Page 111 - Handbook of Civil Engineering Calculations, Second Edition

1.94 STRUCTURAL STEEL ENGINEERING AND DESIGN

9. Calculate the axial force in the cover plate
Calculate the axial force P lb (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 f mean My/I 215,600(12)(9.31)/1634 14,740 lb/sq.in. (101,632.3 kPa).
1
Then P Af mean 3.75(14,740) 55,280 lb (245,885.4 N). Use a /4-in. (6.35-mm) fil-
let weld, which satisfies the requirements of the Specification. The capacity of the weld
4(600) 2400 lb/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).
10. Extend the cover plates
In accordance with the Specification, extend the cover plates 20 in. (508.0 mm) beyond
1
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.
11. 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 V F 35.2 – 8 – 1.2(8.25) 17.3 kips (76.95 kN); V G –30.8 + 1.2(8.36)
–20.8 kips (–92.51 kN). Then q VQ/I 20,800(3.75)(9.31)/1634 444 lb/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, s max 21(0.375) 7.9 in. (200.66 mm). Therefore, use a /4-
1
in. (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 OF A 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:

1. 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).
2. 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).
3. Select the beam size
3
3
Thus, S M/f 117.2(12)/24 58.6 in (960.45 cm ). Use W16 40 with S 64.4 in 3
3
(1055.52 cm ); L c 7.6 ft (2.32 m).