Steel Angle Plastic Section Modulus

[Engineering05]

I am working on making a generalised spreadsheet for steel angles that can handle user input data. The sections to be evaluated will generally come from one steel which are the most commonly available hot-rolled products in Australia.

Link to one steel’s product guide:

http://www.onesteel.com/images/db_images/productspecs/6th Ed_HotRolledCat_web_optimized.pdf

Angles are on pages 21-26.
(Note that in Australia “S” denotes Plastic Section Modulus whilst “Z” denotes Elastic Section Modulus).
Enlarged key diagram:

http://i.imgur.com/Atev7w4.png

I am after trying to find the plastic section modulus about both local axes (x & y) after having calculated them for the global axes (n & p). Is there a way I can transform global to local using Morh’s circle to evaluate plastic section properties?
Any advice would be greatly appreciated.

 

[desertfox]

Hi
Try the links below, on the link ending with pdf scroll down till you find clause 9.10., the links will explain how to use the Mohr circle to get to the principle axis of the angle.

http://books.google.co.uk/books?id=...q=mohr's circle second moment of area&f=false

http://ocw.nthu.edu.tw/ocw/upload/43/763/static_ch9.pdf

http://www.roymech.co.uk/Useful_Tables/Sections/U_Angles_dim_prop.htm

 

[Engineering05]

Thanks for the reply desertfox,

I have been using morh's circle to rotate the second moments of area from global to local (this is a piece of cake). Doing so requires you to find the product of inertia (denoted Ixy when dealing with the second moment of area). In my case, I don't know how to evaluate the plastic section modulus term that would replace the product of inertia. In other words, having already calculated Sn and Sp, how do I calculate Snp - which would be the product of plastic section modulii (does this even exist/mean anything mathematically?)?

 

[johnbridge231]

Mohr's circle is applied to tensors. Inertia moment is a 3x3 tensor, as also stress is.
On the other hand, such transformations are not valid for section moduli. So you will have to recalculate the plastic modulus with respect to the axes x and y. This is time demanding but inevitable if you are doing that by hand..

Analysis and Design of arbitrary cross sections
Reinforcement design to all major codes
Moment Curvature analysis

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

 

[desertfox]

Hi

Sorry I thought you just needed to transform it, its quite complicated and all I could find was this:-

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

scroll down till you see plastic section modulus

 

[johnbridge231]

Transforming can be accomplished easily. On the other hand, rotating of the inertia data is not that easy.

Analysis and Design of arbitrary cross sections
Reinforcement design to all major codes
Moment Curvature analysis

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

 

[BAretired]

A steel angle is an unsymmetrical section. It cannot develop full plastic behavior. What is the meaning of the term 'plastic section modulus' when applied to an angle and how would it be used in calculations of strength?

BA

 

[Engineering05]

Thanks for all the reply's. I really appreciate the input.

You've all confirmed what I thought may be the case - I'll be simplifying the geometry down to a set of rectangles and go from there.

BAretired, why can't an angle go fully plastic? Is it because the case where the unrestrained ends of the legs in compression are likely to buckle before ever going plastic? The Australian steel code (AS4100) will allow you to design an angle based on its slenderness - the first check of which is the "compact section modulus" (I think this is the british equivalent of class 1) which is defined as the minimum of: 1.5 x Elastic Section Modulus and the Plastic Section Modulus.

 

[Jerehmy]

The max strength for a single angle fully laterally-braced according to 2005 AISC seems to be 1.5*My = 1.5*S*Fy. Doing a quick once-over, Z > 1.5S for all the cross-sections I see so I guess AISC doesn't want you using a fully plastic section, just partially.

 

[BAretired]

I am after trying to find the plastic section modulus about both local axes (x & y) after having calculated them for the global axes (n & p). Is there a way I can transform global to local using Morh’s circle to evaluate plastic section properties?

The term "plastic section modulus" is not defined for the global axes (n & p) so it is not clear to me what you calculated. Where would the neutral axis be located?

It may be feasible to calculate the plastic section modulus for the principal (you called them local) axes, particularly for an equal leg angle because the section has one way symmetry about the x axis and a form of symmetry about the y axis.

BA