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CERTIFICATES OF COMPETENCY IN THE MERCHANT NAVY –

MARINE ENGINEER OFFICER

EXAMINATIONS ADMINISTERED BY THE

SCOTTISH QUALIFICATIONS AUTHORITY

ON BEHALF OF THE

MARITIME AND COASTGUARD AGENCY

STCW 95 CHIEF ENGINEER REG. III/2 (UNLIMITED)

041-31 – APPLIED MECHANICS

TUESDAY, 11 DECEMBER 2012

1315 - 1615 hrs

Examination paper inserts:

Notes for the guidance of candidates:

Materials to be supplied by colleges:

Candidate’s examination workbook

Graph paper

1. Non-programmable calculators may be used.

2. All formulae used must be stated and the method of working and ALL intermediate steps must

be made clear in the answer.

[OVER

APPLIED MECHANICS

Attempt SIX questions only

All questions carry equal marks

Marks for each part question are shown in brackets

1. A flat plate in a boiler is supported by bar stays. Each stay is 40 mm diameter, 0.8 m long

and supports a plate area of 0.4 m2. The internal pressure is 6 bar.

Calculate EACH of the following:

(a) the stress in each stay;

(b) the strain energy in each stay;

(c) the strain energy in a hollow stay of the same length and external diameter but an

internal diameter of 18 mm.

Note: Modulus of Elasticity for stay material = 190 GN/m2.

(4)

(6)

(6)

2. A set of shear legs arranged as shown in Fig Q2 is used to lift a load of 200 kg.

Determine EACH of the following:

(a) the load in each front leg;

(b) the load in the back-stay, stating whether this is compressive or tensile.

(12)

(4)

Fig Q2

3m

5 m 3.2 m 1.8 m

3. A welded pressure vessel of circular cross section has an oblique welded seam at an angle

of 60° to the longitudinal joint. The internal diameter of the pressure vessel is 1.9 m, the

shell plate thickness is 32 mm and the working pressure is 28 bar.

(a) Sketch the Forces normal and tangential to the longitudinal joint and the Forces

normal and tangential to the oblique seam.

(b) Calculate EACH of the following:

(i) the tensile stress normal to the circumferential seam;

(ii) the tensile stress normal to the oblique seam;

(iii) the percentage increase in the stress normal to the oblique seam if corrosion leads

to a 10% reduction in shell thickness at the seam.

(4)

(2)

(5)

(5)

4. An intermediate shaft is fitted to an engine of power 14 MW operating at 100 rev/min.

The shaft is to be solid, with a coupling flange at each end with 12 bolt holes on a pitch

circle diameter of 1.6 times the shaft diameter. The limiting shear stress is 190 MN/m2 for

the shaft material and 170 MN/m2 for the bolt material.


(a) the diameter of the shaft for a safety coefficient (factor of safety) of two;

(b) the diameter of the bolts for a safety coefficient (factor of safety) of two.

(8)

(8)

5. A vehicle travels around a bend on a banked track at a constant speed of 25 m/s and at an

effective radius of 100 m. The vehicle has a wheel base width of 1.6 metres and a centre

of gravity 1.4 metres above the track surface.


(a) the minimum angle of banking required to prevent the vehicle from overturning;

(b) the minimum coefficient of friction between the track and the vehicle to prevent the

vehicle sliding when the track is banked at the angle calculated in Q5(a).

(10)

(6)

[OVER

6. A Porter governor has arms of equal length 320 mm and two rotating masses of 0.8 kg

each. At the mean speed of 120 rev/min, with the speed falling, both sets of arms are at

30 degrees to the vertical. Friction at the central sleeve is constant at 20N.


(a) the central sleeve mass;

(b) the speed that would cause the sleeve to rise 20 mm from the mean speed position

given;

(c) the speed that would cause the sleeve to fall 20 mm from the mean speed position

given.

(8)

(5)

(3)

7. An engine fuel injector is operated by fuel oil pressure acting on the underside of a needle

valve. Movement of the needle valve is opposed by a spring with 14 coils of outside

diameter 22 mm and wire diameter 6 mm. Fuel oil pressure acts on an effective area of

34 mm2

on the underside of the needle valve. Fuel injection should not commence until

the fuel pressure has risen to 26 MN/m2. Valve lift is limited to 0.8 mm.


(a) the required initial axial compression of the spring;

(b) the maximum force on the spring;

(c) the maximum torsional stress in the spring.

Note: Modulus of Rigidity for spring material = 80 GN/m2

(8)

(4)

(4)

8. A regular cube of sides 100 mm floats vertically in a tank containing two immiscible

liquids of densities 800 kg/m3 and 1000 kg/m

3.


