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# How to calculate radius of gyration for a channel caps on I beam?

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## How to calculate radius of gyration for a channel caps on I beam?

(OP)
For an I beam with a channel cap attached to compression flange, are we supposedly to use the same formular (F4-10) in page 16.1-51 of AISC-13th to calculate its radius of gyration?

If it is the same formular of (F4-10) as for an I beam without channel cap, then for item bfc in the formular, should we consider channel web as part of the flange components in flexural compression?

Seems AISC-13th does not put it clearly? Any thoughts?

Thanks for your help.

### RE: How to calculate radius of gyration for a channel caps on I beam?

I believe that just under Eqn. F4-11 it describes your situation.  "rt = radius of gyration of the flange components in flexural compression plus 1/3 or the web area..."

Hope it helps.

JWB

### RE: How to calculate radius of gyration for a channel caps on I beam?

(OP)
jberg,

Thank you for your response.

I know this description under Eq.(F4-11), but it does not make me clear, does this description mean that we only need consider the I beam flange and do not need take the web of the channel into consideration (which is attached to the I beam flange)? say if a S12x35 with a C8x11.5 cap, could you please show me how rt is calculated?

Thanks.

### RE: How to calculate radius of gyration for a channel caps on I beam?

The AISC Manual has r-values for channel capped W-Sections in section 1

### RE: How to calculate radius of gyration for a channel caps on I beam?

(OP)

ash060,

firstly AISC-13th Table1-19 to Table1-20 only listed part of the W and S Beam Shapes with Cap Channels. For example, in these two tables, no S12x35 beam with Cap channel was listed.

secondly, in these two Tables, it only listed rx and ry, no rt value was listed.

### RE: How to calculate radius of gyration for a channel caps on I beam?

it does have values, but not for every possible combination of shapes

what I do is take the channel depth and set it as a top flange width, then determine an equivalent flange thickness based on the combined areas of the channel and beam top flange.

then run your calcs based on 1/3rd of the area above n.a. or whatever it is

### RE: How to calculate radius of gyration for a channel caps on I beam?

it does have values, but not for every possible combination of shapes

what I do is take the channel depth and set it as a top flange width, then determine an equivalent flange thickness based on the combined areas of the channel and beam top flange.

then run your calcs based on 1/3rd of the web area above n.a. or whatever it is

### RE: How to calculate radius of gyration for a channel caps on I beam?

There does not appear to be a cookbook equation for this case, especially given the sloped flanges of an S section.

See linked sketch.  That's my interpretation of 1/3 the compression web area...

I'd use AutoCAD to draw the shapes, create a region, then use MASSPROPS command to give me I and A.  r = sqrt(I/A)

I suppose one could break the shape into "simplified" rectangles and triangles and calculate I and A of the individual pieces.  I use the phrase "simplified" lightly though!

### RE: How to calculate radius of gyration for a channel caps on I beam?

PMR06 has it right.  You have the A, Ix and Iy of the channel.  You have it for the S shape, too.  A couple of quick manipulations and you can figure out the A, Ix, and Iy of just the flange, even with the 16 2/3 degree slope.  Add in your little web piece, and you have all you need to calculate Iy and rt.

### RE: How to calculate radius of gyration for a channel caps on I beam?

(OP)

PMR06,

Thank you very much. Your sketch descrcribed the procedure of how to calculate rt very clear.

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