Solid Mechanics

posted by .

A steel block 200 mm X 20 mm x 20 mm is subjected to a tensile force of 40 kN in the direction of its length. Determine the change in volume, if E is 205 kN/mm2 and Poisson's ratio = 0.3.

  • Solid Mechanics -

    E=205 kN/mm²= 205•10⁹ N/m²,
    μ = 0.3

    σ=E•ε(longitudinal)
    F/A = E•ε(longitudinal)
    ε=ε(longitudinal) = F/A•E=
    =40000/(20•10⁻³)²•205•10⁹=4.9•10⁻⁴.
    If a=0.2 m, b=c=0.002 m, ε=4.9•10⁻⁴,

    V=abc = 0.2•0.002•0.002 =8•10⁻⁷ m³
    The deformed volume is
    V₁ =(1+ ε)a•(1- μ ε)b•(1- μ ε)c .
    Neglecting powers of ε, the deformed volume
    V₁ =(1+ ε - 2•μ•ε)V .
    The change in volume is
    ΔV = ε(1- 2•μ)V =
    =4.9•10⁻⁴(1 - 2•0.3)•8•10⁻⁷ =
    =1.57•10⁻¹º m³

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. THEORY OF MACHINE

    A steel block 200 mm * 20 mm* 20 mm is subjected to a tensile force of 40 KN in the direction of its length. Determine the change in volume, if E is 205 KN/mm² poissions ratio = 0.3
  2. mechanics of materials

    A mild steel bar of width 10mm is subjected to a tensile stress of 3,0x105 Pa. Given that Young’s modulus for mild steel is 200 GPa and Poisson’s ration for mild steel is 0.31, calculate the change in width of the bar. Is the width …
  3. solid mechanics

    A steel block 200mm*20mm*20mm is subjected to a tensile force of 40kn in the direction of its length.Determine the change in volume,if Eis 205kn/mm square and poisson's ratio=0.3.
  4. solid mechanics

    A steel plate is subjected to tensile stresses of 200MPa and 150 MPa at right angles to each other. Determine the normal and tangential stresses on a plane inclined at 60 to the 200 MPa stress. Also find the plane on which the resultant …
  5. maths

    Determine the stress in a solid steel rod of diameter 30 mm when subjected to a tensile load of 91 KN (your answer must be in MPa to 2 decimal places).
  6. engineering

    A steel tube 30 mm outside diameter and 25 mm internal diameter and length 500 mm is subjected to a tensile load of 37 KN, determine the change in length in mm to 3 decimal places when the load was applied. For the material E = 210 …
  7. solid mechanics

    A steel block 200mm x 20mm x 20mm is subjected to tensile faro of Gone in the direction of its Length. Determine the change in volume if E is 20KN/mm2 and Poisson’s ratio = 0.3.
  8. solid mechanics

    Under what axial tensile load, the diameter of a steel bar will be reduced from 8 cm to 7.995 cm?
  9. solid mechanics

    Under what axial tensile load, the diameter of a steel bar will be reduced from 8 cm to 7.995 cm?
  10. soild mechanics

    Under what axial tensile load, the diameter of a steel bar will be reduced from 8 cm to 7.995 cm?

More Similar Questions