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

p16.19 The aluminum column shown in Figure P16.19 has a
rectangular cross section and supports an 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).
(a) Determine the critical buckling load of the column for the
following parameters: L = 50 in., b = 0.50 in., h = 0.875 in.,
and E = 10,000 ksi.
(b) Determine the ratio b/h for which the critical buckling load
about the strong axis is the same as that about the weak axis.
but prevent rotation about the weak axis. Determine the allowable
compression load P if a factor of safety of 2.0 is specified. Use the
following parameters: L = 1,200 mm, b = 15 mm, h = 40 mm, and
E = 200 GPa.
h
P
P
b
h
y
L
y
b
z
h
z
b
P
P
FIGURE p16.20
L
x
x
p16.21 A stainless steel pipe with an outside diameter of 100
mm and a wall thickness of 8 mm is rigidly attached to fixed supports
at A and B as shown in Figure P16.21. The length of the pipe
is L = 8 m, the elastic modulus of the pipe material is E = 190 GPa,
and the coefficient of thermal expansion of the pipe is α = 17.3 ×
10 −6 mm/mm/°C. Determine the temperature increase ∆T that will
cause the pipe to buckle.
y
FIGURE p16.19
z
A
B
p16.20 The steel compression link shown in Figure P16.20 has
a rectangular cross section and supports an axial load P. The supports
allow rotation about the strong axis of the link cross section
FIGURE p16.21
L
16.4 The Secant Formula
Many real columns do not behave as predicted by the Euler formula because of imperfections
in the alignment of the loading. In this section, the effect of imperfect alignment is
examined by considering an eccentric loading. We will consider a pinned–pinned column
subjected to compressive forces acting at an eccentricity e from the centerline of the undeformed
column, as shown in Figure 16.8a. (Note: The support symbols have been omitted
from the figure for clarity.) When the eccentricity is nonzero, the free-body diagram for the
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