influence Lines for Statically Indeterminate Structures: Muller-Breslau s Principle Qualitative Influence Lines for Statically Indeterminate Structures: Muller-Breslau s Principle The influence line for a force (or moment) response function is given by the deflected shape of the released

More information

CE 2302 STRUCTURAL ANALYSIS I UNIT-I DEFLECTION OF DETERMINATE STRUCTURES

CE 2302 STRUCTURAL ANALYSIS I UNIT-I DEFLECTION OF DETERMINATE STRUCTURES CE 2302 STRUCTURAL ANALYSIS I UNIT-I DEFLECTION OF DETERMINATE STRUCTURES 1.Why is it necessary to compute deflections in structures? Computation of deflection of structures is necessary for the following

More information

L13 Structural Engineering Laboratory

L13 Structural Engineering Laboratory LABORATORY PLANNING GUIDE L13 Structural Engineering Laboratory Content Covered subjects according to the curriculum of Structural Engineering... 2 Main concept... 4 Initial training provided for laboratory

More information

Foundations and Applications of Engineering Mechanics

Foundations and Applications of Engineering Mechanics Foundations and Applications of Engineering Mechanics 4843/24, 2nd Floor, Ansari Road, Daryaganj, Delhi - 110002, India Cambridge University Press is part of the University of Cambridge. It furthers the

More information

2 marks Questions and Answers

2 marks Questions and Answers 1. Define the term strain energy. A: Strain Energy of the elastic body is defined as the internal work done by the external load in deforming or straining the body. 2. Define the terms: Resilience and

More information

UNIT II SLOPE DEFLECION AND MOMENT DISTRIBUTION METHOD

UNIT II SLOPE DEFLECION AND MOMENT DISTRIBUTION METHOD SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : SA-II (13A01505) Year & Sem: III-B.Tech & I-Sem Course & Branch: B.Tech

More information

UNIT-II MOVING LOADS AND INFLUENCE LINES

UNIT-II MOVING LOADS AND INFLUENCE LINES UNIT-II MOVING LOADS AND INFLUENCE LINES Influence lines for reactions in statically determinate structures influence lines for member forces in pin-jointed frames Influence lines for shear force and bending

More information

ENERGY METHODS OF STRUCTURAL ANALYSIS

ENERGY METHODS OF STRUCTURAL ANALYSIS ENERGY METHODS OF STRUCTURAL ANALYSIS By the same author ESSENTIAL SOLID MECHANICS Theory, Worked Examples and Problems ENERGY METHODS OF STRUCTURAL ANALYSIS Theory, worked examples and problems B. W.

More information

ENGINEERING MECHANICS: STATICS AND DYNAMICS

ENGINEERING MECHANICS: STATICS AND DYNAMICS ENGINEERING MECHANICS: STATICS AND DYNAMICS Dr. A.K. Tayal ENGINEERING MECHANICS STATICS AND DYNAMICS A.K. Tayal Ph. D. Formerly Professor Department of Mechanical Engineering Delhi College of Engineering

More information

If the number of unknown reaction components are equal to the number of equations, the structure is known as statically determinate.

If the number of unknown reaction components are equal to the number of equations, the structure is known as statically determinate. 1 of 6 EQUILIBRIUM OF A RIGID BODY AND ANALYSIS OF ETRUCTURAS II 9.1 reactions in supports and joints of a two-dimensional structure and statically indeterminate reactions: Statically indeterminate structures

More information

Structural Analysis III Compatibility of Displacements & Principle of Superposition

Structural Analysis III Compatibility of Displacements & Principle of Superposition Structural Analysis III Compatibility of Displacements & Principle of Superposition 2007/8 Dr. Colin Caprani, Chartered Engineer 1 1. Introduction 1.1 Background In the case of 2-dimensional structures

More information

UNIT IV FLEXIBILTY AND STIFFNESS METHOD

UNIT IV FLEXIBILTY AND STIFFNESS METHOD SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : SA-II (13A01505) Year & Sem: III-B.Tech & I-Sem Course & Branch: B.Tech

More information

ENGINEERING MECHANICS

ENGINEERING MECHANICS ENGINEERING MECHANICS Engineering Mechanics Volume 2: Stresses, Strains, Displacements by C. HARTSUIJKER Delft University of Technology, Delft, The Netherlands and J.W. WELLEMAN Delft University of Technology,

