Radius of Gyration

[karynalicia]

We are designing a WT-beam with a channel on the bottom to form a composite section. If the channel is positioned so that it's x-axis is oriented in the same location as the beams y-axis can we add the radius of gyration about the y-axis of the the WT beam to the readius of gyration about the x-axis of the channel inorder to find the radius of gyration of the new shape? We were thinking we could but when you look at the composite member section properties in the steel manual it doesn't work out that way. Any thoughts on this would be greatly appreciated as this is driving me crazy.
.
. . = The WT-section
. * = The Channel
* . *
* ....... *
******* Thanks

 

[jhardy1]

karynalicia,

The governing formula is:

Radius of Gyration = (Moment of Inertia / Area)^0.5

You can get the total Moment of Inertia of the composite section by simply adding the two component Moments of Inertia, PROVIDED they are on a common neutral axis. When the centroids are offset, you need to locate the centroid of the composite section, then calculate the offsets for each component, and then use the following formula:

I_composite = I_1 + A_1*e_1^2 + I_2 + A_2*e_2^2 + …

(All moments of inertia and eccentricities are taken about the respective axes.)

In your case, if you are after the Radius of Gyration about the minor (vertical) axis, I assume the components are on a common centre-line, so:

I_composite = I_yy (for the I-Beam) + I_xx (for the channel)

(The channel is rotated 90 degrees, so you need to use the major axis in this case.)

And:

Radius of Gyration = (I_composite / (A_I-beam + A_Channel))^0.5

If you want to calculate the Radius of Gyration about the major (horizontal) axis, you will need to first calculate the centroid location for the composite section, calculate the component offsets etc.

Hope this helps.

 

[ChipB]

Draw the section in Autocad, change it to a region, do a massprop command on it, note the nuetral axis. Move the region's neutral axis to 0,0, and do another massprop on it. It'll kick it out for you.