• Support PF! Buy your school textbooks, materials and every day products Here!

Calculate force required to reduce diameter of bar?

  • Thread starter bensm0
  • Start date
  • #1
20
0
A mild stell bar 40 mm diameter and 100 mm long is subjected to a tensile force along its axis.
Young's modulus of elasticity = 200 GN m -2. Poisson's ratio is 0.3.
Calculate the force required to reduce the diameter to 39.99 mm

It says use the x-y coordinate system?? This i don't understand?

Thank you
 

Answers and Replies

  • #2
nvn
Science Advisor
Homework Helper
2,128
32
bensm0: Hint 1: What is the equation for the definition of Poisson's ratio, in terms of transverse strain εy, and axial strain εx? Hint 2: What is the equation for the bar axial elongation, in terms of the applied tensile force P?

We are not allowed to give you the relevant equations for your homework. You must list relevant equations yourself, and show your work. And then someone might check your math.

Hint 3: The y axis is the bar transverse direction. The y axis is parallel to the bar diameter.

By the way, GN*m^-2 is called GPa. Always use the correct, special name for a unit. E.g., 200 GPa, not 200 GN*m^-2.
 
  • #3
20
0
ok so i think i may have the answer:

poisson's ratio = - transverse strain/axial strain
Transverse strain = (39.99 - 40)/40 = -0.25x10^-3
axial strain = -(-0.25x10^-3/0.3) = 833.333x10^-6
Axial stress = 833.333x10^-6 x 200x10^9 = 166.6666x10^6
Force = stress x area
Force = 166.6666x10^6 x (0.25∏x0.04^2) = 5.236x10^6 N

Am i on the right track?
 
  • #4
nvn
Science Advisor
Homework Helper
2,128
32
bensm0: Nice work, except you did not check your arithmetic, and got the wrong answer.
 
  • #5
Hi there, i am also stuck on this question along with the rest of the assignment to be honest. Bensm0 contact me on here if you want to try and tackle this togeter?
 
  • #6
Hi there,

Ive been working on this for most of today and i have come up with the following :

Axial Strain = 8.333 x 10^-4

Axial Stress = 166.66 x 10^6

Force = Stress x Area
= (166.66 x 10^6) x (1.257 x 10^-3)
= 209491.62 N
 

Related Threads on Calculate force required to reduce diameter of bar?

Replies
9
Views
2K
Replies
8
Views
771
Replies
6
Views
9K
Replies
1
Views
1K
Replies
6
Views
15K
Replies
8
Views
4K
Replies
14
Views
3K
  • Last Post
Replies
8
Views
2K
Replies
1
Views
397
Replies
6
Views
13K
Top