More information

M.S Comprehensive Examination Analysis

M.S Comprehensive Examination Analysis UNIVERSITY OF CALIFORNIA, BERKELEY Spring Semester 2014 Dept. of Civil and Environmental Engineering Structural Engineering, Mechanics and Materials Name:......................................... M.S Comprehensive

More information

(2) ANALYSIS OF INDETERMINATE STRUCTRES

(2) ANALYSIS OF INDETERMINATE STRUCTRES Chapter (2) ANALYSIS OF INDETERMINATE STRUCTRES 1.1 Statically Indeterminate Structures A structure of any type is classified as statically indeterminate when the number of unknown reaction or internal

More information

FLEXIBILITY METHOD FOR INDETERMINATE FRAMES

FLEXIBILITY METHOD FOR INDETERMINATE FRAMES UNIT - I FLEXIBILITY METHOD FOR INDETERMINATE FRAMES 1. What is meant by indeterminate structures? Structures that do not satisfy the conditions of equilibrium are called indeterminate structure. These

More information

Lecture 4: PRELIMINARY CONCEPTS OF STRUCTURAL ANALYSIS. Introduction

Lecture 4: PRELIMINARY CONCEPTS OF STRUCTURAL ANALYSIS. Introduction Introduction In this class we will focus on the structural analysis of framed structures. We will learn about the flexibility method first, and then learn how to use the primary analytical tools associated

More information

Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method

Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method Objectives In this course you will learn the following Deflection by strain energy method. Evaluation of strain energy in member under

More information

Chapter 2: Deflections of Structures

Chapter 2: Deflections of Structures Chapter 2: Deflections of Structures Fig. 4.1. (Fig. 2.1.) ASTU, Dept. of C Eng., Prepared by: Melkamu E. Page 1 (2.1) (4.1) (2.2) Fig.4.2 Fig.2.2 ASTU, Dept. of C Eng., Prepared by: Melkamu E. Page 2

More information

Module 6. Approximate Methods for Indeterminate Structural Analysis. Version 2 CE IIT, Kharagpur

Module 6. Approximate Methods for Indeterminate Structural Analysis. Version 2 CE IIT, Kharagpur Module 6 Approximate Methods for Indeterminate Structural Analysis Lesson 35 Indeterminate Trusses and Industrial rames Instructional Objectives: After reading this chapter the student will be able to

More information

Review of Strain Energy Methods and Introduction to Stiffness Matrix Methods of Structural Analysis

Review of Strain Energy Methods and Introduction to Stiffness Matrix Methods of Structural Analysis uke University epartment of Civil and Environmental Engineering CEE 42L. Matrix Structural Analysis Henri P. Gavin Fall, 22 Review of Strain Energy Methods and Introduction to Stiffness Matrix Methods

More information

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR CE 6602 STRUCTURAL ANALYSIS - II DEPARTMENT OF CIVIL ENGINEERING CE 6501 STRUCTURAL ANALYSIS - I 2 MARK QUESTION BANK UNIT II - INFLUENCE LINES

More information

29. Define Stiffness matrix method. 30. What is the compatibility condition used in the flexibility method?

29. Define Stiffness matrix method. 30. What is the compatibility condition used in the flexibility method? CLASS: III YEAR / VI SEMESTER CIVIL SUBJECTCODE AND NAME: CE 2351 - STRUCTURAL ANALYSIS-II UNIT1 FLEXIBILITY MATRIX METHOD. PART A 1. What is meant by indeterminate structures? 2. What are the conditions

More information

Written as per the revised G Scheme syllabus prescribed by the Maharashtra State Board of Technical Education (MSBTE) w.e.f. academic year

Written as per the revised G Scheme syllabus prescribed by the Maharashtra State Board of Technical Education (MSBTE) w.e.f. academic year Written as per the revised G Scheme syllabus prescribed by the Maharashtra State Board of Technical Education (MSBTE) w.e.f. academic year 2012-2013 Basic MATHEMATICS First Year Diploma Semester - I First

More information

T2. VIERENDEEL STRUCTURES

T2. VIERENDEEL STRUCTURES T2. VIERENDEEL STRUCTURES AND FRAMES 1/11 T2. VIERENDEEL STRUCTURES NOTE: The Picture Window House can be designed using a Vierendeel structure, but now we consider a simpler problem to discuss the calculation

More information

UNIT II 1. Sketch qualitatively the influence line for shear at D for the beam [M/J-15]

UNIT II 1. Sketch qualitatively the influence line for shear at D for the beam [M/J-15] UNIT II 1. Sketch qualitatively the influence line for shear at D for the beam [M/J-15] 2. Draw the influence line for shear to the left of B for the overhanging beam shown in Fig. Q. No. 4 [M/J-15] 3.

