Problem 2 A sector of a steel plate with endurance limit Se = 400 MPa, and ultimate strength Sut = 1000 MPa, has a stress state defining with the following cycle parameters calculated with von Mises criterion: = 130 MPa ση σα max-Mises max-Mises = = 400 MPa. Calculate the useful life in cycles according to Goodman criterion considering an equivalent cycle of completely inverted stress. Take n = 1 and work it in in sector of high cycle and finite life.

A large spherical tank (see figure) contains gas at a pressure of 420 psi. The tank is 45 ft in diameter and is constructed of high-strength steel having a yield stress in tension of 80 ksi. (a) Determine the required thickness (to the nearest 1/4 inch) of the wall of the tank if a factor of safety of 3,5 with respect to yielding is required. (b) If the tank wall thickness is 2.25 in., what is the maximum permissible internal pressure?

A W 360 x 79 steel beam is fixed at A. The beam has a length of 2.5 m and is subjected to a linearly varying distributed load with maximum intensity q0= 500 N/m on segment AB and a uniformly distributed load of intensity qQon segment EC. Calculate the state of plane stress at point D located 220 mm below the top of the beam and 0\3 m to the left of point B. Find the principal normal stresses and the maximum shear stress at D. Include the weight of the beam, See Table F-l(b), Appendix F, for beam properties.

Solve the preceding problem for a steel plate with x= 11,600 psi (tension). y= -5700 psi (compression), x = 450 x 10-6 (elongation), and y = -310 × 10-6 (shortening).

2. Consider a bar of AISI 1015 cold-drawn steel. Using the distortion-energy and maximum-shear-stress theories to determine the factors of safety for a stress state with the following plane principal stresses: 04 = 30 kpsi, OB = 15 kpsi.

A solid cylindrical shaft made of AISI 1020 steel(quenched and tempered at 870oC) rotates at a speedthat produces a safety factor of 2.5 against the stresscausing yielding. To instrument the shaft, a small hole isdrilled in its center for electric wires. At the same timethe material is changed to AISI 1080 steel that has beenquenched and tempered at 800oC. Find the safety factoragainst yielding of the new shaft.

4. A bar of steel has minimum properties of Se= 40 kpsi, Sy = 60 kpsi, and Sut = 80 kpsi. The rotating bar is subjected to a steady torsional stress of 15 kpsi with a completely reversed bending stress of 25 kpsi. Find the factor of safety guarding against first-cycle yielding and either the factor of safety guarding against fatigue failure or the expected life of the part. For the fatigue analysis, use: 1) Goodman criterion 2) Gerber criterion

Consider the 2-D state of stress shown below. Using the provided scales graph the Mohr's Circle for the 2-D state of stress with "full' details Draw the Planes of Principal and Maximum Shear Stresses Provide "full" details and Use 3 Sig. Fig. in this problem Oy = 15 Ksi Tcw → S Txy= -5 ksi Ox = 10 Ksi Tyx = 5 Ksi 10 5 -20 -10 5 10 15 20 5 10 Tccw → S'

= A shaft of circular cross-section with diameter 100 mm is sub- jected to a bending moment of M = 10 kN.m, torque T = 30kN.m, and axial load F = 50 kN. Consider for the material of the shaft a yield strength of oy 750 MPa. Determine the design factor of safety using Tresca and von Mises Theories. Hint: find the point in the shaft that would be subjected to the largest stresses caused by the forces applied. Refer the the lecture. Example of Tresca with the inclusion of safety factor: 01 - 03 2 Where N is the safety factor. = бу 2N

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