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 E for steel as 207 GPa and for cast iron as 100 GPa. F D B 1 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 (G) 20 mm 20 mm 60 mm 100 mm 200 mm 300 mm 10 6.9 MPa ISO 9.8 M12 x 1.75 Bolt spec. The suitable bolt length is 55 mm. The yielding factor of safety is 1.293 The load factor is 11.1 The joint separation factor is 11.8

Answer 1

Grip Length (4)= A+B 20+20 : 40 mm nominal of nuts for 12 mm Dimensions Size he xagonal H = 10.8 mm Height: 9th of fastener length L>ITH L> 40+10.8 L> 50.8 mm suitable for bolt L = 55 mm tength for metric bolt: thread length calculate the LT : 2d +6 LT: 2 (12) +6 LT 30 mm gth of length inthreaded portion in grip Ld - L-LT 55-30 Ld 25 mm of unthreaded portion (Nominal). Ad= I d² I (12)2 = 4 4 → Area Ada 113.097 mm2 CS Scanned with CamScanner

At d = 12 mm tensile stress anea At = 84.3 mm2 OOO from table diam and area pitch of coarge Bolt Stiffness K6= Ad ATE Ad LT + Arld 113.097 x 84.3 x 207 x 103 LT = length 9th of thread 113.097 x 15 + 84.3 X25 in grip = 40-25 - 15 mm Kb - 518.816 MN/m member Stiffness for steel head- Cylindrical Kia 0-5774 T X Ed in (1.155 t + D-d) CDd) (1.155 t + D +d) CD-d) Kia 0-5774 T X (207) (12) en (1.155 (20) + (18-12)) (18+12) (1.155 (20) + (18+12)) (18-12)] [6.15 Kie 4470 MN/m member stiffness for cast iron K2 = 0.5774 TT X (100) (12) en (1.155 (20) + (18-12))(18+12) (1.155 (20) + (18712)) (18-12) K2 - 2159 MM/M mia CS Scanned with CamScanner

→ Member Stiffness for the entire frustum- km. [thit the] -1 Km- . + 4470 2159) km - 1456 MN/m Joint Constanta C- Kb Kot km 518.816 518.816 + 1456 C-0.2627 Pre load for M12 x 1.75 Sp- 650 mpa fi - 0.75 At sp fis 0.75 x 84.3 x 650 # fi- 41.096 KN bolt - Total external load per Pexternal Pg Ag N Pg x I dg² 4 N. = 6.9 XT (100) 4 lo 5.419 KM/bolt CS Scanned with CamScanner

yielding factor of Safety Cop). np = Sp At CP t fi 103 650 X 84.3 'x 0.2627 X 5.419 +- 41.096 X103 np = 1.2887 - overload factor of (n.) = safety ne : SpAt - fi CP 650 x 84.3 41.096 X103 0.2627 x 5.419 x103 ne: 9.622 factor (no) - Joint separation Fi PCI-C) no no 41.096 x103 5.419 x103 (1-0-2627) no - 10.2857 cs Scanned with CamScanner