Young’s · Determine the stiffness by calculating using

 

 

 

Young’s
Modulus of Elasticity

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 Building Science Laboratory
Report

Name: Cosmin Ichim

Student Number: 16008870/1

 

11th
November 2017

 

 

 

 

 

 

Contents
Section 1
1)    Objective. 3
2)    Procedure. 3
3)    Observations. 4
 Young’s Modulus in
Tension – Metal 4
 Young’s Modulus in
Bending – Timber 5
4)    Results. 6
Raw Data. 6
Derived Data. 7
5)    Discussion. 10
1)Comments on E. 10
2) Component stiffness and material stiffness. 9
3) Metal use for structural applications 10
6)    Conclusion. 10
7)    References. 10
Section 2
4)    Results. 15
Raw Data. 15
Derived Data. 15
 

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

Section 1

Objectives

The aims and objectives of the
investigation are the following:

·       To determine the values of   by using Young`s Modulus of Elasticity after
calculations of 0.3% Carbon Steel ( Mild Steel) and 60/40 Brass

 

·       To determine the values of   by using Young`s Modulus of Elasticity after
calculations of Parana Pine and Mahogany timbers.

 

·       Determine the stiffness by calculating using
the data from the graphs and comparing all information gathered with the
published values provided from previous investigations.

 

 

Procedure

The
procedure for this investigation was followed without modification “As per Lab
Sheet”.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Observations

During
the investigation an amount of observations have been collected.

The
observations are gathered into two main sections which represents the nature of
the test (type) and the actual materials which were supplied.

Strength extensometer tensile testing machine

(Young`s
Modulus in tension)

 

·      
Mild Steel –
0.3% Carbon Steel

 

                                                                                                                     
Figure
1

Testing 0.3% Carbon Steel gave out not too many
observational aspects to be recorded.

The results support that as when the graph was calculated
by the software the naked eye couldn`t see the elastic extension as it was
almost 0.05mm.

Taking that in consider, the lack of movement can be explained.

Nothing could be smelt or heard during the experiment,
and it lasted up to 54 seconds.

 

Suggestions

The material
used is a stiff one as all the aspects such as duration, lack of movement, and
force needed to get the limits of elasticity prove this.

 

·      
60/40 Brass

                                                                           Figure
2- Brass Sample

When tested 60/40 Brass, again the
observational aspects are not a strong point as the elastic extension was infima
(0.02mm). Without the performance of the extensometer this variation in terms
of length could be missed. The sample didn`t move at all and nothing could be
smelt or heard during the experiment. It lasted up to 40 seconds

Suggestions

After this test ended, the data gathered
proved that 60/40 is not as stiff as Carbon Steel 0.3%.

Brass took quicker to reach its elastic limit
which indicates that is softer and the force applied its lower which proves
that Carbon Steel 0.3% is stiffer.

3-Point
bending machine

(Young`s Modulus in bending)

 

·       Parana Pine

                                                                                                                                
Figure 3 – 3-point
bending

After 25 seconds the sample of Parana Pine
started to bend in its centre where the force where applied. The bent could be
visible without any problems. Once it reached its elastic limit the timber
sample slightly got back to its original shape and no visible dents could be
seen.

Nothing could be smelt or heard during this
experiment and the test finished relatively quick, lasting up to 38 seconds.

 

Suggestions

The class which Parana pine occupies is
softwood and from the data gathered during the test it could be observed that stiffness
is not as strong feature of this type of timber.

 

·       Mahogany

In this test there wasn’t the impressive type
of bend presented in the Parana Pine`s test.

Once it reached its elastic limit the sample
got back in the shape as it was at the beginning of the process.

Nothing could be smelt or heard during this
experiment and the duration of the test was 30 seconds.

 

Suggestions

The class which Mahogany timber occupies is
hardwood.  The sample rapidly got back to
its original shape when it reached its elastic limit. This might suggest that
based on the observations from the test the Mahogany timber it is stiffer compared
with the Parana pine timber.

The test finished within a couple of seconds
quicker and it needed more force than the sample tested before which again,
might suggest that there is this difference in terms of stiffness.

 

 

 

 

4. Results

Raw Data

Table 1: Measurement of Carbon Steel 0.3% and
Brass 60/40 tested for Young’s Modulus in Tension

 

Metal

Diameter (mm)

Gauge Length (mm)

1

Carbon Steel
0.3%

7.96

50

2

Brass60/40

7.96

50

.

Table 1: Measurement of Parana Pine and
Mahogany tested for Young’s Modulus in Bending

 

Timber

Width (mm)

Thickness (mm)

Beam Span (mm)

1

Parana Pine

20.35

7.20

120

2

Mahogany

20.09

7.36

120

 

Derived Data

 

 

 

 

 

 

 

Figure 4 –
0.3% Carbon Steel Graph

This
graph above presents the load-extension of 0.3% Carbon Steel

 

 

 

 

 

 

 

 

 

 

 

Figure 5 – 60/40
Bra

This
graph above presents the load-extension of 60/40 Brass

 

 

 

 

 

 

 

 

 

Figure 6 –
Parana Pine

This
graph above presents the load extension of Parana Pine

 

 

 

 

 

 

 

 

 

 

                     Figure 7 – Mahogany

This
graph above presents the load extension of Mahogany

 

Young`s
Modulus in tension

0.3% Carbon
Steel:

Diameter
= 7.96mm

Gauge
length= 50mm

Extension(x)
= 0.04-0.01=0.03mm

Axe(y)=
125mm

1mm= 88N

Radius(r)=
3.98mm

Area(

Between
2 horizontal lines = 70mm

F=
88N x 70mm=6160N

E=

E=

 

60/40 Brass (example of
calculation demonstrated above)

x

y

1mm

r

A

F

E

0.01mm

125mm

17.6N

3.98mm

49.739

1284.8N

129154.1848

 

Young`s Modulus
in bending

Parana Pine

Y=
114.5 mm

1mm=5.240N

X
=1.5mm

Length(l)=120mm

Breadth(b)=20.35mm

Depth(d)=7.20mm

Between
2 horizontal lines= 61mm

F=
319.64N

E==1219.644

 

Mahogany (example of calculation
demonstrated above)

x

y

1mm

l

b

d

F

E

1mm

115mm

5.217N

120mm

20.09mm

7.36mm

365.19N

19696.522

Material

Experiment Values

Published Values

Difference

Test 1

 

 

 

0.3% Carbon Steel

206.41GPa

210.GPa(lab sheet)

3.59GPa

60/40 Brass

129.15GPa

100.GPa(lab sheet)

29.15GPa

Test 2

 

 

 

Parana Pine

12.19GPa

7.5GPa – 11GPa
(Building and Civil Engineering Sector
Policy and Strategy Committee, 2002, p.22)
 

4.69GPa
– 1.19GPa
 

Mahogany

19.69GPa

16.1GPa – 19.3GPa
(Building and Civil Engineering Sector
Policy and Strategy Committee, 2002, p.30)
 

(3.59GPa) – (+0.39GPa)

 

 

5.Discussion

1) Comments on E

 

Gordon
(1991, p39) states that E “describes the elastic flexibility of a material”. To
elaborate, it is a measure of stiffness of material and can be used to estimate
the deflection produced in a component by a given load. The higher the value of
E, the stiffer the material. When comparing the values of E produced by the
experiment compared with publish values, it is apparent that there were some
inconsistencies, the main one being carbon steel. The E value produced in the
experiment is significantly lower, which suggests that carbon steel has a lower
stiffness than the published value. This difference could be explained by human
error and the test and calculations would need to be repeated to see if a
similar result was obtained. The machine may not have been calibrated properly
which would affect the results. The sample may have been defective and if this
was the case, the experiment would need to be repeated using a new sample. It
is not likely to be due to tong-term mechanical factors such as creep or
fatigue as “well below the elastic limit the elongation of the material isn’t
affected by time” (Gordon, 1991, p228). Although the values may differ, the
principles still remain the same. That said, carbon steel is the stiffer metal
and Keruing is the stiffer timber.

All of
the graphs show a straight line throughout the testing procedure, which
indicate that stress is proportional to strain (Thompson, 1926, p298). This
theory was introduced by Robert Hooke, and it can be said that that the
materials tested obey Hooke’s Law. The graphs also indicate that the metals
have a much higher Young’s Modulus that the timber samples. The gradient of the
mahogany was slightly steeper, which suggests that is it the stiffer material
out of the two (Desche and Dinwoodie, 1996, p103).

It was
observed in the experiment that visually the deflection levels in the timber
were much more obvious than the extension in the metals samples. Gordon (1991,
p30) states “there is always some deflection”. This suggests that all
materials, no matter how stiff, will show signs of deflection. This may be more
apparent in some materials, such as the timber. Gordon goes on to say that
“these deflections generate forces of resistance which make a solid hard and stiff
and resistant to external loads” (1991, p30). This statement explains that, due
to the level of deflection in the Parana Pine being greater, the Keruing is the
stiffer material.

The
values of E highlight that there are differences not only between different
forms of timber (such as Pine and Mahogany), but also between different samples
of same type of timber, such as the Keruing specimen. Desche and Dinwoodie
outline several factors which determine the elasticity or stiffness of wood.
These include: density, angle of the grain, knots, moisture content,
temperature, age of the wood and any defects it may have. (1996, p117-125).
This would explain any inconsistencies in the varied values of E for the timber
samples.

 

5.2 Component
stiffness and material stiffness

E is
represented as a single unit and can be applied to a sample of any size, and
thus compared. E denotes the inherent stiffness of a particular material. Steel
has high material stiffness, as demonstrated by the large value of E (210 kN /
mm2). Tin, for example, has a low material stiffness, as it only has
an E value of 40 kN / mm2 and shows elasticity.

The
component stiffness of an object depends on the shape of the component and the
distribution of the material. Cardboard is a good example of this. It has a low
material stiffness as, when forces are applied to a sample, it would bend quite
dramatically and eventually break. However, changing the distribution of the
material, such as corrugated cardboard, would mean the specimen had high component
stiffness and when force was applied to the sample the levels of deflection
would be a lot lower.

The idea
of component stiffness could be applied to how the timber beam is used in
construction. We know from the experiment that timber has a lower value of E
than metals such as steel, but one way that the stiffness could be improved
would be to change the dimensions on the beam. In the experiment, the beam was
laid flat with force being applied to the face with the largest surface area.
If the beam were to be rotated 90 degrees on its side, then when the force was
applied from above the levels of deflection would be significantly lower and
therefore it would have a greater stiffness. Likewise with metal, changing the
dimensions and designs of the beam could increase its stiffness. The most
common example of this would be the I-beam. This has a thinner steel beam with
supporting flanges at the top and bottom. When the force is applied to the
flange, there is a larger surface area to take the load and the load is shifted
from the centre of the component. This sees a decrease in the stress that is
applied to the steel beam and therefore increases its stiffness.

In older
buildings, such as those built in the Tudor period, supporting beams were
constructed using timber as this was the most readily available material. In
the present, we know that there are materials available, steel for example,
that would be much better suited for structural applications.  Not only does timber have a lower stiffness,
it can be more susceptible to decay, such as woodworm or rot. In such examples
where timber beams have been originally been used, the wooden beams after often
replaced or reinforced with metal during a renovation. The notion of
reinforcement with a stiffer material is one way to overcome the issue of low
material stiffness.

 

 

 

5.3         Metal use for structural applications

From the
experiment, it is apparent that for structural applications steel should be
used. The results showed that steel had a higher resistance to elastic
deformation and therefore was stiffer and can withstand higher stresses. This
is supported by the published values of E for steel.

Gordon
(1978, p55) stated that “strength of a structure is simply the load which will
just break the structure”. For this experiment, we were testing the stiffness
of a material but not necessarily the strength of it. The test carried out was
non-destructive as we did not want to break the sample. The specimens were
tested between set variables of elasticity and therefore the metals were not
tested to full elastic deformation. The yield point of a material is the
transition from elastic deformation (non-permanent) to plastic deformation
(permanent). For steel this is 300Mpa and 450Mpa for brass (as per lab sheet).  This suggests that brass can withstand a
higher load before fracture and is therefore stronger. However there may be
other factors prohibit the use of brass for construction purposes. Although our
results showed that steel was stiffer as it had the higher resistance to
elastic deformation, for structural application we would need to consider the
maximum strength that could be applied to a steal beam before we could see
signs of plastic deformation. We would need to understand the ultimate tensile
stress which as this point the material would fail. This information can be
gathered by conducting a Tensile Test and the information produced should be
combined with Young’s Modulus testing when decided what material should be
used.

 

Conclusion

 

The
Young’s Modulus in Tension experiment indicated that Carbon Steel had a higher
value of E than Brass and had the ability to withstand a larger amount of force
without deforming. It therefore was the stiffer material. The Young’s Modulus
in Bending demonstrated that Keruing showed a great resistance to elastic
deformation which made it stiffer than the Parana Pine specimen. This
information should be considered when deciding what material to use in
construction, specifically for load bearing applications.  However, it must not be forgotten that
materials that have a lower stiffness can be adapted by changing their
dimensions or by using reinforcement to improve their performance.

 

 

Figure
1: https://www.shimadzu.com/an/sites/default/files/ckeditor/an/industry/petrochemicalchemical/qn5042000000k62u-img/qn5042000000nggy.jpg

Figure
2 : http://modulusandmatrix.co.uk/wp-content/uploads/2017/04/metal-testing-sample.png

Figure
3:   http://www.impactsolutions.co.uk/impact/wpcontent/uploads/2014/09/3pointbend.png

Figure
4: Printed Graph Given

Figure
5: Printed Graph Given

Figure
6: Printed Graph Given

Figure
7: Printed Graph Given

 

 

Section 1

·      The Tensile Test of Metals

 

Results

 Raw Data

 

Metal

Diameter (mm)

Maximum Load(N)

1

Steel 0.1%
Carbon

4.87

7900

2

Steel 0.4%
Carbon

4.99

13315

3

Steel 1.0%
Carbon

4.93

17930

4

Aluminium Alloy

5.06

6759

.

Derived Data

 

 

Figure 8 – Tensile Test 0.1 %, 0.4%,
&1.0% Carbon Steel Graph

 

 

Figure 9 – Tensile
test of Aluminium Alloy Graph

 

0.1%
Carbon Steel

a) Yield Stress==

Radius
(r)=4.87mm2.435mm=2.435

Original
cross-sectional area(A)=

A=x=3.14x 5.99225=18.6177665

Axes(y) = 106mm

1mm=30000N 106mm

1mm=283.018N

From 0 to intersection point = 19mm

Force at yield is = 19 mm x 283.018 N= 5377.342N

Yield stress = = =288.840

 

 

 

b) UTS=

For the purpose of this experiment the calculations
for the ultimate force have been made using the graph provided and the formula
as instructed.

From 0 to intersection
point = 28 mm

Ultimate force = 28 mm x 283.018 N= 7924.504N

 

Sample
Label

Diameter
(mm)

Maximum
Load(N)

Area(A)

Yield
stress

Ultimate
Tensile Strength(UTS)

Proof
Stress
at
0.2%

1

Steel 0.1% Carbon

4.87mm

7900N

18.617

288.840

425.659

 

2

Steel 0.4% Carbon

4.99mm

13315N

19.546

398.188

687.780.

 

3

Steel 1.0% Carbon

4.93mm

17930N

19.078

563.721

942.008

 

4

Aluminium Alloy

5.06mm

6759N

20.098

 

336.786

320.739

 UTS = == 425.659

 

Using the above
calculations all the results have been plotted in the following table:

 

 

 

Sample Label

Elongation %

Reduction in
 Area %

 

1

Steel 0.1% Carbon

36

62

 

2

Steel 0.4% Carbon

25

55

 

3

Steel 1.0% Carbon

19

30

 

4

Aluminium Alloy

15

72

 

 

 

 

Table showing the ductility parameters of percentage
Elongation and percentage Reduction in Area in the table.