{
"metadata": {
"name": "",
"signature": "sha256:2286c67a37dc36a4b2463b6ff90eb31f4de0251dedc09d4493cdbe015dfacf59"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter06 : Levers"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"sum 6-1 : page 296"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sqrt, pi\n",
"Del=10 \n",
"k=500 \n",
"W=k*Del \n",
"#Let load arm be l1\n",
"l1=200 \n",
"#Let effort arm be l2\n",
"l2=500 \n",
"P=W*l1/l2 \n",
"Ro=sqrt(W**2+P**2) \n",
"Ta=40 \n",
"d=sqrt(Ro*4/(2*pi*Ta)) \n",
"d=10 \n",
"pb=10 \n",
"d1=sqrt(Ro/(pb*1.5)) \n",
"d1=20 \n",
"l=1.5*d \n",
"t=10 \n",
"T=Ro*4/(2*pi*d1**2) \n",
"M=(Ro/2*(l/2+t/3))-(Ro/2*l/4) \n",
"sigb=32*M/(pi*d1**3) \n",
"sigmax=(sigb/2)+sqrt((sigb/2)**2+T**2) \n",
"P=Ro/(l*d1) \n",
"D=2*d1 \n",
"\n",
"# Output\n",
"print \"d1 is %0.1f mm \"%d1 \n",
"print \"D is %0.1f mm \"%D"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"d1 is 20.0 mm \n",
"D is 40.0 mm \n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"sum 6-2 : page 297"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sqrt, pi\n",
"d1=80 \n",
"p=0.981 \n",
"Ta=40 \n",
"siga=80 \n",
"pa=15 \n",
"W=pi*(d1**2)*p/4 \n",
"P=W/8 \n",
"Ws=W-P \n",
"d=sqrt(W*4/(pi*2*Ta)) \n",
"l=1.5*d \n",
"D=2*d \n",
"T=W/(2*pi*pa**2/4) \n",
"M1=P*(700-87.5-(D/2)) \n",
"h=50 \n",
"b=h/4 \n",
"Z=b*h**2/6 \n",
"sigb=M1/Z \n",
"pmax=80 \n",
"T=2465.6/h**2 \n",
"pmax=(sigb/2)+sqrt((sigb/2)**2+T**2) \n",
"\n",
"# Output\n",
"print \"h is %0.2f mm \"%h \n",
"print \"pmax is %0.2f MPa \"%pmax\n",
" \n",
"#The difference in the value of pmax is due to rounding-off the digits."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"h is 50.00 mm \n",
"pmax is 74.43 MPa \n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"sum 6-3 : page 303"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sqrt, pi\n",
"P=((4*360)+(2*360))/900 \n",
"Fv=4-2 \n",
"Fh=P \n",
"Fr=sqrt(Fv**2+Fh**2) \n",
"P1=4*0.36/0.9 \n",
"Rf=sqrt(4**2+1.6**2) \n",
"d=sqrt(Rf*10**3/(15*1.25)) \n",
"d=16 \n",
"l=1.25*d \n",
"T=Rf*10**3*4/(2*pi*d**2) \n",
"D=2*d \n",
"M1=Rf*10**3*(360-(D/2)) \n",
"pa=15 \n",
"h=80 \n",
"b=h/4 \n",
"Z=b*h**2/6 \n",
"sigb=M1/Z \n",
"T=4310/(b*h) \n",
"pmax=(sigb/2)+sqrt((sigb/2)**2+T**2) \n",
"\n",
"# Output\n",
"print \"P is %0.1f KN \"%P \n",
"print \"pmax is %0.2f MPa \"%pmax"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"P is 2.0 KN \n",
"pmax is 69.53 MPa \n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"sum 6-4 : page 304"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sqrt, pi\n",
"l=360 \n",
"P=400 \n",
"Mh=2*P*l/3 \n",
"sigb=50 \n",
"l1=60 \n",
"d=(Mh*32/(pi*l1))**(1/3) \n",
"d=30 \n",
"L=420 \n",
"siga=60 \n",
"H=20 \n",
"B=H/3 \n",
"Mx=P*(L-H/2) \n",
"Tx=2*P*l/3 \n",
"sigb1=Mx*18/H**3 \n",
"Td=P/(B*H) \n",
"Tr=17.17*Tx/H**4 \n",
"T=Tr+Td \n",
"sigmax=(sigb1/2)+sqrt((sigb1/2)**2+T**2) \n",
"Tmax=sqrt((sigb1/2)**2+T**2) \n",
"T=P*L \n",
"M=P*(l1+(2/3*l)) \n",
"Te=sqrt(T**2+M**2) \n",
"Ta=40 \n",
"D=(Te*16/(pi*Ta))**(1/3) \n",
"D=round(D) #Rounding off \n",
"# Output\n",
"print \"d is %0.1f mm \"%d \n",
"print \"D is %0.1f mm \"%D"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"d is 30.0 mm \n",
"D is 1.0 mm \n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"sum 6-5 : page 306"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sqrt, pi\n",
"l2=300 \n",
"l=450 \n",
"P=400 \n",
"Mx=2*P*l2/3 \n",
"siga=80 \n",
"dh=(Mx*32/(pi*siga))**(1/3) \n",
"dh=22 \n",
"L=(2*l2/3)+l \n",
"T=P*L \n",
"Ta=40 \n",
"d=(T*16/(pi*Ta))**(1/3) \n",
"d=35 \n",
"d1=1.6*d \n",
"Th=T*16*d1/(pi*(d1**4-d**4)) \n",
"l1=1.5*d \n",
"My=P*(L-(d1/2)) \n",
"B=dh \n",
"H=sqrt(3.66*75) \n",
"H=30 \n",
"Mz=P*l1/2 \n",
"Te=sqrt(T**2+Mz**2) \n",
"d2=(Te*16/(pi*Ta))**(1/3) \n",
"d2=32 \n",
"b=d/4 \n",
"b=round(b)\n",
"t=d/6 \n",
"t=round(t)\n",
"# Output\n",
"print \"d is %0.1f mm \"%d \n",
"print \"dh is %0.1f mm \"%dh \n",
"print \"d1 is %0.1f mm \"%d1 \n",
"print \"l1 is %0.1f mm \"%l1 \n",
"print \"d2 is %0.1f mm \"%d2 \n",
"print \"b is %0.1f mm \"%b \n",
"print \"t is %0.1f mm \"%t "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"d is 35.0 mm \n",
"dh is 22.0 mm \n",
"d1 is 56.0 mm \n",
"l1 is 52.5 mm \n",
"d2 is 32.0 mm \n",
"b is 8.0 mm \n",
"t is 5.0 mm \n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"sum 6-6 : page 307"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sqrt, pi\n",
"L=450 \n",
"P=700 \n",
"T=P*L \n",
"Ta=50 \n",
"d=(T*16/(pi*Ta))**(1/3) \n",
"d=32 \n",
"d1=1.6*d \n",
"d1=52 #Rounding off to nearest whole number\n",
"l1=1.25*d \n",
"My=P*(L-d1/2) \n",
"sigb=65 \n",
"H=(My*18/sigb)**(1/3) \n",
"H=45 \n",
"B=H/3 \n",
"T1=P/(B*H) \n",
"sigmax=(sigb/2)+sqrt((sigb/2)**2+T**2) \n",
"Mx=P*l1/2 \n",
"Te=sqrt((T)**2+(Mx**2)) \n",
"d2=(Te*16/(pi*Ta))**(1/3) \n",
"d2=d2+6 \n",
"d2=round(d2)\n",
"# utput\n",
"print \"d is %0.1f mm \"%d \n",
"print \"d1 is %0.1f mm \"%d1 \n",
"print \"l1 is %0.1f mm \"%l1 \n",
"print \"B is %0.1f mm \"%B \n",
"print \"H is %0.1f mm \"%H \n",
"print \"d2 is %0.1f mm \"%d2 "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"d is 32.0 mm \n",
"d1 is 52.0 mm \n",
"l1 is 40.0 mm \n",
"B is 15.0 mm \n",
"H is 45.0 mm \n",
"d2 is 7.0 mm \n"
]
}
],
"prompt_number": 15
}
],
"metadata": {}
}
]
}