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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2011/
Module Title: Mechanical Materials (2D)
Module Code: MECH
School: School of Mechanical & Process Engineering
Programme Title: Bachelor of Engineering (Honours) in Mechanical Engineering Bachelor of Engineering (Honours) in Biomedical Engineering
Programme Code: EMECH_8_Y EBIOM_8_Y
External Examiner(s): Mr J.J. Hayes, Prof. S. Leen, Mr G. Clerkin, Dr L. McNamara Internal Examiner(s): Mr W.M. Corr
Instructions: Answer any THREE questions.
Duration: 2 Hours
Sitting: Autumn 2012
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. If in doubt please contact an Invigilator.
Q1. (a) Show that for small strains the fractional change in volume is the sum of the normal strain components associated with a set of three perpendicular axes. (4 marks) (b) Using this result, prove that for an isotropic, linearly elastic material,
V
V
x y z ^1 ^2 v
E^ (4 marks)
(c) An elastic material with modulus of elasticity E and Poisson’s ratio v originally fills a square cavity of sides 2a and height L in a rigid block as shown in Figure Q1. A rigid cap is placed on top of the elastic material, and when there is a force F˚ acting on the cap the height of the elastic material is observed to have decreased by an amount c. Calculate the magnitude of the force F˚. (9 marks) (d) For (b) and (c) above, what is the result when Poisson’s ratio approaches 0.50? (3 marks)
Q3. At a point on the free surface of a steel (E = 200 GPa and v = 0.30) machine part, the strain rosette shown below was used to obtain the following normal strain data:
a 875 , b 700 , c 350 .
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 x, y and xy 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 for this loading situation. (4 marks) Note: This is not a “rectangular” rosette.
Q4. (a) For a built-in beam which subsides a distance before loading, show that a “prestressing moment” of magnitude
M ^6 LEI 2
is introduced at the supports. (5 marks) (b) For the beam shown in Figure Q4, (i) Calculate the force and moment reaction V , M at the wall. (4 marks) (ii) Calculate the slope at the tip. (5 marks) (iii) Show that the deflection at the right hand end of the beam can be written
EI
y L^4
^163 (6 marks)
Where the standard notation applies. Hint: Singularity functions probably provide the most direct route to solution.
