Which metal would flex more?

[Desertboy]

If you want to work it out by hand it is not too tricky for a simple shape like that.

1. The geometry of the part (how the material is arranged, into what shape). This is the cross section property and is called the second moment of area:
Ixx = (bd^3)/12
where:
b is the width
d is the depth
For aluminium part this is (100x25^3)/12 = 130208 mm^4
For the steel part this is (100x10^10)/12 = 8333 mm^4

2. The end condition of the beam (how it is restrained at the ends)
Ec = 192 for fully welded
Ec = 48 for simply supported (e.g. pin joint)

3. The material properties for the material being analysed (Young' modulus)
For aluminium Ym = 69000 N/mm2
For steel Ym = 200000 N/mm2

4. The force being applied in the middle of the beam
For the example given this is 200 N

5. The calculation:

Deflection = (force (N) x length^3) / (Ec x Ym x Ixx)

For welded supported ends this is:
Deflection (Aluminium) = (200 x 500^3) / (192 x 69000 x 130208) = 0.01449 mm
Deflection (Steel) = (200 x 500 ^3) / (192 x 200000 x 8333) = 0.07813 mm

These are pretty close to the Fusion FEA results from Zeeflyboy (for fully supported end conditions):
25mm Alu deflection = 0.01471 mm
10mm Steel deflection = 0.06861 mm

If the ends are simply supported pin joints it makes a big difference:
Deflection (Aluminium) = (200 x 500^3) / (48 x 69000 x 130208) =0.0579 mm
Deflection (Steel) = (200 x 500 ^3) / (48 x 200000 x 8333) = 0.312 mm

So there you have it !

Nice one! I always want work it out by hand if I can! I normally do my trig on paper then check it in cad so I already know what numbers I should be getting back.

[Zeeflyboy]

Nice one! I always want work it out by hand if I can! I normally do my trig on paper then check it in cad so I already know what numbers I should be getting back.

By hand gets super complicated super fast when considering more complex shapes and even more so when you are talking complex shapes with complex assemblies... That said always good to have a rough idea as a gross error check for computer simulations (even if nothing more than "hmm... that doesn't sound right"), after all garbage in = garbage out.

[Desertboy]

By hand gets super complicated super fast when considering more complex shapes and even more so when you are talking complex shapes with complex assemblies... That said always good to have a rough idea as a gross error check for computer simulations (even if nothing more than "hmm... that doesn't sound right"), after all garbage in = garbage out.

garbage in garbage out is why I haven't watched TV in 12 years lol ;) the only thing I've watched this year is Rick and Morty and South Park and I feel better for it ;) That said I have never learnt as much since I was a child as I learnt this year lol so so much reading and the brain is better for it.

I've found the router changes you someone along the way nothing scares you any more and you can solve any problem. Drooling over yours and routercnc's work and thinking you know what I can do that is also a healthy thing.

It's good to aspire to better things, although I do wish you'd stop upping the ante every 5 seconds I can't keep up.

Can't you do a bit of crap workmanship for once so us mere mortals can feel good about ourselves for 10 seconds lol.

[Zeeflyboy]

Watching TV right now... perhaps that explains a lot

[PaisleyPCdoctor]

Thanks for all the shared knowledge. Fascinating stuff.

I was handling the 500x100x25mm bar last night and it really does feel solid. I certainly couldn't noticeably deflect the middle without tools. Also the bar hasnt been touched for 5 years (surplus purchase for an old project) and it just happens to be exactly 1mm longer than required. I'll have the sides milled nicely and it'll be perfect.

The alu was destined for its new role.

Thanks again!