Statically Indeterminate Problems with axial loading

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Statically Indeterminate Problems with axial
loading

• John Duke
• Lecture 5

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EX. 2.02
What do we know about deformation?
RIGID END plate? d1d2
1 equation 1 unknown from STATICS
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Deforms
Statics
Solve for P2 then use it to solve for P1
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EX. 2.03
1 eqn 2 unknowns from STATICS
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DEFORMS
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From STATICS
From DEFORMS
Solve for RA then use it to solve for RB.
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2.33
See Example 2.02
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2.39
See Example 2.03
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2.43
See Example 2.03 with the deformation imposed.
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2.45
?
dBERAB?
dDCRDC?
Ay Ax
BE BE
BE
DC DC
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As nut at B is turned force BE develops! dBE
-(1 turn)(deformation due to load) dBE
-(0.1)(PBELBE/AE) LBE 90in-0.1in 90in
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Static Indeterminacy (using superposition)

• Structures for which internal forces and
  reactions cannot be determined from statics alone
  are said to be statically indeterminate.

• A structure will be statically indeterminate
  whenever it is held by more supports than are
  required to maintain its equilibrium.

• Redundant reactions are replaced with unknown
  loads which along with the other loads must
  produce compatible deformations.

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Example 2.04
Determine the reactions at A and B for the steel
bar and loading shown, assuming a close fit at
both supports before the loads are applied.

• SOLUTION
• Consider the reaction at B as redundant, release
  the bar from that support, and solve for the
  displacement at B due to the applied loads.

• Solve for the displacement at B due to the
  redundant reaction at B.

• Require that the displacements due to the loads
  and due to the redundant reaction be compatible,
  i.e., require that their sum be zero.

• Solve for the reaction at A due to applied loads
  and the reaction found at B.

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Example 2.04
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Example 2.04