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

P
t
w
2w
A
a
FIGURE p8.32
p8.33 The beam shown in Figure P8.33 will be constructed
from a standard steel W shape using an allowable bending stress of
30 ksi. The beam span is L = 24 ft, and the beam loads are w =
1.5 kips/ft and P = 20 kips.
(a) Develop a list of five acceptable shapes that could be used for
this beam. Include the most economical W14, W16, W18,
W21, and W24 shapes on the list of possibilities.
(b) Select the most economical W shape for this beam.
A
w
L
2
FIGURE p8.33
B
b
Lever
p8.34 The beam shown in Figure P8.34 will be constructed
from a standard steel W shape using an allowable bending stress
of 30 ksi. The beam span is L = 24 ft, and the beam loads are
w = 1,100 lb/ft and 2w = 2,200 lb/ft.
(a) Develop a list of four acceptable shapes that could be used for
this beam. Include the most economical W10, W12, W14, and
W16 shapes on the list of possibilities.
(b) Select the most economical W shape for this beam.
P
B
h
Cross section
L
2
C
Q
C
A
L
2
FIGURE p8.34
p8.35 The beam shown in Figure
P8.35 will be constructed from
a standard steel W shape using
an allowable bending stress of
165 MPa.
(a) Develop a list of four
acceptable shapes that could
be used for this beam.
Include the most economical
A
W310, W360, W410, and
W460 shapes on the list of FIGURE p8.35
possibilities.
(b) Select the most economical W shape for this beam.
p8.36 The beam shown in Figure P8.36 will be constructed from a
standard steel HSS shape using an allowable bending stress of 30 ksi.
(a) Develop a list of three acceptable shapes that could be used
for this beam. On this list, include the most economical
HSS8, HSS10, and HSS12 shapes.
(b) Select the most economical HSS shape for this beam.
A
FIGURE p8.36
2 kips/ft
16 ft
B
3 m
B
L
2
B
8 ft
C
5 kips
15 kN
40 kN/m
C
8.6 Flexural Stresses in Beams of Two materials
Many structural applications involve beams made of two materials. These types of beams
are called composite beams. Examples include wooden beams reinforced with steel plates
attached to the top and bottom surfaces, and reinforced concrete beams in which steel reinforcing
bars are embedded to resist tensile stresses. Engineers purposely design beams in
this manner so that advantages offered by each material can be efficiently utilized.
The flexure formula was derived for homogeneous beams—that is, beams consisting of
a single, uniform material characterized by an elastic modulus E. As a result, the flexure
formula cannot be used to determine the normal stresses in composite beams without some
additional modifications. In this section, a computational method will be developed so that
a beam cross section that consists of two different materials can be “transformed” into an
equivalent cross section consisting of a single material. The flexure formula can then be used
to evaluate bending stresses in this equivalent homogeneous beam.
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