Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

The Euler buckling load for this compression member can be calculated from Equation
(16.5):
P
cr
2 2 2 4
π EI π (70,000 N/mm )(7,031.25 mm )
= = = 11,498 N
2
2
L
(650 mm)
= 11.50 kN
When the compression member buckles, it bends in the x–z plane as shown.
Ans.
ExAmpLE 16.2
x
z
x–
X
Y ttf
f
X
t w
Y
b f
d
From Appendix B.
y
Lacing
bars
z
y
C10 × 15.3 shapes
aligned toe-to-toe
8.5 in.
Cross section.
A 40 ft long column is fabricated by connecting two
standard steel C10 × 15.3 channels (see Appendix B
for cross-sectional properties) with lacing bars as
shown. The ends of the column are pinned. Determine
the Euler buckling load for the column. Assume that
E = 29,000 ksi for the steel.
Plan the Solution
The column is built up from two standard steel channel
shapes. The lacing bars serve only to connect the two
shapes so that they act as a single structural unit. The
bars do not add to the compressive strength of the
column. Which principal axis of the cross section is
the strong axis, and which is the weak axis? The
answer is not evident by inspection; therefore, the
moments of inertia about both axes must be calculated
at the outset. Since both ends of the column are pinned,
buckling will occur about the axis that corresponds to
the smaller moment of inertia.
SolutioN
The following section properties for a standard steel C10 × 15.3 channel are given in
Appendix B:
A = 4.48 in.
I
I
x
y
= 67.3 in.
= 2.27 in.
2
4
4
x = 0.634 in.
In Appendix B, the X–X axis is the strong axis for the channel and the Y–Y axis is the weak
axis. For the coordinate system defined in this problem, the X–X axis will be denoted the
z′ axis and the Y–Y axis will be denoted the y′ axis.
The cross-sectional area of the built-up column is equal to twice the area of a single
channel shape:
2 2
A = 2(4.48 in. ) = 8.96 in.
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