A metal cylinder with a diameter of 10 cm and a length of 20 cm is subjected to a tensile load of 10 kN. Determine the yield strength of the cylinder according to the Tresca criterion, given that the metal has a shear strength of 200 Mpa.

To determine the yield strength of the metal cylinder according to the Tresca criterion, we need to compare the maximum shear stress experienced by the cylinder with its shear strength. The maximum shear stress can be calculated using the applied tensile load.

Given: Diameter of the cylinder = 10 cm = 0.1 m Length of the cylinder = 20 cm = 0.2 m Tensile load = 10 kN = 10,000 N Shear strength of the metal = 200 MPa = 200,000,000 Pa

To calculate the maximum shear stress, we first need to determine the cross-sectional area of the cylinder.

Cross-sectional area (A) = (π/4) * (diameter)^2 A = (π/4) * (0.1 m)^2 = 0.00785398 m^2

Next, we can calculate the maximum shear stress (τ_max) using the applied tensile load (F).

τ_max = F / A

τ_max = 10,000 N / 0.00785398 m^2 = 1,274,160.93 Pa

Now, we can compare the maximum shear stress (τ_max) with the shear strength of the metal (τ_shear).

If τ_max > τ_shear, the cylinder has exceeded its yield strength according to the Tresca criterion.

In this case, τ_max = 1,274,160.93 Pa and τ_shear = 200,000,000 Pa.

Since τ_max < τ_shear, the cylinder has not exceeded its yield strength according to the Tresca criterion.

Therefore, based on the given information, the yield strength of the cylinder according to the Tresca criterion is not reached with the applied tensile load of 10 kN.