docs/nusa-info/es/truss-element.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Elemento `Truss`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "El elemento `Truss` plano es un elemento finito con coordenadas locales y globales, tiene un modulo de elasticidad $E$, una sección transversal $A$ y una longitud $L$. Cada elemento tiene dos nodos y un ángulo de inclinación $\\theta$ medido en sentido antihorario desde el eje $X$ global, como se muestra en la figura. Sean $C=\\cos(\\theta)$ y $S=\\sin(\\theta)$, entonces la matriz de rigidez por elemento está dada por:\n",
    "\n",
    "$$\n",
    "k = \\frac{EA}{L}\n",
    "\\begin{bmatrix}\n",
    "C^2 & CS & -C^2 & -CS \\\\\n",
    "CS & S^2 & -CS & -S^2 \\\\\n",
    "-C^2 & -CS & C^2 & CS \\\\\n",
    "-CS & -S^2 & CS & S^2 \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "<img src=\"src/truss-element/truss_element.PNG\" width=\"200px\">\n",
    "\n",
    "El elemento `Truss` tiene dos grados de libertad en cada nodo: desplazamientos en `X` e `Y`. \n",
    "\n",
    "La fuerza en cada elemento se calcula como sigue:\n",
    "\n",
    "$$\n",
    "f = \\frac{EA}{L} \\begin{bmatrix} -C & -S & C & S \\end{bmatrix} \\left\\{ u \\right\\}\n",
    "$$\n",
    "\n",
    "Donde $f$ es la fuerza (escalar) en el elemento y $\\left\\{u\\right\\}$ el vector de desplazamientos en el elemento. Una fuerza negativa indica que el elemento está sometido a compresión.\n",
    "\n",
    "El esfuerzo en el elemento se obtiene dividiendo la fuerza $f$ por la sección transversal, es decir:\n",
    "\n",
    "$$\n",
    "\\sigma = \\frac{f}{A}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Ejemplo 1. Estructura simple de tres elementos\n",
    "\n",
    "Como primer ejemplo vamos a resolver una estructura simple de tres elementos, con un apoyo fijo en A, un soporte simple en C y una fuerza horizontal de 500 N en B, como se muestra en la figura.\n",
    "\n",
    "<figure>\n",
    "<img src=\"src/truss-element/example_01.png\" width=\"250px\">\n",
    "<center><figcaption>Fuente: [1]</figcaption></center>\n",
    "</figure>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x80afe70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from nusa import * # Importando nusa\n",
    "\n",
    "E,A = 210e9, 3.1416*(10e-3)**2\n",
    "n1 = Node((0,0))\n",
    "n2 = Node((2,0))\n",
    "n3 = Node((0,2))\n",
    "e1 = Truss((n1,n2),E,A)\n",
    "e2 = Truss((n1,n3),E,A)\n",
    "e3 = Truss((n2,n3),E,A)\n",
    "m = TrussModel()\n",
    "for n in (n1,n2,n3): m.add_node(n)\n",
    "for e in (e1,e2,e3): m.add_element(e)\n",
    "m.add_constraint(n1, ux=0, uy=0)\n",
    "m.add_constraint(n2, uy=0)\n",
    "m.add_force(n3, (500,0))\n",
    "m.plot_model()\n",
    "m.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1a0hOTiY5OZljx4615WnFn08/hb/+1ekqYk7AcM/KMhekx46FP/7RkRpFWqNNwZ6QkIDv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\ngl1ExDL/H57PJpURB5shAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2eeb210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m.plot_deformed_shape()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==========================\n",
      "    NuSA Simple Report\n",
      "==========================\n",
      "\n",
      "Model: Truss Model 01\n",
      "Number of nodes: 3\n",
      "Number of elements: 3\n",
      "\n",
      "NODAL DISPLACEMENTS\n",
      "======  ===========  ===========\n",
      "  Node           UX           UY\n",
      "======  ===========  ===========\n",
      "     1            0            0\n",
      "     2  1.51576e-05            0\n",
      "     3  7.31873e-05  1.51576e-05\n",
      "======  ===========  ===========\n",
