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

y,v
a b c
a
b
x,u
A B C D
p5.18 The truss shown in Figure P5.18 is constructed from three
aluminum alloy members, each having a cross-sectional area A =
850 mm 2 and an elastic modulus E = 70 GPa. Assume that a =
7.0 m, b = 4.5 m, and c = 5.0 m. Calculate the horizontal displacement
of roller A when the truss supports loads of P = 12 kN and
Q = 30 kN acting in the directions shown.
p5.19 Three bars, each with a cross-sectional area of 750 mm 2 and
a length of 5.0 m, are connected and loaded as shown in Figure P5.19.
Bars (1) and (3) are made of steel [E = 200 GPa] and bar (2) is made
of an aluminum alloy [E = 70 GPa]. At D, all three bars are connected
to a slider block that is constrained to travel in a smooth, horizontal
slot. When the load P is applied, the strain in bar (2) is found to be
0.0012 mm/mm. Assume that a = 2.4 m and b = 1.6 m. Determine
(a) the horizontal deflection of D.
(b) the deformations in each of the three bars.
(c) the magnitude of load P.
p5.20 The pin-connected assembly shown in Figure P5.20 consists
of solid aluminum [E = 70 GPa] rods (1) and (2) and solid steel
[E = 200 GPa] rod (3). Each rod has a diameter of 16 mm. Assume
that a = 2.5 m, b = 1.6 m, and c = 0.8 m. If the normal stress in any
rod must not exceed 150 MPa, determine
(a) the maximum load P that may be applied at A.
(b) the magnitude of the resulting deflection at A.
102
P
FIGURE p5.17
a
b
A
L 1
a
Q
FIGURE p5.18
B
C
A
FIGURE p5.19
(1)
(2)
(3)
(1)
C
P
L 2
b
Smooth slot
v
y,v
D
B
(2)
c
P
x,u
Q
u
P
A
FIGURE p5.20
(3)
p5.21 A tie rod (1) A
and a pipe strut (2) are
used to support a load
P = 25 kips as shown in
Figure P5.21. Pipe strut
(1)
(2) has an outside diameter
of 6.625 in. and a
wall thickness of 0.280 in.
B
Both the tie rod and the
pipe strut are made of
(2)
structural steel with a
modulus of elasticity E =
P
29,000 ksi and a yield
C
strength s Y = 36 ksi.
c
For the tie rod, the minimum
factor of safety FIGURE p5.21
with respect to yield is
1.5 and the maximum allowable axial elongation is 0.30 in.
(a) Determine the minimum diameter required to satisfy both
constraints for tie rod (1).
(b) Draw a deformation diagram showing the final position of
joint B.
p5.22 Two axial
members are used to
support a load P =
72 kips as shown in Figure
P5.22. Member (1)
is 12 ft long, has a crosssectional
area A 1 =
1.75 in. 2 , and is made of
structural steel [E = A
29,000 ksi]. Member (2)
is 16 ft long, has a crosssectional
area of A 2 = FIGURE p5.22
4.50 in. 2 , and is made of
an aluminum alloy [E = 10,000 ksi].
(a) Compute the normal stress in each axial member.
(b) Compute the deformation of each axial member.
(c) Draw a deformation diagram showing the final position of
joint B.
(d) Compute the horizontal and vertical displacements of
joint B.
B
(1)
(2)
(1)
C
D
(2)
B
P
c
c
C
55°
a
b