More information

GATE SOLUTIONS E N G I N E E R I N G

GATE SOLUTIONS E N G I N E E R I N G GATE SOLUTIONS C I V I L E N G I N E E R I N G From (1987-018) Office : F-16, (Lower Basement), Katwaria Sarai, New Delhi-110016 Phone : 011-65064 Mobile : 81309090, 9711853908 E-mail: info@iesmasterpublications.com,

More information

Lecture 11: The Stiffness Method. Introduction

Lecture 11: The Stiffness Method. Introduction Introduction Although the mathematical formulation of the flexibility and stiffness methods are similar, the physical concepts involved are different. We found that in the flexibility method, the unknowns

More information

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method Module 2 Analysis of Statically Indeterminate Structures by the Matrix Force Method Lesson 8 The Force Method of Analysis: Beams Instructional Objectives After reading this chapter the student will be

More information

Structural Analysis II Prof. P. Banerjee Department of Civil Engineering Indian Institute of Technology, Bombay Lecture 38

Structural Analysis II Prof. P. Banerjee Department of Civil Engineering Indian Institute of Technology, Bombay Lecture 38 Structural Analysis II Prof. P. Banerjee Department of Civil Engineering Indian Institute of Technology, Bombay Lecture 38 Good morning. We have been looking at influence lines for the last couple of lectures

More information

Igor Emri Arkady Voloshin. Statics. Learning from Engineering Examples

Igor Emri Arkady Voloshin. Statics. Learning from Engineering Examples Statics Igor Emri Arkady Voloshin Statics Learning from Engineering Examples Igor Emri University of Ljubljana Ljubljana, Slovenia Arkady Voloshin Lehigh University Bethlehem, PA, USA ISBN 978-1-4939-2100-3

More information

QUESTION BANK ENGINEERS ACADEMY. Hinge E F A D. Theory of Structures Determinacy Indeterminacy 1

QUESTION BANK ENGINEERS ACADEMY. Hinge E F A D. Theory of Structures Determinacy Indeterminacy 1 Theory of Structures eterminacy Indeterminacy 1 QUSTION NK 1. The static indeterminacy of the structure shown below (a) (b) 6 (c) 9 (d) 12 2. etermine the degree of freedom of the following frame (a) 1

More information

Advanced Structural Analysis Prof. Devdas Menon Department of Civil Engineering Indian Institute of Technology, Madras Module No. # 2.

Advanced Structural Analysis Prof. Devdas Menon Department of Civil Engineering Indian Institute of Technology, Madras Module No. # 2. Advanced Structural Analysis Prof. Devdas Menon Department of Civil Engineering Indian Institute of Technology, Madras Module No. # 2.2 Lecture No. # 08 Review of Basic Structural Analysis-2 Good morning

More information

Chapter 2 Basis for Indeterminate Structures

Chapter 2 Basis for Indeterminate Structures Chapter - Basis for the Analysis of Indeterminate Structures.1 Introduction... 3.1.1 Background... 3.1. Basis of Structural Analysis... 4. Small Displacements... 6..1 Introduction... 6.. Derivation...

