## Rigid Base Plate Analysis - Uni or Biaxial Moments

## Rigid Base Plate Analysis - Uni or Biaxial Moments

(OP)

As extension of the profis discussion in my other thread.

When performing a rigid plate analysis:

1. Should the bolt holes on the compression side of the plate be considered as reducing the available area for compression resistance, both Design Guide 1 and Blodgett don't take the holes into account?

2. If not accounting for the holes then shouldn't the anchors on the compression side of the plate be designed for a minimum tension of the concrete stress x the hole area so that missing resultant force is accounted for?

3. How are folks back checking the rigid plate assumption, or rather how was this checked before tools like RISA Base and the new CBFEM checking in Profis? Based on some limited research I get the feeling this usually doesn't get a whole lot of attention and the plate is designed against yield stress + phi/omega factor and assumed this makes it stiff enough.

When performing a rigid plate analysis:

1. Should the bolt holes on the compression side of the plate be considered as reducing the available area for compression resistance, both Design Guide 1 and Blodgett don't take the holes into account?

2. If not accounting for the holes then shouldn't the anchors on the compression side of the plate be designed for a minimum tension of the concrete stress x the hole area so that missing resultant force is accounted for?

3. How are folks back checking the rigid plate assumption, or rather how was this checked before tools like RISA Base and the new CBFEM checking in Profis? Based on some limited research I get the feeling this usually doesn't get a whole lot of attention and the plate is designed against yield stress + phi/omega factor and assumed this makes it stiff enough.

https://github.com/buddyd16/Structural-Engineering

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## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

2) This is all pretty rough and approximate stuff so it doesn't bother me much for it to be this little bit rougher. In the back of my head, I do kind of monitor the ratio [open:solid] in the compression zone for fear of violating my

little bitassumption.3) I've seen two methods:

a) Design it not to yield as you mentioned.

b) Keep [overhanging projection < 5 x t]. Or some other integer.

While both of these methods encourages a minimum stiffness in the plate, neither explicitly guarantees a

sufficientstiffness in the plate, whatever that is.## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

I think the rigid plate assumption for base plates was always suspect - the concrete elements they bear on are almost always quite stiff - likely stiffer than the plate itself.

## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

I somewhat disagree the load path still has to go through the plate prior to entering the grout bed so my thought is either take out the hole, which seems to marginally impact the results see below, or introduce some compatibility tension in the anchors on the compression side of the plate to restore the missing hole compression which may slightly impact the overall anchor design when checking the tension group. All in all the margin of error of not accounting for the holes is probably largely out weighed by the actually flexibility of the plate anyway so probably not worth splitting hairs over. On board with most of what you said though once the load is in the grout bed it gets to the concrete surface and there will be strain/stress in those areas at the concrete.

Design Guide 1 - Example B.5.2 - W/O Holes Considered and 1" bolts:

Design Guide 1 - Example B.5.2 - W/ Holes Considered and 1" bolts:

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## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

When performing a rigid plate analysis:

1. Should the bolt holes on the compression side of the plate be considered as reducing the available area for compression resistance, both Design Guide 1 and Blodgett don't take the holes into account?

I don't, why? cause even if I consider it, its effects would be mainly a slightly longer bearing length, and bearing length is not really an issue in most cases (spending that time being very precise is not worth the trouble).

2. If not accounting for the holes then shouldn't the anchors on the compression side of the plate be designed for a minimum tension of the concrete stress x the hole area so that missing resultant force is accounted for?

Not really cause of the longer bearing length

3. How are folks back checking the rigid plate assumption, or rather how was this checked before tools like RISA Base and the new CBFEM checking in Profis? Based on some limited research I get the feeling this usually doesn't get a whole lot of attention and the plate is designed against yield stress + phi/omega factor and assumed this makes it stiff enough.

I try not to over complicate things and usually go for hand calculations (I only touch the software you have mentioned in the rarest of occasions)

## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

The spreadsheet makes heavy use of macros so you'll need to enable them for it to function. One thing that the spreadsheet cannot handle is a pure tension case I'm looking into options for that by falling back to just a standard eccentric bolt group analysis.On occasion the default general solution button will pick the wrong solver so I put in (3) buttons below that one for each solver so you can cycle them manually if need be.

