Column strength for member loaded near the base.

[EngDM]

When sizing a typical column, without any intermediate beams, is taken as full height. In my hypothetical scenario I have a 10m tall non-bearing column thats considered pinned-pinned. The load is applied at 1m from the base. Is the unbraced length for calculating strength taken as full height still (the applicator of load may brace it in one direction, but for arguments sake lets say it doesn't)? I can't imagine that the column could start to buckle above where the load is applied and the axial column load is essentially zero.

I was referencing thread507-453669 and have picked up a copy of the book mentioned by CANPRO but it doesn't arrive until later next week. CANPRO mentions that k is what would change, but the equation for the nomograph doesn't appear to be based on where the load is applied.

 

[Eng16080]

Intuitively, it seems to me that designing the column as if it were 1m tall and pinned at both ends and braced at the point of load application should be adequate and perhaps a little conservative.

As I see it, the column would have to be in compression to buckle, and that would not be the case above 1m.

 

[Just Some Nerd]

I'd design it as a 1m tall column fixed at the base, no restraint at the top. The self weight of the column above 1 metre can be taken as an additional applied load at the 1 metre height. I've never actually had to deal with this scenario in my work so I wonder

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Why yes, I do in fact have no idea what I'm talking about

 

[human909]

In interesting question. It would nice to see work out the closed form solution if it exists. The shape is a skewed half sine wave so it states to get challenging.

I will point out that both the above answers are not conservative given the problem posed. Assuming it is braced at 1m when it isn't (as state) is unconservative. Also assuming a base fixity can be unconservative when there is none. (Of course we are currently dealing with a hypothetical here, most columns have baseplates which behave in a semi-rigid fashion under axial compression.)

As I see it, the column would have to be in compression to buckle, and that would not be the case above 1m.

The entire column will participate in the buckling. The member doesn't need to be in compression nor does it even need an explicit force in the section to participate in the buckling change of state. Maybe this sort of thinking is what originated the inflection as a brace point fallacy.

All this can be readily shown using your favourite buckling analysis approach. Software is a great help but also if you start drawing buckling shapes you'll or even playing with a ruler or sheet of paper you can see the buckling shapes form for yourself.

 

[Smoulder]

Agree with Human909. I would do a software buckling analysis. That will be much easier than any hand method. But if need to do it by hand I'd try this way.
1) Take L=1m.
2) Take rotational stiffness at the 1m point equal to stiffness of the 10m column with concentrated torque at the 1m point. Similar for lateral stiffness using point load.
3) Use charts to get K for braced and sway conditions for the 1m column. Calculate the two elastic buckling loads.
4) Interpolate elastic capacity based on ratio of lateral stiffness from step 3 to stiffness required to be considered fully braced.
5) Turn elastic capacity from step 4 into design capacity using column curve.

 

[Just Some Nerd]

Also assuming a base fixity can be unconservative when there is none.

I wouldn't be assuming the fixity at the base, my line of thinking was designing the base connection for it explicitly. I'm generally a concrete kind of guy so I'm not actually sure that sort of fixity works with baseplates and watnot

 

[human909]

I wouldn't be assuming the fixity at the base, my line of thinking was designing the base connection for it explicitly. I'm generally a concrete kind of guy so I'm not actually sure that sort of fixity works with baseplates and watnot

Fair call. You did clearly say that that would be your design approach rather than your assumption. Sorry for my misinterpretation.

In many ways this question and this topic is an edge case and not vitally important. On the other-hand, it can highlight the legacy approaches to buckling which used a buckling length for simplicity this approach focusses on simple idealised solutions and tweaks them to suit. How applicable this is to modern engineering when you can calculate actual critical buckling loads much easier is a great topic of discussion.

 

[EngDM]

The entire column will participate in the buckling. The member doesn't need to be in compression nor does it even need an explicit force in the section to participate in the buckling change of state. Maybe this sort of thinking is what originated the inflection as a brace point fallacy.

Off topic to the original discussion, but this is the best laymans reason I've heard for inflection point as a brace point.

How applicable this is to modern engineering when you can calculate actual critical buckling loads much easier is a great topic of discussion.

For instance, a steel brace bay connection is provided 6" from the top of baseplate instead of connecting to the baseplate and column itself. When designing the column this additional axial load (and bending of course) could not have been checked. Of course during the shop drawing review this should be caught and revised, but say it wasn't.