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Q3. A steel bar, 50 mm diameter and 300 mm long is placed between two supports with an end clearance of 0.3 mm. The temperature is then increased by 180°C. Calculate EACH of the following:

(a) the direct stress in the bar if the supports are perfectly rigid;

(b) the direct stress in the bar if the supports are elastic and the movement of one support relative to the other is 1mm per kN of force applied to them.

Note: Modulus of Elasticity for Steel = 200 GN/m²

Coefficient of Linear Elasticity for Steel = 11 mm/m°C

Q2. A hollow shaft transmits 110 kW at 1800 rev/min. The shaft is 1.5 m long and has an outside diameter of 50 mm and an internal diameter of 36 mm. Calculate EACH of the following:

(a) the angle of twist, in degrees, between each end of the shaft;

(b) the maximum torsional stress in the shaft, stating where it occurs;

(c) the minimum torsional stress in the shaft, stating where it occurs.

Note: Modulus of Rigidity for shaft material = 82 GN/m².

Q1. A short vertical column with the horizontal cross section shown in Fig. has a central vertical compressive load of 120 kN. Calculate the maximum additional vertical load that can be placed at point A without producing tensile stress at any part of the section.

Q2. A circular cam rotates at 360 rev/min and is offset from the centre of rotation by 14 mm. The cam follower has a mass of 0.6 kg and moves with simple harmonic motion.

Calculate EACH of the following:

(a) the maximum velocity of the cam follower;

(b) the maximum acceleration of the cam follower;

(c) the velocity of the cam follower at ¾ lift;

(d) the speed at which the inertia force on the cam follower would be equal to its own weight.

Q1. A basic flapper/nozzle device is shown in Fig Q8. The pneumatic signal for the input bellows unit is proportional to the measured temperature within the range 0-150℃. The output signal range is to be 20-100 kN/m². The characteristic of the input bellows is 4 mm/℃, and the characteristic of the nozzle is 0.2 kN/m² per mm of flapper movement. Calculate EACH of the following:

(a) The flapper movement at the nozzle for 100% input change;

(b) The resulting change in output;

(c) The gain of the device;

(d) The new setting of x, the distance from the pivot to the nozzle, to achieve a gain of 0.5;

(e) The output pressure at 85℃ with a gain of 0.5 if the output pressure was 50 kN/m² at a temperature of 55℃.