International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
ISSN 2319 - 4847
Special Issue for National Conference On Recent Advances in Technology and Management
for Integrated Growth 2013 (RATMIG 2013)
Critical Statistical Analysis of Engineering
Mechanics Results
Vijay G. Kondekar1, Balbir Singh Ruprai2
1
Assistant Professor, GNIEM, Nagpur
vijaykondekar@rediffmail.com
21
Assistant Professor, GNIEM, Nagpur
balbirr@rediffmail.com
ABSTRACT
In today’s technically advanced world, the technical education has become more competitive and challenging. Success of a student
is measured in terms of the percentage of marks scored at the university level and competitive examinations. Undoubtedly, it is a
measure of a student’s intelligence and understanding of basic concepts of engineering. In the engineering curriculum at
university level, Engineering Mechanics (EM) is one of the very important subjects. Not only at national level but also at
international level, it is considered to be one of the toughest subjects for understanding. Engineering Mechanics actually forms the
backbone of engineering career of a student of any branch. It enhances the analytical as well as logical capabilities of a student. It
shall be an undivided opinion that the First Year results are one of the most important factors for the students in their engineering
career and also a crucial factor for any engineering institution. If these results are good, mostly, the results further up to final year
will continue to be good.
This paper presents a critical statistical analysis of results and tries to suggest some optimistic measures to improve them. For the
analysis, two sets of data each consisting marks obtained in unit tests and attendance of about 60 students in each set are studied.
The normal distribution curves and probability functions are drawn which give the quality of students at intake level. For the
analysis the results are categorized into failures, second class, first class and distinction levels. The importance of attendance can
be promptly seen from the analysis. Other critical factors influencing the results are also discussed.
Most of our teaching practices and methodologies are formed by looking at the performance of average students. But it seems that
the weaker and intelligent students need certainly different strategies. If those are adopted, the quality of the results can certainly
be improved. This study highlights distinct aspects of the analysis of Engineering Mechanics results and suggests certain
methodologies to improve the quality of results. This will help in improving the Teaching-Learning process.
Keywords: Engineering Mechanics (EM), Statistical, Modeling, Failures.
1. INTRODUCTION
In today‟s technically advanced world, the technical education has become more competitive and challenging. Success of
a student is measured in terms of the percentage of marks scored at the university level and competitive examinations.
Undoubtedly, it is a measure of a student‟s intelligence and understanding of basic concepts of engineering. In the
engineering curriculum at university level, Engineering Mechanics (EM) is one of the very important subjects. Not only
at national level but also at international level, it is considered to be one of the toughest subjects for understanding. At
national level, the importance given to the subject can be seen from the various two week ISTE workshops funded by
Ministry of Human Resource Development (MHRD), Government of India under the National Mission on Education
through ICT and organized at various institutes [1]. G. Thomas et al. [2] have analyzed the factors for poor performance
of students in Engineering Mechanics from the four participating universities – the University of Wollongong, the
University of Tasmania, the University of Technology Sydney and the Australian Maritime College. Many other authors
[3],[4],[5] have also done similar studies for EM.
This paper discusses some critical factors influencing the results of EM are discussed. It highlights distinct aspects of the
analysis of Engineering Mechanics results and suggests certain methodologies to improve the quality of results. A critical
statistical analysis of results is presented and some optimistic measures are suggested to improve them. For this analysis,
two sets of data each consisting marks obtained in unit tests and attendance of about 60 students in each set are studied.
The normal distribution curves and probability functions are drawn which indicate the quality of students at intake level.
For the analysis the results are categorized into failures, second class, first class and distinction levels.
Organized By: GNI Nagpur, India
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
ISSN 2319 - 4847
Special Issue for National Conference On Recent Advances in Technology and Management
for Integrated Growth 2013 (RATMIG 2013)
2. IMPORTANCE OF EM IN ENGINEERING DISCIPILINE
Engineering Mechanics actually forms the backbone of engineering career of a student of any branch. It enhances the
analytical as well as logical capabilities of a student. It shall be an undivided opinion that the First Year results are one of
the most important factors for the students in their engineering career and also a crucial factor for any engineering
institution. It is observed that if these results are good, further up to final year results continue to be good.
EM studies the effect of various forces on a single or a system of rigid bodies at rest or in motion. The study on bodies at
rest is called as „statics‟ and when the bodies are in motion, it is called as „dynamics‟. Some of the key skills developed
in students by studying EM are listed below.
2.1. The two and three dimensional force systems are based on vector algebra and their study enhances the visualization
and imagination of students.
