Mechanical Engineering Task: Beam Design, Support Structure, and Shaft Torsion

Task 1 - Beam with point load

You are an advanced technician working for a small mechanical engineering company who are installing a range of mechanical hoists and support structures in an assembly plant. You have been asked to confirm the results of some preliminary calculations given in task 1 and 2.

For the simply supported beams shown in Fig 1:

a. Produce a shear force diagram

b. Produce a bending moment diagram

The support reaction at the left-hand end (Ra) in Figure 1 is provided by a column produced from a universal ‘I’ section, due to cost constraints it is to be made from a standard ‘I’ section complying with BS4.  The force of Ra is offset in the x direction from the neutral axis by 0.2 m on the column.

c. Showing full calculations select a suitable column from the table below for the purpose if the tensile stress in the column must not exceed 200MPa.

The customer has identified the need for 2 further beams to carry the same load as shown in figure 1 but with differing support conditions, below are design revisions for the previously investigated arrangement.

To allow for greater access with load handing equipment the support at the right-hand end of the beam in figure 1 (Rb) is to be removed and the support at the left hand altered to be built into heavy masonry creating a cantilever beam (shown below).

d. Produce a shear force diagram for the cantilever beam

e. Produce a bending moment for the cantilever beam.

Fig 2. Revision 1. Beam adapted to a cantilever arrangement.

The other application of the beam design requires minimal deflection under use.  As such the supports at both ends of the beam in figure 1 (Ra and Rb) are to be altered to be built into heavy masonry creating an encastré beam (shown below).

 
f. Produce a shear force diagram for the cantilever beam

g. Produce a bending moment for the cantilever beam.

Fig 4.  Beam under combined point and distributed loading.

A second beam is used within the assembly plant.

For the simply supported beam shown in Fig 4:

a. Produce a shear force diagram

b. Produce a bending moment diagram

For the simply supported beam shown in Fig 4 identify the position of maximum bending Moment and the value at this position on the graph.

The beam in fig 3 is an ‘I’ section beam and the limiting bending stresses is 60MN/m² (compression)

The table has values for the depth (mm) and the Second Moment of Area (m4) for a range of beams.

c. Using this information select the most suitable beam by plotting a graph of the elastic modulus for each beam then identify the most cost effective beam for the loading in Fig 4.

During the instillation of the beams and columns a problem is found with the electrical power supply.  An emergency generator is set up to power the site; however, the only engine available is a six-cylinder tractor unit with a power tack-off. The generator has been linked to the tractor a with a hollow circular prop shaft of 40mm external diameter and 10mm internal diameter and is subjected to a torque of 800 Nm.

The shear modulus (G) of the shaft is 60 GN/m2.

You have been asked to check the suitability of the system in the following ways:

a) Find the maximum and minimum shear stresses in the shaft due to torsion.

b) Find the maximum shear strain in the shaft.

c) Find the angle of twist over 2m length of shaft.

A heavy duty drive shaft is also available with a solid cross section and the same external diameter.

d) Calculate the maximum shear stress for the solid shaft.

e) Find the angle of twist for the solid shaft over 2m length of shaft.

Some concerns have been expressed about the suitability of the material when used in torsion, you have been asked to conduct a torsion experiment to validate the test equipment.

f) From the experimental data you have gather when conducting the torsion test determine the modulus of rigidity and suggest the type of material used in the experiment.

Evaluate the experimental method and the results obtained suggesting possible improvements.

See the experimental procedure for the torsion experiment