If the gap between C and the rigid wall at D is initially 0.15 mm, determine the magnitudes of the support reactions at A and D
when the force P
1 answer:
Answer / Explanation
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If the gap between C and the rigid wall at D is initially 0.15 mm, determine the support reactions at A and D when the force is applied. The assembly is made of A36 steel
Procedure
Recalling the the equation of equilibrium and referencing the free body diagram of the assembly,
Therefore, ∑fₓ = 0 ,
where, 20 ( 10³) - Fₐ - Fₙ = 0 --------------equation (1)
Now, recalling the compatibility equation, while utilizing the superposition method,
Therefore, δₓ - δfₓ
= 0.15 = 200(10³)(600) ÷ π/4 (0.05²)(200)(10⁹) - [ Fₐ (600) / π/4 (0.05²)(200)(10⁹) + Fₐ (600) π / 4 (0.05²)(200)(10⁹) ]
Solving this further,
We get: Fₐ = 20365.05 N
Which is equivalent to = 20.4 kN.
Now, substituting the answer (Fₐ) into equation (1)
Fₙ = 179634.95 N
= 180 kN
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