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)

 

[IDS]

software is not helpful because I want to make my own program in Matlab.

Robbie van Leeuwen's Github site (see links posted by Agent666) has full open source Python code, including torsion and warping constants. If you want to write your own code that would be the best source in my opinion.

You might want to have a look at my section properties spreadsheet because it gives formulas (and open source VBA code) for a wide variety of different shapes, but it doesn't do torsion and warping constants.

https://newtonexcelbach.com/2018/06/24/using-section-properties-group/

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Melad Saad]

Thank you all
I really tried to get Ix and Iy. However, I couldn't understand the parameters of the formula, bxiy^2 AND byix^2.
Could you please send me and helpful example.

Many thanks

 

[BAretired]

I really tried to get Ix and Iy. However, I couldn't understand the parameters of the formula, bxiy^2 AND byix^2.

No example to show you, but:

Ix = [∫b[sub]xi[/sub]y[sup]2[/sup]dy]

This is an integral of b*dy*y[sup]2[/sup] over the section, the definition of moment of inertia. The tricky part is determining b for each sliver of the curved portion where flange meets web. You would need to express b as a function of y throughout the height of the curved sections (which should not be too difficult as it is a circular arc).

Alternatively, you could approximate the curved fillet with a 45[sup]o[/sup] chamfer with x and y dimension of 0.8*radius of curve.

As a further alternative, you could calculate the area of the curved sections and simply add them as a point area at their respective centre of gravity. The only error in this would be that you would be neglecting I[sub]self[/sub] of each little area.

BA

 

[BAretired]

If you want even more accuracy, you could include the fillets, knowing the properties of rectangles and half circles. Areas 1 and 2 represent the top fillets whereas areas 3 and 4 represent the bottom fillets. Including these should provide all the precision you require. It is doubtful that the fabricated shape is as precise.

BA

 

[ESPcomposites]

You can also try the PlasticSection program here. The I-Section tab or General tab could be used.

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

Brian

http://www.espcomposites.com

 

[r13]

If you are an engineering graduate/student, do yourself a favor, buy a copy of "Mechanics of Material" by Timoshenko and Gere. It's free shipping and cost only $5.88 on Amazon.

 

[Agent666]

The centroid of a single fillet from the long edge is:-

r_c = r_1 * (10 - 3 * pi) / (3 * (4 - pi))

The area of a single fillet is:-

A_r = (1 - pi / 4) * r_1^2

The second moment of inertia of a fillet about its centroid is:-

 I_r = r_1^3 * ((1 - 5 * pi / 16) * r_1 - pi / 4 + 5 / 6)

Use the parallel axis theorem to work out Ixx and Iyy of the fillets about the elastic centroid. If you're not sure on that ask....

 

[Mohanlal0488]

Hi

As per your Matlab code, how are you calculating the properties?
Are you using the geometry functions that Matlab has?
I've done the formulations previously for fatigue analysis of welds, I found the best approach is to use built in functionality that Matlab has, less chance of errors occurring.

Keep in mind that most FEA programs go the method of using an exact solution using an integral calculation of the Laplace equation on a discretised representation of the cross section. This allows for the input of any shape of cross section. I would assume that most values that are read from standardized books would use a similar approach or something slightly more simplified as this would give the best results.

This may be the variance you are seeing in your results.

 

[Mohanlal0488]

I have attached a small snip of my code...
Note this is an old revision of the program that does not take into account the fillets, just showing it as the code is more compact and readable.

Hope this helps...