More information

CHENDU COLLEGE OF ENGINEERING &TECHNOLOGY DEPARTMENT OF CIVIL ENGINEERING SUB CODE & SUB NAME : CE2351-STRUCTURAL ANALYSIS-II UNIT-1 FLEXIBILITY

CHENDU COLLEGE OF ENGINEERING &TECHNOLOGY DEPARTMENT OF CIVIL ENGINEERING SUB CODE & SUB NAME : CE2351-STRUCTURAL ANALYSIS-II UNIT-1 FLEXIBILITY CHENDU COLLEGE OF ENGINEERING &TECHNOLOGY DEPARTMENT OF CIVIL ENGINEERING SUB CODE & SUB NAME : CE2351-STRUCTURAL ANALYSIS-II UNIT-1 FLEXIBILITY METHOD FOR INDETERMINATE FRAMES PART-A(2MARKS) 1. What is

More information

Indeterminate Analysis Force Method 1

Indeterminate Analysis Force Method 1 Indeterminate Analysis Force Method 1 The force (flexibility) method expresses the relationships between displacements and forces that exist in a structure. Primary objective of the force method is to

More information

Module 3. Analysis of Statically Indeterminate Structures by the Displacement Method

Module 3. Analysis of Statically Indeterminate Structures by the Displacement Method odule 3 Analysis of Statically Indeterminate Structures by the Displacement ethod Lesson 21 The oment- Distribution ethod: rames with Sidesway Instructional Objectives After reading this chapter the student

More information

Module 3. Analysis of Statically Indeterminate Structures by the Displacement Method

Module 3. Analysis of Statically Indeterminate Structures by the Displacement Method odule 3 Analysis of Statically Indeterminate Structures by the Displacement ethod Lesson 14 The Slope-Deflection ethod: An Introduction Introduction As pointed out earlier, there are two distinct methods

More information

MEG 741 Energy and Variational Methods in Mechanics I

MEG 741 Energy and Variational Methods in Mechanics I MEG 741 Energy and Variational Methods in Mechanics I Brendan J. O Toole, Ph.D. Associate Professor of Mechanical Engineering Howard R. Hughes College of Engineering University of Nevada Las Vegas TBE

More information

3.4 Analysis for lateral loads

3.4 Analysis for lateral loads 3.4 Analysis for lateral loads 3.4.1 Braced frames In this section, simple hand methods for the analysis of statically determinate or certain low-redundant braced structures is reviewed. Member Force Analysis

More information

UNIT-III ARCHES Introduction: Arch: What is an arch? Explain. What is a linear arch?

UNIT-III ARCHES Introduction: Arch: What is an arch? Explain. What is a linear arch? UNIT-III RCES rches as structural forms Examples of arch structures Types of arches nalysis of three hinged, two hinged and fixed arches, parabolic and circular arches Settlement and temperature effects.

More information

Lecture 6: The Flexibility Method - Beams. Flexibility Method

Lecture 6: The Flexibility Method - Beams. Flexibility Method lexibility Method In 1864 James Clerk Maxwell published the first consistent treatment of the flexibility method for indeterminate structures. His method was based on considering deflections, but the presentation

More information

Preliminaries: Beam Deflections Virtual Work

Preliminaries: Beam Deflections Virtual Work Preliminaries: Beam eflections Virtual Work There are several methods available to calculate deformations (displacements and rotations) in beams. They include: Formulating moment equations and then integrating

More information

Module 3. Analysis of Statically Indeterminate Structures by the Displacement Method

Module 3. Analysis of Statically Indeterminate Structures by the Displacement Method odule 3 Analysis of Statically Indeterminate Structures by the Displacement ethod Lesson 16 The Slope-Deflection ethod: rames Without Sidesway Instructional Objectives After reading this chapter the student

More information

Software Verification

Software Verification EXAMPLE 1-026 FRAME MOMENT AND SHEAR HINGES EXAMPLE DESCRIPTION This example uses a horizontal cantilever beam to test the moment and shear hinges in a static nonlinear analysis. The cantilever beam has

More information

GLOBAL EDITION. Structural Analysis. Ninth Edition in SI Units. R. C. Hibbeler

GLOBAL EDITION. Structural Analysis. Ninth Edition in SI Units. R. C. Hibbeler GLOAL EDITION Structural Analysis Ninth Edition in SI Units R. C. Hibbeler STRUCTURAL ANALYSIS NINTH EDITION IN SI UNITS R. C. HIELER SI Conversion by Kai eng Yap oston Columbus Indianapolis New York San

More information

Simplified Structural Analysis and Design for Architects

Simplified Structural Analysis and Design for Architects Simplified Structural Analysis and Design for Architects Second Edition Rima Taher, PhD, PE New Jersey Institute of Technology Bassim Hamadeh, CEO and Publisher Kassie Graves, Director of Acquisitions

