Statement of originality (5 marks)
Compose a truthful statement that describes how you personally produced answers to these assignment questions. Your statement must confirm in some manner, that the analysis, workings, sketches, and answers you have presented to Questions 1, 2 and 3 of this assignment are entirely your own work.
Question 1: Strain gauge laboratory visit (80 marks)
Visit the video record of the strain gauge rosette application: https://www.youtube.com/watch?v=SCuH3AnZgFU
If you cannot access the video on the internet, some key frames from the video are provided in the Assignment 2 folder within the file: “strain_gauge_laboratory.pdf”.
In this video, a 0°-45°-90° strain gauge rosette is bonded to an unopened can of soft drink. The gauges are electrically connected, and the amplifiers are zeroed prior to opening the can of drink. The strains go negative with the opening of the can of drink because the internal pressure is released and the outer dimensions of the can in the 3 axis directions therefore decrease.
(a) Identify reasonable and consistent values for 𝐸, 𝐺, and 𝜈 for aluminium can material from a material properties table in a textbook or similar reference resource, in combination with the use of the known 𝐸-𝐺-𝜈 relationship. [10 marks]
(b) Taking the x-axis direction as aligned with the gauge on the 0° axis (the longitudinal direction of the can), and using the measured strains in the 3 axis directions, specify the strains 𝜖𝑥, 𝜖𝑦, and 𝛾𝑥𝑦. [10 marks]
(c) Using the material properties identified in part (a), determine the stresses 𝜎𝑥, 𝜎𝑦, and 𝜏𝑥𝑦. [15 marks]
(d) Identify the values of the principal stresses 𝜎1 and 𝜎2 and the orientation of the principal stresses 𝜃𝑝 relative to the x-y axis directions. [15 marks]
(e) Should the value of 𝜃𝑝 be zero in this case? Discuss this matter. [10 marks]
(f) Treating the can as a thin-walled pressure vessel with a diameter of 65 mm and a wall thickness of 0.1 mm, calculate values for the internal pressure in the unopened can based on results in (d). [10 marks]
(g) The gauge pressure for the contents of a sealed coke can at 25 ºC is expected to be around 330 kPa. Discuss the results obtained in part (f). [10 marks]
Question 2: Basic stress analysis (25 marks)
For the state of plane stress depicted in the figure to the right: (a) determine the principal stresses and show these on an element in the correct orientation relative to the x axis [10 marks]; and (b) show the magnitudes and directions of all stresses that would exist on an element rotated by 10º in the counter clockwise direction relative to the element orientation shown in the sketch to the right [15 marks]. For both part (a) and part (b), you must show all of your working.
Question 3: Theories of elastic failure (10 marks)
(a) At a certain location on the surface of a steel component, the material is in a state of plane stress with principal stresses of = 90 MPa (a tensile stress) and = -80 MPa (a compressive stress). If the yield strength of the material is = 250 MPa, determine the factor of safety according to the maximum distortion energy theory of failure [5 marks].
(b) At a certain location on the surface of a grey cast iron component, the material is in a state of plane stress with principal stresses of = 90 MPa (a tensile stress) and = –100 MPa (a compressive stress). If the ultimate strengths of the material are = 170 MPa = 655 MPa, determine the factor of safety according to Mohr’s criterion (also known as the Coulomb-Mohr theory) [5 marks].