Structural Responses Of An Arbitrary Wire Problems Assignment

Assignment Task

Problem specification

A wire shape is to be manufactured from the provided length of drawn wire, an example of a bent wire is shown in Figure 1. The structure should then be used to experimentally solve a force‐ displacement problem, followed by the calculation of the natural modes of vibration of the structure (with one fixed‐support).

Analytical and numerical (Finite Element) calculations for the force‐displacement and vibration problems should be presented.

An analysis and discussion of the results should be given with particular focus on any differences between approaches and a discussion of the accuracy of the results due to assumptions associated with each method.

Presentation

A prescribed format for your assignment is provided. The template can be downloaded from the unit site. This is similar to how you would receive a prescribed format if you writing a report in an engineering firm or submitting a research paper to a Journal or Conference. It is an important skill to be able to accurately follow a prescribed format.

Relevant ABAQUS input (.inp) and data (.dat) files must be uploaded with this assignment. See the template document for more information on the file naming convention.

Your report should contain a photograph with the wire dimensions clearly indicated.

Task summary

Experimentally measure the elastic modulus of the wire

• Fix one end of the structure to a solid base (e.g., clamp one end to a desk).
• Add a known load to the Small denomination coins (eg. 2c, 5c, 10c) can be useful for this purpose.

What assumptions are made when deriving the flexure formula for beams? How do these assumptions relate to your problem?

• Calculate Young’s modulus of the material. You know the moments of inertia from geometry, you can calculate the displacement under a known load, and then solve for ‘E’ (this is much easier to calculate with a straight piece of wire!).

 2. Bend the wire into a unique shape, consisting of only straight sections (i.e., no curves). Full marks will be awarded for simple As a rule you should bend the wire so

it has 5 hoops. No two students should have exactly the same wire shape. You should experimentally determine the following (for the bent wire):

• The displacement of the structure when your structure is clamped at one end (fixed boundary conditions) and loaded at the opposite end with a known
• Vibration frequency of the first mode of vibration of:
  1. Just the wire, andb
  2. Wire with a concentrated mass attached

3. Using ABAQUS solve the following problems numerically (for the bent wire):

• Vibration frequency of the first mode of vibration of:
  • Just the wire, and
  • Wire with a concentrated mass attached
• Displacement of the structure when loaded at the opposite end with a known

4. Using your brain and a pen, solve the following problems analytically (for the bent wire):

• Vibration frequency of the first mode (ball‐park figure required only) of:
  • Just the wire, and
  • Wire with a concentrated mass attached
• Displacement of the structure when loaded at the opposite end with a known load (exact solution or ball‐park answer may be It will be marked accordingly).

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