# Core engineering exam paper

PART A
Question 1
Question 2 Answer all ten questions in this part.
This part is worth 40 percent of the total marks in this examination. Plan to spend no more than 40 percent of your time answering this part.

Sketch the distribution of radial stress against radial position on the cross section of a thick walled cylindrical pressure vessel. What is the magnitude of the radial stress at the inside and outside of the pressure vessel wall if the inside pressure is pi and the outside pressure is po?
(4 marks)
A bolted “single-shear” lap joint shown in Figure 1 is pulled apart by equal and opposite forces F at the ends of the plate.
(a) Suggest two possible failure modes for the joint.
(2 marks) (b) Describe where the failure might occur in each case.
(2 marks)

Figure 1 Figure for Question 2 A bolted single-shear lap joint

Question 3 Figure 2 shows a steel column in a structure, with a solid circular cross section, that is subjected to a load along its longitude direction. An assessment of the column’s buckling resistance has indicated that the applied load is too close to the critical buckling load of the column and therefore it is recommended that it should be replaced. However, it is required that the total mass of the column is to remain the same and the same type of steel is to be used in its manufacture. Suggest a replacement shape for the column, which would have a higher critical buckling load. Use the appropriate mathematical expression to explain your reasoning.
(4 marks)

Figure 2 Figure for Question 3 showing a column with a solid circular cross section subjected to a load along its longitudinal direction

Question 4
Question 5 A train accelerates uniformly from rest at a rate of 0.8 m s-2. Sketch a graph with three curves with respect to time for the train’s
• acceleration
• velocity
• displacement
for the first five seconds of its motion.
(4 marks)
The hammer of a pile-driver is raised to a height of 1.25 m above the top of the pile then released, driving the pile onto loose earth such that the hammer does not rebound after striking the pile. If the pile’s mass is 103 kg and the hammer’s is 102 kg, calculate the velocity of
• the hammer immediately before it strikes the pile • the pile after being struck by the hammer.
Assume the gravitational constant to be 10 m s-2 and that air resistance can be ignored. (Where appropriate, state your answer to two significant figures.)
(4 marks)
Question 6 The kinetic energy of a rotating mass is given byEk  I2 where I is the
moment of inertia and  the angular velocity. The kinetic energy of a mass m moving with a velocity v, is given by Ek  mv2.
Using the expression for how I is calculated, show that, for a mass moving about an axis at a large distance compared with its own size, these equations agree.
(4 marks)

Question 7 State the name given to the curved markings on the fracture surface in Figure 3.
Explain what the fracture surface tells you about how the failure started and finished.

Figure 3 Figure for Question 7 showing the fracture surface of a broken bicycle crank (4 marks)

Question 8 Figure 4 Al–Cu phase diagram; shows the phase diagram for part of the aluminium–copper alloy system.

Figure 4 Figure for Question 8

Describe in one or two sentences the intermediate compound CuAl2 and explain why it appears in its pure form on the phase diagram in a very narrow band.
(4 marks)
Question 9 The graphs (a), (b) and (c) in Figure 5 represent three different responses of a material to a fixed stress applied over an interval of time, as a function of time.

Figure 5 Figure for Question 9

For each of the curves, state whether the response of the material is elastic, viscous, or viscoelastic, and estimate the percentage of the overall strain that is permanent.
(4 marks)
Question 10 (a) Briefly explain the role defects play in determining the strength of brittle materials.
(2 marks)
(b) Outline one approach to strengthening ceramics that is intended to reduce the size of defects in the finished product.
(2 marks)
PART B
Question 11 Answer all four questions in this part.
This part is worth 60 percent of the total marks in this examination. Plan to spend no more than 60 percent of your time answering this part.

A thin walled cylindrical pressure vessel with length 0.6 m, radius 0.3 m and wall
thickness 0.002 m is designed to store compressed air and is manufactured from steel with a yield strength of 275 MPa. The pressure vessel experiences a gauge pressure of 2 MPa which is substantially higher than the maximum pressure it was designed to support.