More information

Statics and Influence Functions From a Modern Perspective

Statics and Influence Functions From a Modern Perspective Statics and Influence Functions From a Modern Perspective Friedel Hartmann Peter Jahn Statics and Influence Functions From a Modern Perspective 123 Friedel Hartmann Department of Civil Engineering University

More information

Chapter 11. Displacement Method of Analysis Slope Deflection Method

Chapter 11. Displacement Method of Analysis Slope Deflection Method Chapter 11 Displacement ethod of Analysis Slope Deflection ethod Displacement ethod of Analysis Two main methods of analyzing indeterminate structure Force method The method of consistent deformations

More information

MECHANICS OF MATERIALS

MECHANICS OF MATERIALS STATICS AND MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr, John T. DeWolf David E Mazurek \Cawect Mc / iur/» Craw SugomcT Hilt Introduction 1 1.1 What is Mechanics? 2 1.2 Fundamental

More information

Advanced Structural Analysis. Prof. Devdas Menon. Department of Civil Engineering. Indian Institute of Technology, Madras. Module No. # 1.

Advanced Structural Analysis. Prof. Devdas Menon. Department of Civil Engineering. Indian Institute of Technology, Madras. Module No. # 1. Advanced Structural Analysis Prof. Devdas Menon Department of Civil Engineering Indian Institute of Technology, Madras Module No. # 1.3 Lecture No. # 03 Review of Basic Structural Analysis -1 (Refer Slide

More information

Method of Consistent Deformation

Method of Consistent Deformation Method of onsistent eformation Structural nalysis y R.. Hibbeler Theory of Structures-II M Shahid Mehmood epartment of ivil Engineering Swedish ollege of Engineering and Technology, Wah antt FRMES Method

More information

A New Method of Analysis of Continuous Skew Girder Bridges

A New Method of Analysis of Continuous Skew Girder Bridges A New Method of Analysis of Continuous Skew Girder Bridges Dr. Salem Awad Ramoda Hadhramout University of Science & Technology Mukalla P.O.Box : 50511 Republic of Yemen ABSTRACT One three girder two span

More information

Written as per the revised G Scheme syllabus prescribed by the Maharashtra State Board of Technical Education (MSBTE) w.e.f. academic year

Written as per the revised G Scheme syllabus prescribed by the Maharashtra State Board of Technical Education (MSBTE) w.e.f. academic year Written as per the revised G Scheme syllabus prescribed by the Maharashtra State Board of Technical Education (MSBTE) w.e.f. academic year 2012-2013 Basic MATHEMATICS First Year Diploma Semester - I First

More information

TYPES OF STRUCUTRES. HD in Civil Engineering Page 1-1

TYPES OF STRUCUTRES. HD in Civil Engineering Page 1-1 E2027 Structural nalysis I TYPES OF STRUUTRES H in ivil Engineering Page 1-1 E2027 Structural nalysis I SUPPORTS Pin or Hinge Support pin or hinge support is represented by the symbol H or H V V Prevented:

More information

ENGINEERING MECHANICS

ENGINEERING MECHANICS ENGINEERING MECHANICS ENGINEERING MECHANICS (In SI Units) For BE/B.Tech. Ist YEAR Strictly as per the latest syllabus prescribed by Mahamaya Technical University, Noida By Dr. R.K. BANSAL B.Sc. Engg.

More information

Determinate portal frame

Determinate portal frame eterminate portal frame onsider the frame shown in the figure below with the aim of calculating the bending moment diagram (M), shear force diagram (SF), and axial force diagram (F). P H y R x x R y L

More information

Slender Structures Load carrying principles

Slender Structures Load carrying principles Slender Structures Load carrying principles Basic cases: Extension, Shear, Torsion, Cable Bending (Euler) v017-1 Hans Welleman 1 Content (preliminary schedule) Basic cases Extension, shear, torsion, cable

More information

Ph.D. Preliminary Examination Analysis

Ph.D. Preliminary Examination Analysis UNIVERSITY OF CALIFORNIA, BERKELEY Spring Semester 2017 Dept. of Civil and Environmental Engineering Structural Engineering, Mechanics and Materials Name:......................................... Ph.D.

