# Calculating diameter of steel rod required to not bend over a given length

I want to use steel (or other material) rods to support weight over a 900mm cavity. The weight that needs to be supported is technically unknown, but I'd specify some rough guidelines as:

• 100KG (max) - some give, but no permanent deformity
• <50KG - no real visible bend

I'm not hugely attached to the weights listed above as they could be dropped with max weight advisories etc but I'd say those are probably ideal. Exceeding them would be fantastic, reducing them isn't a huge issue. Ideally I'd be able to calculate myself and adjust the design to use a bigger rod if necessary.

The rod would be used to back a slat of wood which presumably would add to the strength of the unit, and there would be multiple slats (laid horizontally) covering an overall length of about 1.6m. I'd probably add an overlap between the slats also which I would assume would add strength to the system.

I'm trying to find my feet with CAD design and engineering principals so I'm very much new to the (seemingly) advanced maths I've seen glimpses of for this sort of calculation, so a resource I can read through or a breakdown of a calculation would be much appreciated!

• Does it have to be a rod? Would an I beam or similar section work? – Solar Mike Mar 8 '19 at 12:23
• It does have to be circular at the end for the entire supported region - it could be any shape for the unsupported width as long as it is cylindrical at the support point. Would that help at all..? I'm struggling to imagine how weight stress would transfer across shapes - presumably the stress point would then be at the point she shape changes/is joined? – aaronrhodes Mar 8 '19 at 13:19
• Welcome to Engineering! This question is well-written, but we just need a bit more specificity regarding how much deformation is permissible. Any beam of any size and material will deform under any load. So when you say that "some give" is allowed, does that mean that it can have maximum elastic deflection (which disappears when the load is removed) but no plastic deformation (which remains when unloaded)? And what about when you say "no real visible bend"? Also, how would the rod be supported at the ends? – Wasabi Mar 8 '19 at 16:13