ure in each member lies 84 in (2133.6 mm)
from the section of tangency. Design the
knee.
Calculation Procedure:
- Record the relevant
properties of the members
Refer to the Commentary in the AISC Man-
ual. The notational system is the same as
that used in the Manual, plus a = distance
from section of contraflexure to section of
tangency; b = member flange width; x =
distance from section of tangency to given
section; M = ultimate moment at given sec-
tion; Mp = plastic-moment capacity of knee FIGURE 11. Curved knee,
at the given section.
Assume that the moment gradient
dM/dx remains constant across the knee.
The web thickness of the knee is made equal to that of the main material. The flange
thickness of the knee, however, must exceed that of the main material, for this reason: As
jc increases, both M and Mp increase, but the former increases at a faster rate when x is
small. The critical section occurs where dM/dx = dMpldx.
An exact solution to this problem is possible, but the resulting equation is rather cum-
bersome. An approximate solution is given in the AISC Manual.
Record the relevant properties of the the W21 x 82: d = 20.86 in (529.8 mm); b = 8.96
in (227.6 mm); tf= 0.795 in (20.2 mm); tw = 0.499 in (12.7 mm).
- Design the cross section of the knee, assuming tentatively that
flexure is the sole criterion
Use a trial thickness of^1 A in (12.7 mm) for the web plate and a 9-in (228.6-mm) width for
the flange plate. Then a = 84 in (2133.6 mm); n = ald= 84/20.86 = 4.03. From the AISC
Manual, m = 0.14 ± t' = t(\ + m) = 0.795(1.14) = 0.906 in (23.0 mm). Make the flange
plate 1 in (25.4 mm) thick.
- Design the stiffeners; investigate the knee for compliance with
the AISC Commentary
From the Commentary, item 5: Provide stiffener plates at the sections of tangency and at
the center of the knee. Make the stiffener plates 4 x 78 in (102 x 22 mm), one on each side
of the web.
Item 3: Thus, $ = ^(90° - 20°) = 35°; = 35/57.3 = 0.611 rad; L=R = 76(0.611) =
46.4 in (1178.6 mm); or L = 77fl(70°/360°) = 46.4 in (1178.6 mm); Lcr = 6b = 6(9) = 54 in
(1373 mm), which is acceptable.
Item 4: Thus, b/t' = 9; 2RJb = 152/9 = 16.9, which is acceptable.
BASE PLATE FOR STEEL COLUMN
CARRYING AXIAL LOAD
A W14 x 53 column carries a load of 240 kips (1067.5 kN) and is supported by a footing
made of 3000-lb/in^2 (20,682-kPa) concrete. Design the column base plate.
Radius
