path: root/Machine_Design-I_by_Dr._Sadhu_Singh/chapter5.ipynb

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   "source": [
    "# Chapter 5 - Riveted Joints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 5.1 Pg 142"
   ]
  },
  {
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   "execution_count": 1,
   "metadata": {
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    {
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     "text": [
      " DESIGNING LONGITUDINAL JOINT - \n",
      "\n",
      " \n",
      " Plate Thickness\n",
      " , t = 30.30 mm\n",
      " \n",
      " use t = 32 mm\n",
      " \n",
      " Diameter of rivet hole, do = \n",
      " 33.94 mm\n",
      " \n",
      " Use do = 34 mm\n",
      " \n",
      " Diameter of rivet, d = \n",
      " 33.00 mm\n",
      " \n",
      " Pitch of rivets, p = \n",
      " 220.7 mm\n",
      " \n",
      " as per IBR-\n",
      " pitch, pmax = 232 mm\n",
      " \n",
      " Use p = 220 mm\n",
      " \n",
      " pitch of rivets in inner row, pi = 110 mm\n",
      " \n",
      " distance between outer and adjacent row = 82.5 mm\n",
      " \n",
      " take & use this distance = 85 mm\n",
      " \n",
      " distance between inner row for zig-zag riveting = 59.4 mm\n",
      " \n",
      " take & use this distance = 60 mm\n",
      " \n",
      " Thickness of wide butt strap, t= \n",
      "  24 mm\n",
      " \n",
      " Thickness of narrow butt strap, t= 20 mm\n",
      " \n",
      " margin, m = 52 mm\n",
      " \n",
      " strength of the joint = 2350472 N\n",
      " \n",
      " strength of solid plate = 563200 N\n",
      " \n",
      " Efficiency of joint, eta_l = 417.3 %\n",
      " \n",
      "\n",
      " DESIGNING CIRCUMFERENTIAL JOINT- \n",
      "\n",
      " \n",
      " Plate Thickness\n",
      " , t = 32.00 mm\n",
      " \n",
      " Diameter of rivet hole, do = \n",
      " 34.50 mm\n",
      " \n",
      " Diameter of rivet, d = \n",
      " 33.00 mm\n",
      " \n",
      " no. of rivets = 78.8\n",
      " \n",
      " take n = 80\n",
      " \n",
      " pitch of rivets, pc = 4213.00 mm\n",
      " use pc = 4213 mm\n",
      " \n",
      " Efficiency of joint, eta_c = 99.18 %\n",
      " \n",
      " for zig-zag riveting, distance between rows of rivets = 1413.4 mm. use 65 mm\n",
      " \n",
      " margin, m = 52 mm\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import pi,sqrt,ceil\n",
    "# Given Data\n",
    "ps=2.5## MPa\n",
    "D=1.5##m\n",
    "sigma_t=80## MPa\n",
    "tau=60## MPa\n",
    "sigma_c=120## MPa\n",
    "n=5## no. of rivets\n",
    "\n",
    "print ' DESIGNING LONGITUDINAL JOINT - \\n'\n",
    "print ' \\n Plate Thickness'\n",
    "eta_l=80## % (efficiency)\n",
    "t = ps*D*1000/2/sigma_t/(eta_l/100)+1## mm\n",
    "print ' , t = %.2f mm'%(t)\n",
    "t=32##mm (adopted for design)\n",
    "print ' \\n use t = %d mm'%(t)\n",
    "print ' \\n Diameter of rivet hole, do = '\n",
    "d0=6*sqrt(t)##mm (for t>8 mm)\n",
