{
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"name": ""
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"APPENDIX A:Geomatric Properties of an Area"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example A.1:Page no. 786"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"#From fig. A-4(a) The given dimensions are\n",
"l1=8 #inch\n",
"l2=3 #inch\n",
"l3=10 #inch\n",
"l4=5 #inch\n",
"l5=11.5 #inch\n",
"l6=2 #inch\n",
"\n",
"#calculation\n",
"ymean1=((l4*l3*l6)+(l5*l2*l1))/((l3*l6)+(l2*l1))\n",
"#From fig. A-4(b)\n",
"l1_=-8 #inch\n",
"l2_=3 #inch\n",
"l3_=10 #inch\n",
"l4_=-1.5 #\n",
"l5_=2 #inch\n",
"ymean2=((l4_*l2_*-l1_)+(l1_*l3_*l5_))/((l2_*-l1_)+(l3_*l5_))\n",
"d=ymean1-ymean2 #Depth of beam\n",
"#From fig. A-4(c)\n",
"la=8 #inch\n",
"lb=6.5 #inch\n",
"lc=10 #inch\n",
"ld=13 #\n",
"le=5 #inch\n",
"lf=3 #inch\n",
"ymean3=((lb*ld*la)-2*(le*lc*lf))/((ld*la-2*(lc*lf)))\n",
"print\"Location of centroid in fig (a)is\",ymean1,\"inch\" \n",
"print\"Location of centroid in fig (b)is\",ymean2,\"inch\"\n",
"print\"Location of centroid in fig (c)is\",ymean3,\"inch\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Location of centroid in fig (a)is 8.54545454545 inch\n",
"Location of centroid in fig (b)is -4.45454545455 inch\n",
"Location of centroid in fig (c)is 8.54545454545 inch\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example A.2:Page no 789"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"#Dimension in the fig.A-7 a\n",
"#The given dimensions are\n",
"l1=8 #inch\n",
"l2=8.55 #inch\n",
"l3=10 #inch\n",
"l4=5 #inch\n",
"l5=1.5 #inch\n",
"l6=2 #inch\n",
"l7=4.45 #inch\n",
"\n",
"#Calculation\n",
"Ix1=(1/12.0*l6*l3**3)\n",
"A1=l6*l3\n",
"dy1=(l2-l4)\n",
"Ix2=(1/12.0*l1*(l5+l5)**3)\n",
"A2=l1*(l5+l5)\n",
"dy2=(l7-l5)\n",
"I1=(Ix1+A1*dy1**2)+(Ix2+A2*dy2**2)\n",
"print I1\n",
"\n",
"#Dimension in the fig.A-7 b\n",
"l1_= 13 #inch\n",
"l2_= 3 #inch\n",
"l3_=10 #inch\n",
"l4_=5 #inch\n",
"l5_= 2 #inch\n",
"l6_= 6.5 #inch\n",
"l7_=4.45 #inch\n",
"l8_=8.55 #inch\n",
"l9_=6.5 #inch\n",
"\n",
"Ix1_=(1/12.0*l1_*(l2_+l5+l2_)**3)\n",
"A1_=l1_*(l2_+l5+l2_)\n",
"dy1_=(l8_-l9_)\n",
"Ix2_=(1/12.0*l2_*(l3_)**3)\n",
"A2_=l2_*(l3_)\n",
"dy2_=(l7_-l4_)\n",
"I2=(Ix1+A1*dy1**2)+(Ix2+A2*dy2**2)\n",
"\n",
"#Result\n",
"print\"Moment of inertia for fig a is\",round(I1,0),\"inch**4\"\n",
"print\"Moment of inertia for fig a is\",round(I2,0),\"inch**4\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"645.576666667\n",
"645.576666667\n",
"Moment of inertia for fig a is 646.0 inch**4\n",
"Moment of inertia for fig a is 646.0 inch**4\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example A.3 Page no: 790"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"#From fig A-8(a)\n",
"#The given dimensions are\n",
"l1=100 #mm\n",
"l2=400 #mm\n",
"l3=600 #mm\n",
"dx=250 #mm\n",
"dy=200 #mm\n",
"\n",
"#Calculation\n",
"#Rectangle A:\n",
"Ix1=(1/12.0*l1*(l2-l1)**3)\n",
"Ady=(l1*(l2-l1)*dy**2)\n",
"Ix=(Ix1+Ady)\n",
"Iy1=(1/12.0*(l2-l1)*l1**3)\n",
"Adx=(l1*(l2-l1)*dx**2)\n",
"Iy=(Iy1+Adx)\n",
"\n",
"#Rectangle B:\n",
"Ix_=(1/12.0*l3*l1**3)\n",
"Iy_=(1/12.0*l1*l3**3)\n",
"\n",
"#Rectangle C\n",
"Ix3=(1/12.0*l1*(l2-l1)**3)\n",
"Ady_=(l1*(l2-l1)*200**2)\n",
"Ix3_=(Ix3+Ady_)\n",
"Iy3=(1/12.0*(l2-l1)*l1**3)\n",
"Adx_=(l1*(l2-l1)*dx**2)\n",
"Iy3_=(Iy3+Adx)\n",
"\n",
"#Total Moment of inertia\n",
"Itx=(Ix+Ix_+Ix3_)\n",
"Ity=(Iy+Iy_+Iy3_)\n",
"\n",
"#Result\n",
"print\"Moment of inertia across x is \",Itx,\"mm**4\"\n",
"print\"Moment of inertia across y is \",Ity,\"mm**4\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Moment of inertia across x is 2900000000.0 mm**4\n",
"Moment of inertia across y is 5600000000.0 mm**4\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example A.4 :page no. 793"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"#From fig A-12 a\n",
"#The given length of sides are\n",
"l1=100 #mm\n",
"l2=300 #mm\n",
"dy=200 #mm\n",
"dx=250 #mm\n",
"\n",
"#Calculation\n",
"#Rectangle A\n",
"Ixy1=0\n",
"A1=l1*l2\n",
"Ixy1=Ixy1+A1*(-dx)*dy\n",
"\n",
"#Rectangle B\n",
"Ixy2=0\n",
"A2=0\n",
"Ixy2=Ixy2+A2*dx*dy\n",
"\n",
"#Rectangle D\n",
"Ixy3=0\n",
"A3=l1*l2\n",
"Ixy3=Ixy3+A3*(dx)*(-dy)\n",
"Ixy=Ixy1+Ixy2+Ixy3\n",
"\n",
"#Result\n",
"print\"The moment of inertia is\",Ixy,\"mm**4\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The moment of inertia is -3000000000 mm**4\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example A.5 :page no. 796"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"#From fig A-15 and From Example A.3 and A.4\n",
"Ix=2.9*10**9 #moment of inertia along x\n",
"Iy=5.6*10**9 #moment of inertia along y\n",
"Ixy=-3*10**9 #moment of inertia along xy\n",
"\n",
"#Calculation\n",
"import math\n",
"#Using eq. A11\n",
"import math\n",
"thetaP1=1/2.0*math.atan(-Ixy*2/(Ix-Iy))*100\n",
"#As shown in fig. A-15\n",
"thetaP2=-32.9 #degree\n",
"Imax=(Ix+Iy)/2.0+math.sqrt((((Ix-Iy)/2.0)**2)+Ixy**2)\n",
"Imin=(Ix+Iy)/2.0-math.sqrt((((Ix-Iy)/2.0)**2)+Ixy**2)\n",
"\n",
"#Result\n",
"print\"Maximum moment of inertia is\",Imax,\"mm**4\"\n",
"print\"Minimum moment of inertia is\",Imin,\"mm**4\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum moment of inertia is 7539756829.92 mm**4\n",
"Minimum moment of inertia is 960243170.081 mm**4\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example A.6 :page no. 799"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"#From fig. A-17 a and Example A.3 and A.4\n",
"Ix=2.9*10**9 #mm**4, moment of inertia\n",
"Iy=5.6*10**9\n",
"Ixy=-3*10**9\n",
"\n",
"#Calculation\n",
"import math\n",
"d=(Ix+Iy)/2.0 #distance of centre of circle \n",
"#from fig A-17 b\n",
"BC=1.35\n",
"AB=3\n",
"CA=math.sqrt(BC**2+AB**2)\n",
"\n",
"#the circle intersect the I axis at point (7.54,0) and (0.960,0) hence\n",
"Imax=7.54*(10**9) #mm**4\n",
"Imin=0.960*(10**9) #mm**4\n",
"thetap1=1/2.0*(180-(math.atan(AB/BC))*180/math.pi)\n",
"\n",
"#Result\n",
"print\"The maximum moment of inertia is\",Imax,\"mm**4\"\n",
"print\"The minimum moment of inertia is\",Imin,\"mm**4\"\n",
"print\"The angle is \",round(thetap1,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The maximum moment of inertia is 7540000000.0 mm**4\n",
"The minimum moment of inertia is 960000000.0 mm**4\n",
"The angle is 57.1\n"
]
}
],
"prompt_number": 33
}
],
"metadata": {}
}
]
}