**HNEE 102 Engineering Science**

**Learning outcome (LO)**

L01 Be able to determine the behavioural characteristics of elements of static engineering systems

LO 2 Be able to determine the behavioural characteristics of elements of dynamic engineering systems

LO 3 Be able to apply DC theory to solve electrical and electronic engineering problems

LO 4 Be able to apply single phase AC theory to solve electrical and electronic engineering problems

**Scenario:**

You are employed as a trainee engineer in a Megatronics laboratory and the position requires you to have a fundamental understanding of mechanical and electrical oncepts. You have been informed by your potential supervisor that you need to improve and update your knowledge in the following areas : behavioural characteristics of elements of static engineering systems,dynamic mechanical systems, energy transfer in mechanical systems, complex wave forms and ac theory in RLC circuits. Your potential supervisor has set the following tasks in order to assess your suitability to work in the capacity as a trainee engineer.

L01 Be able to determine the behavioural characteristics of elements of static engineering systems

**Task 1 : (LO 1: P1.1)**

Determine distribution of shear force, bending moment and stress due to bending in simply supported beams.

Task1.

A simply supported beam of length 6m supports a vertical point load of 45kN a distance of 4m from one end. If maximum allowable bending stress is 120Mpa:

1. Determine the reaction forces at either end. Fig 1

2. Draw the shear force diagram

3. Make appropriate calculations and draw the bending moment diagram

4. Recalculate the reaction forces at either end, taking into account the actual weight of the beam as a UDL. Assume that the mass of the beam is 39Kg/m and g= 9.81 m/s2

5. Determine the actual maximum bending stress in the selected beam, taking into account the actual weight of the beam as a UDL and check whether your section is still appropriate by comparing this stress with the maximum allowable bending stress. Assume that the beam is a uniform rectangular section of width w, = 100 mm and depth, d = 80mm

6. A cantilever has a length of 2m and a concentrated load of 8 kN is applied to its free end. Determine the shear force and bending moments at distances of (a) 0.5 m, (b) 1.0 m from the fixed end . Neglect the weight of the beam.

**Tasks 2.0 : (LO1: P1.2)**

Select Standard rolled steel sections for beams and columns to satisfy given specifications.

1. Refer to task 1(a). List suitable universal beam sections that will support the 45kN load from table A and then select the lightest.

2. Select the lightest wide flange section that can be used as a steel column 7m long to support an axial load of 450kN with a factor of safety of

3. Use 200MPa as the limit of elasticity, 200GPa as the modulus of elasticity and assume that the column is simply supported

**Tasks 3 : (LO 1**:P1.3**)**

Determine the distribution of shear stress and angular deflection due to torsion in circular shafts.

1. A solid shaft used in the control system of an aircraft is 50 mm in diameter and 0.7 m long is subjected to a torque of 1200 Nm. Calculate :

(i) The shear stress and

(ii) The angle of twist. Take g = 90 GPa. 2. Repeat

(a) but this time the shaft is hollow with an internal diameter of 30 mm.

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