Example


example A A Φ 100 mm nominal pipe is equipped with raised face flanges and a spirally wound asbestos filled gasket, 4 mm thick and of the dimensions sketched. It is proposed to use 8 M20 x2.5 class 5.8 bolts for the joint, which is subjected to a fluid design pressure varying between zero and 7.5 MPa.
Will this class be suitable?

The whole operation of the joint will need to be checked - leakage tendency as indicated by 'm' and 'y' factors, fatigue of the bolts, and so on.

Dimensions & initial loading
The width of the gasket here is (150-125)/2 = 12.5 mm. AS 1210 table 3.21.6.4(B) states that the effective width, allowing for rotation etc, is 2.52√(width/2) = 6.3 mm.
Gasket OD is 150 mm, so gasket effective ID is 150- 2 x 6.3 = 137.4 mm, and gasket effective area is Ag = π( 1502 -137.42 )/4 = 2844 mm2.
The effective area inside the gasket which is subjected to fluid pressure is Ai = 137.42 π/4 = 14 830 mm2.
Bolts' proof load Fp = 245 x 380 = 93 kN
Assume tightening to 75% proof, then total initial tightening load is Fi = 8 x 0.75 x Fp = 560 kN.

Stiffnesses & joint factor
On the basis of a single bolt and the gasket associated with it . . . .

Bolt
Grip = 2 x 35 + 4 = 74 mm. Assume two exposed threads and head/nut height = 0.8 x 20 = 16 mm
1/kb = Σ L/AE = [ (74 -2 x 2.5 +0.5 x 16)/π x 102 + (2 x 2.5 +0.5 x 16)/245 ]/207 ;     kb = 694 kN/mm
Joint
Gasket area associated with one bolt Ag = 1/8 of 2844 = 356 mm2
Table 4 quotes limits for the stiffness of the gasket material 270 to 1800 MPa/mm, or, in units of force ( multiplying by Ag= 356 mm2) 96 ≤ kg ≤ 640 kN/mm.
It is anticipated that a larger value will be more appropriate, but we'll persist with two extreme values using {} to show results for the smaller stiffness. So select estimated gasket stiffness of kg = 600 kN/mm   { 100 kN/mm }.
The portion of each flange in direct compression will be modelled as a 35mm long conical frustum using ( 4)
kf = 207 x 20 x (0.702 +0.654 x 20/35)/(1 -0.12 x 20/35) = 4780 kN/mm
This is so much greater than kg that the approximation inherent in applying the frustum model in this case should not carry over into the overall joint stiffness. So for the two flanges and the gasket in series in the joint :
1/kj = 2/kf +1/kg = 2/4780 +1/600 ;     kj = 480 kN/mm   { 96 kN/mm }
The joint factor follows as :
C = ke /kj = kb /( kb +kj ) = 0.59   { 0.88 }

Gasket stress limitations
Based upon whole gasket . . . .
From Table 3, y = 69 MPa and m= 3.0 for a spiral wound asbestos filled gasket.
The initial gasket stress is Fi/Ag = 560/2844 = 197 MPa > y, so OK.
Check crushing - lacking any recommendations, presume a limiting stress of 2y = 138 MPa ( based on   total not effective gasket area ). Based upon this area, the initial ( ie. maximum ) stress on the gasket is 560 x 4/π( 1502-1252 ) = 104 MPa < 2y and so crushing should not be a problem.

Now consider gasket stress when full fluid pressure of 7.5 MPa is applied. From ( 3b) with external fluid load ( or   hydrostatic load ) of P = pfluid Ai = 7.5 x 14830 = 111 kN
Fj = Fi - ( 1 -C ) P = 560 -(1-0.59) x 111 = 514 kN   { 547 kN }
which corresponds to a gasket stress of pg = Fj /Ag = 514/2844 = 181 MPa   { 192 MPa }
Ratio pg /pfluid = 181/7.5 > m = 3.0 so this criterion is satisfied and the gasket should not leak.

Bolt fatigue
Based upon a single bolt . . . .
From Table 2, Su = 0.5 GPa, so Se' = ( 0.55 -0.088 x 0.5 ) x 0.5 = 253 MPa
Assuming rolled threads, Kf = 2.2 ( Table 6 ) and so Se = Se'/Kf = 253/2.2 = 115 MPa
σi = Fi /As = 560/8 x 245 = 286 MPa
σa = CP/2As = 0.59 x 111/2 x 8 x 245 = 17 MPa   { 25 MPa }

Applying ( 6a), the safety factor for the load on the bolts themselves ( Fb) is
1/n = σi /Su + σa (1/Su + 1/Se ) = 286/500 +17 x ( 1/500 +1/115) ;     n = 1.33   { 1.19 - note effect of small kj }
Alternatively, applying ( 6b) for the safety factor on fluid pressure loading ( P) against bolt fatigue failure
1 = σi /Su + n σa (1/Su + 1/Se ) = 286/500 + n x 17 x ( 1/500 +1/115) ;     n = 2.35   { 1.60 }

All-in-all, the joint is satisfactory as it stands. The bolt class is therefore suitable.
 


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