(+1) shows an additional lecture per week to deliver the content in desired depth and within the available time frame.
Grades/Marks for Practical Exam include submission of term work, assignments and viva-voce.

Syllabus

Unit

Unit Contents

Total Hours

1

Fundamentals of CAD:
1. Introduction, Reasons for implementing a CAD system, Computer Aided
Process application, Conventional design vs CAD. Benefits of a CAD system.
2. Hardware, CAD software, Elements of Programming, CAD programming.
3. Technical specification of CAD workstation, computer software-operating system

03

2

Computer Graphics:
1. Scan conversions,
2. DDA and Breshnham’s algorithm for generation of various figures,
3. 2D and 3D transformations: Scaling, Translation, Rotation,
4. Mirroring,Clipping, Homogeneous matrix.

04

3

Geometrical Modeling:
1. Types & mathematical representation of curves,
2. Wire frame models,
3. Entities, representations,
4. Parametric representations [A]
5. Review of vector algebra, lines, circle, ellipse, parabolas,
6. Parametric representation of synthetic curves,
7. Cubic curves, b - spline,
8. Bezier spline, sweep curves
9. --- : Reserve Lecture : --- [B]
10. Surfaces & solids – model, entities, representations,
11. Fundamentals of surface and solid modeling,
12. B-rep, constructive solid geometry (CSG),
13. Analytical modeling, sweep. [C]
14. Solid manipulation, visual realism.
15. Computer aided design of Mechanical Elements & Mechanical Assembly with animation.
16. Capabilities of various commercially available software in the area of CAD.

16

4

Graphics Standards:
1. Standards for graphics programming, features of GKS, other graphics standards,
2. PHIGS, IGES, PDES. Standards in CAD.

02

5

Finite Element Analysis:
1. Types of elements, types of error,
2. Derivation equitation finite element procedure,
3. Stress – deflection – stiffness matrix,
4. Global matrix, conductivity table. [A]
5. Elimination approach,
6. Penalty approach,
7. Effect of temperature,
8. Principle of min. Potential energy, [B]
9. Mesh generation,
10. Capability of different FEA software.

10

6

Optimization:
1. Introduction, design synthesis, Engineering vs Optimum Design,
2. Objectives of Optimization,
3. Classification of Optimization problems and their procedure,
4. Techniques of optimization,
5. Optimized design of machine components,
6. Optimization Software.
7. --- : Reserve Lecture : ---
8. --- : Reserve Lecture : ---

08

Midterm Exam Syllabus:Units 1, 2, 3-A, 5

Teachers

Units 1, 2, 3, 4 will be taught by Dr. Keyur Thakkar
Units 5, 6 will be taught by Mr. Sachin Daxini

Course Calendar

Lecture Notes/Presentations/Videos

(Click the link to go to individual lecture contents) Lecture 01: [Introduction, Reasons for implementing a CAD system, Computer Aided Process application, Conventional design vs CAD. Benefits of a CAD system.] Lecture 02: [Hardware, CAD software, Elements of Programming, CAD programming] Lecture 03: [Technical specification of CAD workstation, computer software-operating system] Lecture 04: [Review, Assignment 1]

Lecture 05: [Scan conversions] Lecture 06: [DDA and Breshnham’s algorithm for generation of various figures] Lecture 07: [2D and 3D transformations: Scaling, Translation, Rotation] Lecture 08: [Mirroring,Clipping, Homogeneous matrix] Lecture 09: [Review, Assignment 2]

Lecture 10: [Types & mathematical representation of curves] Lecture 11: [Wire frame models] Lecture 12: [Hardware, CAD software, Elements of Programming, CAD programming] Lecture 13: [Entities, representations] Lecture 14: [Parametric representations] Lecture 15: [Review of vector algebra, lines, circle, ellipse, parabolas] Lecture 16: [Parametric representation of synthetic curves] Lecture 17: [Cubic curves, b - spline] Lecture 18: [Bezier spline, sweep curves] Lecture 19: [Midterm Exam Revision, Instructions and Tips]

Lecture 20: [Review, Assignment 3 & 4, Surfaces & solids – model, entities, representations]
Lecture 21: [Fundamentals of surface and solid modeling]
Lecture 22: [B-rep, constructive solid geometry (CSG)]
Lecture 23: [Analytical modeling, sweep]
Lecture 24: [Solid manipulation, visual realism]
Lecture 25: [Computer aided design of Mechanical Elements & Mechanical Assembly with animation]
Lecture 26: [Capabilities of various commercially available software in the area of CAD]