    "print ' %.2f mm'%(d0)\n",
    "d0=34.5## suggested for design\n",
    "print ' \\n Use do = %.f mm'%(d0)\n",
    "print ' \\n Diameter of rivet, d = '\n",
    "d=d0-1.5##mm \n",
    "print ' %.2f mm'%(d)\n",
    "print ' \\n Pitch of rivets, p = '\n",
    "Ps=(4*1.875+1)*pi/4*d0**2*tau## N\n",
    "# Putting Pt=Ps where Pt=(p-d0)*t*sigma_t## N\n",
    "Pt=Ps##N\n",
    "p=Pt/(t*sigma_t)+d0## N\n",
    "print ' %.1f mm'%(p)\n",
    "C=6## for 5 no. of rivets\n",
    "pmax=C*t+40## mm (as per IBR)\n",
    "print ' \\n as per IBR-\\n pitch, pmax = %.f mm'%(pmax)\n",
    "p=220## mm (adopted for design)\n",
    "print ' \\n Use p = %.f mm'%(p)\n",
    "pi=p/2## mm \n",
    "print ' \\n pitch of rivets in inner row, pi = %.f mm'%(pi)\n",
    "\n",
    "#Distance between rows of rivets\n",
    "dis1=0.2*p+1.115*d0## mm \n",
    "print ' \\n distance between outer and adjacent row = %.1f mm'%(dis1)\n",
    "dis1=85##mm (adopted for design)\n",
    "print ' \\n take & use this distance = %.f mm'%( dis1)\n",
    "dis2=0.165*p+0.67*d0## mm \n",
    "print ' \\n distance between inner row for zig-zag riveting = %.1f mm'%( dis2)\n",
    "dis2=60##mm (adopted for design)\n",
    "print ' \\n take & use this distance = %.f mm'%( dis2)\n",
    "print ' \\n Thickness of wide butt strap, t= '\n",
    "t1=0.75*t## mm (wide butt strap)\n",
    "print '  %.f mm'%(t1)\n",
    "t2=0.625*t## mm (narrow butt strap)\n",
    "print ' \\n Thickness of narrow butt strap, t= %.f mm'%(t2)\n",
    "#margin\n",
    "m=ceil(1.5*d0)## mm\n",
    "print ' \\n margin, m = %.f mm'%(m)\n",
    "# Efficiency of joint\n",
    "Pt=(p-d0)*t*sigma_t## N\n",
    "Ps=Ps## N (shearing resistance of rivets)\n",
    "Pc=n*d0*t*sigma_c## N (crushing resistance of rivets)\n",
    "sigma_com = (p-2*d0)*t*sigma_t+pi/4*d0**2*tau## N\n",
    "print ' \\n strength of the joint = %d N'%(sigma_com)\n",
    "P=p*t*sigma_t##N (strength of solid plate)\n",
    "print ' \\n strength of solid plate = %d N'%(P)\n",
    "eta_l=sigma_com/P*100## % (efficiency)\n",
    "print ' \\n Efficiency of joint, eta_l = %.1f %%'%(eta_l)\n",
    "\n",
    "print ' \\n\\n DESIGNING CIRCUMFERENTIAL JOINT- \\n'\n",
    "t=32## mm\n",
    "d0=34.5##mm\n",
    "d=33##mm\n",
    "print ' \\n Plate Thickness'\n",
    "print ' , t = %.2f mm'%(t)\n",
    "print ' \\n Diameter of rivet hole, do = '\n",
    "print ' %.2f mm'%(d0)\n",
    "print ' \\n Diameter of rivet, d = '\n",
    "print ' %.2f mm'%(d) \n",
    "n=(D*1000/d0)**2*(ps/tau)## no. of rivets\n",
    "print ' \\n no. of rivets = %.1f'%(n)\n",
    "n=80## adopted for design\n",
    "print ' \\n take n = %d'%(n)\n",
    "# Pitch of rivets\n",
    "n1=n/2## no. of rivets per row\n",
    "pc=pi*(D*1000+t)/n1## mm (pitch of rivets)\n",
    "print ' \\n pitch of rivets, pc = %.2f mm\\n use pc = %.f mm'%(pc,pc)\n",
    "eta_c=(pc-d0)/pc*100## % (efficiency of joint)\n",
    "print ' \\n Efficiency of joint, eta_c = %.2f %%'%(eta_c)\n",
