There are two unknown forces in this bar, namely, F1 and F2; therefore, two simultaneous equations will be required.
The first of these simultaneous equations can be obtained by considering compatibility, i.e.
deflection of bar (1) = deflection of bar (2)
The second simultaneous equation can be obtained by considering the equilibrium of the compound bar.
Let F1 = tensile force in bar (1)
and F2 = tensile force in bar (2)
Now, from equilibrium conditions
P = F1 + F2
i.e. P = σ1A1 + σ2A2 ....(1.7)
Substituting equation (1.6) into equation (1.7) gives:
N.B. If P is a compressive force, then both σ1 and σ2 will be compressive stresses (i.e. negative), and vice-versa if P were tensile.