How Is Stress Calculated in a Bar Using Transposed Formulas?

[anthonyk2013]

Need to find stress in a bar

(α1L1ΔT1+x1)+(α2L2ΔT2+x2)=0

(α1L1ΔT1+ε1L1)+(α2L2ΔT2+ε2L2)=0

(α1L1ΔT1+σ1/E1*L)+(α2L2ΔT2+σ2/E2*L)=0

(α1L1ΔT1+α2L2ΔT2)+σ1/E1*L1+σ2/E2*L2=0

αΔT(L1+L2)+1/E(σ1L1+σ2L2)=0

I can work out most of this formula but i don't understand how we got the highlighted line 1/E(σ1L1+σ2L2)=0

 

[haruspex]

i don't understand how we got the highlighted line 1/E(σ1L1+σ2L2)=0

You don't mean the '=0' there, right?
I presume it should be (σ1/E1)*L1+(σ2/E2)*L2 and (1/E)(σ1L1+σ2L2), which are the same if E=E1=E2. With no context, I cannot tell whether E1=E2.

 

[anthonyk2013]

No=0 fine. It 1/E where did that come from.

 

[haruspex]

No=0 fine. It 1/E where did that come from.

You have (σ1/E1)*L1+(σ2/E2)*L2. If E1=E2=E then that reduces to (σ1/E)*L1+(σ2/E)*L2 = (1/E)(σ1)*L1+(1/E)(σ2)*L2 = (1/E)(σ1L1+σ2L2).