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diff --git a/Electronic_Measurements_and_Instrumentation_by_Er.R.K.Rajput/R.K.RAJPUT_CHAPTER_7.ipynb b/Electronic_Measurements_and_Instrumentation_by_Er.R.K.Rajput/R.K.RAJPUT_CHAPTER_7.ipynb new file mode 100644 index 00000000..697d4b21 --- /dev/null +++ b/Electronic_Measurements_and_Instrumentation_by_Er.R.K.Rajput/R.K.RAJPUT_CHAPTER_7.ipynb @@ -0,0 +1,957 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 7:Sensors And Transducers"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.2,Page No:401"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "displacement 5.75 mm\n",
+ "displacement 12.800 mm\n",
+ "resolution of potentiometer 0.050 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "R =10000; #resistance in Ω\n",
+ "R1 = 3850; #resistance of potentiometer Ω\n",
+ "R2 = 7560; #resistance of potentiometer Ω\n",
+ "l = 50*10**-3; #length of uniform wound wire in m\n",
+ "x = 10;\n",
+ "\n",
+ "#calculations\n",
+ "\n",
+ "R3 = (R/float(2)); #resistance of potentiometer in .normal position in Ω\n",
+ "r = (R/float(l)); #resistance of potentiometer wire per unit length Ω/mm\n",
+ "dR1 = R3-R1; #change in resistance of potentiometer from its normal position Ω\n",
+ "D1 = (dR1/float(r)); #displacement in mm\n",
+ "dR2 = (R2-R3); #change in resistance of potentiometer from its normal position in Ω\n",
+ "D2 = (dR2/float(r)); #displacement in mm\n",
+ "RE = (x/float(r)); #resolution of potentiometer in mm\n",
+ "\n",
+ "#result\n",
+ "print'displacement %3.2f'%(D1*10**3),'mm';\n",
+ "print'displacement %3.3f'%(D2*10**3),'mm';\n",
+ "print'resolution of potentiometer %3.3f'%(RE*10**3),'mm';\n",
+ " \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.3,Page No:403"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "resistance at 35°C is 50 Ω\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "R25 = 100; #resistance of thermistor at 25°C\n",
+ "t2 = 35; #temperature in °C\n",
+ "t1 = 25; #temperature in °C\n",
+ "alpha = 0.05; #temperature coefficient\n",
+ "\n",
+ "#calculations\n",
+ "t = t2-t1; #temperaturre difference in °C\n",
+ "x = alpha*t;\n",
+ "R35 = (R25)*(1-x); #resistance in Ω\n",
+ "\n",
+ "#result\n",
+ "print'resistance at 35°C is %d'%R35,'Ω';"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.4,Page No:406"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "inductance = 0.04 mH\n",
+ "ratio of change in inductance to the original inductance =0.02\n",
+ "ratio of change in inductance to the original inductance =0.02\n",
+ "Hence dl is directly proportional to displacement\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "l = 1.00; #length in mm\n",
+ "L = 2; #inductance in mH\n",
+ "d = 0.02; #displacement in mm\n",
+ "\n",
+ "#calculations\n",
+ "la = l-d; #length of air gap when d=0.02\n",
+ "dl = (2*(1/float(la)))-L; #change in inductance in mH\n",
+ "r = dl/float(L); #ratio of change in inductance to the original inductance\n",
+ "dd = r/float(l); #ratio of displacement to original gap length\n",
+ "\n",
+ "#result\n",
+ "print'inductance = %3.2f'%dl,'mH';\n",
+ "print'ratio of change in inductance to the original inductance =%3.2f'%r;\n",
+ "print'ratio of change in inductance to the original inductance =%3.2f'%dd;\n",
+ "print'Hence dl is directly proportional to displacement';\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.5,Page No:409"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "percentage linearity 0.25 %\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "d = 1.8; #output voltage at maximum displacement in V\n",
+ "de = 0.0045; #deviation from straight line through the origin\n",
+ "\n",
+ "#calculations \n",