    "dis=0.33*pc+0.67*d0## mm (distance between rows of rivets)\n",
    "print ' \\n for zig-zag riveting, distance between rows of rivets = %.1f mm. use 65 mm'%( dis)\n",
    "m=1.5*d0## mm (Margin)\n",
    "print ' \\n margin, m = %.f mm'%(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 5.2 Pg 147"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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      " \n",
      " Diameter of rivet, do = \n",
      " 26.83 mm\n",
      " \n",
      " Standard diameter of rivet hole, do = 29 mm & corresponding diameter of rivet = 27 mm\n",
      " \n",
      " no. of rivets, n = 9.629. Use n = 10 \n",
      " \n",
      " thickness of inner butt strap, t1 = 15 mm\n",
      " \n",
      " thickness of outer butt strap, t2 = 15 mm\n",
      " \n",
      " efficiency of joint = 92.75 %\n",
      " \n",
      " pitch of rivets = 92 mm. Use 100 mm\n",
      " \n",
      " margin,\n",
      " m = 43.5 mm. Use 50 mm\n",
      " \n",
      " w = 400 mm\n",
      " \n",
      " distance between rows = 72.5 mm. Use 75 mm\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt,pi,ceil\n",
    "# Given Data\n",
    "w=400##mm\n",
    "t=20##mm\n",
    "sigma_t=90## MPa\n",
    "tau=60## MPa\n",
    "sigma_c=140## MPa\n",
    "\n",
    "print ' \\n Diameter of rivet, do = '\n",
    "d0=6*sqrt(t)##mm (for t>8 mm)\n",
    "print ' %.2f mm'%(d0)\n",
    "d0=29##mm (standard)\n",
    "print ' \\n Standard diameter of rivet hole, do = %.f mm & corresponding diameter of rivet = 27 mm'%(d0)\n",
    "Pt=(w-d0)*t*sigma_t##N max. tearing strength of plate\n",
    "Ps=1.75*pi/4*d0**2*tau## N (shearing strength of one rivet)\n",
    "n1=Pt/Ps## no. of rivets\n",
    "n=ceil(n1)#\n",
    "print ' \\n no. of rivets, n = %.3f. Use n = %.f '%(n1,n)\n",
    "t1=0.75*t## mm\n",
    "t2=t1## mm\n",
    "print ' \\n thickness of inner butt strap, t1 = %.f mm'%( t1)\n",
    "print ' \\n thickness of outer butt strap, t2 = %.f mm'%( t2)\n",
    "# section 1-1 \n",
    "P1=(w-d0)*t*sigma_t##N\n",
    "# section 2-2 \n",
    "P2=(w-2*d0)*t*sigma_t+1.75*pi/4*d0**2*tau##N\n",
    "# section 3-3 \n",
    "P3=(w-3*d0)*t*sigma_t+1.75*3*pi/4*d0**2*tau##N\n",
    "# section 4-4\n",
    "P4=(w-4*d0)*t*sigma_t+1.75*6*pi/4*d0**2*tau##N\n",
    "Ps=10*Ps## N (shearing stress of all rivets)\n",
    "Pc=10*d0*t*sigma_c## N (shearing stress of all rivets)\n",
    "Pj=P1## N (strength f joint)\n",
    "P = w*t*sigma_t## N (strength of solid plate)\n",
    "eta=P1/P*100# # % (efficiency of joint)\n",
    "print ' \\n efficiency of joint = %.2f %%'%( eta)\n",
    "p1=3*d0+5## mm (pitch of rivets)\n",
    "p=100##mm (adopt for design)\n",
    "print ' \\n pitch of rivets = %.f mm. Use %.f mm'%(p1,p)\n",
    "m1=1.5*d0## mm (margin)\n",
    "m=50##mm\n",
    "w=3*p+2*m## mm\n",
    "print ' \\n margin,\\n m = %.1f mm. Use %.f mm'%( m1,m)\n",
    "print ' \\n w = %.f mm'%(w)\n",
    "dis=2.5*d0## mm\n",
    "print ' \\n distance between rows = %.1f mm. Use 75 mm'%(dis)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 5.3 Pg 150"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      " diameter of rivets = 16.99 mm. Use d0 = 17.5 mm & d=16 mm for design.\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt,pi,ceil,acos,cos\n",
    "# Given Data\n",
    "n=6## no. of rivets\n",
    "P=54## kN\n",
    "e=200##mm \n",
    "a=50##mm (from fig.5.13(a))\n",
    "b=100##mm (from fig.5.13(a))\n",
    "tau=120## MPa\n",
    "\n",
    "Pd=P/n*1000## N (direct shear load in rivet)\n",
    "C=P*e## kN.mm (Couple)\n",
    "#l1=l3=l4=l6\n",
    "l1=sqrt(a**2+b**2)## mm\n",
    "l3=l1#l4=l1#l6=l1#mm\n",
    "l2=a#l5=a##mm\n",
    "# F1/l1*(4*l1**2+2*l2**2)=C\n",
    "F1=C*1000/(4*l1**2+2*l2**2)*l1## N\n",
    "theta1=acos(a/l1)## radian\n",
    "R1=sqrt(Pd**2+F1**2+2*Pd*F1*cos(theta1))## N (resultant force in rivet 1)\n",
    "#R1=pi/4*d0**2*tau\n",
    "d0=sqrt(R1/(pi/4*tau))## mm\n",
    "print ' \\n diameter of rivets = %.2f mm. Use d0 = 17.5 mm & d=16 mm for design.'%(d0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 5.4 Pg 151"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " DESIGNING LONGITUDINAL JOINT - \n",
      "\n",
      " \n",
      " Plate Thickness\n",
      " , t = 9.61 mm\n",
      " \n",
      " use t = 10 mm\n",
      " \n",
      " Diameter of rivet hole, do = \n",
      " 18.97 mm\n",
      " \n",
      " Use do = 19.5 mm\n",
      " \n",
      " Diameter of rivet, d = \n",
      " 18.00 mm\n",
      " \n",
      " Pitch of rivets, p = \n",
      " 89.18 mm\n",
      " \n",
      " as per IBR-\n",
      " pitch, pmax = 75 mm\n",
      " \n",
      " Use p = 75 mm\n",
      " \n",
      " distance between rows of rivets = 37.8 mm\n",
      " \n",
      " take & use this distance = 40 mm\n",
      " \n",
      " Thickness of butt strap, t= \n",
      "  6.25 mm\n",
      " \n",
      " Use thickness = 7 mm\n",
      " \n",
      " margin, m = 30 mm\n",
      " \n",
      " strength of the joint = 49950 N\n",
      " \n",
      " strength of solid plate = 67500 N\n",
      " \n",
      " Efficiency of joint, eta_l = 74.00 % = 75 % as given\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import ceil,sqrt,pi\n",
    "# Given Data\n",
    "D=0.75##m\n",
    "ps=1.55## N/mm.sq\n",
    "eta_l=0.75## efficiency\n",
    "sigma_t=90## MPa\n",
    "sigma_c=140## MPa\n",
    "tau=56## MPa\n",
    "n=2## no. of rivets\n",
    "\n",
    "print ' DESIGNING LONGITUDINAL JOINT - \\n'\n",
    "print ' \\n Plate Thickness'\n",
    "t = ps*D*1000/2/sigma_t/eta_l+1## mm\n",
    "print ' , t = %.2f mm'%(t)\n",
    "t=ceil(t)##mm (adopted for design)\n",
    "print ' \\n use t = %d mm'%(t)\n",
    "\n",
    "print ' \\n Diameter of rivet hole, do = '\n",
    "d0=6*sqrt(t)##mm (for t>8 mm)\n",
    "print ' %.2f mm'%(d0)\n",
    "d0=19.5## suggested for design\n",
    "print ' \\n Use do = %.1f mm'%(d0)\n",
    "print ' \\n Diameter of rivet, d = '\n",
    "d=d0-1.5##mm \n",
    "print ' %.2f mm'%(d)\n",
    "\n",
    "print ' \\n Pitch of rivets, p = '\n",
    "Ps=(2*1.875)*pi/4*d0**2*tau## N\n",
    "# Putting Pt=Ps where Pt=(p-d0)*t*sigma_t## N\n",
    "Pt=Ps##N\n",
    "p=Pt/(t*sigma_t)+d0## N\n",
    "print ' %.2f mm'%(p)\n",
    "C=3.5## for 2 no. of rivets\n",
    "pmax=C*t+40## mm (as per IBR)\n",
    "print ' \\n as per IBR-\\n pitch, pmax = %.f mm'%(pmax)\n",
    "p=75## mm (adopted for design)\n",
    "print ' \\n Use p = %.f mm'%(p)\n",
    "\n",
    "#Distance between rows of rivets\n",
    "dis=0.33*p+0.67*d0## mm \n",
    "print ' \\n distance between rows of rivets = %.1f mm'%(dis)\n",
    "dis=40##mm (adopted for design)\n",
    "print ' \\n take & use this distance = %.f mm'%( dis)\n",
    "\n",
    "print ' \\n Thickness of butt strap, t= '\n",
    "t1=0.625*t## mm\n",
    "print '  %.2f mm'%(t1)\n",
    "t1=7## mm (adopted for design)\n",
    "print ' \\n Use thickness = %.f mm'%(t1)\n",
    "\n",
    "#margin\n",
    "m=ceil(1.5*d0)## mm\n",
    "print ' \\n margin, m = %.f mm'%(m)\n",
    "\n",
    "# Efficiency of joint\n",
    "Pt=(p-d0)*t*sigma_t## N\n",
    "Ps=Ps## N (shearing resistance of rivets)\n",
    "Pc=n*d0*t*sigma_c## N (crushing resistance of rivets)\n",
    "sigma_com = (p-2*d0)*t*sigma_t+pi/4*d0**2*tau## N\n",
    "print ' \\n strength of the joint = %d N'%(Pt)\n",
    "P=p*t*sigma_t##N (strength of solid plate)\n",
    "print ' \\n strength of solid plate = %d N'%(P)\n",
    "eta_l=Pt/P*100## % (efficiency)\n",
    "print ' \\n Efficiency of joint, eta_l = %.2f %% = 75 %% as given'%(eta_l)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 5.6 Pg 153"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      " diameter of rivets = 22.81 mm. Use d0 = 21.5 mm & d=20 mm for design.\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import cos,pi,sqrt,sin,atan,tan\n",
    "# Given Data\n",
    "n=5## no. of rivets\n",
    "P=45## kN\n",
    "alfa=30## degree\n",
    "tau=120## MPa\n",
    "\n",
    "\n",
    "Pd=P/n*1000## N (direct shear load in rivet)\n",
    "# C.G. of rivet group\n",
    "# values below are collected direct from figure\n",
    "x_bar=(3*200)/5## mm\n",
    "y_bar=(1*50+1*150+1*100+1*200)/5## mm\n",
    "ex=300+x_bar+y_bar##mm\n",
    "ey=100##mm\n",
    "l1=sqrt(x_bar**2+(y_bar/2)**2)## mm\n",
    "l2=l1##mm\n",
    "l3=sqrt(100**2+80**2)## mm\n",
    "l4=80##mm\n",
    "l5=l3##mm\n",
    "\n",
    "#2*F1*l1+2*F3*l3+F4*l4=P*cos(alfa)*ex+P*sin(alfa)*ey\n",
    "F1=(P*1000*cos(pi/180*alfa)*ex+P*1000*sin(pi/180*alfa)*ey)/(2*l1**2+2*l3**2+l4**2)*l1##N\n",
    "# rivet 1 is nearest\n",
    "Beta = atan(x_bar/(y_bar/2))*180/pi## degree\n",
    "theta1=Beta-(90-alfa)## degree\n",
    "R1=sqrt(Pd**2+F1**2+2*Pd*F1*cos(pi/180*theta1))## N (resultant force in rivet 1)\n",
    "#R1=pi/4*d0**2*tau\n",
    "d0=sqrt(R1/(pi/4*tau))## mm\n",
    "print ' \\n diameter of rivets = %.2f mm. Use d0 = 21.5 mm & d=20 mm for design.'%(d0)\n",
    "# Note -  Ans in the textbook is wrong."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 5.7 Pg 155"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Diameter of rivets, d0 = 11.46 mm. Take d0=13.5 mm & d=12 mm\n",
      " \n",
      " Distance between rows of rivet = 35.2 mm = 35 mm\n",
      " \n",
      " back pitch = 21 mm\n",
      " \n",
      " tearing strength = 28380 N\n",
      " \n",
      " shearing strength = 28628 N\n",
      " \n",
      " crushing strength = 24300 N\n",
      " \n",
      " joint strength = 24300 N\n",
      " \n",
      " strength of solid plate = 46200 N\n",
      " \n",
      " efficiency of joint = 52.6 %\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import pi,sqrt,floor\n",
    "# Given Data\n",
    "t=6##mm\n",
    "sigma_t=220## MPa\n",
    "tau=100## MPa\n",
    "sigma_c=150## MPa\n",
    "n=2## no. of rivets / pitch length\n",
    "#Ps=n*pi/4**d0**2*tau## shearing strength of rivets\n",
    "#Pc=2*d0*t*sigma_c## Crushing strength of rivets\n",
    "d0=2*t*sigma_c/(n*pi/4*tau)## mm (equating Ps=Pc)\n",
    "print ' Diameter of rivets, d0 = %.2f mm. Take d0=13.5 mm & d=12 mm'%(d0)\n",
    "d0=13.5##mm\n",
    "d=12##mm\n",
    "#Pt=(p-d0)*t*sigma_t## tearing strength\n",
    "# equating Pt=Ps\n",
    "#p= n*pi/4**d0**2*tau/(t*sigma_t)+d0##mm\n",
    "p= n*pi/4*d0**2*tau/(t*sigma_t)+d0\n",
    "print ' \\n Distance between rows of rivet = %.1f mm = %.f mm'%(p,p)\n",
    "p=floor(p)##mm\n",
    "pb=0.6*p##mm (back pitch)\n",
    "print ' \\n back pitch = %.f mm'%(pb)\n",
    "Pt=(p-d0)*t*sigma_t##  N (tearing strength)\n",
    "print ' \\n tearing strength = %.f N'%(Pt)\n",
    "Ps=n*pi/4*d0**2*tau## N ( shearing strength)\n",
    "print ' \\n shearing strength = %.f N'%(Ps)\n",
    "Pc=2*d0*t*sigma_c##N (Crushing strength of rivets)\n",
    "print ' \\n crushing strength = %.f N'%(Pc)\n",
    "joint_strength = Pc## N\n",
    "print ' \\n joint strength = %.f N'%(joint_strength)\n",
    "P=p*t*sigma_t##N (strength of solid plate)\n",
    "print ' \\n strength of solid plate = %.f N'%(P)\n",
    "eta = joint_strength/P*100## % (efficiency)\n",
    "print ' \\n efficiency of joint = %.1f %%'%( eta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 5.8 Pg 156"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Diameter of rivets - \n",
      " d0 = 11.654 mm\n",
      " \n",
      " Use d0 = 13.5 mm & d = 12 mm\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt,pi\n",
    "# Given Data\n",
    "P=20## kN\n",
    "e=80##mm\n",
    "tau=150## MPa\n",
    "\n",
    "\n",
    "Pd=P/4## kN\n",
    "C=P*e## kN.mm (Couple)\n",
    "# As C.G. lies at 45mm from top rivet\n",
    "l1=45;l4=45##mm \n",
    "l2=15;l3=15##mm\n",
    "#(F1/l1)*(2*l1*l4+2*l2*l3) = C\n",
    "F1= C*1000/(2*l1*l4+2*l2*l3)*l1##N\n",
    "R1=sqrt(Pd**2+F1**2)## N\n",
    "#R1=pi/4*d0**2*tau\n",
    "d0=sqrt(R1/(pi/4*tau))##mm\n",
    "print ' Diameter of rivets - \\n d0 = %.3f mm'%(d0)\n",
    "print ' \\n Use d0 = 13.5 mm & d = 12 mm'"
   ]
  }
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