Question

QUESTION 2 The end-cap of a pressure vessel as shown in Figure 2 is secured by 10 off M10 x SAE class 10.9 bolts (with rolled threads). A soft gasket is used such that the clamped member stiffness is one quarter of the bolt stiffness. The internal diameter of the pressure vessel is 140 mm and the pressure in the vessel varies from 0 to P MPa gauge. Assuming that the bolts are initially tightened to 80% of their yield strength determine : (a) the required initial tension in the bolts and describe how this would be achieved; (b) the maximum value of P that would not cause separation of the joint; (c) the maximum value of P that would not cause eventual fatigue failure of the bolts; and (d) the minimum practical wall thickness required for the pressure vessel for this maximum pressure P. 230 mm 140 mm 280 mm Figure 2. Pressure vessel end-cap [100 marks]

Answer 1

SOLUTION : PAGE 1 Given parameters, Internal Pressure in diameter 2 Premsune Vessel = 140mm Vessal varies from o to P MPa Xet, Botts are ikitially tightened to 80.4 09 Yield Strength their 230 mm 140mm 280 MM PRESSURE VESSEL END CAP (a) CALCULATION 30 LT OF TENSION The Exitial tension required in the bolts, f 1600 od 16000 C 0.010+ 39.370) ft 28.02 KN VALUE OF P: OF MAX سد (6) CALCULATION Choke)? Kb to=ft Kotke where te → clamping force for a tension force

PAGE 2: fe: - 28.02 P'tko 366+ Kb cdis K¢:3ko fined, Clamping At joldt seperation and bolt fonce is Zero fo:0 28.02 - Ś? P'=112.08 KN Man Value & Goa ? is ola P 112.08*103 (140) 2 T 4 Manimum Value q P 2 7.28x10 3 KP a CC MAXIMUM VALUE of P WHICH WOULD NOT CAUSE OF 30LTS EVENTUAL FAILURE FATIGUE duial Kood for fx + ( ko k) p' [ke: 13 Kb fo= p' la se ka 28.024 bolt Stress, oa cola x p' 78.53 oĀ 4:7 72 103 Fatique Stoengte la si C₂ CG & SCCR

PAGE 3: Sin sa 830 2 = 415 MP CG ( Endurance liquid) - 0.9 [s C ( anial Xoading) cs ( Surface Comerial) ( Fatique Strength)-1 CR ( Reliability ) SG taken as 8hora Sa OMPA Sn=415 teto.9 * 14 1x1 Sn=375.5 MPa Siners firectuation fi ДЕ Kf 28.02 t 3 78.03 Stress fluctuation 1070.41 MPa