Question

Problem 5. A thin-walled cylindrical pressure vessel of radius 50 mm and thickness 5 -mm, made of steel, is subjected to an internal pressure which is fluctuating from -0.2P to P. (i) Determine the safe pressure P according to each of the following criteria': (a) The Soderberg Criterion, (b) The Goodman Criterion, and (c) The Gerber Criterion (ii) Draw these criteria on same coordinates and include the load line. (iv) If a 20-MPa pressure is used what would be the safety factor according to each criterion*? Assume that the vessel is made of 4130 steels, annealed (S,-360, S-560, S,-200 MPa). See the "Fatigue Design Tools." The most conservative criterion is the Soderberg; the Gerber is Criterion is relatively less conservative, and the Modified Goodman is widely used. Hint: The actual safety factor of a typical fatigue scenario can be obtained from: sf-OB/OA, as shown in the attached Figure(s). Note: sf-1 for points at the border line of the criterion; sf>1 for points inside the region; and sf<1 for points outside the criterion border. C

Answer 1

S Given Sy 3 6oMPa, Su 560MPa Sn 200M fa RSom m D D 2R: oD mm t- Smm -o.2P to P. P, Amin = - o-2P. fm ax To find PAssuming sf1) The 3tat of ^tress eve the element cylinder is shaon A on the Sur face on 6n= Cy 6 6 P D 4t (longitu dina! stress) (haop atro Nou Mean ampli tude of Jnside fre ssure P Pimax Pimin PD.2P. 4 P - (Mean) Pim imez-fimin (Amplitude P+o2P 2 similariy for Pim D 4-t MPa 4 x So Pia D Gza 3 PMfa 4 Pimp o.4P Mfa Gym 64a o. 6f Mfe. 2 t Com bine meam Van- mises cri te i q, the ccot dina stress amplitu de wiu bhe ' to Nd A -Stress o. 346 P Mfa Gm Gzm6-Gxm 6ym O.52P Mfa 2 62a 6ya- 6x Can app fatigue failune theonies'. Nou we Sodexberg Crieria (a) m GA Sn Sy o. 3u6 3 280.81MPa 6m 96.8 ? Mf Ga - 46 02Mfa

(b Goodman crideria: ms d.346P o.S2 zao S6 P 310.76Mfa 16 1.6Ma &6m17.5 2M fa, 6a Ce) Gerbet Cviteria: Sutsf Snt o.S2 S Go + 2.6xlP = / (Pz0). 3. 81y1 P 365.0S mfa 126. 3 Mfa, 6a = 1 89.83 Mfa & 6m (i piagTam 6a Gewd man's lins Sn 2MP (b Gevbes Parab ok (a) Soderbergline Sr S6sMfa Gm Sy 36 oMfa. 49 g.b c ae (a Smi 6 = ( 96-87, 146.2 M Pa (b) (Gm, 6a ) = (101.52 , 16.6)Pe (6m, 6 The co-ordinate (126.3 189P3) MP

NI Given Suder berg Citeria be fore using equations wed O. 3u6 Y20 3 60 4. 04 S f (b ood man's ctena 0 34 6X20 s f - 15.s4 (c) Gerber's cjteia' O.S2Y20sf O.34 6x2 o X Sf S6 sf8 2S