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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2011/
Module Title: Mechanical Materials (3D)
Module Code: MECH
School: School of Mechanical and Process Engineering
Programme Title: Bachelor of Engineering (Honours) in Mechanical Engineering
Programme Code: EMECH_8_Y
External Examiner(s): Prof. Sean Leen, Mr J. J. Hayes Internal Examiner(s): Mr S.F. O Leary
Instructions: Answer THREE questions. All questions carry equal marks.
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) Assuming the three dimensional components of surface traction equations, derive the following expressions for direct stress, , and shear stress, , acting on an oblique plane in terms of the principal stresses and the direction cosines:-
[ ]½
Hence, derive expressions for the octahedral direct stress, , and the octahedral shearing stress,. (18 marks)
(b) The state of stress at a critical point in a polymer component is given with respect to a set of axes x,y,z by the following tensor:-
/^2
MN m XYZ
Another set of axes exists whose rotational matrix with respect to x, y, z, is given by:-
R
Determine the value of the direct and shear stress components with respect to the set of axes. Hence, or otherwise, calculate the magnitudes of the octahedral direct stress and the octahedral shearing stress at this critical point. Comment on the relevance of and in determining elastic failure at this point. (16 marks)
Q3. (a) Clearly explain the term Auto-Frettage and comment on its beneficial use. In assessing the stress at which plastic yielding occurs in a thick cylinder, which theory of failure is normally used? Is this theory of failure applicable for all types of material? (12 marks)
(b) A thick cylinder of external radius 600mm and internal radius 400m is subjected to a gradually increasing internal pressure p. Find the value of p when: (a) The material of the cylinder first commences to yield (b) Yielding has progressed
- One third of the depth
- Mid-depth
- Two thirds of the depth of the cylinder wall (c) The cylinder material suffers complete collapse. Comment, using these results, on the relationship between depth of yielding and remaining strength in the cylinder. Take σy = 600 MN/m^2 (22 marks)
Q4. (a) Calculate the shape factor of a T-Section beam of flange width 125mm and depth 10mm and of web depth (excluding flange) 140mm and width 10mm. (10 marks)
(b) A beam of length 9m is constructed from the above section and is designed to carry a point load at 2m from one support. Determine the value of the point load to cause complete plastic collapse of this structure when the beam is (1) Simply supported at both ends (2) Built-in at both ends (10 marks)
(c) Find the maximum value of the point load that can be carried by the simply supported beam if yielding is permitted over the lower part of the web to a depth of 20mm. (14 marks) Given: Yield stress of material = 250N/mm^2
