Show that the support reactions are RL = 22·2 kN and RR = 32·8 kN

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1. For the loaded simply supported beam shown:

Note: All parts of this question relate to the beam shown above

(a) Show that the support reactions are RL = 22·2 kN and RR = 32·8 kN. ₄

(b) Draw the SFD and BMD. Use the table below when evaluating the bending moments. You may add extra values to those shown, if you consider it necessary. ³²

(c) Identify the positions of any points of contraflexure. 2

(d) Find the magnitude and position of the maximum bending moment. 2

(e) State if the beam is hogging or sagging where the bending moment is greatest. 2

(f) State the value of the shear force and the bending moment at the mid-span of the beam. 2

In cross-section, the beam you are working on is a gantry girder, the maximum bending stress in the girder must not exceed 25 MN/m² and the modulus of elasticity can be assumed to be 210 GN/m².

(g) Determine a suitable size for the beam, selected from standard section tables. 6

(h) Determine the actual value of maximum stress in the chosen beam. 4

(i) Determine the radius of curvature for the chosen beam. 4

(j) Discuss what factors would need to be incorporated into your calculations in order to give more accurate answers, and indicate how this can be achieved. ²

Distance from LHE (m)	Moments (kN x m)	M (kNm)
2
3
4
5
9
11
13
15

2.(a)	A ship’s propeller shaft transmits 9·5 MW at 400 rev/min. The shaft has an external diameter of 225 mm. Calculate the maximum permissible bore diameter if the shearing stress in the shaft is to be limited to 150 MN/m². The modulus of rigidity for the shaft material is 79 GN/m².			Marks
				12
(b)	What is the minimum stress in the shaft material?			5
(c)	If the angle of twist is not to exceed 3° determine the maximum length of the shaft.			5
(d)	Assuming the torque and maximum shear stress values to be the same for both shafts, determine the size of a suitable solid shaft which could have been used instead of the hollow one.
				6
(e)	Compare the angles of twist for the two shafts.			7
(f)	Recommend, with reasons, whether a solid or hollow section should be used for the propeller shaft. Research and evidence must be used to justify your reasoning.			10
3.	A hoist is used to move material in a facility; the following details apply:
	The winding drum of the hoist has a mass of		150 kg
	The winding drum of the hoist has an outer diameter of		600 mm
	The winding drum of the hoist has a radius of gyration of		220 mm
	The mass moved by the hoist is		110 kg
	The distance moved by the mass is		4·5 m
	The frictional resistance at the bearings is		7 Nm
	The frictional resistance to linear motion is		160 N
The cable used to support the load is considered to be massless.
If the hoist is used to lower the mass, while the velocity is increased from 2·0 m/s to 3·5 m/s, determine:
	(a)	The input torque applied.		22
	(b)	The work energy transfer.		6
	(c)	The maximum input power delivered by the motor.		6
4.	The rotating parts of an engine are equivalent to a mass of 60 kg concentrated at a radius of 120 mm. Calculate:
	(a)	The mean torque if the power output at 1500 rev/min is 40 kW.		5
	A second shaft and flywheel, on the same axis as the engine, is suddenly connected by means of a clutch. This second shaft and flywheel (combined) has a mass of 120 kg and a diameter of 325 mm and is initially rotating at 750 rev/min in the opposite direction to the engine. Determine:
	(b)	The common speed of rotation, once the clutch slippage has stopped.		14
	(c)	The change in angular kinetic energy for the engine.		7
	(d)	The change in angular momentum for the engine.		5

Overall presentation [professional]	Marks 10
Bibliography and referencing [evidence of wider reading]	10
Total Marks Available:	190

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