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ENGG2400 Mechanics of Solids 1

Assignment 2 – Mechanical Modelling and Analysis

Introduction:

Through this assignment you create a link between objects in the real world with the mechanical models you have learnt throughout ENGG2400. This assignment will also allow you to work on your communication skills through report writing, an essential skill to share your ideas with other engineers!

For this assignment, you are required to select a simple object to model and conduct a loading analysis. This can be any object which is mechanically loaded. Through your analysis you will determine the expected stresses in your chosen object, the safety of your object to loading, and likely failure modes.

Each step of this modelling and analysis task will require extensive thought and consideration on your part. It is essential that you clearly communicate these thoughts through text and allow the reader to understand your ideas and analyses.

Assignment Overview:

Preliminary Task – Choice of object and preliminary modelling (1 mark)

You are to upload three files into the Form:

1. Image of the object, uploaded as an image file (PNG or JPEG).

2. Free body diagram of the object, uploaded as an image file (PNG or JPEG).

3. Short description of the object, the procedure of converting to a free body diagram, and analysis plan. This is to be uploaded as a text file.

Prior to selecting an object, make sure to read this entire document to get an idea of what analysis you will be required to do.

This will be due prior to the actual report.

Main Task – Mechanical analysis and written report (9 marks)

You are to upload a PDF report into Teams Assignment. The report should complete the following tasks:

1. Modelling of a real-world system

2. Analysis of loads on the model

3. Safety/failure of the design

4. Discussion of your model

Details of expectations are given through the rest of this document.

Preliminary Task: Choice of object and preliminary modelling

The preliminary task is to get you started with a few simple tasks before you dive into a more detailed mechanical analysis. You will be required to select an object in your surroundings that supports a mechanical load as part of its usage. You may want to consider objects such as: furniture, structures, equipment, vehicles, household objects, etc.

Do not feel obligated to analyse the whole object; you may choose to analyse only the part of the object—like the leg of a chair—most likely to fail under a loading. The object you choose and the loads you model for your object can be very simple or very complex; the choice is up to you. The only requirement we set is that the object must support a mechanical load that is not just the self-weight of the object.

After selecting your object, you are to submit three responses to the Preliminary Assignment Form:

1. An image of your object (this must be your own image) and ensure the object is clearly visible in the image. This is to be submitted as an image file and must be either of PNG or JPEG file formats.

2. Create a mechanical model by drawing a free body diagram of your object. Include the following:

a. Geometry, dimensions, axes, and necessary labels. If you can’t get precise measurements of your object, just make your best guess as to what these values are.

b. Reaction forces and moments.

c. Applied forces or force distributions.

d. Applied torques/moments or torque/moment distributions.

Your free body diagram may be hand drawn for this preliminary assignment; however, it will need to be converted to a digital drawing for the second part (formal report) of the assignment.

This is to be submitted as an image file and must be either of PNG or JPEG file formats.

3. Write a short paragraph (under 200 words) describing the object, what you are planning to analyse and what mechanical loads are applied on it.

Write a second short paragraph (under 200 words) describing how you converted the object and mechanical loads into a mechanical model.

If you are unsure of whether your object is suitable for this assignment, work through the following questions.

If you answer yes to any of these questions, the system is acceptable for analysis.

• Does your object have a mechanical function that involves supporting or outputting a force, moment (torque) or distributed load?

• Do other objects mechanically interact with your object, involving a transfer of force?

• Is your object placed somewhere such that environmental interactions may exert forces, moments (torque) or distributed loads?

Something else to consider is the complexity of your object; can your mechanical analysis be conducted within the time frame provided? Make sure you read this entire document to get an idea of what analyses are expected.

Main Task: Mechanical analysis and written report

Part 1: Modelling of a real-world system

In creating the model, you will need to estimate any loading distributions and magnitudes for one (or more) standard use cases of your object. A use case is a typical scenario where your object is subject to any mechanical loads. An example of this is illustrated below, for a person standing on a picnic table.

