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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2012/
Module Title: Mechanical Materials (3D)
Module Code: MECH
School: School of Mechanical, Electrical & Process Engineering
Programme Title: Bachelor of Engineering (Honours) in Mechanical Engineering
Programme Code: EMECH_8_Y
External Examiner(s): Prof. Sean Leen, Mr. Tom O’Connor Internal Examiner(s): Mr S.F. O Leary
Instructions: Answer THREE questions. All questions carry equal marks.
Duration: 2 Hours
Sitting: Winter-Spring 2012/
Requirements for this examination: Graph paper and Logarithmic Books to be provided
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 classical flexural formula for curved bars of large initial curvature, show that the eccentricity, ℮, of the neutral axis from the centroid of a rectangular sectioned bar of width b and depth d is given by the formula:-
( ⁄⁄ )
where Rm is the mean radius of curvature of the bar. (14 marks)
(b) A curved bar, of square cross-section of 30mm side and of mean radius of curvature of 45mm, is initially unstressed. The bar is then subjected to a pure bending moment of magnitude 300Nm across a critical cross-section causing the bar to straighten. Calculate the maximum tensile and compressive stresses developed in the critical section. Using the provided graph paper, plot the stress variation throughout the depth of the section recording stress magnitudes at 2mm depth intervals. (20 marks)
Q4. (a) Determine the shape factor of a T-section beam of flange width 150 mm and depth 15 mm, and of web depth (excluding flange) 175 mm and width 12 mm. (15 marks)
(b) A cantilever is to be constructed from a beam with the above cross-section and is designed to carry a uniformly distributed load over its complete length of 4 m. Determine the maximum uniformly distributed load that the cantilever can carry if yielding is permitted over the lower part of the web to a depth of 30 mm. The yield stress of the cantilever material is 250 MN/m^2. (19 marks)
