Finding axial force N from fiber stress and strain

[billy722]

Homework Statement

i can not find the N.
what i can only found is:
D₀=0.02mm;V=0.25;E=10G Pa;A=π(0.02mm/2)²
ΔD=ε_shear×D₀
ε_shear=ε_axial×V
ε_axial=σ_axial / E
σ_axial=N/A

Homework Equations

The Attempt at a Solution

 

[haruspex]

I don't see anything in the question about a tension being applied, so why should it change diameter?

 

[billy722]

stress_Shear= E×I
R=0.01mm,E=10GPa, I₀= (π/4)×(0.01×10^(-3))⁴=7.85 zm⁴
Stress_shear=(10×10⁹×7.85×10^-21)
=78.5p Pa

Shear modulus=E/[2(1+V)] = 10G/[2(1+0.25)]=4GPa
Shear modulus= Stress_shear/ε_shear
ε_shear=78.5p/4G=19.625z

ΔD=ε_shear×D₀
=19.625z×0.02m
=0.3925y m
Is it right?

 

[haruspex]

stress_Shear= E×I
R=0.01mm,E=10GPa, I₀= (π/4)×(0.01×10^(-3))⁴=7.85 zm⁴
Stress_shear=(10×10⁹×7.85×10^-21)
=78.5p Pa

Shear modulus=E/[2(1+V)] = 10G/[2(1+0.25)]=4GPa
Shear modulus= Stress_shear/ε_shear
ε_shear=78.5p/4G=19.625z

ΔD=ε_shear×D₀
=19.625z×0.02m
=0.3925y m
Is it right?

You seem to be using the given Young's modulus as though it is the applied stress. They happen to have the same dimension, pressure, but they are not the same thing. Specifically, the modulus is that stress which would, in theory, double the wire's length.
If the problem statement does not specify an applied load then there is no way to answer it.

Even then, I am unable to follow the rest of your calculation. Not sure what all those ys and zs mean. It makes no sense that the change in diameter can be 20 times the initial diameter.

 

[billy722]

Stress_shear=E×I=F/A
V=strain_shear/strain_axial
⇒strain_shear=Vχstrain_axial=ΔD/D₀
⇒ΔD=D₀χVχStrain_axial
=D₀χVχ(stress_axial/E)
=D₀χVχ(1/E)χ(FχA)
F in shear and F in axial are same?

 

[billy722]

However, I calculate out 3.925*10^-26 again
I think that's wrong

 

[haruspex]

Stress_shear=E×I=F/A
V=strain_shear/strain_axial
⇒strain_shear=Vχstrain_axial=ΔD/D₀
⇒ΔD=D₀χVχStrain_axial
=D₀χVχ(stress_axial/E)
=D₀χVχ(1/E)χ(FχA)
F in shear and F in axial are same?

If the problem statement does not specify an applied load then there is no way to answer it.

If the problem statement does not specify an applied load then there is no way to answer it.

If the problem statement does not specify an applied load then there is no way to answer it.

If the problem statement does not specify an applied load then there is no way to answer it.

If the problem statement does not specify an applied load then there is no way to answer it.

Am I getting through?