Lecture 27: [Standards for graphics programming, features of GKS, other graphics standards]
Lecture 28: [PHIGS, IGES, PDES. Standards in CAD]
Lecture E1: [Extra Lecture - Revision]
Lecture 29: [---:Reserve Lecture:---]
Lecture 30: [---:Reserve Lecture:---]

Lecture 31: [Types of elements, types of error]
Lecture 32: [Derivation equitation finite element procedure]
Lecture 33: [Stress – deflection – stiffness matrix]
Lecture 34: [Global matrix, conductivity table]
Lecture 35: [Elimination approach]
Lecture 36: [Penalty approach]
Lecture 37: [Effect of temperature]
Lecture 38: [Principle of min. Potential energy]
Lecture 39: [Mesh generation]
Lecture E2: [Capability of different FEA software, Revision, Midterm Exam Tips]

Lecture 40: [Introduction, design synthesis, Engineering vs Optimum Design, Objectives of Optimization]
Lecture 41: [Classification of Optimization problems and their procedure]
Lecture 42: [Techniques of optimization]
Lecture 43: [Optimized design of machine components]
Lecture E3: [Optimization Software, Revision]

Assignments

1. There will be 6 assignments, one from each unit, by the concerned teacher.
2. Failure to submit the assignment before deadline shall result in zero grades. Late assignments will not be accepted under any circumstances.

3. Mode of Submission: Paper Copy, soft copies to be mailed or uploaded as requested, within the prior set deadlines.
4. Grades : A-F system (equivalent to 0 - 10 scale, 0 - 20 for a 20 Mark assignment)
5. Penalty : The penalty for late submission is a deduction of (0.1 X No. of Days) from original grades. i.e., If you are late by 10 or more days, you will not get any grades for the assignment.
6. For subject related queries, please feel free to communicate with

Term Work

1. There will be 10 Experiments/Experiences to be learned/performed and each one is to be submitted individually within the prescribed deadlines.
2. The date of submission will be the subsequent lab. e.g., if the term work is given on Monday the 19th, the date of submission is next Monday, that is, 26th of the same month.
3. Late term works shall not be accepted under any circumstances unless prior approval is obtained with a proper justification.
4. Prepare a record book/file and a journal to submit your findings as instructed. Use diagrams/figures as and when required.

Experiments/Experiences

Ex.No.

Title/Aim/Objectives

Activities/Submission

1

Introduction to Computer Aided Design

- To Study basic concepts and content of subject
- To get an awareness about selection of hardware and software
for a CAD Workstation.

Lab Activity:Discussion
The Lab Instructor should...
a. Begin a discussion about what inspires a Design Engineer to
move from conventional paper based drafting and designing to a computer based drafting, designing
and analysis.
b. From the comparison, advantages and limitations the discussion should move on to various elements
of a CAD workstation (software as well as hardware) and their present specifications. Submission :Q/A
(Record book as well as Journal)
1. What is CAD?
2. Distinguish between conventional design and computer aided design?
3. Discuss advantages & limitation of CAD.
4. List of hardware requirements for a CAD workstation.
5. List CAD software used commercially with their capabilities.

2

Computer Graphics I: Line and Circle

- To understand basics of programming language and use of the compiler.
- To learn the DDA and Bresenham Algorithms
- Use the algorithms to create C programs

Lab Activity :Demonstration and individual programming
The Lab Instructor should instruct and demonstrate on a CAD workstation about the origin of a CAD software,
DDA and Bresenham algorithms.
a. Prepare a ‘C’ program for generation of a line using DDA algorithm
b. Prepare a ‘C’ program for generation of a line using Bresenham algorithm
c. Prepare a ‘C’ program for generation of a circle using Bresehnam algorithm
Submission :
1. Basics of 'C' language
2. Details of DDA algorithm
3. Details of Bresenham algorithm

3

Computer Graphics II: 2D & 3D Transformation

- To learn the 2D and 3D transformations
- Create C programs for them.

Lab Activity: On the basis of discussion, prepare ‘C’ programs for following 2D & 3D Transformations:

Ø Two Dimensional Transformation

1) Translation of Triangle.
2) Program to Translate and Rotate Rectangle about origin.
3) Rotation of Triangle about a point.

Ø Three Dimensional Transformation

1) Program to Scale and Rotate a 3D Box

4

Design of Machine Elements Generation of ‘C’ programs for designing machine elements– Shaft and Spring design

Prepare ‘C’ programs for designing a Shaft and a Spring for following problems:Shaft Design:A shaft is supported by two bearings placed 1 m apart . A 600 mm diameter pulley is mounted at a distanceof 300 mm to the right of left hand bearing and this drives a pulley directly below it with the help of belt havingmaximum tension of 2.25 kN. Another pulley 400 mm diameter is placed 200 mm to the left of right handbearing and is driven with the help of electric motor and belt, which is placed horizontally to the right.The angle of contact for both the pulleys is 180° and µ=0.24. Determine the suitable diameter for a solid shaft.Take allowing stress in tension 63 MPa and in shear 42 MPa for shaft material.Assume that the torque on one pulley is equal to that on the other pulley. Spring Design:It is required to design a helical compression spring subjected to a maximum force of 1250 N. The deflectionof the spring corresponding to the maximum force should be approximately 30 mm. the spring index is 6 andthe UTS and modulus of rigidity of spring material are 1090 and 81370 N/mm2, respectively. The permissibleshear stress for the spring wire should b taken as 50% of UTS. Design the spring and calculate wire diameter,mean coil diameter, no. of active coils and total no. of coils, free length of spring.

5

Geometric Modeling and Graphic Standards To study Geometric Modeling and significance of Graphics Standards

On the basis of discussion, answer following questions: EXERCISE:
1) Explain the Constructive Solid Geometry (CSG) scheme of solid modeling.
2) Explain the following surface types:
Lofted surface
Tabulated surface
Bezier surface
3) What are the differences among 3D wire frame, surface and solid models? State their advantages, limitations and applications.
4) Why standardization is needed in computer graphics. State the various graphics standard available. Explain them.

6

Solid ModelingPreparation of 3D models of given parts using Pro/Engineer and generating detailed drawing

Prepare a 3D model for the following object using Pro/Engineer software:Prepare a 3D model of the part from following detailed drawing and generate similar drawing for the model prepared using Pro/Engineer software:- Sectional View- Projection View- Detailed View- General View

7

Assembly Modeling Preparation of Assembly of given parts in Pro/Engineer

Assembly Creation: Pro/Engineer is ideal for feature based design and cumulative building up of successive parts. But once these complex parts are in place, they have to be assembled in ways that work. Creating workable assemblies and machines is the desired end result and the most important aspect of learning to work with Pro/Engineer.To create an assembly model, you must constrain components by selecting surfaces and features. Always begin an assembly with a base component, a component that you are unlikely to remove from the assembly later on. Begin your assembly with default datums. Add the first part or subassembly onto the default assembly datum.Constraint Options: Placement constraints create a parent/child relationship between the already assembled components and the new component being added to the assembly. Careful consideration is advised in choosing constraint types and references.Most commonly used constraints are: Mate: - Normal Vectors of selected surfaces point in opposite directions and become co-planar. Mate Offset: - Normal Vectors of selected surfaces point in opposite directions and are offset by a specified negative or positive value.Align: - Normal vectors of selected surfaces point in the same direction and are made co-planar. Align will also make two axes co-axial.Align Offset: - Normal vectors of selected surfaces point in the same direction and are offset by a specified negative or positive value.Insert: - Selected cylindrical surfaces of revolution become co-axial. Three surfaces do not need to be full 360 degree cylinders.Packaging or Under-Constrained Components: - Packaging allows you to add components to an assembly without adding all its necessary constraints. Similarly when you over-constrain a component, you add more constraints than is necessary.Since Pro/E is associative, you can make changes to all components in sub assemblies while working in the assembly. When you save assembly, the system automatically saves any changes that you made to any of the parts in that assembly.

8

Finite element Method Study Finite Element Method – 1D, 2D & 3D analysis in Pro/Engineer, Pro/Mechanica

The objective of this exercise is to know the basic steps while performing Static Stress Analysis using a FEA software package. One dimensional and three dimensional problems are considered here. An example of bar loaded axially is taken as one dimensional problem.While a simple solid model is considered for three dimensional analysis. The main steps involved are:* Creation of the model

Specifying model type

Setting up constraints, loads, and material definitions

Meshing – generation of elements in problem domain

Running the solution

Setting up and showing result displays for displacements, stresses

EXERCISE: One Dimensional Problem:1) The problem of bar loaded axially is taken for study. To work in software, such problems can be formulated by beam idealization. Consider the bar shown in Fig. below loaded as shown. Determine the nodal displacement, element stresses and support reactions, theoretically by adopting the penalty approach. Verify the results obtained using a Software package available. Take, P = 300 kN, P’ = 600 kN, A1 = 250 mm2, A2 = 400 mm2 Esteel = 200 x 109 N/m22) Formulate a Plane stress/strain problem for 2D analysis.3) Formulate a 3 D analysis problem for the geometry shown below in Pro/Engineer:

9

Design OptimizationTo study optimization in mechanical design problems

On the basis of discussion, answer following questions:1) List various application areas of optimization and discuss role of computers in Optimization.2) State linear programming problem in standard form.3) Differentiate between linear and non linear programming problems.4) Differentiate between design variables and preassigned parameters.5) Define Design space, constraints and objective functions.6) Differentiate between a bound point and a free point in design space.

## Table of Contents

## Teaching Scheme

Teaching SchemeEvaluation SchemeTotalCreditsFinal Exam(External)

[E]

Midterm Exam(Internal)

[M]

Practical Exam(External)

[I]

Grades/Marks for Practical Exam include submission of term work, assignments and viva-voce.

## Syllabus

UnitUnit ContentsTotal HoursFundamentals of CAD:1. Introduction, Reasons for implementing a CAD system, Computer Aided

Process application, Conventional design vs CAD. Benefits of a CAD system.

2. Hardware, CAD software, Elements of Programming, CAD programming.

3. Technical specification of CAD workstation, computer software-operating system

Computer Graphics:1. Scan conversions,

2. DDA and Breshnham’s algorithm for generation of various figures,

3. 2D and 3D transformations: Scaling, Translation, Rotation,

4. Mirroring,Clipping, Homogeneous matrix.

Geometrical Modeling:1. Types & mathematical representation of curves,

2. Wire frame models,

3. Entities, representations,

4. Parametric representations

[A]5. Review of vector algebra, lines, circle, ellipse, parabolas,

6. Parametric representation of synthetic curves,

7. Cubic curves, b - spline,

8. Bezier spline, sweep curves

9. --- : Reserve Lecture : ---

[B]10. Surfaces & solids – model, entities, representations,

11. Fundamentals of surface and solid modeling,

12. B-rep, constructive solid geometry (CSG),

13. Analytical modeling, sweep.

[C]14. Solid manipulation, visual realism.

15. Computer aided design of Mechanical Elements & Mechanical Assembly with animation.

16. Capabilities of various commercially available software in the area of CAD.

Graphics Standards:1. Standards for graphics programming, features of GKS, other graphics standards,

2. PHIGS, IGES, PDES. Standards in CAD.

Finite Element Analysis:1. Types of elements, types of error,

2. Derivation equitation finite element procedure,

3. Stress – deflection – stiffness matrix,

4. Global matrix, conductivity table.

[A]5. Elimination approach,

6. Penalty approach,

7. Effect of temperature,

8. Principle of min. Potential energy,

[B]9. Mesh generation,

10. Capability of different FEA software.

Optimization:1. Introduction, design synthesis, Engineering vs Optimum Design,

2. Objectives of Optimization,

3. Classification of Optimization problems and their procedure,

4. Techniques of optimization,

5. Optimized design of machine components,

6. Optimization Software.

7. --- : Reserve Lecture : ---

8. --- : Reserve Lecture : ---

## Teachers

Units 1, 2, 3, 4 will be taught by

Dr. Keyur ThakkarUnits 5, 6 will be taught by

Mr. Sachin Daxini## Course Calendar

## Lecture Notes/Presentations/Videos

(Click the link to go to individual lecture contents)Lecture 01: [Introduction, Reasons for implementing a CAD system, Computer Aided Process application, Conventional design vs CAD. Benefits of a CAD system.]

