Page 284 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

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DESIGN OF BUILDING MEMBERS

6.6 CHAPTER SIX

Because

 KL = 19 ×12   E 29 000 
,
.
.
 r 225 = 101 3 .  ≤  471 F y = 471 36 = 133 7 .  

.
The elastic critical stress, from Eq. (6.8), is
π 2 × 29 000
,
F = = 27 87 ksi
.
e
101 3 . 2
Equation (6.9) yields the critical stress
F cr = (0.658 36/27.87 ) × 36 = 20.97 ksi
The design strength of the 6-in pipe, then, from Eqs. (6.6) and (6.7), is
φP n = 0.90 × 5.58 × 20.97 = 105.3 kips > 93.6 kips OK

6.6 EXAMPLE—LRFD FOR WIDE-FLANGE SECTION
WITH AXIAL COMPRESSION

A wide-flange section is to be used for columns in a five-story steel building. A typical interior
column in the lowest story will be designed to support gravity loads. (In this example, no eccentricity
will be assumed for the load.) The effective height of the column is 18 ft. The axial loads on the column
from the column above and from the steel girders supporting the second level are dead load 420 kips
and live load (reduced according to the applicable building code) 120 kips.
The factored axial load is the larger of the following:
P u = 420 × 1.4 = 588 kips
P u = 420 × 1.2 + 120 × 1.6 = 696 kips (governs)
Use of the column design tables of the AISC “Manual of Steel Construction” presents the fol-
lowing options:
For a column of A36 steel, select a W14 × 99, with a design strength φP n = 745 kips.
For a column of A992 steel, select a W12 × 87, with a design strength φP n = 758 kips.
Both steels cost about the same, so the W12 × 87 of A992 steel is the most economical wide-flange
section.

6.7 EXAMPLE—LRFD FOR DOUBLE ANGLES
WITH AXIAL COMPRESSION

Double angles are the preferred steel shape for a diagonal in the vertical bracing part of the lat-
eral framing system in a multistory building (Fig. 6.2). Lateral load on the diagonal in this
example is due to wind only and equals 65 kips. The diagonals also support the steel beam at
midspan. As a result, the compressive force on each brace due to dead loads is 15 kips, and that
due to live loads is 10 kips. The maximum combined factored load is P u = 1.2 × 15 + 1.3 × 65 +
0.5 × 10 = 107.5 kips.
The length of the brace is 19.85 ft, neglecting the size of the joint. A36 steel is selected because
slenderness is a major factor in determining the nominal capacity of the section. Selection of the size
of double angles is based on trial and error, which can be assisted by load tables in the AISC “Manual

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