AISC Design Guide 1 - Appendix B

[Jerehmy]

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 > e_kern. I for the life of me cannot figure out where the error is.

P_u = 110.55 kip
M_u = 47 kip-ft
B = 20 in
N = 16 in
N' = 14.5 in
A' = 6.5 in
f_pn = 2.224ksi (nominal concrete bearing capacity)

e = M_u/P_u = 5.102 in
e_kern = N/6 = 2.667 in

e > e_kern, thus large eccentricity moment

A = 0.5 * (3N` ± [ (3N`)² - 24(P_uA` + M_u)/(f_pnB) ]^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)

T_u = f_pnAB/2 - P_u

f_pnAB/2 = (2.224 ksi)(4.428 in)(20 in)/2 = 99.5 kip

T_u = 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.

 

[BadgerPE]

In A, should Mu be in k*in vs k-ft?

 

[Jerehmy]

yes, I use mathcad so it automatically does it. I also cerified mathcad on the calculator but I should have shown it above.

 

[BadgerPE]

I wonder if there is no error, but rather due to the axial force being so large, the anchors are really in compression. If you look at Example B.5.2 the eccentricity is higher than yours with a lower axial force and smaller base plate dimensions. This resulted in a "small" anchor tension demand of 12k.

 

[BadgerPE]

If you play around with your Mathcad design by lowering Pu, there should be a point when the anchors do go into tension.

 

[Jerehmy]

The point is, based on the design guide, the anchors should be in tension whenever e > e_kern. The anchors here are NOT in tension even though e > e_kern. That's the issue.

 

[Leftwow]

What size is your beam? I made a spreadsheet for the aisc designguide one

 

[Leftwow]

After messing around with the values you gave, the largest controlling factor I noticed was beam size. If I go with a 10 inch depth and a 10 inch bf I'm having no bolt tension, however, if I go 8 inch and 8 inch, it gives me 28.77 kips of tension

 

[Jerehmy]

The anchor rod tension is independent of the beam size, so use whatever one you want. Let me know what you find.

Also, this is triangular distribution method. It works fine with the uniform distribution method.

 

[BadgerPE]

Yeah I am stumped a bit too. Reducing B to 10 in puts the AB in tension, but that is all I have found. Have you asked AISC yet? I am wondering what their response would be.

 

[Leftwow]

Ah I C now, B.5.2, will take me a while to work it out.

 

[DaveAtkins]

I don't have that Design Guide, but it is possible to have zero tension in anchor rods, even if the load is outside the Kern limit. If the resultant vertical force is still within the base plate, there will be triangular bearing pressure below the base plate, but no tension in the anchor rods.

DaveAtkins

 

[Jerehmy]

David, if that's the case, then the design guide had a glaring error because it explicitily states that if the eccentricity is outside of the kern then there will be tension in the anchor rods.

 

[Leftwow]

Jerehmy, my A formula is different. It comes from the 2006 design guide, which is the latest. I attached my formula, let me know if you can't see it.

 

[DaveAtkins]

Then I disagree with the Design Guide--to a point. Until the triangular bearing pressure exceeds the capacity of the concrete, there is no need to use the anchor rods in tension. At some point, the resultant load will get too close to the leading edge of the base plate, and the anchor rods will be needed to prevent the bearing capacity of the concrete from being exceeded.

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

 

[BadgerPE]

Dave,

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?

 

[Jerehmy]

Dave, I'm aware of the similarities to spread footings, but I think the equations were set up in a way that you should always get tension when the eccentricity is outside the kern. That's why it makes no sense.

 

[DaveAtkins]

BadgerPE has a good point. Perhaps in reality, when the load is outside the Kern, the anchors go into tension and the bearing pressure at the leading edge is less than the allowable bearing pressure. I think if the Design Guide is not making sense, use statics to figure out what is really happening.

DaveAtkins

 

[BadgerPE]

Jerehmy,

Did you come to a resolution on this issue?

 

[structSU10]

I entered this into RAM baseplate. they have a check box for 'enforce strain compatibility' - if you leave this unchecked it uses AISC DG1 equations to determine the bearing and anchor tension. In this case, it said it could not converge using the AISC method and turned strain compatibility on. It has to do with the fact that the maximum bearing pressure is assumed at the leading edge, which for some reason blows up the equilibrium computation.