Analysis of Structures

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ME 221 StaticsLecture 15bSections 6.1 6.4
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Chapter 6 Analysis of Structures

• The knowledge of internal forces is a
  fundamental requirement for true design

• The Structural elements are
• Trusses
• Frames
• Machines

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Trusses
Composed of slender straight pieces connected
together by frictionless pins where all the loads
(no moments) are applied.
Each member will act as a two-force member
(either in tension or compression). All the
forces acting on a truss member are axial.
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Frames Are designed to support, prevent or
transmit loads (forces, no moments). At least
one member is not a two-force member.
Machines Are designed to transmit force, motion
or energy (forces and moments). Will always have
at least one member with multiple forces.
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Planar Trusses
If the planar truss (2-D) is statically
determinant, then the number of joints is related
to the number of reactions and internal members
by
2j m r j number of joints m number of
internal members r number of reactions
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Analysis of Trusses Using the Method of Joints
We need to solve for (1) - Internal forces
FAB, FAC, and FBC (2) - Reactions Ax, Ay and Cy
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Joint A
FAB cosa FAC Ax -Pax .(1) FAB sina
Ay -Pay (2)
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At Joint C
FCB
PCy
b
FCA
PCx
C
Cy
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At Joint B
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Using Matrix Notation
-1

Using manual calculations
Look for joints with 2 unknowns
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Example
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Example
6 kN
A
B
3 kN
0.9 m
C
D
E
1.2 m 1.2 m
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6 kN
A
B
4
4
5
9
15
3 kN
9
15
5
C
16
4
4
16
E
D