Page 313 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch06.qxd 9/29/05 5:15 PM Page 6.35

DESIGN OF BUILDING MEMBERS

DESIGN OF BUILDING MEMBERS 6.35

Use of the AISC “Manual of Steel Construction” tables for design axial strength of compression
members simplifies evaluation of the trial column size. For the W14 × 426, A992 section, a table
indicates that for K y L y = 13 ft, φP n = 4830 kips.
Moment Capacity. Next, the nominal bending-moment capacities are calculated. For strong-axis
bending moment, K y L y = 13 ft is assumed for the flange lateral buckling state. The limiting lateral
unbraced length L p (in) for plastic behavior for the W14 × 426 is

300 r 300 × 4 34
.
L = y = = 184 in = 15 3 ft >13 ft
.
p
F y 50
Since the unbraced length is less than L p ,
⋅
×
.
φM nx = 0 9 869 × 50 = 3259 kip ft
12
×
⋅
.
φM = 09 . Z F = 09 434 × 50 = 1628 kip ft
y y
ny
12
Interaction Equation for Dead Load. For use in the interaction equation for axial load and bend-
ing [see Art. 5.7.1, Eq. (5.102)], the factored dead load is
P u = 1.4(750 + 325 + 0.426 × 13) = 1513 kips
The factored moments applied to columns due to any general loading conditions should include the
second-order magnification. When the frame analysis does not include second-order effects, the fac-
tored column moment can be determined from Eq. (5.3).
Computer analysis programs usually include the second-order analysis (P–∆ effects). Therefore,
the values of B 2 for moments about both column axes can be assumed to be unity. However, B 1
should be determined for evaluation of the nonsway magnifications. For a braced column (drift pre-
vented), the slenderness coefficient K x is determined from Fig. 6.9a with G A = 0.49 and G B = 0.98,
calculated previously. The nomograph indicates that K s = 0.73.
For determination of B 1 , the column when loaded is assumed to have single curvature with end
moments M 1 = M 2 . Hence C m = 1.
4
Determine the elastic buckling load P ex for the column moment of inertia I x = 6600 in :
π 2 × 29 000 6600
×
,
P = = 247 000 kips
,
ex
−
(
[. ×12 13 3)] 2
073
With these values, the magnification factor for M ux is
.
B = C m = 10 = 1 006
.
ex
,
/
1 − PP / ex 1 −1513 247 000
u
The elastic buckling load P ey with respect to the y axis is
×
π 2 × 29 000 2360
,
P = = 247 000 kips
,
ex
×
( 113 ×12) 2
Application of the magnification factor of the dead-load moments due to gravity loads yields
M ux = 1.006 × 1.4 × 180 = 253.5 kip⋅ft
M uy = 1.058 × 1.4 × 75 = 111.1 kip⋅ft
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