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

ExERcISES
m8.16 A composite-beam cross section consists of two rectangular
bars securely bonded together. The beam is subjected to a
specified bending moment M. Determine
(a) the vertical distance from K to the centroidal axis.
(b) the bending stress produced at H.
(c) the bending stress produced at K.
m8.17 A composite-beam cross section consists of two rectangular
bars securely bonded together. From the indicated allowable
stresses, determine
(a) the vertical distance from K to the centroidal axis.
(b) the maximum allowable bending moment M.
(c) the bending stress produced at H.
(d) the bending stress produced at K.
FIGURE m8.16
FIGURE m8.17
pRoBLEmS
p8.37 A simply supported composite beam spans a distance
L = 24 ft and carries a uniformly distributed load w, as shown in
Figure P8.37a. The beam is fabricated by bolting two wooden
boards (b = 3 in. and d = 12 in.) to the sides of a steel plate
(t = 0.5 in. and d = 12 in.), as shown in Figure P8.37b. The
moduli of elasticity of the wood and the steel are 1,800 ksi and
30,000 ksi, respectively. Neglect the weight of the beam in your
calculations, and
t
d
(a) determine the maximum bending stresses produced in the
wooden boards and the steel plate if w = 400 lb/ft.
(b) determine the largest acceptable magnitude for distributed
load w. (Assume that the allowable bending stresses of
the wood and the steel are 1,200 psi and 24,000 psi,
respectively.)
A
280
L
4
FIGURE p8.37a
B
w
L
2
C
L
4
D
FIGURE p8.37b
p8.38 A flitch beam can be
fabricated by sandwiching two
steel plates (2) between three
wooden boards (1), as shown in
Figure P8.38. The dimensions of
the cross section are b = 1.5 in.,
d = 7.25 in., and t = 0.5 in. The
elastic moduli of the wood and
steel are E 1 = 1,800 ksi and
E 2 = 30,000 ksi, respectively.
For a bending moment M z =
+12 kip ⋅ ft, determine
b
b
z
a
H
b
(2)
FIGURE p8.38
t
y
(1) (1) (1)
b
(2)
t
b
d