analysis of statically - wikispaces. classify each of the trusses in the figure below as stable,...
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1. Classify each of the trusses
in the figure below as stable,
unstable, statically determinate,
or statically indeterminate. The
trusses are subjected to
arbitrary external loadings that
are assumed to be known and
can act anywhere on the
trusses.
Problem Set 5
2. Classify each of the trusses
in the figure below as stable,
unstable, statically determinate,
or statically indeterminate. The
trusses are subjected to
arbitrary external loadings that
are assumed to be known and
can act anywhere on the
trusses.
Problem Set 5
METHOD OF JOINTS
In the method of joints, the axial forces in the members of a
statically determinate truss are determined by considering the
equilibrium of its joints.
1. Always assume the unknown member forces acting on the joint’s
free-body diagram to be in tension (i.e. pulling on the pin). If this is
done, then numerical solution of the equilibrium equations will
yield positive scalars for members in tension and negative scalars for
members in compression. Once an unknown member force is found,
use its correct magnitude and sense (T or C) on subsequent joint
free-body diagrams.
2. The correct sense of direction of an unknown member force can,
in many cases, be determined by inspection.
METHOD OF JOINTS
Identification of Zero-Force Members
1. If only two noncollinear members are connected to a joint
that has no external loads or reactions applied to it, then the
force in both members is zero.
2. If three members, two of which are collinear, are connected
to a joint that has no external loads or reactions applied to it,
then the force in the member that is not collinear is zero.
METHOD OF SECTIONS
The method of sections involves cutting the truss into two
portions by passing an imaginary section through the members
whose forces are desired. Sections should be chosen that do
not pass through more than three members with unknown
forces. The desired members forces are then determined by
considering the equilibrium of one of the two portions of the
truss.
1. Using the method of joints, indicate all the members of the
truss shown in the figure below that have zero force.
Problem Set 6
2. Determine all the member forces and identify zero-force
members. Use method of sections to double-check the force in
members CD, ID, and IH.
Problem Set 6
3. Determine the force in members GF and GD of the truss
shown in the figure below. State whether the members are in
tension or in compression. The reactions at the supports have
been calculated.
Problem Set 6
4. Determine the force in members BC and MC of the K-truss
shown in the figure below. State whether the members are in
tension or in compression. The reactions at the supports have
been calculated.
Problem Set 6