Calculations for the glide rail

The following are the formulas used in the calculations for the designed boom of the crane:


Equations courtesy of:

http://www.efunda.com/math/areas/SquareIBeam.cfm

Mechanics of engineering materials, second edition, by PP Benham, RJ Crawford & CG Armstrong

Elements of Strength of Materials, International Student Edition, by S Timoshenko

Legend
E – Young’s modulus of the material (Pa)
I – second moment of area (m^4)
w – Uniformly distributed load (N/m)
P –point load (N)
L –total length of glide rail (m)

Using the properties of superposition it is possible to obtain the combined loading effect on a structure by adding the individual effects caused by the different loading conditions.


Courtesy of:
Mechanics of engineering materials, second edition, by PP Benham, RJ Crawford & CG Armstrong

Elements of Strength of Materials, International Student Edition, by S Timoshenko

The ORIGINAL I BEAM possesses the following values:



This particular glide rail beam possesses several disadvantages, particularly the total mass. This would make it difficult to be carried by 4 people over 100m of rough ground. The deflection however complies with the BS 5950-12000 part 1:



The maximum deflection for the given length would be 5.1m/180=0.02833m.

Several improvements would need to be carried out on the beam particularly choosing a beam with a low manufacturing cost. Currently choosing this type of beam would have large cost implications due to its custom made quality.

Alternative options were therefore researched (courtesy of http://www.structural-drafting-net-expert.com/steel-selections-IPE.html):





Using the values of the original I beam structure as a template three standards were chosen IPE140, IPE120 and IPE160.
These were also selected as the beam width fell within an acceptable range 50-220mm to be able to use the selected travel trolleys for the hoists.

The following results were obtained:



From these calculations it can be deduced that not only has an effect been created on the mass but also on the deflection value, falling within the acceptable range.

According to the standard, the new max deflection value= 4.7m/180=0.02611.

The length was selected due to the dimensions of the loads that will be dealt with.

It is likely that beam IPE140 will not be used in the final design as the deflection is too close to the upper range of the specified BS 5950-12000 part 1 standard.


As we can see the mass has decreased to a weight which could be carried by 2 people however the I beam dimensions caused the deflection to be greater than the accepted standard for structural steel. Therefore beam IPE120 will not be used in the final design.




It is clear from these results and from the δmax equation that the higher the second moment of area the lower the deflection but the greater the area and the overal mass of the beam, an appropriate balace always needs to be found.