m2. Calculate the stress and strain and the final length under this load?

Question

A rod 500mm long with a cross sectional area of 0.000035m2 is subjected to a tensile force of2.5kn. The modules of elasticity for the material is 17.85gn/m2. Calculate the stress and strain and the final length under this load?

Answer 1

This is the most fundamental concept of strength of materials.  Use the following formulas

 

S = F / A      ----> formula 1

 

where:
S = stress  (N/m²)
F = tensile force  (N)
A = cross-sectional area (m²)

 

 

ε = ΔL / L       ---->  formula 2

 

where:

ε = strain (unitless)

ΔL = elongation (m)

L = original length (m)

 

 

E = S / ε      ----->  formula 3

 

where:

E = elastic modulus

 

 

First, we need to convert our SI units of the given values.

 

F = 2.5 x 10³ N

A = 3.5 x 10^-5 m

L = 500 x 10^-3 m

E = 17.85 x 10⁹  N/m²

 

We can easily find the stress.

 

S = (2.5 x 10³ N) / (3.5 x 10^-5 m²)

S = 71428571 x 10^-8 N/m²

 

 

Now we use this value of stress and the elastic modulus to find the strain.

 

ε = S / E 

ε = (71428571 x 10^-8 N/m²) / (17.85 x 10⁹ N/m²)

 

 

Then plug in this strain result into the strain formula to get the elongation.

 

ΔL = εL

 

 

Final length = L + ΔL     (because of tension)

 

 

If you had compressive force, then

 

Final length = L -  ΔL