(a) the depth of the lighter liquid if 10 mm of the cube remains above the liquid surface;

(b) the mass of steel which should be attached to the base of the cube to ensure that the

cube is just submerged.

Note: Density of Cube material = 850 kg/m3

Density of Steel = 7800 kg/m3

(10)

(6)

9. A pump has a suction lift of 0.5 m and delivers 24 tonnes per hour of fresh water to a tank

whose water level is 16 m above the pump. The delivery pipe is 28 m long and 90 mm

bore, with a friction coefficient of 0.02.


(a) the power output of the pump;

(b) the pump discharge pressure.

Note: Assume the friction loss in the suction pipeline is negligible.

(10)

(6)





ON BEHALF OF THE




TUESDAY, 16 OCTOBER 2012

1315 - 1615 hrs





Graph paper




[OVER

APPLIED MECHANICS




1. A steel shaft 240mm outside diameter is 2 m long. The shaft is solid for 0.8 m of its

length and hollow for the remainder, with an inside diameter of 160 mm. The shaft is

fixed at both ends and a torque of 25 kNm is applied at the junction of the solid and hollow

sections.

Calculate the maximum shear stress in the shaft material.

(16)

2. A solid rectangular section beam is loaded as shown in Fig Q2. It is simply supported at

points B and D and carries a uniformly distributed load of 6 kN/m over a 3 m length from

A to C. The breadth of the beam is 80 mm and the maximum stress due to bending is not

to exceed 140 MN/m2.

(a) Sketch the shear force diagram, indicating the values of shear force at points A, B, C

and D.

(b) Sketch the bending moment diagram, stating the maximum bending moment and

where it occurs.

(c) Calculate the minimum allowable depth of the beam.

(4)

(6)

(6)

Fig Q2

1.5 m

D C B A

50 kN UDL = 6 kN/m

1.5 m 2 m

3. An overhead camshaft operated valve moves with Simple Harmonic Motion. The valve

lift is 40 mm and the valve is opened and closed within 120° of camshaft rotation. The

mass of the valve is 0.8 kg. The valve moves against a spring and the maximum and

minimum spring forces are 900 N and 180 N respectively. The camshaft speed is

480 rev/min.


(a) the maximum velocity of the valve;

(b) the maximum acceleration of the valve;

(c) the force between the valve and the cam when the valve first starts to open;

(d) the force between the valve and the cam when the valve is fully open.

(4)

(2)

(5)

(5)

4. A winch drum has a mass of 300 kg and a radius of gyration of 320 mm. The winch has a

single brake shoe acting on a brake drum of 0.4 m diameter. The coefficient of friction

between the shoe and the drum is 0.8. Friction in the winch bearings is constant at 4 Nm.


(a) the force to be applied at the brake shoe to slow the winch down from 240 rev/min to

120 rev/min in 30 seconds;

(b) the work done by the brake to bring the drum to rest from 240 rev/min using the brake

force calculated in Q4(a).

(10)

(6)

5. A Hartnell governor has three rotating balls each of mass 0.3 kg. The length of the ball

arms are 150 mm and the length of the sleeve arms are 100 mm. When at the mean speed

of 480 rev/min and rising the balls are at a radius of 110 mm. The governor spring

stiffness is 14 kN/m and friction at the sleeve is 50 N.


(a) the spring compression at the mean speed;

(b) the vertical movement of the sleeve if the speed increases by 5%.

(8)

(8)

[OVER

6. A short vertical hollow cylindrical column, 160 mm high and fixed at the base, is 70 mm

outside diameter and 8 mm thick. It carries concentrated loads of 10 kN and 6 kN as

shown in Fig Q6.


(a) the maximum compressive stress in the column;

(b) the maximum tensile stress in the column.

(8)

(8)

7. A horizontal nozzle is supplied with sea water at a gauge pressure of 5 bar. The water

inlet velocity may be assumed to be negligible. The nozzle has a diameter of 30 mm and a

coefficient of velocity of 0.95. Water from the nozzle then strikes a curved fixed vane that

deflects the water jet through 45°. Due to friction across the vane, the velocity of the

water leaving the fixed vane is 6% lower than the initial velocity of the jet.


(a) the velocity of the water jet leaving the nozzle;

(b) the magnitude and direction of the force exerted by the jet on the fixed vane.

Note: Density of sea water = 1025 kg/m3

(4)

(12)

160mm

45°

10kN

6kN

50mm 50mm

Fig Q6

8. Two oil tanks are separated by a vertical bulkhead fitted with a circular flap valve, 600 mm

diameter. The valve is hinged at its top edge, which is 2.5 m above the bottom of the tank.

