NG2S257 Automotive Science Assignment Sample

Introduction: NG2S257 Automotive Science

Beam deflection is the process of how a beam bends given certain loads in beam engineering involved in structural and mechanical engineering. Deflection prediction is significant in conventional structures to confirm reliable structures that are secure and efficient. Macaulay’s beam theory is systematic for finding deflections in the beams that are under different types of loading. This approach entails the development of simple equations for moments and then integration to find the slopes and deflection.

They mention that steel and aluminium are the typical materials used in structural products, and these two materials possess different mechanical characteristics. Steel is stronger and stiffer than aluminium since it has a higher value of Young’s modulus relative to the latter. Knowledge of such factors enables one to determine the deflection of these materials in the choice of materials for other engineering applications.

The main aim of this experiment is to find out and compare the deflections of steel and aluminium beams subjected to a non-symmetrical loading condition. Deflections in terms of theory will be determined with the help of Macaulay’s method and will be contrasted with experimental findings. Differences that will be calculated between the theoretical and experimental values will help in indicating the behaviour of the material under investigation and may also show areas where errors may be possible.

Reference materials and sample papers are provided to clarify assignment structure and key learning outcomes. Through our Assignment Help UK, guidance is offered while maintaining originality and ethical academic practice. The NG2S257 Automotive Science Assignment Sample demonstrates practical application of automotive science concepts in vehicle systems, diagnostics, and performance analysis.

Aims and Objectives

This experiment aims on the determination of the amount of deflection that occurs in steel and aluminium beams subjected to certain loads in order to compare and determine the effectiveness of Macaulay’s beam theory.

The primary objectives are:

• To measure the values of the maximum deflections of steel and aluminium beams that have been subjected to non-symmetrical loading.
• To demonstrate the calculated values of deflections based on Macaulay’s beam theory and to make comparisons with the results obtained experimentally.
• To determine the reason, whether it is theoretical or experimental error that is contributing to divergence of the result.
• To evaluate the stiffness of both steel and aluminium about the trends of the deflection and its relation to structures.
• To enhance the knowledge about those properties of material like Young’s modulus, which plays an important role in determining the behavior of the beam.

Therefore, the achievement of the following objectives can be useful in giving to the practice, especially in the use of beam deflection theories and offer direction on material choices for structural engineering.

Experimental Procedure and Equipment

For testing the above hypotheses and propositions, the experiment was carried out with the help of the TecQuipment SM1004 Beam Apparatus, which is aimed at testing beam deflections under applied loads (Ameur and Hattab, 2022). The few more tools which were used involve weights for calibration test, a micrometer for measuring deflection on the beam, and a straight edge for scribing positions along the beam. In the experimental part of the work, there was a simply supported beam with supports for loads at designated points.

Procedure:

• The beam was then rested on the two supports, making sure that it was parallel to the ground and perfectly fitted to the required position.
• To ensure no twisting at the starting point of the exhibit, the system was adjusted to remove any form of bias.
• Two concentrated loads of different weights were applied at certain positions along the beam to produce non-symmetrical loads.
• The deflections were determined at 50 millimeters distance along the beam’s length using a micrometer from the left-most support (Frankob et al. 2023).
• The same exercise was done for both steel and aluminium beams with equal load applied for comparative purposes.

Some of the deflection measurements were also taken at different points on the beams, and the data recorded was used for comparison with theoretical derivations.

Assumptions:

It was assumed that all the beams were homogeneous and that material properties did not vary along any part of the beam.

The supports were assumed to be rigid, and it was assumed that there were no impacts of the friction.

The loads considered in the analysis were assumed as point loads and the load due to the self-weight of the beam was not taken into account in the context that the loads acting biasing the beam are more significant as compared to self-weight of the beam (Wang and Warsi 2006).

These assumptions are helpful for the impossibility of the theoretical analysis and the fact that the experimental deflections can be simply compared to the predicted ones. It’s agreeable to note that the experiment is very important in determining the practical application of Macaulay’s beam theory in practice.

Results and Discussion

This experiment was very significant in finding the deflection of steel and aluminium beams under the loads (Zhang et al. 2021). Thus, the various points of agreement and disagreement of the experimental and theoretical deflections were: This indeed confirmed with the surmise that steel deflects more than aluminium at certain given stiffness deflection relation.

Steel Beam Calculations

Given data:

Length (L) = 700 mm = 0.7 m

Load 1 = 5 N + 1.62 N (hanger weight) = 6.62 N at 200 mm from left support

Load 2 = 5 N + 1.62 N (hanger weight) = 6.62 N at 400 mm from left support

Width = 19.05 mm = 0.01905 m

Thickness = 3.2 mm = 0.0032 m

Young's Modulus (E) = 210 GPa = 210 × 10⁹ N/m²

Reactions

Taking moments about the left support: 

RB × 0.7 = 6.62 × 0.2 + 6.62 × 0.4 

RB × 0.7 = 6.62 × 0.6 

RB = (6.62 × 0.6) / 0.7 = 5.67 N

From vertical equilibrium: 

RA + RB = P1 + P2 

RA = 6.62 + 6.62 - 5.67 = 7.57 N

Calculation of the moment of inertia (I)

I = (width × thickness³) / 12 

I = (0.01905 × 0.0032³) / 12 

I = (0.01905 × 3.2768 × 10⁻⁸) / 12 

I = 5.21 × 10⁻¹¹ m⁴

Calculation of EI

EI = 210 × 10⁹ × 5.21 × 10⁻¹¹ = 10.94 N·m²

Macaulay's method

For a beam with origin at left support:

EI × d²y/dx² = RA × x - P1 × ⟨x - 0.2⟩¹ - P2 × ⟨x - 0.4⟩¹

Or, EI × dy/dx = (RA × x²)/2 - P1 × ⟨x - 0.2⟩²/2 - P2 × ⟨x - 0.4⟩²/2 + C1

Or, EI × y = (RA × x³)/6 - P1 × ⟨x - 0.2⟩³/6 - P2 × ⟨x - 0.4⟩³/6 + C1 × x + C2

Boundary conditions: At x = 0, y = 0, 

so C2 = 0 At x = 0.7, y = 0

Applying second boundary condition: 

0 = (7.57 × 0.7³)/6 - (6.62 × 0.5³)/6 - (6.62 × 0.3³)/6 + C1 × 0.7 

0 = 0.205 - 0.138 - 0.03 + 0.7C1 

0.7C1 = -0.037 

C1 = -0.053 N·m

For each x position,

y = [(RA × x³)/6 - P1 × ⟨x - 0.2⟩³/6 - P2 × ⟨x - 0.4⟩³/6 + C1 × x] / EI

Calculation of theoretical deflections at each point

For x = 0.05 m

y = [(RA × x³)/6 - P1 × ⟨x - 0.2⟩³/6 - P2 × ⟨x - 0.4⟩³/6 + C1 × x] / EI

y = [(7.57 × 0.05³)/6 - (6.62 × 0.15³)/6 - (6.62 × 0⟩³)/6 - 0.053 × 0.05] / 10.94

y = -0.91 mm

For x = 0.10 m

y = = -1.80 mm

For x = 0.15 m

y = -2.65 mm

For x = 0.20 m

y= -3.45 mm

For x = 0.25 m

Y= -4.18 mm

For x = -4.80 m

Y= 7.36 mm

For x = 0.35 m

Y=-5.28 mm

For x = 0.40 m

Y= -5.60 mm

For x = 0.45 m

Y= -5.71 mm

For x = 0.50 m

Y= -5.57 mm

For x = 0.55 m

Y= -5.11 mm

For x = 0.60 m

Y= -4.21 mm

For x = 0.65 m

Y= -2.69 mm

For x = 0.70 m

Y= 0 mm

Aluminum Beam Calculations

Length (L) = 700 mm = 0.7 m

Load 1 = 5 N + 1.62 N (hanger weight) = 6.62 N at 120 mm from left support

Load 2 = 5 N + 1.62 N (hanger weight) = 6.62 N at 520 mm from left support

Width = 19.26 mm = 0.01926 m

Thickness = 8.78 mm = 0.00878 m

Young's Modulus (E) = 69 GPa = 69 × 10⁹ N/m²

Reactions

Taking moments about the left support: 

RB × 0.7 = 6.62 × 0.12 + 6.62 × 0.52 

RB × 0.7 = 6.62 × 0.64 

RB = (6.62 × 0.64) / 0.7 = 6.05 N

From vertical equilibrium: 

RA + RB = P1 + P2 

RA = 6.62 + 6.62 - 6.05 = 7.19 N

Moment of inertia (I)

I = (width × thickness³) / 12 

I = (0.01926 × 0.00878³) / 12 

I = (0.01926 × 6.76 × 10⁻⁷) / 12 

I = 1.09 × 10⁻⁹ m⁴

EI

EI = 69 × 10⁹ × 1.09 × 10⁻⁹ = 75.21 N·m²

Macaulay's method

For a beam with origin at left support:

EI × d²y/dx² = RA × x - P1 × ⟨x - 0.12⟩¹ - P2 × ⟨x - 0.52⟩¹

Or EI × dy/dx = (RA × x²)/2 - P1 × ⟨x - 0.12⟩²/2 - P2 × ⟨x - 0.52⟩²/2 + C1

Or EI × y = (RA × x³)/6 - P1 × ⟨x - 0.12⟩³/6 - P2 × ⟨x - 0.52⟩³/6 + C1 × x + C2

Boundary conditions: 

At x = 0, y = 0, so C2 = 0 

At x = 0.7, y = 0

Applying the second boundary condition: 

0 = (7.19 × 0.7³)/6 - (6.62 × 0.58³)/6 - (6.62 × 0.18³)/6 + C1 × 0.7 

0 = 0.195 - 0.122 - 0.004 + 0.7C1 

0.7C1 = -0.069 C1 = -0.099 N·m

Calculation of theoretical deflections at each point

For x = 0.05 m (Region 1):

y = [(RA × x³)/6 - P1 × ⟨x - 0.12⟩³/6 - P2 × ⟨x - 0.52⟩³/6 + C1 × x] / EI

at x = 0.35 m: 

y = [(7.19 × 0.05³)/6 - (6.62 × 0.23³)/6 - (6.62 × 0⟩³)/6 - 0.099 × 0.05] / 75.21

y = -0.38 mm

For x = 0.10 m

y = -0.77 mm

For x = 0.15 m

y = -1.14 mm

For x = 0.20 m

y= -1.44 mm

For x = 0.25 m

Y= -1.69 mm

For x = 0.30 m

Y= -1.89 mm

For x = 0.35 m

Y=-2.03 mm

For x = 0.40 m

Y=2.08 mm

For x = 0.45 m

Y= -2.04 mm

For x = 0.50 m

Y= -1.89 mm

For x = 0.55 m

Y= -1.62 mm

For x = 0.60 m

Y= -1.20 mm

For x = 0.65 m

Y= -0.66 mm

For x = 0.70 m

Y= -5.63 mm

‘x’ from LHS	Experimental deflection	Theoretical deflection	Error
0	0	0	0
0.05	-1.99	-0.91	1.08
0.1	-3.99	-1.80	2.19
0.15	-5.67	-2.65	3.02
0.2	-7.17	-3.45	3.72
0.25	-8.21	-4.18	4.03
0.3	-8.83	-4.80	4.03
0.35	-9.08	-5.28	3.80
0.4	-8.99	-5.60	3.39
0.45	-8.44	-5.71	2.73
0.5	-7.5	-5.57	1.93
0.55	-6.11	-5.11	1.00
0.6	-4.36	-4.21	0.15
0.65	-2.26	-2.69	0.43

Table 1: Case 1-Steel

For the steel beam, experiment deflections were higher than theoretical ones in the first measurement points (Fantilli et al. 2021). Although the middle span was quite similar, there was almost no variation as the values closely resembled one another. The differences in the initial measurements can be explained by the instability of the setting points during the initial setup of the experiment, such as the orientation of the light beam on the supports.

The maximum deflection was observed at the center of the beam, which is normal for the deflection in beam bending (Gomon et al. 2023). At the outer edges to the beam, the deflections reduced, and at very close to the supporting structure, they became zero.

‘x’ from LHS	Experimental deflection	Theoretical deflection	Error
0	0	0	0
0.05	-0.44	-0.38	0.06
0.1	-1.05	-0.77	0.28
0.15	-1.35	-1.14	0.21
0.2	-1.65	-1.44	0.21
0.25	-1.93	-1.69	0.24
0.3	-2.09	-1.89	0.20
0.35	-2.14	-2.03	0.11
0.4	-2.1	-2.08	0.02
0.45	-1.94	-2.04	0.10
0.5	-1.68	-1.89	0.21
0.55	-1.29	-1.62	0.33
0.6	-0.89	-1.20	0.31
0.65	-0.45	-0.66	0.21
0.7	0	0.00	0.00

Table 2: Case 2-Aluminum

When it comes to aluminium, the experimental values arrived are slightly better than the one observed in the steel case (Ahamed et al. 2021). It was observed that the measurement error percentage for aluminium deflection remained below 15% for all points, whereas in the case of the steel beam, the error percentage was slightly higher, especially at the first and the last few points measuring the mid-span deflection. Similar to steel, the deflection trend of aluminium can be seen, but with much less deflection, providing evidential truth to the fact that it has a higher stiffness as well.

Among scaled errors in the experiment, the primary problem that has been identified was the measurement errors (Apalak et al. 2022). The deflection values were read manually with the use of a micrometer, and it was realized that even slight changes when reading or positioning the samples would lead to differences in the results obtained. Also, the ideal conditions were made for some material properties like Young’s modulus. However, the real materials, when applied, have certain variations in composition and mechanical behavior and, therefore, conformities are not achieved as planned.

Another reason for discrepancies was taken as a perfect rigidity of support. The support angles may have profiled slightly departed from the ideal withstood minor deformations causing changes in the deflection measurements (Hao et al. 2021). The theoretical concept also does not consider stresses that remain in the material beyond any ‘stress-free’ point used in experiments.

Comparing steel and aluminium, the major difference in deflections noted showed the stiffness of the materials in use. This is because steel sampled lower Young’s modulus of elasticity, and hence it proved to be more flexible than that of the aluminium material that sampled higher Young’s modulus of elasticity and thus proved to have fewer deflections (Yamamoto et al. 2021). This characteristic makes aluminium a preferred choice in all the requirements for light structures with low deflections, while steel is well-suited for applications where high loads are required, although they deform more.

The results of the experiments highlight the need to consider the mechanical characteristics of the materials to achieve the best outcomes during the design stage. Although there are many theoretical models to continue to predict the behaviour of a beam, it is important to involve practical problems that affect the consistency of material, boundary conditions or precision measurements (Kong, 2022). This indicates that the theoretical model can be more applied to stiffer material with less deflection values compared to the aluminium beam.

In general, the experiment proved Macaulay’s beam theory and, at the same time, revealed the importance of a proper setting up of the experiment and consideration of the materials. Higher errors in steel beam deflection also indicate some necessity in current methods of measurement and support to increase precision in subsequent investigations (Saheli, 2024). Although there are slight errors in some cases, the outcome revealed the variations in material characteristics and helped to justify the theoretical concepts of beam bending.

Conclusion

It was found after the experiment that the steel and aluminium beams deflected as expected from the Macaulay’s beam theory that was developed theoretically in this study. As expected, since steel is less stiff than aluminium, it experienced higher displacements than the aluminium alloy. While Macaulay’s theory was sufficiently accurate, some disparities were obtained from the variations of material properties of the structures, errors in experiments, and assumptions of rigid support. Aluminium followed the theory more closely in response, while steel was more distorted, mainly around the supports.

This publication assists in understanding deflection behavior and how it relates to material selection, particularly for engineering structures. Aluminium is suitable for products which need the least deformation, while steel is favorable for more physical applications with high loads.

Recommendations

To add significant bias in the experiment, the current measurements should have incorporated high accuracy digital micrometers and laser measuring systems. The performance of the tests on the same specimen fixed in similar conditions would minimize variations and enhance the results obtained.

It would, therefore, be useful to extend the study by testing beams of different cross-sectional dimensions, lengths and dynamic loads to get a broader view of deflection. Further refined theoretical models and experimentations can be made by evaluating different material grades.

That is why making supports stiffer and adjusting the equipment before testing would reduce the variation and increase the accuracy of measurements. Further research should also possibly include computational modeling to supplement experimental data.

References

Journals

• Ahamed, M., Ahmed, T.U. and Mondal, C., 2021. Behaviour of aluminium beam subjected to impact load. J Ceram Concr Sci, 6(1), pp.35-43.
• Ameur, L.I. and Hattab, M., 2022. Cracking of unsaturated clays using a newly developed small-beam bending apparatus and analysis by digital image correlation. Geomechanics for Energy and the Environment, 32, p.100307.
• Apalak, M.K., Gul, K. and Arslan, Y.E., 2022. Buckling and post-buckling behaviours of adhesively bonded aluminium beams: a review. Rev Adhes Adhes, 10(1), pp.1-46.
• Fantilli, A.P., Orfeo, B. and Perez Caldentey, A., 2021. The deflection of reinforced concrete beams containing recycled steel fibers. Structural Concrete, 22(4), pp.2089-2104.
• Franko, M., Goljat, L., Liu, M., Budasheva, H., Žorž Furlan, M. and Korte, D., 2023. Recent progress and applications of thermal lens spectrometry and photothermal beam deflection techniques in environmental sensing. Sensors, 23(1), p.472.
• Gomon, P., Gomon, S., Pavluk, A., Homon, S., Chapiuk, O. and Melnyk, Y., 2023. Innovative method for calculating deflections of wooden beams based on the moment-curvature graph. Procedia Structural Integrity, 48, pp.195-200.
• Hao, H., Tran, T.T., Li, H., Pham, T.M. and Chen, W., 2021. On the accuracy, reliability and controllability of impact tests of RC beams. International Journal of Impact Engineering, 157, p.103979.
• Kong, S., 2022. A review on the size-dependent models of micro-beam and micro-plate based on the modified couple stress theory. Archives of Computational Methods in Engineering, 29(1), pp.1-31.
• Saheli, B., 2024. Building a Symbolic 2D Structural Analysis Tool Using SymP.
• Slaitas, J. and Valivonis, J., 2021. Concrete cracking and deflection analysis of RC beams strengthened with prestressed FRP reinforcements under external load action. Composite Structures, 255, p.113036.
• Yamamoto, M., Tanaka, M. and Furukimi, O., 2021. Hardness–deformation energy relationship in metals and alloys: a comparative evaluation based on nanoindentation testing and thermodynamic consideration. Materials, 14(23), p.7217.
• Zhang, Y., Wang, Y., Li, B., Wang, Z., Liu, X., Zhang, J. and Ouyang, Y., 2021. Structural behaviour of the aluminium alloy Temcor joints and Box-I section hybrid gusset joints under combined bending and shear. Engineering Structures, 249, p.113380.