HOW TO CALCULATE THE FOLLOWING?

Question

A tensile load of 10 kN is applied to a bar with a square cross sectional area. The lengths of the sides are 194 mm each and the bar is TWO metres long. The total change in length is 0,231 mm. Calculate, The stress, The strain, Young's Modulus of Elasticity

Answer 1

Given,

Tensile load ,P = 10 kN =10000 N

Side length of the square bar, a = 194 mm =0.194 m

Length of the bar, l =2 m

Change in length of the bar, Δl  = 0.231 mm =0.000231 m

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Calculate area of the square bar.

A = a²

    = 0.194²

   = 0.037636 m²

Calculate the young modulus of the bar:

Δl = Pl / AE

E =Pl / Δl A

E = (10000)(2) / (0.000231)(0.037636)

   = 23×10⁸ Pa

 

Therfore, the young modulus of the bar is 23×10⁸ Pa

 

     

Answer 2

Calculate stress in the bar.

σ= P / A

  =  10000/ 0.037636

  =26.57 ×10⁴ Pa

 

Therfore, the stress in the bar is 26.57×10⁴ Pa

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Calculate the strain (ε ) in the bar.

ε = σ/ E

  =  26.57 ×10⁴  /  23×10⁸

   =   1.155 ×10^-4 m/m

 

Therfore, the strain (ε ) in the bar is 1.155 ×10^-4  m/m

 

Comments

strain (ε) = change in length) / (original length).

ε = Δl / l

  = 0.000231 m/2 m (Remeber Units must be same)

  =1.155 ×10^-4