AISC Design Guide 1 - Appendix B
AISC Design Guide 1 - Appendix B
(OP)
I have spreadsheets for both methods from AISC Design Guide 1 edition #2. I sent the triangular distribution method to a friend and he found an interesting situation where the anchor rod tension is negative even though e > ekern. I for the life of me cannot figure out where the error is.
Pu = 110.55 kip
Mu = 47 kip-ft
B = 20 in
N = 16 in
N' = 14.5 in
A' = 6.5 in
fpn = 2.224ksi (nominal concrete bearing capacity)
e = Mu/Pu = 5.102 in
ekern = N/6 = 2.667 in
e > ekern, thus large eccentricity moment
A = 0.5 * (3N` ± [ (3N`)2 - 24(PuA` + Mu)/(fpnB) ]0.5)
A = 0.5 * ((43.5 in ) ± [ (43.5 in)2 - 24((110.55 kip)(6.5 in) + 47 kip-ft)/((2.224 ksi)(20in))]0.5)
A = 39.072 in ; 4.428 in (4.428 in is obviously correct one)
Tu = fpnAB/2 - Pu
fpnAB/2 = (2.224 ksi)(4.428 in)(20 in)/2 = 99.5 kip
Tu = 98.5 kip - 110.6 kip = -12.1 kip
Can't figure out why. I thought it might be an error calculating A but I have triple checked it.
Pu = 110.55 kip
Mu = 47 kip-ft
B = 20 in
N = 16 in
N' = 14.5 in
A' = 6.5 in
fpn = 2.224ksi (nominal concrete bearing capacity)
e = Mu/Pu = 5.102 in
ekern = N/6 = 2.667 in
e > ekern, thus large eccentricity moment
A = 0.5 * (3N` ± [ (3N`)2 - 24(PuA` + Mu)/(fpnB) ]0.5)
A = 0.5 * ((43.5 in ) ± [ (43.5 in)2 - 24((110.55 kip)(6.5 in) + 47 kip-ft)/((2.224 ksi)(20in))]0.5)
A = 39.072 in ; 4.428 in (4.428 in is obviously correct one)
Tu = fpnAB/2 - Pu
fpnAB/2 = (2.224 ksi)(4.428 in)(20 in)/2 = 99.5 kip
Tu = 98.5 kip - 110.6 kip = -12.1 kip
Can't figure out why. I thought it might be an error calculating A but I have triple checked it.






RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
Also, this is triangular distribution method. It works fine with the uniform distribution method.
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
DaveAtkins
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
Think of a spread footing with a moment. The load CAN be outside of the Kern limit, as long as the allowable bearing pressure under the footing is not exceeded.
DaveAtkins
RE: AISC Design Guide 1 - Appendix B
For your spread footing analogy, wouldn't a load outside of the kern result in the foundation "lifting" off of the soil on the back side? If a base plate tries to rotate because the load is outside of the kern, wouldn't the anchors then go into tension?
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
DaveAtkins
RE: AISC Design Guide 1 - Appendix B
Did you come to a resolution on this issue?
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
BA
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
BA
RE: AISC Design Guide 1 - Appendix B
Mu = 47'k or 564"k
e = 564/110 = 5.13"
Effective width = (8-5.13)3 = 8.61"
Average pressure = 110/8.61(20) = 0.6388ksi
Maximum pressure = 1.28ksi
Minimum pressure = 0
Check
C = 0.6388(8.61)20 = 110k
M = 110(8 - 2.87) = 564"k = 47'k
This means the bolts are not stressed and the triangular pressure diagram extends over 8.61".
BA
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
A=[f+/-(f^2-4*f*B*(P*A'+M)/6)^0.5]/(f*B/3)
It looks like the equation you are using is similar but has been edited algebraicly. The algebra appears to have lead to the answer.
RE: AISC Design Guide 1 - Appendix B
I didn't use the equation in the design guide; it's at the top of page 58. I am attaching a pdf of it. It doesn't seem to yield the correct answer, but I haven't really checked it thoroughly yet.
I found that A = 8.61" based on the fact that the eccentric load occurs at the kern of an area measuring 8.61" x 20". The pressure varies from 0 to a maximum of 1.28 ksi.
BA
RE: AISC Design Guide 1 - Appendix B
I also derived it but I am getting the same answer as Jerehmy.
Jerehmy,
I think that the issue maybe the bearing pressure.
I think the pressure used in the equation may the allowable bearing pressure (f_allow). Can you confirm?
Should the pressure be the applied pressure and not the allowable pressure?