Both tanks contain oil of relative density 0.9, one to a depth of 2.5 m, the other to a depth

of 3.2 m.

Calculate the horizontal force required at the bottom edge of the door to open the door

against the hydrostatic force.

(16)

9. A hydraulic control piston is shown in Fig Q9. The input piston of 20 mm diameter is

displaced by the input force P. The system is filled with an incompressible liquid and the

movement of the 80 mm diameter output piston is resisted by a spring of stiffness

60 kN/m.

Calculate the force P required to achieve a 40 mm movement of the input piston

Fig Q9

(16)

P

Vent

Output Piston

Input Piston





ON BEHALF OF THE




TUESDAY, 27 MARCH 2012

1315 - 1615 hrs





Graph paper




[OVER

APPLIED MECHANICS




1. A shaft consists of a bronze sleeve 390 mm outside diameter shrunk onto a solid steel shaft

of 340 mm diameter. The shaft is to transmit a power of 4.8 MW at a speed of 120 rev/min.


(a) the torque transmitted by the bronze sleeve;

(b) the percentage of the total power which is transmitted by the steel.

Note: Modulus of Rigidity for Bronze = 40 GN/m2

Modulus of Rigidity for Steel = 80 GN/m2.

(12)

(4)

2. A hollow brass tube, 24 mm outside diameter and 12 mm inside diameter is 260 mm long

and at a temperature of 18°C. It is then heated to 180°C and then rigidly secured at each

end to prevent any contraction.


(a) the length of the tube immediately after heating;

(b) the temperature to which the tube must be cooled so that the stress in the brass is

55 MN/m2;

(c) the strain energy in the bar at this lower temperature.

Note: Modulus of Elasticity for Brass = 80 GN/m2

Coefficient of linear expansion of Brass = 16 x 10 -6

/ oC.

(3)

(8)

(5)

3. An electric motor is running at 1500 rev/min when the power is shut off. The total

frictional resistance to motion is equivalent to a torque of 6 Nm, and forty seconds later the

speed of the motor has fallen to 800 rev/min.


(a) the moment of inertia (I) of the motor;

(b) the total time taken to come to rest;

(c) the total number of revolutions made after the power is shut off before coming to rest.

(8)

(4)

(4)

4. A steel beam is 5 m long and has a symmetrical cross section shown in Fig Q4 and is

simply supported at each end. The weight of the beam itself is 480 N per metre length and

the maximum allowable bending stress for the beam is 110 MN/m2.


(a) the maximum additional uniformly distributed load which can be carried;

(b) the least radius of curvature when carrying the load in Q4(a).

Note: Modulus of Elasticity for Steel = 210 GN/m2

(13)

(3)

5. A ship heading due South at 9 knots sights another ship dead ahead at a distance of

5 nautical miles. The second ship is heading in a direction 40° East of North at 20 knots.


(a) the relative velocity of the second ship to the first ship;

(b) the distance of nearest approach of the two ships;

(c) the time taken to reach the point of nearest approach.

(8)

(4)

(4)

80mm

10mm

Fig Q4

Cross Section

(not to scale)

300mm

12mm

12mm

[OVER

6. In a four-ram hydraulic steering gear the centre line of the rams is 1.2 m from the

centreline of the rudder stock. The diameter of the rams is 280 mm and the diameter of

the rudder stock is 420 mm.

Movement of the rudder is limited to 35° on either side and the maximum allowable shear

stress in the rudder stock is 70 MN/m2.


(a) the maximum allowable torque on the rudder stock;

(b) the pressure to which the relief valves on the rams should be set.

(6)

(10)

7. A pressurised spherical tank 12 m diameter is partly filled with liquefied gas. The

pressure at the bottom of the tank is 820 kN/m2

(gauge) whilst that in the gas space at the

top of the tank is 780 kN/m2 (gauge).


(a) the depth of liquid in the tank;

(b) the weight of liquid in the tank.

Note:

Where r = radius of the sphere

h = depth of the segment

Relative density of liquefied gas = 0.52

(7)

(9)

8. Two bodies A and B are connected by a light cord over a frictionless pulley as shown in

Fig Q8. The mass of A is 100 kg, its weight acts at its geometric centre and it stands on a

rough inclined plane. Mass B is gradually increased until mass A overturns.


(a) the mass of B that will just cause A to overturn;

(b) the minimum value of the coefficient of friction between the plane and body A to

prevent sliding when A is about to overturn.

