Page 290 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch06.qxd 9/29/05 5:15 PM Page 6.12

DESIGN OF BUILDING MEMBERS

6.12 CHAPTER SIX

In this example, the load due to the weight of the floor system is from Table 6.1 with the weight
of the beam added:
+
3
=
W = (45 + )(40 25 ) + 55 1615 lb /ft
wt
2
The deflection due to this load is
×
.
∆ = 5 ×1 615 30 4 ×12 = 0 746 in
.
wt
,
384 × 29 000 ×1 360
,
3
Therefore, cambering the beam / 4 in at midspan is recommended.
For review of the shear capacity of the section, the depth/thickness ratio of the web is
h  29 000 
,
= 54 6 . < 245 = 59 0. 
 .
t w  50 
From Eq. (6.14), the design shear strength is
φV n = 0.9 × 0.6 × 50 × 23.6 × 0.395 = 252 kips
The factored shear force near the support is

V = 4 461 × 30 = 66 92. kips < 252 kips OK
.
u
2
As illustrated in this example, it usually is not necessary to review the design of each simple beam
with uniform load for shear capacity.

6.10 EXAMPLE—LRFD FOR FLOOR BEAM
WITH UNBRACED TOP FLANGE

A beam of A992 steel with a span of 20 ft is to support the concentrated load of a stub pipe column
at midspan. The factored concentrated load is 55 kips. No floor deck is present on either side of the
beam to brace the top flange, and the pipe column is not capable of bracing the top flange laterally.
The weight of the beam is assumed to be 50 lb/ft.
The factored moment at midspan is

⋅
.
M = 55 × 20 + 0 050 × 20 2 = 277 5 . kip ft
u
4 8
A beam size for a first trial can be selected from a load-factor design table for steel with F y = 50 ksi
in the AISC “Steel Construction Manual.” The table lists several properties of wide-flange shapes,
including plastic moment capacities φM p . For example, an examination of the table indicates that the
lightest beam with φM p exceeding 277.5 kip⋅ft is a W18 × 40 with φM p = 294 kip⋅ft. Whether this
beam can be used, however, depends on the resistance of its top flange to buckling. The manual table
also lists the limiting laterally unbraced lengths for full plastic bending capacity L p and inelastic tor-
sional buckling L r . For the W18 × 40, L p = 4.5 ft and L r = 12.0 ft (Table 6.2).
In this example, then, the 20-ft unbraced beam length exceeds L r , so the design strength will be
less than M p . From the table in the manual for the W18 × 40 (Grade 50), design strength φM r =
205 kip⋅ft < 277.5 kip⋅ft. Therefore, a larger size is necessary.

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