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?

 

[miecz]

If I'm right, calculating the moment at the bottom of the beam has not solved the problem, but made it worse. I would try to turn the columns 90[°] to bend on their weak axis.

 

[miecz]

Also, a stiffer beam should help reduce bending in the columns, by limiting the rotatiion at the end of the beam.

 

[csd72]

miecz,

even with the increased stiffness from the rigid offset I would still be very surprised if the increase in the moment from the rigid offsets is greater than the reduction by taking it at the bottom of the beam.

 

[Lion06]

Why would taking the moment at the bottom of the beam result in a higher moment. You aren't using a smaller h, you are just taking the moment at a different location along the height, right? Or am I thinking about it incorrectly?

 

[miecz]

I'm thinking of the length of column from the bottom of the beam to the center of the beam as being stiffened by the beam, so, while H is the same, the length of column free to flex is shorter by half the beam depth. This effectively stiffens the column, drawing more moment when the end of the beam rotates.

 

[miecz]

See the attached sketch. If you model this with H=14', L=30' and x=1.5ft, I_c=I_x=999 in⁴, I_b=9040 in⁴, w₁=1.8 klf, you'll get a bending moment of 34.5 k' at points A and C, the theoretical intersection of the beam and column.

Now, if you change I_x where the column is attached to the beam, to 9040 in⁴, the moment at points E and F, representing the column at the bottom of the beam, is 39.0 k', a 13% increase. My analysis ignores shear flexibility.

 

[kslee1000]

If this is my design, I will tempted to do two things:

1. Place plate elements in between the columns (beam elements), and perform analysis.
1. Change the support mechanism, let the columns end (fixed/pinned) at bottom of the beam, perform the analysis and compare results of the models.

 

[JStephen]

Just an update- by changing where I evaluated bending stress in the columns and making a couple of minor corrections in the loading, I was able to make things work out okay.

This is actually a simplified version of a more involved assembly. Beam length is 162", height to beam centerline is about 39". Columns are pipe so rotating them doesn't help. Wind forces were pretty insignificant compared to gravity forces on the beam, so drift wasn't a problem.

Thanks for the help and the input on it.