Calculating Thickness of Base Plate

[MrFurleyEIT]

I am trying to determine all the possibilities for the hickness of a column base plate, t (ASD Method) for axial loads only without any substantial moments. The AISC Manual 9th Ed on Pg. 3-106 provides that t be the larger of or {2m or 2n} * SQRT(fp/Fy). My CERM 8th Ed also states that this is also equal to {m or n} * SQRT (3fP/Fb), where Fb, tensile bending stress, = 0.75 Fy. I am cool with this.

My CERM also states that if m or n are small, then t = L * SQRT(3 * fp/Fb) must also be checked. L has to be solved from an quadratic equation, Fp = P/A = P/(2L * (d + b - 2L)). Even though this is more tedious and less frequently encountered, I am also cool with this.

However, I have come across other calculations for t that I am not very clear about. Two such ones are from the "green book" that states that tp = 2 * n' * SQRT (fp/Fy) and tp = 2 * lambda * n' * SQRT (fp/Fy). While the note for these equations state that these equations are for more heavily loaded small plates, how do we decide when to use them? Hope someone can elaborate on this. Under what conditions do we check the base plate thickness with these equations.

Another such one is from the AISC Design Guide 1, 2nd Ed which is from the AISC 13th Manual that states that t min = l * SQRT (2 * OMEGA * Pa/( Fy * B * N) where l is the max of {m or n or lambda * n'). Lambda * n' = lambda * SQRT (d * bf/4). Do we need to check for this each and every time, too?

Also, another confusing thing is the value of OMEGA. In the AISC SDG-1 on Page 32, OMEGA is given as 1.67. However, on Page 31 of the same design guide, the value of OMEGA was provided as 2.50. Can someone please explain why the discrepancy, and which value of OMEGA should I use.

Appreciate any and all responses from all of you familiar with this topic, and please provide references, page nos, and sample calcs, if possible, to help us understand why this is so. Thanks a bunch.

 

[DaveAtkins]

I think you are looking at too many different design procedures. I use only the 9th Edition ASD (the "green" book), and so OMEGA does not apply.

In the 9th edition procedure, you need not decide if the base plate is a heavily loaded small base plate--the design procedure takes care of that.

DaveAtkins

 

[dgkhan]

If you are using ASD than omega in 1.67, if using LRFD than omega is 2.5, hope your problem is solved now.

 

[JLNJ]

My favorite out of the 9th Edition is Example 13 where "Solving for L reveals L to be an imaginary number".

Nice.

 

[MrFurleyEIT]

Thanks for the quick responses, DaveAtkins, dgkhan and JLNJ, and please keep it up. Can anyone elaborate on the thickness of base calculation with the lambda and OMEGA terms, please?

dgkhan, I went back to the AISC Steel Design Guide 1, and it appears that OMEGA equal to 2.5 might not actually be when when using LFRD. On page 31 of the Design Guide, the required base plate area, a1 req'd. for LFRD is Pu/(phi * 0.85 * f'c). When using ASD, A1 req'd. is OMEGA * Pa/(0.85 * f'c). The note that follows states that: "Throughout these examples, a resistance factor for bearing on concrete of phi = 0.65 has been applied, per ACI 318-02. This resistance factor is more liberal than the resistance factor of phi = 0.60 presented in the 2005 AISC Specification. Although it was intended that the AISC provision would match the ACI provision, this deviation was overlooked, As both documents are consensus standards endorsed by the building code, and ACI 318-02 has been adopted by reference intothe 2005 AISC Specification for Structural Steel Buildings, the authors consider a phi factor of 0.65 appropriate for use in design. However, ACI 318 is written using strength design only and does not publish an equivalent OMEGA factor. Therefore, an OMEGA = 2.50 has been used in the ASD calculations presented here to remain consistent wit the value published in the AISC Specification."

So you see, the OMEGA factor of 2.50 is actually meant for the ASD calculation. However, in the calculation for minimum thickness of base plate using the ASD method on Page 32, an OMEGA = 1.67 was used. What gives? Can anyone explain this anamoly or discrepancy, please? Thanks again, everyone.

 

[BENDOG]

There are different OMEGA values depending on what you are designing. The value shown on page 31 is for column bases bearing on concrete and the value is 2.5 (also see AISC 2005 Section J8). The value shown for calculating base plate thickness is for flexure and the value should be 1.67 (see AISC F1). Also look at page 34 and you will see OMEGA = 2.0 for tensile strength of the anchor rod (see AISC D2(b).