# Ch:5 Introduction to pressure vessels¶

## exa 5-1 - Page 138¶

In :
p=2#
Rm=220#
#tensile hoop or circumferential stress= sigt
sigr=-2#
#sigt=(p*Rm)/t#
Sa=230/2#
#t1=thickness according to maximum principal stress theory
#t2=thickness according to maximum shear stress theory
t1=(p*Rm)/Sa#
t2=(p*Rm)/(Sa+sigr)#
print "t1 is %0.2f mm "%(t1)#
print "\nt2 is %0.3f mm "%(t2)#

t1 is 3.83 mm

t2 is 3.894 mm


## exa 5-2 - Page 139¶

In :
from math import sqrt
from __future__ import division
#Elastic limit=sige
sige=310#
#inside diameter=di
di=300#
p=1.8#
FOS=2#
#design stress=sigd#
sigd=sige/2#
c=0.162#
d=380#
#cover plate thickness=t#
t=d*sqrt(c*p/sigd)#
t=17#
M=di*p*t/4#

z=(1/6)*1*t**2#
#bending stress=sigb#
sigb=M/z#
print "t is %0.1fmm "%(t)#
print "\nM is %0.1fmm "%(M)#
print "\nsigb is %0.1fmm "%(sigb)#
if (sigb<=sigd):
print 'sigb is below allowable sigd.'

t is 17.0mm

M is 2295.0mm

sigb is 47.6mm
sigb is below allowable sigd.


## exa 5-3 - Page 140¶

In :
from math import sqrt
sige=220#
v=0.29#
Ri=175#
FOS=3#
Sa=sige/3#
p=10#
#t1=thickness according to maximum principal stress theory
#t2=thickness according to maximum shear stress theory
x=Sa+(p*(1-(2*v)))#
y=Sa-(p*(1+v))#
t1=(sqrt(x/y)-1)*Ri#
t1=24#
#t1=((sqrt((Sa+(p*(1-(2*v)))))/(Sa-(p*(1+v))))-1)*Ri#
t2=Ri*((sqrt(Sa/(Sa-(2*p))))-1)#
# printing data in scilab o/p window
print "t1 is %0.1fmm "%(t1)#
print "\nt2 is %0.3fmm "%(t2)#
#The answer to t2 is not calculated in the book.

t1 is 24.0mm

t2 is 30.206mm


## exa 5-4 - Page 141¶

In :
p=16#
Ri=250#
#Yield strength =sigy#
sigy=330#
v=0.3#
FOS=3#
Sa=sigy/3#
t=Ri*((sqrt(Sa/(Sa-(2*p))))-1)#
t=50#

print "t is %0.1fmm "%(t)#

t is 50.0mm


## exa 5-5 - Page 141¶

In :
from math import pi,sqrt
d=15#
Eg=480#
t=3#
#flange thickness=ft#
ft=12#
A=pi*d**2/4#
l=d+t+(ft/2)#
E=210#
kb=A*E/l#
Ag=pi*(((ft+t+d)**2)-(d**2))/4#
kg=Ag*Eg/t#
# printing data in scilab o/p window
print "kb is %0.3f N/mm "%(kb)#
kb=kb*10**-3#
kg=kg*10**-3#
if (kb<=kg):
print "\nThe combines stiffness of bolt and gasket is %0.3f kN/mm"%(kg)

#The difference in the value of kb is due to rounding-off the value of A


kb is 1546.253 N/mm

The combines stiffness of bolt and gasket is 84.823 kN/mm