- Calculate the axial force in the cover plate
Calculate the axial force P Ib (N) in the cover plate at its end by computing the mean
bending stress. Determine the length of fillet weld required to transmit this force to the W
shape. Thus/mean = MyII= 215,600(12)(9.31)/1634 = 14,740 lb/in^2 (101,632.3 kPa). Then
P = ^/mean = 3.75(14,740) = 55,280 Ib (245,885.4 N). Use a^1 X 4 -Ui (6.35-mm) fillet weld,
which satisfies the requirements of the Specification. The capacity of the weld = 4(600) =
2400 Ib/lin in (420,304.3 N/m). Then the length L required for this weld is L =
55,280/2400 = 23.0 in (584.20 mm). - Extend the cover plates
In accordance with the Specification, extend the cover plates 20 in (508.0 mm) beyond
the theoretical cutoff point at each end, and supply a continuous /4-in fillet weld along
both edges in this extension. This requirement yields 40 in (1016.0 mm) of weld as com-
pared with the 23 in (584.2 mm) needed to develop the plate. - Calculate the horizontal shear flow at the inner surface
of the cover plate
Choose F or G, whichever is larger. Design the intermittent fillet weld to resist this shear
flow. Thus Vp = 35.2 - 8 - 1.2(8.25) - 17.3 kips (76.95 kN); V 0 = -30.8 + 1.2(8.36) =
-20.8 kips (-92.51 kN). Then q = VQII = 20,800(3.75)(9.31)/1634 = 444 Ib/lin in
(77,756.3 N/m).
The Specification calls for a minimum weld length of 1.5 in (38.10 mm). Let s denote
the center-to-center spacing as governed by shear. Then s = 2(1.5)(2400)/444 = 16.2 in
(411.48 mm). However, the Specification imposes additional restrictions on the weld
spacing. To preclude the possibility of error in fabrication, provide an identical spacing at
the top and bottom. Thus, smax = 21(0.375) = 7.9 in (200.66 mm). Therefore, use a^1 X 4 -Ui
(6.35-mm) fillet weld, 1.5 in (38.10 mm) long, 8 in (203.2 mm) on centers, as shown in
Fig. 4a.
DESIGN OFA CONTINUOUS BEAM
The beam in Fig. 5a is continuous from A to D and is laterally supported at 5-ft (1.5-m)
intervals. Design the member.
Calculation Procedure:
- Find the bending moments at the interior supports; calculate
the reactions and construct shear and bending-moment diagrams
The maximum moments are +101.7 ft-kips (137.9 kN-m) and -130.2 ft-kips (176.55
kN-m). - Calculate the modified maximum moments
Calculate these moments in the manner prescribed in the AISC Specification. The clause
covering this calculation is based on the postelastic behavior of a continuous beam. (Refer
to a later calculation procedure for an analysis of this behavior.)
Modified maximum moments: +101.7 + 0.1(0.5)(115.9 + 130.2) = +114.0 ft-kips
(154.58 kN-m); 0.9(-130.2) - -117.2 ft-kips (-158.92 kN-m); design moment = 117.2
ft-kips (158.92 kN-m). - Select the beam size
Thus, S = MIf= 117.2(12)724 = 58.6 in^3 (960.45 cm^3 ). Use W16 x 40 with S = 64.4 in^3
(1055.52 cm^3 ); Lc = 7.6 ft (2.32 m).