Question

Question 1 An end capped cylindrical pressure vessel with internal pressure p = fully supported at one end, is also subjected to a force F= 10 kN in the y direction at the other end as shown. The internal diameter of the pressure vessel is d= 160 mm and its thickness is t= 10 mm 3 MPa, assumed to be Determine the magnitudes of the stress components in x, y and z coordinates at points H and K and sketch the state of stress elements representing these points (include coordinate axes Note: you do NOT have to determine the principal 0.2 on for reference) 0.8 m stresses 0.2 m (Centroidal moment of inertia for a circle, = d/64 Polar moment of inertia for a circle, J = /d*/32 Centroid of semi-circle = 4r/3n) F= 10 kN

Answer 1

Moment due te due to boYce F-10KN OccuYs about -axiS in C.G.w TOVYUE F X0.2 KN m MzこT = T: 10X02 KNm G.G.W. T: 2KNM Moment (bending moment) accus due to F= 10KN HEK Points section about -axis at MX C.W FXO. 8 10X0.8 KNIM Mx =8 )くNm At that tHans vevse load, V- F= 10KN section Given d 160mm t 1omm ->2 P= 3MPa K pvemare Psremes at Due to intevnad HEK (o) lo) strem Hoop strens/cicum fevential 3X160 Pd 2t 2 X10 ory 24 MPa 07 xtPxdxt Pd Aial strer/ongitudinal shem (0z) Px

Pd t4t 3X160 0z 12MPa shear strens y Zyz txy *0- ho TXz- O-02 24-12 2 2. 2 24-12 = 6 MPa - 2 Coty0, z = 6MPa, yz= 6 MPa. Point H: due to. Bending srers : XW Here, a is in ension since GW de 9omm (idistance to H 2 (- d) 64 = 160+20 - 37. 19 MPa . T 64 TovguP shear shres due to C da 90 TXc 2x10 x90 N.mm2 32 (d80160 ) 32 4.65 MPa shear 1oad vi- to ttansveyse due is given by =2 31s Know we NiA to Poind heYe, y Ro Pant K strem due to Mti Bendng Point K is on the same axis 07-0 (x-axis shear strem due to taveue,T 2X106X90 GE90mm =4.65MPa 1 32 G991-1061

Sheav due lad transveyse to (R 31x here, y, oK is on ZR2 10X10 3*T0160) only he (16 RER 90 mm 64 1.395 MPa Sheas state at Hi- 24MPa, y24 MPa, 0712+37.19 0= 49.19MPa Cy=o742 = 6+4.65 10-65MPa, Tz 6MPa stres State at k 24MPa, 0 12 MPa, O 24 MPa, oy 6M Pa Cy=0, Zyz 6+4.65+1395 y2-12.045MPa K strers elementi- tStess element 01 7 01