Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.


Link To This Forum!

Partner Button
Add Stickiness To Your Site By Linking To This Professionally Managed Technical Forum.
Just copy and paste the
code below into your site.

Optimum shape of a simply supported beam

Optimum shape of a simply supported beam


figure 3 in particular.

This shape surprises me a little, any comments? I'd have expected a direct compression strut running down from the force application point to each support.



Greg Locock

New here? Try reading these, they might help FAQ731-376: Forum Policies

RE: Optimum shape of a simply supported beam

Must be an
He dosn't specify optimization with respect to what: refers to strength and lightness, but what about stiffness, cost, aesthetics,etc. (the last being possibly what really he is caring about). And of course the result will depend on allowed materials, available equipment,etc.
Chatter, though the argument is quite serious, of course.

prex : Online engineering calculations : Magnetic brakes and launchers for fun rides : Air bearing pads

RE: Optimum shape of a simply supported beam

Getting past the author's verbal diarrhea, it appears to be a system of rounded trusses. Expensive, suitable for monumental buildings. I don't want my stamp on one of these. I admit though, I have pondered the use of organic shapes, but not seriously, just as an exercise for the mind.

I wonder how one specifies for the program, it looks like  big change in approach.

Timing has a lot to do with the outcome of a rain dance.

RE: Optimum shape of a simply supported beam

He seems to be talking about optimization to include aesthetics, which I interpret to mean that he's found a way to stick his thumb into an optimizer and diddle with it until he likes the solution it comes up with.

I get the impression he's using Figure 4 as a _bad_ example, where the optimizer went from a pierced sheet rib to a bit of lovely Zeppelin structure, without his diddling.

Or something like that; I couldn't bring myself to study his prose.


Mike Halloran
Pembroke Pines, FL, USA

RE: Optimum shape of a simply supported beam

Well figure 3 follows generic a strut and tie form for this support condition and loading, but is influenced by whatever optimization objective is taking place.  

While we'd expect to have a node at each support the offset of those sames nodes towards the center of the beam suggests some sort of balance of compressive behavior with tension behavior.  In other words minimizing huge compressive regions in favor of introducing tension in smaller regions where SEs would overlook them as they are refinements without benefits to us on the whole.  

It definitely reeks of organic structural development.  Something that as a matter of evolution is great after possibly 2 million years of adaption to a possibly stable load and support but definitely not something I'd design for 20+ years subject to who knows what!


Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

RE: Optimum shape of a simply supported beam

Interesting.  It looks like a cross between a two hinged arch and a bowstring truss.  I wonder about the two large trapezoids each side of the central triangle and also about the horizontal member within the central triangle.

It would be interesting to learn what load combinations were considered in the optimization.


RE: Optimum shape of a simply supported beam

Seems to have a lot of holes in his design...  Reminds me of bone structure actually.

Kinda looks like one of the sleezy cult leader actors on "Big Love" too.  Can his opinion really be trusted?

Mike McCann
MMC Engineering

RE: Optimum shape of a simply supported beam

My first thought was similar to BAretired's...bowstring truss.  If you do FEA and plot the stress contours, you'll probably see a similar pattern.

RE: Optimum shape of a simply supported beam

I assume what he means by "topology optimization" is the arrangement of structural members. Topological optimization of structural arrangements has been studied by many engineers and researchers. The thing that is interesting is the notion to include aesthetics in the optimization procedure. This can easily be formulated as an index in a multi-objective optimization procedure.
It severely lacks any logical engineering assessment. "It" is much more Architect than Engineer.  His flaw is his "weight" on aesthetics is much much to high...haha... leaving for a structure that intuitively to an engineer is weaker than is should be...not to mention the construction of those elaborate curves.

One other thing. He uses "user friendly technology" referring to software that does all the work. ... Although technology is great, understanding it is equally important.


Fe (IronX32)

RE: Optimum shape of a simply supported beam

It is a step forward and a good idea nonetheless.  

Fe (IronX32)

RE: Optimum shape of a simply supported beam

In terms of what the software is doing, it is fairly easy, Ron is on the right lines, it reduces the density and hence stiffness of elements that are under stressed, so to some extent all it does is throw away all the blue bits in a typical FEA stress plot. It has a few goes at that, and reinforces the overstressed areas at the same time.

Then it slaps a surface around the remaining highly stressed bit and you have a structure.

You can get the same effect by hand with a bit of thought, I've done it with spaceframes where I started with all nodes connected, then reduce the diameter of the tubes that are understressed, and increased the diameter of those that are overstressed. What's interesting is when you have stiffness requirements and strength requirements.


Greg Locock

New here? Try reading these, they might help FAQ731-376: Forum Policies

RE: Optimum shape of a simply supported beam

One would wonder about constructability and cost to construct?  Perhaps the Romans had it right?

RE: Optimum shape of a simply supported beam

"Perhaps the Romans had it right? "

Slaves labor?
No OSHA and minimum wage/maximum work week laws, no environmental worries, and pay for it all (by conquering somebody else) and grabbing their loot?          8<)

RE: Optimum shape of a simply supported beam

I'm not sure what product he is using, but there's a feature in Solidworks Premium (I forget the analysis engine behind it) that allows you to visualize an "optimized" (or something like that) design.

I believe it uses the stress plots and effectively "grays" out the less stressed areas depending on well, how far you move the slider.  

"We shape our buildings, thereafter they shape us." -WSC

RE: Optimum shape of a simply supported beam

I like the optimized shelter.

"This tent packs so lightly. It does have some drawbacks, though."

RE: Optimum shape of a simply supported beam

   That organic looking bridge looks cool.  I wonder if he accounted for the water flow underneath it.


RE: Optimum shape of a simply supported beam

I agree totally Greg.
I guess I was referring to the fact that this seems kind of like the Architect is now trying to eliminate the engineer with software he does not totally understand. He likely understands that it reduces density etc. , but does he understand the underlying principles, likely not.

Also, I implied that there does not exist an index for aesthetics yet.  This could be the subject of some research. By index I mean the index we use in the optimization procedure like Stiffness, Strength, Dexterity, Weight, Cost. Seems like they need one that defines "Good Looking" smile. Consequently, this could be formulated exactly like a typical structural engineering problem within FEA (or other). And the "weights" upon which give the "best" compromise between say Strength, Stiffness, and Aesthetics could be formulated.

One of the problems I have with the article is just that. What is their definition of "aesthetics"? They don't say.  

Fe (IronX32)

RE: Optimum shape of a simply supported beam

hey raecookpe1978,
re: The Romans.
Was actually just commenting on their arches and viaducts as a structural form that have, in some cases, 'stood' the test of time, if you'll pardon the pun.  Not sure about there politics etc., though.

RE: Optimum shape of a simply supported beam

I suspect this problem gets even more involved than it appears.  If you optimize a typical beam based on stress only, you come up with something made out of aluminum foil.  So to properly optimize it, you need to analyze very accurately for buckling as well.  Even then, whatever your constraints are, are likely to define the solution moreso than the analysis.

RE: Optimum shape of a simply supported beam

Right and when you try to connect all the members (nodes)... things get more complicated and expensive I would suspect and perhaps the elegance and logic and organics all get lost.

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close