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Assessment Essay Example
 Category:Engineering and Construction
 Document type:Assignment
 Level:Undergraduate
 Page:2
 Words:1030
Assignment 1: Laboratory Investigation
Lab report
Assignment 1: Laboratory Investigation
Group members:
Abstract
Stiffness is important for many applications such as when building bridges, and is dependent on both the geometry of the structure and the material from which it is made. The objective of this experiment was to study the stiffness of different materials such as mild steel, brass and aluminium under the load. In this experiment, we examined the deflection of a beam by increasing the load on the beam for different materials in order to find the relationship between their deflection and the load applied. A material in form of a beam with a rectangular cross section was supported at both ends so as to bear the load. Then a load was applied in a perpendicular direction to the horizontal beam that resulted in to deflection. We found out that the defection increases with increase in load and aluminium deflects more than brass and mild steel for each load. The Young modulus of elasticity obtained from this experiment for mild steel was 172.3GPa, for brass was 109.7 GPa and for aluminium was 69.9 GPa. Stiffness of a material is related to the deflection such that stiffer materials deflect less compared to less stiff ones.
(Words = 195)
Table showing the dimensions for the specimens
Mild steel 
Aluminium 

Length (mm) 

Thickness (mm) 

Width (mm) 
Table below shows the deflection of the specimens for procedure 1a
Load (W) Newtons 
Deflection (Δ) in mm 

Mild steel 
Aluminium 

0 
0 
0 
0 
Beam size 
500 x 3.3 x 19 
500 x 3.3 x 19 
500 x 3.1 x 18 
The graph of load verses deflection is shown below.
Figure 1: A graph of Load verses deflection for procedure 1a

Results table for 1b
Table showing the deflection of the specimens for procedure 1b
Mild steel
Load (W) Newtons 
Deflection (Δ) in mm 
^{3}48ΔI/L 

0 
0 
0 
0 
1.8299E12 
2.85923E11 

3.74174E12 
5.84648E11 

5.57165E12 
8.7057E11 

7.45618E12 
1.16503E10 

9.44995E12 
1.47656E10 

Experiment 1b 
Material 

I = 

= 125000000^{3}L 
^{4} mmThe second moment of area, I =
for mild steel^{3}48ΔI/LThe graph of load verses
for mild steel^{3}48ΔI/LFigure 2: The graph of load verses
Modulus of elasticity for mild steel from the load verses graph
= 172.3 Gpa
Aluminium Table showing the deflection of the specimens for
Load (W) Newtons 
Deflection (Δ) in mm 
^{3}48ΔI/L 

0 
0 
0 
0 
4.50648E12 
7.04138E11 

9.17683E12 
1.43388E10 

1.37379E11 
2.14655E10 

1.7944E11 
2.80375E10 

2.29148E11 
3.58043E10 

Experiment 1b 
Material 

I = 

= 125000000^{3}L 
^{4} mmThe second moment of area, I =
for aluminium ^{3}48ΔI/LThe graph of load verses
for aluminium^{3}48ΔI/LThe graph of load verses Figure 3:
Modulus of elasticity for aluminium from the load verses graph is
= 69.9 Gpa
Table showing the deflection of the specimens for Brass
Load (W) Newtons 
Deflection (Δ) in mm 
^{3}48ΔI/L 

0 
0 
0 
0 
2.91736E12 
4.55838E11 

5.83473E12 
9.11676E11 

9.0095E12 
1.40774E10 

1.15193E11 
1.79989E10 

1.44581E11 
2.25908E10 

Experiment 1b 
Material 

I = 

= 125000000^{3}L 
^{4} mmThe second moment of area, I =
below for brass is shown ^{3}48ΔI/LThe graph of load verses
for brass ^{3}48ΔI/LFigure 4:The graph of load verses
Modulus of elasticity for brass from the load verses graph is
= 109.7 Gpa
Discussion
From the graphs above, it can be concluded that the load applied is directly propositional to the deflection for the beams for mild steel, brass and aluminium. In other words;
Deflection, D L where, L = the load applied.
It means that as the load increase, the deflection increase too (Ashby, 2010). However, the deflection value for aluminium is high for both brass and mild steel for each load. Mild steel has the least deflection among the three materials.
. Thus modulus of elasticity for mild steel is higher compared to that of brass and aluminium. ^{11} compared to brass whose gradient is 1.085 x 10^{11}From the graphs above, the slopes, as seen from the gradients, vary with the materials being tested. For example, mild steel has 2 x 10
The table below shows the comparison between the theoretical and the experimental values of Young’s modulus.
Theoretical value 
Experimental value 

Mild steel 
172.3GPa 

108.5 GPa 
109.7GPa 

Aluminium 
As seen from the table above, the values obtained from this experiment were different from the theoretical values (calculated values). The percentage error for brass and aluminium are 1.11% and 1.28% respectively which is low compared to mild steel, which is 13.85%. The factors that may have caused the difference between the experimental values and the theoretical values include the following.

Temperature – as the temperature increase, the materials used in the experiment soften and expands.

The impurities in the material may cause difference in Young’s modulus. Holes or substances inside the beam may harden or soften it, thus the deflection is affected.

Oxidation on the surface layer of the beam may cause may harden the material. For example, the oxide of aluminium is harder than aluminium itself. This affects the deflection which affects the accuracy in the experiment.

Another factor is the level of the beam. Unbalanced beam affect the moment of the segment.
The second moment of the area of the beam affects the stiffness of a material. It can be concluded from this experiment that the higher the value of Young’s modulus, the higher the stiffness and the less the structure deflects.
Deflection is useful in our daily lives. Deflection is used to construct buildings and bridges, since a curved beam can support more loads. Some cases where deflection is undesirable include deflection of the shaft of the engine. Such a beam will rotated out of its axis and make it unstable (Duggal, 2009).
conclusion
From this experiment, it has been shown that the deflection for mils steel, aluminium and brass are directly proportional to the load applied. But aluminium deflects more compared to mild steel and brass. We also found out that the Young’s modulus is related to the stiffness of the material. The materials with higher Young’s modulus are stiffer compared to those with low Young’s modulus.
REFERENCES
. New Delhi: Tata McGrawHill.Design of steel structuresDuggal, S. K. (2009).
. Burlington: Elsevier Science.Materials Selection in Mechanical DesignAshby, M. F. (2010).
Bird J., & Ross C. T. F., (2012). Mechanical Engineering Principles, Routledge