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| author | kinitrupti | 2017-07-13 15:05:55 +0530 |
|---|---|---|
| committer | kinitrupti | 2017-07-13 15:05:55 +0530 |
| commit | 920fbc095386afd4dfcd95d85ef7ef9072b3d5d7 (patch) | |
| tree | 0f57da126a244c6daabbbdaf93f43ac6a7d8f2be /Engineering_Mechanics/chapter_1.ipynb | |
| parent | ed35da23b7069c9de29859cf02c33d3c7a9c1d49 (diff) | |
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Modified Engineering_Mechanics/
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| -rw-r--r-- | Engineering_Mechanics/chapter_1.ipynb | 866 |
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diff --git a/Engineering_Mechanics/chapter_1.ipynb b/Engineering_Mechanics/chapter_1.ipynb new file mode 100644 index 00000000..ea9d90ce --- /dev/null +++ b/Engineering_Mechanics/chapter_1.ipynb @@ -0,0 +1,866 @@ +{
+ "metadata": {
+ "name": "chapter_1.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 1:Fundamental Of Engineering Mechanics"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.1,Page No.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "P=10 #N #Force1\n",
+ "Q=8 #N #Force2\n",
+ "alpha=60 #Degrees #Angle Between Two Forces\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Magnitude of Resultant Force \n",
+ "R=(P**2+Q**2+2*P*Q*cos(alpha*pi*180**-1))**0.5 #N\n",
+ " \n",
+ "#Result\n",
+ "print\"Magnitude of Resultant Force\",round(R,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Resultant Force 15.62 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.2,Page No.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "alpha=60 #Degrees #Angle between Forces\n",
+ "R=20*(3)**0.5\n",
+ "\n",
+ "#Let P & Q be the Two forces\n",
+ "#As Two Forces are equal i.e P=Q\n",
+ "\n",
+ "#Magnitude of Resultant Force \n",
+ "#R=(P**2+Q**2+2*P*Q*cos(alpha*pi*180**-1))**0.5 #N\n",
+ "#After Sub values and Furhter simplifying above equations we get\n",
+ "#R=2*P*cos(alpha*2**-1*pi*180**-1)\n",
+ "\n",
+ "#Further on Simplifying we get\n",
+ "P=R*((3)**0.5)**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Force is\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Force is 20.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.3,Page No.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "#Case-1\n",
+ "R1=14 #N #Resultant1\n",
+ "alpha1=60 #Degrees #Angle between two forces\n",
+ "\n",
+ "#Case-2\n",
+ "R2=(136)**0.5\n",
+ "alpha2=90 #Degrees #Angle between two Forces\n",
+ "\n",
+ "#Let P And Q be the two forces\n",
+ "#R=(P**2+Q**2+2*P*Q**cos(alpha))\n",
+ "\n",
+ "#Now For case-1,we get Resultant as\n",
+ "#P**2+Q**2+P*Q=196 ............................(1)\n",
+ "\n",
+ "#For case-2,we get Resultant as\n",
+ "#P**2+Q**2=136 ...................................(2)\n",
+ "\n",
+ "#Subtracting Equation 2 from equation 1 we get\n",
+ "#P*Q=60 .........................................(3)\n",
+ "\n",
+ "#Multiplying abovw equation by 2 we get\n",
+ "#2*P*Q=120 .......................................(4)\n",
+ "\n",
+ "#Adding equation 4 to equation 2 we get\n",
+ "#P**2+Q**2+2*P*Q=256\n",
+ "#After Further simplifying we get\n",
+ "#P=16-Q ..........................(5)\n",
+ "\n",
+ "#Sub value of P in equation 3 we get\n",
+ "#Q**2-16*Q+60=0\n",
+ "a=1\n",
+ "b=-16\n",
+ "c=60\n",
+ "\n",
+ "X=b**2-4*a*c\n",
+ "\n",
+ "Q1=(-b+X**0.5)*(2*a)**-1\n",
+ "Q2=(-b-X**0.5)*(2*a)**-1\n",
+ "\n",
+ "#Now sub value of Q in equation 5 we get\n",
+ "P1=16-Q1\n",
+ "P2=16-Q2\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of two Forces is:P2\",round(P2,2),\"N\"\n",
+ "print\" :Q1\",round(Q2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of two Forces is:P2 10.0 N\n",
+ " :Q1 6.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.4,Page No.10 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "P=50 #N #Force acting at pt O\n",
+ "Q=100 #N #force acting at pt O\n",
+ "alpha=30 #DEgree #Angle Between Two Forces\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#MAgnitude of Resultant\n",
+ "R=(P**2+Q**2+2*P*Q*cos(alpha*pi*180**-1))**0.5 #N\n",
+ "\n",
+ "#Angle Made by resultant with the direction of P\n",
+ "X=(Q*sin(alpha*180**-1*pi)*(P+(Q*cos(alpha*pi*180**-1)))**-1)\n",
+ "theta=np.arctan(X)*(180*pi**-1) #Degrees\n",
+ "\n",
+ "#Angle made by resultant with x-axis is\n",
+ "Y=theta+alpha*2**-1 #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Resultant in the Magnitude is\",round(R,2),\"N\"\n",
+ "print\"Resultant in the Direction is\",round(Y,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resultant in the Magnitude is 145.47 N\n",
+ "Resultant in the Direction is 35.1 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.5,Page No.10 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "R=1500 #N #REsultant of two Forces\n",
+ "alpha=90 #Degrees #Angle between two Forces\n",
+ "theta=36 #Degrees #Angle Made by Resultant with one Force\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Now From Equation of Direction of Resultant,we get\n",
+ "#tan(theta)=(Q*sin(alpha))*(P+Q*sin(alpha))**-1\n",
+ "#After Further sub values and simplifying we get\n",
+ "#Q=0.726*P .......................................(1)\n",
+ "\n",
+ "#Now From Equation of Resultant\n",
+ "#R=(P**2+Q**2+2*P*Q*cos(alpha))\n",
+ "#After sub values and further simplifying we get\n",
+ "#R=1.527*P**2 \n",
+ "#Therefore,we get value of P After simplifying above equation\n",
+ "P=(R**2*(1.527)**-1)**0.5\n",
+ "\n",
+ "#Sub value of P in equation 1 we get\n",
+ "Q=0.726*P \n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude Of Forces:P\",round(P,2),\"N\"\n",
+ "print\" :Q\",round(Q,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude Of Forces:P 1213.87 N\n",
+ " :Q 881.27 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.6,Page No.11"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "#P+Q=120\n",
+ "R=180 #N #Resultant of two Forces\n",
+ "theta=90 #Degrees #Angle between force and Resultant\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Now From Equation of Direction of Resultant,we get\n",
+ "#Tan(theta)=Q*sin(alpha)*(P+Q*sin(alpha))**-1\n",
+ "#After Further ssub values a in above equation and further simplifying we get\n",
+ "#P=-Q*cos(alpha) ..........(1)\n",
+ "\n",
+ "#Now From equation of Resultant we get\n",
+ "#R=(P**2++Q**2+2*P*Q*cos(alpha))**0.5\n",
+ "#After sub values and further simplifying\n",
+ "#Q-P=120 ......................................(1)\n",
+ "#P+Q=270 ......................................(2)\n",
+ "\n",
+ "#After Adding above equations i.e equations 1 and 2 we get\n",
+ "Q=390*2**-1 #N\n",
+ "\n",
+ "P=270-Q #N\n",
+ "\n",
+ "#Value of angle alpha\n",
+ "alpha=np.arccos(-P*Q**-1)*(180*pi**-1) #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Each Force:P\",round(P,2),\"N\"\n",
+ "print\" :Q\",round(Q,2),\"N\"\n",
+ "print\"Angle between Two Forces\",round(alpha,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Each Force:P 75.0 N\n",
+ " :Q 195.0 N\n",
+ "Angle between Two Forces 112.62 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.7,Page No.13"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "W=1000 #N #Weight\n",
+ "#Angles\n",
+ "CAB=30 #Degrees\n",
+ "CBA=CBD=60 #Degrees\n",
+ "ACB=90 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "#Angle\n",
+ "CAD=30 #Degrees\n",
+ "\n",
+ "#In Right-Angle Triangle,Angle ADC\n",
+ "ACD=90-CAD #Degrees\n",
+ "\n",
+ "#In Right-Angle Triangle,Angle BDC\n",
+ "#Angle\n",
+ "BCD=90-CBD #Degrees\n",
+ "ACE=180-ACB-90-60 #DEgrees\n",
+ "BCE=180-ACE-ACB #DEGrees\n",
+ "\n",
+ "#Applying LAmi's Theorem at Point C\n",
+ "#T1*(sin150)**-1=T2*(sin(120)**-1=1000*sin(90)**-1\n",
+ "\n",
+ "#After Further simp;ifying we get\n",
+ "T1=W*sin(150*pi*180**-1) #N\n",
+ "T2=W*sin(120*pi*180**-1) #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Tension in Chain is:T1\",round(T1,2),\"N\"\n",
+ "print\" :T2\",round(T2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Tension in Chain is:T1 500.0 N\n",
