Question

The figure illustrates the nonpermanent connection of a steel cylinder head to a grade 30 cast-iron pressure vessel using N bolts. 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. E -D Head thickness (A) Cylinder thickness (8) Cylinder ID ( Gasket sealing diameter (0) Bolt circle diameter (2) Head outer diameter ( Number of bolts (1) Cylinder pressure (Pg) Bolt grade (6) Bolt spec. 20 mm 20 mm 60 mm 100 mm 200 mm 300 mm 10 6.15 MPa ISO 9.8 M12 * 1.75

please show clear working and box and label each answer! thank you

Answer 1

M12 From Table A 31, the but height for bolt is H= 10 8 mm L=l+H = 40 + 10.8 = 50.8 mm & A+B = 20 + 20 - 40mm Since available, is readily 55mm Round upto L = 55 mm For L$125, (2x12) +6 = 30 mm Ly=ad +6 Now, 55-30 = 25 mm la L-LT 40 25 = 15 mm lt l-la ld le Length of unthreaded portion in grip Length of threaded portion in grip. Ad. x 12 = 113-12 A Table 8.1 [from 1] & 4.3 mm² ko 518.8mN/m Ad A E Adlet Arld 113.1 x 84,3 x 207 (113-1 X15) + (84:3x25)

stiffness, 0: 57747 Ed k en (1.155+ +D-d) (D+d) (1.155+ +D+d) CD-d) Members: Steel cyli head: t = =20mm, D. 12X1,5 = 18mm, d = 12mm, E = 2076 Pa. = 4470 TOMN/m ki ln 0.57747 x 207x12 [1.155(20) +18-12] (18+12) [1.155(20) +18 +12] C18-12) Cast iron: t = 20mm, d=12mm, D=18mm, E-100Pa the material The only difference from K, is * 4470 = 2159 MNIM ke 100 201 + k km ko - 1 km Lisetas .: km 1456 Malm Fraction of external load P carried by bolt, ke C= 0.263 kbtkm 518.87 1456 518.8

proof strength for 0.75 X 84.3 x 650 x103 3 Minimum Iso 9.8 M12x1.75 is Sp = 650 MPa Assume non-permanent connections Fi = 0.75 Ar sp Fi 41.1kn 07 The total external load is, Ptotal = Pg x x Ac where, Ac is als area of cylinder with bolt diameter 60mm; The external load per. is, P= Protal N, T/AX60 x 10 1:1396Nombolt P = -3 - Thm, 6.15 x 7/4x60² 10 3 Yielding factor of Safety, SpA 650 x84,3x10 up CP+ Fi (0.263 x 1.739)+ A1:1 on mp = 1,32

4 Overload factor of safety, SpĄŁ - Fi (650x84·3x103) – +11 n = CP (0.263+1,739) 29:9 Separation factor of safety bo Fi 4111 PC1-e) 173961-0.263) 32.07 are, The answers 55 mm Bolt length, La Factor of Safety, Yielding np 132 Overload Factor of Safety, n = 29.9 Separation Factor of Safety, mo 32:07

Table A .31 for finding value of H for M12 regular hexagonal bolt

Nominal Size, in Width Height H Regular Thick or Hexagonal Slotted W JAM MI2 18 10.8 12.0 6.0

Reference: Budynas, R.G. and Nisbett, J.K., 2008. Shigley's mechanical engineering design (Vol. 8). New York: McGraw-Hill.

Table 8.1 for finding A_t

Nominal Coarse-Pitch Series Major Tensile Minor- Diameter Pitch Stress Diameter Pitch d р Area A. Area A, р mm mm mm mm mm Fine-Pitch Series Tensile Minor- Stress Diameter Area A Area A. mm mm2 12 1.75 84.3 76.3 1.25 92.1 86.0

Reference: Budynas, R.G. and Nisbett, J.K., 2008. Shigley's mechanical engineering design (Vol. 8). New York: McGraw-Hill.