A cylindrical tank with flat endplates is constructed from two sections that are welded together circumferentially.The outer diameter of the tank is 1.20, and the wall of the tank is 20.0 mm thick and the mamimum internal pressure is 2.00 MPa.

(a) Calculate the maximum hoop stress in the tank
(b) Calculate the maximum tensile stress in the tank
(c) The tensile strength of the weld is 350 MPa and the shear strength of the weld is 40% of the tensile strength. what is the magnitude of the tensile stress that will cause the weld to burst open

To calculate the maximum hoop stress in the tank, you'll need to use the formula for hoop stress in a cylindrical vessel:

Hoop stress (σ_h) = (P * D) / (2 * t)

where:
P is the internal pressure (2.00 MPa),
D is the inner diameter of the tank (since it has flat endplates) which can be calculated as (outer diameter - 2 * wall thickness),
t is the wall thickness (20.0 mm).

Substituting the values into the formula:

D = 1.20 - 2 * 20.0 = 1.20 - 40.0 = 1.16 m (convert mm to m)

σ_h = (2.00 * 1.16) / (2 * 0.020)
= 116 / 0.040
= 2900 MPa

Therefore, the maximum hoop stress in the tank is 2900 MPa.

To calculate the maximum tensile stress in the tank, you'll need to use the formula for tensile stress in a cylindrical vessel:

Tensile stress (σ_t) = P * D / (4 * t)

Using the same values as before,

σ_t = (2.00 * 1.16) / (4 * 0.020)
= 116 / 0.080
= 1450 MPa

Therefore, the maximum tensile stress in the tank is 1450 MPa.

To determine the magnitude of the tensile stress that will cause the weld to burst open, we need to consider the tensile strength and shear strength of the weld material.

Given:
Tensile strength of the weld (σ_ts) = 350 MPa
Shear strength of the weld (σ_ss) = 0.40 * σ_ts = 0.40 * 350 = 140 MPa

The tensile stress that will cause the weld to burst open is the minimum of the tensile strength of the weld material and the shear strength of the weld:

Magnitude of tensile stress = min(σ_ts, σ_ss)
= min(350 MPa, 140 MPa)
= 140 MPa

Therefore, the magnitude of the tensile stress that will cause the weld to burst open is 140 MPa.