Question

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

Answer 1

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 + σ₂A_{2 ....}(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.

Comments

Yes correct ans.