3. A thin-walled cylindrical pressure vessel of radius r and thickness t and the material has a Young's modulus E and Poisson ratio v = 0.3. The vessel is subjected to an internal pressure p while the two F р F ends are held fixed through solid supports, which ensure there is zero longitudinal strain in the cylinder walls. Show that the axial force at the solid supports is F = 0.4 πr²p. Hints to use as needed (see how far you can get without each one): 1) This is a combined load, so remember to decompose the loads, solve, and superimpose stresses. 2) Consult the Laplace's law derivations for the relevant cross-sectional area of a thin-walled cylinder, in a convenient form. 3) Zero longitudinal strain does not mean zero longitudinal stress because the material is not subjected to uniaxial stress since there are also stresses in the pressure vessels. 4) If you are still stuck, make sure you use Hook's law in 3D AFTER superimposing the stresses. What do you set to zero to solve for F?

3. A thin-walled cylindrical pressure vessel of radius r and thickness t and the material has a Young's modulus E and Poisson ratio v = 0.3. The vessel is subjected to an internal pressure p while the two F р F ends are held fixed through solid supports, which ensure there is zero longitudinal strain in the cylinder walls. Show that the axial force at the solid supports is F = 0.4 πr²p. Hints to use as needed (see how far you can get without each one): 1) This is a combined load, so remember to decompose the loads, solve, and superimpose stresses. 2) Consult the Laplace's law derivations for the relevant cross-sectional area of a thin-walled cylinder, in a convenient form. 3) Zero longitudinal strain does not mean zero longitudinal stress because the material is not subjected to uniaxial stress since there are also stresses in the pressure vessels. 4) If you are still stuck, make sure you use Hook's law in 3D AFTER superimposing the stresses. What do you set to zero to solve for F?