      "\n",
      "NODAL FORCES\n",
      "======  ====  ===========\n",
      "  Node    FX           FY\n",
      "======  ====  ===========\n",
      "     1  -500         -500\n",
      "     2     0          500\n",
      "     3   500  1.13687e-13\n",
      "======  ====  ===========\n",
      "\n",
      "ELEMENT FORCES\n",
      "=========  ========\n",
      "  Element         F\n",
      "=========  ========\n",
      "        1       500\n",
      "        2       500\n",
      "        3  -707.107\n",
      "=========  ========\n",
      "\n",
      "ELEMENT STRESSES\n",
      "=========  ============\n",
      "  Element             S\n",
      "=========  ============\n",
      "        1   1.59155e+06\n",
      "        2   1.59155e+06\n",
      "        3  -2.25079e+06\n",
      "=========  ============\n",
      "\n",
      "\n",
      "FINITE-ELEMENT MODEL INFO\n",
      "\n",
      "NODES:\n",
      "======  ===  ===\n",
      "  Node    X    Y\n",
      "======  ===  ===\n",
      "     1    0    0\n",
      "     2    2    0\n",
      "     3    0    2\n",
      "======  ===  ===\n",
      "\n",
      "ELEMENTS:\n",
      "=========  ====  ====\n",
      "  Element    NI    NJ\n",
      "=========  ====  ====\n",
      "        1     1     2\n",
      "        2     1     3\n",
      "        3     2     3\n",
      "=========  ====  ====\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "m.simple_report()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Ejemplo 2.\n",
    "\n",
    "\n",
    "<img src=\"src/truss-element/example_02.png\" width=\"300px\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OXf+14at5Onn0XuXlX1HpPf+ncE5YGx/caPBKAG7xW99OOdoXLlzQCy+8oLfffls7duzQ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bc7f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "E,A = 200e9, 0.01\n",
    "n1 = Node((0,0))\n",
    "n2 = Node((6,0))\n",
    "n3 = Node((6,4))\n",
    "n4 = Node((3,4))\n",
    "e1 = Truss((n1,n2),E,A)\n",
    "e2 = Truss((n2,n3),E,A)\n",
    "e3 = Truss((n4,n3),E,A)\n",
    "e4 = Truss((n1,n4),E,A)\n",
    "e5 = Truss((n2,n4),E,A)\n",
    "m = TrussModel()\n",
    "for n in (n1,n2,n3,n4): m.add_node(n)\n",
    "for e in (e1,e2,e3,e4,e5): m.add_element(e)\n",
    "m.add_constraint(n1, uy=0)\n",
    "m.add_constraint(n3, ux=0, uy=0)\n",
    "m.add_force(n2, (600,0))\n",
    "m.add_force(n4, (0,-400))\n",
    "m.plot_model()\n",
    "m.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DkW2pcS9b5rKrGLqj1q3pz81f/AVUq+Yyc7XDwsKQmJho93Z2R9pmsznv84CAAPj5+d1b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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8410630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m.plot_deformed_shape()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==========================\n",
      "    NuSA Simple Report\n",
      "==========================\n",
      "\n",
      "Model: Truss Model 01\n",
      "Number of nodes: 4\n",
      "Number of elements: 5\n",
      "\n",
      "NODAL DISPLACEMENTS\n",
      "======  =========  ===========\n",
      "  Node         UX           UY\n",
      "======  =========  ===========\n",
      "     1  2.575e-06            0\n",
      "     2  3.925e-06        4e-07\n",
      "     3          0            0\n",
      "     4      9e-07  -1.0875e-06\n",
      "======  =========  ===========\n",
      "\n",
      "NODAL FORCES\n",
      "======  ============  ===========\n",
      "  Node            FX           FY\n",
      "======  ============  ===========\n",
      "     1  -2.84217e-14          600\n",
      "     2           600  1.13687e-13\n",
      "     3          -600         -200\n",
