Radius of Gyration

[GalileoG]

The radius of gyration for a rectangular solid section is r = 0.3h. I am curious as to which "h" should be taken.

Say I have a rectangular column b = 200, h = 500, and a moment about the strong axis, would I take h = 500 or h = 200?

I am assuming h should always be about the weak buckling side, which is why h should be 200 mm.

CSA A23.3-04 does not clarify, it simply states "take r = 0.3h, h being the design dimension of the column)"

Any input is appreciated.

 

[IceNine]

Radius of gyration equals square root of (I/A). It will be different for each axis of a rectangular column. Evaluate the slenderness in each direction based on the unbraced length in each direction, and use the worst case.

 

[civilperson]

Skipped that lecture did you? Radius of gyration is the square root of the quantity of: (Moment of Inertia divided by the cross section area). The Moment of Inertia is with respect to axis crossing the height, (I=(bh<3)/12)

 

[Lion06]

You two are rough. Even ACI allows you to use 0.3h for the radius of gyration, it's not that big of a deal. the 0.3h depends about which axis you are talking. Sor a section with an x dimension of 10" and a y dimension of 20", the radius of gyration about the y axis 0.3*10" (the x-dimension)=3", and the radius of gyration about the x axis is 0.3*20" (the y-dimension) = 6".

Clearly the radius of gyration of any section is (I/A)^.5, but there's nothing wrong with the down and dirty number of 0.3h...... especially if ACI allows it, right?!

 

[kslee1000]

"r" is taken in the direction under consideration = 0.3*h (h = member depth in that direction).

 

[GalileoG]

I am fully aware of how one can calculate the radius of gyration folks, I was merely asking about the code equation.

Thank you for the helpful responses.

 

[kslee1000]

We have mis-read your post.
Put simply this way, in the AISC (ASD), when checking allowable compression stress, we have to check kx*Lx/rx & ky*ly/ry, Lx & Ly representing unbraced length in each direction respectively. And rx & ry are radius of gyration in the cooresponding direction, kx & ky are effective length factor in the corresponding direction. Therefore, for a rectanglar section a x b, h for cal r can be "a" or "b" depending the "direction" under consideration (either one could govern).

 

[asixth]

Clansman,

Which national code is CSA (I'll assume it is Canadian). The Australian concrete code also allows the radius of gyration to be calculated using 0.3*D where D is the direction under consideration. For you example, your column will have a stiff axis (bending the 500 dimension) and a weak axis (bending the 200 dimension). If you are designing your column for buckling in the weak axis, your dimension to use will be 200.

 

[swearingen]

It's a derived equation:

I = bh^3/12
A = bh

Divide I by A and you get:

I/A = h^2/12

Take the square root of this and you get:

SQRT(I/A) = r = SQRT(1/12) x h

The square root of 1/12 equals 0.288675 and some change, so they round it to 0.3 - an error of a little over 3%.

If you can't sleep at night with 0.3, use 0.288675...


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