Ch:9 Threaded Fasteners

exa 9-1 - Page 266

In [1]:
from math import pi
p1=2#
d=16#
dt1=d-(0.93825*p1)#
At1=pi*dt1**2/4#
p2=1.5#
d=16#
dt2=d-(0.93825*p2)#
At2=pi*dt2**2/4#

print " At1 is %0.1f mm**2     "%(At1)#
print "\n At2 is %0.1f mm**2     "%(At2)#

 At1 is 156.7 mm**2     

 At2 is 167.2 mm**2

exa 9-2 - Page 266

In [2]:
W=20*10**3#
n=4#
#Let the load on each bolt be W1
W1=W/n#
At=W1/80#

print "At is %0.1f mm**2     "%(At)#

At is 62.0 mm**2

exa 9-3 - Page 267

In [3]:
from math import atan, tan, cos,pi
d=18#
p=2.5#
dr=d-(1.2268*p)#
dm=(d+dr)/2#
alpha=atan(p/(pi*dm))#
theta=pi*30/180#
u1=0.15#
u2=0.13#
x=(tan(alpha)+(u1/cos(theta)))/(1-(tan(alpha)*u1/cos(theta)))#
K=dm*x/(2*d)+(0.625*u2)#
print "K is %0.5f      "%(K)#

K is 0.18343

exa 9-4 - Page 267

In [4]:
from math import log,pi
d=20#
t=4#
Lg=84#
Ad=pi*d**2/4#
Eb=205*10**3#
Ed=105*10**3#
kb=Ad*Eb/Lg#
lg=80#
x=5*(lg+(0.5*d))/(lg+(2.5*d))#
kp=pi*Ed*d/(2*log(x))#
At=245#
sigb=105#
Pe=20*10**3#
Pb=Pe*kb/(kb+kp)#
sigad=Pb/At#
finalst=sigb+sigad#

print "final stress is %0.2f N/mm**2      "%(finalst)#

final stress is 123.28 N/mm**2

exa 9-5 - Page 268

In [5]:
from math import atan, tan, cos,pi,log
Eb=207*10**3#
Ec=105*10**3#
sigp=650#
At=115#
Pi=0.75*sigp*At#
F=sigp*At#
#Let the additional load Fadd
Padd=F-Pi#
d=14#
Ad=pi*d**2/4#
Lg=63#
kb=Ad*Eb/Lg#
lg=60#
x=5*(lg+(0.5*d))/(lg+(2.5*d))#
km=pi*Ec*d/(2*log(x))#
C=kb/(kb+km)#
Pe=Padd/C#
K=0.2#
Ti=Pi*K*d*10**-3#

print "Ti is %0.2f Nm      "%(Ti)#

Ti is 156.97 Nm

exa 9-6 - Page 269

In [6]:
from math import atan, tan, cos,pi
d=20#
sigp=600#
At=245#
Pi=120*10**3#
Pe=30*10**3#
C=0.35#
Pb=C*Pe#
P=Pi+Pb#
sigi=Pi/At#
sigf=P/At#
K=0.18#
T=K*d*Pi*10**-3#
E1=sigi/sigp#
E2=sigf/sigp#

print " sigi is %0.1f MPa     "%(sigi)#
print "\n sigi is %0.2f MPa     "%(sigf)#
print "\n T is %0.0f Nm     "%(T)#
print "\n E1 is %0.3f      "%(E1)#
print "\n E2 is %0.3f      "%(E2)#
  
#Value upto tenthth place is considered in the book for value of final stress in bolt, 'sigf'

 sigi is 489.0 MPa     

 sigi is 532.65 MPa     

 T is 432 Nm     

 E1 is 0.000      

 E2 is 0.888

exa 9-7 - Page 269

In [7]:
from math import sqrt,pi
p=2#
d=16#
dt=d-(0.938*p)#
At=pi*dt**2/4#
r=60*sqrt(2)#
Td=1/(4*At)#
Ta=120#
T=8.722*10**-3#
P=Ta/T*10**-3#

print "P is %0.3f kN      "%(P)#
  
#Value upto hundredth place is considered in the book for value of permissible load, 'P'

P is 13.758 kN

exa 9-8 - Page 270

In [1]:
sigyp=460#
FOS=2#
Ts=0.577*sigyp/FOS#
At=245#
r=100#
P=Ts*At/1.453*10**-3#
print "The eccentric load is %f N       "%(P)
print "P is %0.3f kN      "%(P)#
#Value of thousandth place of eccentric load, 'P' is misprinted in the book. 

The eccentric load is 22.377116 N       
P is 22.377 kN

exa 9-9 - Page 271

In [2]:
P=4*10**3#
e=200#
l1=150#
l2=550#
sigyp=420#
FOS=3#
siga=sigyp/3#
M=P*e#
At=12.5#
At=14.2#

# printing data in scilab o/p window
print "At is %0.1f mm**2      "%(At)

At is 14.2 mm**2

exa 9-10 Page 271

In [4]:
from math import atan
Pi=10*10**3#
sigyp=420#
FOS=2#
sige=sigyp/FOS#
K1=0.85#
K2=0.74#
K4=0.868#
SCF=2.4#
K3=1/SCF#
sige=sige*K1*K2*K3*K4#
Pe=10*10**3/3#
Pmax=Pi+Pe#
Pmin=Pi#
Pa=(Pmax-Pmin)/2#
Pm=(Pmax+Pmin)/2#
theta=atan(Pa/Pm)#
siga=21.132#
At=Pa/siga#
At=84.2#

# printing data in scilab o/p window
print "At is %0.1f mm**2      "%(At)
print 'M12 coarse-pitch bolt with 1.75 mm pitch is used'#

At is 84.2 mm**2      
M12 coarse-pitch bolt with 1.75 mm pitch is used

exa 9-11 Page 272

In [5]:
Pi=15#
Pmax=15+3.75#
Pmin=15+1.25#
Pa=(Pmax-Pmin)/2#
Pm=(Pmax+Pmin)/2#
K1=0.85#
K2=0.7#
K4=0.897#
SCF=2.4#
K3=1/SCF#
sige=900/4*K1*K2*K3*K4#
siga=28.115#
At=Pa*10**3/siga#
At=58#

# printing data in scilab o/p window
print "At is %0.0f mm**2      "%(At)#

At is 58 mm**2