The adjacent drawing shows two brass cylinders brazed togeth

The adjacent drawing shows two brass cylinders brazed together. The cylinder AB has a diameter of 15 mm and the cylinder BC has a diameter of 10 mm. The total length of cylinders AB and BC is 100 m. Also it b given that the density of brass is 8470 kg/m^3. Calculate the length of cylinder AB such that the normal stress within cylinder AB equals to the normal stress within cylinder BC.

Solution

we can calculate the length of AB by using deflection formula

PL / AE

given L₁ + L₂ =100

L₁ / A₁ = L₂ / A₂

L₁ / 225 = L₂ /100

(100 - L₂ ) /225 = L₂ /100

(100 - L₂ ) / 9 = L₂ / 4

13L₂ = 400

L₂ = 30.7

L₁ = 69.3