Question

The bar in the figure has constant cross sectional area A . The top half of the bar is made of material 1 with mass density ro1 , and Young’s modulus E1 . The bottom half of the bar is made of material 2 with density ro2 and Young’s modulus E2=2E1 . The total length of the bar is L . When the bar is hung from the ceiling, it stretches under its own weight. No other loads are applied. Assume p2 >> p1 [so you can neglect the gravity load on the top half of the bar].

1. Obtain a symbolic expression for .
For 0 <x< L/2, fx(x)=
For 0 <x< L, fx(x)=

2. Obtain a symbolic expression for .
For 0 <x< L/2, N(x)=
For 0 <x< L, N(x)=

3. Obtain a symbolic expression for
For 0 <x< L/2, ea(x)=
For 0 <x< L, ea(x)=

4. btain a symbolic expression for the total elongation of the bar

Answer 1

for part 4

(rho_2*g*L^2)/(4*E_1)+(rho_2*g*L^2)/(8*E_2)