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

fixed at base A with respect to bending about both the strong and
weak axes of the HSS cross section. At upper end B, the column is
restrained against rotation and translation in the x–z plane (i.e.,
bending about the weak axis) and against translation in the x–y
plane (i.e., the column is free to rotate about the strong axis). Use
the AISC equations to determine the allowable axial load P allow that
may be supported by the column, on the basis of (a) buckling in the
x–y plane and (b) buckling in the x–z plane. Assume that E = 29,000
ksi and σ Y = 46 ksi.
p16.31 A column with an effective length of 28 ft is fabricated
by connecting two C15 × 40 steel channels (see Appendix B for
cross-sectional properties) with lacing bars as shown in Figure
P16.31/32. Use the AISC equations to determine the allowable
axial load P allow that may be supported by the column if d = 10 in.
Assume that E = 29,000 ksi and σ Y = 36 ksi.
FIGURE p16.31/32
Lacing
bars
C shapes
aligned toe-to-toe
p16.32 A column is fabricated by connecting two C310 × 45
steel channels (see Appendix B for cross-sectional properties) with
lacing bars as shown in Figure P16.31/32. (a) Determine the distance
d required so that the moments of inertia for the section about
the two principal axes are equal. (b) Using the value of d obtained
in part (a), determine the allowable axial load P allow that may be
supported by a column with an effective length KL = 9.5 m. Use the
AISC equations and assume that E = 200 GPa and σ Y = 340 MPa.
p16.33 A compression chord of a small truss consists of two
L127 × 76 × 12.7 steel angles arranged with long legs back-to-back
as shown in Figure P16.33. The angles are separated at intervals by
spacer blocks. (a) Determine the spacer thickness required so that
the moments of inertia for the section about the two principal axes
are equal. (b) Using the spacer thickness obtained in part (a), determine
the allowable axial load P allow that may be supported by a
compression chord with an effective length KL = 7 m. Use the
AISC equations and assume that E = 200 GPa and σ Y = 340 MPa.
d
Spacer block
76 mm
FIGURE p16.33
Spacer thickness
76 mm
Double angles
L127 × 76 × 12.7
Long legs back-to-back
p16.34 Develop a list of three acceptable structural steel WT
shapes (from those listed in Appendix B) that can be used as an
18 ft long pin-ended column to carry an axial compression load of
30 kips. Include the most economical WT8, WT9, and WT10.5
shapes on your list, and select the most economical shape from the
available alternatives. Use the AISC equation for long columns
[Eq. (P16.25)], and assume that E = 29,000 ksi and σ Y = 50 ksi.
p16.35 A 6061-T6 aluminum-alloy pipe column with pinned
ends has an outside diameter of 4.50 in. and a wall thickness of
0.237 in. Determine the allowable axial load P allow that may be supported
by the aluminum pipe column for the following effective
lengths: (a) KL = 7.5 ft and (b) KL = 15 ft. Use the Aluminum
Association column design formulas.
p16.36 A 6061-T6 aluminum-alloy rectangular tube shape has
cross-sectional dimensions b = 100 mm, d = 150 mm, and t = 5 mm
as shown in Figure P16.36. The tube is used as a compression
member that is 7.5 m long. For buckling about the z axis, assume
that both ends of the column are pinned. For buckling about the y
axis, however, assume that both ends of the column are fixed.
Determine the allowable axial load P allow that may be supported by
the rectangular tube. Use the Aluminum Association column
design formulas.
z
t
(typ.)
y
b
FIGURE p16.36
p16.37 The aluminum column shown in Figure P16.37 has a rectangular
cross section and supports a compressive axial load P. The
base of the column is fixed. The support at the top allows rotation of
the column in the x–y plane (i.e., bending about the strong axis) but
prevents rotation in the x–z plane (i.e., bending about the weak axis).
d
705