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posted by  Minicaky on 10/3/2009 6:18:55 PM  |  status: Closed  |  Earned Karma: 50

Mechanis of Materials 5th ed

Course Textbook Chapter Problem Needs by
Mechanics of Materials Mechanics of Materials (5th) by Beer, Johnston, DeWolf 2 76P 10/6/2009 at 6:00:00 PM
Question Details:
A vibration isolation unit consists of two blocks of hard rubber bonded to plate AB and to rigid supports as shown (see bk). For type and grade of rubber used allowable τ = 220psi and G=1800psi. Knowing that a centric vertical force of magnitude P=3.2kips must cause a 0.1in vertical deflection of plate AB, determine smallest allowable dimensions a and b of block.
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posted by PhysicsPhanatic on 10/4/2009 2:02:51 PM  |  status: Live
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Response Details:
First, consider the rubber block on the right. It carries a shearing force equal to (1/2)P. Then the shearing stress is given by or required . But A = (3.0)b, and therefore b = A / 3.0 = 7.2727 / 3.0 = 2.42 in.
Next Step:

Now use b = 2.42 in and τ = 220 psi
Shearing strain:
But . Therefore, we find that
a = δ / γ
   = 0.1 / 0.12222
   = 0.818 in
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