diff options
Diffstat (limited to 'Engineering_Mechanics,_Schaum_Series_by_McLean/chapter7_3.ipynb')
| -rwxr-xr-x | Engineering_Mechanics,_Schaum_Series_by_McLean/chapter7_3.ipynb | 669 |
1 files changed, 669 insertions, 0 deletions
diff --git a/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter7_3.ipynb b/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter7_3.ipynb new file mode 100755 index 00000000..297dc26a --- /dev/null +++ b/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter7_3.ipynb @@ -0,0 +1,669 @@ +{
+ "metadata": {
+ "name": "chapter7.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 7: Trusses And Cables"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-1, Page no 99"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of variables\n",
+ "F1=2000 #lb\n",
+ "F2=4000 #lb\n",
+ "l1=10 #ft\n",
+ "l2=30 #ft\n",
+ "l3=20 #ft\n",
+ "l4=40 #ft\n",
+ "# as t=60 degrees\n",
+ "sint=sqrt(3)*2**-1\n",
+ "cost=2**-1\n",
+ "\n",
+ "#Calculations\n",
+ "#Taking moment about point B and A\n",
+ "Ra=(F1*l2+F2*l1)/l4 \n",
+ "Rb=(F2*l2+F1*l1)/l4\n",
+ "#Consider fig 7-4(c)\n",
+ "A=np.array([[1,-cost],[0,-sint]])\n",
+ "B=np.array([[0],[-2500]])\n",
+ "C=np.linalg.solve(A,B)\n",
+ "#Consider figure 7-4(d)\n",
+ "A1=np.array([[1,cost],[0,-sint]])\n",
+ "B1=np.array([-C[1]*cost,-C[1]*sint+F1])\n",
+ "C1=np.linalg.solve(A1,B1)\n",
+ "#Consider figure 7-4(e)\n",
+ "CD=577\n",
+ "CE=C[0]+C1[1]*cost+CD*cost\n",
+ "#Consider figure 7-4(f)\n",
+ "DE=Rb/sint\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print'The reactions are:Ra=',round(Ra),\"lb\",'and Rb=',round(Rb),\"lb\"\n",
+ "print'Force in member AB=',round(C[1]),\"lb (C)\",'and AC=',round(C[0]),\"lb (T)\"\n",
+ "print'Force in member BC=',round(C1[1]),\"lb (T)\",'and BD=',round(C1[0]),\"lb (-ve sign indicates compression)\"\n",
+ "print'Force in member CD=',round(CD),\"lb (C)\",'and CE=',round(CE),\"lb (T)\"\n",
+ "print'Force in member DE=',round(DE),\"lb (C)\"\n",
+ "\n",
+ "#Decimal Accuracy causes discrepancy in answers.Thus answers wary as compared to the textbook.\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The reactions are:Ra= 2500.0 lb and Rb= 3500.0 lb\n",
+ "Force in member AB= 2887.0 lb (C) and AC= 1443.0 lb (T)\n",
+ "Force in member BC= 577.0 lb (T) and BD= -1732.0 lb (-ve sign indicates compression)\n",
+ "Force in member CD= 577.0 lb (C) and CE= 2021.0 lb (T)\n",
+ "Force in member DE= 4041.0 lb (C)\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-2, Page no 101"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "s=4 #m length of sides\n",
+ "l=2 #kN load acting on each node\n",
+ "r=7 #kN by inspection reaction at A\n",
+ "sin60=sqrt(3)*2**-1\n",
+ "tan30=sqrt(3)**-1\n",
+ "tan60=sqrt(3)\n",
+ "\n",
+ "#Calculation\n",
+ "#Taking Moment about point G\n",
+ "FH=(-r*12+2*10+2*6+2*2)/(2*tan60) #kN Compressive\n",
+ "#Taking moment about point H\n",
+ "GI=(r*14-2*12-2*8-2*4)/(2*tan30) #kN Tension\n",
+ "#Summing forces in the vertical direction\n",
+ "HG=-(r-(l*3))/sin60 #kN Compression\n",
+ "#Taking moment about point J yields\n",
+ "IK=(-2*4-2*8+r*10)/(2*tan60) #kN\n",
+ "\n",
+ "#Result\n",
+ "print'The value of the forces in the components are as follows'\n",
