Page 120 - 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 105

is limited by the bearing strength of the parts; thus the bolt shear
strength is equal to the bearing strength, so
R R 78.5 kips
y p
3. Piece W16 57: The limit states for this part of the connection are
Whitmore section yield and buckling, bearing, and prying action in
conjunction with the W16 flange to W18 flange bolts. Because there
is only one line of bolts, block shear is not a limit state. Bearing has
already been considered with the angle checks.
a. Whitmore section: This is the section denoted by l on Fig. 2.25. It
w
is formed by 30 lines from the bolt furthest away from the end of
the brace to the intersection of these lines with a line through and
perpendicular to the bolt nearest to the end of the brace. Whitmore
(1952) determined that this 30 spread gave an accurate estimate
of the stress in gusset plates at the end of the brace. The length
of the Whitmore section l 3(tan 30 )2 3.46 in.
w
(1) Whitmore yield:
R 0.9 50 3.46 0.430 67.0 kips
wy
where 0.430 is the web thickness of a W16 57.
(2) Whitmore buckling:
Tests (Gross, 1990; Dowswell, 2006) have shown that the
Whitmore section can be used as a conservative estimate for
gusset buckling. In the present case, the web of the W16 57
is a gusset. If the load P is a compression, it is possible for the
gusset to buckle laterally in a sidesway mode. For this mode
of buckling, the K factor is 1.2. The buckling length is l 5
b
in in Fig. 2.25. Thus the slenderness ratio is
Kl 1.2 3 5 3 212
5 5 48.3
r 0.430
Since Kl/r 25, Section J4.4 on strength of elements in com-
pression does not apply; the column buckling equations of
Chapter E apply. Thus, from Section E3,

2
p 3 29000
F 5 5 123
e
s28.3d 2
50
F 5 c0.658a bd50 5 42.2 ksi
cr
123
F 5 0.9 3 42.2 5 38.0 ksi
cr
5 38.0 3 3.46 3 0.430 5 56.5 kips
and R wb

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