Bolt Sizing Example for Pressure Vessel Cap

Bolt sizing for pressure vessel cap

A closed-end steel cylindrical pressure vessel shown in the figure is to work under 15 bar gauge pressure. The end cover is planned to fix to the vessel with 10 bolts (8.8 Grade). The weight of the cover is 55 kg. Estimate the proper bolt size for the design. (Use design factor as 4).

Note: Ignore gasket stiffness and the force occurred due to compression of gasket.

Note 2: Assume that transverse forces on the bolts occur only due to weight of the cover.


Step 1 : Write down input parameters which are defined in sample example including material properties.

Parameter Value
Gage pressure pg 15 bar
Vessel inner diameter di 250 mm
Design factor nd 4  
Earth gravity g 9.81 m/s2
Number of Bolts n 10  
Mass of Cover mc 55 kg

Step 2 : We need to calculate forces experinced on a single bolt. To be able to do the calculation, bar to MPa unit conversion shall be done. Go to "Unit Converter"  page to convert bar to MPa. Convert 15 bar to Mpa.

Physical Quantity Pressure
From To
atmosphere standard [atm] megapascal [MPa]
15 atmosphere(standard) [atm] 1.51988 megapascal [MPa]

Pressure inside the vessel is 1.52 Mpa.

Step 3 : Calculate the axial and transverse force per bolt.

Faxial = nd*pg*π*di2 / (4*n) = 4*1.52*π*2502/(4*10) =29830 N  (Note that this force is eccentric to bolt axis. See figure.)

Ftransverse = nd*mc*g / n= 4*55*9.81/(10) =216 N

Step 4 : Calculate the required bolt size by using input parameters given in Step 1 and Step 3 .

Parameter Value
Axial Load [FA] 29830 N
Transverse Load [FQ] 216
Min. friction coef. between clamped parts [μ]+ 0.1 -
Axial load type and introduction location * Static and eccentric
Tightening technique Torque wrench
Bolt Strength Grade   G8.8

Minimum friction coefficient between clamped parts is entered 0.1 which is minimum static dry friction value between steel -steel as suggested in VDI 2230 Part-1. 

Since pressure is not dynamically changing, loading is static. Axial force introduction location is eccentric to bolt axis.

Bolts are assumed to be tightened with torque wrench.

Parameter Value
Required preload FMmax 100000 N
Required bolt size for selected grade M20 ---

According to calculation results, minimally 10 bolts of M20 with 8.8 strength grade is needed to meet design requirments. As mentioned in bolted joint calculator, this calculator is just to give an initial estimate for the bolt sizing. Further calculations are needed for detailed bolt sizing.


The problem is completely solved with calculators which are summarized as follows.

Calculator Usage
Rough Calculation of Metric Bolt Size To estimate size and strength grade of the bolt according to axial and transverse load. Results depend on axial load type, load introduction location, tigtening technique and friction coeffcient.
Unit Converter To convert from one unit type to another one. In sample problem conversion is done from bar to MPa.