Experiment: Determining Young's Modulus of Wood, Analysis and Results

This report details an experiment to determine the Young's modulus of wood, a crucial mechanical property. The experiment involved bending a timber sample and measuring its deflection under increasing loads. The report outlines the objectives, apparatus used (including bending apparatus, timber samples, dial gauge, weights, and Vernier gauge), and the procedure, which involved measuring the dimensions of the wood sample, applying loads in increments, and recording the resulting deflections. Data was collected and presented in tables and graphs, showing the relationship between load and deflection during both loading and unloading phases. Analysis included calculating the second moment of area and the Young's modulus based on the experimental data. The discussion section compares the calculated Young's modulus value with theoretical values, discusses the viscoelastic properties of wood, and highlights the significance of Young's modulus in engineering design and timber stress grading. The report concludes with a summary of findings and references to relevant sources.

(Institution)
(Name)
(Course)
(Unit)
(Unit Code)
Experiment No 3: Young modulus for wood.
(Professor’s Name)
(Date)

INTRODUCTION
The strength of materials is determined through load application. The two main techniques of
testing the strength are destructive testing and the non-destructive testing. The destructive testing
ends up destroying the sample while in non-destructive testing the sample is not destroyed.
The two types of destructive testing are compressive load and tensile load. Compressive load is
mainly reserved for brittle materials such as concreate and brick which have small plastic range
while tensile load is usually used for ductile materials.
Non-destructive testing is used for timber testing since it is an organic material. In this
experimental setup the timber is bent, the deflection noted using the bending theory and the value
of young modulus of stiffness is determined. Material is not destroyed during testing.
OBJECTIVES
The main objective of this experiment is to determine the Young’s modulus of a timber sample.
APPARATUS
Bending apparatus, Timber samples, dial gauge weights and Vernier gauge.
PROCEDURE
1. Vernier gauge was used to measure both the height (h) and width (w) of the wood
samples and results used to calculate the second moment of area (I) of the sample.
2. The equipment to be used was set in position and the timber sample was fixed in the
clamp.
3. Dial gauge was situated at a position from the clamp and recorded the distance this
measurement represents L1 . Dial gauge was reset to zero and the load carriers were fixed
immediately bellow dial gauge. The process was repeated for L2.
4. In steps of 50g Loads were applied up to a maximum of 500g while taking care of the
loads to stabilize before recording the deflection.
5. The process done was carried out in reverse.

RESULTS
Table 1
Load in
grams
Load in
Newton’s
Deflection
loading mm
Deflection
unloading
mm
0 0 0 0.12
50 0.4905 0.3 0.4
100 0.981 0.48 0.62
150 1.4715 0.74 0.79
200 1.962 0.95 1
250 2.4525 1.15 1.26
300 2.943 1.4 1.49
350 3.4335 1.64 1.65
400 3.924 1.88 1.85
450 4.4145 2.1 2.11
500 4.905 2.33 2.33
Table 2
Load
in
grams
Load
in
newton
Deflection
loading
mm
Deflection
unloading
mm
0 0 0 0.42
50 0.4905 0.97 1.22
100 0.981 1.86 1.98
150 1.4715 2.56 2.72
200 1.962 3.24 3.51
250 2.4525 3.86 4.28
300 2.943 7.74 5
350 3.4335 5.49 5.78
400 3.924 6.62 6.79
450 4.4145 7.22 7.48
500 4.905 7.91 7.91

Using the data obtained to plot graphs of mass verses deflection loading and unloading
Table 1 graph
0 0.5 1 1.5 2 2.5
0
100
200
300
400
500
600
Agraph of load verses Deflection loading & unloading
Deflection
loading mm
Linear
(Deflection
loading mm)
Deflection
unloading mm
Deflection loading & unloading mm
Load (g)
Table 2 graph
0 100 200 300 400 500 600
0
1
2
3
4
5
6
7
8
9
Agraph of load verses Deflection loading & unloading mm
Deflection
loading
mm
Linear
(Deflection
loading
mm)
Deflection
unloading
mm
Deflection loading & unloading mm
Load (g)

ANALYSIS
Calculating the slope of the graph during loading
Slope= load∈ grams ( g )
Deflection loading ( mm )
Graph1 slope= 150−0
0.74−0 = 150
0.74
Dimension of the wood sample used.
Width (w)=18mm
Height (h)=6mm
Length (L)=215.5mm
Calculating the second moment of area I
I= w h3
12 = 18∗63
12 =324 m m4
Calulating the youngs modulus E
E=
g L3
3 I ∗m
δ
E=
9.81∗215.53
3∗324 ∗150
0.74 =20.4741∗106 N /m m2
Youngs modulus of wood ( E)=20.4741Gpa
DISCUSSSION
The calculated value of Young’s modulus is 20.4741 Gpa, this value indicates that the wood
sample used and all woods have reasonable amount of stiffness wich depend on the wood
cellulose microfibrils being stretched. The young modulus value of the wood depend on the cells
spaces in the wood that is filled by water or air and it can decrease the value depending on the
size.

The theoriticallly measured range of wood young modulus value is 10GPa to 60Gpa of which the
experimental value obtained through calculation lies within the range indicating an accuracy of
the experiment. The mechanical behaviour of the wood is determined by the composite model of
the cell wall.
The graphical drawing of both loading and unloading data does not coincide exactly indicating
that the wood has some viscoelastic properties during deformation which is very important in
damping vibrations that leads to deflection and damage of wood. The area between the loading
and the unloading curves on the graph represents strain energy that stored in in the woood.
(Construction, 2012)
Asssignments
The accuracy of the experiment was very high becouse the caluclated value of Young’s
Modulus lie between the acceptable limits. The accuarrcy of the experiment can be
improved by using different types of woods with know value of Young’s modulus and
the experimentally calculated value of individual wood be compared with the theoritical
value of that wood.
The reuslts of calculated value of Young’s modulus is 20.4741 Gpawhile the accepted
value is between 10GPa- 60Gpa, this indicates that the results are accurate. The graphical
data plots of loading and unloading does not coincide proofing that the wood sample has
viscoelastic properties that responds instantly to strain and slow during unloading. In the
graph there is a space in between the loading and the unloading indicating that the wood
sample has some reserved strain energy and finally there is a liner relationship between
loading and unloading which indicates that the wood has some elastic properties.
Young’s modulus indicates the relationship between material stress and strain under
deformation. It is very essential both to the engineers and scientist in designing a
component since they are able to predict the mechanical properties of the material or
structure under during deformation and thus able to design a suitable body to fit the
usage. (CodeCogs, 2013)
Timber stress grading is done to determine the strength of the timber for structural
purposes. The grading methods for timebr are machine based and visually based:
 Machine grading: this is done mechanically by using a technique that relate
strength directly with the stiffnes

 Visual grading: The strength group is used to determine stress grade of the
species and the grade or visual quality of the timber. The structural properties of
the individual stress grade are described and they are used in determining the
grade of the timber. (Government, 2016)
 Proof grading: This grading is taken form the ability of the timber to take proof
load when subjected to bending. (boeingconsult.com, 2017)
The other techniques used for stress grading are.
1. Stress grades determination theough in-grade testing:
2. Using the traditional stress grades that has beenconfirmed or adjusting the by in-
grade testing
3. Using traditional stress grades (‘F’ grades) that is based on strength grouping
CONCLUSION
The Young’s Modulus value for every component used for structural designed should be known
so as to ensure greater accuracy during design and to determine the exact points where the
material will deform under particular size of load.
References
boeingconsult.com. (2017). GradingPresentation. Retrieved from Grading:
https://www.boeingconsult.com/tafe/mat/Timber/Grading.pdf
CodeCogs. (2013, May 11). Youngs Modulus. Retrieved from
https://www.codecogs.com/library/engineering/structures/youngs-modulus.php
Construction, A. I. (2012). Timber construction manual. Wiley.
Government, Q. (2016). Strength groups and stress grades. Retrieved from
https://qtimber.daf.qld.gov.au/guides/strength-groups-and-stress-grades