from __future__ import division
import math
#Given
#Variable declaration
L=4*(10**3) #Length of the bar in mm
b=30 #Breadth of the bar in mm
t=20 #Thickness of the bar in mm
P=30*(10**3) #Axial pull in N
E=2e5 #Young's modulus in N/sq.mm
mu=0.3 #Poisson's ratio
#Calculation
A=b*t #Area of cross-section in sq.mm
long_strain=P/(A*E) #Longitudinal strain
delL=long_strain*L #Change in length in mm
lat_strain=mu*long_strain #Lateral strain
delb=b*lat_strain #Change in breadth in mm
delt=t*lat_strain #Change in thickness in mm
#Result
print "change in length =",delL,"mm"
print "change in breadth =",delb,"mm"
print "change in thickness =",delt,"mm"
#Given
#Variable declaration
L=30 #Length in cm
b=4 #Breadth in cm
d=4 #Depth in cm
P=400*(10**3) #Axial compressive load in N
delL=0.075 #Decrease in length in cm
delb=0.003 #Increase in breadth in cm
#Calculation
A=(b*d)*1e2 #Area of cross-section in sq.mm
long_strain=delL/L #Longitudinal strain
lat_strain=delb/b #Lateral strain
mu=lat_strain/long_strain #Poisson's ratio
E=int((P)/(A*long_strain)) #Young's modulus
#Result
print "Poisson's ratio =",mu
print "Young's modulus = %.e N/mm^2"%E
#Given
#Variable declaration
L=4000 #Length of the bar in mm
b=30 #Breadth of the bar in mm
t=20 #Thickness of the bar in mm
mu=0.3 #Poisson's ratio
delL=1.0 #delL from problem 2.1
#Calculation
ev=(delL/L)*(1-2*mu) #Volumetric strain
V=L*b*t #Original volume in mm^3
delV=ev*V #Change in volume in mm^3
F=int(V+delV) #Final volume in mm^3
#Result
print "Volumetric strain =",ev
print "Final volume =",F,"mm^3"
from __future__ import division
#Given
#Variable declaration
L=300 #Length in mm
b=50 #Width in mm
t=40 #Thickness in mm
P=300*10**3 #Pull in N
E=2*10**5 #Young's modulus in N/sq.mm
mu=0.25 #Poisson's ratio
#Calculation
V=L*b*t #Original volume in mm^3
Area=b*t #Area in sq.mm
stress=P/Area #Stress in N/sq.mm
ev=(stress/E)*(1-2*mu) #Volumetric strain
delV=int(ev*V) #Change in volume in mm^3
#Result
print "Change in volume =",delV,"mm^3"
import math
#Given
#Variable declaration
L=5*10**3 #Length in mm
d=30 #Diameter in mm
P=50*10**3 #Tensile load in N
E=2e5 #Young's modulus in N/sq.mm
mu=0.25 #Poisson's ratio
#Calculation
V=int(round((math.pi*d**2*L)/4,-2)) #Volume in mm^3
e=P*4/(math.pi*(d**2)*E) #Strain of length
delL=round(e*L,3) #Change in length in mm
lat_strain=round(mu*round(e,7),7) #Lateral strain
deld=lat_strain*d #Change in diameter in mm
delV=round(V*(0.0003536-(2*lat_strain)),2) #Change in volume in mm^3
#Result
print "Change in length =",delL,"mm"
print "Change in diameter =",deld,"mm"
print "Change in volume =",delV,"mm^3"
#Given
#Variable declaration
E=1.2e5 #Young's modulus in N/sq.mm
C=4.8e4 #Modulus of rigidity in N/sq.mm
#Calculation
mu=(E/(2*C))-1 #Poisson's ratio
K=int(E/(3*(1-2*mu))) #Bulk modulus in N/sq.mm
#Result
print "Poisson's ratio =",mu
print "Bulk modulus = %.0e N/mm^2"%K
#Given
#Variable declaration
A=8*8 #Area of section in sq.mm
P=7000 #Axial pull in N
Ldo=8 #Original Lateral dimension in mm
Ldc=7.9985 #Changed Lateral dimension in mm
C=0.8e5 #modulus of rigidity in N/sq.mm
#Calculation
lat_strain=(Ldo-Ldc)/Ldo #Lateral strain
sigma=P/A #Axial stress in N/sq.mm
mu=round(1/((sigma/lat_strain)/(2*C)-1),3) #Poisson's ratio
E=round((sigma/lat_strain)/((sigma/lat_strain)/(2*C)-1),-1) #Modulus of elasticity in N/sq.mm
#Result
print "Poisson's ratio =",mu
print "Modulus of elasticity = %.4e N/mm^2"%E