Question

The figure illustrates the nonpermanent connection of a steel cylinder head to a grade 30 cast-iron pressure vessel using Nbolts. A confined gasket seal has an effective sealing diameter D. The cylinder stores gas at a maximum pressure Pg. For the specifications given in the table for the specific problem assigned, select a suitable bolt length, assuming bolts are available in increments of 5 mm. Then determine the yielding factor of safety np, the load factor nL, and the joint separation factor no. Take the value of Efor steel as 207 GPa and for cast iron as 100 GPa. D Head thickness (A) Cylinder thickness (B) Cylinder ID Gasket sealing diameter (D) Bolt circle diameter (E) Head outer diameter (A) Number of bolts (M) Cylinder pressure (Pg) Bolt grade (6) Bolt spec. 20 mm 20 mm 60 mm 100 mm 200 mm 300 mm 10 6.3 MPa ISO 9.8 M12 x 1.75

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Answer 1

= 20t6 Sultable length 2= 60mm (table A-17) Threaded length LT LT = 2(12) +6 – 30mm Length of unthreaded portion in grip (lt): - ld L-LT 60 - 30 Length of Ihreaded portion in grip Clo): - lt l-ld 40 - 30 Area of anth readed portion (Ad) :- Ad=N/ud2 1 13.097 mm? 30 mm 10 mm /u (122 Balt stiffness (Ab) = Ad At E Ad lo + At ld (123.097) (84.3) (207X109) (113.097) (10) + (84.3) (30) kb 53.9226.32 N/mm) a Member stiffness :- wildth ) = 18 mm (table A-30) stiftneas of steel cylinder head :- RL = 0.5774 * (Esd In [.a55t+o-d] [o+d] [.isSt+D+d] D -d] ky 0.577420 7X103) (12) IS 1.157(20) + 18-12] [18+12) CE 355 (20)+(48) +12] [18-12) Ki=4470108.6 N/mm Stiffness of pressure vessel of cast iron: - (similar to ki, except tcast iron)-

K2= Kex Ecastinon Esteel 4470108.6 X 100 207 TK2=2159472.75 N/mm n member stiffness, I 1 / 2 [km RA 1 + 1 1470108.6 2159472.75 km km = 1456061.43 N/mm $ Toint constant (C) = kb Kbt km 539 226.32 539226.32 + 1 456061.43 Pg X /4X02 e To 0.27025 - Total load gas pressure y area Platal 6.3X X(100)? {p.total 49480.08 Ny load per bault (P) = Ptotal 49480.08 N 10 = 4948 NI O P - Ans (a): - The suitable bolt length is 60 mm yielding factos of safety choi- Spat (650)(84.3) rpa (P+ Fi (0.27025) (4948) +41096.25 Ans(: - The sp= 1.29

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