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

(a) If the screws are uniformly spaced at an interval s = 200 mm
along the span, what is the maximum concentrated load P that
can be supported by the beam, given the strength of the screw
connections? Demonstrate that the maximum bending and
shear stresses produced by P are acceptable.
(b) Determine the magnitude of the load P that produces the
allowable bending stress in the span (i.e., σ b = 8,300 kPa).
What screw spacing s is required to support this load?
p9.28 The wooden box beam shown in Figure P9.28a is fabricated
from four boards fastened together with nails (see Figure
P9.28b) installed at a spacing s = 125 mm (see Figure P9.28a).
Each nail can provide a resistance V f = 500 N. In service, the beam
will be installed so that bending occurs about the z axis. Determine
the maximum shear force V that can be supported by the beam,
given the shear capacity of the nailed connections.
s
z
y
25 mm 140 mm 25 mm
50 mm
150 mm
50 mm
FIGURE p9.29b
p9.30 A wooden beam is fabricated by bolting together three
members, as shown in Figure P9.30a/31a. The cross-sectional
dimensions are shown in Figure P9.30b/31b. The 8 mm diameter
bolts are spaced at intervals s = 200 mm along the x axis of the
beam. If the internal shear force in the beam is V = 7 kN, determine
the shear stress in each bolt.
y
y
z
V
s
z
x
FIGURE p9.28a
x
y
25 mm
FIGURE p9.30a/31a
V
40 mm
z
250 mm
40 mm
40 mm
90 mm
40 mm 120 mm 40 mm
25 mm
FIGURE p9.28b
300 mm
p9.29 The wooden box beam shown in Figure P9.29a is fabricated
from four boards fastened together with screws, as shown in
Figure P9.29b. Each screw can provide a resistance of 800 N. In
service, the beam will be installed so that bending occurs about the
z axis and the maximum shear force in the beam will be 9 kN. Determine
the maximum permissible spacing interval s (see Figure
P9.29a) for the screws.
s
z
y
x
FIGURE p9.29a
FIGURE p9.30b/31b
p9.31 A wooden beam is fabricated by bolting together three
members, as shown in Figure P9.30a/31a. The cross-sectional dimensions
are shown in Figure P9.30b/31b. The allowable shear
stress of the wood is 850 kPa, and the allowable shear stress of the
10 mm diameter bolts is 40 MPa. Determine
(a) the maximum internal shear force V that the cross section can
withstand, given the allowable shear stress in the wood.
(b) the maximum bolt spacing s required to develop the internal
shear force computed in part (a).
p9.32 The cantilever beam shown in Figure P9.32a is fabricated
by connecting two hat shapes with rivets that are spaced longitudinally
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