Question

A 500 mm long bar has rectangular cross-section 20 mm × 40 mm. The bar is subjected to: 

(i) 40 kN tensile force on 20 mm × 40 mm face. 

(ii) 200kN compressive force on 20 mm × 500 mm face 

(iii) 300kN tensile force on 40 mm × 500 mm face. 

Find the change in dimensions and volume, if E = 2 × 10⁵ N/mm² and poisson ratio = 0.3.

Answer 1

E = 2 × 10⁵ N/mm², 1/ m = µ = ⋅3

Change in length in x direction ∆l = l × e_x

= 500 × ⋅000257 

∆lx = ⋅1285 mm 

 in y direction ∆b = e_y × b 

= – ⋅000197 × 90 

= – ⋅0076 mm (decreases) 

 in z direction ∆w = e_z × w 

= ⋅00003 × 20 

eυ = e_x + e_y + e_z 

= ⋅00009 

∆v = υ × e_υ = 20 × 40 × 500 × ⋅00009 

= 36 mm³