Two rods of identical dimensions, with Young’s moduli Y1 and Y2 are joined end to end. The equivalent Young’s modulus for the composite rod is
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To get Y effective we assume a rod of new material but having same dimension as combind given rod.
Now use change in new rod is equals to sum of change in two given rods while there are under same stress.
F2l / AY = Fl / AY1 + Fl / Ay2
Y=2Y1Y2 / (Y1+Y2)