Overall the sheet isn't very polished at this point and I've only back checked a handful of cases so would love any feedback from folks that try to use it.

Enhineyero:

1. somewhat agree, there may be special cases where bearing length becomes an issue

2. somewhat agree, when proceeding beyond the analysis to design the plate a longer bearing length coupled with a higher starting stress will produce higher design moments (this ultimately may be better because you would need slightly more thickness getting you closer to the rigid pl assumption)

3. I like hand calcs as well but how are you verifying the plate is rigid, criteria similar to KootK?

Another global question for the folks that are doing hand calcs for this are you doing a triangular stress distribution or doing a constant rectangular distribution similar to AISC Design Guide 1 section 3.4.

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## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

1. somewhat agree, there may be special cases where bearing length becomes an issue.

My approach when making standard calculations or programs is to design for those you will encounter 95% of the time and reserve those rare 5% to further discussion with engineers (may be in these instances use FEA or apply engineering judgement)

2. somewhat agree, when proceeding beyond the analysis to design the plate a longer bearing length coupled with a higher starting stress will produce higher design moments (this ultimately may be better because you would need slightly more thickness getting you closer to the rigid pl assumption).

No comment

3. I like hand calcs as well but how are you verifying the plate is rigid, criteria similar to KootK?

Base plate 'rigidity' is basically the bending moment capacity of a connection. (i.e. bolt failure, plate bending failure). Others also look at the amount of deformation/rotation, however, I usually neglect this as deformation of a base plate is really small.

## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

The analysis assume a triangle stress distribution and it works perfect for a uniaxial eccentricity and converge very fast since you iterate only one variable (N.A. Depth).

for biaxial eccentricity it seems reasonable to me to rotate the section in an angle equal to ATAN(Mx/My) and calculate the new coordinates (including eccentricity point) by maintaining the N.A horizontal, then solve for also one variable by using GoalSeek function, a further iteration then is preformed by using solver.xlsm to iterate the angle of rotation and the N.A. depth.

For a case where the base plate is under pure tension and biaxial moment it can be divided into two sub-cases:

1) when the tension and the moment doesn't result in plate bearing on concrete: a standard eccentric bolt group analysis.

2) when the tension and the moment result in plate bearing on concrete: the same analysis method descried above is valid

The challenge I am facing now is how to design a base plate for this, there is no guide or reference that explain how to design the base plate in case of biaxial bending, if anyone knows about a reference please share with us.

## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

I did not read in detail the previous responds. The approach with elastic analysis with the assumption of the plane sections remain plane , ignores the flexibility of the base plate , concrete and anchor bolts. Although this approach is satisfactory , does not represent real behavior of base plate and concrete. The reduction of the bolt holes on the compression side of the plate will not reduce compression resistance of concrete . Eurocode 3 approach is different and based on the effective compression area and T - stub.

I will suggest you to look to EC-3 and the following document at link= https://people.fsv.cvut.cz/~wald/CESTRUCO/Texts_of...

I uploaded the same doc.

## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

take a look at this resource: Link

This works out to be an OK starting point but the final angle needed to reach equilibrium is usually somewhere within a range of +/- 90 degrees from the load angle.

not sure I follow you here, If you are adhering to strain compatibility you end up with three unknowns Neutral Axis Angle, Length of Bearing (Neutral Axis Depth), and the Peak Bearing stress. If allow for the AISC design guide 1 method then strain compatibility is no longer followed and the peak anchor tension becomes a fourth unknown.

Agree with your approach for plates in tension, you can do an initial elastic analysis to determine if there is pure tension then switch to the bolt group analysis.

HTURKAK:

Thank you for the resource and the recommendation to look at EC-3.

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## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

2. No, see 1.

3. Ok with it as long as the plate doesn't yield. Concrete crushing strain is higher enough that I don't worry about it otherwise - do you think you are going to crush concrete below the W section before engaging the plate? Seems impossible unless you have a very tiny pier.

## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

Remove the concrete for a moment and look at a pure axial case, for equilibrium with the applied load the reaction force is just the integral of the bearing stress with respect to the plate area. If there is a hole that area is reduced and thus the resulting required pressure increases. The net result when considering the bolt holes is less than 1/8 ksi for standard 1" bolt holes so for hand design can be likely be ignored without significant impact to the design.

3. Not worried about the concrete more the dishing/cupping and prying action that would come with a flexible plate.

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## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

allowablebearing pressure at the concrete surface is unchanged.Hilti put out an ok tech background document on the rigid vs flexible topic: Link

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## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

I will elaborate more:

- First you have to calculate moment of inertia of the areas and the moment areas about the “e” line for both the bolts and the concrete area which is under compression.

- The moment of inertia divided by the moment area will then be the location of the neutral axis.

- The process iterates on the value of q until it is determined to a sufficient degree of accuracy.

- Definitions:

modular ratio = n

effective are of bolt = Ab

Abolt = n x Ab

Depth of N.A. = Y

Width of plate = B

Calculating the Area:

Area of the bolt in tension zone, Abolts = Σ n x Ab

Area of concrete in compression zone, Ac = B x Y

Total area = Abolts + Ac

Calculating the Moment of Area:

Moment of Area of concrete, Qc = Area of concrete in compression zone x (q - distance from c.g. of concrete to edge of plate)

Moment of Area of the bolts, Qbolts =

Total moment of Area, Q = Qc + Qbolts

Calculating the Moment of Inertia:

Moment of inertia of the concrete, Ic = moment of inertia of the concrete zone in compression about the line of eccentricity (e)

Moment of inertia of the bolts, Ibolts =

Total moment of Inertia, I = Ic + Ibolts

q = I/Q, then I/Q - q = 0

Where q = e + Y - Depth of the section/2

Since the method of Horn described above calculates the moment of areas and moment of inertia about the eccentricity line, the only variable in this case is the depth of neutral axis, by iterating the value of "Y" you will be able to find an exact solution which takes into account the actual concrete compressive stress and it can be calculated as shown below:

fp = P Y/(q A - Q)

In case of biaxial bending the same method can be used by rotating the section an angle θ so that the N.A. is parallel to the eccentricity line, in this case there will be two variable (The N.A. depth and the angle θ).

The challenge in this case is to create the transformed geometry of the section and to calculate the volume of the bearing pressure, it's basically just a mathematical challenge (if you need more information let me know).

Thanks for sharing, this is alternative analysis method, what I am looking for is how to design the base plate after you get the final analysis results for biaxial bending, since the pressure distribution is not constant along a slice across the width of the plate as it is the case for uniaxial bending, the design method described in D.G. 1 is not valid, there is no resources on an appropriate method to be used in this case.

Reference: Design of Monopole Bases, By Daniel Horn, P.E.

## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

I'm trying to back check it by making some assumptions and not getting right answers:

fp - assume the stress block is taken to be rectangular, constant stress over the compression region or do they assume linear stress distribution?

fp - what is A in this equation?

Q,bolts - assume this isn't the signed first moment of area, because if summing moments about the eccentricity line if using the signed first moments Q,bolts+Q,c should = 0 which leads to a div/0 error in your step of q = I/Q.

I,bolts - shouldn't Abolt here also be the transformed area, n*A,bolt

Flip the problem upside down and look at the plate as if it were a concrete slab supported by walls taking the form of the column section. Load the plate with the pressure and point loads from the tension anchors. You can then use something like the strip method in concrete or look into a yield line analysis.

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## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

Linear Distribution

Yes, probably this is something I should add to the definition to make things clear.

Abolt = n x Ab, where Ab is the net area of bolt.

They should not be equal.

Qbolts = Σ n x Ab (e - yi)

for case of uniaxial bending:

Qc = Area of bearing pressure (q - Y/2)

## RE: Rigid Base Plate Analysis - Uni or Biaxial Moments

I see where I was going astray Q,bolts and I,bolts should also include (n-1) components for the bolts within the assumed compression block.

I uploaded a new version of my spreadsheet with Horn's Example 2.4 problem and get close agreement, I only allow 9 coordinates for holes so approximated the opening with points at every 45 degrees.

Link to Sheet Download Page

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