A frame question

[JStephen]

See the attached diagram. A larger beam is supported by two smaller columns, which in turn are pinned at the bases. When the larger beam is loaded, you get a certain amount of end rotation which in turn induces moments in the columns. The problems I'm running into are that when the height H is reduced, it actually increases the moment in the columns due to their increased stiffness. And trying to upsize the columns to the required strength just increases the moment.

The pinned connections are actually anchor points to a foundation. If one of those anchor points can slide about 1/16 of an inch, it eliminates the moment in the columns. Is it an acceptable design solution to assume that this happens? For that matter, if the the columns yield in bending, it shouldn't hurt anything. Any comments or suggestions here?

 

[csd72]

Are you checking the moment in the column at the bottom of the beam or at the beam center? It should be at the bottom.

 

[hokie66]

As you are connecting the beam to the column flanges, design the column for the vertical load combined with the moment from the connection. This will not change with the deflection of the beam, but the eccentricity will increase slightly with column deflection.

 

[civilperson]

Model the ends of the beam as simple,(pinned), connections. Use shear tabs to the web of the beam sufficient for the shear. Takes the column out of the flexure region on the column interaction diagram.

 

[JStephen]

csd72- I was checking moment at the beam center; that will help some to check at the bottom of the beam.

hokie66- I think what you're saying is what I was already doing.

civilperson- I was trying to avoid having to brace for lateral loads which is why the connections weren't already pinned.

 

[JStephen]

Looking at it some more, I think checking the moment at the bottom of the beam instead of the center will be enough to make things work out. Thanks for the input.

 

[civilperson]

Your columns must have an interaction diagram with greater strength than the bending and axial loading imposed. The location vertically in the beam means nothing. Extreme fiber at the top and the bottom are where yield will occur.

 

[apsix]

civilperson
For a moment connection the actual maximum moment in the column is located at the beam bottom flange, which is less than that by modelling at the member centrelines.

 

[civeng80]

Just as a matter of interest why is the design moment at the bottom of the beam rather than at centreline of the beam?

 

[GalileoG]

I have the same question as civeng.

I have always done it to centerline.

 

[apsix]

For a rigid connection the column is stiffened by the beam above the level of the bottom flange and therefore will not fail in flexure there. Critical flexure will then occur at bottom flange level, if it is a typical frame with maximum moment at the column-beam connection.

 

[civeng80]

Makes sense, thanks apsix !

 

[csd72]

This also actually works for a bolted connection as well.

The reasonining is a little different though.

When you design the connection you treat the beam as if there is a horizontal force at each flange giving a moment couple. The coonection formulii used in portal knee connection design are based roughly on this truss analogy.

now if you apply these two forces to the column with a support at the base you get a triangular moment distribution that is largest at the bottom of the beam and tapers off to zero at the top and bottom of the column.

 

[JAE]

And another way to look at it: Hooke's Law.

Basically, the length of column across the depth of the beam is most likely connected with angles or plate such that the column will not bend along the depth of the beam.

If a member doesn't bend, there is no stress and thus no corresponding moment.

 

[asixth]

If your attached sketch is to scale, it looks to be a very strong beam and weak column, despite the fact the columns are short, not much moment should be transferred from beam to column in frame action. Despite this, the columns are small, so they won't have much capacity in flexure.

I have always modelled and designed to centreline, however, as csd and others have indicated, the push-pull of the beam flanges will result in the greatest bending moment of the column at the level of the bottom beam flange.

However, you mentioned that you are relying on frame action to resist lateral forces, may I asked how the frame performed with respect to drift?

 

[miecz]

JStephen said in the OP, "when the height H is reduced, it actually increases the moment in the columns due to their increased stiffness." With that in mind, I would think that checking the moment at the bottom of the beam would increase the moment. as "H" is now to the bottom of the beam, rather than to the middle.

 

[csd72]

miecz, no H remains the same in the analysis.

Well actually if you want to be really specific you can provide rigid offsets to the face of column and bottom of beam. But it wont make much difference.

 

[apsix]

miecz does raise an interesting point; how accurate is the analysis when the beam depth is significant compared to the column length?
Perhaps the use of rigid offsets will make a difference and will result in better accuracy.

 

[miecz]

csd72-

The difference may not be much, but I would expect the column moment to increase. Perhaps my intuition is wrong (again). I'll have to run some numbers.

 

[csd72]

miecz,

In this case you are probably right.