Radius of Gyration
Radius of Gyration
(OP)
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.
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.






RE: Radius of Gyration
RE: Radius of Gyration
RE: Radius of Gyration
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?!
RE: Radius of Gyration
RE: Radius of Gyration
Thank you for the helpful responses.
RE: Radius of Gyration
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).
RE: Radius of Gyration
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.
RE: Radius of Gyration
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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