2 X 18 X 1392

Use a V4-in fillet weld.

The weld to the beam web is subjected to the shear plus a small couple. Using AISC LRFD Manual Table 8-42, l = 18 in, kl = 4.25 in, k = 0.24, x = 0.04, xl = 0.72 in al = 4.28 in, a = 0.24, c = 2.04, and thus,

A 5/16-in fillet weld is satisfactory.

Next consider the beam web thickness. To support a 5/i6 fillet weld on both sides of a plate, AISC LRFD Manual Table 9-3, shows that a 0.72-in thick web is required. For a 5/i6-in fillet on one side, a 0.36 in thick web is required. Since the W21 X 62 web is 0.400 in thick, it is OK.

Design of Beams Nos. 3 and 4. These beams are W21 X 44 sections of Grade 50 steel and are composite. The flange connection is a full penetration weld so again, no design is required for the connection. Section A-A of Fig. 5.56a shows the arrangement in plan. See also Fig. 5.56c. The connection plates A are made V4 in thicker than the W21 X 44 beam flange to accommodate under and over rolling and other minor misfits. Also, the plates are extended beyond the toes of the column flanges by 3/4 to 1 in to improve ductility. Plates A should also be welded to the column web, even if not required to carry load, to provide improved ductility.

The flange force for the W21 X 44 is based on the full moment capacity as required in this example, so faMp = 358 ft-kip and

Figure 5.59 shows the distribution of forces on Plates A, including the forces from the strong axis connection. The weak axis force of 213 kips is distributed V4 to each flange and V2 to the web. This is done to cover the case when the beams may not be reacting against each other. In this case, all of the 213 kips must be passed to the flanges. To see this, imagine that beam 4 is removed and Plate A for beam 4 remains as a back-up stiffener. One-half of the 213 kips from beam 3 passes into the beam 3 near side column flanges, while the other half is passed through the column web to the back-up stiffener, and thence into the far side flanges, so that all of the load is passed to the flanges. This is the load path usually assumed, although others are possible.

t213 k

| WORST FLGE

FIGURE 5.59 Distribution of forces on Plates A of Fig. 5.56c. (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.)

| WORST FLGE

FIGURE 5.59 Distribution of forces on Plates A of Fig. 5.56c. (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.)

Merging of Stiffeners from Strong and Weak Axis Beams. The strong axis beam, beam 1, required stiffeners V2 X 6V2 X 12V2 in. Weak axis beams 3 and 4 require Plates A which are 3/4 X 8 X 12V/2 in. These plates occupy the same space because the beams are all of the same depth. Therefore, the larger of the two plates is used, as shown in Fig. 5.56a.

Since the stiffeners are merged, the welds that were earlier determined for the strong axis beam must be revisited. For the weld to the flanges, from Fig. 5.59, the worst case combined flange loads are 53 kips shear and 29 kips axial. The length of weld is 6/4 in. Thus, the weld size is

V292 + 532

which indicates a V4-in fillet weld. This is also the AISC minimum size. However, remember that for axial load, the contact strength of the stiffener must be developed. The contact strength in this case is 0.9 X 36 X 6.25 X 0.75 = 152 kips, because the stiffener has increased in size to accommodate the weak axis beams. But the delivered load to this stiffener cannot be more than that which can be supplied by the beam, which is 229/2 = 114.5 kips. Thus

which indicates that a 5/i6 in fillet weld is required. This is the fillet weld that should be used as shown in Fig. 5.56c.

For the weld to the web, from Fig. 5.59, calculate the size as

Use a Vi-in fillet weld.

Stresses in Stiffeners (Plate A). The weak axis beams are 50 ksi yield point steel and are butt welded to Plates A. Therefore, Plates A should be the same strength steel. Previous calculations involving this plate assumed it was A36, but changing to a higher strength will not change the final results in this case because the stiffener contact force is limited by the delivered force from beam 1 rather than the stiffener strength. The stiffener stresses for the flange welds are, from Fig. 5.59

f = „f53 ^ = 11.3 ksi < 0.9 x .6 x 50 = 27 ksi OK. Jv 0.75 x 6.25

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