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Q2. 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.

Q1. 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.

Q1. 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. Calculate EACH of the following:

(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.

Q1. 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. Calculate EACH of the following:

(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).

Q7. 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. Calculate EACH of the following:

(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.

Q1. 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 m. Calculate EACH of the following:

(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