effective buckling length for post restrained at midheigh

huangyhg

effective buckling length for post restrained at midheight
can anybody tell me how i would determine the "k" value for a post fixed at it's base and laterally supported at midheight? the axial load is applied at the top of the post.
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if the top and bottom are pinned and the restraint at mid-height is only for lateral translation (and not any moment connections) then i would use a k would be 1.0 since the column will buckle in an "s" shape and each segment would be a pure simple curve.  your l is 1/2 the total length (base to restraint at mid-height or mid-height to top).
sorry, i should have specified that the top of the post is unbraced, (like a propped cantilever running vertically). the restraint at midheight is only for lateral translation.
the easiest thing is to let a computer solve it.
i did so and got k = 2.7, where l is half the total length.
tomfh - i would wonder what computer program you used and what its basis is?
maturin - if the top of the column is cantilevered above the floor, then the lower half would still be k=1 but i would think the upper section would be at least 2.0 as tomfh suggests.  check the aisc nomographs for sway condition and no beam stiffness.
as a practical point, does it have to be pinned at the exact mid point, i suspect that moving the restraint up a bit would help.
cheers
greg locock
i used microstran and ran a linear buckling analysis.
i should point out that k=2.7 is for a pinned base. a rigid base gives k=2.5
these values make sense if you draw your buckled shape. the tip to crest distance will be approximately 1/2 of your effective length.
thanks for all the input.
tomfh, i agree with your values. i ran a model to determine the section displacement due to a lateral load applied at the tip assuming that this deflected shape would approximate the buckled shape. using tip to crest distance as 1/2 of the buckled length gave approximate values of k=2.75 (pinned) and k=2.58 (fixed).
is the mid-support constrinaing lateral deflections in both directions (x- and y-, assuming z- is along the column) ?
the mid-support is restraining in one direction only. cross-bracing restrains the post in the other lateral direction so that the k-value is 1.0.
if the column is fixed at the ground, isn't k=2 (assuming that you use k as l' = (l/k)^2.
if the mid-support is effective in one lateral direction only, is there something different happening between the two directions (loads?, geoometry?) ?  if there isn't, then does this mid-support affect the column buckling at all ?