Mechanical engineering type question

[slow-poke]

I'm trying to determine deflection of a round steel bar of various diameters, for example 16mm and 25mm
The bar would be supported at both ends (12" long) and the force would be say 1lb, 5lbs in the center

I for 16mm = 0.1184 in^4, is that correct?
I for 25mm = 0.736 in^4, is that correct?

16mm: with 1lb, 0.002", with 5lb, 0.012"
25mm: with 1lb, 0.0004", with 5lb, 0.002"

Does that sound correct?

Now assume the length, diameter, force are all fixed so just focusing on the material, Modulus of elasticity (E) for "steel" is 30,000,000 psi
I would have thought hardened steel would be less flexible, but I just read this:


Does hardening steel change Young's modulus?

When certain solid materials, pure metal, steel or an alloy of a certain composition, gets strengthened by cold working or by heat treating, the Young's modulus stays exactly the same as before even though the yield strength of that material gets doubled, and the elongation gets reduced by an order of magnitude.Mar


So it sounds like hardened steel is "harder" as in less prone to plastic deformation (heavy load) but no stiffer under light load, if that's the case interesting.

 

[JRaut]

That's exactly right.

Elastic Modulus is a material-specific property and does not change based on how you heat treat it.

If you need less deflection, your options are (assuming you want to stay in the so-called 'elastic range of response'):
- Make it bigger (larger dia.)
- Use a smaller force
- Make it shorter
- Make it out of a new material that's stiffer than steel (Tungsten Carbide is about your only option, and a very expensive one at that)

As a pretty good rule of thumb:
- If we say that steel has a 'normal' elastic modulus (29,000ksi), then
- Aluminum is about 1/3 as stiff (10,000ksi) and
- Tungsten carbide is about 3x as stiff (100,000ksi)

 

[slow-poke]

JRaut,

Thanks for that, when I read the explanation of what heat treating does and it makes sense, but was not intuitive based on my first thoughts of "hardened" steel.

Back in my racing days I broke a lot of driveline parts at the drag strip. At one point I was ordering a new set of axles from Moser Engineering and one of the questions they wanted to know was was the car ever driven on the street?

Moser had numerous alloys they could use and some were stronger overall but were not as tolerant for day to day use. It would be interesting to know what alloy they were using.

 

[JRaut]

There's a whole world of stuff to learn about materials. Neat stuff.

Also worth a google is toughness vs. brittleness in the true engineering sense --- area under the stress-strain curve and all that jazz.

With Moser's question about your driveline parts, I suspect what the engineering department was really after is the proper heat treatment for your application. A wild-ish guess at the steel would be 4140 or 4340 --- both can be pretty well tailored with respect to toughness / strength through heat treat.

There's always a tradeoff between hardness and toughness. Can't really have both, so it's a give/take sort of thing. For track applications, they'd probably make it harder (and thus stronger) at the expense of some toughness. For street application, they wouldn't need all the strength, so could gain back some of the toughness (and longevity).

(Also, toughness goes WAY down at cold temperatures. So the baseline toughness for a street ride would necessarily have to be quite a bit higher than a track rig, assuming you're not racing in the snow.)

 

[benmychree]

There is a chapter in the book "Tool Steel Simplified" by the Carpenter Steel Co., manufacturers of tool steel, that explains the whole subject of deflection and Modulus of Elasticity. This was one of the required textbooks for my apprentice classes.

 

[Ischgl99]

This is a pretty good video of stress, strain, and toughness. He also has a bunch of other really good videos on engineering subjects.

 

[slow-poke]

Thanks everyone, fabricating and machining is a really fun hobby, so much to learn and that's what makes it fun.

 

[gard]

I'm trying to determine deflection of a round steel bar of various diameters, for example 16mm and 25mm
The bar would be supported at both ends (12" long) and the force would be say 1lb, 5lbs in the center

I for 16mm = 0.1184 in^4, is that correct?
I for 25mm = 0.736 in^4, is that correct?

16mm: with 1lb, 0.002", with 5lb, 0.012"
25mm: with 1lb, 0.0004", with 5lb, 0.002"

Does that sound correct?

Now assume the length, diameter, force are all fixed so just focusing on the material, Modulus of elasticity (E) for "steel" is 30,000,000 psi
I would have thought hardened steel would be less flexible, but I just read this:


Does hardening steel change Young's modulus?

When certain solid materials, pure metal, steel or an alloy of a certain composition, gets strengthened by cold working or by heat treating, the Young's modulus stays exactly the same as before even though the yield strength of that material gets doubled, and the elongation gets reduced by an order of magnitude.Mar


So it sounds like hardened steel is "harder" as in less prone to plastic deformation (heavy load) but no stiffer under light load, if that's the case interesting.

I come up with different values for I and thus deflection, not sure if it might be mixed units. 16 mm is 0.63 inches, I is 0.007725 and deflection of 12 inch simply supported with 1 lb in center is 0.00016 inchs, with E at 30e6psi, deflection is linear so 5x at 5 lb. This is from a spreadsheet I used years ago so its possible it has an error.

 

[ChazzC]

Sticking my nose in: basic question is Structural Engineering, and the developed discussion Materials Science.