+ "print'FH=',round(FH,1),\"kN (C)\",',GI=',round(GI,1),\"kN (T)\",',HG=',round(HG,2),\"kN (C)\",'and IK=',round(IK,1),\"kN (T)\"\n",
+ "print'The answer in the text book for GI is wrong'\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The value of the forces in the components are as follows\n",
+ "FH= -13.9 kN (C) ,GI= 43.3 kN (T) ,HG= -1.15 kN (C) and IK= 13.3 kN (T)\n",
+ "The answer in the text book for GI is wrong\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-3, Page no 101"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "# as theta=30 degrees,\n",
+ "sin30=2**-1\n",
+ "EF=40000 #lb\n",
+ "l=36 #feet\n",
+ "\n",
+ "#Calculation\n",
+ "#Taking moment about point D and setting EF=40000lbs\n",
+ "P=-(EF*sin30*l)/l #lb\n",
+ "\n",
+ "#Result\n",
+ "print'The maximum value of P is',round(P),\"lb\"\n",
+ "print'The negative sign indicates the downward direction'\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The maximum value of P is -20000.0 lb\n",
+ "The negative sign indicates the downward direction\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-4, Page no 102"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "l=12 #m\n",
+ "# as theta1=30 degrees\n",
+ "cos30=sqrt(3)*2**-1\n",
+ "cos60=2**-1\n",
+ "sin30=2**-1\n",
+ "\n",
+ "F1=1000 #N\n",
+ "F2=2000 #N\n",
+ "\n",
+ "#Calculation\n",
+ "FG=l*cos30 #m\n",
+ "DG=(l+(l/2))/cos30 #m\n",
+ "#Taking moment about point G\n",
+ "A=(F1*l+F2*FG+F1*DG)/(l*3) #N\n",
+ "#Summing forces in horizontal direction\n",
+ "G_x=(2*F1+F2)*sin30 #N\n",
+ "#Summing forces in the vertical direction\n",
+ "G_y=(2*F1+F2)*cos30+F1-A #N\n",
+ "#Taking moment about point C\n",
+ "BD=-(A*l)/(l/2) #N\n",
+ "#Taking moment about point D\n",
+ "CE=(A*(l+(l/2)))/FG #N\n",
+ "theta=arctan((l/2)/FG) #degrees \n",
+ "#Summing forces in the vertical direction\n",
+ "CD=(A+(BD*cos60))/cos(theta) #N\n",
+ "\n",
+ "#Result\n",
+ "print'The values of the forces are as follows'\n",
+ "print'A=',round(A),\"N\",',G_x=',round(G_x),\"N\",',G_y=',round(G_y),\"N\",',BD=',round(BD),\"N (C)\",',CE=',round(CE),\"N (T)\",'and CD=',round(CD),\"N(T)\"\n",
+ "#Decimal Accuracy causes discrepancy in answers\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The values of the forces are as follows\n",
+ "A= 1488.0 N ,G_x= 2000.0 N ,G_y= 2976.0 N ,BD= -2976.0 N (C) ,CE= 2577.0 N (T) and CD= 0.0 N(T)\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-5, Page no 103"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "A=2000 #lb\n",
+ "E=2000 #lb\n",
+ "# as theta=60 degrees and theta1=30 degrees, which means:\n",
+ "sin60=sqrt(3)*2**-1\n",
+ "cos60=2**-1\n",
+ "sin30=2**-1\n",
+ "cos30=sqrt(3)*2**-1\n",
+ "\n",
+ "#Sign convention positive means Tension and negative means Compression\n",
+ "#Taking sum of forces along x and y direction in fig7-13\n",
+ "AB=-A/sin60 #lb\n",
+ "AG=-AB*cos60 #lb\n",
+ "#Taking sum of forces along x and y direction in fig7-14\n",
+ "BG=((-AB*cos30)-1000)/(cos30) #lb\n",
+ "BC=((AB*sin30)-(BG*sin30)) #lb\n",
+ "#Taking sum of forces along x and y direction in fig7-15\n",
+ "GC=-(BG*sin60)/sin60 #lb\n",
+ "GF=AG+BG*cos60-GC*(cos60) #lb\n",
+ "#By symmetry of structure\n",
+ "DE=AB #lb\n",
+ "FE=AG #lb\n",
+ "DF=BG #lb\n",
+ "CD=BC #lb\n",
+ "\n",
+ "#Result\n",
+ "print'The forces in the truess are'\n",
+ "print'AB=DE=',round(AB),\"lb (C)\",',AG=FE=',round(AG),\"lb (T)\",',BG=DF=',round(BG),\"lb (T)\",',BC=CD=',round(BC),\"lb (C)\",'and CG=CF=',round(GC),\"lb (C)\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The forces in the truess are\n",
+ "AB=DE= -2309.0 lb (C) ,AG=FE= 1155.0 lb (T) ,BG=DF= 1155.0 lb (T) ,BC=CD= -1732.0 lb (C) and CG=CF= -1155.0 lb (C)\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-6, Page no 104"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "F=500 #N\n",
+ "A=1000 #N\n",
+ "# as theta=60 degrees,\n",
+ "sin60=sqrt(3)*2**-1\n",
+ "l=20 #m\n",
+ "\n",
+ "#Calculations\n",
+ "#Taking moment about point G\n",
+ "R_c=(20*3*A+50*F+30*F+10*F)/40 #N\n",
+ "#Returning to fig7-17\n",
+ "#Taking moment about point C\n",
+ "BD=(l*A+(l/2)*F)/(l*sin60) #N\n",
+ "#Taking sum of forces in vertical direction\n",
+ "CD=(A+F-R_c)/sin60 #N\n",
+ "\n",
+ "#Result\n",
+ "print'The forces in the members are as follows'\n",
+ "print'BD=',round(BD),\"N (T)\",'and CD=',round(CD),\"N (C).\",'Also the reaction at C is',round(R_c),\"N\"\n",
+ "#Decimal accuracy causes discrepancey in answers\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The forces in the members are as follows\n",
+ "BD= 1443.0 N (T) and CD= -1299.0 N (C). Also the reaction at C is 2625.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-7, Page no 104"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "w=800 #lb/ft\n",
+ "a=600 #ft\n",
+ "d=40 #ft\n",
+ "\n",
+ "#Calculations\n",
+ "T=0.5*w*a*(sqrt(1+(a**2/(16*d**2)))) #lb\n",
+ "H=(w*a**2)/(8*d) #lb\n",
+ "#Taking the first two terms of the series\n",
+ "l=a*(1+(8/3)*(d*a**-1)**2-(32/5)*0.00002) #ft\n",
+ "\n",
+ "#Result\n",
+ "print'The value of T=',round(T),\"lb\",'and that of H=',round(H),\"lb.\",'Also l=',round(l),\"ft\"\n",
+ "#Deciaml accuracy causes discrepancy in answers\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The value of T= 929516.0 lb and that of H= 900000.0 lb. Also l= 605.0 ft\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-8,Page no 105"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "l=800*300 #lb\n",
+ "\n",
+ "#Calculations\n",
+ "#Summing forces in horizontal and vertical direction\n",
+ "theta=arctan(40*150**-1) #degrees\n",
+ "H=l/tan(theta) #lb\n",
+ "T_max=sqrt(l**2+H**2) #lb\n",
+ "\n",
+ "#Result\n",
+ "print'The maximun tension is',round(T_max),\"lb\",'and H=',round(H),\"lb\"\n",
+ "#Decimal accuracy causes discrepancy in answers"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The maximun tension is 931450.0 lb and H= 900000.0 lb\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-9,Page no 105"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "#For simplicity a1 and a2 values are being considered as constant free of H\n",
+ "a_1=sqrt(10*14.7**-1)\n",
+ "a_2=sqrt(30/14.7)\n",
+ "y=10 #m\n",
+ "\n",
+ "#Calculations\n",
+ "H=(300/(a_1+a_2))**2 #N\n",
+ "#Now reconsidering a1 and a2 actual values\n",
+ "a1=a_1*sqrt(H) #m\n",
+ "a2=a_2*sqrt(H) #m\n",
+ "#Theta calculations\n",
+ "x=a1\n",
+ "theta=arctan(2*y/x)\n",
+ "#T calculations\n",
+ "T=sqrt((864*a2**2)+H**2) #N\n",
+ "\n",
+ "#Result\n",
+ "print'The tension in the cable is',round(T,2),\"*10**-3 kN\"\n",
+ "# The answer may wary due to decimal point descrepancy"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The tension in the cable is 18585.57 *10**-3 kN\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-10, Page no 106"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "T=140000 #N\n",
+ "w=2000 #N/m\n",
+ "a=20 #m\n",
+ "\n",
+ "#Calculations\n",
+ "#Calculation step by step\n",
+ "lhs=(140000*2)*(2000*20)**-1 \n",
+ "d=sqrt(1/((((lhs**2)-1)*16)/(20**2))) #m\n",
+ "l=a*(1+(8/3)*(d/a)**2) #m\n",
+ "\n",
+ "#Result\n",
+ "print'The sag in the cable is',round(d,2),\"m\"\n",
+ "print'The required length is',round(l,2),\"m\"\n",
+ "\n",
+ "# Value of l is off by 0.2 m"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The sag in the cable is 0.72 m\n",
+ "The required length is 20.05 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-11, Page no 106"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "w=10*16**-1 #lb/ft\n",
+ "a=80 #ft\n",
+ "P=500 #lb\n",
+ "\n",
+ "#Calculations\n",
+ "lhs=(P*2)/(w*a)\n",
+ "d=sqrt(1*((((lhs**2)-1)*16)/(80**2))**-1) #ft\n",
+ "\n",
+ "#Result\n",
+ "print'The sag in the cable is',round(d),\"ft\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The sag in the cable is 1.0 ft\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-12, Page no 107"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of variables\n",
+ "w=0.518 #lb/ft\n",
+ "d=50 #ft\n",
+ "l=500 #ft\n",
+ "#Plot coding\n",
+ "A=linspace(0,800,9) #defined x axis\n",
+ "B=A+50\n",
+ "C=[50000,500*(2*100)**-1,500*(2*200)**-1,500*(2*300)**-1,500*(2*400)**-1,500*(2*500)**-1,500*(2*600)**-1,500*(2*700)**-1,500*(2*800)**-1]\n",
+ "D=cosh(C)\n",
+ "E=([D[0]*A[0],D[1]*A[1],D[2]*A[2],D[3]*A[3],D[4]*A[4],D[5]*A[5],D[6]*A[6],D[7]*A[7],D[8]*A[8]])\n",
+ "plot(A,B,A,E) #plotting two lines on the same plot\n",
+ "\n",
+ "#Calculations\n",
+ "#By close observation of plot taking c around 650\n",
+ "#consider c=635\n",
+ "c=635\n",
+ "T_max=w*(c+d) #lb\n",
+ "a=c+d\n",
+ "l=(4*(a*a-c*c))**0.5\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print'The maximum tension is',round(T_max),\"lb\",'and length required is',round(l),\"ft respectively.\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The maximum tension is 355.0 lb and length required is 514.0 ft respectively.\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEACAYAAACwB81wAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x62f93d0>"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7-13, Page no 108"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "m=0.6 #kg/m\n",
+ "l=240 #m\n",
+ "d=24 #m\n",
+ "\n",
+ "#Calculations\n",
+ "c=((((1*4**-1)*(l**2))-(24*24)))/(2*d)\n",
+ "T_max=9.8*m*(c+d) #N\n",
+ "a=arcsinh((l)/(2*c))*576\n",
+ "\n",
+ "#Result\n",
+ "print'The maximun tension is',round(T_max),\"N\"\n",
+ "print'The value of a is',round(a)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The maximun tension is 1835.0 N\n",
+ "The value of a is 234.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |