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

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