2.2.. The statics portion of EM deals with the various engineering structures like working of pulleys, cranes, beams,
trusses and various parts of a machine which are day-to-day real objects or structures in the world. The students are
opened to the live problems which they have to work on in their future careers. The analysis which consists of finding
unknown forces in the various parts of the structure enhances their analytical and mathematical capabilities. This aspect
is very important for students of Civil, Mechanical, Electrical, Aerospace and other core disciplines of engineering.
2.3. The concept of free body diagram (FBD) teaches to students to analyze a difficult problem by breaking into smaller
parts.
2.4. Newton's laws of motion, impulse-momentum principles (linear and angular) and the work-energy principle are the
key theorems for solving any dynamic problem.
3. CAUSES OF FAILURES IN ENGINEERING MECHANICS
There are many causes which lead to failures or poor results of students in EM and some of the major reasons are
described below.
3.1 Application of basic concepts of physics to real practical problems in EM
The physics course taken at college level forms the basis of entry level understanding of Engineering Mechanics course.
The modeling of real structures or objects through FBD becomes difficult to comprehend. This can be overcome by
telling the students the significance and usage of various objects and structures in real life. In EM, modeling is a process
of abstraction in which real-world objects are represented by mathematical models for analysis. In engineering
mechanics, modeling is a process of abstraction in which real-world objects are represented by mathematical models
amenable to rigorous analysis. Streveler et al. [3] represented the two-step process schematically as shown in Figure 1
and it shows the complexity of engineering analysis which leads to failure or less results due to poor understanding.
Figure 1: Schematic depiction of the modeling process in EM, adapted from [3]
It is also observed that the students do not understand for what purpose the various unknown forces are found in various
parts of structures and objects. It is difficult to explain to the students at first year level about their future use in design
process, but the future process of engineering should be told in general. This can solve many of their difficulties and
misunderstandings.
3.2 Numerical problems based on real mechanisms
In the EM course, students often have to solve problems with multiple interconnected bodies which are more relevant to
engineering. Typically, this creates more difficulties in solving. The most important contribution that the engineering
Organized By: GNI Nagpur, India
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
ISSN 2319 - 4847
Special Issue for National Conference On Recent Advances in Technology and Management
for Integrated Growth 2013 (RATMIG 2013)
mechanics course makes toward the undergraduates' education is the systematic engineering approach to modeling,
analysis, and problem-solving that is inculcated into the students early in the curriculum.
In their higher courses, the students will use the same process in the study of mechanics of materials, vibrations in
mechanical systems, the dynamics of fluid systems, jet propulsion, and many more. Also, it is worth mentioning that the
difficult concepts can be understood by supplementing them by experimentation [6-11].
3.3 Entry level of students in Engineering
Looking at present scenario of admission process for engineering, the students can be distinguished into two categories
viz. academically excellent and good students and weak students looking at the levels of understanding. A self
explanatory flow chart below explains the difference in entry level input and Teaching-Learning (T-L) processes at
various institutions.
Table 1: Entry level input and Teaching-Learning (T-L) processes
Hence there is a vast difference in the level of understanding the subject between the above institutes if we compare from
the input point of view. Most of our teaching practices and methodologies are formed by looking at the performance of
average students. It can be very clearly seen that the processes A, B and C should be different to suit for various types of
institutes and the weaker and intelligent students need certainly different strategies. If those are adopted, the quality of
the results can certainly be improved.
3.4 Regularity of the students
Irregularity is the key aspect in understanding this difficult subject. This subject is of cohesive nature and the next topic
depends on previous. Unless they understand the operations on forces in two and three dimensional systems, it becomes
difficult to understand equilibrium concepts of various structures. The students are unable to solve even the simple
problems in private institutes as compare to the IIT due to level difference of understanding among the students. This key
factor is taken for statistical analysis of results.
3.5 Competency level of teaching faculty
This is also a very important aspect and is also highlighted in the statistical analysis. This factor becomes more prominent
and effective when the understanding level of students are weak particularly in private institutions, as shown in process B
and C in Table 1.
4. METHODOLOGY
As seen from Table 1, it is a challenging task for Processes B and C to improve the results and to bring out excellent
product comparable to a Process A of a premier institute as the duration of the semesters, syllabus and other guidelines of
governing bodies like AICTE, NBA being the same.
Thus, to achieve this, creative methodologies are needed to improve the results.
Looking at the various factors listed above, the controlling key parameters are mainly regularity of the students,
punctuality in attending all the classes. Also, sincere efforts at home for solving additional problems and assignments can
lead to better results in Engineering Mechanics. A case study is presented of two classes which analyzes unit test marks
and this important factor, attendance. The sample data consists of two classes, each of about 60 students. The data is
chosen such that sample data „D‟ represents Process-B and sample data „C‟ represents Process-C. The normal
distribution curves and probability functions are presented for the analysis.
5. RESULTS AND DISCUSSIONS
The statistical analysis of about 120 students is represented in normal distribution curves shown in Figures 2 and 3. The
marks obtained are the average marks for that interval for Sample D and C respectively. The relative frequency
Organized By: GNI Nagpur, India
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
ISSN 2319 - 4847
Special Issue for National Conference On Recent Advances in Technology and Management
for Integrated Growth 2013 (RATMIG 2013)
represents the ratio of number of students in a particular interval to the total number of students and gives the relative
probability.
Figure 2: Normal Distribution Curve for Sample D
Figure 3: Normal Distribution Curve for Sample C
Similarly, probability functions are plotted in Figures 4 and 5. They represent the cumulative frequency of that interval of
students.
Figure 4: Probability Function for Sample D
Figure 5: Probability Function for Sample C
From the normal distribution curves and the probability functions, it is seen that Figures 2 and 4 represents Process-B
showing mixed type of students, ranging from good to weak understanding. It is also clearly seen that Figure 3 and 5
represents Process-C showing weak understanding of students.
The regularity of students which is a key factor which can be controlled plays a vital role in the results of EM. It is
mapped for the various categories of students viz. failures, II nd class, Ist class and distinction. The various strategies
adopted by the teaching faculty are also logically represented for both the data sets.
Table 2: Regularity of students and the various categories
Data D Average Attendance Data C
Categories
(Mixed)
(Weak)
(%)
Failures (Below 40%)
18
53.85
36
Average
Attendance (%)
69.05
IInd Class (Below 60%)
13
78.11
15
84.76
I Class (Above 60%)
10
77.69
7
71.43
Distinction (Above 75%)
14
89.01
0
-
st
Strategies adopted by teaching faculty
Fundamentals and concepts
more focus
enough time not given
Practice of fundamental problems
more
less
Application oriented problems
more
less
Organized By: GNI Nagpur, India
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
ISSN 2319 - 4847
Special Issue for National Conference On Recent Advances in Technology and Management
for Integrated Growth 2013 (RATMIG 2013)
Experience of faculty
more
less
It is seen from Table 2, the better results are achieved by regular students in case of students having good understanding.
But for weak students, more vital role is played by the competence and strategies of teaching faculty. In both cases,
failures are more for irregular students.
6. CONCLUSIONS
The importance of the subject of Engineering Mechanics is immense and it plays a vital role in any engineering
discipline. The various causes of failures are due to the nature of the subject being application oriented using basic
concepts of physics to real practical problems and numerical and analytical based. Looking at the admissions at number
of institutions, the understanding level of students vary from excellent for premier institutes like IIT/NIT to weak or
mixed for private institutions at the entry level of students in Engineering. In such cases improvement of results depends
mainly on two key factors viz. attendance and regularity of the students and competency level of teaching faculty. It is
seen that the better results are achieved by regular students in case of students having good understanding. But for weak
students, the competence and strategies of teaching faculty play more vital role. Failures are more observed for irregular
students. The teaching strategies should be changed as per the understanding of students and the good results can be
achieved through proper analysis.
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student performance in engineering mechanics”, Australasian Journal of Engineering Education, Vol 17 No 1, p
19-25.
[3] B.D Coller, “An Experiment in Hands- on Learning in Engineering Mechanics-Statics” , International Journal of
Engineering Education, Volume 24, Number 3, March 2008 , pp. 545-557(13)
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Organized By: GNI Nagpur, India
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
ISSN 2319 - 4847
Special Issue for National Conference On Recent Advances in Technology and Management
for Integrated Growth 2013 (RATMIG 2013)
AUTHOR
Vijay G Kondekar received the B.E. degree from VRCE, Nagpur and M.S. degree in Civil Engineering from IIT
Madras, Chennai and currently doing Ph.D. from VNIT, Nagpur. He is having about 20 years of teaching
experience and has taught Engineering Mechanics for more than 10 years. He has received fellowship from
Ministry of Culture, Government of India, New Delhi. His 18 publications include a paper in an International
Journal and in International and National conferences.
Balbir Singh Ruprai received the B.E in Civil Engineering from KDKEC Nagpur and M.Tech (Structural
Engineering) from YCCE Nagpur and currently perusing Phd from VNIT, Nagpur. He is having 16 years of
industrial and teaching experience and has taught Engineering Mechanics from the beginning of his teaching
carrier.
Organized By: GNI Nagpur, India