Aula5.ipynb

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    "Universidade Federal do Rio Grande do Sul (UFRGS)   \n",
    "Programa de Pós-Graduação em Engenharia Civil (PPGEC)   \n",
    "\n",
    "\n",
    "# Python aplicado à análise de estruturas\n",
    "---\n",
    "## <center> Aula 5: Aplicação: Resolução de uma treliça plana</center>\n",
    "\n",
    "[1. Fundamentação teórica](#section_1)\n",
    "\n",
    "[1.1. Matriz de rigidez de uma treliça plana](#section_11)\n",
    "\n",
    "[1.2. Montagem da matriz de rigidez global da estrutura](#section_12)\n",
    "\n",
    "[1.3. Montagem do vetor de forças externas](#section_13)\n",
    "\n",
    "[1.4. Aplicação das condições de contorno ](#section_14)\n",
    "\n",
    "[1.5. Cálculo dos deslocamentos ](#section_15)\n",
    "\n",
    "[1.6. Determinação das reações de apoio ](#section_16)\n",
    "\n",
    "[1.7. Determinação dos esforços em cada barra ](#section_17)\n",
    "\n",
    "[2. Introdução ](#section_2)\n",
    "\n",
    "[2.1. Estrutura em estudo ](#section_21)\n",
    "\n",
    "[3. Entrada de dados ](#section_3)\n",
    "\n",
    "[4. Plotagem da estrutura ](#section_4)\n",
    "\n",
    "[5. Comprimento das barras e cossenos diretores ](#section_5)\n",
    "\n",
    "[6. Montagem da matriz de rigidez ](#section_6)\n",
    "\n",
    "[7. Aplicação das condições de contorno ](#section_7)\n",
    "\n",
    "[8. Montagem do vetor de forças  ](#section_8)\n",
    "\n",
    "[9. Resolução da equação de equilíbrio ](#section_9)\n",
    "\n",
    "[10. Plotagem da treliça deformada ](#section_10)\n",
    "\n",
    "[11. Plotagem das reações de apoio ](#section_111)\n",
    "\n",
    "[12. Determinação dos esforços ](#section_112)\n",
    "\n",
    "\n",
    "\n",
    "---\n",
    "\n",
    "_Eng.Msc Eduarto Pagnussat Titello_\n",
    "\n",
    "_Eng.Daniel Barbosa M. Matos_"
   ]
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    "# Fundamentação teórica. <a name=\"section_1\"></a>\n",
    "\n",
    "Nesta sessão serão apresentados todos os conceitos necessários de análise matricial de estruras para o compreendimento e realização da aplicação prática.\n",
    "\n",
    "## Matriz de rigidez de uma barra de treliça plana.<a name=\"section_11\"></a>\n",
    "\n",
    "A análise de estruturas por elementos de barra é o princípio do ** método dos elmentos finitos**, sendo a barra de treliça plana o elemento finito mais simples, que sofre apenas carregamentos axiais em torno dos seus eixos locais, como mostrado na figura abaixo.\n",
    "\n",
    "![sistema_local.PNG](Resources/sistema_local.PNG)\n",
    "\n",
    "Num sistema local, a barra de treliça plana possui apenas um grau de liberdade (gdl) por nó, tendo sua matriz de rigidez expressa por:\n",
    "\n",
    "\\begin{align}\n",
    "K_l^l = \\frac{EA}{L}\n",
    "\\begin{bmatrix}\n",
    "1&-1\\\\\n",
    "-1&1\n",
    "\\end{bmatrix}\n",
    "\\end{align}\n",
    "\n",
    "A partir do momento em que se deseja realizar uma análise global da estrutura, é necessário reescrever a matriz de rigidez local de forma que essa possua um grau de liberdade por eixo do espaço adotado. Isso ocorre porque devem existir graus de liberdade suficientes para a correta decomposição dos deslocamentos de todos os nós, indiferentemente da orientação das barras. Dessa forma, em uma treliça plana devem haver 2 graus de liberdade, o gdl de translação horizontal (x) e o gdl de translação vertical (y), conforme a figura a seguir:\n",
    "\n",
    "![sistema.PNG](Resources/sistema.PNG)\n",
    "\n",
    "Adotando o eixo x' (local) sobre o eixo da barra (conforme figura anterior), a matriz local, considerando o grau de liberdade adicional y' perpendicular ao eixo x', tem a seguinte configuração, que não altera suas propriedades. \n",
    "\n",
    "\\begin{align}\n",
    "K_l^l = \\frac{EA}{L}\n",
    "\\begin{bmatrix}\n",
    "1&0&-1&0\\\\\n",
    "0&0&0&0\\\\\n",
    "-1&0&1&0\\\\\n",
    "0&0&0&0\n",
    "\\end{bmatrix}\n",
    "\\end{align}\n",
    "\n",
