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

p11.44 A timber [E = 12 GPa] beam is loaded and supported as
shown in Figure P11.44. The cross section of the timber beam is
100 mm wide and 300 mm deep. The beam is supported at B by a
12 mm diameter steel [E = 200 GPa] rod that has no load before the
distributed load is applied to the beam. A distributed load of 7 kN/m
is applied to the beam. Determine
(a) the force carried by the steel rod.
(b) the maximum bending stress in the timber beam.
(c) the deflection of the beam at B.
v
70 kN/m
A
10 mm B C
4.5 m
1.5 m
FIGURE p11.46
x
v
A B C
FIGURE p11.44
p11.45 A W360 × 72 structural steel [E = 200 GPa] wide-flange
shape is loaded and supported as shown in Figure P11.45. The
beam is supported at B by a timber [E = 12 GPa] post having a
cross-sectional area of 20,000 mm 2 . A uniformly distributed load of
50 kN/m is applied to the beam. Determine
(a) the reactions at supports A, B, and C.
(b) the maximum bending stress in the beam.
(c) the deflection of the beam at B.
v
300 mm
100
mm
50 kN/m
7 kN/m
4 m
(1)
5 m
2 m
x
p11.47 Steel beam (1) carries a concentrated load P = 13 kips
that is applied at midspan, as shown in Figure P11.47/48. The steel
beam is supported at ends A and B by nondeflecting supports and
at its middle by simply supported timber beam (2). In the unloaded
condition, steel beam (1) touches, but exerts no force on, timber
beam (2). The length of the steel beam is L 1 = 30 ft, and its flexural
rigidity is EI 1 = 7.2 × 10 6 kip · in. 2 . The length and the flexural rigidity
of the timber beam are L 2 = 20 ft and EI 2 = 1.0 × 10 6 kip · in. 2 ,
respectively. Determine the vertical reaction force that acts
(a) on the steel beam at A.
(b) on the timber beam at C.
p11.48 In Figure P11.47/48, a W10 × 45 steel beam (1) carries
a concentrated load P = 9 kips that is applied at midspan. The steel
beam is supported at ends A and B by nondeflecting supports and at
its middle by simply supported timber beam (2) that is 8 in. wide
and 12 in. deep. In the unloaded condition, steel beam (1) touches,
but exerts no force on, timber beam (2). The length of the steel
beam is L 1 = 24 ft, and its modulus of elasticity is E 1 = 29 × 10 3 ksi.
The length and the modulus of elasticity of the timber beam are L 2 =
15 ft and E 2 = 1.8 × 10 3 ksi, respectively. Determine the maximum
flexural stress
(a) in the steel beam.
(b) in the timber beam.
(c) in the steel beam if the timber beam is removed.
A B C
x
L 1
2
6 m 7 m
(1)
5 m
A
(1)
P
L 1
2
E
FIGURE p11.45
p11.46 A W530 × 66 structural steel [E = 200 GPa] wide-flange
shape is loaded and supported as shown in Figure P11.46. A uniformly
distributed load of 70 kN/m is applied to the beam, causing
the roller support at B to settle downward (i.e., be displaced downward)
by 10 mm. Determine
(a) the reactions at supports A and B.
(b) the maximum bending stress in the beam.
C
(2)
L 2
2
FIGURE p11.47/48
D
L 2
2
B
477