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If the solid bar of Problem 19 did not suffer temperature change, but instead was subjected to a tensile axial force P, as shown in Figure 1.14, determine σ1 and σ2.

Compound bar under axial tension

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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.

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