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

pRoBLEmS
p16.42 The structural steel column shown in Figure P16.42/43 is
fixed at its base and free at its upper end. At the top of the column, a
load P is applied to the stiffened seat support at an eccentricity
e = 9 in. from the centroidal axis of the wide-flange shape. Use the
AISC equations given in Section 16.5, and assume that E = 29,000 ksi
and σ Y = 36 ksi. Employ the allowable-stress method to determine
(a) whether the column is safe for a load P = 15 kips. Report the
results in the form of the stress ratio σ x /σ allow .
(b) the magnitude of the largest eccentric load P that may be
applied to the column.
(a) determine whether the column is safe for a load P = 125 kN.
Report the results in the form of the stress ratio σ x /σ allow .
(b) determine the magnitude of the largest eccentric load P that
may be applied to the column.
y
x
Eccentricity e
P
Eccentricity e
8 in.
P
x
0.50 in. 7 in. 0.50 in.
z
y
12 ft
FIGURE p16.42/43
p16.43 The structural steel column shown in Figure P16.42/43
is fixed at its base and free at its upper end. At the top of the column,
a load P is applied to the stiffened seat support at an eccentricity
e from the centroidal axis of the wide-flange shape. Apply the
AISC equations given in Section 16.5, and assume that E = 29,000
ksi and σ Y = 50 ksi. Using the allowable-stress method, determine
the maximum allowable eccentricity e if
(a) P = 15 kips.
(b) P = 35 kips.
z
y
0.35 in.
8 in.
p16.44 A W200 × 46.1 structural steel shape (see Appendix B
for cross-sectional properties) is used as a column to support an
eccentric axial load P. The column is 3.6 m long and is fixed at its
base and free at its upper end. At the upper end of the column (see
Figure P16.44), the load P is applied to a bracket at a distance e =
170 mm from the x axis, creating a bending moment about the
strong axis (i.e., the z axis) of the W200 × 46.1 shape. Apply the
AISC equations given in Section 16.5, and assume that E =
200 GPa and σ Y = 250 MPa. On the basis of the allowable-stress
method,
z
Cross section
FIGURE p16.44
p16.45 An eccentric compression
load P = 32 kN is applied at an eccentricity
e = 12 mm from the centerline
of a solid 45 mm diameter 6061-T6
aluminum-alloy rod. (See Figure P16.45/
46.) Employing the interaction method
and an allowable bending stress of
150 MPa, determine the longest effective
length L that can be used.
p16.46 An eccentric compressive
load P = 13 kips is applied at an
eccentricity e = 0.75 in. from the centerline
of a solid 6061-T6 aluminum-
A
alloy rod. (See Figure P16.45/46.) The
FIGURE p16.45/46
rod has an effective length of 45 in.
Employing the interaction method and an allowable bending stress
of 21 ksi, determine the smallest diameter that can be used.
p16.47 A sawn wood post of rectangular cross section (Figure
P16.47) consists of Select Structural Spruce–Pine–Fir lumber
(F c = 700 psi; E′ min = 440,000 psi). The finished dimensions of the
post are b = 5.5 in. and d = 7.25 in. The post is 12 ft. long and the
ends of the post are pinned. Using the interaction method and an
allowable bending
x Eccentricity e
stress of 1,000 psi,
determine the maximum
allowable load
y
7.25 in. z
that can be supported
P
by the post if the
load P acts at an eccentricity
of e = 6 in.
from the centerline
of the post. Use the
AWC NDS column
design formula. FIGURE p16.47
5.5 in.
B
P
Eccentricity e
L
714