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

p9.23 A W14 × 34 standard steel section is used for a simple
span of 6 ft 6 in. Determine the maximum uniform load that the
section can support if the allowable bending stress is 30 ksi and the
allowable shear stress is 18 ksi. Assume bending about the strong
axis of the W shape.
p9.24 A simply supported beam with spans of L AB = 9 ft and
L BC = 27 ft supports loads of w = 5 kips/ft and P = 30 kips, as
shown in Figure P9.24a. The cross-sectional dimensions of the wideflange
shape shown in Figure P9.24b are b f = 10 in., t f = 0.64 in.,
d = 27.7 in., and t w = 0.46 in. Determine the magnitude of
(a) the maximum horizontal shear stress in the beam.
(b) the maximum bending stress in the beam.
P
w
beam is a rectangular tube (Figure P9.25b) with dimensions b =
100 mm, d = 180 mm, and t = 5 mm. Determine, at point H, which
is located at a distance a = 40 mm to the right of the z centroidal axis,
(a) the vertical shear stress magnitude,
(b) the normal stress in the y direction produced by the bending
moment. State whether it is a tensile or a compressive normal
stress.
(c) the normal stress in the y direction produced by the axial force.
State whether it is a tensile or a compressive normal stress.
y 1
A
y
H
x
C
A B C
LAB
LBC
y 2
B
FIGURE p9.24a
b f
y
t f
P
D
y 3
x 1 x 2
Figure p9.25a
t w
b
z
d
FIGURE p9.24b
p9.25 Vertical beam AD supports a horizontal load P = 120 kN
as shown in Figure P9.25a. Dimensions of this structure are x 1 =
220 mm, x 2 = 5.78 m, y 1 = 0.85 m, y 2 = 3.15 m, and y 3 = 1.60 m. The
d
z
x
H
Cross section at point H.
a
t
(typ.)
Figure p9.25b
9.8 Shear Flow in Built-Up members
While standard steel shapes and other specially formed cross sections are frequently used
to construct beams, there are instances in which beams must be fabricated from components
such as wooden boards or metal plates to suit a particular purpose. As has been shown
in Section 9.2, nonuniform bending creates horizontal forces (i.e., forces parallel to the
longitudinal axis of the beam) in each portion of the cross section. To satisfy equilibrium,
additional horizontal forces must be developed internally between these parts. For a cross
section made from disconnected components, fasteners such as nails, screws, bolts, or
other individual connectors must be added so that the separate pieces act together as a unified
flexural member.
The cross section of a built-up flexural member is shown in Figure 9.14a. Nails connect
four wooden boards so that they act as a unified flexural member. As in Section 9.3,
we will consider a length ∆x of the beam, which is subjected to nonuniform bending
(Figure 9.14b). Then, we will examine a portion A′ of the cross section in order to assess
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