MMAN3400 Mechanics of Solids Case study Report

Introduction

You are hired as a structural engineer in Knowitall, an engineering consulting firm. Your company recently secured a contract to help a client, Sweeties Confectionery, to design a sugarcane juice storage tower in their new factory in Honeyville, NSW. The sugarcane juice storage tower consists of a thinwalled tank and a supporting structure similar to Figure 1. The specific requirements from the client and the specific tasks assigned to you by the lead engineer in your company are listed in the next section.

Estimate the total weight of the entire system. This information will be used by a separate team of engineers in your firm to design the ground support.

Your Tasks

The client would like to install a sugarcane juice storage tower in their new facility, and your task is to design the structure to prevent failure and choose appropriate materials for construction. The overall system might look a little complicated, but the problem can be simplified by viewing it as a combination of the following separate components:

• A pressure vessel
• Vertical supporting columns
• Bracings between columns

To help you kickstart the design process, the client has outlined some key requirements for each component in the sections below. Note that the final design, including dimensions and materials, is completely your decision, as long as it meets all the specified requirements. You are expected to demonstrate the validity of your design and justify your design decisions by applying relevant theories of mechanics of solids.

However, please be practical and realistic with budgeting in mind. You do not need to complete a cost analysis, but you should think twice before designing an excessively huge/thick pressure vessel or using rare/expensive materials such as gold/crystal! In your calculations, a safety factor of 2 – 3 should be sufficient in most cases.

Design of Pressure Vessel

Client Requirements:

1. The designed capacity of the storage tank is 10 tonnes of sugarcane juice.
2. The storage tank should have the shape of a cylindrical and a conical shell, similar to Figure 1.
3. The tank must be constructed using non-toxic sheet metal with uniform thickness.
4. To avoid fracture of the pressure vessel, inspections of cracks in the storage tank are conducted monthly to ensure the storage tower has a long service life.

Your Tasks:

1. Design the shape and dimension of the tank to satisfy the capacity requirement. You may neglect the details at the cone tip and assume it has a pointy tip. Hint: Research the density of sugarcane juice to convert the mass requirement to volume requirement. Always be on the safe side!
2. Determine the membrane stresses at all important points in the shell. Ignore the effects of discontinuity at the cone tip and at the connection between the cylinder and the cone.
3. Choose the appropriate sheet metal for construction for the vessel by specifying its material and thickness.
4. Conduct research to find out the fracture toughness of the material you chose to construct the storage tank.
5. Suggest critical crack length value(s) to be included in the maintenance procedure when conducting crack inspections. Hint: Consider cracks developing at different orientations and/or locations of the vessel. Assume stress intensity factor,

Design of Supporting Columns

Client Requirements:

1. The storage tank is to be supported by eight (8) vertical columns below the tank.
2. The bottom of the storage tank (cone tip) must be at least one metre from the ground.
3. The vertical supporting columns are to be constructed using standard I beams.

Your Tasks:

Choose the appropriate standard I beam (material, length, and cross-sectional dimensions) for these supporting columns.

Ensure the columns do not buckle. Hint: Consider the weight of both the sugarcane juice and the tank itself. Ignore the bracings for now.

Ensure the columns will not yield under the same compressive load. Again, ignore the bracings for now.

Design of Bracings Between Columns

Client Requirements:

1. The bracings between the columns are to be constructed by welding circular rods together, with a configuration as shown in Figure 2.
2. During the monthly safety inspections of the structure, safety inspectors may need to climb up the tower using the horizontal members of the bracings.

Your Tasks:

1. Ensure the horizontal members of the bracing are able to support the weight of a human (around a safe upper limit, 100~130 kg) by choosing the appropriate circular rods (material, diameter and length) for these bracings. Hint: Consider a statically indeterminate beam with fixed ends, and a point load due to human weight. Ensure the maximum vertical deflection of the member does not exceed 2 mm when a human stands on it, by applying the principle of virtual-work and the method of superposition. Ignore the bracings from the other neighbouring columns for now.
2. Discuss the practical function of the bracings (the whole configuration including the horizontal and diagonal members), and discuss how these bracings may affect your design calculation of the vertical columns. Note that you are not required to perform any quantitative calculations for this task.
3. Estimate the total weight of the entire system. This information will be used by a separate team of engineers in your firm to design the ground support.

