Calculation of steel section properties 3

[Melad Saad]

Dear All,, Hope you could help me with this...
I need to work on design optimisation of steel space structures, using Continuous design variables. I am using different sections from that in the Universal Tables (UBs & UCs) by assuming new section dimensions.
I would like to know to calculate the following section properties of Universal Steel Beams and Columns:
- Second moment of area (Iy and Iz)
- Radius of gyration (iy and iz)
- Elastic modulus (Wel.y & Wel.z)
- Plastic modulus (Wpl.y & Wpl.z)
- Warping constant (Iw)
- Torsional constant (It)

 

[phamENG]

What is your background? Don't mean this to be mean, but those things are taught in the second year of most engineering curricula. Your mechanics of materials textbook should have detailed explanations.

 

[johnie134]

Why not buy a software

 

[KootK]

This may help with some of the torsional properties: Link

 

[robyengIT]

if you know french :
1 -

http://www.cticm.com

2 - >>>> logiciels
3 - looking for "logiciel PropSection" as per image

 

[Agent666]

Like phamENG noted, this stuff is covered by most undergraduate textbooks. Similarly most commercial analysis software will have basic routines to determine these values from user input sections. Though they may not fully account for complexities like fillets or torsional properties of built up shapes.

With a little searching you'll find for basic shapes like UB/UCs that there are readily available equations for determining these properties. They aren't perfect but give a fairly good estimate. Kootk's link includes some of these relationships.

If you are after a comprehensive free alternative to spending a lot of money on a commercial software package and know a little python I'd highly recommend this package. It'll analyse any section you could think up and has a lot of inbuilt sections. The readthedocs documentation has plenty of examples to get you started.

 

[johnie134]

i would suggest that one instead

https://www.engissol.com/cross-section-analysis-design.html

 

[Agent666]

IES shapebuilder is another commercial package I've used in the past if you'd prefer to part with your hard earned cash.

 

[Mohanlal0488]

Have a look at Octave GNU, the matgeom package has a number of tools which are useful for calculating sectional properties for polygons.

 

[SarkTower]

I have written a lot of design software over the years and have routines which calculate all the information you're looking for. Are you simply looking to select a section size and display these properties on screen? Or do you want to be able to set the values depth, breadth, etc. yourself?

 

[MarkDi]

In the UK there is the Blue Book

https://www.steelforlifebluebook.co.uk/

 

[johnie134]

MarkDi, excellent post.

 

[SarkTower]

Something like this?

 

[Melad Saad]

Dear all ,, Thanks a lot for your responses..

I am looking for formulas to calculate all the Universal Beams and columns section properties. software is not helpful because I want to make my own program in Matlab.
I tried some formulas, but not giving me exact results as it shown in the universal beams table..
Any suggestions please ...

Many thanks

 

[PEinc]

You will always have a problem calculating the exact properties for a beam compared to the property tables published by beam manufacturers and steel associations. I-shaped, H-shaped, and C-shaped beams, for example, are not made only of three rectangular plates as you may be using to calculate the properties.

http://www.PeirceEngineering.com

 

[Agent666]

If you want the exact properties for the torsion and warping constants you need to evaluate the fundamental integrals. There are estimates, they do a reasonable job but have their limitations.

Most of the other properties can be worked through knowing the centroids of rectangular sections and fillet shapes and their areas and the parallel axis theorem.

Second moment of inertia - use parallel axis theorem, or solve the fundamental integrals.

Radius of gyration = (I/A)^0.5

Elastic modulus = I/y_max (y_max is the max distances to the extreme fibres (edit - from the elastic centroid/neutral axis), for unsymmetric sections there will be a different moduli for each direction of bending)

Plastic modulus - determine the plastic neutral axis (based on area weighted by yield strength of various components), then the plastic modulus is determined by the sumproduct of the areas either side of the plastic neutral axis multiplied by their respective leverarm to centroids of the constituent shapes.

Torsion and warping constants - you really need to resort to FEM methods to numerically solve the fundamental integrals. But for UB shapes their is a paper from 1960's by Darwish and Johnson that has soon reasonably accurate formulas for the torsion constant.

If you're setting up solving the fundamental integrals for torsion and warping constants, then you might as well be solving the remaining properties by using the fundamental integrals for these as well.

Some examples of the integrals are discussed in the following links and how to numerically evaluate them, Wikipedia also covers them, as does any student textbook:-

https://robbievanleeuwen.github.io/finite element analysis/calculating-section-properties-part1/

https://leancrew.com/all-this/2018/01/greens-theorem-and-section-properties/

If you want accuracy, as soon as you have curved fillets or corners you're not going to get it with simplified formulas. They do all right in terms of getting an end capacity that is about right, but you won't match published properties which are worked out using the methods I linked to.

 

[Agent666]

Review this one also, and the paper linked there regarding numerical evaluation of the integrals.

https://robbievanleeuwen.github.io/finite element analysis/finite-element-preliminaries/

 

[BAretired]

I tried some formulas, but not giving me exact results as it shown in the universal beams table..
Any suggestions please ...

How inexact are your results and are they consistently high or low? If the error is small, particularly if it is consistently low, I would ignore it as being sufficiently accurate for engineering purposes.

BA

 

[JStephen]

In working with US-sized beams, going from the published data, you have to work backwards to derive the fillet radiuses to make everything work. I think the tabulated dimensions show the largest fillet size and the tabulated properties are based on the smallest fillet size. Not sure if this is an issue elsewhere or not.

 

[EDB9]

Hope this helps...

How off are your numbers in your setup from your table values?