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 R= 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

 

 

Don’t forget the requirement that the work you submit must be of a professional standard, and this includes both the content and the presentation of your work.

The Assessment is now complete – well done.

 

 


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