You will also be required to include an image and description of your object, any measurements or geometry (measured or estimated) of your object, the assumed material of your object with its mechanical properties, and the procedure and assumptions in creating the model.

In summary, your mechanical model should include:

1. An image of your original object.

2. A basic description of the object and its function.

3. A description of one or more load case(s) applicable to your object.

4. The assumed material of your object with mechanical properties required for any further calculations.

5. A free body diagram of your chosen object with all necessary information for further calculations such as geometry and loads. The diagram must be digitally drawn. Consider using Adobe Illustrator, draw.io, or PowerPoint for this.

6. A description of use cases and assumed loads that the object is subject to.

7. A diagram of relevant geometry of your object for determining geometric properties, such as a drawing of the object’s cross-section.

8. Any assumptions that you have applied in creating your model.

This part of the report will overlap with the preliminary analysis. For the final report we expect your model to be more complete, presented clearly, and for all drawings to be digitally created.

Part 2: Analysis of loads on the model

Using the mechanical model developed in Part 1, analyse the effect of the loading on the object. You may want to consider one or more of the following effects of loading on the material.

• Normal stresses and strains due to:

o Axial loads

o Bending loads

o Pressure loads (from vessels)

• Shear stresses and strains due to:

o Torsional loads

o Transverse shear loads

• Bearing stresses and strains induced by:

o Fasteners (screws, bolts)

Your analysis should contain the following general procedure. You will need to give enough information such that the reader can understand every step and reproduce it without any additional assumptions or hidden information.

1. Calculation of the internal loads within your object. You should express this through one or more of the following, depending on the nature of the loads you have selected.

• Axial load diagram

• Shear force diagram

• Bending moment diagram

• Torque diagram

• Estimated pressure inside and outside of your system.

2. Calculation of the cross-sectional properties (from your assumed geometry in Part 1) required for subsequent stress calculations. This may include:

• Cross-sectional area

• Location of centroid and neutral axes

• First / Second moment of areas

• Polar moment of area

3. Identify one or more points where failure is expected to occur and calculate the stress states at those points.

All equations must be typed and the substitution of numbers for calculations should be given if it makes it easier for the reader to understand. If you have utilised software to obtain your results, you must give the name and version of the software and a description of the procedure for software usage.

Always use standard notation where possible e.g. use E for Young’s modulus, use σ for normal stress. Non-standard notation can make it impossible for a reader to understand without a glossary and difficult to follow. Notation you introduce must be clearly explained.

Part 3: Safety/failure of the design

Using the information gathered in Parts 1 and 2, you are to determine the safety of the design and predict failure modes. Note that the content required to complete this section to a satisfactory level won’t be taught until Week 8.

1. Using the stress states at your selected critical points of failure from Part 2 and the material properties you found from Part 1, evaluate the failure and yield stresses of your points for a particular failure criterion. Examples include:

o Tresca (maximum shear stress)

o Von Mises (maximum elastic distortional energy)

o Maximum Stress Criterion

2. Identify likely failure modes and calculate the factor or margin of safety for the object.

The factor of safety (FoS) equation is as follows:

The margin of safety (MoS) equation is as follows:

MoS = FoS − 1

Part 4: Discussion of your model

From the preceding analysis, you should have gained some interesting insights about how your object responds to the mechanical loads and its consequent safety. As with any theoretical analysis, there will be limitations that prevent complete fidelity with the real-world behaviour. You should discuss those in this section. Some questions worth considering are:

1. What insights did you gain about your object from this mechanical analysis?

2. How might you expect the assumptions you have made in your modelling to have affected its accuracy compared with the real-world object?

3. What methods, strategies or improvements could be made to mitigate or minimise the risks of these discrepancies? What factor / margin of safety should we be designing for?

4. What phenomena does your model not consider? How might your model be refined to include these phenomena? We aren’t expecting much detail here; your thoughts on the matter are sufficient.

