# Chapter 2: Strain¶

## Example 2.1 page no. 70¶

In [19]:
#Given
e_z= 4     #Constant
ab = 0.200 #m, dimension
from scipy import integrate
#Calculations
#Part a)
import math
def f(z):
return(1+(40*10**-3)*(math.sqrt(z)))
z=integrate.quad(f,0,ab) #Strain formula for short line segment = delta(sdash) =(1+e_z)delta(s)
deltaB= z[0]-ab
deltaB_mm= deltaB*1000

#Part b)

e_avg = deltaB/ab#  Normal strain formula  e = (delta(sdash) -delta(s))/delta(s)

#Display
print"The displacement at the end of the rod is =   ",round(deltaB_mm,2),"mm"
print"The average normal strain in the rod is   =",round(e_avg,4),"mm"
The displacement at the end of the rod is =    2.39 mm
The average normal strain in the rod is   = 0.0119 mm

## Example 2.2 page no. 71¶

In [12]:
#Given
theta = 0.05      #degree, angle
L1=300.0          #mm, length
L2 = 400.0        #mm

#Calculations
import math
alpha=math.atan(L2/L1)*180/3.14
phi=90-alpha+theta
epsilonBD=(Lbd-L1)/(L1)
dLbd=(theta*3.14/180.0)*L2

#Display
print"The average normal strain =",round(epsilonBD,3),"mm/mm"
The average normal strain = 0.001 mm/mm

## Example 2.3 page no. 72¶

In [13]:
#Given
#The given dimension are
ab= 250.0        #mm
bbdash_x = 3.0   #mm
bbdash_y = 2.0   #mm
ac = 300.0       #mm

#calculations
#Part(a)
import math
abdash = math.sqrt((ab - bbdash_y)**2 + (bbdash_x)**2)  #Pythagoras theorem
avg_normal_strain = (abdash-ab)/ab

#Part(b)
gamma_xy = math.atan(bbdash_x/(ab - bbdash_y)) #shear strain formula

#Display
print"The average normal strain along AB is    =",round(avg_normal_strain,4),"mm/mm"
The average normal strain along AB is    = -0.0079 mm/mm
The average shear strain                 = 0.0121 rad

## Example 2.4 page no. 73¶

In [22]:
#Given
ab = 150 #mm
bc = 150 #mm
disp_cd= 2 #mm
ab_half = ab/2.0

#Calculations
#Part(a)
import math
ac = sqrt((ab)**2 + (bc)**2)  #Pythagoras theorem in mm
ac_m = ac/1000.0 #in m
acdash = sqrt((ab)**2 + (bc+disp_cd)**2)  #Pythagoras theorem in mm
acdash_m = acdash/1000.0 #in m
avg_strain_ac = (acdash_m - ac_m)/ac_m    #Normal strain formula

#Part(b)