Fig Q8

(8)

(8)

9. A fire-fighting launch discharges three identical jets of sea water through 40 mm diameter

nozzles, each jet being inclined upwards at 40° to the horizontal. The discharge velocity

of the water is 42 m/s and the velocity at the suction side can be ignored.


(a) the vertical force created by the jets;

(b) the increase in the immersed volume of the launch due to the operation of the jets.

Note: Density of Sea Water = 1025 kg/m3

(10)

(6)





ON BEHALF OF THE




TUESDAY, 17 JULY 2012

1315 - 1615 hrs





Graph paper




[OVER

APPLIED MECHANICS




1. A Porter governor has arms of equal length, three flyweights each of mass 3 kg and a

central mass of 18 kg. Friction at the sleeve is constant at 22 N.

Calculate the maximum and minimum speeds for a governor height of 120 mm.

(16)

2. A hollow propeller shaft of 380 mm outside diameter and 320 mm inside diameter runs at

90 rev/min and propels a ship through the water at 17 knots. The total resistance of the

ship through the water at this speed is 300 kN and the propeller efficiency is 78%.


(a) the power transmitted by the shaft;

(b) the angel of twist of the shaft per metre length in degrees;

(c) the maximum torsional stress in the shaft.

Note Modulus of Rigidity of Shaft Material 80 GN/m2

1 knot = 0.514 m/s

(6)

(6)

(4)

3. A short vertical column consists of a hollow steel tube of 52 mm outside diameter and

40 mm inside diameter with a concentric solid brass rod of 35 mm diameter within it. The

steel tube is 380 mm long and the brass rod is 1 mm shorter.

The maximum allowable stress in the brass rod is 55 MN/m2.

Calculate the maximum vertical compressive load that can be placed on the column.

Note: Modulus of Elasticity for Steel = 210 GN/m2

Modulus of Elasticity for Brass = 80 GN/m2

(16)

4. An “I” section beam as shown in Fig Q4 is simply supported at both ends. It carries a

uniformly distributed load of 6 kN/m along its entire length and has a concentrated load of

18 kN at mid-span. The safety coefficient (factor of safety) of the beam is limited to 4.

Determine the maximum permissible length of the beam.

Note: UTS of Beam Material = 120 MN/m2

Fig Q4

(16)

5. When subjected to a tensile load of 80 kN, a uniform metal rod 30 mm diameter and 3 m

long extends by 1.8 mm.

The unloaded rod is then placed vertically with its upper end fixed and a collar fitted at its

free lower end. A load mass is then allowed to drop onto the collar from a height of

180 mm, and the instantaneous extension of the rod is found to be 3.6 mm.


(a) the Modulus of Elasticity for the rod;

(b) the magnitude of the load mass.

(4)

(12)

[OVER

6. An engine has rotating parts of mass 160 kg with a radius of gyration of 0.5 m. The

frictional torque for the engine may be assumed constant at 8 Nm. It is to be accelerated

from rest to its full speed of 720 rev/min and then clutched on to a stationary pump having

rotating parts of mass 50 kg and radius of gyration 0.3 m.


(a) the driving torque required to accelerate the engine from rest to 720 rev/min in

15 seconds;

(b) the common speed of the engine and pump just after engagement;

(c) the loss of kinetic energy due to the clutching operation.

(6)

(5)

(5)

7. A connecting rod has a mass of 1.43 tonne, is 3 m long and its centre of gravity is 1.8 m

from the top. It is to be freely suspended from the crosshead bearing, with the bottom end

bearing removed.


(a) the horizontal force required at the lower end of the con-rod to hold the rod at 20o to

the centre-line of the engine;

(b) the magnitude and direction of the minimum force required at the lower end of the

con-rod to hold the rod at 20o to the centre-line of the engine;

(c) the magnitude and direction of the reaction at the crosshead for condition in Q7(b).

(5)

(5)

(6)

8. A sluice has a square door with sides of length 1.8 m hinged at point A, 3 m below the

waterline as shown in Fig Q8. The mass of the door is 700 kg. The channel is full of sea

water on the left hand side of the door.

Calculate the magnitude of the minimum force, applied at right angles to the door at B to

open the door.

Note; Density of Sea Water = 1025 kg/m3

Fig Q8

(16)

9. A centrifugal pump has an impeller with inner and outer diameters of 280 mm and 580 mm

respectively. The pump runs at 8 rev/sec and the fluid enters the pump with a radial

velocity of 2.8 m/s. The absolute velocity of the water at exit from the pump is 11 m/s.


(a) the angles of the impeller vanes at entry and exit so that the fluid enters and leaves the

impeller without shock;

(b) the theoretical head delivered by the pump.

(10)

(6)

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