Lecture 02: [Hardware, CAD software, Elements of Programming, CAD programming]

Lecture 03: [Technical specification of CAD workstation, computer software-operating system]

Lecture 04: [Review, Assignment 1]

Lecture 05: [Scan conversions]

Lecture 06: [DDA and Breshnham’s algorithm for generation of various figures]

Lecture 07: [2D and 3D transformations: Scaling, Translation, Rotation]

Lecture 08: [Mirroring,Clipping, Homogeneous matrix]

Lecture 09: [Review, Assignment 2]

Lecture 10: [Types & mathematical representation of curves]

Lecture 11: [Wire frame models]

Lecture 12: [Hardware, CAD software, Elements of Programming, CAD programming]

Lecture 13: [Entities, representations]

Lecture 14: [Parametric representations]

Lecture 15: [Review of vector algebra, lines, circle, ellipse, parabolas]

Lecture 16: [Parametric representation of synthetic curves]

Lecture 17: [Cubic curves, b - spline]

Lecture 18: [Bezier spline, sweep curves]

Lecture 19: [Midterm Exam Revision, Instructions and Tips]

Lecture 20: [Review, Assignment 3 & 4, Surfaces & solids – model, entities, representations]

Lecture 21: [Fundamentals of surface and solid modeling]

Lecture 22: [B-rep, constructive solid geometry (CSG)]

Lecture 23: [Analytical modeling, sweep]

Lecture 24: [Solid manipulation, visual realism]

Lecture 25: [Computer aided design of Mechanical Elements & Mechanical Assembly with animation]

Lecture 26: [Capabilities of various commercially available software in the area of CAD]

Lecture 27: [Standards for graphics programming, features of GKS, other graphics standards]

Lecture 28: [PHIGS, IGES, PDES. Standards in CAD]

Lecture E1: [Extra Lecture - Revision]

Lecture 29: [---:Reserve Lecture:---]

Lecture 30: [---:Reserve Lecture:---]

Lecture 31: [Types of elements, types of error]

Lecture 32: [Derivation equitation finite element procedure]

Lecture 33: [Stress – deflection – stiffness matrix]

Lecture 34: [Global matrix, conductivity table]

Lecture 35: [Elimination approach]

Lecture 36: [Penalty approach]

Lecture 37: [Effect of temperature]

Lecture 38: [Principle of min. Potential energy]

Lecture 39: [Mesh generation]

Lecture E2: [Capability of different FEA software, Revision, Midterm Exam Tips]

Lecture 40: [Introduction, design synthesis, Engineering vs Optimum Design, Objectives of Optimization]

Lecture 41: [Classification of Optimization problems and their procedure]

Lecture 42: [Techniques of optimization]

Lecture 43: [Optimized design of machine components]

Lecture E3: [Optimization Software, Revision]

## Assignments

1. There will be 6 assignments, one from each unit, by the concerned teacher.

2. Failure to submit the assignment before deadline shall result in zero grades. Late assignments will not be accepted under any circumstances.

AssignmentNoTitleMax. MarksDate of AssignmentSubmission DeadlineGraded Homeworkto be returned4. Grades : A-F system (equivalent to 0 - 10 scale, 0 - 20 for a 20 Mark assignment)

5. Penalty : The penalty for late submission is a deduction of (0.1 X No. of Days) from original grades. i.e., If you are late by 10 or more days, you will not get any grades for the assignment.

6. For subject related queries, please feel free to communicate with

## Term Work

1. There will be 10 Experiments/Experiences to be learned/performed and each one is to be submitted individually within the prescribed deadlines.

2. The date of submission will be the subsequent lab. e.g., if the term work is given on Monday the 19th, the date of submission is next Monday, that is, 26th of the same month.

3. Late term works shall not be accepted under any circumstances unless prior approval is obtained with a proper justification.

4. Prepare a record book/file and a journal to submit your findings as instructed. Use diagrams/figures as and when required.

## Experiments/Experiences

Introduction to Computer Aided Design- To Study basic concepts and content of subject

- To get an awareness about selection of hardware and software

for a CAD Workstation.

Lab Activity:DiscussionThe Lab Instructor should...

a. Begin a discussion about what inspires a Design Engineer to

move from conventional paper based drafting and designing to a computer based drafting, designing

and analysis.

b. From the comparison, advantages and limitations the discussion should move on to various elements

of a CAD workstation (software as well as hardware) and their present specifications.

Submission :Q/A(Record book as well as Journal)

1. What is CAD?

2. Distinguish between conventional design and computer aided design?

3. Discuss advantages & limitation of CAD.

4. List of hardware requirements for a CAD workstation.

5. List CAD software used commercially with their capabilities.

Computer Graphics I: Line and Circle- To understand basics of programming language and use of the compiler.

