rt formula for I-shape with channel cap?

[RobertEIT]

I am looking at AISC-13th, page 16.1-51, at bottom paragraph, it read as follows:

"(ii) For I-shape with channel cap.....:

rt=radius of gyration of the flange components in flexural compression plus one-third of the web area in compression due to application of majar axis bending moment alone, in."

Can anybody help me to translate it into an exact formula, what it should look like? Does this flange components includes all the channel cap section plus the I-shape flange?

Thanks a lot for your help!

 

[Lion06]

It will include all of the flange (channel cap and WF flange) that is actually in compression in the elastic range. If the ENA doesn't extend into the web (it almost certainly will), then you just figure out the r of the portion of the flange that is in compression. If the ENA is in the web, then it's figured out for you. You will need to find the radius of gyration of the T about the y-axis of the section because even though the rt will be smaller about the x-axis of the section, it can't buckle in that direction.

 

[RobertEIT]

Thanks, StructuralEIT.

So it is the radius of gyration of the top T-shape in Y-Y(horizontal) axis(including C-channel), not the axis Y-Y radius of gyration in Table 1-19 or Table 1-20. Right?

That will give a larger LTB capacity than use Table 1-19 or Table 1-20 ry value.

 

[Lion06]

correct, rt (per F4) will be larger than ry in table 1-19 or 1-20. The reason is that as the ENA moves toward the compression flange (assuming the channel is on the compression side) less of the web is in compression and the section (the T) has more of its area farther from its ENA, which increases its radius of gyration.

 

[JAE]

RobertEIT:


r_T = square root of (I_T / A_T)

I_T equals the sum of the following:

Moment of inertia of the channel
(about the channel major axis) Ix

Moment of inertia of the top flange of the beam
(t_f x b_f^3 / 12)

Moment of inertia of the compression portion of the web
b_cw x t_w^3 / 12
where b_cw is the compression portion of the web.

A_T is the sum of the areas of those parts.