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

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

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

(OP)
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.

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

(OP)
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

 

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

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...


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

(OP)
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.

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