# Chapter 10 : Torsion¶

## Example 10.1 Page No : 229¶

In [1]:
import math

# Variables
L = 50. 			#ft
Do = 2 			#in
Di = 1.5 			#in
Mt = 10000. 			#lb in
G = 12.*10**6

# Calculations
Tmax = 16*Mt*Do/(math.pi*(Do**4-Di**4))
angle = (Mt*L*12*32)*57.3/(G*math.pi*(Do**4-Di**4))

# Results
print  'Maximum shearing strees = %.f psi'%(round(Tmax,-1))
print  'twist angle = %.1f degrees'%(angle)

Maximum shearing strees = 9310 psi
twist angle = 26.7 degrees


## Example 10.2 Page No : 229¶

In [2]:
import math

# Variables
d = 4. 			#ft
T = 5000. 			#psi
angle = 0.1 			#degrees

# Calculations
T1 = (math.pi*d**3)*T/16
T2 =angle*math.pi*G*math.pi*d**4/(180*12*32)

# Results
if (T1<T2):
print  'Safe torque = %.2f lb in'%(T1)
else:
print  'Safe torque = %.2f lb'%(T2)

# note : anwer is wrong in book. plz check.

Safe torque = 43864.91 lb


## Example 10.3 Page No : 229¶

In [4]:
from numpy import linalg

# Variables
Ds = 1.  			#in
Db = 1.5 			#in
Ls = 4. 			#in
Lb = 6. 			#in
Gs = 12.*10**6 			#psi
Gb = 6.4*10**6 			#psi
T = 10000.   			#lb in

# Calculations
A = [[1,1],[(Ls*12/(Gs*Ds**4)),(-Lb*12/(Gb*Db**4))]]
b = [T,0]
c = linalg.solve(A,b)
Tab = c[0]
Tbc = c[1]

# Results
print  'Torque in section AB = %.f lb in'%(Tab)
print  'Torque in section AB  = %.f lb in'%(Tbc)

# note : Answers are slightly different because of inbuilt solve function of python.

Torque in section AB = 3571 lb in
Torque in section AB  = 6429 lb in


## Example 10.4 Page No : 230¶

In [2]:
import math

# Variables
T = 10000. 			#lb in
G = 12.*10**6
Dab = 1.5 			#in
Lab = 4. 			#in
Dcd = 1. 			#in
Lcd = 3. 			#in

# Calculations
F = T/2
Tab = F*Lab
angle = ((T*32*12*Lcd/(G*math.pi*Dcd**4))+2*(Tab*32*12*Lab/(G*math.pi*Dab**4)))*(180/math.pi)

# Results
print  'angle of twist = %.0f degrees'%(angle)

angle of twist = 36 degrees


## Example 10.5 Page No : 231¶

In [5]:
import math

# Variables
Tallowable = 5000. 			#psi
power = 250. 	    		#hp
n = 1800.        			#rpm

# Calculations
T = 63000*power/n
d = (16*T/(math.pi*Tallowable))**(1/3.)

# Results
print  'Torque = %.2f lb in'%(T)
print  'diameter =%.2f in'%(d)

Torque = 8750.00 lb in
diameter =2.07 in


## Example 10.6 Page No : 232¶

In [6]:
import math

# Variables
ds = 2. 			#in
n = 315. 			#rpm
Gs = 12.*10**6
Lab = 5. 			#in
Lbc = 15. 			#in
Pa = 10. 			#hp
Pc = 40. 			#hp
Pb = 50. 			#hp

# Calculations
Tab = 63000*Pa/n
Tbc = 63000*Pc/n
angle = ((32*Tbc*Lbc*12/(math.pi*ds**4*G))-(32*Tab*Lab*12/(math.pi*ds**4*G)))*(180/math.pi)

# Results
print  'angle of twist of gear C releative to a = %.2f degrees'%(angle)

angle of twist of gear C releative to a = 4.01 degrees


## Example 10.7 Page No : 234¶

In [7]:
import math

# Variables
T = 10000. 			#lb in

# Calculations
ke = 1/((1/k1)+(1/k2)+(1/k3))
angle = T*180/(ke*math.pi)

# Results
print  'equivalent spring constant = %.2e lb in/rad'%(ke)
print  'angle of twist d/a = %.2f degrees'%(angle)

equivalent spring constant = 1.00e+06 lb in/rad
angle of twist d/a = 0.57 degrees


## Example 10.8 Page No : 234¶

In [3]:
import math

# Variables
T = 20000.   			#lb in

# Calculations
ke = k1+k2
angle = T*180/(ke*math.pi)

# Results
print  'equivalent spring consmath.tant = %.2e lb in/rad'%(ke)
print  'angle of twist at B = %.3f degrees'%(angle)

equivalent spring consmath.tant = 5.00e+06 lb in/rad
angle of twist at B = 0.229 degrees


## Example 10.9 Page no : 238¶

In [7]:
import math

# variables
n = 10        # coils
P = 1200.     # axial load lb
R = 2.
K = 1.33      # factor
d = 1.

# Calculations
Tmax = round(K*(16*P*R)/(math.pi*d**3),-2)
delta = 64*P*R**3*n/(12*10**6*d**4)

# Results
print "Stress = %d psi"%Tmax
print "The deflection = %.3f in"%delta

Stress = 16300 psi
The deflection = 0.512 in


## Example 10.10 Page No : 239¶

In [9]:

# Variables
di = 0.2 			#in
dm = 2. 			#in
n = 10.
F = 10. 			#lb
G = 12.*10**6

# Calculations
k = G*di**4/(64*dm**3*n)
ke = 1/((1/(k+k))+(1/k)+(1/k))
delta = F/ke

# Results
print  'elongation = %.2f in'%(delta)

elongation = 6.67 in


## Example 10.11 Page No : 241¶

In [10]:
import math

# Variables
d = 0.5 			#in
n = 315. 			#rpm
t1 = 5000. 			#psi
r1 = 8. 			#in
r2 = 4. 			#in
n1 = 6.
n2 = 4.

# Calculations
t2 = r2*t1/r1
T = r1*n1*(math.pi/4)*d**2*t1+r2*n2*(math.pi/4)*d**2*t2
hp = T*n/63000

# Results
print  'Premissible horsepower = %.f hp'%(hp)

Premissible horsepower = 275 hp