Problem 6.57
Determine if each truss is statically determinate, statically indeterminate, or a
mechanism.
(a) (b)
(c) (d)
Problem 6.58
Determine if each truss is statically determinate, statically indeterminate, or a
mechanism.
(a) (b)
(c) (d)
Problem 6.59
For the K truss shown, determine the force supported by members
EH
,
FH
,
F I
, and
GI
.Hint: Use the method of sections twice with cuts such as those
described in Example 6.5 on p. 390.
Problem 6.60
For the K truss shown, determine the force supported by members
HJ
,
HK
,
IK
, and
IL
.Hint: Use the method of sections twice with cuts such as those
described in Example 6.5 on p. 390.
Problem 6.61
Agambrel room-in-attic truss is shown.
(a)
Use equation counting, Eq. (6.22) on p. 383, to show that this truss is a
mechanism.
(b)
This truss type is popular for many applications. Discuss why this
truss design does not collapse in view of the fact that it is a mechanism
according to truss theory, as shown in Part (a).
(c)
If the roller support at
J
is replaced by a pin support, equation counting
indicates that the number of equations and the number of unknowns is
the same. With a pin support at
J;
is the structure no longer a mechanism
according to truss theory? Explain.
Problem 6.62
The two truss designs differ only in their depths.
(a)
Determine the forces supported by all members of both trusses, and compare values for corresponding
members in each truss.
(b) Offer reasons why truss (b) is the better design.
(c) Offer reasons why truss (a) is the better design.
(d)
Overall, which of the two trusses do you believe is stronger, assuming all members are of the same
material and have the same cross-sectional shape?
Statics 2e 887
Part (c)
Even though members
AB
and
DF
in truss (a) have higher com-
pressive forces than in truss (b), they are shorter and hence will
require higher forces in order to cause buckling than the correspond-
ing members in truss (b).
Part (d)
A definitive answer to this question requires knowledge of the actual mode of failure, which
requires knowledge of the material and cross-section shape for all of the members. Such issues are discussed
in mechanics of materials. Nonetheless, if we assume failure is due to in-plane buckling, which is a typical
mode of failure for trusses, then we will compare the buckling loads for member
AB
in each of the two
trusses (member AB is both the longest and most highly loaded member in compression). For truss (a),
where the constants in these equations are the same if the material and cross-section shape of member
AB
is
the same. The ratio of the buckling loads in member AB for the two trusses is
Problem 6.63
A bar
AB
is supported by a pin at
A
and a horizontal spring
BC
with stiffness
k
. When
the bar is vertical, the force in the spring is zero. The force
P
applied to the bar is vertical.
Determine the value of
P
at which the structure buckles (i.e., becomes unstable). Express
your answer in terms of parameters like
k
,
L
, etc. Hint: For small angles, with
measured
in radians, sin and cos 1.
Problem 6.64
A bar
AB
is supported by a pin at
A
and a torsional spring at
B
with stiffness
kt
. When the bar
is vertical, the moment in the spring is zero. The force
P
applied to the bar is vertical. Determine
the value of
P
at which the structure buckles (i.e., becomes unstable). Express your answer in
terms of parameters like
kt
,
L
, etc. Hint: For small angles, with
measured in radians,
sin
and cos 1.
L:(8)
890 Solutions Manual
Problem 6.65
The truss shown has a socket support at point
D
, rollers at points
E
and
F
, and
a link from Eto Gthat prevents motion in the xdirection.
(a) Does the truss have partial fixity or full fixity?
(b)
Determine if the truss is statically determinate or statically indeterminate.
(c)
Determine the force supported by all members of the truss if
PD1kip
,
QD2kip, and RD3kip.
Statics 2e 891
Problem 6.66
The truss shown has a socket support at point
A
and rollers at points
B
and
C
.
Points A,B, and Clie in the xy plane, and point Elies in the y´ plane.
(a) Does the truss have partial fixity or full fixity?
(b)
Determine if the truss is statically determinate or statically indeterminate.
(c)
Determine the force supported by all members of the truss if
PD1kN
.
Force Pis vertical.
Problem 6.67
The box shown has cardboard sides and wood strips along
the edges and from corner to corner. The strength of the
box is provided primarily by the wood strips, and a truss
model with 18 members for the wood strips is also shown.
Let the truss be supported by rollers at points
A
and
B
, a
socket at point
C
, and a short link at
E
that is parallel to
the
y
direction. For the
100
N and
150
N forces shown,
determine the force supported by the six members that
emanate from joint A.
Problem 6.68
Repeat Prob. 6.67 to determine the force supported by
the six members that emanate from joint C.