Question

THO4 (10 pts) Take Home Date Due: 9:30am Wednesday, October 23, 2019 Name: Consider a cylindrical pressure vessel with spherical end caps made of ASTM A516 Grade 70 steel with yield stress a,eld Tated at 335 MPa that has diameter D-3.0m, thickness t-25mm and length L-24.0m for the cylindrical portion of the pressure vessel. The cylindrical pressure vessel is pressurized internally at pressure p-2.5 MPa. Assume externally pressure to be zero. The material has modulus E-200 GPa and Poisson's ratio v-0.29. See Figures A-C, section of length b, for examples of how stresses are manifested. mp B Fig. A. Pressure vessel with Section "m-n to p-q" Fig. B. Longitudinal cut Fig. C. Circumferential cut Determine values, the locations in cylindrical pressure vessel and the stress element orientations for each of the following worsst.cases (I) The maximum shear stress tn (2) The maximum normal stress m (3) The minimum normal stress onis For full credit, show all work: FBDS, Eqs. of Static Equilibrium, appropriate equations for calculating stresses as functions of applied loads together with Stress Element Diagrams, stress element orientation 8 diagrams, and Mohr Circle Analyses. Indicate all uses of Mohr circle analysis.

Answer 1

Solution :- D: 3m 3000 mm. t. 25 mm. P: 2.5 MPa. Ý : : 120 > 20 :- Pressure vessel is treated as thin. On Moope shers > . 2-5x3000 2*25 150 MPa G , Longitud nal shress : PD, .5*3000 75 MPa. 9. Largitarat those senden de stage - 75 M** 9) Martimum stay stres - Free Game 159.75 1x25 Maximum sheay strass Imax : - 150-75 Imer = 37.5 MPa. 5] Maximum Normad stress - Pmax • Hoope shers. 577 » | Some + 150 MM. 1 - male omax = 150 MPa. / Minimum Normal Shress Longitudna. Creumeranti Slyers. Amin | Oma = 75 mma. - Ang min : 75 MPa. 11