(a) Calculate the hoop stress in the pressure vessel at the gauge pressure of 2 MPa.
(2 marks)
(b) Calculate the longitudinal stress in the pressure vessel at the gauge pressure of 2 MPa.
(1 mark)
(c) Use your answers from parts (a) and (b) to draw the 2D stress element for a point on the cylindrical surface of the pressure vessel.
(2 marks)
(d) Use the Tresca yield criteria to determine whether the pressure vessel will yield at this pressure.
(4 marks)
(e) Considering this type of pressure vessel in general, suggest three possible failure modes.
(3 marks)
(f) Explain three features of how proof testing is used to assure the safety of pressure vessels before they enter service.
(3 marks)

Question 12 The drum of a washing machine is suspended vertically by a spring with a damper as shown in Figure 6. The drum is free to move vertically but fixed horizontally. The drum is set in rotation with an offset load causing the machine to vibrate. The maximum spin speed is 1800 rpm.

Figure 6 Figure for Question 12 showing a schematic drawing of the drum of a washing machine

(a) List three key attributes of a harmonic oscillator which cause the machine to vibrate.
(3 marks)
(b) State three ways of changing the features of the system to reduce the amplitude of vibration for a given spin speed.
(3 marks) (c) Convert the maximum spin speed to angular frequency.
(2 marks)
(d) The forces acting on the machine can be modelled by the differential equation mx  xkx F0sint
Identify what each term in the equation describes.
(4 marks)
(e) A simplified part of the differential equation from part (d) is used to study the machine’s behaviour. x104x0
Solve this equation to show that it is consistent with an angular speed of 100 rad s-1.
(3 marks)

Question 13 In certain environmental conditions the steel within steel reinforced concrete can be at risk of corrosion. Repairs to reinforced concrete structures affected by corrosion often include the attachment of zinc sacrificial anodes to the reinforcing metal structure, to provide targeted protection to affected areas. Figure 7 shows an example – the hole would be filled once the anodes are in place.

Figure 7 Figure for Question 13 showing zinc sacrificial anode used to protect reinforced concrete (a) basic design (b) two anodes in position

You may find this data useful for answering the questions that follow:

Standard electrode potential of zinc = -0.76 V
Standard electrode potential of steel in concrete = 0.14 V to -0.01 V
Mass of sacrificial anode = 100 g
Atomic mass of zinc = 65.4
Faraday’s constant (charge on one mole of electrons) = 96 500 C

(a) For the situation illustrated in Figure 7 part (b)
(i) Explain how this arrangement satisfies the four requirements for galvanic corrosion to occur.
(ii) Calculate the minimum and the maximum voltage that could be generated by the corrosion cell.
(iii) Write a half equation to represent the corrosion reaction that will occur and identify it as an oxidation or a reduction reaction.
(6 marks)
(b) The anodes will need to be replaced before they have completely corroded. If the average corrosion current is 0.50 mA, how long will it take for 60% of the sacrificial anode to corrode? Give your answer in days, to the nearest day.
(5 marks)
(c) Briefly describe how an impressed current could be used as an alternative means of corrosion protection in this situation. Suggest one advantage and one disadvantage of using this alternative method.
(4 marks)

Question 14 (a) Outline what happens at an atomic level when a metal deforms plastically.
Describe and briefly explain one way of modifying a metal to increase its yield strength. The following concepts may help you prepare your answer.
Concepts: dislocation, lattice.
(6 marks) (b) Outline what happens at an atomic level when a polymer deforms plastically.
Describe and briefly explain one way of modifying a polymer to increase its stiffness. The following concepts may help you prepare your answer.
Concepts: chain, bond angle.
(6 marks)
(c) Explain why ceramic materials generally show no plastic deformation under normal operating conditions.
(3 marks)
[END OF QUESTION PAPER]

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