This assignment relates to the analysis of static & dynamic engineering systems.
There are six questions. Answer all questions.
The assignment forms Element 1 of the module’s assessment criteria that covers
Learning Outcomes 1, 2, 3 and 6 as indicated below.
Knowledge and Understanding
1 Demonstrate a detailed understanding of mechanical engineering principles.
2 Analyse and apply solutions to a variety of loading systems and the behaviour
of loaded beams and cylinders.
3 Understand the effects that constraints have on the performance of a dynamic
mechanical system through the applications of force and energy transfer.
4 Analyse and apply the dynamics of geared systems and power transmission
system elements for a variety of engineering problems.
5 Analyse natural and damped vibrations within translational and rotational mass-
spring systems.
Key Transferable Skills
6 Act with increased autonomy, with reduced need for supervision to assess and
suggest limitations to a range of mechanical systems.
Determine the vertical reactions at the supports.
(b) Sketch the shear force diagram for the beam.
(c) Calculate the bending moment at 1m intervals along the beam.
(d) Sketch the bending moment diagram for the beam.
(e) State the position and magnitude of the maximum bending moment
in the beam.
For the I-section shown in Figure 2, calculate the values of the second
moments of area about axis X-X and axis Y-Y.
A beam of rectangular cross section 200 mm deep and 100 mm wide. If
the beam is 3m long, simply supported at either end and carries point
loads as shown in Figure 3.
Calculate the maximum bending moment.
(b) Calculate the maximum stress in the beam.
(c) At the point of maximum stress sketch a graph of the stress
distribution through the thickness of the beam, indicating which are
tensile and compressive stresses.
(d) Determine the dimensions of the cross section which will minimize
the maximum stress value if:
• the cross sectional area of the beam can be increased by 20%;
• the beam section is to remain a solid rectangle;
• neither the breadth or depth of the beam section can be reduced
below their original dimensions.
Show the dimensions of the proposed beam cross section with the aid
of a sketch.
(e) Determine the percentage reduction of the maximum stress value
when the new cross section is used.
