1. The problem statement, all variables and given/known data
A mild steel bar 40 mm diameter and 100 mm long is subjected to a tensile force along its axis.
Young’s modulus of elasticity for mild steel = 200 GN m–2.
Poisson’s ratio is 0.3.
Calculate the force (F) required to reduce the diameter to 39.99 mm.
Use the x–y coordinate system as shown above.
2. Relevant equations
Poissson's Ratio = - (transverse strain / axial strain)
force = Stress x Area
3. The attempt at a solution
transverse strain = (39.99 - 40) / 40 = -0.25x10^-3
axial strain = - (-0.25x10^-3 / 0.3) = 833.333 x 10^-6
axial stress = (833.333 x 10^-6) x (200 x 10^9) = 166.666 x 10^6
force (F) = 166.666x10^6 x (0.25∏ x 0.04^2) = 209439.51 N
A mild steel bar 40 mm diameter and 100 mm long is subjected to a tensile force along its axis.
Young’s modulus of elasticity for mild steel = 200 GN m–2.
Poisson’s ratio is 0.3.
Calculate the force (F) required to reduce the diameter to 39.99 mm.
Use the x–y coordinate system as shown above.
2. Relevant equations
Poissson's Ratio = - (transverse strain / axial strain)
force = Stress x Area
3. The attempt at a solution
transverse strain = (39.99 - 40) / 40 = -0.25x10^-3
axial strain = - (-0.25x10^-3 / 0.3) = 833.333 x 10^-6
axial stress = (833.333 x 10^-6) x (200 x 10^9) = 166.666 x 10^6
force (F) = 166.666x10^6 x (0.25∏ x 0.04^2) = 209439.51 N
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