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An internal crack has been detected with ultrasonics in the shell of a large cylindrical steel pressure vessel. The stresses in the region of the crack are: (longitudinal tensile stress of 60,000 psi, circumferential tensile stress of 140,000 psi, radial compressive stress of 5,000 psi. The pressure vessel is so large that there is no appreciable variation of stress over the region containing the crack. The crack is oriented so that its normal makes an angle of 40o with the longitudinal direction and 60o with the circumferential direction.
(i) What is the normal stress on the plane of the crack? What is the shear stress in the plane of the crack?
(ii) If KI for the steel is 50 ksi. in ½ , what is the smallest size crack that will cause fracture of the pressure vessel?
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