      "     4   1.56319e-13         -400\n",
      "======  ============  ===========\n",
      "\n",
      "ELEMENT FORCES\n",
      "=========  ====\n",
      "  Element     F\n",
      "=========  ====\n",
      "        1   450\n",
      "        2  -200\n",
      "        3  -600\n",
      "        4  -750\n",
      "        5   250\n",
      "=========  ====\n",
      "\n",
      "ELEMENT STRESSES\n",
      "=========  ======\n",
      "  Element       S\n",
      "=========  ======\n",
      "        1   45000\n",
      "        2  -20000\n",
      "        3  -60000\n",
      "        4  -75000\n",
      "        5   25000\n",
      "=========  ======\n",
      "\n",
      "\n",
      "FINITE-ELEMENT MODEL INFO\n",
      "\n",
      "NODES:\n",
      "======  ===  ===\n",
      "  Node    X    Y\n",
      "======  ===  ===\n",
      "     1    0    0\n",
      "     2    6    0\n",
      "     3    6    4\n",
      "     4    3    4\n",
      "======  ===  ===\n",
      "\n",
      "ELEMENTS:\n",
      "=========  ====  ====\n",
      "  Element    NI    NJ\n",
      "=========  ====  ====\n",
      "        1     1     2\n",
      "        2     2     3\n",
      "        3     4     3\n",
      "        4     1     4\n",
      "        5     2     4\n",
      "=========  ====  ====\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "m.simple_report()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Ejemplo 3\n",
    "\n",
    "<figure>\n",
    "<img src=\"src/truss-element/example_03.png\" width=\"350px\">\n",
    "<center><figcaption>Fuente: [2]</figcaption></center>\n",
    "</figure>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x829e1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "E,A = 29e6, 0.1\n",
    "n1 = Node((0,0)) # A\n",
    "n2 = Node((8*12,6*12)) # B\n",
    "n3 = Node((8*12,0)) # C\n",
    "n4 = Node((16*12,10*12)) # D\n",
    "n5 = Node((16*12,0)) # E\n",
    "n6 = Node((24*12,6*12)) # F\n",
    "n7 = Node((24*12,0)) # G\n",
    "n8 = Node((32*12,0)) # H\n",
    "\n",
    "e1 = Truss((n1,n2),E,A)\n",
    "e2 = Truss((n1,n3),E,A)\n",
    "e3 = Truss((n2,n3),E,A)\n",
    "e4 = Truss((n2,n4),E,A)\n",
    "e5 = Truss((n2,n5),E,A)\n",
    "e6 = Truss((n3,n5),E,A)\n",
    "e7 = Truss((n4,n5),E,A)\n",
    "e8 = Truss((n4,n6),E,A)\n",
    "e9 = Truss((n5,n6),E,A)\n",
    "e10 = Truss((n5,n7),E,A)\n",
    "e11 = Truss((n6,n7),E,A)\n",
    "e12 = Truss((n6,n8),E,A)\n",
    "e13 = Truss((n7,n8),E,A)\n",
    "\n",
    "m = TrussModel(\"Gambrel Roof\")\n",
    "for n in (n1,n2,n3,n4,n5,n6,n7,n8): m.add_node(n)\n",
    "for e in (e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13): m.add_element(e)\n",
    "\n",
    "m.add_constraint(n1, uy=0)\n",
    "m.add_constraint(n8, ux=0, uy=0)\n",
    "m.add_force(n2, (0,-600))\n",
    "m.add_force(n4, (0,-600))\n",
    "m.add_force(n6, (0,-600))\n",
    "m.add_force(n8, (0,-600))\n",
    "m.add_force(n1, (0,-600))\n",
    "m.plot_model()\n",
    "m.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PpmIpWuMsHKDQFqcRhX9gC/zx7bBPcNzQBj17Fvbrolqge3dg3Tpk79yLF5ssh9Pq5bhP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\nUZgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x81e9690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m.plot_deformed_shape()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==========================\n",
      "    NuSA Simple Report\n",
      "==========================\n",
      "\n",
      "Model: Gambrel Roof\n",
      "Number of nodes: 8\n",
      "Number of elements: 13\n",
      "\n",
      "NODAL DISPLACEMENTS\n",
      "======  ==========  =========\n",
      "  Node          UX         UY\n",
      "======  ==========  =========\n",
      "     1   -0.158897          0\n",
      "     2  -0.0421247  -0.259144\n",
      "     3   -0.119172  -0.259144\n",
      "     4  -0.0794483  -0.273323\n",
      "     5  -0.0794483  -0.288219\n",
      "     6   -0.116772  -0.259144\n",
      "     7  -0.0397241  -0.259144\n",
      "     8           0          0\n",
      "======  ==========  =========\n",
      "\n",
      "NODAL FORCES\n",
      "======  ============  ============\n",
      "  Node            FX            FY\n",
      "======  ============  ============\n",
      "     1   9.09495e-13           900\n",
      "     2  -9.09495e-13          -600\n",
      "     3  -9.09495e-13   1.62897e-12\n",
      "     4             0          -600\n",
      "     5   2.27374e-12  -9.09495e-13\n",
      "     6  -1.36424e-12          -600\n",
      "     7             0   1.90023e-13\n",
      "     8             0           900\n",
      "======  ============  ============\n",
      "\n",
      "ELEMENT FORCES\n",
      "=========  ===========\n",
      "  Element            F\n",
      "=========  ===========\n",
      "        1        -1500\n",
      "        2         1200\n",
      "        3  2.23587e-12\n",
      "        4     -1073.31\n",
      "        5         -300\n",
      "        6         1200\n",
      "        7         -360\n",
      "        8     -1073.31\n",
      "        9         -300\n",
      "       10         1200\n",
      "       11            0\n",
      "       12        -1500\n",
      "       13         1200\n",
      "=========  ===========\n",
      "\n",
      "ELEMENT STRESSES\n",
      "=========  ===========\n",
      "  Element            S\n",
      "=========  ===========\n",
      "        1       -15000\n",
      "        2        12000\n",
      "        3  2.23587e-11\n",
      "        4     -10733.1\n",
      "        5        -3000\n",
      "        6        12000\n",
      "        7        -3600\n",
      "        8     -10733.1\n",
      "        9        -3000\n",
      "       10        12000\n",
      "       11            0\n",
      "       12       -15000\n",
      "       13        12000\n",
      "=========  ===========\n",
      "\n",
      "\n",
      "FINITE-ELEMENT MODEL INFO\n",
      "\n",
      "NODES:\n",
      "======  ===  ===\n",
      "  Node    X    Y\n",
      "======  ===  ===\n",
      "     1    0    0\n",
      "     2   96   72\n",
      "     3   96    0\n",
      "     4  192  120\n",
      "     5  192    0\n",
      "     6  288   72\n",
      "     7  288    0\n",
      "     8  384    0\n",
      "======  ===  ===\n",
      "\n",
      "ELEMENTS:\n",
      "=========  ====  ====\n",
      "  Element    NI    NJ\n",
      "=========  ====  ====\n",
      "        1     1     2\n",
      "        2     1     3\n",
      "        3     2     3\n",
      "        4     2     4\n",
      "        5     2     5\n",
      "        6     3     5\n",
      "        7     4     5\n",
      "        8     4     6\n",
      "        9     5     6\n",
      "       10     5     7\n",
      "       11     6     7\n",
      "       12     6     8\n",
      "       13     7     8\n",
      "=========  ====  ====\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "m.simple_report()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Referencias\n",
    "\n",
    "* [1] Hibbeler, R.C. (2010). *Engineering Mechanics, Statics*. Pearson\n",
    "* [2] Beer, F.P. et. al. (2013) *Vector Mechanics for Engineers, Statics and Dynamics*. McGraw-Hill"
   ]
  }
 ],
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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