- To learn the DDA and Bresenham Algorithms

- Use the algorithms to create C programs

Lab Activity :Demonstration and individual programmingThe Lab Instructor should instruct and demonstrate on a CAD workstation about the origin of a CAD software,

DDA and Bresenham algorithms.

a. Prepare a ‘C’ program for generation of a line using DDA algorithm

b. Prepare a ‘C’ program for generation of a line using Bresenham algorithm

c. Prepare a ‘C’ program for generation of a circle using Bresehnam algorithm

Submission :

1. Basics of 'C' language

2. Details of DDA algorithm

3. Details of Bresenham algorithm

- To learn the 2D and 3D transformations

- Create C programs for them.

On the basis of discussion, prepare ‘C’ programs for following 2D & 3D Transformations:

- Ø

1) Translation of Triangle.Two Dimensional Transformation2) Program to Translate and Rotate Rectangle about origin.

3) Rotation of Triangle about a point.

- Ø

1) Program to Scale and Rotate a 3D BoxThree Dimensional TransformationGeneration of ‘C’ programs for designing machine elements– Shaft and Spring design

Spring Design:It is required to design a helical compression spring subjected to a maximum force of 1250 N. The deflectionof the spring corresponding to the maximum force should be approximately 30 mm. the spring index is 6 andthe UTS and modulus of rigidity of spring material are 1090 and 81370 N/mm2, respectively. The permissibleshear stress for the spring wire should b taken as 50% of UTS. Design the spring and calculate wire diameter,mean coil diameter, no. of active coils and total no. of coils, free length of spring.

To study Geometric Modeling and significance of Graphics Standards

EXERCISE:1) Explain the Constructive Solid Geometry (CSG) scheme of solid modeling.

2) Explain the following surface types:

Lofted surface

Tabulated surface

Bezier surface

3) What are the differences among 3D wire frame, surface and solid models? State their advantages, limitations and applications.

4) Why standardization is needed in computer graphics. State the various graphics standard available. Explain them.

Preparation of Assembly of given parts in Pro/Engineer

Assembly Creation:Pro/Engineer is ideal for feature based design and cumulative building up of successive parts. But once these complex parts are in place, they have to be assembled in ways that work. Creating workable assemblies and machines is the desired end result and the most important aspect of learning to work with Pro/Engineer.To create an assembly model, you must constrain components by selecting surfaces and features. Always begin an assembly with a base component, a component that you are unlikely to remove from the assembly later on. Begin your assembly with default datums. Add the first part or subassembly onto the default assembly datum.

Constraint Options:Placement constraints create a parent/child relationship between the already assembled components and the new component being added to the assembly. Careful consideration is advised in choosing constraint types and references.Most commonly used constraints are:

Mate:- Normal Vectors of selected surfaces point in opposite directions and become co-planar.Mate Offset:- Normal Vectors of selected surfaces point in opposite directions and are offset by a specified negative or positive value.Align:- Normal vectors of selected surfaces point in the same direction and are made co-planar. Align will also make two axes co-axial.Align Offset:- Normal vectors of selected surfaces point in the same direction and are offset by a specified negative or positive value.Insert: -Selected cylindrical surfaces of revolution become co-axial. Three surfaces do not need to be full 360 degree cylinders.Packaging or Under-Constrained Components: -Packaging allows you to add components to an assembly without adding all its necessary constraints. Similarly when you over-constrain a component, you add more constraints than is necessary.Since Pro/E is associative, you can make changes to all components in sub assemblies while working in the assembly. When you save assembly, the system automatically saves any changes that you made to any of the parts in that assembly.Study Finite Element Method – 1D, 2D & 3D analysis in Pro/Engineer, Pro/Mechanica

- Specifying model type
- Setting up constraints, loads, and material definitions
- Meshing – generation of elements in problem domain
- Running the solution
- Setting up and showing result displays for displacements, stresses

EXERCISE: One Dimensional Problem:1) The problem of bar loaded axially is taken for study. To work in software, such problems can be formulated by beam idealization. Consider the bar shown in Fig. below loaded as shown. Determine the nodal displacement, element stresses and support reactions, theoretically by adopting the penalty approach. Verify the results obtained using a Software package available. Take, P = 300 kN, P’ = 600 kN, A1 = 250 mm2, A2 = 400 mm2 Esteel = 200 x 109 N/m22) Formulate a Plane stress/strain problem for 2D analysis.3) Formulate a 3 D analysis problem for the geometry shown below in Pro/Engineer: