Stress calculations for alluminium sliding beam

It would have been great to 'get the hopper' or just 'get that hopper in' , however, it seems as though destiny does not want it to be dear team mates . After doing some calculations for stress , the grasshopper design has some problems, hence why me and andy have decided that it would be a lot less problematic to do the second design we came up with as it fits the specification ; does its job and is a lot more simple to calculate the stresses and strain on the struts.



Moving on to the important stuff now, lets recall the second design which had 4 struts as legs with a sliding bar in the middle to move the load in the x direction. Calculations below have been done for this bar which will lift the load . Calculations for other struts ( e.g the legs) will be done during the course of this week. For the sliding strut, different combinations of length , materials ( steel or alluminium) , etc have been taken into consideration when doing the calculations. I have pointed these points out below. The first set of calculations were done to these specifications :

• material: alluminium




• length : 1.25m




• deflection : 1mm or 0.001
  
  


• weight of beam : 1020 g ( 1000kg of load plus 20 kg for winch ) = 10006.2 N
  

The calculations are below.

By using the formula y ( deflection) = wl cubed divided by 48 EY i could work out the second moment of area . This allowed me to work out the dimensions of the beam . The weight of the beam would be 18.71 kg and the level of stress the beam would withstand with such loading at a 1mm deflection would be 32.21 MN/m2. However, in reality, the properties of alluminium do indicate that alluminium is not as stiff as some other metals although it has good tensile strength. In reality, under such loading, alluminium would not deflect by 1mm and would rather deflect by up to 5 mm hence i did another set of calculations with the deflection value set at 4mm but with every other value as the same. What i wanted to gain from doing this was to see how much extra stress the beam would have to take if there was more deflection. Below are the calculations :

















































By changing the level of deflection of the beam to a more realistic estimate, the level of stress went up to 81.7 MN/m2 from 32.21 MN/m2. This shows that the level of deflection has a positive correlation with the amount of stress being applied to the beam . Also the yield stress of alluminium is 100 mPA . This shows that the alluminium strut at a deflection of 4 mm would be nearing the yield stress . In reality deflection could be even more than 4mm which is why the sliding beam should NOT be made out of alluminium. In the next post, the same calculations have been made for steel to see if it is more suitable for the sliding beam .