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UNIVERSITY OF MAURITIUS

FACULTY OF ENGINEERING

SECOND SEMESTER / YEARLY EXAMINATIONS

MAY 2008

PROGRAMME BEng (Hons) Manufacturing Engineering/

BEng (Hons) Mechanical Engineering/

Level IIIMODULE NAME Mechanics of Materials and Machines III

DATE Saturday 17

May 2008

MODULE CODE MECH 3001Y(5)

TIME 9:30 12:30 Hours DURATION 3 Hours

NO. OFQUESTIONS SET

7 NO. OF QUESTIONSTO BE ATTEMPTED

5

INSTRUCTIONS TO CANDIDATES

There are SEVEN (7) questions in this paper.

Answer any FIVE (5) questions.

All questions carry equal marks.

Fig Q1, Fig Q4, Fig Q7 are enclosed.

All equations are given with the usual notations.

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MECHANICS OF MATERIALS AND MACHINES III MECH 3001Y(5)

Answer any FIVE (5) questions.

All questions carry equal marks.

Question 1

(a) State THREE assumptions made with reference to material behaviour in PlasticLimit Design. [3 marks]

(b) A steel beam of symmetrical I-section , as shown in Fig Q1, of length 5 m issimply supported at each end and carries a uniformly distributed load of 114kN/m over the full span. Steel reinforcing plates 12 mm thick are welded to eachflange and are made of elastic-perfectly plastic material.

Determine the plate width b such that yielding has just spread through eachreinforcing plate, at mid-span under the given load.

Mpp = B y. [ 3D2

d2. ]

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[17 marks]

Question 2

(a) Sketch the idealized stress/strain curve for torsion of a shaft beyond the elasticlimit. [3 marks]

(b) A solid circular shaft is subjected to pure torsion and the material is elastic-perfectly plastic with a yield stress in shear of 152 MN/m2. The shear stress atonethird of the radius from the centre of the shaft reaches the yield stress.

Determine:

(i) the shear strain on the outer surface [5 marks]

(ii) the ratio of the torque carried in the above conditions to the maximumelastic torque for the shaft. G = 83 GN/m2.

Tpp = y [ 4R3 R13 ] /6 [12 marks]

Question 3

(a) Express by means of an equation the condition for pure bending for a givencross-section . [3 marks]

(b) A horizontal cantilever of rectangular section , 40 mm wide 60 mm deep, issubjected to a load P in a transverse vertical plane at the free end. The load isinclined at 250 to the vertical. If the length of the cantilever is 2 metres and themaximum stress due to bending is not to exceed 200 MN/m2, determine thevalue of P. [17 marks]

= M [v cos/Iuu + u sin/Ivv]

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MECHANICS OF MATERIALS AND MACHINES III MECH 3001Y(5)

Question 4

(a) For a short column with an eccentric load the stress is given by

= W [ 1/A + au/Ivv + bv/Iuu ].

Show that the neutral axis does not pass through the centroid of the section.[5 marks]

(b) A short column of 200 mm external diameter and 150 internal diameter issubjected to a load parallel to the longitudinal axis, with eccentricity e. Thestresses induced are as indicated in Fig Q4.

Determine:

(i) the magnitude of the load [8 marks]

(ii) the distance of the line of action of the load from the axis of the column[7 marks]

Question 5

A steel disc of 400 mm external diameter is of uniform thickness and has a 50 mm holeat the centre.

Determine:

(i) the speed of rotation about an axis perpendicular to the plane of the disc whichwill produce a maximum tensile stress of 80 MN/m2. [12 marks]

(ii) the maximum radial stress and the radius at which it occurs. [4 + 4 marks]

The radial stress r and thecircumferential stress, c, is given by

r= A B/r2

2

r2

(3+ )/8.

c = A+ B/r2 - 2r2( 1+ 3 )/8.

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MECHANICS OF MATERIALS AND MACHINES III MECH 3001Y(5)

Question 6

A diaphragm of uniform thickness t is of radius R. It is freely supported at its edge andloaded on one face with a uniform pressure q. If the maximum stress induced is max,

show that:

(i) the maximum bending moment, Mmax, is given byMmax = qR2( 3 + )/16 [8 marks]

(ii) max = 3qR2(3+ )/8t2 [6marks]

(iii) the maximum deflection , ymax, is given by ` [6 marks]ymax= qR4 (5 + )/64D(1+ ).

d/dr[1/r . d/dr{ rdy/dr} ]= - Q/D

Mr = D[d/dr + /r ]

= My/I

D = Et3/12(1- 2)

Question 7

(a) State the condition for free vibrations in a body. [2 marks]

(b) What type of motion is characteristic of free vibration? [2 marks]

(c) In the linkage shown in Fig Q7, the bars AB and CD are uniform in cross-sectionand each has a mass of 1.2 kg. The disc at D, carried by the bar CD, is 150 mm indiameter and has a mass of 1 kg. The mass of the connecting link BE and that ofthe spring may be ignored. The spring has a stiffness of 400 N/m.

Determine the frequency of vibrations of the system. [16 marks]

END OF QUESTION PAPER

sg/

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