I need to determine the bending stresses in a base plate for a circular column supported by 4 anchor bolts. The column carries a lateral load producing a bending moment through the connection. Levelling nuts raise the plate a few inches above the foundation. The connection is ungrouted, so all the forces go through the bolts. Any suggestions?
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Pole Base Plate 2
- Thread starter miecz
- Start date
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1
- #2
The guideline which most closely addresses your question that I have found is in AISC Hollow Structural Section Connections Manual.
Refer to Page 7-9, first paragraph headed AXIAL COMPRESSION LOADING. You will need to have your AISC LRFD 3rd Ed right next to you.
Hope this is helpful....
Refer to Page 7-9, first paragraph headed AXIAL COMPRESSION LOADING. You will need to have your AISC LRFD 3rd Ed right next to you.
Hope this is helpful....
Sum moments about cross sections just outside the radius of the column, in line with bolts and at 45 degrees to the bolt pattern, and you can find average moment on those cross sections.
Sum moments about a plate centerline with axial load only (applied moment will cancel out) as an additional check.
Sum moments about a plate centerline with axial load only (applied moment will cancel out) as an additional check.
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- #4
Thanks, terdburd. Unfortunately I haven't sprung for the HSS Connections manual.
Thanks, JStephen. While your suggestion gets the average bending moment, I'm not sure how to then convert that to bending stresses. It seems that the area near the bolt and the pole is stressed a lot higher than the rest of the section on the diagonal.
Thanks, JStephen. While your suggestion gets the average bending moment, I'm not sure how to then convert that to bending stresses. It seems that the area near the bolt and the pole is stressed a lot higher than the rest of the section on the diagonal.
How you convert the average bending moment to stress is to just treat it as if it was a uniform moment about that cross section, so you use Mc/I.
This is not exact, but not as terrible an approximation as you might imagine either. If the stress across that width varies from zero to some maximum, the maximum shouldn't be much more than 1.5 times the average. Try to visualize how that plate would bend if it failed. It's not going to yield in the center, but not at the edges, or vice versa. If the application is super critical, reduce your allowable stress some to compensate.
By the way, some of the older flat-plate formulas solved the rectangular flat-plate-bending problem by assuming that moment was uniform on a diagonal. So the concept is not that off-the-wall.
This is not exact, but not as terrible an approximation as you might imagine either. If the stress across that width varies from zero to some maximum, the maximum shouldn't be much more than 1.5 times the average. Try to visualize how that plate would bend if it failed. It's not going to yield in the center, but not at the edges, or vice versa. If the application is super critical, reduce your allowable stress some to compensate.
By the way, some of the older flat-plate formulas solved the rectangular flat-plate-bending problem by assuming that moment was uniform on a diagonal. So the concept is not that off-the-wall.
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- #7
JStephen,
You're right; it's a very good approximation, at least for this case. I took the time (2 hours) to model this up with finite elements, and the highest stressed elements were 1.41 times the average. Right or wrong, I like my calculations to look more sophisticated than - calculating an average and bumping the result by 50%. Can't you develop some formula, preferably containing natural logarithms, that looks more scientific? Seriously though, this is such a common application, I would have thought that someone would have studied it and developed a formulation.
You're right; it's a very good approximation, at least for this case. I took the time (2 hours) to model this up with finite elements, and the highest stressed elements were 1.41 times the average. Right or wrong, I like my calculations to look more sophisticated than - calculating an average and bumping the result by 50%. Can't you develop some formula, preferably containing natural logarithms, that looks more scientific? Seriously though, this is such a common application, I would have thought that someone would have studied it and developed a formulation.
DaveAtkins
Structural
I use the method developed in Gaylord and Gaylord. You set the compressive bearing stress at one edge of the base plate equal to 0.35f'c, and you sum moments about the two tension anchor bolts to solve for the depth of the compressive stress block (it is a quadratic equation). Once you know the volume of the compressive stress block, you sum vertical forces to solve for the tension in the anchor bolts. Many times the tension in the anchor bolts controls the bending in the plate.
DaveAtkins
DaveAtkins
- Thread starter
- #9
DaveAtkins
Structural
Then that's even simpler. There are two compression anchor bolts and two tension anchor bolts, correct? The two tension (or compression) forces added together, times the distance between the anchor bolt pairs, must equal the moment. Then the bending in the base plate at each anchor bolt is just the bolt force times the distance to the column. If there is any shear in the anchor bolts, it will cause them to bend, so they will need to be a hefty diameter.
DaveAtkins
DaveAtkins
When all things are considered and calculations performed, the final base plate size selected will be sufficiently thicker than the actual required thickness. Of course it depends on total number of plates on a given contract. If there are one or two, making it 50% thicker will not cause a impact on cost.
J1D
Structural
- Feb 22, 2004
- 259
jmiec,
Levelling nuts raise the plate a few inches above the foundation. What the a few here is? 3" or 9"? This sounds quite unusual. Without grout and shear key, all the shear from the lateral load, vertical load and the resulted bending (or torsion as well) will be taken by the bolts. You need to check the combined stress and deflection of the pole since the base will be somehow like a spring. Also check if the fatigue is a concern.
Levelling nuts raise the plate a few inches above the foundation. What the a few here is? 3" or 9"? This sounds quite unusual. Without grout and shear key, all the shear from the lateral load, vertical load and the resulted bending (or torsion as well) will be taken by the bolts. You need to check the combined stress and deflection of the pole since the base will be somehow like a spring. Also check if the fatigue is a concern.
