Trusses and Machines

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Trusses and Machines

• ENGR 221
• February 24, 2003

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Lecture Goals

• 7-2 Plane Trusses
• 7-3 Space Trusses
• 7-4 Frames and Machines

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Equilibrium Problem Example
A beam is supported by a ball and socket joint
two cables . Determine the reactions at support
A and tension in two cables.
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Equilibrium Problem Example
Draw the free-body diagram of the beam.
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Equilibrium Problem Example
Obtain the unit vectors of DB and DC for the
tension in the cables.
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Equilibrium Problem Example
Take the moment about A.
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Equilibrium Problem Example
Take the moment about A.
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Equilibrium Problem Example
Using the summations of moments about A and look
at the components.
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Equilibrium Problem Example
Look at the summation of forces
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Equilibrium Problem Example
The resultant force at A is
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Trusses -Definition
Trusses are structures composed entirely of two
force members . They consists generally of
triangular sub-element and are constructed and
supported so as to prevent any motion.
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Truss
Space Trusses - are structures that are not
contained in a single plane and/or are loaded out
of the plane of the structure.
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Truss Assumptions
There are four main assumptions made in the
analysis of truss
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Simple Truss
The basic building block of a truss is a
triangle. Large truss are constructed by
attaching several triangles together A new
triangle can be added truss by adding two members
and a joint. A truss constructed in this
fashion is known as a simple truss.
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Simple Truss
It has been observed that the analysis of truss
can be done by counting the number member and
joints on the truss to determine the truss is
determinate, unstable or indeterminate.
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Simple Truss
A truss is analysis by using m2j-3, where m is
number of members, j represents the number of
joints and 3 represents the external support
reactions.
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Simple Truss
If mlt 2j-3, then the truss is unstable and will
collapse under load.
If mgt 2j-3, then the truss has more unknowns
than know equations and is an indeterminate
structure.
If m 2j-3, ensures that a simple plane truss is
rigid and solvable, it is neither sufficient nor
necessary to ensure that a non-simple plane truss
is rigid and solvable.
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Method of Joints -Truss
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Method of Joints -Truss
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Truss Example Problem
Determine the loads in each of the members by
using the method of joints.
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Truss Example Problem
Draw the free-body diagram. The summation of
forces and moment about B result in
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Truss Example Problem
Look at Joint B
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Truss Example Problem
Look at Joint D and find the angle
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Truss Example Problem
Look at Joint C and find the angle
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Method of Joints Class Problem
Determine the forces in the truss using the
method of joints.
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Method of Sections -Truss
The method of joints is most effective when the
forces in all the members of a truss are to be
determined. If however, the force is only one or
a few members are needed, then the method of
sections is more efficient.
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Example Problem
Determine the forces in members FH, DH,EG and BE
in the truss using the method of sections.
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Truss Example Problem
Draw the free-body diagram. The summation of
forces and moment about H result in
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Truss Example Problem
Do a cut between BD and CE
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Truss Example Problem
Take moment about A
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Truss Example Problem
Do a cut between HD and GE
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Truss Example Problem
Take the moment about I Take the moment about D
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Truss Example Problem
Do a cut between HD and HI
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Truss Example Problem
Take the sum of forces in y direction
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Truss - Class Problem
Determine the forces in members AE and BE in the
truss using the method sections.
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Truss Class Problem
Determine the loads in members,BC, HD FG, and DE.
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Homework (Due 3/3/03)
Problems
7-9, 7-11, 7-13, 7-15, 7-16