Page 128 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch03.qxd 9/29/05 5:05 PM Page 3.60

CONNECTIONS

3.60 CHAPTER THREE

Bearing on the W16 × 57: φR p = 44.0 kips
Tear-out on the angles: φR to = 0.75 × 1.2(3 − 0.9375) × 2 × 0.25 × 58 = 53.8 kips
Tear-out on the W16 × 57: φR to = 0.75 × 1.2(2 − 0.5 × 0.9375) × 0.430 × 65 = 38.5 kips

The shear/bearing/tear-out strength of the lower bolt is thus 38.5 kips, and the capacity of the con-
nection in these limit states is φR vp = 40.0 × 1 + 38.5 × 1 = 78.5 kips.
BOLTS FOR ANGLES TO PIECE W16. The limit state for the bolts is shear. The shear capacity of one
A325N bolt is
π
×
φr = 075 48 × × 0 875 2 = 21 6 kips
.
.
.
v
4
In this case, the bolts are in double shear and the double-shear value per bolt is 21.6 × 2 = 43.3 kips/
bolt. Note that because of bearing limitations, shown in the preceding calculations, this value cannot
be achieved. The bolt shear strength is limited by the bearing strength of the parts. Thus the design
strength for the bolts in shear is limited to the bearing strength, so
φR v =φR p = 78.5 kips
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.
Whitmore Section. The Whitmore section is denoted by l w on Fig. 3.36. It is formed by 30°
lines from the bolt farthest away from the end of the brace to the intersection of these lines with a
line through and perpendicular to the bolt nearest 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 w = 3(tan 30°)2 = 3.46 in.
The design strength for the limit state of yielding on the Whitmore section in the W16 × 50 with
a web thickness of 0.430 in is

φR wy =φF y A g = 0.90 × 50 × 3.46 × 0.430 = 67.0 kips
Tests (Gross, 1990) have shown that the Whitmore section can be used as a conservative estimate
for buckling of a gusset, such as the web of the W16 × 57. If the load P is compression, the gusset can
buckle laterally in a sidesway mode and, for this mode, the K factor is 1.2. The buckling length is
l b = 5 in in Fig. 3.36. The radius of gyration of the rectangular section is r = t/ 12 . Thus the slenderness
ratio is

5
Kl 12 . ×× 12
= = 48 3 .
r 0. 430
Since (Kl/r) > 25, AISC Specification Sec. J4.4 on strength of elements in compression does not
apply. Instead, the column buckling equations of Sec. E3 apply. Thus,

π 2 E π 2 × 29 000,
F = = = 123 ksi
e
( KL r / ) 2 ( 48 3) 2
.
y /
F = (. 0 658 FF e F ) y
cr
= [. 0 658 (50 /123 ) ]50 = 42 .2 ksi
φF cr = 0.9 × 42.2 = 38.0 ksi
φR wb = 38.0 × 3.46 × 0.430 = 56.5 kips

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