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 nu and the joint separation factor no. Take the value of Efor steel as 207 GPa and for cast iron as 100 GPa. F E D B

Answer 1

Giren, Bolt Spec M12 X 1-75 &d=12mm lg = 4 for is H = 10.8 mm Fasther length ? 40+10-8 750.8 mm 4 L = 55mm the expression for length of unthreaded portion ingrip Sovetian i Grip length lg- AtB do + 20 = Homm from the "table A- 31 Dimensions of Hexogual nuets" the nut - height Nominal Size 12mm L3 lg tH & Suitable bolt length 1 l = 55mm thread length metric but 4 = 2d +6 = 2(12) + 6 4= 30mm ld L-4 = 55-30 do z 25mm For length of threaded portion in grip f = lg-ld = 40-as 4 = 18mm Area of withreaded portion 7T 4 A = 13-1mm fon 21 Table 8-a Suggested procedure for finding fastener slithess". is • (12) 2

from table 8.1 Dicauetes and areas of Coarse pitch and fine pitch melic threads "for d - 12mm The tensile stress corea At. [ Ester = 84.3 mm ² . Bolt stitness - 27 14Pa] A ALE (113.1) (84.3) (207) (113:1X15) + (84.3x25) + - 514. f Malim 6 i. Member Stiftues do Steel Cylindrice herd K, - 0.5774Ted [Crosst+0-1) (0+d) (busst+otd) Co-d) [Here, t= domm 0.5774 X IT X 807812 DEIB am] an [(1-55(20) + 18-12) (18 Hz) LC-sslac) +18+2) (18-11) K : 4470 MWM . Member Stiftnes for Cast iron 0.5474 T5 E d en Cl55440-4) (o tay (1:SSH+D+) (0-02 (0.5774) u (100) (12) (Eco = 100 gpa) en FOSS (20) 414-12) (1842) 441-55(20) +18H2) (18-12) . K₂ = 2159 Malim Stiffnes for entire frustum 1. Member + сч - [*+ +J" + [uto 2159 kry= 1456 MNIM

518.8 Jonat Constant Istkm 578.4 + 486 " poeload Fi = 0 C = 0.261 Fortable 8-11 Metre mecheri al property classes for Skel bolte, screws and Bredy " for M 12x1-75 Proof Strength sp = 650 MPa 0.75 Ay Sp Mla -0.75 X 849.3 x 650 xio (lepas Mpa Fi = 41.1 IN Total external load Probet but per Pg Ag Pg x 7 de N Given, = 6.9 hPa dga 1260mm N=10 pg & Ptotal 6.9x10 let ope] * (60) lo -3 kPa Ptotal 1. 949 kN/bolt 4 yielding factor of Safety 650 MPa Xo Mia (0-263) (1.9.49)+ 4011 X 84.3 21-316 2 CProt ffi np = 1.316 load factor - lepa . x 84.5 - 411 650 Paxto? Mpa 26. 777 n = p At - R CP total (0.263) (1949) nes 26.777

.: Joint factor Seperection 41.1 - 28.613 no Fi PCI-C) 4.949 (1-0-263) no = 28.613 Auswers The suitable bolt length is 55 mm the yielding factor The load factor is 126. 17 the joint Seperation factor is (080613 of safety is [1.316 please like the Answer, Thenk you