Solve using a computer not by hand please Write explanations

Solve using a computer not by hand please. Write explanations for every step thanks.

A tensile impact bar, shown on the left hand side of the figure below, fractured in service. Because the failure happened to occur near the center, a naive technician makes a new bar exactly like the old one except that the middle third is enlarged to twice the diameter of the ends. Assuming that stress concentration can be neglected (not very realistic), how do the impact capacities of the new and old bars compare?

Solution

The old bar if failed in tension at the center, then increasing the cross-section at the center won\'t really help.

Because if the old bar has failed due to tensile loading then it is due to the fact that the stress applied (Force/Cross-section area) is more than the ultimate tensile strength of the bar.

Now, the cross-section has doubled at the centre but not all along the length. But the force is equally applied all along the length of the new bar. So, the new bar will surely not fail at the centre but it will fail where the cross-section area is same as the old bar.

Because, stress at the centre will reduce but not at other places.

So, increasing the cross-section at the centre will prevent the failure at the centre but it will fail at some other point as the stress (Force/area) will be same as it was in the old rod.