# How to calculate the swl of aluminium?

I am designing a roof rack for my car that attaches to my canopy and extends over the roof of the cab. I am deciding what size of aluminum.

It would need to support me walking on it ideally (80kg).

It would be a 1800x3600mm rectangle that is welded onto the canopy for 2400mm from one end, leaving the 1200mm overhanging the cabin. There will be 8 cross supports including the ends. Options are all in box section:

• 32 x 32 in 2 and 3mm
• 40 x 40 in 2 and 3mm
• 50 x 50 in 2,3 and 5mm.

if needed, I can add a central support.

• You need to provide a drawing or two - we can’t guess your design... it may be fine or may need improving - types of joints, spacing of bars etc May 26 '18 at 7:10
• sorry, does this help? May 26 '18 at 7:17
• Are there sides - these can add a huge amount of stiffness? May 26 '18 at 7:19
• so the plan at the moment is to have the 8 supports in pairs with solid rods between them to offer multiple tie down points. May 26 '18 at 7:29

Depending on what series of aluminum section you use the tensile strength varies greatly. But generally these are the steps.

I of a square aluminum section is $$5\times 5^3 /12 - 4.7\times 4.7^3/12 = ~ 12 cm^4$$ for 3mm thickness profile.

And $$S = 2I/H = 4.5 cm^3$$

You multiply your weight by 2.8 for dynamic load factor 80. 2.8 = 224 kg. Moment of your weight is 224. 1.2 = 268 kgm. = 26800 kgcm

now we have $$\sigma = m/S = 26800/4.5 = ~6000kg/ cm^2$$ I did not check my calcs but basically this is the stress your aluminum profile should be able to take.

You need to check the data sheet of the section.

• i appreciate to answer and im sure that its correct, however im not an engineer and my math skills arent up to scratch to use that formula. i dont undestand where you got the 5x5^3, 12, 4.7x4.7^3, 12. i dont understand what 12cm^4 means... basically i could go on. is this for a 50x50(thats why you - the 4.7 to find the area of the aluminium minus the cavity)? 26800kgcm would be the same for all the formulas. i dont know what the 4.5cm^3 is for. how would i apply the end result? is that how much weight it will be able to support at the end? May 30 '18 at 2:18
• It shows the stress per square cm of your material, if your roof rack section is strong enough to support your weight. It is not! 6000kg/cm, sqr is on par with strongest steel alloys limit of allowable stress, not aluminum. I recommend you use a truss configuration or make the over-hang part suspended by a 10mm thick bar from a post in the middle like a suspended bridge. May 30 '18 at 3:50
• Thank you very much. I guess i will have to rethink my design or restrict its use. Jun 1 '18 at 9:13