Chapter 16:Torsion of Shafts and Springs

Problem 16.1,page no.675

In [1]:
import math
#Given
#Variable declaration
D=150                  #Diameter of the shaft in mm
tau=45                 #Maximum shear stress in N/sq.mm

#Calculation
T=int(math.pi/16*tau*D**3)*1e-3  #Maximum torque transmitted by the shaft in N-m

#Result
print "Maximum torque =",T,"N-m"

Maximum torque = 29820.586 N-m

Problem 16.3,page no.677

In [2]:
import math

#Given
#Variable declaration
Do=200     #Outer diameter in mm
Di=100     #Inner diameter in mm
tau=40     #Maximum shear stress in N/sq.mm

#Calculation
T=int(round((math.pi)/16*tau*((Do**4-Di**4)/Do),-1))*1e-3 #Maximum torque transmitted by the shaft in Nm

#Result
print "Maximum torque transmitted by the shaft =",T,"Nm"

Maximum torque transmitted by the shaft = 58904.86 Nm

Problem 16.7,page no.682

In [4]:
from __future__ import division
import math

#Given
#Variable declaration
Do=120          #External diameter in mm
P=300*1000      #Power in W
N=200           #Speed in r.p.m
tau=60          #Maximum shear stress in N/sq.mm

#Calculation
T=round((P*60)/(2*math.pi*N),1)*1e3                         #Torque transmitted in Nmm   
Di=round(((Do**4)-((T*16*Do)/(math.pi*tau)))**(1/4),1)      #Maximum internal diameter in mm

#Result
print "Maximum Internal diameter =",Di,"mm"

Maximum Internal diameter = 88.5 mm

Problem 16.8,page no.683

In [4]:
import math
#Given
#Variable declaration
D=15*10        #Diameter of shaft in mm
P=150*1e3      #Power transmitted in W
N=180          #Speed of shaft in r.p.m

#Calculation
T=(P*60)/(2*math.pi*N)*1e3        #Torque transmitted in Nmm
tau=int((16*T)/(math.pi*D**3))    #Maximum shear stress in N/sq.mm

#Result
print "Maximum shear stress =",tau,"N/mm^2"

Maximum shear stress = 12 N/mm^2

Problem 16.9,page no.683

In [5]:
from __future__ import division
import math
#Given
#Variable declaration
P=300*1000      #Power in W
N=100           #Speed in r.p.m
tau=80          #Maximum shear stress in N/sq.mm

#Calculation
#case(a):
T=(P*60)/(2*math.pi*N)*1e3                              #Torque transmitted in Nmm
D=round(((16*T)/(math.pi*tau))**(1/3),0)                #Diameter of solid shaft in mm
#case(b):
Do=round(((T*16)/(math.pi*tau*(1-0.6**4)))**(1/3),0)    #External diameter of hollow shaft in mm
Di=0.6*Do                                               #Internal diameter of hollow shaft in mm
Per=(D**2-(Do**2-Di**2))/(D**2)*100                     #Percentage saving in weight

#Result
print "Diameter of solid shaft =",D,"mm"
print "Percentage saving in weight = %.2f%%"%Per

Diameter of solid shaft = 122.0 mm
Percentage saving in weight = 29.55%

Problem 16.10,page no.685

In [6]:
import math
#Given
#Variable declaration
P=75e3      #Power transmitted in W
N=200       #R.P.M of the shaft 
tau=70      #Shear stress in N/sq.mm

#Calculation
T=P*60/(math.pi*2*N)*1e3                        #Mean Torque transmitted in Nmm
Tmax=1.3*T                                      #Maximum Torque transmitted in Nmm
D=round((16*Tmax/(math.pi*tau))**(1/3),0)       #Suitable diameter of the shaft in mm

#Result
print "Diameter of the shaft = %d mm"%D

Diameter of the shaft = 70 mm

Problem 16.11,page no.685

In [7]:
import math
#Given
#Variable declaration
P=300e3     #Power transmitted in W
N=80        #speed of the shaft in r.p.m
tau=60      #Maximum shear stress in N/sq.mm

#Calculation
T=P*60/(math.pi*2*N)*1e3                                 #Mean Torque transmitted in Nmm
Tmax=1.4*T                                               #Maximum Torque transmitted in Nmm
D=round((16*Tmax/(math.pi*tau))**(1/3),0)                #Suitable diameter of the shaft in mm
Do=round(((Tmax*16)/(math.pi*tau*(1-0.6**4)))**(1/3),0)  #External diameter of hollow shaft in mm
Di=0.6*Do                                                #Internal diameter of hollow shaft in mm

#Result
print "External diameter of hollow shaft = %d mm"%Do
print "Internal diameter of hollow shaft = %d mm"%Di

External diameter of hollow shaft = 170 mm
Internal diameter of hollow shaft = 102 mm
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