Ch:7 Struts and Columns

exa 7-1 - Page 192

from math import pi
sigc=550#
FOS=4#
sigw=sigc/FOS#
l=4000#
le=l/2#
A=pi*(1-0.7**2)/4#
K=(1+0.7**2)/16#
Pr=800*10**3#
a=1/1600#
D=130# #Rounding off to nearest whole number
d=D*0.7#
print "D is %0.1f mm     "%(D)#
print "\nd is %0.1f mm     "%(d)#

D is 130.0 mm     

d is 91.0 mm     

exa 7-2 - Page 192

from math import sqrt,pi
l=500#
E=70*10**3#
P=20*10**3#
FOS=2#
d=P*2*12*4*l**2/((pi)**2*E)#
d=(sqrt(8)*d)**0.25#
b=d/sqrt(8)#
print "d is %0.2f mm     "%(d)#
print "\nb is %0.2f mm     "%(b)#

d is 37.44 mm     

b is 13.24 mm     

exa 7-3 - Page193

from math import sqrt,pi
Ixx=(2*1696.6)+115.4#
Iyy=1696.6+(2*115.4)+(2*25.27*10.27**2)#
A=3*25.27#
Kmin=sqrt(Ixx/75.81)#
L=600#
k=L/Kmin#
sigc=110#
c=1/200#
sigw=sigc*(1-(c*k))#
Pw=sigw*A#
a=1/7500#
sigc1=320#
Pr=(sigc1*A)/(1+(a*(L/Kmin)**2))#
FOS=Pr/Pw#
print "FOS is %0.2f      "%(FOS)#

FOS is 2.91      

exa 7-4 - Page 194

from math import sqrt,pi
Iyy=193.4+(2*1.2*1.5**3/12)#
E=200*10**3#
l=500#
Pe=(pi**2)*E*Iyy*10**5/(l**2)#
A=35.53+(2*1.2*15)#
sige=Pe/7530#
k=sqrt(Iyy/A)#
xc=75#
sig=80#
sigo=20.875#
A=A*100#
P=sigo*A#
P=P*10**-3#
print "P is %0.1f kN     "%(P)#
  
#The difference in the value of P is due to rounding-off the digits.

P is 149.3 kN     

exa 7-5 - Page 195

from math import sqrt,pi
sigc=330#
a=1/7500#
t=4#
A=14.5*t**2#
l=300#
Kx=sqrt(1.4626*t**2)#
Pr=sigc*A/(1+(a*(l/Kx)**2))#
FOS=2#
P=Pr/FOS*10**-3#
print "P is %0.4f KN     "%(P)#

P is 38.2800 KN     

exa 7-6 - Page 195

from math import sqrt,pi
P=1500#
FOS=2#
Pd=FOS*P#
l=280#
E=207*10**3#
I=Pd*l**2/(pi**2*E)#
D=(64*I/(pi*(1-0.8**4)))**(1/4)#
D=8#
d=6.4#
print "D is %0.1f mm     "%(D)#
print "\nd is %0.1f mm     "%(d)#

D is 8.0 mm     

d is 6.4 mm     

exa 7-7 - Page 196

from math import sqrt,pi
D=500#
p=0.3#
E=208*10**3#
sigc=320#
a=1/7500#
l=2000#
le=l/2#
W=pi*D**2*p/4#
FOS=4#
Wd=W*FOS#
I=Wd*l**2/(pi**2*E)#
d=(64*I/pi)**(1/4)#
A=pi*d**2/4#
k=d/4#
d=45# #Rounding off to nearest whole number
print "d is %0.1f mm     "%(d)#

d is 45.0 mm