Question

1. The lid on a pressure vessel is held down with 10 bolts that pass through the lid and a flange on the pressure vessel (similar to example 8-4, in the text). The bolts are secured with nuts under the flange. There are no washers. The thickness of the lid is 28 mm and the thickness of the flange is 28 mm. The vessel and lid are both made of steel. The vessel is pressurized to 8 MPa, and the area of the lid exposed to the pressure is 31.4e3 mm². The modulus of elasticity is 207 GPa. The chosen bolts are ISO property class 9.8 (see table 8-11) and are coarse-pitch series, M12. (a) Find the external load, P, on each bolted joint. (b) Consult tables A-17 and A-31 to select a bolt of the correct length, L. State your choice for L (pick the first bolt on the list that is long enough). (c) Find the spring constant of the bolt, using Table 8-7 for guidance. (d) Use the curve-fit, equation 8-23, p. 440, to find the spring constant of the members. Note that A and B in this equation are parameters from Table 8-8. The FE review sheet has something similar. (e) Now find the stiffness coefficient of the joint, c. (f) Calculate the recommended preload, F, assuming that the lid will be re- moved and reinstalled repeatedly (See equation 8-31). Also, determine the required tightening torque (See equation 8-27; Use K 0.20) (g) Draw and annotate a diagram similar to what we constructed in class for this type of problem. The external load goes on the horizontal axis. F, and Fm go on the vertical axis. (h) Calculate the factors of safety against overproofing (n.) and joint separation (no). Which threat is greater?

please just do #1

Answer 1

Number of bolts : (N) = 10 Thickness of lid - aь гом Thickness of Hanger = 28 mm All the material to steel Pressure in the Vessel ( Puessel ) = 8 MPa borea of the lid ( And) = 3d un mo? 2 31-4e3 mm modulus of Slouhilly (E) = 207 Q. Pa class 9.8 M12 Coarse pitch bolt. (a) And the Eternal load, P on each bolted soint. Protal = Total external load applied to the joint Protal = (Pressure) * (Area) Pressed to Aed = BX 105 X 31-4*108 -4 to M Protal 25102 x 103 m Eternal tensile loud per bolt P= Rotal N 3 2512X10 10 P 25.1 x 10tr (1) And the sopping constant of bolt (Kb) : Theranded Sength (LT) àd + 6 mm ; L 125 mm, d = 48 = 2 (12) + 6 30 mm (b) Select the bolt of lorrect length (2) - length of unthreaded poston in golp eld: L-LT I thickness of bott & nut squeezed material b/w them. 80 - 30 a Somm S6 l28 mm 28 mm length of faccided pootton in golp lf: doeld 56 - 50 6 mm Foother langth (2) L>H Rerea untioneaded por Hon (Ad) : па“, : M (127343 = 113.04 mm? H-thickness of rut from table A-29 * [from shlyley Machine design book] Arsea of threaded postren (At) : From table 8.1* Fou MIR H 4.45 mm For MIB coorse pitch series L> 56 17.95 Az = 84.3mm 1763-95 MM Now Now foom table A-144 [ Rounding off Kb = Ad. At. E (807 63.95 > 60) Sinta Ad-lz + Atld L 90 mm Bom The required fastner dength Kb 19x106 ( N/mm²) (13.04) -(84-3). 207 x 10 x 10 (113-04)(6) + (84-3)(50) | Ko= 4.031 x 105 N/mm с е 0.153 (d) Spoling constant jou member ( km) :- (f) calculate the pereload (FF) & Tooque (T) From Jable 8.6 fi 0.75 #fp (tos non permanent joint) For stoel medestal where ATIS Fp - Poootload BE062813 fp = Aq* Sp Fi = 0.75* At * Sp km- Eid A. Poep (Bd/a) where foom table 8-11* km = 207 x 10 (mm) 120m (0.28715) Class 9.5 Sp= 650 MPa x Cap • L 0-62873 +12 56 13] Sp= 650 N/mm² N/mm 22.372 x 10 km = F = 0.75 * 843 (mon?) x 650 (mm) Fi = 41696.25 Fi = 41.096 KN ie Stiffness Constant of joint , c : Kb C = Now Kbtkm Torque (T) T=K*Fixd 4.031 x 10² (4.031 + 22-372) x 105 where Klo too que factor = 0.20 C penebally) T= 0.2 * 41.096 810 * 12 x 10 m T- 98.63 Nim Doow and annobate dagram >> Bol Plate 0 0 Top view 0 o P = 504.545N c Ls BOOM Top Fm Hube maneber It's a rough diagram : (h) Safety against overproofing (n) joint soperation (no) :- m2 = SpAt-Fi CP AL 650 * 84.3 - 41096.25 (0.153) * 25100 n2= 3.567 safety against overproofing no = Fi PC1-C) 41096.25 25100 (1-0.153) no = 1.933 safety against joint seperation. Any doubts, post below in the comments If you like this solution, please give a thumbs up, thanks.