More information

ERM - Elasticity and Strength of Materials

ERM - Elasticity and Strength of Materials Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2018 205 - ESEIAAT - Terrassa School of Industrial, Aerospace and Audiovisual Engineering 712 - EM - Department of Mechanical Engineering

More information

Matrix Method of Structural Analysis Prof. Amit Shaw Department of Civil Engineering Indian Institute of Technology, Kharagpur

Matrix Method of Structural Analysis Prof. Amit Shaw Department of Civil Engineering Indian Institute of Technology, Kharagpur Matrix Method of Structural Analysis Prof. Amit Shaw Department of Civil Engineering Indian Institute of Technology, Kharagpur Lecture 01 Introduction Hello everyone, welcome to the online course on Matrix

More information

Module 1. Energy Methods in Structural Analysis

Module 1. Energy Methods in Structural Analysis Module 1 Energy Methods in Structural Analysis esson 5 Virtual Work Instructional Objecties After studying this lesson, the student will be able to: 1. Define Virtual Work.. Differentiate between external

More information

Ph.D. Preliminary Examination Analysis

Ph.D. Preliminary Examination Analysis UNIVERSITY OF CALIFORNIA, BERKELEY Spring Semester 2014 Dept. of Civil and Environmental Engineering Structural Engineering, Mechanics and Materials Name:......................................... Ph.D.

More information

STATE UNIVERSITY OF NEW YORK COLLEGE OF TECHNOLOGY CANTON, NEW YORK COURSE OUTLINE ENGS STATICS

STATE UNIVERSITY OF NEW YORK COLLEGE OF TECHNOLOGY CANTON, NEW YORK COURSE OUTLINE ENGS STATICS STATE UNIVERSITY OF NEW YORK COLLEGE OF TECHNOLOGY CANTON, NEW YORK COURSE OUTLINE PREPARED BY: ARTHUR HURLBUT, Ph.D. P.E.(October 2006) UPDATED BY: MICHAEL J. NEWTOWN, P.E. (October 2006) REVISED BY:

More information

Module 3. Analysis of Statically Indeterminate Structures by the Displacement Method. Version 2 CE IIT, Kharagpur

Module 3. Analysis of Statically Indeterminate Structures by the Displacement Method. Version 2 CE IIT, Kharagpur odule 3 Analysis of Statically Indeterminate Structures by the Displacement ethod Version CE IIT, Kharagpur Lesson The ultistory Frames with Sidesway Version CE IIT, Kharagpur Instructional Objectives

More information

QUESTION BANK. SEMESTER: V SUBJECT CODE / Name: CE 6501 / STRUCTURAL ANALYSIS-I

QUESTION BANK. SEMESTER: V SUBJECT CODE / Name: CE 6501 / STRUCTURAL ANALYSIS-I QUESTION BANK DEPARTMENT: CIVIL SEMESTER: V SUBJECT CODE / Name: CE 6501 / STRUCTURAL ANALYSIS-I Unit 5 MOMENT DISTRIBUTION METHOD PART A (2 marks) 1. Differentiate between distribution factors and carry

More information

ELASTICITY AND FRACTURE MECHANICS. Vijay G. Ukadgaonker

ELASTICITY AND FRACTURE MECHANICS. Vijay G. Ukadgaonker THEORY OF ELASTICITY AND FRACTURE MECHANICS y x Vijay G. Ukadgaonker Theory of Elasticity and Fracture Mechanics VIJAY G. UKADGAONKER Former Professor Indian Institute of Technology Bombay Delhi-110092

More information

Supplement: Statically Indeterminate Trusses and Frames

Supplement: Statically Indeterminate Trusses and Frames : Statically Indeterminate Trusses and Frames Approximate Analysis - In this supplement, we consider an approximate method of solving statically indeterminate trusses and frames subjected to lateral loads

More information

2. Determine the deflection at C of the beam given in fig below. Use principal of virtual work. W L/2 B A L C

2. Determine the deflection at C of the beam given in fig below. Use principal of virtual work. W L/2 B A L C CE-1259, Strength of Materials UNIT I STRESS, STRAIN DEFORMATION OF SOLIDS Part -A 1. Define strain energy density. 2. State Maxwell s reciprocal theorem. 3. Define proof resilience. 4. State Castigliano

More information

Method of Least Work. Theory of Structures II M Shahid Mehmood Department of Civil Engineering Swedish College of Engineering & Technology, Wah Cantt

Method of Least Work. Theory of Structures II M Shahid Mehmood Department of Civil Engineering Swedish College of Engineering & Technology, Wah Cantt Method of east Work Theor of Structures II M Shahid Mehmood epartment of ivil Engineering Swedish ollege of Engineering & Technolog, Wah antt Method of east Work / astigliano s Second Theorem Staticall

More information

Theory of structure I 2006/2013. Chapter one DETERMINACY & INDETERMINACY OF STRUCTURES

Theory of structure I 2006/2013. Chapter one DETERMINACY & INDETERMINACY OF STRUCTURES Chapter one DETERMINACY & INDETERMINACY OF STRUCTURES Introduction A structure refers to a system of connected parts used to support a load. Important examples related to civil engineering include buildings,

More information

Deflections. Deflections. Deflections. Deflections. Deflections. Deflections. dx dm V. dx EI. dx EI dx M. dv w

Deflections. Deflections. Deflections. Deflections. Deflections. Deflections. dx dm V. dx EI. dx EI dx M. dv w CIVL 311 - Conjugate eam 1/5 Conjugate beam method The development of the conjugate beam method has been atributed to several strucutral engineers. any credit Heinrich üller-reslau (1851-195) with the

More information

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method Module 2 Analysis of Statically Indeterminate Structures by the Matrix Force Method Lesson 10 The Force Method of Analysis: Trusses Instructional Objectives After reading this chapter the student will

More information

BOOK OF COURSE WORKS ON STRENGTH OF MATERIALS FOR THE 2 ND YEAR STUDENTS OF THE UACEG

BOOK OF COURSE WORKS ON STRENGTH OF MATERIALS FOR THE 2 ND YEAR STUDENTS OF THE UACEG BOOK OF COURSE WORKS ON STRENGTH OF MATERIALS FOR THE ND YEAR STUDENTS OF THE UACEG Assoc.Prof. Dr. Svetlana Lilkova-Markova, Chief. Assist. Prof. Dimitar Lolov Sofia, 011 STRENGTH OF MATERIALS GENERAL

More information

Shear Force V: Positive shear tends to rotate the segment clockwise.

Shear Force V: Positive shear tends to rotate the segment clockwise. INTERNL FORCES IN EM efore a structural element can be designed, it is necessary to determine the internal forces that act within the element. The internal forces for a beam section will consist of a shear

More information

ME 025 Mechanics of Materials

ME 025 Mechanics of Materials ME 025 Mechanics of Materials General Information: Term: 2019 Summer Session Instructor: Staff Language of Instruction: English Classroom: TBA Office Hours: TBA Class Sessions Per Week: 5 Total Weeks:

More information

Advanced Structural Analysis Prof. Devdas Menon Department of Civil Engineering Indian Institute of Technology, Madras

Advanced Structural Analysis Prof. Devdas Menon Department of Civil Engineering Indian Institute of Technology, Madras Advanced Structural Analysis Prof. Devdas Menon Department of Civil Engineering Indian Institute of Technology, Madras Module - 6.2 Lecture - 34 Matrix Analysis of Plane and Space Frames Good morning.

More information

202 Index. failure, 26 field equation, 122 force, 1

202 Index. failure, 26 field equation, 122 force, 1 Index acceleration, 12, 161 admissible function, 155 admissible stress, 32 Airy's stress function, 122, 124 d'alembert's principle, 165, 167, 177 amplitude, 171 analogy, 76 anisotropic material, 20 aperiodic

More information

Experimental Lab. Principles of Superposition

Experimental Lab. Principles of Superposition Experimental Lab Principles of Superposition Objective: The objective of this lab is to demonstrate and validate the principle of superposition using both an experimental lab and theory. For this lab you

More information

STATICALLY INDETERMINATE STRUCTURES

STATICALLY INDETERMINATE STRUCTURES STATICALLY INDETERMINATE STRUCTURES INTRODUCTION Generally the trusses are supported on (i) a hinged support and (ii) a roller support. The reaction components of a hinged support are two (in horizontal

More information

Lecture 8: Flexibility Method. Example

Lecture 8: Flexibility Method. Example ecture 8: lexibility Method Example The plane frame shown at the left has fixed supports at A and C. The frame is acted upon by the vertical load P as shown. In the analysis account for both flexural and

More information

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK. Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK. Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV UNIT I STRESS, STRAIN DEFORMATION OF SOLIDS PART A (2 MARKS)

More information

STATICS Chapter 1 Introductory Concepts

STATICS Chapter 1 Introductory Concepts Contents Preface to Adapted Edition... (v) Preface to Third Edition... (vii) List of Symbols and Abbreviations... (xi) PART - I STATICS Chapter 1 Introductory Concepts 1-1 Scope of Mechanics... 1 1-2 Preview

More information

MECHANICS OF SOLIDS Credit Hours: 6

MECHANICS OF SOLIDS Credit Hours: 6 MECHANICS OF SOLIDS Credit Hours: 6 Teaching Scheme Theory Tutorials Practical Total Credit Hours/week 4 0 6 6 Marks 00 0 50 50 6 A. Objective of the Course: Objectives of introducing this subject at second

More information

ESE TOPICWISE OBJECTIVE SOLVED PAPER I

ESE TOPICWISE OBJECTIVE SOLVED PAPER I C I V I L E N G I N E E R I N G ESE TOPICWISE OBJECTIVE SOLVED PAPER I FROM 1995-018 UPSC Engineering Services Eamination, State Engineering Service Eamination & Public Sector Eamination. Regd. office

More information

Mechanics of Solids and Structures, Second Edition

Mechanics of Solids and Structures, Second Edition Mechanics of Solids and Structures, Second Edition A revision of a popular textbook, this volume emphasizes the development of analysis techniques from basic principles for a broad range of practical problems,

More information

Continuing Education Course #207 What Every Engineer Should Know About Structures Part B Statics Applications

Continuing Education Course #207 What Every Engineer Should Know About Structures Part B Statics Applications 1 of 6 Continuing Education Course #207 What Every Engineer Should Know About Structures Part B Statics Applications 1. As a practical matter, determining design loads on structural members involves several

More information

QUESTION BANK DEPARTMENT: CIVIL SEMESTER: III SUBJECT CODE: CE2201 SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A

QUESTION BANK DEPARTMENT: CIVIL SEMESTER: III SUBJECT CODE: CE2201 SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A DEPARTMENT: CIVIL SUBJECT CODE: CE2201 QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State

More information

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method Module 2 Analysis of Statically Indeterminate Structures by the Matrix Force Method Lesson 11 The Force Method of Analysis: Frames Instructional Objectives After reading this chapter the student will be

More information

A New Jacobi-based Iterative Method for the Classical Analysis of Structures

A New Jacobi-based Iterative Method for the Classical Analysis of Structures 2581 A New Jacobi-based Iterative Method for the Classical Analysis of Structures Abstract Traditionally, classical methods of structural analysis such as slope-deflection and moment distribution methods

More information

METHOD OF COMPUTING GEOMETRIC RELATIONS IN STRUCTURAL ANALY IS

METHOD OF COMPUTING GEOMETRIC RELATIONS IN STRUCTURAL ANALY IS Solid Mechanics, Plasticity, and Limit Analysis METHOD OF COMPUTING GEOMETRIC RELATIONS IN STRUCTURAL ANALY IS LiBRARY by. Wai F. Chen Fritz Engineering Laboratory Report No. 356..3 Solid Mechanics, Plasticity,

More information

STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS

STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1 UNIT I STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define: Stress When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The

More information

Only for Reference Page 1 of 18

Only for Reference  Page 1 of 18 Only for Reference www.civilpddc2013.weebly.com Page 1 of 18 Seat No.: Enrolment No. GUJARAT TECHNOLOGICAL UNIVERSITY PDDC - SEMESTER II EXAMINATION WINTER 2013 Subject Code: X20603 Date: 26-12-2013 Subject

More information

Structural Analysis of Truss Structures using Stiffness Matrix. Dr. Nasrellah Hassan Ahmed

Structural Analysis of Truss Structures using Stiffness Matrix. Dr. Nasrellah Hassan Ahmed Structural Analysis of Truss Structures using Stiffness Matrix Dr. Nasrellah Hassan Ahmed FUNDAMENTAL RELATIONSHIPS FOR STRUCTURAL ANALYSIS In general, there are three types of relationships: Equilibrium

More information