Applied Pressure from Moment - maximum magnitude at edge
f_m = (6*M)/(B*N^2) = 0.661 ksi
Applied Pressure from point load - evenly distributed
f_p = P/(B*N) = 0.345 ksi
Max Applied Pressure
f_max = F_m + f_p = 1.006 ksi <= 2.224 psi = f_allow
Using f_max instead of f_allow yields the following:
A = 12.224"
Tu = 161.3 kip
It is worth noting that the value of Tu is greater than if it was calculated as a simple couple between two anchors (not what I was expecting).
tension from simple couple between anchors
Tu = (N'/2 + e)*P/N' = 94.2 k
RE: AISC Design Guide 1 - Appendix B
P = 110.5k
fp = 2.224ksi
N = 16", B = 20"
If the volume of the stress block is equal to Pu
i.e. 2.224AB/2 = 110.5
so A = 110.5*2/2.224(20) = 4.97"
e = N/2 - A/3 = 6.34"
The base plate can handle an ultimate load of 110.5k at an eccentricity of 6.34" without relying on tension in the anchor bolts.
The kern of the plate is at N/6 = 2.67" from the center of plate.
The actual eccentricity, e = 47*12/110.5 = 5.1"
Conclusion:
The kern of the base plate is not where the AISC method starts to apply. The proper location is at an eccentricity of N/2 - A/3 when A is calculated assuming the compression block carries the total load by itself without help from the anchor bolts. If the eccentricity exceeds that, the AISC method works properly.
BA
RE: AISC Design Guide 1 - Appendix B
the value 'fpn' given was defined as follows:
fpn = 2.224ksi (nominal concrete bearing capacity)
I do not think the 'bearing capacity' is appropriate to use.
What if the column overturns prior to inducing the maximum bearing pressure of 2.224 psi?
I think the bearing capacity is a design constraint, the applied pressure cannot exceed the bearing capacity, but the actual load analysis should be based on the applied loads.
RE: AISC Design Guide 1 - Appendix B
That is not possible with four anchor bolts present. Failure cannot occur until two bolts are stressed to their yield point and the ultimate compressive stress is reached under the opposite end of the base plate.
I agree; applied loads for ASD, factored loads for LRFD. In my earlier analysis I found the maximum pressure fp to be 1.28ksi, less than 60% of fpn.
BA
RE: AISC Design Guide 1 - Appendix B
I think it is unlikely that the anchors and the concrete bearing will reach failure at the same time. The anchors may or may not fail first. The anchors if very weak could fail before the bearing strength is reached.
The equation for e_kern is derived using the 'Applied loads'. The reason the tension is coming out negative is because the stress used in the original question is not the applied stress but the bearing capacity. See quote below.
RE: AISC Design Guide 1 - Appendix B
The reason the tension is coming out negative is explained in the attached pdf file.
BA
RE: AISC Design Guide 1 - Appendix B
I do not think this is always true. What if there is anchor pullout or breakout?
What if there was not an applied moment? Is the bearing pressure the concrete bearing capacity or is it P/A?
Applied stress:
σ_a = P/A; not f_allow (axial load)
σ_b = M/S; not f_allow (flex Ural load)
If there is combined loading
σ_a +/- σ_b = P/A +/- M/S
E_kern is defined as the location the load acts (e = M/P) that causes the magnitude of the stress distribution at the bolt side of the base plate to be zero
σ_a - σ_b = P/A - M/S = 0
Therefore P/A = M/S
P/(N*B) = P*e/(B*N^2/6)
Solving for e
e=e_kern=N/6
The triangular stress on the concrete used must be caused by 'Applied Loads', using the bearing capacity will lead to ubconservatice tension loads in the anchors.
I am only questioning, because I want to understand why I am incorrect, if I am.
RE: AISC Design Guide 1 - Appendix B
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: AISC Design Guide 1 - Appendix B
With no moment, the actual bearing pressure is P/A and the factored bearing pressure is Pu/A
The above is true when the bearing stress is covering the entire area of plate, but that is not the range that we are considering in this discussion.
That is true, but it is the same principle we use in determining the required area of reinforcement in a concrete beam. The difference is that in a beam, we use a Whitney stress block whereas in the AISC guide, a triangular stress block is used. It is certainly a point which could be argued as noted in Section B.1 Introduction to Appendix B.
As well you should. You are not necessarily incorrect and you are entitled to use more conservative assumptions in determining the tension force in the anchor bolts if you wish.
My only goal was to explain why the tensile force in the OP's example turned out negative, so I did not quarrel with the basic assumptions made by AISC. In actual fact, there may be several contentious points in the proposed method.
BA
RE: AISC Design Guide 1 - Appendix B
If Appendix B does not work for all situations, they should say so. Also, to quote the design guide "B.4.2 Design Procedure for a Large Moment Base - When the effective eccentricity is large (greater than ekern), there is a tensile force in the anchor rods due to the moment." If this isn't always the case, they should have a corollary to the equations.
