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QUESTION 1

The segment of shaft shown in Figure 1 is made of AISI 1095 annealed steel. The shaft is fine turned

with a diameter of D=20 mm and with a transverse hole of d=3 mm diameter. The segment as shown

is part of a drive shaft for a mixing machine.

Under normal operating conditions the shaft segment rotates at 60 rpm and is subject to the following

fluctuating loads:

A torque that varies from -120 Nm to +120 Nm once every five seconds;

An axial tensile load that varies from 0 to 8 kN at the same rate as the torque variation; and

A bending moment that varies between 10 Nm and 40 Nm once every second.

Determine the expected life of this segment of shaft.

(If you determine life in excess of the Endurance limit then determine the factor of safety).

[100 m

QUESTION 2

The end-cap of a pressure vessel as shown in Figure 2 is secured by 10 off M12 x SAE class 8.8 bolts

(with rolled threads). A soft gasket is used such that the clamped member stiffness is one third of the

bolt stiffness. The internal diameter of the pressure vessel is 300 mm and the pressure in the vessel

varies from 0 to P kPa gauge. Assuming that the bolts are initially tightened to 80% of their yield

strength determine :

(a) the maximum value of P that would not cause separation of the joint;

(b) the maximum value of P that would not cause eventual fatigue failure of the bolts; and

(c) the wall thickness required for the pressure vessel for this maximum pressure P.

QUESTION 3

A particle is projected to the right from the position x = 0 with an initial velocity 9m/s. if the

acceleration of the particle is defined by the relation a = −0.6 v

3/2 where a and v are

expressed in m/s2

and m/s, respectively. Determine

1. The distance the particle will have travelled when its velocity is 4m/s. (8 marks)

2. The time when v = 1m/s (6 marks)

3. The time required for the particle to travel to 6m

Q2. (Marks 25/100)

At a given instant in an airplane race, airplane A is flying horizontally in a straight line, and its

speed is being increased at the rate of 8m/s2

. Airplane B is flying at the same altitude as airplane

A and, as it rounds a pylon, is following a circular path of 300 m radius. Knowing that at the

given instant the speed of B is being decreased at the rate of 3m/s2

. Determine, for the position

shown in Figure Q2

1. The velocity of B relative to A (10 marks)

2. The acceleration of B relative to A (15 marks )

QUESTION 5

The motion of rod OA about O is defined by the relation θ = F(t), where θ and t are expressed

in radian and second, respectively. Collar B slides along the rod so that its distance from O is

r = G(t) , where r and t are expressed in dm and second, respectively. When t = 1s determine

1. The velocity of the collar, (10 marks : 5(A) + 5(B))

2. The total acceleration of the collar , (10 marks: 5(A) + 5(B))

3. The acceleration of the collar relative to the rod (10 marks: 5(A) + 5(B))

In the two following cases

A. 𝜃 = 𝐹(𝑡) = 𝜋(4𝑡

2 − 8𝑡) ; 𝑟 = 𝐺(𝑡) = 10 + sin 𝜋𝑡

B. 𝜃 = 𝐹(𝑡) =

2

𝜋

sin 𝜋𝑡 ; 𝑟 = 𝐺(𝑡) =

25

𝑡+4

4. Use a software/programing language you know to draw the trajectory of the collar

relative to O

QUESTION 6

The system shown in Figure Q4 starts from the rest, and the length of the upper cord is adjusted

so that A, B, and C are initially at the same level. Each component moves with a constant

acceleration, and after 2 s the relative change in position of block C with respect to block A is

280 mm upward. Knowing that when the relative velocity of collar B with respect to block A is

80 mm/s downward, the displacement of A and B are 160mm downward and 320mm

downward, respectively. Determine

1. The accelerations of A and B if 𝑎𝐵 > 10𝑚𝑚/𝑠

2

(10 marks)

2. The change in position of block D when the velocity of block C is 600 mm/s upward