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Mechanical and structural analysis miscellaneous

Mechanics and Structural Analysis

Direction: Consider a propped cantilever beam ABC under two loads of magnitude P each as shown in the figure below. Flexural rigidity of the beam is EI.

  1. The reaction at C is
    1. 9Pa
      (upwards)
      16L
    2. 9Pa
      (downwards)
      16L
    3. 9Pa
      (upwards)
      8L
    4. 9Pa
      (downwards)
      8L
Correct Option: C

Remove support C.
deflection (at C)

=
2p.a.L2
+
2p.aL
× L
2EIEI

=
3PaL2
EI

Deflection at C due to
RC =
RC × (2C)3
3EI

=
RC × 8L3
3EI

Equating, (by compatibility equation)
2paL2
=
RC × 8L3
EI3EI

⇒ RC =
9Pa
8L



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