Flexural capacity of a column with Lb>Lr (360-05)

[engco]

now I am designing a column, 11.81x0.55 in flange and 11.81x0.31 web built up element. Its flexural capacity Mn, for Lb=118 in 2984 kip-in

for Lb=236 in Mn=2578 kip-in

and for Lb=354 in Mn=1967 kip-in

but for Lb=393.7 and although this dimension is bigger than Lr, Fcr=31.51 ksi (Fy=32.63 ksi)

And this leads to a bigger flexural capacity? (Sorry for dimensions, i converted them from SI)

Fcr*Sx is bigger than a value in a zone for Lp<Lb<Lr..

am I doing a mistake?Thanks.

 

[engco]

In calculations;

i use there formulas,

Lr=pi*rts?E/(0.7Fy)

Fcr=Cb*pi²*E/(Lb/rts)²*sqrt(1+0.078Jc/Sxho(Lb/rts)²)

h = 300mm 11.81103in
b = 300mm 11.81103in
tf = 14mm 0.5511814in
tw = 8mm 0.3149608in

Used values kip-inch
E= 210000 N/mm2 29000.00
Fy= 225 N/mm2 32.63
Fu= 340 N/mm2 49.31
G= 81000.00 N/mm2 11200
bf= 300.00 mm 11.81
tw= 8.00 mm 0.31
tf= 14.00 mm 0.55
h-2c= 300.00 mm 11.81
Ag= 108.00 cm2 16.74
I1-1= 22518.88 cm4 541.0194247
S1-1= 1373.10 cm3 83.79
r1-1= 14.44 cm 5.68
I2-2= 6301.28 cm4 151.3891846
S2-2= 420.09 cm3 25.64
r2-2= 7.64 cm 3.01
Z1-1= 1498.80 cm3 91.46
Z2-2= 634.80 cm3 38.74
J= 60.00 cm4 1.44150888
Cw= 1553202.51 cm6 5783.98543
rts= 8.28 cm 3.26

 

[swearingen]

In the latest AISC code, when you are in the zone Lp<Lb<Lr, all the equation does is draw a straight line from the maximum plastic bending stress at Lp to the value of the Euler equation at Lr. This means that you will never get an Fcr at lengths over Lr greater than an Fcr at lengths between Lp and Lr. I haven't got time to check the math now, but I think you've done something wrong...


If you "heard" it on the internet, it's guilty until proven innocent. - DCS

http://www.eng-tips.com/supportus.cfm

 

[engco]

I found the answer. In spec. it is specified for the Lr value I mentioned before as "Note that this approximation can be extremely conservative".When i use the exact value of Lr, everything goes ok!. But the situation i said before is surprisingly true for the approximate formula for Lr.For your information.