This is a common support detail. I noticed several traffic light poles done like this on the way home.
As far as generating a generic Roark-type formula, I think there are several complications. One is the base plate will usually have a hole in the center, which could be the size of the column, or could be any size smaller. Secondly, the column itself, and the attachment details to the plate, will have some effect on the stiffness and stress in the plate. Then also, the plates usually have nuts below them and above them on the supporting bolts. While it is reasonable to treat these as point loads/ reactions, in fact, there are some moment effects there that would be difficult to analyze exactly even with FEA. I would treat the distribution of the pole moment on the plate with the MC/I equation, but that is actually only applicable away from supports on a beam, so you don't really know this distribution.
I notice it is also common to have base plates that are circular, essentially a flange, with multiple bolts, but mounted up on the bolts as you indicate.
You don't say what your application is, but there might be some design literature or standards applicable to this situation in literature dealing with either utility poles or sign/ traffic light poles.
As far as generating a generic Roark-type formula, I think there are several complications. One is the base plate will usually have a hole in the center, which could be the size of the column, or could be any size smaller. Secondly, the column itself, and the attachment details to the plate, will have some effect on the stiffness and stress in the plate. Then also, the plates usually have nuts below them and above them on the supporting bolts. While it is reasonable to treat these as point loads/ reactions, in fact, there are some moment effects there that would be difficult to analyze exactly even with FEA. I would treat the distribution of the pole moment on the plate with the MC/I equation, but that is actually only applicable away from supports on a beam, so you don't really know this distribution.
I notice it is also common to have base plates that are circular, essentially a flange, with multiple bolts, but mounted up on the bolts as you indicate.
You don't say what your application is, but there might be some design literature or standards applicable to this situation in literature dealing with either utility poles or sign/ traffic light poles.
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- #14
J1D,
The distance from the bottom of the plate to the top of the concrete is 3-1/2 inches. As there is a nut under the plate, the bolt has a clear distance of 1-1/2 inches. You're right, the bolt carries shear and resulting bending and is subject to fatigue. But I'm just focusing on the plate for now,and ignoring the fixety between the bolts and the plate.
Jim
The distance from the bottom of the plate to the top of the concrete is 3-1/2 inches. As there is a nut under the plate, the bolt has a clear distance of 1-1/2 inches. You're right, the bolt carries shear and resulting bending and is subject to fatigue. But I'm just focusing on the plate for now,and ignoring the fixety between the bolts and the plate.
Jim
- Thread starter
- #15
JStephen,
This kind of detail is very common in transportation applications exposed to weather. That's why I'm surprised that solutions aren't published in Roarke, for instance. This is a Highway application and is covered by the Standard Specification for Structural Supports for Highwy Signs, Luminaires and Traffic Signals. I can't find any guidelines in this publication for analysis for the plate.
A small hole in the center of the plate shouldn't affect things much. You're right though. Sometimes, the hole in the plate is the diameter of the pole. Yikes!
The pole is typically thin compared to the plate and welded all around. There are always nuts above and below the plate, and they do transfer bending to the bolt, but I think it's conservative to ignore this for the design of the plate.
Finally, I think a circular plate with many bolts would be easier to analyze, as the distribution can be taken as a function of the bolt spacing.
This kind of detail is very common in transportation applications exposed to weather. That's why I'm surprised that solutions aren't published in Roarke, for instance. This is a Highway application and is covered by the Standard Specification for Structural Supports for Highwy Signs, Luminaires and Traffic Signals. I can't find any guidelines in this publication for analysis for the plate.
A small hole in the center of the plate shouldn't affect things much. You're right though. Sometimes, the hole in the plate is the diameter of the pole. Yikes!
The pole is typically thin compared to the plate and welded all around. There are always nuts above and below the plate, and they do transfer bending to the bolt, but I think it's conservative to ignore this for the design of the plate.
Finally, I think a circular plate with many bolts would be easier to analyze, as the distribution can be taken as a function of the bolt spacing.
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- #16
This type of connection is also very common in the electric utility field. Try a search of this site as I know there are other threads on the subject.
Make sure you look at the worst case loading. It may be that you have one bolt in tension, one in compression and the other two are on the neutral axis. Your circular column may have the same strength in all directions, but your bolt pattern does not.
We ignore bending in the bolt if the distance from the top of concrete to the bottom of the base plate is less than 2 bolt diameters. For the type of structures we do the bolt design is governed by high structure moments and very low shear anyway.
When determining the section modulus of the base plate resisting the moment, care should be exercised in using an effective bend line which may be less than the width of the base plate. Lots of different opinions on this subject and not much research back it up. I find it funny how often the base plate thickness matches the anchor bolt diameter.
Make sure you look at the worst case loading. It may be that you have one bolt in tension, one in compression and the other two are on the neutral axis. Your circular column may have the same strength in all directions, but your bolt pattern does not.
We ignore bending in the bolt if the distance from the top of concrete to the bottom of the base plate is less than 2 bolt diameters. For the type of structures we do the bolt design is governed by high structure moments and very low shear anyway.
When determining the section modulus of the base plate resisting the moment, care should be exercised in using an effective bend line which may be less than the width of the base plate. Lots of different opinions on this subject and not much research back it up. I find it funny how often the base plate thickness matches the anchor bolt diameter.
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