A 6.1-m-long solid circular metal rod (E = 150 GPa) must not stretch more than 10 mm when a load of 109 kN is applied to it. Determine the smallest diameter rod that should be used. State your answer in mm.

To solve this problem we will apply the concepts related to the deformation of a body and the normal effort, from which we will obtain the area. From this area applied to the geometric concept of a circular bar we will find the diameter.

The deformation equation in a rod tells us that

Here,

P = Load

L = Length

A = Cross-sectional area

E = Elastic Modulus

Rearranging the Area,

Replacing we have that the area is,

Using the geometric expression for the Area we have,

Therefore the smalles diameter rod is 7.51mm

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