Specimen of steel has a rectangular cross section 20 mm wide and 40 mm thick, an elastic modulus of 207 GPa, and a Poisson’s ratio of 0.30. If this specimen is pulled in tension with a force of 60,000 N, what is the change in width if deformation is totally elastic? (A) Increase in width of 3.62  10−6 m (B) Decrease in width of 7.24  10−6 m (C) Increase in width of 7.24  10−6 m (D) Decrease in width of 2.18  10−6 m

(D) Decrease in width of 2.18 x m

Explanation:

Given:

force 'F'= 60,000 N

elastic modulus 'E' = 207 GPa => 2.07 x  N/m²

cross section area ' '= 20 mm x 40 mm => 800mm² =>8 x m²

∈z = б/E => (F/ )/E => F/ E

∈z = 60,000/(8 x x 2.07 x  )

∈z =3.62 x  

Lateral strain is given by,

∈x= -v∈z => -(0.30)(3.62 x  )

∈x=1.09  x  

Next is to calculate the change in width

ΔW= Wo x ∈x =>20 x 1.09  x  

ΔW= -2.18 x   m

Therefore, the correct option is 'D'