AISC LRFD Deisgn of Slender HSS Column
AISC LRFD Deisgn of Slender HSS Column
(OP)
Has anyone come across a problem with calculating the reduced effective width be of a rectnagular section neede for deriving the Q factor used in assessing the compression capacty of a rectangular HSS section. I cannot find any literature which addresses this thoroughly enough.
I rever to:
HSS 10x2x1/4
lambda_b (b/t)wall slenerness of 5.6
lambda_h (h/t) wall slenderness of 39.92
Pu = 0.87 kip
Ag = 5.24 in*in
Non Compact wall slenderness lambda_r=1.4 SQRT(E/Fy) = 35.2
hence, Lambda_h > lambda_r
hence, in acccordancwe with HSS provisions for LRFD design - see p.16.2-6 LRFD 3rd Edtion, Section 4.2., EQ 4.2-7
be= 1.91*t*SQRT(E/f)*((1-(0.381/lambda_b)*SQRT(E/f))
f = Pu/Ag = 0.166ksi
E= 29000 ksi
I always get a NEGATIVE value of be that is 100 times or so larger than b. I can only get teh equation to work if the lambda_b value i ssomething like 200 which is crazy.
For the current values
lambda_b gives -5118.001 in !!!!!
lambda_h gives -5555.917 in !!!
I ahve checked noth the 2000 and 1996 HSS specificaitons produced by AISC and they are the same for this equation!
Any help would be apreciated!
thanks
I rever to:
HSS 10x2x1/4
lambda_b (b/t)wall slenerness of 5.6
lambda_h (h/t) wall slenderness of 39.92
Pu = 0.87 kip
Ag = 5.24 in*in
Non Compact wall slenderness lambda_r=1.4 SQRT(E/Fy) = 35.2
hence, Lambda_h > lambda_r
hence, in acccordancwe with HSS provisions for LRFD design - see p.16.2-6 LRFD 3rd Edtion, Section 4.2., EQ 4.2-7
be= 1.91*t*SQRT(E/f)*((1-(0.381/lambda_b)*SQRT(E/f))
f = Pu/Ag = 0.166ksi
E= 29000 ksi
I always get a NEGATIVE value of be that is 100 times or so larger than b. I can only get teh equation to work if the lambda_b value i ssomething like 200 which is crazy.
For the current values
lambda_b gives -5118.001 in !!!!!
lambda_h gives -5555.917 in !!!
I ahve checked noth the 2000 and 1996 HSS specificaitons produced by AISC and they are the same for this equation!
Any help would be apreciated!
thanks






RE: AISC LRFD Deisgn of Slender HSS Column
2.64 ksi is a very low stress and probably runs off the chart for the equation as most stresses in economical designs are closer to the 0.4 to 0.6 times Fy. For HSS with Fy = 46 ksi, a "normal" design would be in the range of 18.4 ksi to 27.6 ksi. Your stress of 0.166 ksi is very very low.
If you calculated f = 25 ksi (as an example), then the equation for the b/t = 39.9 results in
be = 10.22" - which is greater than b = 9.29" (39.9 x .233")
So you'd use be = 9.29" for the long sides.
For the short sides, the equation zeros out so the effective width of those is zero.
So your total effective widths would be 2 x 9.29 = 18.59 inches. Taking that times 0.233" thick - effective area = 4.33 sq. in.
Q = 4.33 / 5.24 = 0.8268
Fcr = 0.8268(0.658(.8268)(λc^2)46
This is my initial take on it. It does look that the equation goes negative pretty easy so I guess you assume that you can't have a negative and so you get 0 in those cases.
I think your specific problem is the low stress - 0.166 ksi.
RE: AISC LRFD Deisgn of Slender HSS Column
The way this equation "blows up" for small values of "f", which doesn't really make sense, suggests to me that the be equation is empirical. Does any know if this is true? I would just follow the note and for b/t<50 and Fy<50ksi use f=Fy.
RE: AISC LRFD Deisgn of Slender HSS Column
thanks for the response. It seems to me that AISC needs to add an extra clause to this equaiton to stop it blowing up. Unless, what UcfSE is referring to some additional clause/note that would allow me to bypass this slender wall requirement. UcfSE; where is the note re: b/t<50 and Fy <50ksi you are referring to in the AISC 3rd Manual? I didnt see such a note in the manual for the Section 4.2., EQ 4.2-7
cheers!
RE: AISC LRFD Deisgn of Slender HSS Column
UcfSE - I agree - the short sides going to 0 and the long sides counting for something doesn't seem to be logical.
RE: AISC LRFD Deisgn of Slender HSS Column
cheers
RE: AISC LRFD Deisgn of Slender HSS Column
When you think about it, a larger stress should cause more of a section susceptible to local instability to buckle more. At very low stresses no instability should be observed. After all, if there is little or no stress on an element there is nothing to make it buckle. A larger stress should cause more of an element to buckle, starting farthest from its support. In the case of a rectangular HSS, that is in the middle of the element. Given that, using a larger stress to calculate effective properties should be more conservative. The draft version of the 4th edition LRFD gives those limits on Fy and b/t and states that within these parameters, using f=Fy yields conservative results that are about 9% off. Using f=Fy is also much easier than iterating using f equal to its real value. Once you have your effective section properties, you have to go back and re-evaluate your Qa with a new f. That can potentially take a long time and for 9% I doubt it worth it unless it really has to work.
RE: AISC LRFD Deisgn of Slender HSS Column
RE: AISC LRFD Deisgn of Slender HSS Column
So I guess in reality I should have used the limiting non-compact value for compression AND flexure acting simultaneously, the provosions in the HSS specificaiotns of the LRFD 3rd edition gives a higher value. Something like 3 times more. So, I guess the "blowing up" of the equaiton due to a snall value of f will not occur as my wall slenderness limit is not exceeded for case of compression and flexurem and I dont need to reduce Q.
cheers
RE: AISC LRFD Deisgn of Slender HSS Column
Regards,
chichuck
RE: AISC LRFD Deisgn of Slender HSS Column
can you direct to where that note for the substitution of F?
cheers
RE: AISC LRFD Deisgn of Slender HSS Column
It is in the new combined spec, section E7.2(b). I found it on page 43 of the new spec, right after they have Eq. (E7-18). Its in a grey bar near the top of the page.
regards,
chichuck
RE: AISC LRFD Deisgn of Slender HSS Column
F has also been revised and is now given by Pn/Ae isnatead of teh previous HSS specifcaitons of Pu/Ag. f is now an iterative calculaitons as be and f are dependant on one another.
Unfortuantelt when i set f to Fy I still got teh equaiton to blow up for the calculaiton of be :(
RE: AISC LRFD Deisgn of Slender HSS Column
That expression assumes you are designing an HSS compression member for near its full design capacity. For very small loads over large gross areas, local buckling of stiffened slender elements may not occur and the expression begins to fall apart.
However, further guidance is available in Section E7.2 of the 2005 AISC Specification (a free download from www.aisc.org/2005). One can use f = Fy, and that will result in a slightly conservative estimate of column capacity.
RE: AISC LRFD Deisgn of Slender HSS Column
I guess the answer is to only use this expression for "be" when you have a member being designed purely in compression, where here the wall limits would not requries you to calculate "be" for such a small axial load.
RE: AISC LRFD Deisgn of Slender HSS Column
RE: AISC LRFD Deisgn of Slender HSS Column
RE: AISC LRFD Deisgn of Slender HSS Column