Page 309 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch06.qxd 9/29/05 5:15 PM Page 6.31

DESIGN OF BUILDING MEMBERS

DESIGN OF BUILDING MEMBERS 6.31

the plastic neutral axis and for several values of the distance Y 2 from the top of the steel beam to the
centroid of the effective concrete flange force (∑Q n ) (see Art. 5.8). Try ∑Q n = 260 kips. The cor-
responding depth of the concrete compression block is
a = 260 = 1 133. in
085 × 30 90. ×
.
From Eq. (6.29), Y 2 = 5.25 – 1.133/2 = 4.68 in. The manual table gives the corresponding design
strength for Case 6 and Y 2 = 4.68 in, by interpolation, as
φM n = 546 kip⋅ft > (M u = 509.6 kip⋅ft)
The maximum positive moment M u occurs 13.25 ft from the left support (Fig. 6.8). The inflec-
tion points occur 0.49 and 0.19 ft from the left and right supports, respectively.

Shear Connectors. Next, the studs required to develop the maximum positive moment and the
moments at the concentrated loads are determined. Welded studs / 4 in in diameter are to be used. As
3
in Art. 6.13, the nominal strength of a stud is Q n = 17.7 kips.
For development of the maximum positive moment on both sides of the point of maximum
moment, with ∑Q n = 260 kips, at least 260/17.7 = 14.69 studs are required. Since the negative-
moment region is small, it is not practical to limit the stud placement to the positive-moment region
only. Therefore, additional studs are required for placement of connectors over the entire 30-ft span.
Stud spacing on the left of the point of maximum moment should not exceed
(.
.
S = 12 13 25 − 0 49) = 10 42 in
.
L
.
14 69
Stud spacing on the right of the point of maximum moment should not exceed
(
.
− .
S = 12 30 −13 25 0 19) = 13 53 in
.
R
14 69
.
For determination of the number of studs and spacing required between the concentrated load P
10 ft from the left support (Fig. 6.8) and the left inflection point, the maximum moment at that load
is calculated to be M Lu = 502.1 kip⋅ft. For the W21 × 44 Grade 50 beam, the manual table indicates that
for ∑Q n = 260 kips and Y 2 = 4.68 in, as calculated previously, the design strength is φM n = 546 kip⋅ft.
3
For / 4-in studs and ∑Q n = 260 kips, the required number of studs is 14.69. Spacing of these studs,
which may not exceed 10.42 in, is also limited to
.
(
.
S PL = 12 10 − 0 49) = 777 in
.
14 69
Hence the number of studs to be placed in the 10 ft between P and the left support is 10 × 12/7.77 =
15.4 studs. Use 16 studs.
For determination of the number of studs and spacing required between the concentrated load
P 10 ft from the right support (Fig. 6.8) and the right inflection point, the maximum moment at that
load is calculated to be M Ru = 481.2 kip⋅ft. For the W21 × 44, the manual table indicates that, for
Case 7, ∑Q n = 163 kips and φM n = 486 kip⋅ft. The required number of studs for ∑Q n = 163 kips is
163/17.7 = 9.21 studs. Spacing of these studs, which may not exceed 13.53 in, is also limited to
.
(
.
S PR = 12 10 − 0 19) = 12 78 in
.
921
The number of studs to be placed in the 10 ft between P and the right support is 10 × 12/12.78.
Use 10 studs.
The number of studs required between the two concentrated loads equals the sum of the number
required between the point of maximum moment and P on the left and right. On the left, the required
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