Plastic Section Modulus Calculator 1

[novr4]

Hi All,

I know what a plastic section modulus is but I can't seem to find a calculator that can quickly calculate the plastic section modulus (full yielding) for steel sections?

Regards
Annoyed Engineer

 

[pointseventhree]

For rectangular shapes you can probably do it faster just using your calculator - b x d(squared) / 4
But if you wanted to here is one for rectangular section plastic modulus

For I section there are many i section plastic section modulus calculators available on the internet - you should verify for yourself though..

 

[klaus.]

most the time this value is given in the Tables for the different sections....

 

[phamENG]

Depends on how versatile you want it to be. If you want basic shapes, or the ability to add flat plates to reinforce an I shaped section, you can get CSISections for your phone (they have a suite of free apps that are pretty handy). If you want something more powerful, that can do custom fabricated shapes, extruded shapes, or a built up shape comprised of several standard shapes, then you may need to pay for it. I'm working my way through the SkyCiv trial right now, and they have one. Haven't used it much but it may be worth a try.

If you don't have to use them very much, though, it's probably worthwhile to do it by hand. Either that, or use the REGION, MASSPROP method in AutoCAD. It doesn't output the plastic section modulus directly, but you can locate the PNA pretty easily and then find the centroids of each half. Then it's a simple moment calculation.

 

[robyengIT]

if you can read french, here a very good one (attached from CTICM site)

 

[Celt83]

If you don't mind working from a command line there is this project on github: Link

I believe IDS created a spreadsheet that can interface with that program as well: Link

Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[dauwerda]

The plastic section modulus is defined as the sum of all elemental areas above or below the centroid of the cross section multiplied by the distance from each of the individual elemental centroids to the centroid of the cross section as a whole. You can create a spreadsheet for different typical cross sections pretty quickly using basic geometry.

 

[BridgeSmith]

Darn, dauwerda beat me to it - plastic section modulus is the summation of A * y for the component parts, where "A" is the area of the component part and "y" is the distance from the centroid of the component part to the plastic neutral axis (centroid) of the section. The areas can be split up into component parts in any convenient way, other than the areas have to be separated where they cross the neutral axis.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[Agent666]

I was going to post a recommendation the same as Celt83, even if you don't know python it's fairly easy to get started.

Otherwise it's fairly easy to calculate by hand for sections without any curvy bits, find plastic neutral axis (same area weighted by yield strength above/below the axis). Then do a first moment of Area calc, weighted area times lever arm to each bit of area will give you the plastic section modulus. Use it with whatever yield stress you weighted the areas with (moment strength = plastic modulus x yield stress, if all the plates are the same yield stress then it's even easier (otherwise use min of all plates yield stress will be conservative, often for I-sections codes just have you use the flange yield stress with no account of the web often being a higher yield stress).

 

[BridgeSmith]

...for I-sections...the web often being a higher yield stress).

That's interesting. When we do hybrid plate girders for bridges, it's always the flanges with the higher yield strength.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[Agent666]

I was referring to hot rolled sections. Web undergoes more rolling so becomes more strain hardened. With plate girders often as well for the same base grade of steel if the flanges are thicker then the plate will have a lower yield stress. For example in my market, grade 300 plate at 10mm thick has a yield strength of 310MPa, but at 40mm thick its a yield strength of 280MPa.

 

[BridgeSmith]

That's good to know, Agent666, but doesn't affect what we do for design. We use the specified minimum yield for design, so variations in actual yield strength across the section, or for different plate thicknesses, doesn't change our designs.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[Agent666]

Yeah I guess most codes for flexure say to simply use the flange yield stress without taking benefit of the slightly higher strength web. The NZ steel standard does let you use for compression the actual yield stress of each plate element. For working out effective section moduli for flexure, you also use the actual plate strengths for evaluating local plate buckling, so it stands to reason you can sharpen your pencil and use the same philosophy for actually working out the plastic modulus and effective section modulus. It's not something I regularly rely on, but it can get you that few extra percent capacity if you're looking for that little bit more to make something work.

 

[ukbridge]

https://pdfs.semanticscholar.org/14d6/f9c2d195c541d855a5789e22022393a09744.pdf

This paper gives a method for a (simple) spreadsheet implementation which I've used in the past.

 

[atrizzy]

To add to the great comments already posted, if you have a copy of Staad.Pro with 'section wizard' installed (I believe they all do) you can quite easily define the geometry of a variety of different common shapes, press a button, and out pops not just the plastic modulus, but just about every other geometrical property you'd ever want.

 

[P1ENG]

What kind of sections are we talking; HRS or cold formed? What design standard? If you are looking specifically for AISC plastic section modulus, then download AISC's shape database. Then in Excel (or Google Sheets or OpenOffice), do a vlookup() to find the value of a cell based on the name of the shape.

I've actually done it for you in the attachment below. Just enter the name of a shape in cell C1 and the Zx value is reported in cell C2.

Juston Fluckey, SE, PE, AWS CWI
Engineering Consultant

 

[ESPcomposites]

I just updated the "PlasticSection" program and it may be able to do what you need (free for non-commercial use and also has a free trial). It is an immediate download and no installation is required so you can test it out quickly. It can handle up to 5 rectangular segments for bending about the horizontal axis. I have not explored other programs, but some users have said they could not find this capability in other programs.

https://www.espcomposites.com/software/download.html