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 ρ1, and Young’s modulus E1. The bottom half of the bar is made of material "2" with density ρ2 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 ρ2>>ρ1[so you can neglect the gravity load on the top half of the bar].

Obtain a symbolic expression for N(x).

For 0≤x<L/2, N(x)=
For L/2<x≤ L, N(x)=


Obtain a symbolic expression for ϵa(x).

For 0≤x<L/2, ϵa(x)=
For L/2<x≤ L, ϵa(x)=


Obtain a symbolic expression for the total elongation of the bar, δ.

Answer 1

for problem 1,part 4

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