Need Help with Mechanical Principles: Calculating Stress, Strain, and Extension

[Curly91]

Hey guys. Just signed up hear after finding the website. I really need some help on Mechanical Principles as i have just been handed work to do once i came back from my car crash. I don't have a clue what any of it means so i could really do with your help.

One of the questions is: A steel bar of 70mm dia is subjected to a pull of 120kN. If E=200GN/m2 and the length is 400mm, calculate:
a) the tensile stress
b) the tensile straing
c) the extension

Any help at all would be appreciated.

 

[Q_Goest]

Can you write down any of the relevant equations? How does stress relate to strain and modulus (E)? If you know strain, and the total length, how would you find extension?

 

[piercas]

Hi there,

I am sorry to hear about your car crash and I am here to help with your mechanical principles work. Let's break down the question to better understand it.

First, we have a steel bar with a diameter of 70mm, which is being pulled with a force of 120kN. The length of the bar is 400mm.

To calculate the tensile stress, we will use the formula stress = force/area. In this case, the area of the bar can be calculated using the formula area = π*(diameter/2)^2, where π is the mathematical constant pi. Plugging in the values, we get an area of approximately 3848 mm^2.

Now, plugging this into the stress formula, we get: stress = 120kN / 3848 mm^2 = 31.2 N/mm^2.

Moving on to the tensile strain, we will use the formula strain = change in length/original length. In this case, the change in length is the extension of the bar, which we will calculate next. The original length is given as 400mm.

To calculate the extension, we will use the formula extension = force*length/area*E, where E is the modulus of elasticity for steel (200GN/m^2). Plugging in the values, we get an extension of approximately 0.015 mm.

Now, we can calculate the tensile strain: strain = 0.015 mm / 400 mm = 0.0000375.

Finally, to calculate the extension, we will use the formula extension = force*length/area*E. Plugging in the values, we get an extension of approximately 0.015 mm.

I hope this helps you understand how to calculate stress, strain, and extension in mechanical principles problems. If you need further clarification, please let me know. Good luck with your work!