+ " :T2 866.03 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.8,Page No.18"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "W=900 #N #Weight at C\n",
+ "#Length\n",
+ "AC=4 #m \n",
+ "BC=3 #m\n",
+ "AB=5 #m\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#In Triangle ABC\n",
+ "X=AC**2+BC**2 \n",
+ "Y=AB**2 \n",
+ "\n",
+ "#Therefore,\n",
+ "#X=Y\n",
+ "\n",
+ "#Therefore,\n",
+ "#Triangle ABC is Right Angle Triangle,In Which Angle ACB=90 Degrees\n",
+ "alpha=np.arcsin(BC*AB**-1)*(180*pi**-1)\n",
+ "Beta=90-alpha\n",
+ "\n",
+ "#In Right Angle Triangle ADC,\n",
+ "theta1=90-alpha\n",
+ "\n",
+ "#In Right Angle Triangle BDC,\n",
+ "theta2=90-Beta\n",
+ "\n",
+ "#Now,Angles\n",
+ "ACE=180-theta1\n",
+ "BCE=180-theta2\n",
+ "\n",
+ "#Now applying ami's Theorem\n",
+ "#T1*(sin(BCE))**-1=T2*(sin(ACE))**-1=W*(sin(90))**-1\n",
+ "\n",
+ "#Tensions in chains \n",
+ "T1=W*sin(BCE*180**-1*pi) #N\n",
+ "T2=W*sin(ACE*180**-1*pi) #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Tension in Chains are:T1\",round(T1,2),\"N\"\n",
+ "print\" :T2\",round(T2,2),\"N\"\n",
+ "\n",
+ "#Answer in hte book For T2 is incorrect"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Tension in Chains are:T1 540.0 N\n",
+ " :T2 720.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.9,Page No.18"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "W=15 #N #Weight at Pt C\n",
+ "OAC=FAC=60 #Degrees\n",
+ "CBD=BCF=45 #Degrees\n",
+ "FCA=90-FAC #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Using Lami's theorem,\n",
+ "#W*(sin(BCA))**-1=T1*(sin(ACE))**-1=T2*(sin(ACE))**-1\n",
+ "\n",
+ "#Angles\n",
+ "BCA=BCF+FCA #Degrees\n",
+ "ACE=180-FCA #Degrees\n",
+ "BCE=180-BCF #Degrees\n",
+ "\n",
+ "#Force's in the string AC\n",
+ "T1=W*sin(ACE*180**-1*pi)*(sin(BCA*180**-1*pi))**-1 #N\n",
+ "T2=W*sin(BCE*180**-1*pi)*(sin(BCA*180**-1*pi))**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Force's in the string:T1\",round(T1,2),\"N\"\n",
+ "print\" :T2\",round(T2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force's in the string:T1 7.76 N\n",
+ " :T2 10.98 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.10,Page No.16"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "#Forces\n",
+ "P=50 #N\n",
+ "Q=100 #N\n",
+ "alpha=30 #Angle Between Two Forces\n",
+ "theta=15 #Degrees #Angle Made By Force P with x-axis\n",
+ "theta2=alpha+theta #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Sum Of COmponents of forces along X-Axis is\n",
+ "H=P*cos(theta*pi*180**-1)+Q*cos(theta2*pi*180**-1) #N\n",
+ "\n",
+ "#Sum Of COmponents of forces along Y-Axis is\n",
+ "V=P*sin(theta*pi*180**-1)+Q*sin(theta2*pi*180**-1) #N\n",
+ "\n",
+ "#MAgnitude Of Resultant Force is\n",
+ "R=(H**2+V**2)**0.5 #N\n",
+ "\n",
+ "#Let Direction Of Resultant Force be beta\n",
+ "#Direction Of Resultant Force is\n",
+ "beta=np.arctan(V*H**-1)*(180*pi**-1) #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Resultant Force is\",round(R,2),\"N\"\n",
+ "print\"Direction of Resultant Force is\",round(beta,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Resultant Force is 145.47 N\n",
+ "Direction of Resultant Force is 35.1 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.11,Page No.17"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "#Let 3Forces Be\n",
+ "R1=40 #KN\n",
+ "R2=15 #KN\n",
+ "R3=20 #KN\n",
+ "\n",
+ "#Angles Made by respective forces with X-Axis\n",
+ "theta1=60 #Degrees\n",
+ "theta2=120 #Degrees\n",
+ "theta3=240 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Now sum of components of all forces along X-Axis\n",
+ "H=R1*cos(theta1*pi*180**-1)+R2*cos(theta2*pi*180**-1)+R3*cos(theta3*pi*180**-1)\n",
+ "\n",
+ "#Now sum of components of all forces along Y-Axis\n",
+ "V=R1*sin(theta1*pi*180**-1)+R2*sin(theta2*pi*180**-1)+R3*sin(theta3*pi*180**-1)\n",
+ "\n",
+ "#MAgnitude of Resultant Force is\n",
+ "R=(H**2+V**2)**0.5 #N\n",
+ "\n",
+ "#Direction of Resultant Force is\n",
+ "theta=np.arctan(V*H**-1)*(pi**-1*180)\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Resultant Force is\",round(R,2),\"KN\"\n",
+ "print\"Direction of Resultant Force is\",round(theta,2),\"Degrees\"\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "#Let 3Forces Be\n",
+ "R1=40 #KN\n",
+ "R2=15 #KN\n",
+ "R3=20 #KN\n",
+ "\n",
+ "#Angles Made by respective forces with X-Axis\n",
+ "theta1=60 #Degrees\n",
+ "theta2=120 #Degrees\n",
+ "theta3=240 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Now sum of components of all forces along X-Axis\n",
+ "H=R1*cos(theta1*pi*180**-1)+R2*cos(theta2*pi*180**-1)+R3*cos(theta3*pi*180**-1)\n",
+ "\n",
+ "#Now sum of components of all forces along Y-Axis\n",
+ "V=R1*sin(theta1*pi*180**-1)+R2*sin(theta2*pi*180**-1)+R3*sin(theta3*pi*180**-1)\n",
+ "\n",
+ "#MAgnitude of Resultant Force is\n",
+ "R=(H**2+V**2)**0.5 #N\n",
+ "\n",
+ "#Direction of Resultant Force is\n",
+ "theta=np.arctan(V*H**-1)*(pi**-1*180)\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Resultant Force is\",round(R,2),\"KN\"\n",
+ "print\"Direction of Resultant Force is\",round(theta,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Resultant Force is 30.41 KN\n",
+ "Direction of Resultant Force is 85.28 Degrees\n",
+ "Magnitude of Resultant Force is 30.41 KN\n",
+ "Direction of Resultant Force is 85.28 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.12,Page No.18"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "#Let 4 Forces Be\n",
+ "R1=10 #KN\n",
+ "R2=15 #KN\n",
+ "R3=20 #KN\n",
+ "R4=40 #KN\n",
+ "\n",
+ "#Angles Made by respective forces with X-Axis\n",
+ "theta1=30 #Degrees\n",
+ "theta2=60 #Degrees\n",
+ "theta3=90 #Degree\n",
+ "theta4=120 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Now sum of components of all forces along X-Axis\n",
+ "H=R1*cos(theta1*pi*180**-1)+R2*cos(theta2*pi*180**-1)+R3*cos(theta3*pi*180**-1)+R4*cos(theta4*pi*180**-1)\n",
+ "\n",
+ "#Now sum of components of all forces along Y-Axis\n",
+ "V=R1*sin(theta1*pi*180**-1)+R2*sin(theta2*pi*180**-1)+R3*sin(theta3*pi*180**-1)+R4*sin(theta4*pi*180**-1)\n",
+ "\n",
+ "#MAgnitude of Resultant Force is\n",
+ "R=(H**2+V**2)**0.5 #N\n",
+ "\n",
+ "#Direction of Resultant Force is\n",
+ "theta4=np.arctan(V*H**-1)*(pi**-1*180)\n",
+ "theta=180+theta4 #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Resultant Force is\",round(R,2),\"KN\"\n",
+ "print\"Direction of Resultant Force is\",round(theta,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Resultant Force is 72.73 KN\n",
+ "Direction of Resultant Force is 93.03 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.13,Page No.19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "L=10 #m #Length of beam\n",
+ "W=200 #N #Pt Load\n",
+ "\n",
+ "#Distances\n",
+ "L_AC=4 #m\n",
+ "L_CB=6 #m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A & R_B be the forces acting at A & B\n",
+ "#Taking Moment at A\n",
+ "R_B=(W*L_CB)*L**-1 #N\n",
+ "R_A=W-R_B #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Beam Reactions are:R_A\",round(R_A,2),\"N\"\n",
+ "print\" :R_B\",round(R_B,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Beam Reactions are:R_A 80.0 N\n",
+ " :R_B 120.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.14,Page No.20"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "#Let 4 Forces be\n",
+ "F1=10 #N\n",
+ "F2=20 #N\n",
+ "F3=30 #N\n",
+ "F4=40 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Net Forces in Horizontal direction is\n",
+ "H=F1-F3 #N\n",
+ "\n",
+ "#Net Forces in Vertical direction is\n",
+ "V=F2-F4 #N\n",
+ "\n",
+ "#Resultant Force is given by\n",
+ "R=(H**2+V**2)**0.5 #N\n",
+ "\n",
+ "#Direction of resultant Forces\n",
+ "theta=np.arctan(V*H**-1)*(pi**-1*180) #Degrees\n",
+ "\n",
+ "#Since H & V are negative theta lies between 180 & 270\n",
+ "theta2=180+theta #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Force is\",round(R,2),\"N\"\n",
+ "print\"Direction of Force is\",round(theta2,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Force is 28.28 N\n",
+ "Direction of Force is 225.0 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |