Two Equations Involving F1 and F2  
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The figure shows the free body diagram around the flange at B. The free body diagram cuts across the rod above and the post below. The axial forces on the rod and the post are F subscript 1 directed vertically upwards and F subscript 2 directed vertically downwards respectively. The parameters corresponding to the rod are A subscript 1, L subscript 1, alpha subscript 1 and E subscript 1. The parameters corresponding to the post are A subscript 2, L subscript 2, alpha subscript 2 and E subscript 2.

Two equations involving the unknown forces F1 and F2 have been developed. The following equation was derived from equilibrium:

∑Fy=F1-F2=0

The compatibility equation was derived from the deformations involved in this particular problem:

F1L1A1E1+α1∆TL1        +F2L2A2E2+α2∆TL2=0

These two equations can be solved simultaneously to compute the forces F1 and F2.