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UNIVERSITY OF MAURITIUS

FACULTY OF ENGINEERING

SECOND SEMESTER EXAMINATIONS

MAY 2011

PROGRAMME BEng (Hons) Manufacturing Engineering Year 2

BEng (Hons) Mechanical Engineering Year 2

BEng (Hons) Mechatronics Year 2

MODULE NAME Mechanics of Materials & Machines 1

DATE Tuesday

10 May 2011 MODULE CODE MECH 1001Y(1)

TIME 9:30 12:30 hrs DURATION 3 Hours

NO. OF

QUESTIONS SET

6 NO. OF QUESTIONS

TO BE ATTEMPTED

5

INSTRUCTIONS TO CANDIDATES

Answer any 5 Questions.

All questions carry equal marks.

g = 9.81m/s2

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MECHANICS OF MATERIALS & MACHINES 1 MECH 1001Y(1)

Answer any 5 questions.

All questions carry equal marks.

Question 1

(a) The brass rodAB and aluminum rod BC are joined at B and fixed connected attheir ends (Fig. Q1a). Both rods have the same cross-sectional area of1000 mm2. If there is no load in the members when T1= 10C, determine:

(i) the average normal stress in each member when T2= 50C;

(ii) the distance B will move.

(Ebr= 100 GPa, br= 18 X 10-6/0C; Eal= 70 GPa, al= 23 X 10-6/0C)

Fig. Q1a[10 marks]

(b) The concrete column shown in Figure Q1b is reinforced using four steelreinforcing rods, each having a diameter of 18 mm. Determine the averagenormal stress in the concrete and the steel if the column is subjected to an

axial load of 800 kN.

(Est= 200 GPa, Ec= 25 GPa)

Figure Q1b[10 marks]

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MECHANICS OF MATERIALS & MACHINES 1 MECH 1001Y(1)

Question 2

(a) Determine the tension in the cable and the horizontal and vertical componentsof reaction of the pin A shown in Figure Q2a. The pulley at D is frictionlessand the cylinder weighs 80 N.

Figure Q2a [8 marks]

(b) A homogeneous plate (Fig. Q2b) has a mass of 100 kg and is subjected to aforce and couple moment along its edges. It is supported in the horizontalplane by means of a roller at A, and a ball-and-socket joint at B, and a cord atC. Draw the free body diagram and determine the components of reaction atthe supports.

Fig. Q2b

[12 marks]

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MECHANICS OF MATERIALS & MACHINES 1 MECH 1001Y(1)

Question 3

(a) An open-endedpipe has a wall thickness of 2 mm and an internal diameter of40 mm. Calculate the maximum pressure on the interior wall of the pipe if the

maximum stress that the material can support is 360 MPa.

Show the hoop and axial stresses acting on a small element of material.

[6 + 2 marks]

(b) Draw the shear force and bending moment diagrams for the beam shown in

Figure Q3. Determine the position and magnitude of the maximum bendingmoment

Figure Q3[12 marks]

Question 4

(a) Prove that the total moment of resistance, IR

EM , where

Eis Youngs Modulus;

Ris the radius of curvature; and

Iis the second moment of area of the section about the neutral axis.[6 marks]

(b) Figure Q4 shows the section of a cantilever beam 3m long, which is to carry a

concentrated load of 700 kg at its free end. Calculate the maximum tensilestress in the beam if the flange of the channel is uppermost.

Figure Q4[14 marks]

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MECHANICS OF MATERIALS & MACHINES 1 MECH 1001Y(1)

Question 5

(a) Determine the force in each member of the truss (Fig Q5a) and state if themembers are in tension or compression, given that P1= 2 kN and P2= 1.5 kN.

Figure Q5a

[12 marks]

(b) The thin disc shown in Figure Q5b shows three masses (A, B and C) on a disc.To statically balance the disc, a 4thmass (D) should be added on it at a radiusof 50 mm. Find the mass of D and its position on the disc relative to A.

Mass A is 1.0 kg at 100 mm radius;

Mass B is 1.5 kg at 75 mm radius ;

Mass C is 2.0 kg at 90 mm radius.

Figure Q5b [8 marks]

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MECHANICS OF MATERIALS & MACHINES 1 MECH 1001Y(1)

Question 6

(a) The torque-angle diagram for a four stroke petrol engine is shown in FigureQ6a. The speed of the shaft must be maintained between 490 and 510rev/min. Calculate the following:

(i)

moment of inertia of a suitable flywheel;

(ii) mass of flywheel required if the radius of gyration is to be 0.3 m.

Figure Q6a[10 marks]

(b) The mechanism shown in Figure Q6b (attached) is driven by link AB at aspeed of 14 rev/s anti-clockwise. LM is perpendicular to BC and is rigidly

attached to it. Usethe method of instantaneous center of zero velocity to findthe instantaneous velocities of points B, C, L, and M at the instant shown.

[10 marks]

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MECHANICS OF MATERIALS & MACHINES 1 MECH 1001Y(1)

Question 6(b)

Figure Q6b

(OA = 3.0 cm; AB = 8.0 cm; BC = 12.0 cm; BL = 6.0 cm; LM = 2.5 cm)

Note: Figure Q6b has been drawn to scale and does not need to be reproduced.Kindly attach the sheet to your answer book in case you have used it to solveQuestion 6b.

END OF QUESTION PAPER

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