# Chapter 9:Mechanical Properties of Materials¶

## Example 9.1,Page No:9.3¶

In [1]:
import math

#variable declaration
F   = 8482;                    # Tensile force in newtons
lo  = 0.30;                    # length of steel wire in cm
Y   = 207*10**9;               # Youngs modulus of steel Gpa
r   = 3*10**-3;                # radius of steel wire  in m
v   = 0.30;                    # poisson ratio

# Calculations

dl  = (F*lo)/float(Y*math.pi*r**2);       #elongation in mm
e1  = dl/float(lo);                       #longitudanl strain
e2  = v*e1                                # lateral strain
dr  = e2*r;                               # lateral contraction in m

# Result
print'Elongation = %3.3f'%(dl*10**3),'mm';
print'Lateral contraction = %3.2f '%(dr*10**6),'um';

Elongation = 0.435 mm
Lateral contraction = 1.30  um


## Example 9.3,Page No:9.7¶

In [2]:
import math

#variable declaration
P   = 400;                      # tensile force in newtons
d   = 6*10**-3;                 # diameter of steel rod m

# Calculations
r   =d/float(2);
E_stress = (P)/float((math.pi/float(4))*d*d);         #e_stress in N/m**2

#Result

print'Engineering stress = %3.2f '%(E_stress*10**-6),'MPa';

Engineering stress = 14.15  MPa


## Example 9.4,Page No:9.7¶

In [3]:
import math

#variable declaration
Lf  = 42.3;         #guage length after strain mm
Lo  = 40;           # guage length in mm

# Calculations
e   = ((Lf - Lo)/float(Lo))*100      #Engineering Strain in %

#Result
print'Percentage of elongation = %3.2f '%e,'%';

Percentage of elongation = 5.75  %


## Example 9.5,Page No:9.7¶

In [4]:
import math

#variable declaration
dr  = 12.8;      # original diameter of steel wire in mm
df  = 10.7;     # diameter at fracture in mm

# Calculations
percent_red = (((math.pi*dr*dr) - (math.pi*df*df))/float(math.pi*dr*dr))*100;  #Percent reduction in area  in %

# Result
print'Percent reduction in area = %3.1f'%percent_red,'%';

Percent reduction in area = 30.1 %