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A spherical tank of diameter 1.2 m and wall thickness 50 mm contains compressed air at a pressure of 17 MPa. The tank is constructed of two hemispheres joined by a welded seam (see figure).

(a) What is the tensile load f (N per mm of length of weld) carried by the weld?

(b) What is the maximum shear stress τmax (Mpa) in the wall of the tank?

A pressurized steel tank is constructed with a helical weld that makes an angle α = 55°with the longitudinal axis (see figure). The tank has radius r = 0.6 m, wall thickness t = 18 mm, and internal pressure p = 2.8 MPa. Also, the steel has modulus of elasticity E = 200 GPa and Poisson’s ratio v = 0.30.

Determine the following quantities for the cylindrical part of the tank.

(a) The circumferential and longitudinal stresses.

(b) The maximum in-plane and out-of-plane shear stresses.

(c) The circumferential and longitudinal strains.

(d) The normal and shear stresses acting on planes parallel and perpendicular to the weld (show these stresses on a properly oriented stress element).

A cylindrical pressure vessel with flat ends is subjected to a torque T and a bending moment M (see figure). The outer radius is 300 mm and the wall thickness is 25 mm. The loads are as follows: T 90 kN-m, M 100 kN-m, and the internal pressure p 6.25 MPa. M Determine the maximum tensile stress ?, maximum compressive stress ?c, and maximum shear stress Tmax in the wall of the cylinder.

 A sign is supported by a pipe (see figure) having outer diameter 110 mm and inner diameter 90 mm. The dimensions of the sign are 2m x 1m, and its lower edge is 3.0 m above the base. Note that the center of gravity of the sign is 1.05 m from the axis of the pipe. The wind pressure against the sign is 1.5 kPa. Determine the maximum in-plane shear stresse (MPa) due to the wind pressure on the sign at points A located on the outer surface at the base of the pipe.

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