For a solid A36 steel rectangular bar 1 wide by 0125 thick b

For a solid A36 steel rectangular bar 1\" wide by 0.125\" thick by 12\" long that is pulled with a load of 4,000 lbs, what will the change in thickness be? If it were made out of annealed aluminum alloy 6061 instead, would the change in thickness be different or the same and why?

Solution

First We need to calculate change in length of steel bar due to force of 4000 lbs

For Steel Stress is directly proportional to strain

So , Stress = Youngs modulus * (Strain)

Stress = Force / cross sectional area = 4000/0.0125 * 1 = 32000 psi

Strain = Change in length / Original length

and Youngs modulus for steel is = 29000000 psi

So, Strain = Stress / Youngs modulus

Strain = 32000 / 29000000 = 0.001103448 = change in length / original length

Change in length = 120 *  0.001103448 = 0.0132414 in

Now Original Volume of Bar = Cross section area * Original length

Original Volume of Bar = 1 * 0.125 * 12 = 1.5 in³

After extension Volume remains same , so there wil be change in thickness

Volume = 1* New thk (t) * (change in length + original length)

1.5 = 1 * t * (0.0132414 + 12)

New thickness after extension of bar t = 0.12486222 in

So change in thk is = 0.125 -  0.12486222 = 0.0001378 in

If bar is of Aluminium Alloy 6061 there will be change in thickness after loading becase of change in Youngs modulus of Aluminium than Steel.