The reason it doesn't work is because of B, it's too wide. Maybe it's because the equations they use for kern distance are elastic equations and the design equations are plastic/failure equations?
Seems the ekern only works with square plates, which is fine butthey should change the verbiage in the Appendix to indicate this is so or change the equation for when eccentricity counts as large v small moment.Just for reference, it doesn't count as large eccentricity per the new design method which has:
ecrit = N/2 - P/(2*qmax) = 6.76in > e = 5.108in
RE: AISC Design Guide 1 - Appendix B
Agreed. I think they overlooked that fact.
I agree that B = 20" is too wide, but that is not the reason it doesn't work. It doesn't work because e < ecrit = N/2 - 2Pu/3B.fpn = 8 - 110.5/(20*2.224) = 6.34" which I showed in a pdf attachment earlier.
The actual e = 47*12/110.55 = 5.10" which is less than 6.34". If the anchor bolts are considered a reaction, it stands to reason they would be in compression when the load falls between them and the centroid of concrete compression. The force T would be 110.55*1.24/(6.5 + 6.34) = 10.7k compression while the force C would be 110.55*(6.5 + 5.1)/12.84 = 99.9k and C + T = P as expected.
Pete600 would object to the "new" design method even more than the AISC suggestion, but it appears more in keeping with the usual concept of limit design.
BA
RE: AISC Design Guide 1 - Appendix B
I am unsure of the spirit of this comment, but I do not object to either design method.
The original question was why is the anchor in compression, when e_kern says it should not be.
I still believe my original conclusion is correct. Using the triangular design method noted (not the only the acceptable method) the bearing stress should be the applied bearing stress not the allowable bearing stress.
I was unable to open the MathCad spreadsheet.
See MathCAD spreadsheet in link.baseplate
RE: AISC Design Guide 1 - Appendix B
AISC has said it shouldn't and it seems you are saying that it shouldn't, but e-kern is not the critical value of e which determines whether or not the anchor rods are in tension or compression.
Consider a footing A by A with a load P at its kern point, i.e. A/6 from center. The bearing pressure will vary from 0 to 2P/A. Now, suppose P is placed at A/3 from center which is outside the kern point. The new position is still a kern point, but not of the whole footing. It is a kern point of only half of the footing; there is no pressure over half of the footing, then it varies from 0 to 4P/A. Provided 4P/A does not exceed permissible soil bearing pressure, that is considered acceptable to many engineers (although there are some who insist on staying within the kern of the whole footing).
I don't dispute your claim if you insist upon using elastic design but I think AISC are looking at more of an ultimate strength criterion.
BA
RE: AISC Design Guide 1 - Appendix B
RE: AISC Design Guide 1 - Appendix B
BA
RE: AISC Design Guide 1 - Appendix B
1) As discussed above, the AISC procedure represents an ultimate capacity condition and assumes non-linearity and some degree of plastic behavior (the anchors if not the concrete). In comparison, the kern business is predicated upon a linear elastic stress distribution. The two procedures were never destined to jive. Shame on the design guide for suggesting otherwise.
2) As discussed above, "the problem is B". I've considered this hypothetically in detail C below where I've studied the case of a base plate with an infinite B dimension. In that scenario, the concrete compression block reduces to a line of resistance at the leading edge of the base plate. Clearly, for any eccentricity that would put the applied load over the base plate, the anchor bolt tension would be negative.
3) I believe that BA's sketch (below) does not represent the eccentricity at which we would first expect tension in the anchor bolts. Rather, his sketch represents the eccentricity at which no additional ultimate capacity could be gained without tension in the anchor bolts. There's an important difference there.
4) I think that the kern business actually would be a pretty good predictor of the eccentricity at which bolt tension would first manifest itself. See detail A below (classic presentation where the kern is based on the base plate perimeter). A modified version of the kern concept based on the anchor bolts (detail B below), would produce more accurate results still.
5) There must be a range of eccentricity somewhere between my detail B and BA's detail where the anchor bolts are in significant tension but the ultimate procedure would not indicate any design tension demand. That's a little disconcerting.
6) Of the misleading things built into the AISC design guide, the most misleading has not yet been discussed. The ultimate capacity procedure often implies anchor bolt strains in the post-yield range. And anyone who's dabbled with appendix D knows that an embedded anchor's ability to develop it's plastic capacity is anything but given in many cases.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: AISC Design Guide 1 - Appendix B
I agree with the above statement. Using an elastic analysis, tension will occur in the anchor bolts whenever strain exceeds zero. Using an ultimate strength approach, coupled with a triangular stress distribution proposed by the AISC Design Guide, anchor bolt tension is not needed until the eccentricity exceeds N/2 - x/3.
BA