+ "a = (de/float(d))*100; #percentage linearity indicating in both -ve and +ve\n",
+ "\n",
+ "#result\n",
+ "print'percentage linearity %3.2f'%a,'%';\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.6,Page No:409"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "sensitivty of LVDT 3.00 mV/mm\n",
+ "resolution 0.0067 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "Vo = 1.8; #output voltage in mV\n",
+ "Vi = 0.6; #input voltage in mV;\n",
+ "a = 500; #amplification factor\n",
+ "r = 1/float(4); #scale can read \n",
+ "v = 4; #output of voltmetr in V\n",
+ "D = 100; #millivoltmeter readings\n",
+ "\n",
+ "#calculation\n",
+ "s = Vo/float(Vi); #sensitivity in mV/mm\n",
+ "sm = a*s; #sensitivity of measurement in mV/mm\n",
+ "s1 = (v/float(D))*10**3; # 1 scale division in mV\n",
+ "Vm = r*s1; #minimum voltage that can be read on voltmeter\n",
+ "R = Vm/float(sm); #resolution in mm\n",
+ "\n",
+ "#result \n",
+ "print'sensitivty of LVDT %3.2f'%s,'mV/mm';\n",
+ "print'resolution %3.4f'%R,'mm';\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.7,Page No:413"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "capacitance = 13.275 pF\n",
+ "change in capacitance 1.475 pF\n",
+ "ratio ofper unit change of capacitance to per unit change in displacement = 1.111111\n",
+ "capcitance when mica is inserted = 13.88 pF\n",
+ "change in capacitance when mica sheet is inserted = 1.62 pF\n",
+ "ratio ofper unit change of capacitance to per unit change in displacement = 1.168\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "A = 300*10**-6; #area of plate in m**2\n",
+ "d = 0.2*10**-3; #distance between plates in mm\n",
+ "e0 = 8.85*10**-12; #permittivity in F/m\n",
+ "er2 = 8; #dielectric constant of mica \n",
+ "d1 = 0.18*10**-3; #distance between plates in mm\n",
+ "er1 = 1; #dielectric constant\n",
+ "D1 = 0.19;\n",
+ "D2 = 0.01; #thickness of mica sheet in mm\n",
+ "D3 = 0.17; #displacement in mm\n",
+ "D4 = 0.01;\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "#calculation\n",
+ "C = ((e0*A)/float(d)); #value of capacitance in pF\n",
+ "dD = d-d1; #change in displacement in mm\n",
+ "dC = ((e0*A)/(float(d1)))-C; #change in capacitance in capacitance\n",
+ "x1 = (dC/float(C)); #per unit change in capacitance \n",
+ "x2 = (dD/float(d)); #per unit change of displacement\n",
+ "d3 = d-d1; #length of air gap between plates in mm\n",
+ "x = x1/float(x2); #ratio of unit change of capacitance to unit change in displacement\n",
+ "D = (D1/(float(er1)))+((D2/float(er2)));\n",
+ "C1 = (e0*A)/float(D*10**-3); #initial capacitance of transducer in mm\n",
+ "d4 = d1-d3; #length of air gap in mm\n",
+ "d1 = (D3/float(er1))+(D4/float(er2));\n",
+ "C2 = (e0*A)/float(d1*10**-3); # capacitance with displacement is applien in pF\n",
+ "dC2 = C2-C1; #change in capacitance in pF\n",
+ "y1 = (dC2/float(C1)); #per unit change in capacitance \n",
+ "y2 = (dD/float(d)); #per unit change of displacement\n",
+ "Y = y1/float(y2); #ratio of unit change of capacitance to unit change in displacement\n",
+ "\n",
+ "#result\n",
+ "print'capacitance = %2.3f'%(C*10**12),'pF';\n",
+ "print'change in capacitance %3.3f'%(dC*10**12),'pF';\n",
+ "print'ratio ofper unit change of capacitance to per unit change in displacement = %f'%x;\n",
+ "print'capcitance when mica is inserted = %3.2f'%(C1*10**12),'pF';\n",
+ "print'change in capacitance when mica sheet is inserted = %2.2f'%(dC2*10**12),'pF';\n",
+ "print'ratio ofper unit change of capacitance to per unit change in displacement = %3.3f'%Y;\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.8,Page No:417"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "output voltage = 192.50 V\n",
