1.0 Overview

Analysis of deflection is of great importance in design, any

structure without prior testing and analysis when working in engineering could

have major ramifications. Excessive deflection has the possibility to result in

damage of moving parts, broken or jammed parts. This means that knowledge of Deflection

in materials is of paramount importance for many engineers. Therefore it is

necessary for students aspiring to become engineers to have a firm understanding

of Materials.

During first year study in mechanical engineering students

are exposed to many forms of stress and bending which results from this. These stresses

are as follows; shear, torsion and compression. The form of stress and

resulting deformation being considered in this study is shear stress which

results in bending.

These stresses are applicable in the real worlds with many

examples through experience students have seen these occur. However these

examples that students have experienced have limited aid in helping students

understand the underlying principals and concepts. Therefore For many students

it will be helpful in gaining a deeper understanding of bending theory through

experimentation and help students integrate theory into practical knowledge.

Laboratories allow student to appreciate and verify theories

taught and therefore my purpose is to review and improve the existing

laboratories using the latest teaching methods with the intent to improve the

students experience and learning while ensuring that students are adequately

prepared and have sufficient understanding of the theory demonstrated.

To ensure students have sufficient preparation to perform

the correct calculations and understanding relevant to the experiment thorough research

into teaching methods is necessary. This will be extremely useful in finding

the most useful techniques and methodologies which will both aid students in

the long term retention of information and prepare the students for the

experiments which will allow them to gain the most out of the experience.

2.0 Literature review

This projects aim is to improve existing laboratories and

therefore research and understanding into both teaching methods and Bending

theory are necessary as such this literature review will be divided up into 3

sections as follows;

·

Bending theory

·

Teaching methods

·

Applying teaching methods to bending theory

2.1Bending theory

Bending is a process that occurs when force is acted upon a

material which produces a V shape along an axis in ductile materials. When bending

occurs the inside surface is getting compressed with the outer surface is in

tension.

Generally literature at the level required for students at

this level is uniform with theories and ideas ingrained over many years and

therefore it is quite difficult to find opposing views on any theory

considered.

The strain caused can also decrease or increase due to the

radius of the bend with the strain being higher the smaller the bend. When testing

a material many factor must be considered including the thickness, width and

materials properties e.g. young’s modulus and poisons ratio. (2.1 Byars EF,

(1963))

2.1.1 Initial restrictions

In the experiment a concentrated load is used which is a

load of which has a small area of contact compared to the area of the metal

bar.

When experimenting with bending there are many other forms

of failure which have the possibility of occurring if care is not taken

including buckling and twisting which could be a problem when demonstrating to

student as at this time students are unfamiliar with these concepts and the

purpose of the experiment is to demonstrate bending and as such bending should

be the only form of failure observed.

To ensure that these effects are controlled restrictions

must be placed on the beams geometry:

·

The beam must be straight with a constant square

cross section, made from homogeneous material.

·

Loads must be applied in the longitudinal plane

of symmetry

Internal reactions in a cross section of any of the beam

could incorporate a resultant shear force or a resultant normal force. To

ensure that bending effects are examined alone restrictions must be placed to

restrict the loading to which the resultant shear and normal forces are zero on

any one section which is perpendicular along the axis that is longitudinal on

the beam.

The lack of the shear force means that every cross section

of the beam is since the beam is loaded with only pure

couples at the end applied in the same plane of symmetry. This means that the

beam is considered to be in pure bending and the plane of symmetry is also

known as the plane of bending.

This means the beam has the correct

geometry to allow for deformation and reasonable conclusions can be drawn since

there is both no other forms of deformation and there is negligible undesirable

forces on the bar.

2.1.2 Strain

In the diagram below U is the distance between the neutral

axis which is shown as EF and the parallel line GH which is the plane of symmetry.

It can be assumed that the difference between these lines is the same Loaded as

when it is loaded.

Therefore the definition for the neutral surface is assumed

to be

The deformation on a fibre of which the original position

was G’H’ then becomes

The definition of axial strain

Since this case considers pure bending

the radius is constant for the length of the entire beam. This means the axial

strain on the longitudinal axis is directly proportional with the distance “u'”

from the neutral surface. The negative symbol shows ta negative strain for a

positive value which is of u. (Benham,

Crawford and Armstrong, 1996) (Gere and Goodno, 2009)

2.1.3 Stress

Hookes law is used for stress in this

case.

For elastic strain:

In this case is the normal stress which is due to bending

known as flexure stress.

(Benham, Crawford and

Armstrong, 1996) (Hibbeler, n.d.)

2.1.4 Euler-Bernoulli bending theory

In Euler bending theory the fibres in a bent beam form arcs,

the top fibres are compressed and the bottom fibres are stretched as mentioned

above. The Euler-Bernoulli theory of slender beams the assumption must be made

that Plane sections remain plane.

It also means that there isn’t any deformation due to shear.

This linear distribution only applies if the maximum shear stress which the

material undergoes is less than the yield stress. If stresses exceed the yield

stress it is then known as plastic bending.

The equation for the bending of beaming of beams is:

E I d4w(x) /

dx 4 = q(x)

In the equation; E is youngs modulus, I is the area moment

of inertia, W(x) is also the deflection which the neutral axis of the

beam. When a solution has been found for

the displacement the beam is under has been found, the shear force (Q) and also

the bending moment (M) can be found using the equations below.

M(x) = -EI d2w(x) /

dx2

Q(x) = dm / dx

Beam bending generally analysed using the Euler Bernoulli

beam equation. The conditions necessary for using the Euler-Bernoulli simple

bending equations are;

(Cook and Young, 1999)

(Benham, Crawford and Armstrong, 1996)

·

The beam must be subject to pure bending as to

ensure that the shear force is zero with no torsional and no axial loads would

be present.

·

The material used must be homogeneous and

isotropic.

·

The materials used must obey Hookes law.

·

And the bar must be initially straight with a

cross section that is uniform throughout the bar

·

It must have axis of symmetry in the plane of

bending

·

The dimensions must be that it wouldn’t fail by

sideways buckling, crushing or wrinkling but by bending.

Bending stress can be determined

with the formula:

= M y / I

In this formula Is the bending stress, y is the perpendicular

distance to the neutral axis M is the moment around the neutral axis, I is the

second moment of area around the neutral axis (x). this equation is considered

a classical equation which gets extended if considering other variations of

bending.

(Hibbeler, n.d.) (Boresi

and Schmidt, n.d.)

2.2 Teaching methodology in Laboratories

2.2.1 The goals of Laboratory experiences

Laboratories have a number of goals for students. Most of

these goals are also the goals of science educations in general. (Lunetta, 1998;

Hofstein and Lunetta, 1982). These goals can vary however the core set is

generally consistent. These goals were reviewed then discussed, a list of goals

and desired outcomes for laboratory experiences was compiled (Anderson, 1976;

Hofstein and Lunetta, 1982; Shulman and Tamir, 1973; Lazarowitz and Tamir, 1994).

·

To enhance the mastery of a subject. – The experiences

may enhance a student’s comprehension and understand of concepts and facts.

·

To Develop Scientific reasoning – These laboratory

experiences can help develop a student’s ability to understand and identify

questions and concepts.

·

Developing practical skill – These Laboratories

are used to allow students to learn then use the tools and the conventions

commonly used in science. (Using scientific equipment in the correct manner,

making observations based on findings, carrying out procedures and taking

measurements in the correct manner).

·

Developing Teamwork abilities – these experiences

can help promote the ability of the student to collaborate effectively with

others.

2.2.2 Recent research in laboratory experiences and its

design

Generally laboratory experiences have lacked clear learning

goals and in general this approach is still common. Due to this Researchers

tested students in experiments or other scientific activities to determine if

the students underlying understanding of the activity had increased. This was

compared with other methods including videotapes, discussions and lectures. To determine

which were the most effective when compared.

It was found that the best method was to integrate laboratories

in support of other teaching methods was the best methodology. (National

Research Council, 1999), (Glaser, 1994; National Research Council, 1999)

(National Research Council, 2005)

2.2.3 common laboratory experiences

It is commonly claimed that laboratory classes help students

in understanding scientific concepts largely are a resultant of the argument

that these opportunities to observe and manipulate materials can be used to

directly help students to gain a much more substantial grasp of scientific

concepts as a whole. Many researchers and teachers believe that these experience

would help force many students in identifying any misunderstandings they may

have in a concept and therefore change their thoughts towards a more

scientifically accurate way.

However these claims have no direct evidence. These laboratory

experiences that are generally isolated from any flow of instruction and

therefore have no evidence to back up claims that they aid in the learning of

any content of a scientific nature (Hofstein and Lunetta, 1982, 2004;

Lazarowitz and Tamir, 1994).

2.2.4 Development of investigative skills

Research on development of investigative skills has shown the

possibility that students can learn certain aspects of scientific reasoning

using laboratory instruction (Reif and St. John, 1979, cited in Hofstein and

Lunetta, 1982).

However recent research has shown that during Laboratories

Teaches tend to prioritise procedures in laboratories rather than discussion

for how to plan an investigation or to interpret the results that laboratories

findings have given (Tobin, 1987). Therefore it may be beneficial to

encourage the design and interpretation of the laboratories to encourage the

development of this skills.

This is because Average Laboratories appear to have a low

impact on improving more complex aspects related to scientific reasoning. This can

include the capacity of students to find their own research questions and to

then design experiments and drawing conclusions from the data observed then use

these conclusions to make inferences (Klopfer, 1990, cited in White, 1996).

2.2.5 Developing Teamwork Abilities

Commonly in laboratories teamwork is an integral aspect and

is beginning to be seen as an outcome itself, these laboratory experiences are

now being viewed as an ideal opportunity for developing these skills which are

essential in any scientific pursuit. These team working skills are now seen as

an essential skill for workers in any industry.

2.2.6. Principles for the design of effective experiences in

the laboratory

The research found shows that there are a number of key

factors in the development of good laboratory lessons these are believed to be

Clearly Communicated purposes – Laboratories with clear

goals to guide the experience. These goals should be clearly communicated to

allow students to gain a clear understanding for the reasons behind the

laboratory activity.

Ongoing Discussion and reflection – Laboratory experiences

shown are generally more effective when focus is placed on the discussion of

activities done during a laboratory and the reflection of the reasons for them rather

than the actual performing of the laboratory activities themselves. The

findings found from research shows that the focus of the laboratories and the

activities surrounding the emphasis should be placed on the development of

explanations to understand the data further rather than confirming the ideas

presented.