# Chapter 7 : Mechanical Properties¶

### Example 7.3 pageno : 166¶

In [1]:
%matplotlib inline

from matplotlib.pyplot import *

# Variables
a1 = 222.*10**9;			#in N
a2 = 168.*10**9;			#in N
e1 = 1.90;  	    		#in sqm
e2 = 1.42;  		    	#in sqm
da = a1-a2; 			    #in N
de = e1-e2;	    	    	#in sqm
MPa = [14,28,56,84,110,138,193,221,276]
strain = [.1,.21,.44,.67,.88,1.14,1.7,1.95,2.9]

# Calculations
e_math_tan = da/de;
e_math_tann = e_math_tan*10**-9;			#in Gpa
a3 = 180.*10**9;                   			#in N
e3 = 1.46;			                        #in sqm
e_sec = 10**-9*a3/e3;			            #in Gpa
a = 85*10**6;
e = .68*10**-3;
e_y = 10**-9*a/e;			                #in Gpa
plot(strain,MPa)
plot(strain,MPa,"go")
xlabel("STRAIN")
ylabel("STRESS(MPa)")
suptitle("Stress-strain diagram")

# Results
print "Tangent Modulous of elasticity (in Gpa)  =  %.1f GPa"%e_math_tann
print "Secant modulous of elasticity (in Gpa)  =  %d GPa"%e_sec
print "Youngs modulous (in Gpa)  =  %d GPa"%e_y

Populating the interactive namespace from numpy and matplotlib
Tangent Modulous of elasticity (in Gpa)  =  112.5 GPa
Secant modulous of elasticity (in Gpa)  =  123 GPa
Youngs modulous (in Gpa)  =  125 GPa


### Example 7.4 page no : 179¶

In [2]:
%matplotlib inline

from matplotlib.pyplot import *

# Variables
t = [0,1,2,4,8,16,24,32,40,48,60,72]       #time
s = [0,.02,.029,.041,.057,.078,.094,.109,.122,.136,.156,.176]     # strain E (mm/mm)

# calculations
min_creep_rate = 12./14            # from curve
creep_intercept = .055              # from curve

#results
plot(t,s)
plot(t,s,"go")
suptitle("Strain-Time Curve")
xlabel("Time(minute)")
ylabel("Strain")

print "Minimum Creep rate : %.3f mm/mm"%min_creep_rate
print "The creep intercept : %.3f mm/mm"%creep_intercept

Populating the interactive namespace from numpy and matplotlib
Minimum Creep rate : 0.857 mm/mm
The creep intercept : 0.055 mm/mm

WARNING: pylab import has clobbered these variables: ['draw_if_interactive', 'e']
%pylab --no-import-all prevents importing * from pylab and numpy


### Example 7.5 pageno : 183¶

In [19]:
import math
#Find Stress

# Variables
n = 3.;
a = 300.;
t = 365. * 24;			#in hours
e = 2.*10**6;			#kgf/sqcm
ai = 750.;	    		#in kgf/sqcm

# Calculations
v_cr = 2.8*10**-8;			# in cm/cm/hour creep rate
x = math.log(v_cr)-n*math.log(a);
a1 = math.exp(x);
a_tf = round(math.sqrt(1./((1./ai**(n-1))+(a1*e*(n-1)*t))),-2);

# Results
print "Stress Remaining (in kgf/sq cm)  =  %.f kgf/cm**2"%a_tf

Stress Remaining (in kgf/sq cm)  =  200 kgf/cm**2