Report Format

You are to present the assignment as a formal scientific report which will effectively communicate your ideas and methodology to the reader. A scientific report usually contains the following sections:

• Title and abstract

• Introduction and Aims

• Methodology

• Results

• Discussion

• Conclusion

• References

The report should be no longer than 10 pages in length, from Abstract to Conclusion (i.e. excluding title page, appendices (if any), and references.)

Mark Distribution

This assignment is worth 10 marks. This corresponds to a 10% weighting towards the course. The preliminary analysis is worth 1 mark. The written report is worth 9 marks.

Preliminary Task: Choice of object and preliminary modelling

Main Task: Mechanical analysis and report writing

FAQ

Q: Why is there no template provided for this assignment?

A: This assignment is open-ended, and it is up to you to write, structure and present the report in a way that makes information clear and concise for the reader. You should write your report to a level of detail sufficient for a student in your cohort to understand. For example, you don’t need to define what normal stress is, but you do need to clearly state what the relevant force and area are.

In the real world, a senior engineer will go through your report, understanding and checking every aspect before approving or denying your analysis. If information is not clear or if the report is not clear, mistakes might be missed and result in not predicting the failure of the system. If the information is not presentable, the report may not even be read.

If you are still unsure about how reports should be presented, refer to past assignment templates or search online for examples of technical/scientific reports.

Q: I do not know exactly what to do. This assignment is quite vague.

A: This assignment gives you the freedom to come up with a unique analysis. We do not want to limit what you are allowed or not allowed to do. Instead, we provide a lot of suggestions to get you started. You can get a general idea of what we will expect in your report by reading the document and marking criteria. If you want to discuss your ideas, feel free to post in the xLab Channel on Teams, where your colleagues and the Demo Team will be able to lend a hand.

Q: The marking criteria is also vague! How do I get all the marks?

A: With regards to all the technical parts of the assignment, we will be looking at how well you understand the course material. Correct application of the theory, correct calculation and correct explanations will make sure you are on the path to a good grade in this assignment.

The report writing itself will be marked as a whole. What this means is a marker will determine the quality of your report after reading through it. The mark you get will depend on what the marker thinks of your layout, writing, clarity of writing, etc. We provide a list of standard headings but recommend that you structure the report such that all the information is easy to understand and well-presented.

First impressions are important; if a reader can get through your report without re-reading multiple times, or stopping and pondering what you have done, you will be on the path to a good grade!

Q: Where in the suggested report format do I place each of the parts for the main task (report writing)?

A: This is up to your discretion based on how you can best convey your methodology and results to the reader.

For a typical lab report, the methodology section should detail any methods or procedures you applied in calculating each step of your analysis. The results section should detail any key numbers from your calculation which provide insights into discussing the safety of your object or are interesting observations you wish to discuss. The discussion should detail the insights gained from your results and include mention of any errors or discrepancies from your methodology.

Q: What kind of questions are appropriate to ask in Teams?

A: We are happy to discuss whether your assumptions may/may not be valid. We will not be looking through working.

Q: How many loads are you expecting for the system?

A: We require at least one external load to be acting on your system of choice. More than 4–5 loads will likely be too complicated for this report, so you should be aiming for anything in that range.

Q: Does self-weight count as a mechanical load?

A: It does, however it should not be the primary or dominant load for your object. The primary load should relate to the main function or operation of your object.

Q: If my object carries a mass as part of its mechanical function, does that count as a mechanical load suitable for this assignment?

A: If your object’s function is to take or transfer the weight force from other objects, that is acceptable as a mechanical load, making the object suitable for analysis.

Q: How do I draw a free-body diagram for my object? The shape is so complex.

A: As you have learnt through the course, a free-body diagram does not need to include every aspect of the system in question; it only needs to define the relative position between all the forces to complement any calculations for mechanical analysis (such as applying Newton’s Laws).

In general, you just need to simplify the shape using more simple shapes. You can even construct composite shapes like stacking a rectangle and a circle.

Q: Do my diagrams need to be digitally produced?

A: For the written report (main task), all diagrams must be digitally produced and not hand drawn. You may use any software such as draw.io, GeoGebra, Adobe Illustrator, InkScape or Microsoft PowerPoint to create these diagrams.

