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PROBLEM 16.47
Solve Prob. 16.46, assuming that the effective length of the column is decreased to
20 ft.
PROBLEM 16.46 A square structural tube having the cross section shown is used
as a column of 26-ft effective length to carry a centric load of 65 kips. Knowing
that the tubes available for use are made with wall thicknesses ranging from
1
4
in.
to
3
4
in. in increments of
1
16
in., use allowable stress design to determine the
lightest tube that can be used. Use
36 ksi
Y
s
=
and
6
29 10 psi.E= ×
consent of McGraw-Hill Education.
PROBLEM 16.48
Two
11
22
3 2 -in.×
angles are bolted together as shown for use as a column of 6-
ft effective length to carry a centric load of 54 kips. Knowing that the angles
available have thickness of
1
4
,
3
8,
and
1
2 in.,
use allowable stress design to
determine the lightest angles that can be used. Use
36 ksi
Y
s
=
and
6
29 10 psi.E= ×
SOLUTION Continued
22
22
36/50.058
cr
cr
all
72 75.616 133.68
0.9522
(29000) 50.058 ksi
( / ) (71.616)
[0.658 ](36) 26.64 ksi
(26.64)(2.88) 45.9 kips 54 kips (not allowed)
1.67 1.67
pp
s
s
s
= = <
= = =
= =
= = = <
e
ee
L
r
E
Lr
A
P
Use
1 13
3 2 in.
2 28
L××
consent of McGraw-Hill Education.
PROBLEM 16.49
A column with the cross section shown has a 13.5-ft effective length. Using a factor
of safety equal to 2.8, determine the allowable centric load that can be applied to
the column. Use E = 29 × 106 psi.
SOLUTION
( ) ( )
min 1 2
3
3
4
2
cr 2
26 4
2
all
2
11 1 1
2 in. 6 in. 10 in. in.
12 2 12 4
18.0130 in
(29 10 psi)(18.0130 in )
[(13.5 ft)(12 in./ft)]
196.451kips
196.451 kips
2.8
e
I II
EI
PL
P
= +
= +
=
=
×
=
=
=
p
p
all
70.2 kips
=P
PROBLEM 16.50
The rigid bar AD is attached to two springs of constant k and is in
equilibrium in the position shown. Knowing that the equal and
opposite loads
P
and
′
P
remain horizontal, determine the
magnitude
cr
P
of the critical load for the system.
PROBLEM 16.51
A rigid block of mass
m
can be
supported in each of the four ways
shown. Each column consists of an
aluminum tube that has a 44-mm outer
diameter and a 4-mm wall thickness.
Using
70 GPaE=
and a factor of safety
of 2.8, determine the allowable load for
each support condition.
SOLUTION Continued
Allowable capacity:
Case (1):
4 m
e
LL= =
2
5108
(4)
m=
319 kgm=
Case (2):
2 8 m
e
LL
= =
2
5108
(8)
m=
79.8 kgm=
Case (3):
4 m
e
LL= =
2
5108
(4)
m=
319 kgm=
Case (4):
0.699 2.796 m
e
LL= =
2
5108
(2.796)
m=
653 kgm=
PROBLEM 16.52
The steel rod BC is attached to the rigid bar AB and to the fixed
support at C. Knowing that
6
11.2 10 psi,G= ×
determine the
diameter of rod BC for which the critical load
cr
P
of the system is
80 lb.
PROBLEM 16.53
Supports A and B of the pin-ended column shown are at a fixed distance L from each
other. Knowing that at a temperature T0 the force in the column is zero and that buckling
occurs when the temperature is
10
,TT T= +∆
express ∆T in terms of b, L, and the
coefficient of thermal temperature
α
.
consent of McGraw-Hill Education.
PROBLEM 16.48
Two
11
22
3 2 -in.×
angles are bolted together as shown for use as a column of 6-
ft effective length to carry a centric load of 54 kips. Knowing that the angles
available have thickness of
1
4
,
3
8,
and
1
2 in.,
use allowable stress design to
determine the lightest angles that can be used. Use
36 ksi
Y
s
=
and
6
29 10 psi.E= ×
SOLUTION Continued
22
22
36/50.058
cr
cr
all
72 75.616 133.68
0.9522
(29000) 50.058 ksi
( / ) (71.616)
[0.658 ](36) 26.64 ksi
(26.64)(2.88) 45.9 kips 54 kips (not allowed)
1.67 1.67
pp
s
s
s
= = <
= = =
= =
= = = <
e
ee
L
r
E
Lr
A
P
Use
1 13
3 2 in.
2 28
L××
consent of McGraw-Hill Education.
PROBLEM 16.49
A column with the cross section shown has a 13.5-ft effective length. Using a factor
of safety equal to 2.8, determine the allowable centric load that can be applied to
the column. Use E = 29 × 106 psi.
SOLUTION
( ) ( )
min 1 2
3
3
4
2
cr 2
26 4
2
all
2
11 1 1
2 in. 6 in. 10 in. in.
12 2 12 4
18.0130 in
(29 10 psi)(18.0130 in )
[(13.5 ft)(12 in./ft)]
196.451kips
196.451 kips
2.8
e
I II
EI
PL
P
= +
= +
=
=
×
=
=
=
p
p
all
70.2 kips
=P
PROBLEM 16.50
The rigid bar AD is attached to two springs of constant k and is in
equilibrium in the position shown. Knowing that the equal and
opposite loads
P
and
′
P
remain horizontal, determine the
magnitude
cr
P
of the critical load for the system.
PROBLEM 16.51
A rigid block of mass
m
can be
supported in each of the four ways
shown. Each column consists of an
aluminum tube that has a 44-mm outer
diameter and a 4-mm wall thickness.
Using
70 GPaE=
and a factor of safety
of 2.8, determine the allowable load for
each support condition.
SOLUTION Continued
Allowable capacity:
Case (1):
4 m
e
LL= =
2
5108
(4)
m=
319 kgm=
Case (2):
2 8 m
e
LL
= =
2
5108
(8)
m=
79.8 kgm=
Case (3):
4 m
e
LL= =
2
5108
(4)
m=
319 kgm=
Case (4):
0.699 2.796 m
e
LL= =
2
5108
(2.796)
m=
653 kgm=
PROBLEM 16.52
The steel rod BC is attached to the rigid bar AB and to the fixed
support at C. Knowing that
6
11.2 10 psi,G= ×
determine the
diameter of rod BC for which the critical load
cr
P
of the system is
80 lb.
PROBLEM 16.53
Supports A and B of the pin-ended column shown are at a fixed distance L from each
other. Knowing that at a temperature T0 the force in the column is zero and that buckling
occurs when the temperature is
10
,TT T= +∆
express ∆T in terms of b, L, and the
coefficient of thermal temperature
α
.
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