Application of Weighted Objective Method in Searching Appropriate

Teaching Aids for Lecturing Column Buckling in Mechanical

Engineering Department of Andalas University

Eka Satria

, Jhon Malta

, and Hendery Dahlan

Mechanical Engineering Department, Faculty of Engineering, Andalas University, Padang, Indonesia

Keywords: Teaching Aids, Weighted Objective, Column Buckling.

Abstract: This paper shows how the appropriate teaching aid was selected in lecturing column stability (buckling),

which is considered as the most challenging topic in the subject of Strength of Materials in Mechanical

Engineering Department of Andalas University. However, most students are not interested in this topic as it

contains a number of mathematical derivations. Teaching aid such as a presentation of materials and figures

taken from reference books are not able to stimulate student’s interest in the topic. In order to select the best

way to explain theoretical concepts without making students bored, the teaching staffs are suggested to use

the teaching aid which can stimulate the curiosity of students. For this reason, this paper describes how to use

a weighted objective method in determining appropriate teaching aids for the intended topic. The method is

usually applied based on several criteria of evaluation, decided by both students and teaching staff. The criteria

should be able to fulfill all the demands of the students and the teaching staff. The selected teaching aid

theoretically should be able to increase students' curiosity and understanding of students about the topic.

1 INTRODUCTION

The Strength of Material is one of the compulsory

courses which is offered by a curriculum of bachelor

degree program of Mechanical Engineering

Department of Andalas University. It has 3 credits

and has 12 topics. According to the survey given to

the students, the most challenging topic in this subject

is the column buckling. The main reason for this fact

is that the topic has too many mathematical

derivations. Besides, most students are not good at

mathematics. On the other side, the current teaching

aids, such as material presentation and reference

books are still traditional aids; they are not able to

stimulate students’ interest in this topic.

In addition, the class size which is big also made

the situation worse. That is why in the current

situation, the class is quite boring for some students.

Most of the science teachers do not pay attention to

scientific and technological methods, and this reflects

the difficulties that are teaching science (Nasab,

Esmaelli, and Sareem, 2015). Since 75% of learning

is learned by sight and vision, therefore the use of

technological teaching aids are considered very

efficient to achieve student’s attention.

Shabiralyani (Shabiralyani, et.al, 2015) explored

the opinions of selected teachers on the use of visual

aids as a motivational tool in enhancing students’

attention in reading literary texts in the district of

Dera Gazi Khan. The results show that 70% of the

students and teachers agree that the visual aids help

in motivation; 75% agree that they help in

clarification of contents under researching; 68%

agree that they increase the vocabulary; 82% agreed

that they help save the time in preparing the lessons;

71% agree that they help avoid the dullness; and 92%

agree that through visual aids the direct experience

increased to observe the things.

Although there are many works have been done

related to the effectiveness of the use of teaching aids

in teaching, there is still a few works which

investigate how to select the best teaching aid among

many available aids. Edward (2008) used four

specific criteria to evaluate learning resources. The

criteria are content, instructional design, technical

design, and social considerations. The criteria are

intended to encourage teaching staffs to think

critically about the resource and evaluate some of its

more detailed aspects. Andambi and Kariuki (2013)

describes several criteria for selecting relevant

Satria, E., Malta, J. and Dahlan, H.

Application of Weighted Objective Method in Searching Appropriate Teaching Aids for Lecturing Column Buckling in Mechanical Engineering Department of Andalas University.

DOI: 10.5220/0008678700220028

In Improving Educational Quality Toward International Standard (ICED-QA 2018), pages 22-28

ISBN: 978-989-758-392-6

learning resources by teachers of social education and

ethics in Bungoma District, Kenya. However, the

selection was done only for available learning

resources, and the main criteria are based on the

relevancy of teaching resources with the subject of

the lecture.

This paper focussed on how to select an

appropriate teaching aid for a lecturer to teach column

stability. The aim is to select the best teaching aid to

stimulate students' interest in the topic and to involve

the student’s role when the aid is used. In order to

understand this current problem properly, two quick

surveys were given to the students. The first is aimed

to see the students' level of understanding to the topic

of column buckling. The data are taken from the

students who took a subject the Strength of the

Material in even semester 2017/2018. The result of

this survey is given in Fig.1, showing that about

61.5% of the students are in the medium, weak, and

very weak level of understanding. Only 38.5% of the

students are in good and very good level of underst .

It means that in general the course outcome is not

reached yet.

Figure 1: Level of understanding of students for the topic of

column buckling.

