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

pRoBLEmS
p16.15 An HSS152.4 × 101.6 × 6.4 structural steel [E = 200 GPa]
section (see Appendix B for cross-sectional properties) is used as
a column with an actual length of 6 m. The column is supported
only at its ends and may buckle in any direction. If a factor of
safety of 2 with respect to failure by buckling is specified, determine
the maximum safe load for the column for the following end
conditions:
(a) pinned–pinned
(b) fixed–free
(c) fixed–pinned
(d) fixed–fixed
P
L
p16.16 A W250 × 80 structural steel [E = 200 GPa] section
(see Appendix B for cross-sectional properties) is used as a
column with an actual length L = 12 m. The column is supported
only at its ends and may buckle in any direction. The column
is fixed at its base and pinned at its upper end, as shown in
Figure P16.16. Determine the maximum load P that may be supported
by the column if a factor of safety of 2.5 with respect to
buckling is specified.
P
FIGURE p16.17
p16.18 A long, slender structural steel [E = 29,000 ksi] HSS8 ×
4 × ¼ shape (see Appendix B for cross-sectional properties) is used
as a 32 ft long column. The column is supported in the x direction
at base A and pinned at ends A and C against translation in the y and
z directions. Lateral support is provided to the column, so deflection
in the x-z plane is restrained at midheight B; however, the column is
free to deflect in the x–y plane at B (Figure P16.18). Determine the
maximum compressive load the column can support if a factor of
safety of 1.92 is required. In your analysis, consider the possibility
that buckling could occur about either the strong axis (i.e., the
z axis) or the weak axis (i.e., the y axis) of the steel column.
x
L
1
HSS8 × 4 ×
4
P
y
C
z
16 ft
FIGURE p16.16
Lateral
bracing
B
16 ft
p16.17 A W14 × 53 structural steel [E = 29,000 ksi] section
(see Appendix B for cross-sectional properties) is used as a column
with an actual length L = 16 ft. The column is fixed at its
base and unrestrained at its upper end, as shown in Figure P16.17.
Determine the maximum load P that may be supported by the
column if a factor of safety of 2.5 with respect to buckling is
specified.
FIGURE p16.18
z
y
A
689