+ "charge sensitivity = 2.233 pC/N\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "t = 2.5*10**-3; #thickness in m\n",
+ "g = 0.055; #voltage intensity in Vm/N\n",
+ "p = 1.4*10**6; #pressure in N/m**2\n",
+ "e = 40.6*10**-12; #permittivity of quartz in F/m\n",
+ "\n",
+ "#calculation\n",
+ "E = g*t*p; #output voltage in V\n",
+ "q = e*g; #charge sensitivity in pC/N\n",
+ "\n",
+ "#result\n",
+ "print'output voltage = %3.2f'%E,'V';\n",
+ "print'charge sensitivity = %3.3f'%(q*10**12),'pC/N';"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.9,Page No:417"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "force = 43.64 N\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "r = 6*10**-3; #radius in m\n",
+ "t = 1.8*10**-3; #thickness in m\n",
+ "g = 0.055; #voltage intensity in Vm/N\n",
+ "E = 120; #voltage developed in V\n",
+ "\n",
+ "#calculation\n",
+ "A = r*r; #area in m**2\n",
+ "p = E/(float(g*t)); #pressure in N/m**2\n",
+ "F = p*A; #force in N\n",
+ "\n",
+ "\n",
+ "#result\n",
+ "print'force = %3.2f'%F,'N';\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.10,Page No:417"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "strain = 0.01392\n",
+ "charge = 900.0 pC\n",
+ "capacitance = 300 pf\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "r = 6*10**-3; #radius in m\n",
+ "t = 1.5*10**-3; #thickness in m\n",
+ "e = 12.5*10**-9; #permittivity in F/m\n",
+ "F = 6; #force in N\n",
+ "d = 150*10**-12; #charge density in pC/N\n",
+ "E = 12*10**6; #modulus of elasticity in N/m**2\n",
+ "s = 0.167*10**6; #stress \n",
+ "\n",
+ "#calculation\n",
+ "A = r*r;\n",
+ "p = F/float(A); #pressure in MN/m**2\n",
+ "p1 = p*10**-6;\n",
+ "e1 = s/float(E); #strain \n",
+ "g = d/float(e); #voltage sensitivity in V*m/N;\n",
+ "E1 = g*t*p; #voltage generated in V\n",
+ "Q = d*F; #charge in C\n",
+ "C = (Q)/float(E1); #capacitance in F\n",
+ "\n",
+ "#result\n",
+ "print'strain = %3.5f'%e1;\n",
+ "print'charge = %3.1f'%(Q*10**12),'pC';\n",
+ "print'capacitance = %3.3d'%(C*10**12),'pf';\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.11,Page No:421"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "hall angle 1.55 °\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "p = 0.00912; #resistivity in Ωm\n",
+ "B = 0.48; #flux density in Wb/m**2\n",
+ "RH = 3.55*10**-4; #hall coefficient in m**3/C\n",
+ "\n",
+ "#calculation\n",
+ "Ex = p; #Ex in terms of Jx in °\n",
+ "Ey = RH*B; #ey interms of Jx in °\n",
+ "x= Ex/float(Ey);\n",
+ "t = math.atan(x);\n",
+ "\n",
+ "print'hall angle %3.2f'%t,'°';\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.12,Page No:421"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "voltage between contacts = 0.00256 V\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "p = 0.00912; #resistivity in Ωm\n",
+ "B = 0.48; #flux density in Wb/m**2\n",
+ "RH = 3.55*10**-4; #hall coefficient in m**3/C\n",
+ "I = 0.015; # current in A\n",
+ "l = 15*10**-3; #length in m\n",
+ "b = 10**-3; #breadth in m\n",
+ "\n",
+ "\n",
+ "#calculation\n",
+ "A = l*b; #area in m**2\n",
+ "Jx = I/float(A); #current density in A/m**2\n",
+ "Ey = RH*B*Jx; #Ey in V/m\n",
+ "V = Ey*I; #voltage between contacts in V\n",
+ "\n",
+ "#result\n",
+ "print'voltage between contacts = %5.5f'%V,'V';"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.13,Page No:432"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "poissons ratio = 1.6\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "Gf = 4.2; #guage factor of resistance \n",
+ "\n",
+ "#calculation\n",
+ "u =(Gf-1)/float(2); #poisson's ratio\n",
+ "\n",
+ "#result\n",
+ "print'poissons ratio = %1.1f'%u;"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.14,Page No:432"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "change in resistance = 48.00 mΩ\n",
+ "Note:Ans printing mistake in textbook\n",
+ "change in resistance = 48.00 mΩ\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "R = 120; #resistance in Ω\n",
+ "Gf = 2; #guage factor \n",
+ "s = 400*10**6; #elastic limit stress in N/m**2\n",
+ "E = 200*10**9; #modulus of elasticity in N/m**2\n",
+ "alpha = 20*10**-6; #resistance temperature coefficient in /°C\n",
+ "x = 1/float(10); #cahnge in stress \n",
+ "dt = 20; #change in temperature in °C\n",
+ "\n",
+ "#calculations\n",
+ "sc = s*x; #change in stress in N/m**2\n",
+ "e = sc/float(E); #strain \n",
+ "dR = Gf*e*R; #change in resistance in mΩ\n",
+ "dR1 = R*alpha*dt; #change in resistance in mΩ\n",
+ "\n",
+ "#result\n",
+ "print'change in resistance = %3.2f'%(dR*10**3),'mΩ';\n",
+ "print'Note:Ans printing mistake in textbook';\n",
+ "print'change in resistance = %3.2f'%(dR1*10**3),'mΩ';\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.15,Page No:433"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "change in length = 3.72e-06 m\n",
+ "force = 2.438 kN\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "L = 0.12; #length in m\n",
+ "A = 3.8*10**-4; #area in m**2\n",
+ "R = 220; #resistance in Ω\n",
+ "Gf = 2.2; #guage factor\n",
+ "dR = 0.015; #change in resistance in Ω\n",
+ "E = 207*10**9; #elasticity in N/m**2\n",
+ "\n",
+ "#calculations\n",
+ "dL = (dR*L)/float(R*Gf); #change in length in m \n",
+ "s = (E*dL)/float(L); \n",
+ "F = s*A; #force in kN \n",
+ "\n",
+ "#result\n",
+ "print'change in length = %2.2e'%dL,'m';\n",
+ "print'force = %3.3f'%(F*10**-3),'kN';\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.16,Page No:444"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "strain = 594.5 microstrain\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "Rg = 100; #resistance in Ω\n",
+ "Rsh = 80000; #resistance in Ω\n",
+ "Gf = 2.1;\n",
+ "\n",
+ "#calculations\n",
+ "x = (Rg/float(Rg+Rsh)); #equivalent strain\n",
+ "eeq = x/(float(Gf)); #strain in microstrain\n",
+ "\n",
+ "#result\n",
+ "print'strain = %3.1f'%(eeq*10**6),'microstrain';\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.17,Page No:445"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "strain = 356.43 microstrain\n",
+ "Note:calculation mistake in text book,Rg value is taken wrong in calculating s\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "n = 4; #four arm bridge\n",
+ "Rg = 200; #resistance in Ω\n",
+ "Rsh = 100*10**3; #resistance in Ω\n",
+ "x = 140; #number of divisions\n",
+ "Gf = 2.0; #guage factor\n",
+ "\n",
+ "#calculation\n",
+ "eeff = Rg/float(n*Gf*(Rg+Rsh)); #effective strain\n",
+ "d = eeff/float(x); #1 division scale\n",
+ "s = float(d)*Rg; #strain when loaded\n",
+ "\n",
+ "#result\n",
+ "print'strain = %3.2f'%(s*10**6),'microstrain';\n",
+ "print'Note:calculation mistake in text book,Rg value is taken wrong in calculating s';\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.18,Page No:447"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "longitudinal stress = 70.01 MN/m**2\n",
+ "longitudinal stress = 146.2 MN/m**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "ex = 0.00016; #strain values in axial \n",
+ "ey = 0.00064; #strain values in circumferential direction\n",
+ "E = 200*10**9; #modulus of elasticity in N/,**2\n",
+ "u = 0.26; #poisson's ratio \n",
+ "\n",
+ "#calculation\n",
+ "sigmax = (E*(ex+(u*ey)))/float(1-(u**2)); #longitudinal stress in N/m**2\n",
+ "sigmay = (E*(ey+(u*ex)))/float(1-(u**2)); #hoop stress in N/m**2\n",
+ "\n",
+ "#result\n",
+ "\n",
+ "print'longitudinal stress = %3.2f'%(sigmax/10**6),'MN/m**2';\n",
+ "print'longitudinal stress = %3.1f'%(sigmay/10**6),'MN/m**2';\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.19,Page No:447"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 39,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "227272727.273\n",
+ "modulus of elasticity = 147.5797 GN/M**2\n",
+ "poissons ratio = 0.2727\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "A = 110*10**-6; #area in m**2\n",
+ "P = 25*10**3; #load in N\n",
+ "ex = 1540*10**-6; #strain values in axial direction\n",
+ "ey = -420*10**-6; #strain values in transvers direction\n",
+ "\n",
+ "#calculation\n",
+ "sigmax = P/float(A); #axial stress in N/M**2\n",
+ "E = sigmax/float(ex); #modulus of elasticity in N/M**2\n",
+ "u = (-ey*E)/float(sigmax); #poisson's ratio\n",
+ "\n",
+ "#result\n",
+ "print sigmax\n",
+ "print'modulus of elasticity = %3.4f'%(E*10**-9),'GN/M**2';\n",
+ "print'poissons ratio = %3.4f'%u;\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.21,Page No:450"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 55,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "emax = 6.73e-05\n",
+ "emin = -1.927e-05\n",
+ "sigmamax = 13.514 MN/m**2\n",
+ "sigmamin = 0.201 MN/m**2\n",
+ "maximum shear stress = 6.656 MN/m**2\n",
+ "location of principle planes = 0.29 °\n",
+ "location of principle planes = 106.85 °\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "e1 = 60*10**-6; #strain in microstrains\n",
+ "e2 = 48*10**-6; #strain in microstrain\n",
+ "e3 = -12*10**-6; #strain in microstrain\n",
+ "E = 200*10**9; #modulus of elsticity in N/m**2\n",
+ "u = 0.3;\n",
+ "\n",
+ "#calculation\n",
+ "x = (e1+e3)/float(2); #average of strains\n",
+ "a = math.sqrt(((e1-e2)**2)+((e2-e3)**2));\n",
+ "b = 1/math.sqrt(2);\n",
+ "y = a*b;\n",
+ "emax = x+y; #principle strains\n",
+ "emin = x-y; #principle strains\n",
+ "x1 = x/float(1-u);\n",
+ "y1 = y/float(1+u); \n",
+ "sigmamax = E*(x1+y1); #principle stress\n",
+ "sigmamin = E*(x1-y1); #principle stress\n",
+ "tmax = E*y1; #maximum shear stress in MN/m**2\n",
+ "k = ((2*e2)-e1-e3)/float((e1-e3));\n",
+ "theta = (math.atan(k)); #location of principle planes\n",
+ "theta1 = (math.atan(k))/float(2); #location of principle planes\n",
+ "theta2 = 180+((theta)*180/float(math.pi));\n",
+ "theta3 = theta2/float(2); #location of principle planes\n",
+ "\n",
+ "print'emax = %2.2e'%(emax);\n",
+ "print'emin = %2.3e'%(emin);\n",
+ "print'sigmamax = %3.3f'%(sigmamax*10**-6),'MN/m**2';\n",
+ "print'sigmamin = %3.3f'%(sigmamin*10**-6),'MN/m**2';\n",
+ "print'maximum shear stress = %3.3f'%(tmax*10**-6),'MN/m**2';\n",
+ "print'location of principle planes = %3.2f'%(theta1),'°';\n",
+ "print'location of principle planes = %3.2f'%(theta3),'°';\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example:7.22,Page No:454"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 56,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "sensitivity of load = 13.79 uV/kN\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "d = 0.06; #diameter in m\n",
+ "Rg = 120; #nominal resistance of each guage Ω\n",
+ "Gf = 2.0; #guage factor \n",
+ "v = 6; #supply voltage in V\n",
+ "E = 200*10**9; #modulus of elasticity in N/m**2\n",
+ "u = 0.3; #poisson's ratio\n",
+ "P = 1000; #load in N\n",
+ "\n",
+ "#calculation\n",
+ "\n",
+ "A = (math.pi/float(4))*d*d;\n",
+ "s = P/float(A); #stress in N/m**2\n",
+ "e = s/float(E); #strain \n",
+ "x = Gf*e; #fraction change in resistence i.e dR/R\n",
+ "a = v/float(4);\n",
+ "y = 2*(1+u)*(x)*a; #output volatge in uV\n",
+ " \n",
+ "#result\n",
+ "print'sensitivity of load = %3.2f'%(y*10**6),'uV/kN';"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.6"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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