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# Rigid Base Plate Analysis - Uni or Biaxial Moments4

## 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.

My Personal Open Source Structural Applications:
https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:
https://github.com/open-struct-engineer

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

1) It theoretically should be taken into account but, from what I've seen, is not.

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 bit assumption.

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 sufficient stiffness in the plate, whatever that is.

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

2
My general though on area reduction is that as long as the base plate is on a grout bed the load spread through that grout bed creates uniform pressure over that surface. I also think that due to strain compatibility, the hole technically doesn't affect the stress seen by the concrete, as the concrete below the hole isn't just going to see zero strain since it is note being contacted - it moves with the rest of the top surface. No idea how the shake the number our directly though beyond ignoring the holes.

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

(OP)
structSU10:
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:

My Personal Open Source Structural Applications:
https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:
https://github.com/open-struct-engineer

### 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

(OP)
If anyone is interested I've posted the spreadsheet I used for the screenshots here: Link

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.

My Personal Open Source Structural Applications:
https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:
https://github.com/open-struct-engineer

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

Enhineyero (my responses in red):
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

Impressive effort, I have a spreadsheet which also solve biaxial bending in base plate, I use a method developed by Horn for square base plates with a circular opening which takes into account individual bolts locations to calculate bolts tension and concrete stresses by taking sum of first moment of area for bolts and compression zone and 2nd moment of area for the same about the eccentricity line and the result of dividing the 2nd moment of area over 1st moment of area will be the distance from N.A. to eccentricity line.

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...

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

(OP)
Mohd Yousef:
take a look at this resource: Link

#### Quote:

...seems reasonable to me to rotate the section in an angle equal to ATAN(Mx/My)...
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.

#### Quote:

..a further iteration then is preformed by using solver.xlsm to iterate the angle of rotation and the N.A. depth.
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.

My Personal Open Source Structural Applications:
https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:
https://github.com/open-struct-engineer

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

1. You use a prismatic increase in bearing area, so the bolt holes do not affect the design area for bearing. For plate bending the holes have no effect on the simple beam analysis, a slightly higher bearing pressure over a slightly smaller area yields the same resultant force.
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

(OP)
Canwesteng:
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.

My Personal Open Source Structural Applications:
https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:
https://github.com/open-struct-engineer

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

Sure, remove the concrete and the pressure on the plate is higher. The pressure in the concrete is not (assuming you are using ACI or CSA codes). There is no physical way to have bearing pressure control for a steel plate in compression like this. Re: the cupping, no significant cupping can occur before plate yield. I also don't think the prying is possible with any stiffness of plate. Basically, your possible options are a-the plate is stiff enough to distribute the load over the concrete b-the plate is not and concrete crushes below the column. For some fictitious meters wide base plate with a tiny column, I guess elastic deflections could amount to enough to cause the cupping to occur, but this is so far from ordinary practice that you shouldn't be using a design guide.

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

(OP)

#### Quote (canwesteng)

Sure, remove the concrete and the pressure on the plate is higher.
I disagree the pressure on the concrete surface in those sketches is exactly the same as the pressure reacted by the plate, under the rigid plate assumption. The allowable bearing pressure at the concrete surface is unchanged.

Hilti put out an ok tech background document on the rigid vs flexible topic: Link

My Personal Open Source Structural Applications:
https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:
https://github.com/open-struct-engineer

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

#### Quote (celt83)

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

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).

#### Quote (Celt83)

take a look at this resource: Link
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

(OP)
Are you able to share the resource that has those equations noted?

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

#### Quote:

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.
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.

My Personal Open Source Structural Applications:
https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:
https://github.com/open-struct-engineer

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

#### Quote (Celtt83)

Are you able to share the resource that has those equations noted?
Design of Monopole Bases

#### Quote (Celt83)

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

#### Quote (Celt83)

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

#### Quote (Celt83)

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
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

(OP)

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.

My Personal Open Source Structural Applications:
https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:
https://github.com/open-struct-engineer

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