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PROBLEM 16.2
Knowing that the torsional spring at B is of constant K and that the bar AB is rigid,
determine the critical load
cr.P
SOLUTION
PROBLEM 16.3
Two rigid bars AC and BC are connected as shown to a spring of constant k.
Knowing that the spring can act in either tension or compression, determine the
critical load
cr
P
for the system.
SOLUTION
PROBLEM 16.4
Two rigid bars AC and BC are connected by a pin at C as shown. Knowing that
the torsional spring at B is of constant K, determine the critical load
cr
P
for the
system.
SOLUTION
PROBLEM 16.5
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 vertical, determine the magnitude
cr
P
of the critical
load for the system. Each spring can act in either tension or compression.
SOLUTION
PROBLEM 16.6
The rigid rod AB is attached to a hinge at A and to two springs, each of
constant k. If
450 mm,h=
300 mm,d=
and
200 kg,m=
determine the
range of values of k for which the equilibrium of rod AB is stable in the
position shown. Each spring can act in either tension or compression.
SOLUTION
PROBLEM 16.7
Determine the critical load of a round wooden dowel that is 48 in. long and has a diameter of (a) 0.375 in.,
(b) 0.5 in. Use
6
1.6 10 psi.E= ×
PROBLEM 16.8
Determine the critical load of a pin-ended steel tube that is 5 m long and has a 100-mm
outer diameter and a 16-mm wall thickness. Use
200 GPa.E=
SOLUTION
150 mm 50 16 34 mm
2
o o io
c d cct= = = −= − =
( )
4 4 6 4 64
3.859 10 mm 3.859 10 m
4
oi
I cc
π
−
= −= × = ×
22 9 6 3
cr 22
(200 10 )(3.859 10 ) 305 10 N
(5.0)
EI
PL
ππ
−
××
= = = ×
cr 305 kNP=
consent of McGraw-Hill Education.
PROBLEM 16.9
A compression member of 20-in. effective length consists of a solid 1-in.-
diameter aluminum rod. In order to reduce the weight of the member
by 25%, the solid rod is replaced by a hollow rod of the cross section shown.
Determine (a) the percent reduction in the critical load, (b) the value of the
critical load for the hollow rod. Use
6
10.6 10 psiE= ×
.
PROBLEM 16.10
Two brass rods used as compression members, each of 3-m effective length,
have the cross sections shown. (a) Determine the wall thickness of the
hollow square rod for which the rods have the same cross-sectional area.
(b) Using
105 GPa
E=
, determine the critical load of each rod.
PROBLEM 16.2
Knowing that the torsional spring at B is of constant K and that the bar AB is rigid,
determine the critical load
cr.P
SOLUTION
PROBLEM 16.3
Two rigid bars AC and BC are connected as shown to a spring of constant k.
Knowing that the spring can act in either tension or compression, determine the
critical load
cr
P
for the system.
SOLUTION
PROBLEM 16.4
Two rigid bars AC and BC are connected by a pin at C as shown. Knowing that
the torsional spring at B is of constant K, determine the critical load
cr
P
for the
system.
SOLUTION
PROBLEM 16.5
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 vertical, determine the magnitude
cr
P
of the critical
load for the system. Each spring can act in either tension or compression.
SOLUTION
PROBLEM 16.6
The rigid rod AB is attached to a hinge at A and to two springs, each of
constant k. If
450 mm,h=
300 mm,d=
and
200 kg,m=
determine the
range of values of k for which the equilibrium of rod AB is stable in the
position shown. Each spring can act in either tension or compression.
SOLUTION
PROBLEM 16.7
Determine the critical load of a round wooden dowel that is 48 in. long and has a diameter of (a) 0.375 in.,
(b) 0.5 in. Use
6
1.6 10 psi.E= ×
PROBLEM 16.8
Determine the critical load of a pin-ended steel tube that is 5 m long and has a 100-mm
outer diameter and a 16-mm wall thickness. Use
200 GPa.E=
SOLUTION
150 mm 50 16 34 mm
2
o o io
c d cct= = = −= − =
( )
4 4 6 4 64
3.859 10 mm 3.859 10 m
4
oi
I cc
π
−
= −= × = ×
22 9 6 3
cr 22
(200 10 )(3.859 10 ) 305 10 N
(5.0)
EI
PL
ππ
−
××
= = = ×
cr 305 kNP=
consent of McGraw-Hill Education.
PROBLEM 16.9
A compression member of 20-in. effective length consists of a solid 1-in.-
diameter aluminum rod. In order to reduce the weight of the member
by 25%, the solid rod is replaced by a hollow rod of the cross section shown.
Determine (a) the percent reduction in the critical load, (b) the value of the
critical load for the hollow rod. Use
6
10.6 10 psiE= ×
.
PROBLEM 16.10
Two brass rods used as compression members, each of 3-m effective length,
have the cross sections shown. (a) Determine the wall thickness of the
hollow square rod for which the rods have the same cross-sectional area.
(b) Using
105 GPa
E=
, determine the critical load of each rod.
