How to determine the following?

Question

A round cast iron bar is placed in tension by a force of 100 kN.
Calculate the diameter of the bar if the stress in the bar is not to exceed 300 kPa.
If the bar has a length of 50 cm before the load is applied, and a final length of 50,010 cm after the load is applied, then calculate the strain in the bar.

Answer 1

Given data

Load ,P = 100 kN =100000 N

Stress, σ ≤ 300 kPa = 300000 Pa

Length of the bar ,l =50 cm = 0.5 m

Increased length, Δl = 50.010 - 50 =0.01 cm =0.0001 m

Young modulus of the cast iron,E =110 GPa = 110×10⁹ Pa

Calculate the diameter of the bar:

Δl = Pl / AE

A =Pl / Δl E 

A= (100000)(0.5) / (0.0001 )(110×10⁹)

   = 0.004545

Here A = (π/4)d ²

(π/4)d ² = 0.004545

d ² =0.0058

d = 0.0761 m =7.61 cm

Therefore, the diameter of the bar is 7.61 cm

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Calculate the strain (ε).

ε = Δl / l

  = 0.0001/0.5

  =0.0002 cm/cm

Therefore, the strain in the bar is 0.0002 cm/cm

 

Comments

I know strain is a dimensional less quantity, can we write units?

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Although strain is a unit less quantity, it is common practice to express the strain as the ratio of two length units, for example, as m/m or in/in. It is not compulsory to write the units.