Relationship Between Young's Modulus and Section Modulus.

[aftr9]

I am trying to find a relationship between the Young's Modulus and the Section Modulus.

I am currently comparing different structural shapes made out of different materials and was wondering if there was a relationship between the two moduli (?) which would allow me to compare different shapes with different materials.

To be more specific, I am comparing steel structural shapes with aluminum ones trying to design a lighter, stronger/stiffer profile for us to use.

If anyone can help me with this or point me in the right direction I would greatly appreciate it. Thank you.

 

[SnTMan]

Youngs modulus is a material property, section modulus is a shape property, in other words, no relation.

Regards,

Mike

 

[drawoh]

aftr9,

Are you talking about Section Modulus, or Shear Modulus?

JHG

 

[SnTMan]

aftr9, I suggest you brush up on your strength of materials, then ask the question.

Regards,

Mike

 

[aftr9]

Thank you for the quick replies.

I'm talking about Section Modulus. S = I/c.

I didn't think there was a relationship but a coworker brought it up. He mentioned he remembered working on a project a long time ago dealing with this.

He told me to look at composites and that he believed there was a relationship between the two.

 

[aftr9]

SnTMan,

Thanks for the suggestion. Just thought I'd ask.

 

[FeX32]

No relation whatsoever.
Your co-worker must not understand mechanics. Or maybe he is thinking section modulus and strain...
Here is something relating the 'related' modulus's

http://www.sciencedirect.com/science/article/pii/S0921509308000622

Fe

 

[aftr9]

Thank you FeX32.

I was just wondering if anyone else had heard of that. He is one of our senior engineers who deals with FEA so I thought maybe he knew something I didn't.

 

[rb1957]

"composite" makes me think if the structure is strain controlled then you might get something like ...

allowable strain = 0.2%
bending stress = Mc/I
bending strain = Mc/(IE)
so allowable moment = 0.002*E*(I/c) ?

 

[JohnRBaker]

aftr9, if I'm reading your 'problem' correctly, it appears that you're attempting to derive the MINIMUM 'Section Modulus' needed (to reduce material cost and/or live within some size/space constraint) while meeting certain performance specifications (maximum stress, deflection, etc.) of a structural member of a certain material. If this is the case then I guess one could argue that once the equations were written out that there was indeed an ALGEBRAIC 'relationship' between what the 'derived' Section Modulus would need to be relative to the material (and thus the Young's Modulus) chosen. If THAT is what your senior engineer had in mind then perhaps it was just a matter of everyone doing a better job of explaining exactly was being asked for and how one was expected to go about getting the answer(s) needed.

John R. Baker, P.E.
Product 'Evangelist'
Product Design Solutions
Siemens PLM Software Inc.
Industry Sector
Cypress, CA

http://www.siemens.com/plm

http://www.plmworld.com/museum/

To an Engineer, the glass is twice as big as it needs to be.

 

[Compositepro]

What is the proper term the product of section modulus and Young's modulus?

 

[dhengr]

I think it’s Young’s Section Modulus squared.

 

[MikeHalloran]

Re lighter/stronger/stiffer, the ratio of Young's Modulus for aluminum versus steel is roughly 1:3. Oddly enough, the ratio of their specific weights is also roughly 1:3. So for a structure of a given stiffness, neither has a strong weight advantage.

As an example, once upon a time, I worked on a flight simulator, where extreme stiffness was a primary design criterion. I designed the structure as a truss of 5x5x5/16 steel tube. The Chairman asked me why not aluminum. I replied that I could do the same structure at the same weight from 4x4 aluminum bar, but it was much more difficult to get full strength joints in that material.

Aluminum structurals are extruded, not rolled, so there are limits on how big your profile can get to compensate for the reduced E. At the time I did the FS, 40-ish years ago, the biggest extrusion press in the world was in Arkansas, and could handle any shape that would fit in a 13" circle. Because extruded aluminum comes out annealed, it's possible to extrude shapes in a curled form and then unwrap them before heat treat, but there are limits to that. I think there's a bigger press now, but I don't know who owns it or what the minimum run is (5000 lb, one stroke, for the one in Arkansas).

You have a really interesting problem there, but it's not going to yield nicely to just one or two equations.




Mike Halloran
Pembroke Pines, FL, USA

 

[JohnRBaker]

There is one very significant advantage with Aluminum and that is that it CAN be extruded, which means that it's much easier to engineer a profile where the Section Modulus has been optimized if you have space and packaging issues. I spent several weeks back during my actual 'sitting at a drawingboard' part of my engineering career laying out and calculating the section moduli of customized aluminum extrusion profiles for a project where we needed to replace a series of painted steel members with something which would meet some new and updated FDA sanitation rules (we manufactured machinery used in the production of food products). Our first thought was to simply replace the rolled steel shapes with stainless, but that was deemed too expensive and besides not every mild-steel rolled shape was available in stainless, so we decided to go with aluminum since we could get any shape we wanted (the aluminum extruders would refund us the cost of tooling after so many pounds of stock was purchase so in the end the cost of custom tooling was never a real consideration and at the quantities that we were ordering, the vendors were more than willing to deal when it came to tooling).

Anyway, what we needed to do was design the profiles so as to be as 'stiff' as possible yet still fit into the space we had to work in and yet still get something which we could fabricate and still meet the sanitary rules, which involved more than just the materials used. BTW, if anyone has every tried to do these sorts of calculations using a mechanical 'planimeter' working with 2D drawings of proposed profiles, you'll appreciate why when we installed our first CAD system a couple of years later and I discovered that there was a built-in tool which would do this for me virtually automatically. All I had to do was draw the profile and the system would give me all the 2D Section properties virtually in seconds, I was hooked. I could do a week's worth of work in a single afternoon, which included producing the final purchasing drawings without having to beg for some detailer's time from the drafting pool.

BTW, for those of you who've never had the joy of doing section property calculations prior to the advent of CAD, this planimeter looked very much like the one we had in our office (and they were NOT cheap, costing several hundred dollars each and this was back in the early 70's):

For information about how they worked, go to:

http://en.wikipedia.org/wiki/Planimeter

http://whistleralley.com/planimeter/planimeter.htm

John R. Baker, P.E.
Product 'Evangelist'
Product Design Solutions
Siemens PLM Software Inc.
Industry Sector
Cypress, CA

http://www.siemens.com/plm

http://www.plmworld.com/museum/

To an Engineer, the glass is twice as big as it needs to be.

 

[dvd]

For self-supported objects the aluminum/steel tradeoff is okay: close to one-third the weight of steel and one-third the Young's modulus of steel provides roughly the same deflection given similar shape/section modulus. But put a load on it and you've got lots of deflection with the aluminum member.

Be very careful welding aluminum and pay attention to fatigue strength of welds.

 

[msquared48]

Young Section Modulus is 362436.

Old Section Modulus is 324048.



Mike McCann
MMC Engineering

 

[SnTMan]

Yes, but what units?

 

[rb1957]

does it matter ?

maybe furlongs/fortnight

 

[JohnRBaker]

maybe furlongs/fortnight

Have you ever seen one of my demos? When I'm asked whether the Siemens NX CAD software can utilize customized units, the example I always use is 'Furlongs/Fortnight' in a Velocity calculation ;-)

John R. Baker, P.E.
Product 'Evangelist'
Product Design Solutions
Siemens PLM Software Inc.
Industry Sector
Cypress, CA

http://www.siemens.com/plm

http://www.plmworld.com/museum/

To an Engineer, the glass is twice as big as it needs to be.

 

[rb1957]

don't know that i'd like to make a model with units of furlongs ... sounds like i'd be using a whole bunch of decimal places ...