Page 311 - Handbook of Structural Steel Connection Design and Details

Partially Restrained Connections

296 Chapter Four

the plate. Compute the elongation of the plate and add 1/32 in for the slip of
the bolts:

s plate,yield sL>2d s1.1 3 50 ksidds20 in>2d 1
conn 5 1 slip 5 1
E 29000 ksi 32
5 0.019 1 0.031 5 0.050 in

From this computation, elastic strains in the plate contribute approximately
40% and slip approximately 60% to the total deformation. Assume that the
connection rotates about the center of the beam. The connection rotation is

0.050 in
conn
conn 5 5 5 0.00478 rad
sd>2d s20.99 in>2d
The connection stiffness is

s1.1 3 50ds9.5 3 0.75ds20.99d
M yield,plate
K conn 5 5
conn 0.00478 rad
6
5 1.89 3 10 kip-in/rad
The relative stiffness, assuming the beam is 24 ft long is

6
s1.89 3 10 ds24 3 12d
K conn L beam
5 5 5 14.1
EI beam s29000ds1330d
Note that this will put this connection in the strong PR range after slip
occurs. This calculation can only be considered as an estimate as from the
computations above it is clear that slip is the main contributor to the defor-
mation. The assumed slip (1/32 in) is considered a reasonable value. The
moment-rotation curve for this connection indicates rigid behavior at the ser-
vice level, and PR behavior between the service and ultimate load level.
13. Moment and rotation at ultimate: Assume that the plate has yielded and
reached a stress halfway between the expected yield strength (55 ksi) and
ultimate strength (71.5 ksi), or approximately 63.25 ksi. The corresponding
moment at the column face is 9459 kip-in. At the critical location in the
beam, that is, just under the first row of bolts, the moment is much higher
than the beam can take (approximately 7700 kip-in based on net section and
ultimate strength with no resistance factor). Thus extensive yielding and a
plastic hinge in the beam would be expected before the connection reaches
even its initial yield. The rotation at this level correspond to full yielding
along the plate, plus 1/8 in of slip and bearing deformation top and bottom for
a rotation of 9.56 mrad. The final moment-rotation curve for the connection is
shown in Fig. 4.11.
Figures 4.12 and 4.13 show some typical details and variations proposed by
Astaneh-Asl for this type of connections. Figure 4.12 shows a variation where the
bottom flange is welded rather than bolted, while Fig. 4.13 shows a connection to
the weak axis of the column.

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