Page 72 - Handbook of Structural Steel Connection Design and Details

Design of Connections for Axial, Moment, and Shear Forces

Design of Connections for Axial, Moment, and Shear Forces 57

and the normal stress at point A is

f 5 f 1 f 5 15.9 1 9.97 5 25.9 ksi
a
1
n A
and at point B
f 5 f 2 f 5 35.8 2 9.97 5 25.9 ksi
a
2
n B
Now the entire section is uniformly stressed. Since
f 9.24 ksi 21.6 ksi
v
f 25.9 ksi 32.4 ksi
n
at all points of the section, the design yield stress is nowhere exceeded
and the connection is satisfactory.
It was stated previously that there is an alternative to the use of the
inappropriate slender beam formulas for the analysis and design of
gusset plates. The preceding analysis of the special section a-a demon-
strates the alternative that results in a true limit state (failure mode or
mechanism) rather than the fictitious calculation of “hot spot” point
stresses, which since their associated deformation is totally limited by
the remaining elastic portions of the section, cannot correspond to a
true failure mode or limit state. The UFM performs exactly the same
analysis on the gusset horizontal and vertical edges, and on the associ-
ated beam-to-column connection. It is capable of producing forces on all
interfaces that give rise to uniform stresses. Each interface is designed
to just fail under these uniform stresses. Therefore, true limit states are
achieved at every interface. For this reason, the UFM achieves a good
approximation to the greatest lower bound solution (closest to the true
collapse solution) in accordance with the lower bound theorem of limit
analysis.
The UFM is a complete departure from the so-called traditional
approach to gusset analysis using slender beam theory formulas. It has
been validated against all known full-scale gusseted bracing connection
tests (Thornton, 1991, 1995b). It does not require the checking of gusset
sections such as that studied in this section (section a-a of Fig. 2.4). The
analysis at this section was done to prove a point. But the UFM does
include a check in the brace-to-gusset part of the calculation that is
closely related to the special section a-a of Fig. 2.4. This is the block shear
rupture of Fig. 2.7 (Hardash and Bjorhovde, 1985, and Richard, 1983),
which is included in section J4 of the AISC Specification (AISC, 2005).
The block shear capacity was previously calculated as 877 kips.
Comparing the block shear limit state to the special section a-a
877 2 855
limit state, a reserve capacity in block shear 100 5 2.57 %
855

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