Handbook of Civil Engineering Calculations

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  1. 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).

  2. 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.

  3. 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:



  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
    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).

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