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A V4 in fillet weld is indicated, or use the AISC minimum if larger. The factor 1.5 in the denominator above comes from the AISC LRFD Specification Appendix J, Section J2.4 for transversely loaded fillets. The weld to the web has a length 12.5 - 0.75 - 0.75 = 11.0 in, and is designed to transfer the unbalanced force in the stiffener to the web. The unbalanced force in the stiffener is 29 kips in this case. Thus,

Because only a Vi6 in weld is indicated, the AISC minimum fillet weld size governs.

Doubler Plate Design The beam flange force (required strength) delivered to the column is Ff = 229 kips. The design shear strength of the column (Vv = 0.9 x 0.6 x 50 x 0.485 x 14.16 = 185 kips < 229 kips, so a doubler appears to be required. However, if the moment that is causing doublers is (f>Mp = 389 ft-kips, then from Fig. 5.57, the column story shear is v = M Vs H

where H is the story height. If H = 13 ft

FIGURE 5.57 Relationship between column story shear and beam end moments. (From W. A. Thornton and T. Kane, "Connections," Chapter 7, Steel Design Handbook—LRFD Method, A. R. Tamboli, Ed., 1997, McGraw-Hill, 1997 with permission.)

V = 13 = 30 kiPs and the shear delivered to the column web is Ff - Vs = 229 - 30 = 199 kips. Since 199 kips > 185 kips, a doubler plate (or plates) is still indicated. However, if some panel zone deformation is acceptable, and is considered in the analysis, the panel zone strength may be increased. AISC LRFD Specification Eq. K1-11 or Eq. K1-12, contain the following extra term which acts as a multiplier on the basic strength 4>Vv:

3bfctfc2 = 3 x 14.565 x 0.7802 = 0 dbdctwc 20.66 x 14.16 x 0.485 .

If the column load is less than 0.75 Py = 0.75 x AcFyc = 0.75 x 29.1 x 50 = 1091 kips, which is the usual case, Eq. K1-11 applies and

Since 220 kips > 199 kips, no doubler is required. In a high-rise building where the moment connections are used for drift control, the extra term can still be used, but an analysis which includes inelastic joint shear deformation should be considered.

Doubler Plate Placement. If a doubler plate or plates had been required in this example, the most economical arrangement would be to place the doubler plate against the column web between the stiffeners (the panel zone) and to attach to weak axis shear connection plates, plates B, to the face of the doubler. This is permissible provided that the doubler is capable of carrying the entire weak axis shear load R = 107 kips (specified shear load for W21x44 G50 beam) on one vertical cross section of the doubler plate. To see this, consider Fig. 5.58. The portion of the shear force induced in the doubler plate by the moment connection flange force Ff is H. For the doubler to be in equilibrium under the forces H, vertical shear forces V = Hd/w exist. The welds of the doubler at its four edges develop the shear strength of the doubler. Let the shear force R from the weak axis connection be applied to the face of the doubler at or near its horizontal center as shown in Fig. 5.58. If it is required that all of the shear R can be carried by one vertical section a-a of Fig. 5.58, (0.9 x 0.6 x Fyd > R, where td is the doubler thickness and Fy is the yield stress of the doubler and the

Weakest Axis Column
FIGURE 5.58 Force equilibrium diagram for doubler plate with weak axis shear load. (From W. A. Thornton and T. Kane, "Connections," Chapter 7, Steel Design Handbook—LRFD Method, A. R. Tamboli, Ed., 1997, McGraw-Hill, 1997 with permission.)

column), then the free body diagram of Fig. 5.58 is possible. In this figure, all of the shear force R is delivered to the side of the doubler where it is opposite in direction to the shear delivered by the moment connection, thereby avoiding over-stressing the other side where the two shears would add. Since the doubler and its welds are capable of carrying V or R alone, they are capable of carrying their difference. The same argument applies to the top and bottom edges of the doubler. Also, the same argument holds if the moment and/or weak axis shear reverse(s).

Associated Shear Connections—Beam 1. The specified shear for the web connection is R = 163 kips, which is the shear capacity of the W21 X 62 A36 beam. The connection is a shear plate with two erection holes for erection bolts. The shear plate is shop welded to the column flange and field welded to the beam web. The limit states are plate gross shear, weld strength, and beam web strength.

For plate gross shear try a plate V2 X 18 in. the gross shear strength is

$Rgv = 0.5 X 18 X 0.9 X 0.6 X 36 = 175 kips > 163 kips OK.

Plate net shear need not be checked because it is not a valid limit state.

The weld to the column flange is subjected to shear only. Thus, the weld size in number of sixteenths of an inch is

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