Calculating Extension & Stress in Machined Steel Bar

[wock]

Homework Statement

1. A steel bar 375mm long is machined to give a diameter of 75mm for the first 175mm length, a diameter of 45mm for the next 100mm length and a diameter of 37mm for the final 100mm length. Determine:

(i) The total extension of the bar when it’s subjected to an axial tensile load of 84 kN.

(ii) The tensile stress in each portion of the bar.
Assume E = 200 GN/m2

Homework Equations

The Attempt at a Solution

can this be solved by working out each part as if it were 3 separate bars ?

 

[vector3]

The simple answer is yes. A bar with varing diameter as noted is nothing more that 3 springs in "series" with 3 different spring constants "k". An axial force applied to springs in series would be equal to the sums of the $k_i \cdot x_i$.

$$k_i$$ in this problem would be $\frac{A_{i}E}{L_i}$

 

[wock]

thanks