Bonus Task

Although the client did not have any specific requirements on the following topics, the senior engineer in your firm offered you a bonus (up to 10 bonus marks) if you could explain to him, with or without calculations, how unsymmetric bending, shear flow and shear centre, and fatigue theories may be relevant in the design of this structure.

Writing Your Report

In writing an engineering report, you are expected to provide information which is specific and precise. Please adopt the following points in writing your report:

• Page Limit: The length of the report from introduction to conclusion should NOT be longer than twenty (20) pages. Marks for this report will be awarded on quality and not quantity of the work.
• Paper Size and Margins: A4 pages should be used, with 25 mm margins. The text should be justified.
• Font: Body text needs to be 11-point Times New Roman with a line spacing of 1.5 (or equivalent). The font used must be consistent throughout the report.
• Type your report (including equations). No hand drawings/calculations will be accepted.
• Tables and Figures:
• All figures and tables should have a descriptive caption.
  • For figures, the caption should be below the images.
  • For tables, the caption should be above the table.
  • Proper references should be added to the captions of figures and/or tables if necessary.
• All figures, tables and equations should be referenced within the report.
• Formal Language: Engineering reports should be written in third-person narrative. Avoid the use of informal and personal language, such as “I think ….”, “We did ….”.
• Page Numbering: The title page should not have a page number, but everything after that should. All page numbering before the introduction should be in roman numerals (i.e. i, ii, iii, iv, etc.) with the numbering switching to numbers at the Introduction (the introduction section is on page 1)
• Multi-level headings are standard practice in engineering reports and assist in the creation of the table of contents. Please be sensible with the number of levels, especially in a short report like this one. Three levels should be ample, e.g., “2.2.1 Buckling Analysis”.

  In general, your report should include the following:

  • • Title Page
      • Include the course code, the title of the report, the name and zID of the author, the date of submission, and the authorship statement.
      • Authorship statement: By submitting this work, I acknowledge that the intellectual content of this report is my own, except where the contributions of others are explicitly described and/or properly cited. I am familiar with my responsibilities under the UNSW Student Code and understand how UNSW defines plagiarism and academic integrity.
    • Abstract
      • In less than 200 words ... what was the problem, how was it investigated, what did you find out and what do your findings mean?
      • This section should be a snapshot, not a narrative. Tell the reader about what was done and what was discovered, not a story about the process.
    • Table of Contents
      • A list of the major and minor sections of your report.
      • Introduction

        File Submission

        The project report is due at 11:55 pm on Friday Week 10. You must submit your .pdf file named ‘zID_Project_Report.pdf’ to the Moodle submission box before this time.

        Late Policy: Standard UNSW Late policy applies. Work submitted late without an approved extension by the course coordinator or delegated authority is subject to a late penalty of five percent (5%) of the maximum mark possible for that assessment item, per calendar day. The late penalty is applied per calendar day (including weekends and public holidays) that the assessment is overdue. There is no pro-rata of the late penalty for submissions made part way through a day. This is for all assessments where a penalty applies. Work submitted after five days (120 hours) will not be accepted and a mark of zero will be awarded for that assessment item.

        • Set the scene; give some background information about the topic. State the aim/purpose of the investigation. Outline the body sections.
        • Main Body
          • Organise the sections in a logical sequence: what you investigated, what you found, what interpretations and what judgements you made. Use short informative headings and subheadings.
          • Show the complete working (including detailed calculations and necessary diagrams such as FBDs, shear/bending moment/torque diagrams, etc) and final answers to support your design decisions. For tasks where a calculation step is to be repeated, you may show one complete sample calculation of that step and include the rest of the results in a table. You must organise your working in a neat and legible format.