A 2D thin plate with modulus of elasticity, 𝐸 = 1.0 N/m², and Poisson’s ratio, 𝜇 = 0.5, is in plane stress condition. The displacement field in the plate is given by 𝑢 = 𝐶𝑥²𝑦 and 𝑣 = 0, where 𝑢 and 𝑣 are displacements (in m) along the 𝑋 and 𝑌 directions, respectively, and 𝐶 is a constant (in m⁻²). The distances x and y along X and Y, respectively, are in m. The stress in the 𝑋 direction is 𝜎_𝑋𝑋 = 40𝑥𝑦 N/m², and the shear stress is 𝜏_𝑋𝑌 = 𝛼𝑥² N/m². What is the value of 𝛼 (in N/m⁴, in integer)? ________

The infinitesimal element shown in the figure (not to scale) represents the state of stress at a point in a body. What is the magnitude of the maximum principal stress (in N/mm2, in integer) at the point? ________

For the stress state (in MPa) shown in the figure, the major principal stress is 10 MPa.

The shear stress $$\tau $$ is

For the state of plane stress (in $$MPa$$) shown in the figure below, the maximum shear stress (in $$MPa$$) is ___________