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Key Concept:
A
truss is a structure where each member connects to adjoining members
by a pin and where all
forces on the truss act at the pin connections. Each member is a
two-force member with
one force at each end of the member.
These forces are equal in
magnitude, opposite in
direction, and collinear. Thus truss members are either in tension,
in compression, or have no force in them. i.e.
a zero force member
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In a Nut Shell: Since each member connects to the next member by a pin, the
resultant force
in each truss member acts
along the member. There can be no
bending nor shear in a truss
member. Common examples of trusses are roof trusses
and bridge trusses.
Strategy (detailed in the table below)
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Draw
a FBD of the entire truss to determine the support reactions. Sometimes
this
step is not needed and you can proceed to find the forces in each member.
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For analysis use the method of joints,
the method of sections, or perhaps a combination of both
methods. A recommendation is to
assume each truss member
is in tension. Then a negative
result indicates that the member is in compression.
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In the method of joints isolate each joint, construct a FBD, and apply
the two equations of equilibrium ΣFx = 0 and ΣFy
= 0 at each joint. (for planar
trusses)
Then proceed from one joint to the next until you find the forces desired. You can only solve for two unknowns at any
given joint . If more than two unknowns occur at a
joint, then you need to move to another joint in the truss that has only
two unknowns. |
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In the method of sections pass a section within the truss, cutting the
truss along
any desired line or curve. In this
case there will be three equilibrium equations
for a planar truss. They are ΣFx
= 0 , ΣFy
= 0 and Σ M = 0 about a convenient point. For each FBD you will then have three
equations. So you can only solve for
three unknowns for each section. |
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The method of sections
has the advantage that you can investigate forces in members
within the middle of the truss without
proceeding from one end of the truss to the
other end of the truss moving from joint
to joint.
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Click
here to continue with discussion of trusses.
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