Plan the Solution  
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The figure shows the free body diagram around the flange. The flange connects the post with the rod. The free body diagram cuts across the post labeled 1 and the rod labeled 2. The force on the post is F subscript 1 directed horizontally to the left and the force on the rod is F subscript 2 directed horizontally to the right.

A five-step process will be used to solve this problem:

Step 1. Equilibrium equation
Draw a free-body diagram (FBD) of flange B after the gap has been closed. Write the equilibrium equation.

Step 2. Geometry of deformation equation
Determine the relationship between the deformations in members (1) and (2).

Step 3. Force-deformation relationships
Express the force-deformation relationships for members (1) and (2).

Step 4. Compatibility equation
Substitute the force-deformation relationships into the geometry of deformation equation.

Step 5. Solve equations simultaneously
Solve the equilibrium and compatibility equations simultaneously for the unknown forces F1 and F2.