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{
"metadata": {
"name": "chapter5.ipynb"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 5: General Case Of Forces In Plane"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.5-2,Page No:111"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Inilization of variables\n",
"\n",
"W=2000 #N\n",
"Lab=2 #m #length of the member from the vertical to the 1st load of 2000 N\n",
"Lac=5 #m #length of the member from the vertical to the 2nd load of 2000 N\n",
"Lpq=3.5 #m\n",
"\n",
"#Calculations\n",
"\n",
"Rq=((W*Lab)+(W*Lac))/Lpq #N #take moment abt. pt P\n",
"Xp=Rq #N #sum Fx=0\n",
"Yp=2*W #N #sum Fy=0\n",
"Rp=(Xp**2+Yp**2)**0.5 #N\n",
"\n",
"#Resuts\n",
"\n",
"print\"The reaction at P is \",round(Rp,1),\"N\"\n",
"print\"The reaction at Q is \",round(Rq),\"N\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The reaction at P is 5656.9 N\n",
"The reaction at Q is 4000.0 N\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.5-3,Page No:112"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"import numpy as np\n",
"#Initilization of vaiables\n",
"\n",
"W=25 #N # self weight of the ladder\n",
"M=75 #N # weight of the man standing o the ladder\n",
"theta=63.43 #degree # angle which the ladder makes with the horizontal\n",
"alpha=30 #degree # angle made by the string with the horizontal\n",
"Loa=2 #m # spacing between the wall and the ladder\n",
"Lob=4 #m #length from the horizontal to the top of the ladder touching the wall(vertical)\n",
"\n",
"#Calculations\n",
"\n",
"#Using matrix to solve the simultaneous eqn's 3 & 4\n",
"\n",
"A=np.array([[2 ,-4],[1, -0.577]])\n",
"B=np.array([100,100])\n",
"C=np.linalg.solve(A,B)\n",
"\n",
"#Results\n",
"\n",
"print\"The reaction at A i.e Ra is \",round(C[0],2),\"N\"\n",
"print\"The reaction at B i.e Rb is \",round(C[1],2),\"N\"\n",
"\n",
"#Calculations\n",
"\n",
"T=C[1]/cos(alpha*(pi/180)) #N # from (eqn 1)\n",
"\n",
"#Results\n",
"\n",
"print\"The required tension in the string is \",round(T,2),\"N\"\n",
"\n",
"#answer may vary due to decimal variance"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The reaction at A i.e Ra is 120.27 N\n",
"The reaction at B i.e Rb is 35.14 N\n",
"The required tension in the string is 40.57 N\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.5-4,Page No:113"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Initilization of variables\n",
"\n",
"W=100 #N\n",
"theta=60 #degree #angle made by the ladder with the horizontal\n",
"alpha=30 #degree #angle made by the ladder with the vertical wall\n",
"Lob=4 #m # length from the horizontal to the top of the ladder touching the wall(vertical)\n",
"Lcd=2 #m # length from the horizontal to the centre of the ladder where the man stands\n",
"\n",
"#Calculations\n",
"\n",
"Lab=Lob*(1/cos(alpha*(pi/180))) #m #length of the ladder\n",
"Lad=Lcd*tan(alpha*(pi/180)) #m\n",
"Rb=(W*Lad)/Lab #N #take moment at A\n",
"Xa=Rb*sin(theta*(pi/180)) #N # From eq'n 1\n",
"Ya=W+Rb*cos(theta*(pi/180)) #N #From eq'n 2\n",
"\n",
"#Results\n",
"\n",
"print\"The reaction at B i.e Rb is \",round(Rb),\"N\"\n",
"print\"The horizontal reaction at A i.e Xa is \",round(Xa,2),\"N\"\n",
"print\"The vertical reaction at A i.e Ya is \",round(Ya,1),\"N\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The reaction at B i.e Rb is 25.0 N\n",
"The horizontal reaction at A i.e Xa is 21.65 N\n",
"The vertical reaction at A i.e Ya is 112.5 N\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.5-5,Page No:114"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Initilization of variables\n",
"\n",
"W=100 #N #self weight of the man\n",
"alpha=30 #degree # angle made by the ladder with the wall\n",
"Lob=4 #m # length from the horizontal to the top of the ladder touching the wall(vertical)\n",
"Lcd=2 #m\n",
"\n",
"#Calculations\n",
"\n",
"# using the equiblirium equations\n",
"\n",
"Ya=W #N # From eq'n 2\n",
"Lad=Lcd*tan(alpha*(pi/180)) #m #Lad is the distance fom pt A to the point where the line from the cg intersects the horizontal\n",
"Rb=(W*Lad)/Lob #N # Taking sum of moment abt A\n",
"Xa=Rb #N # From eq'n 1\n",
"\n",
"#Results\n",
"\n",
"print\"The horizontal reaction at A i.e Xa is \",round(Xa,2),\"N\"\n",
"print\"The vertical reaction at A i.e Ya is \",round(Ya),\"N\"\n",
"print\"The reaction at B i.e Rb is \",round(Rb,2),\"N\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The horizontal reaction at A i.e Xa is 28.87 N\n",
"The vertical reaction at A i.e Ya is 100.0 N\n",
"The reaction at B i.e Rb is 28.87 N\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.5-6,Page No:115"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Initilization of variables\n",
"\n",
"d=0.09 #m #diametre of the right circular cylinder\n",
"h=0.12 #m #height of the cyinder\n",
"W=10 #N # self weight of the bar\n",
"l=0.24 #m #length of the bar\n",
"\n",
"#Calculations\n",
"\n",
"theta=arctan(h/d)*(180/pi) # angle which the bar makes with the horizontal\n",
"Lad=(d**2+h**2)**0.5 #m # Lad is the length of the bar from point A to point B\n",
"Rd=(W*h*cos(theta*(pi/180)))/Lad #N # Taking moment at A\n",
"Xa=Rd*sin(theta*(pi/180)) #N # sum Fx=0.... From eq'n 1\n",
"Ya=W-(Rd*cos(theta*(pi/180))) #N # sum Fy=0..... From eq'n 2\n",
"Ra=(Xa**2+Ya**2)**0.5 #resultant of Xa & Ya\n",
"\n",
"#Results\n",
"\n",
"print\"The horizontal reaction at A i.e Xa is \",round(Xa,2),\"N\"\n",
"print\"The vertical reaction at A i.e Ya is \",round(Ya,2),\"N\"\n",
"print\"Therefore the reaction at A i.e Ra is \",round(Ra,2),\"N\"\n",
"print\"The reaction at D i.e Rd is \",round(Rd,2),\"N\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The horizontal reaction at A i.e Xa is 3.84 N\n",
"The vertical reaction at A i.e Ya is 7.12 N\n",
"Therefore the reaction at A i.e Ra is 8.09 N\n",
"The reaction at D i.e Rd is 4.8 N\n"
]
}
],
"prompt_number": 10
}
],
"metadata": {}
}
]
}
|
