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INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous)

Dundigal, Hyderabad -500 043

Aeronautical Engineering

COURSE INFORMATION SHEET

Course Title THEORY OF STRUCTURES

Course Code AAE002

Semester B Tech III Semester

Course Type Core

Regulation IARE - R16

Course Structure Lectures Tutorials Practicals Credits

3 1 - 4

Course

Coordinator

Dr. D Govardhan, Professor and Head

Department of Aeronautical Engineering

Course Faculty Mr. G.S D Madhav, Assistant Professor

Ms. Y Shwetha, Assistant Professor

Mr. G Ram Vishal, Assistant Professor

I. COURSE OVERVIEW:

The primary objective of this course is to introduce the concept of algorithm as a precise

mathematical concept, and study how to design algorithms, establish their correctness, study

their efficiency and memory needs. The course consists of a strong mathematical component

in addition to the design of various algorithms.

II. COURSE PRE-REQUISITES:

Level Course Code Semester Prerequisites Credits

UG AHS007 I Applied physics 4

UG AME002 II Engineering Mechanics 4

III. MARKS DISTRIBUTION

Subject SEE

Examination

CIA

Examination Total Marks

Theory of Structures 70 Marks 30 Marks 100

Semester End Examination (SEE):

The SEE is conducted for 70 marks of 3 hours duration. The syllabus for the theory courses is

divided into FIVE units and each unit carries equal weightage in terms of marks distribution.

The question paper pattern is as follows: two full questions with ‘either’ ‘or’ choice will be

drawn from each unit. Each question carries 14 marks.

Continuous Internal Assessment (CIA):

CIA is conducted for a total of 30 marks, with 25 marks for Continuous Internal Examination

(CIE) and 05 marks for Quiz / Alternative Assessment Tool (AAT).

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Continuous Internal Examination (CIE):

The CIE exam is conducted for 25 marks of 2 hours duration consisting of two parts.

Part–A shall have five compulsory questions of one mark each. In part–B, four out of

five questions have to be answered where, each question carries 5 marks. Marks are

awarded by taking average of marks scored in two CIE exams.

Quiz / Alternative Assessment Tool (AAT):

Two Quiz exams shall be online examination consisting of 20 multiple choice questions

and are be answered by choosing the correct answer from a given set of choices

(commonly four). Marks shall be awarded considering the average of two quizzes for

every course. The AAT may include seminars, assignments, term paper, open ended

experiments, micro projects, five minutes video and MOOCs.

IV. DELIVERY / INSTRUCTIONAL METHODOLOGIES:

CHALK & TALK QUIZ ASSIGNMENTS MOOCs

LCD / PPT SEMINARS MINI PROJECT VIDEOS

OPEN ENDED EXPERIMENTS

V. ASSESSMENT METHODOLOGIES – DIRECT

CIE EXAMS SEE EXAMS ASSIGNEMNTS SEMINARS

LABORATORY

PRACTICES

STUDENT

VIVA MINI PROJECT CERTIFICATION

TERM PAPER

VI. ASSESSMENT METHODOLOGIES – INDIRECT

ASSESSMENT OF COURSE

OUTCOMES (BY FEEDBACK, ONCE)

STUDENT FEEDBACK ON FACULTY

(TWICE)

ASSESSMENT OF MINI PROJECTS BY EXPERTS

VII. COURSE OBJECTIVES:

The course should enable the students to:

I Understand the several of Concepts of stress and strain in mechanical components by

stressing the fundamentals

II Calculate bending stresses and shear stresses for in a beam of symmetric and un-

symmetric sections

III Explain the deflections of beams with various load conditions by different approaches

IV Discuss the buckling behavior of columns with different load and boundary

conditions

V Explain the components of the stress and strain tensors and conditions of

compatibility and equations of equilibrium.

VI Describe statically indeterminate structure by using different approximate methods.

VII Demonstrate curvature beams and how to determine deflection using various

approximation methods.

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VIII . COURSE LEARNING OUTCOMES:

Students, who complete the course, will have demonstrated the ability to do the following:

CAAE002.01 Calculate the stress strain relations in conjunction with elasticity and material properties

CAAE002.02 Describe the resistance and deformation in members which are subjected to axial, flexural

and torsion loads.

CAAE002.03 Discuss thermal explanations in solid bars and induced thermal stresses

CAAE002.04 Solve for bending and shear stresses of symmetric and un-symmetric beams under loading

conditions

CAAE002.05 Calculate the shear stresses developed in various sections of beams.

CAAE002.06 Calculate the flexural developed in various sections of beams of real field problems.

CAAE002.07 Differentiate between redundant structures and determinate structures.

CAAE002.08 Analyze the redundant complex structural components subjected to different loading and

boundary conditions.

CAAE002.09 Solve for deflections of beams under loading with various approaches

CAAE002.10 Calculate the stability of structural elements and determine buckling loads.

CAAE002.11 Discuss critical buckling load for column with various loading and end conditions

CAAE002.12 Apply a theories and to predict the performance of bars under axial loading including

buckling.

CAAE002.13 Describe the behavior of structural components subjected to various loading and support

conditions based on principles of equilibrium and constitutional relationships.

CAAE002.14 Explain the stress transformation and concept of principle plane and principle stresses

CAAE002.15 Evaluate principal stresses, strains and apply the concept of failure theories for design

CAAE002.16 Acquire Basic knowledge to solve real time problems in Aircraft structure with different

loading conditions

CAAE002.17 Posses the knowledge skills for employability and to succeed in national and international

level competitive examinations

IX. HOW PROGRAM OUTCOMES ARE ASSESSED:

Program Outcomes Level Proficiency

assessed by

PO 1

Engineering knowledge: Apply the knowledge of mathematics, science,

engineering fundamentals, and an engineering specialization to the

solution of complex engineering problems.

H Assignments

PO 2

Problem analysis: Identify, formulate, review research literature, and

analyze complex engineering problems reaching substantiated

conclusions using first principles of mathematics, natural sciences, and

engineering sciences.

H Assignments

PO 3

Design/development of solutions: Design solutions for complex

engineering problems and design system components or processes that

meet the specified needs with appropriate consideration for the public

health and safety, and the cultural, societal, and environmental

considerations.

S Mini Project

PO 4

Conduct investigations of complex problems: Use research-based

knowledge and research methods including design of experiments,

analysis and interpretation of data, and synthesis of the information to

provide valid conclusions.

S Open ended

experiments /

PO 5

Modern tool usage: Create, select, and apply appropriate techniques,

resources, and modern engineering and IT tools including prediction and

modeling to complex engineering activities with an understanding of the

S Mini Project

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Program Outcomes Level Proficiency

assessed by

limitations.

PO 6

The engineer and society: Apply reasoning informed by the contextual

knowledge to assess societal, health, safety, legal and cultural issues and

the consequent responsibilities relevant to the professional engineering

practice.

N ---

PO 7

Environment and sustainability: Understand the impact of the

professional engineering solutions in societal and environmental contexts,

and demonstrate the knowledge of, and need for sustainable development.

N ---.

PO 8 Ethics: Apply ethical principles and commit to professional ethics and

responsibilities and norms of the engineering practice. N ---

PO 9 Individual and team work: Function effectively as an individual, and as

a member or leader in diverse teams, and in multidisciplinary settings. N ---

PO 10

Communication: Communicate effectively on complex engineering

activities with the engineering community and with society at large, such

as, being able to comprehend and write effective reports and design

documentation, make effective presentations, and give and receive clear

instructions.

S

Seminars /

Term Paper /

5 minutes

video

PO 11

Project management and finance: Demonstrate knowledge and

understanding of the engineering and management principles and apply

these to one’s own work, as a member and leader in a team, to manage

projects and in multidisciplinary environments.

N ---

PO 12

Life-long learning: Recognize the need for, and have the preparation and

ability to engage in independent and life-long learning in the broadest

context of technological change.

S Certifications

N= None S= Supportive H = Highly Related

X. HOW PROGRAM SPECIFIC OUTCOMES ARE ASSESSED:

Program Specific Outcomes Level

Proficiency

assessed

by

PSO 1

Professional skills: Able to utilize the knowledge of

aeronautical/aerospace engineering in innovative, dynamic and

challenging environment for design and development of new products

H Lectures,

Assignments

PSO 2

Problem solving skills: imparted through simulation language skills and

general purpose CAE packages to solve practical, design and analysis

problems of components to complete the challenge of airworthiness for

flight vehicles

H Projects

PSO 3

Practical implementation and testing skills: Providing different types of

in house and training and industry practice to fabricate and test and

develop the products with more innovative technologies

S Guest

Lectures

PSO 4

Successful career and entrepreneurship: To prepare the students with

broad aerospace knowledge to design and develop systems and subsystems

of aerospace and allied systems and become technocrats

S Guest

Lectures

N - None S - Supportive H - Highly Related

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XI. SYLLABUS:

UNIT I

INTRODUCTION

Mechanical properties of materials; Stresses and strains; Hooke‘s law, elastic constant, relation between

modulii, working stress, factor of safety, poisons ratio ; bars of varying cross section; Thermal stresses.

Torsion of solid and hollow circular shafts and shear stress variations; Power transmission in shafts; Shear

force and bending moment diagrams for different types of beams with various loads.

UNIT II

STRESSES IN BEAMS

Bending stresses and Shear stress variation in beams of symmetric and un-symmetric sections; Beams of

uniform strength; Flexural stresses: Bending equations, calculation of bending stresses for different

sections of beams like I, L, T, C, angle section.

UNIT III

BEAMS AND COLUMNS

Deflection of beams by Double integration method, Macaulay‘s method, moment area method, conjugate

beam method; Principle of superposition.

Columns, types of columns, Euler‘s formula instability of columns, Rakine‘s and Jonson‘s formula, Eigen

values and Eigen modes, concept of beam-column.

UNIT IV

REDUNDANT STRUCTURES

Trusses, perfect frames, analysis of trusses; Determinate and indeterminate structures, order of redundancy;

Redundant analysis, analysis of determinate structures, area movement method, Clayperons method, slope

deflection method, moment distribution method

UNIT V

THEORY OF ELASTISITY

Equilibrium and compatibility conditions and constitute relations for elastic solid and plane: generalized

plane strain cases Airy‘s stress function Stress on inclined planes, stress transformations determination of

principal stresses and strains by analytical method and graphical method - Mohr‘s circles and its

constructions.

TEXT BOOKS:

1 R. K Bansal, ―Strength of Materials‖, Laxmi publications, 5th

Edition, 2012.

2 T. H. G. Megson, ―Aircraft Structures for Engineering Students‖, Butterworth-Heinemann Ltd, 5th

Edition, 2012 .

3 Gere, Timoshenko, ―Mechanics of Materials‖, McGraw Hill, 3rd

Edition, 1993.

REFERENCES:

1 Dym, C. L, Shames, I. H, ―Solid Mechanics‖, McGraw Hill, Kogakusha, Tokyo, 7th

Edition,

2007.

2 Stephen Timoshenko, ―Strength of Materials‖, Vol I & II, CBS Publishers and Distributors,

3rd

Edition, 2004.

3 R. K. Rajput, ―Strength of Materials‖, S. Chand and Co., 1st Edition, 1999.

4 Timoshenko, S, Young, D. H. ―Elements of Strength of Materials‖, T. Van Nostrand Co.

Inc., Princeton N.J, 4th

Edition, 1977.

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XII. COURSE PLAN:

The course plan is meant as a guideline. There may probably be changes.

Lecture

No

Topic Outcomes Topic/s to be covered Reference

1-3 Define stress and strain. Equations

associated with them

UNIT 1

INTRODUCTION

Equilibrium and Compatibility

conditions for elastic solids, 2D

elasticity equations for plane

stress,

T1

4-6 Examine stress functions associated

with stress and strain

2D elasticity equations plane strain and

generalized plane strain cases Airy’s stress

function

T1

7-8 Analyze bars of varying cross

sections and thermal stresses

Simple problems in bars of varying cross

sections and thermal stresses T1

9-11 Relate torsion of solids an hollow

circular shafts

2D Elastic equations of torsion of solids an

hollow circular shafts T3

12-14 Describe Power transmission in

shafts

Concept of principal planes, principal

stress and Strains Power transmission in

shafts

T3

15-17 Evaluate Shear force and bending

moment diagrams for different types

of beams with various loads

Problems on different beams of Shear

force and bending moment diagrams for

different types of beams with various loads

T3

18-20 Describe symmetrical and

unsymmetrical bending equation for

beams

UNIT 2

STRESSES IN BEAMS

Bending stresses and Shear stress variation

in beams of symmetric and un-symmetric

sections;

T2

21-23 Evaluate Beams of uniform strength;

Flexural stresses

Beams of uniform strength; Flexural

stresses T2

24-26 Evaluate Bending equations, for

different sections of beams like I, L,

T, C, angle section.

Bending equations, calculation of bending

stresses for different sections of beams like

I, L, T, C, angle section.

T2

27-30 Explain importance of deflection of

beams.

UNIT 3

BEAMS AND COLOUMNS

Deflection of beams by Double

integration method, Macaulay‘s

method

-

31-33 Discuss deflection methods for

different bemas

Deflection of beams using moment area

method, conjugate beam method; Principle

of superposition.

-

34-37 Define column and strut and types

column

Columns, types of columns, Euler‘s

formula instability of columns, T3

38-39 Discuss Rankine method to solve

different failure of column

Rakine‘s and Jonson‘s formula, Eigen

values and Eigen modes, concept of beam-

column.

T3

39-41 Describe statically indeterminate

structures and equations

UNIT 4

REDUNDANT STRUCTURES

Indeterminate structures and order of

redundancy, Introduction to redundant

analysis, Statically determinate models,

T3

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Lecture

No

Topic Outcomes Topic/s to be covered Reference

Use of free body diagrams to explain

compatibility and redundant analysis

principles.

42-44 Evaluate methods of analysis of

statically indeterminate beams

Statically determinate models- Area

movement method use of free body

diagrams to explain compatibility and

redundant analysis principles.

T3

45-47 Evaluate methods of analysis of

statically indeterminate beams

Statically determinate models- Clayprons

method use of free body diagrams to

explain compatibility and redundant

analysis principles.

T3

48-50 Explain methods of analysis of

statically indeterminate beams

Singularity method for uniform beams

with various boundary and support

conditions (props, hinges and fixities)

subjected to distributed / discrete loads

(including moments).

T3

51-53 Discuss equilibrium equations and

compatibility conditions

UNIT 5

THEORY OF ELASTISITY

Equilibrium and compatibility

conditions and constitute relations

for elastic solid and plane.

T2

54-56 Explain importance of Airys stress

functions

generalized plane strain cases

Airy‘s stress function). T2

57-59 Discuss various expressions for

transformation equations

Stress on inclined planes, stress

transformations T2

60-62 Explain the determination of

principle stresses using both

analytical and graphical method

determination of principal stresses and

strains by analytical method and graphical

method - Mohr‘s circles and its

constructions..

T2

XIII. GAPS IN THE SYLLABUS - TO MEET INDUSTRY / PROFESSION

REQUIREMENTS:

S NO

DESCRIPTION

PROPOSED

ACTIONS

RELEVANCE

WITH POs

RELEVANCE

WITH PSOs

1

Broad knowledge of

engineering materials and

material properties

Seminars / Guest

Lectures / NPTEL

PO 1, PO 2, PO 12

PSO 1

2

Practical Exposure about the

stress deflections and stability

of elements

Seminars / Guest

Lectures / NPTEL

PO 2, PO 12

PSO 2

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XIV. MAPPING COURSE OBJECTIVES LEADING TO THE ACHIEVEMENT OF

PROGRAM OUTCOMES AND PROGRAM SPECIFIC OUTCOMES:

Course

Objectives

Program Outcomes Program Specific

Outcomes

PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 PSO1 PSO2 PSO3 PSO4

I H H S S H

II H H S S S H S

III H S S H

IV H H S H S

V H S H

VI H H S H S

VII H H S S H

S= Supportive H = Highly Related

XV. MAPPING COURSE LEARNING OUTCOMES LEADING TO THE ACHIEVEMENT

OF PROGRAM OUTCOMES AND PROGRAM SPECIFIC OUTCOMES:

Course

Learning

Outcomes

Program Outcomes Program Specific

Outcomes

PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 PSO1 PSO2 PSO3 PSO4

CAIT001.01 H H S H

CAIT001.02 H H S S H

CAIT001.03 H H S H

CAIT001.04 H H S H

CAIT001.05 H H S H

CAIT001.06 H H S H

CAIT001.07 H S H

CAIT001.08 H H S H

CAIT001.09 H H S H

CAIT001.10 H H S S H

CAIT001.11 H H S S H

CAIT001.12 H H S H

CAIT001.13 H H S H

CAIT001.14 H S H

CAIT001.15 H H S H

CAIT001.16 H H S H

CAIT001.17 H H S H

S= Supportive H = Highly Related

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XVI. DESIGN BASED PROBLEMS (DP) / OPEN ENDED PROBLEM:

1. Task is to design a mechanical scale for making rough measurements of the weight of

passengers’ checked luggage at a local airport located in New Delhi. The boss has proposed

the system shown in the figure - 1. A party’s luggage is placed on the platform AB and the

cable DCE, originally in the no load configuration indicated by the lengths Lo, takes up the

new state indicated by the lengths L. The circles indicate pulleys meant to offer no

resistance to rotation. The spring extends, the pointer moves and a reading is made. You are

given the following specifications and constraints.

The scale is to be read with the naked eye.

The measured weight should be accurate to within 5%. Of particular interest is

determining the weight of baggage which may be excessive.

Two springs are available for use - one with stiffness of 500 lb/in, another of 100 lb/in.

The dimension b is constrained to be less than 4 feet and must be greater than 1.5 ft.;

1.5 < b< 4 ft.

Your boss wants to see a non-dimensional analysis justifying your choice of spring and of

cable geometry as well as a figure showing the details of the scale against which the position

of the pointer is read. If you use a spread sheet, and this is encouraged, you are to label all

columns on your print out of same and indicate units, if needed.

Figure -1

2. A hollow aluminum shaft, two meters long, must transmit a torque of 20 KN-m. and bear a

compressive load of 100 KN. The total angle of twist over the full length of the shaft is not

to exceed 2.0o, and of course, we do not want the shaft to yield. Size the outside and inside

diameters of the shaft striving to keep the volume of material a minimum.

3. A truss structure is needed to support a hoist in a garage which services ordinary passenger

vehicles. The hoist’s major load is the engine block. The truss must span the twenty feet

overhead, from wall to wall. All diagonal members are to have the same cross-sectional

area. Horizontal members at the top and bottom are to have the same cross-sectional area,

but may be different from that of the diagonals.

Develop a layout of a (statically determinant) truss structure which will support the load

with a factor of safety of 2. (This material fails in tension if the member stress equals the

yield stress of 50,000 psi).

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Consider several alternative designs, exploring how their cost varies one to another taking,

as a first approximation, the cost as proportional to the total volume of the material. You do

not have time to optimize. Rather, limit your concern to identifying the parameters that will

determine the cost and how their variation will affect the same.

Figure -3

4. A truss structure is needed to support a 1 kilometer stretch of roadway. The structure is

supported, at equally spaced intervals of length b, atop 1 ft.-square pads which, in turn, rest

directly on the sandy soil.

The equivalent spring stiffness of the soil is 50 to 150 lb/in per square-in of surface area.

Anticipated traffic includes fully loaded trucks as well as passenger vehicles.

Specifications include:

Drivers should not experience disorienting rotation of their vehicle as they travel the

roadway (e.g., as if they were going over hills and dale).

The roadway is to accommodate but one lane of traffic.

The structure should not yield.

Truss members are to be made of steel. Take the allowable design stress to be

20,000psi.

While cost will ultimately be a factor in the design, you need only describe which features

of the design will matter when costs are considered. Also, while existing codes will further

circumscribe and even dictate the choice of some design parameters; these too are to be left

aside for the moment. However, you do have available Truss-works to explore and fix on

candidate structures worth further detailed design.

Figure - 4

Prepared By:

Dr. D Govardhan, Professor

HOD, AE

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