Effective Radius of Gyration (rts) 2

[Usman3301]

Hi there,
I was recently assigned a task of determining flexural strength of a given Steel cross-section against given loading conditions. This involves determining "rts-effective radius of gyration". Since the cross-section is not a standard one, I had to manually calculate rts value but I think there's a mistake in my calculation. Kindly help me out. Your help is highly appreciated.

 

[rb1957]

why do you need the radius of gyration ? rho = sqrt(I/A)
you'll have two values, for major (strong) and minor (weak) axis I

you may need to investigate the principal axes (though I think they're the same as the orthogonal axes, as per sketch).

another day in paradise, or is paradise one day closer ?

 

[Usman3301]

@rb1957
I have attached an image showing necessary steps to calculate flexural strength of steel section as per Lothers (Design in structural steel)

 

[r13]

rts - Effective radius of gyration used in the determination of Lr for the lateral-torsional buckling limit state for major axis bending of doubly symmetric compact I-shaped members and channels.

I don't think your member belongs to either shape.

 

[JStephen]

I'm assuming your shape is loaded vertically? That is, top of page is "up" and load is gravity loading down?
If I remember right, that rts comes in for evaluating wide flange beams bent about the major axis, which your shape is not. Refer to the criteria for channels bent around the weak axis and for rectangular bars bent around the weak axis, which is what your geometry most closely resembles. I think you would have another failure mode with the section buckling into a flat shape at some point, which is not addressed by the AISC criteria and needs to be addressed by other means. This is a small shape, and it may be quicker to form one and test it than to analyze it properly for that.

 

[Guest090822]

retired is correct - this shape isn’t appropriate for rts in the lateral torsional buckling (LTB) determination for I-beams.

If this is sheeting used as a beam then LTB doesn’t apply. The memeber is wider than it is deep.

 

[Usman3301]

@JStephen
Yes, the shape is loaded vertically by concrete slab, with compression at top and tension at bottom. As "retired13" and you correctly pointed out that "rts" is limited to doubly symmetric compact I-shaped members and channels. I'll try to check it against both cases (rectangular bars and channel section bent about their weak axis). I hope it works. Thanks a lot for helping out.

 

[Usman3301]

@TheRick109
I had reservations when my boss told me to analyze it as a beam. It is in fact a steel deck supporting concrete slab. For simplicity, he told me to consider 1 foot portion of deck and then analyze it against given loads.

 

[Guest090822]

You can just determine the elastic or plastic section modulii and use one of them. Since LTB won’t come into play then the capacity is is just Fy Zx.

If this is for a concrete deck then it’s likely sheet metal. Make sure you have the right material properties.

Don’t forget to check deflection. You don’t want your forms to sag.....

 

[Celt83]

Check out the AISI and SDI specifications instead of AISC, similar provisions with a few extra checks for localized failure and more applicable to what your are looking at.

My Personal Open Source Structural Applications:

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

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[BAretired]

h = 1.50 - 0.06 = 1.44"
diagonal length = 1.52"
Area = 2(2.75)t + 5.5t + 2*1.52t = 14.0t in²
I = 2*5.5t(.72)² + 2(1.44)³*1.07t/12 = 6.23t
rho = sqrt(I/A) = sqrt(6.23t/14t) = 0.667"

Section Modulus S = I/y_max = 6.23t/0.75 = 0.498 in³
M = 15,840 "#
Fb = M/S = 31,780 psi

The material is 0.06 " thick, less than 1/16", so it may be governed by cold formed light gauge steel design code. This could mean that the effective width of top flange is less than the flat width of 2.75" by code.


BA

 

[r13]

Note the code specified parameter usually was derived through a series of evaluations/calculations around a particular structural behavior/phenomenon of a member, thus the limitations it set shouldn't be altered to fit your case, because it usually will be resulted in wrong prediction/conclusion.

For this case, pay attention to the "T" in subscript, it ties the parameter to torsional effect on members with particular geometry characteristics, that is noted in the code provision - "rts maybe approximated accurately and conservatively as the radius of gyration of the compression flange plus one-sixth of the web", a very definite attribute of doubly symmetrical I shapes and channels, for which localized twisting capacity is the concern. This parameter, therefore, is not applicable to any shape without the afore mentioned geometry attributes.

 

[JAE]

Usman3301,
Is this a composite decking or a non-composite decking?
I presume since your supervisor suggested you design 1 1 ft. section of it as a "beam" then the concrete is only a load on the deck and not used for flexure(i.e. non-composite?).

If so, are you using AISI design methods I would hope? (vs. AISC).
I'm a bit confused by why you are even doing this. For non-composite decking there are numerous catalogs showing maximum deck-only loads for various spans, etc.

 

[Usman3301]

@TheRick109
I did the elastic analysis, and "BAretired's" solution confirms my calculations.
@JAE
Yes, it's a non-composite deck, with 3" concrete slab. You are quite right in saying that instead of using AISC, I should refer to AISI design methods. Since I am fresh graduate with zero experience, my Boss just wanted to give this as a little assignment to me, and because of time constraint, he couldn't explain in detail the whole thing. He just draw the image and told me to refer to Lother's structural steel design book. But it's from these comments, I have started developing an understanding of what's actually going on. I hope you'll understand my situation. Besides, can you refer to catalogs with specifics, so I can go through them as well.

My utmost respect for you two guys. @BAretired and @retired13, just wanted to let you know that your suggestions on my previous thread "tributary area method" were very valuable and now, I have developed an intuition of how load distributes. Thanks a lot for you valuable comments and being so helpful back then.

@Celt83 I am not familiar with Github, but I did go through your project and it seems pretty cool. I'll definitely use your code, once I learn how to run python code on desktop.

 

[r13]

You are very welcome.

 

[Celt83]

AISI specifications are provided free of charge by CFSEI here: Link

If you have any questions on the python stuff feel free to reach out to me on GitHub. I'm not as active with my programming right now due to some other life influences but I check in on GitHub pretty regularly.

My Personal Open Source Structural Applications:

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

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer