Limit state of shear yielding (punching) According to AISC Specification Section K3.2b(b), the limit state of shear yielding (punching) need not be checked when B (1 1/G). Because B b (1 1/G), which reduces to Db 4.00 in. < (D 2t) 5.30 in., this limit state must be considered. From AISC Specification Section K3.2b(b), the nominal strength is: 1 3sin M n 0.6 Fy tDb2 2 4sin
(Spec. Eq. K3-4 and Table 9-1)
2 â&#x17D;Ą 1 + 3sin 45° â&#x17D;¤ = 0.6 ( 42 ksi ( 0.349 in. ( 4.00 in. â&#x17D;˘ â&#x17D;Ľ 2 â&#x17D;Ł 4sinn 45° â&#x17D;Ś = 220 kip-in.
)
)
)
The available flexural strength of the connection is: LRFD M n 0.95 220 kip-in.
209 kip-in. 209 kip-in. > 180 kip-in.
o.k.
ASD Mn 220 kip-in. = 1.58 = 139 kip-in. 139 kip-in. > 120 kip-in.
o.k.
Example 9.2}Vierendeel Connection with Square HSS (In-Plane Bending) Given: A planar Vierendeel frame has an interior connection subject to the loads shown in Figure 9-3. The loads indicated consist of 50% dead load and 50% live load. For a fully rigid connection, it is recommended that such a connection have a width ratio, B 1.0, and a chord overall width-to-thickness ratio not exceeding 16 (Packer and Henderson, 1997). It can be seen that these conditions are fulfilled with these selected members. Determine the adequacy of the connection under these in-plane branch loads. Assume the welds are strong enough to develop the yield strength of the connected branch wall at all locations around the branch. From AISC Manual Table 2-3, the material properties are as follows: Both members ASTM A500 Grade B Fy = 46 ksi Fu = 58 ksi
Fig. 9-3. Vierendeel connection with square HSS. AISC DESIGN GUIDE 24 / HOLLOW STRUCTURAL SECTION CONNECTIONS / 131