huangyhg

radius of gyration
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.
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.
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)
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?!
"r" is taken in the direction under consideration = 0.3*h (h =
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.
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).
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.
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...
if you "heard" it on the internet, it's guilty until proven innocent. - dcs

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