Sample Problem : Bolt Sizing for Pressure Vessel Cap
A closedend 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.
Solution:
Step 1 : Write down input parameters which are defined in sample example
including material properties.
INPUT PROPERTIES SUMMARY 
Parameter 
Symbol 
Value 
Unit 
Gage pressure 
p_{g} 
15 
bar 
Vessel inner diameter 
d_{i} 
250 
mm 
Design factor 
n_{d} 
4 

Earth gravity 
g 
9.81 
m/s^{2} 
Number of Bolts 
n 
10 

Mass of Cover 
m_{c} 
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.
Pressure inside the vessel is 1.52 Mpa.
Step 3 : Calculate the axial and transverse force per bolt.
F_{axial} = n_{d}*p_{g}*π*d_{i}^{2 }/ (4*n) = 4*1.52*π*250^{2}/(4*10) =29830 N (Note that
this force is eccentric to bolt axis. See figure.)
F_{transverse }= n_{d}*m_{c}*g / n= 4*55*9.81/(10) =216 N
Minimum friction coefficient between clamped parts is entered 0.1 as suggested in
VDI 2230 Part1.
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.
Summary
The problem is fully 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. 