Download Strain Rosette - Mechanical Materials - Exam and more Exams Mechanical Engineering in PDF only on Docsity!
CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2008/
Module Title: Mechanical Materials (2D)
Module Code: MECH 7011
School: Mechanical & Process Engineering
Programme Title: Bachelor of Engineering (Honours ) in Mechanical Engineering – Year 2
Programme Code: EMECH_8_Y2 EBIOM_8_Y
External Examiner(s): Mr. Peter Clarke and Prof. Robin Clarke Internal Examiner(s): Mr. William M. Corr
Instructions: Answer any three questions.
Duration: 2 hours
Sitting: Winter 2008
Requirements for this examination:
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
Q1. At a point on the free surface of a steel (E = 200 GPa and v = 0.30) machine part, the strain rosette shown in the figure was used to obtain the following normal strain data:
ε a = + 875 μ, ε b =+ 700 μ, ε c =+ 350 μ.
Determine: (a) The principal strains and the maximum shearing strain at the point. Prepare a material sketch showing all of these strains. (5 marks) (b) The stress components σx , σy and τxy at the point. (6 marks) (c) The principal stresses and the maximum shearing stress at the point. Prepare a material sketch showing all of these stresses. (5 marks) (d) Sketch Mohr’s Circles of stress and strain on a single plot for this loading situation. (4 marks) Note: This is not a “rectangular” rosette.
Q4. A rubber plug has a diameter of 30 mm and fits within a rigid sleeve having an inner diameter of 32 mm. Both the plug and the sleeve are 50 mm long. (a) Determine the axial pressure p that must be applied to the top of the plug to cause it to contact the sides of the sleeve. (8 marks) (b) Also, how far must the plug be compressed downward in order to do this? The plug is made from a material for which Ε = 5 MPa. v = 0.45. (4 marks) (c) Finally, if a total downward compression of 10 mm is required, what additional pressure is required to achieve this? (8 marks) Hint: Treat the before-contact and after-contact situations separately.
Q5. A viewing platform in a wild animal park is supported by a row of aluminium pipe columns having length L = 3.25 m and outer diameter d = 100 mm. The bases of the columns are set in concrete footings and the tops of the columns are supported laterally by the platform. The columns are being designed to support compressive loads P = 100 kN each. Determine the minimum required thickness t of the columns if a factor of safety N = 3 is required with respect to Euler buckling. (15 Marks)
What is the factor of safety against yielding? (5 Marks)
(For the aluminium, use E = 72 GPa for the modulus of elasticity and 480 MPa for the yield strength).