The second survey is aimed to determine which area

of the topic of structural stability is considered very

difficult for the students. Fig. 2 shows the list of

difficult sub-topics chosen by students in

understanding the concept of column buckling. The

result shows that the six sub-topics with the number

of choices greater than 50% of the total survey are:

Q3 (76.9%), Q10 (76.9%), Q7 (69.2%), Q8 (61.5%),

Q5 and Q6 (both are 53.8%). The detail description

of sub-topics can be seen in Fig. 2. Based on this

condition, the criteria of teaching aid should be based

on these 6 sub-topics. Other criteria, from the

perspective of the students and the teaching staff, are

discussed later.

Figure 2: List of difficult topics chosen by students in

understanding column buckling.

Q1. How does column buckling occur?

Q2. How to calculate the theoretical and

critical buckling load?

Q3. How to determine the mode shapes of

buckling?

Q4. How the geometrizal sizes and shapes

affect the critical buckling load?

Q5. How to determine the direction of

buckling?

Q6. :How the types of support can affect the

critical buckling load?

Q7. How the geometrical imperfections can

affect the critical buckling load?

Q8. How the eccentricity of load can affect the

critical buckling load?

Q9. How to determine the minimum length of

the column that create the buckling?

Q10. How to use the standards such as CRC,

AISC in determining the critical buckling

load?

As a number of criteria must be considered in this

selection, it is essential to have a specific method for

evaluation. This method should be able to guide the

selection for the best result. Thus, this paper adopts a

weighted objective method (WOM), a well-known

method for evaluation solutions in the procedure of

design, to evaluate all the used criteria in the design

process. WOM is frequently used to evaluate several

alternatives and to select the best alternative based on

several evaluation criteria (Diaz and Diaz, 2015;

Kota

and Chakrabakti, 2007; Hongjiu and Yanrong, 2015)

23,1

38,5

76,9

46,2

53,8 53,8

69,2

61,5

38,5

76,9

0,0

20,0

40,0

60,0

80,0

100,0

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10

Application of Weighted Objective Method in Searching Appropriate Teaching Aids for Lecturing Column Buckling in Mechanical

Engineering Department of Andalas University

2 METHOD AND GENERATING

ALTERNATIVES

The method of weighted objectives aims to compare

the utility values of alternative designs, by

performance against differentially weighted

objectives [8]. The procedure is as follows: (i).list

design objectives or evaluation criteria, (ii). Rank

order the list objectives, (iii). Assign relative

weightings to the objectives, (iv). Establish

performance parameters or utility scores for each of

objectives, and (v).calculate and compare the relative

utility values of the alternative designs and multiply

each parameter score by its weighted value. The best

alternative has the highest sum value comparison and

discussion of utility value profiles may be a better

design aid than simply choosing the best.

There are three types of alternatives of the

teaching aids which are selected: 3D_Model,

Program_Simulation, and Poster, as shown in Table

I. The 3D_Model is a prototype of a column structure

under axial loading, the Program_Simulation is result

of a computational program in the form of animation

and video, and the Poster is a group of figures or

pictures with a simple explanation about the

characteristics of column buckling.

Table 1: Types of Alternatives to Solution

Types Description

3D_Model 3D Real Model of Column

Program

Simulation

Video and Animation from

Numerical Program

Poster Pictures/ Figures

3 RESULT AND DISCUSSION

3.1 Evaluation Criteria

The general criteria are taken from some

considerations in the perspective of students,

lecturers, and easiness of design process. The best

method to derive the criterion of evaluation is through

the application of the objective tree method (OTM).

The OTM offers a clear and useful format for such a

statement of objectives (Cross, 2000). It shows a

diagrammatic form how different objectives are

related to each other, and the hierarchical pattern of

objectives and sub-objectives. The procedure of this

method is listed as follows: (i) prepare a list of design

objectives, (ii) order the list into sets of higher-level

and lower-level objectives, and (iii) draw a

diagrammatic tree of objectives showing hierarchical

relationship and interconnections.

Fig. 3 Finding EC through the application of the objective tree method

High

Level

Low

Level

ICED-QA 2018 - International Conference On Education Development And Quality Assurance

Tabel 2. Criteria of Evaluation of Teaching Aids

No. Perspective Criteria of

Evaluation

(High-Level

Objectives)

Sub Criteria of Evaluation (Low-Level Objectives) Rank Weighted

Factor

(%)

1. Students

(60%)

EC1: Ability to

Increase

Student’s

Understanding

(50%)

SC1. How does buckling of the column occurs?

SC2. How to calculate the theoretical critical buckling

load?

SC3. How to determine the mode shapes of buckling?

SC4. How do the geometrizal sizes and shapes affect

the critical buckling load?

SC5. How to determine the direction of buckling?

SC6. How the types of support can affect the critical

buckling load?

SC7. How the geometrical imperfections can affect the

critical buckling load?

SC8. How the eccentricity of load can affect the

critical buckling load?

SC9. How to determine the minimum length of

column that create the buckling?

SC10. How to use standards such as CRC, AISC in

determining the critical buckling load?

1 2%

10%

EC2: Ability to

Stimulate

Student;s

Interesting

(10%)

SC11. Interesting Appearance

SC12. Easy to Understand

4 4%

2. Teaching

Staffs

(32%)

EC3: Good

Accuracy

(20%)

SC13. Good in accuracy

SC14. Easy to show the basic phenomena of buckling

2 10%

10%

EC4: Easiness in

Delivering

Material

(12%)

SC15. Easy to use

SC16. Safe to use

SC17. Easy to bring and operate

3 4%

3 Design

Process

(8%)

EC5: Design

Process

(8%)

SC18. Easy to make

SC19. Cost

5 4%

=100% =100%

=100%

Figure 3 shows 5 criteria (EC) of evaluation (as

higher-level objectives). They are (i) ability to

increase student’s understanding; (ii) ability to

stimulate student’s interesting; (iii good in the

accuracy, (iv) easiness in delivering material of

lecture, and (v) easiness in the design process. From

these five criteria, 19 sub-criteria (SC1-SC19) of

evaluation, as lower-level objectives, to evaluate the

appropriate teaching aid is derived. Ten sub-criteria

is from the derivation of EC1, two from EC2, two

from EC3; three from EC4; and two from EC5. A

detailed description of SC can be seen in Table 2.

3.2 Rank Order of Evaluation Criteria

The next step is to give a rank order for EC. For this

purpose, the level of importance of each criterion will

be compared to each other. For example, if the first

criterion is decided more important than the second

one, the first will be given a score “1” while the

second will be given a score “0”. Then the

comparison is continuously repeated for other

criterions. In the end, the highest rank order is given

to the highest score, as the most important criterion

among all criteria. In contrary, the lowest rank order

is given to the criterion whose score is the lowest.

From Table II, the rank order of EC is started by EC1,

EC3, EC4, EC2 and the last by EC5..

Table 3. Simple Method of Rank Order of EC

EC1 EC2 EC3 EC4 EC5 Total

EC1 - 1 1 1 1 4

EC2 0 - 0 0 1 1

EC3 0 1 - 1 1 3

EC4 0 1 0 - 1 2

EC5 0 0 0 0 - 0

Application of Weighted Objective Method in Searching Appropriate Teaching Aids for Lecturing Column Buckling in Mechanical

Engineering Department of Andalas University

The next step is to give a weighted factor (WF) for

each EC. Off course, the highest rank is assumed to

have a higher percentage than the lowest one. From

Table II, the WF of each EC is 50% for EC1, 20% for

EC3, 12% for EC4, 10% for EC2 and 8% for EC5

(totally 100%).

The same procedure is also applied to all

subcriteria (SC) for each EC. Therefore, every SC

should also have their weighted factor, as shown in

the last column in Table II.

3.3 Establish Performance Parameters

For each SC, a scale with a range between 1 to 5

is used as a score of performance. A score of 1 shows

the worst condition, 3 shows medium condition, and

5 shows the best condition, as shown in Table IV.

Table V shows the description of the performance of

each SC and scales to measure the performances. The

values later are called ‘utility values’ (see Tabel VI).

The utility value is given based on the performance of

evaluated alternatives for each SC. For example, SC-

16: Safe to Use, where 3D_Model is given 3 points

(medium), Program_Simulation is given 5 points (the

safest), and the poster is given 4 points (between

medium and the safest).

Tabel 4. Criteria of Evaluation of Teaching Aids

Score Description

Not Understand/Ugly/Most Expensive/ Not

Safe

3 Medium

5 Very Understand/Good/Cheap/Very Safe

Tabel 5. Performance Parameters

Score Description

SC1-

5: Most Difficult, 3: Medium, 1:Easiest

SC11 5: Most Interesting, 3: Medium, 1:Ugliest

SC12 5: Easiest, 3: Medium, 1: Most Difficult

SC13

5: Very Accurate, 3: Medium, 1:Not

Accurate

SC14

SC15

SC16

SC17

SC18

SC19

5: Easiest, 3: Medium, 1: Most Difficult

5: Safest, 3: Medium, 1: Most Dangerous

5: Easiest, 3: Medium, 1: Most Difficult

5: Most Expensive, 3: Medium, 1: Cheapest

3.4 Comparison of Alternative Solutions

The value of each SC is given from

multiplication of WF and utility values. Again, if SC-

16 is taken as an example, the value 3D_Model is

4%×3=0.12, Program_Simulation is 4%×5=0.20, and

Poster is 4%×4=1.6. The same procedure is given for

the other SCs. Table VI shows the result of evaluation

using the method of WOM. Based on this method, the

best teaching aid for lecturing the column buckling is

through program simulation, because the relative

utility value of this program simulation is the highest

among the others. Its value is about 4.18 compared to

3.18 for 3D_Model and 3.56 for Poster, in the scale

of 1 to 5.

3.5 Actual Design

Based on the result, the next step is preparing

some data for computational programming based on

finite element analysis to make a numerical

simulation which is later used as a part of lecturing

video. This video can show several characteristics

asked by EC1 and EC3. Both ECs are criteria of

evaluation which cover some technical aspects of

column buckling. There are some procedures for this

work as generally described in the following section:

(1). Prepare numerical models of the column. It

must be in a variety of lengths (slenderness

ratios) and also types of cross-sections. This

step is prepared for SC4.

(2). Prepare numerical models of a variation of

supports for column (pin-roller, clamped-

roler, and clamped-clamped). This step is

prepared for SC3 and SC6.

(3). Prepare a variety of geometrical imperfections

to the length of columns. This step is prepared

for SC7.

(4). Prepare a variation of eccentricity loads to the

columns. This step is prepared for SC7.

(5). Prepare material properties of the column.

Use a finite element package software to calculate the

buckling loads.

ICED-QA 2018 - International Conference On Education Development And Quality Assurance

Table 6. The result of Total Grade for Every Alternative solution

Subcriteria of Evaluation (SC)

Weighted

Factor

(%)

Alternatives of Solution

3D_Model

Program

Simulation

Poster

Utility Value Utility Value Utility Value

SC1. How buckling of column occurs?

SC2. How to calculate the critical buckling load?

SC3. How to determine the mode shapes of

buckling?

SC4. How the geometrizal sizes and shapes

affect the critical buckling load?

SC5. How to determine the direction of

buckling?

SC6. How the types of support can affect the

critical buckling load?

SC7. How the geometrical imperfections can

affect the critical buckling load?

SC8. How the eccentricity of load can affect the

critical buckling load?

SC9. How to determine the minimum length of

column that create the buckling?

SC10. How to use the standards such as CRC,

AISC

SC11. in determining the critical buckling load?

10%

0,08

0,18

0,08

0,24

0,18

0,08

0,2

0,1

0,08

0,30

0,16

0,06

0,24

0,3

0,2

0,4

0,04

0,16

0,18

0,12

0,04

0,18

0,24

0,16

0,4

SC12. Interesting Appearance

SC13. Easy to Understand

0,12

0,24

0,2

0,24

0,08

0,18

SC14. Good in accuracy

SC15. Easy to show the basic phenomena of

buckling

10%

0,4

0,3

SC16. Easy to use

SC17. Safe to use

SC18. Easy to bring and operate

0,16

0,12

0,2

0,16

SC19. Easy to make

SC20. Cost

0,12

0,08

0,12

0,20

0,16

Skor Total



=3,18



=4,18

=3,56

(6). Convert the results to numerical animation

forms using post-processor software.

(7). Compare the results to the variation of

standard designs. This step is prepared for

SC10.

(8). Use all animations, resulted in figures, result

of the comparison to design standards to

produce a lecturing video which is very

interesting in visual.

(9). Asked students in a group to prepare their data

to create their animation.

4 CONCLUSION

Through this paper, the method in how to select the

best teaching aid for teaching column buckling in the

subject of strength of the material is detailly

described. The result shows how the simulation of the

program is selected as the best teaching aid based on

several criteria given by students, teaching staffs and

design process. They are (i) ability to increase

student’s understanding (weighted factor=50%); (ii)

ability to stimulate student’s interesting (weighted

factor=10%); (iii) good in accuracy (weighted

factor=20%), (iv) easiness in delivering material of

lecture (weighted factor=12%); and (v) easiness in

design process (weighted factor=8%).

ACKNOWLEDGMENT

This paper is funded by Andalas University through a

research grant for improving teaching-learning

effectiveness. The research grant is provided by

LP3M of Andalas University in the 2018 financial

year.

Application of Weighted Objective Method in Searching Appropriate Teaching Aids for Lecturing Column Buckling in Mechanical

Engineering Department of Andalas University

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ICED-QA 2018 - International Conference On Education Development And Quality Assurance