Q: My object experiences many loads and/or can be subject to an infinite number of load cases. How do I decide what to include?

A: Technically, all objects have infinite loads that they can be subject to. For this assignment, it is expected that you identify key or dominant loads that apply a majority of the load onto your object. To help decide this, consider what the primary mechanical function of your object is, and the loads associated with such function.

For example, an office chair probably is not subject to large amounts of wind forces, so it is not a consideration you need to add to your model.

Q: How can I tell what material my object is?

A: You can make assumptions about what your object is made of. To help with this, find examples of similar objects and identify their material. You don’t have to get the exact material either, any close-enough material with a general justification is sufficient.

Once you know the general material class (wood, metal, glass, plastic), try to find a more specific material relevant to your object (hard wood, steel, hardened glass, polycarbonate) and search online for their general material properties. You don’t need to specify materials to their exact classification (though you can if you wish), e.g. A36 Steel or 6061 Aluminium.

Q: I cannot find the material properties for my specific material. What do I do?

A: If you find your material selection is too specific, find a similar material where their properties are available and use those in your analysis. Make sure to state what material properties you are using and make your reasoning for such choice clear. A table is a very good way to present data like this.

Note that you only require properties relevant to your calculations. For example, you might need the Elastic Modulus (E), Shear Modulus (G), Poisson’s Ratio (V), Yield Stresses (σY ) among others.

Q: What references am I expected to include?

A: There are various references to feature:

1. Any online sources you used to gather information about your object including basic description, function, material, loads, and geometry

2. Any software you used to assist your calculation procedure

3. Any calculations/equations not covered by course content (lectures, PSS, exams)

Q: Which failure mode should I be considering? There are so many.

A: Objects can fail in many ways. We are not expecting you to develop a perfect model of your object’s failure. You should consider the main load or stress that your object is subjected to and calculate the respective factor of safety. It is important to also calculate other stresses (if applicable) in case those end up being the predominant sources of stress.

You can search online for various failure criteria which can be used to evaluate the failure of a part. The most common are the Tresca (maximum shear stress) or the von Mises (maximum elastic distortional energy) criteria.

Q: What is considered ‘failure’ for a mechanical part?

A: For general mechanical systems, failure is defined as the point when the stress at any point in the system exceeds the material’s yield stress, not the ultimate failure stress. When the material begins to yield, the part is unable to sustain continued use at such stresses.

The material may also fail by cracking or rupturing, and you may consider that in this assignment, though we don’t expect you to have a well-developed understanding of these failure modes.

Q: What if I calculated that my part ‘failed’?

A: We expect errors to occur from the simplification, modelling and assumptions that we conduct through this procedure. A ‘failure’ result does not necessarily mean you have done anything wrong as we are more focused on the analysis and modelling procedure than the result.

If you do calculate that your part should have failed, review your calculations and discuss the consequent failure modes. The object you have selected is hopefully functional and safe, so you should identify why there are discrepancies between your analysis and the real-world.

Q: Margin or Factor of Safety?

A: You can select either one. They are both acceptable as long as you understand how they are used or what they imply.

Q: Do I need to justify every assumption I make?

A: Generally speaking, yes. The reader will need to understand the logic and reasoning behind why you modelled the system the way you did, and to do this, justifications must be detailed. You do not have to go into excessive detail; one line is often sufficient for this sort of reasoning.

Q: I am still confused with how I am to conduct this analysis. Please help.

A: Your PSS questions demonstrate the typical calculation process from first seeing the system to getting some stress values out. You should be following a similar process to those, for which there are plenty of examples (in lectures and your PSS). If you follow the general steps from your PSS problems, you should at least be able to determine the stress distributions of your object.

Q: What if my image is in a different format? (Like .HIEF for Apple Devices)

A: You are able to configure Apple Devices to take photos in JPEG, the procedure for which is available online. Alternatively, applications such as Microsoft Office Lens can be used to take photos in JPEG format.