There are two unknown forces in this bar, namely, F_{1} and F_{2}; 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 F_{1} = tensile force in bar (1)

and F_{2} = tensile force in bar (2)

Now, from equilibrium conditions

P = F_{1} + F_{2}

i.e. P = σ_{1}A_{1 }+ σ_{2}A_{2 ....}(1.7)

Substituting equation (1.6) into equation (1.7) gives:

N.B. If P is a compressive force, then both σ_{1} and σ_{2 }will be compressive stresses (i.e. negative), and vice-versa if P were tensile.