    "Perceba que, para transformar as coordenadas globais em coordendadas locais, podem-se usar as seguintes equações:\n",
    "\n",
    "\\begin{align}\n",
    "u_{i'} &= u_i\\cos{\\theta} + v_i\\sin{\\theta} \\\\\n",
    "v_{i'} &= -u_i\\sin{\\theta} + v_i\\cos{\\theta} \\\\\n",
    "u_{j'} &= u_j\\cos{\\theta} + v_j\\sin{\\theta} \\\\\n",
    "v_{j'} &= -u_j\\sin{\\theta} + v_j\\cos{\\theta} \n",
    "\\end{align}\n",
    "\n",
    "Colocando o sistema de equações acima em forma matricial, tem-se o exposto abaixo:\n",
    "\n",
    "\\begin{align}\n",
    "\\begin{bmatrix}\n",
    "u_{i'}  \\\\\n",
    "v_{i'}  \\\\\n",
    "u_{j'}  \\\\\n",
    "v_{j'}\n",
    "\\end{bmatrix}\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "\\cos\\theta&\\sin\\theta&0&0 \\\\\n",
    "-\\sin\\theta&cos\\theta&0&0 \\\\\n",
    "0&0&\\cos\\theta&\\sin\\theta \\\\\n",
    "0&0&-\\sin\\theta&\\cos\\theta\n",
    "\\end{bmatrix} \n",
    "\\begin{bmatrix}\n",
    "u_{i} \\\\\n",
    "v_{i} \\\\\n",
    "u_{j}  \\\\\n",
    "v_{j}\n",
    "\\end{bmatrix}\n",
    "\\end{align}\n",
    "Ou ainda:\n",
    "\\begin{align}\n",
    "U^l = \\Theta U^G\n",
    "\\end{align}\n",
    "\n",
    "Em que $\\Theta$ é chamada de matriz de rotação.\n",
    "\n",
    "\\begin{align}\n",
    "\\Theta = \n",
    "\\begin{bmatrix}\n",
    "\\cos\\theta&\\sin\\theta&0&0\\\\\n",
    "-\\sin\\theta&cos\\theta&0&0\\\\\n",
    "0&0&\\cos\\theta&\\sin\\theta\\\\\n",
    "0&0&-\\sin\\theta&\\cos\\theta\n",
    "\\end{bmatrix}\n",
    "\\end{align}\n",
    "\n",
    "Escrevendo, agora, as equações de equilíbrio local (de uma barra de treliça plana) e equilibrio global (de toda estrutura), temos:\n",
    "\n",
    "\\begin{align}\n",
    "K_l^L U^l = F^l \\\\\n",
    "K^G U^G = F^G\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "Sabendo que o vetor de forças globais $F_G$ pode ser escrito como \n",
    "\n",
    "\\begin{align}\n",
    "F^G = \\Theta^T F^l\n",
    "\\end{align}\n",
    "\n",
    "E utilizando a relação entre deslocamentos locais e globais,é possível reescrever a equação de equilíbrio multiplicando ambos os lados pelo transposto da matriz de rotação:\n",
    "\n",
    "\\begin{align}\n",
    "\\Theta^T K_l^L \\Theta U^G &= \\Theta^TF^l\\\\\n",
    "K_l^G U^G &= F^G\n",
    "\\end{align}\n",
    "\n",
    "Sendo possível afirmar que a matriz de rigidez em coordendas globais pode ser expressa por:\n",
    "\\begin{align}\n",
    "K_l^G = \\Theta^T K_l^L \\Theta\n",
    "\\end{align}"
   ]
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    "## Montagem da matriz de rigidez global da estrutura<a name=\"section_12\"></a>\n",
    "\n",
    "A matriz de rigidez total da estrutura é uma matriz que comtempla todos os graus de liberdade das barras utilizadas, sendo necessário o correto acoplamento dos mesmos. Abaixo será realizado um exemplo de como deve ser realizado este procedimento.\n",
    "\n",
    "![exemplo.PNG](Resources/exemplo.PNG)\n",
    "\n",
    "Neste exemplo é possível verificar a presença de 4 barras de treliça plana, 4 nós e 8 gdl (2 por nó). A numeração dos graus de liberdade é feita nó a nó, onde a direção x tem o primeiro gdl do nó e a direção y o segundo, dessa forma, a numeração dos gdls para o nó n é dada por:\n",
    "\\begin{align}\n",
    "gdl_h &= 2n-1\\\\\n",
    "gdl_v &= 2n\n",
    "\\end{align}\n",
    "Montando as matrizes de rigidez locais (já rotacionadas) de cada um dos elementos temos:\n",
    "\\begin{matrix}\n",
    "& & & & & &1& 2& 3& 4\\\\\n",
    "\\end{matrix}\n",
    "\\begin{align}\n",
    "K_1 &= \\frac{29.5* 10^6}{40}\n",
    "\\begin{bmatrix}\n",
    "1&0&-1&0\\\\\n",
    "0&0&0&0\\\\\n",
    "-1&0&1&0\\\\\n",
    "0&0&0&0\n",
    "\\end{bmatrix}\n",
    "\\begin{matrix}\n",
    "1\\\\\n",
    "2\\\\\n",
    "3\\\\\n",
    "4\n",
    "\\end{matrix}\n",
    "\\end{align}\n",
    "\\begin{matrix}\n",
    "& & & & &5&6&3&4\\\\\n",
    "\\end{matrix}\n",
    "\\begin{align}\n",
    "K_2 &= \\frac{29.5 *10^6}{30}\n",
    "\\begin{bmatrix}\n",
    "0&0&0&0\\\\\n",
    "0&1&0&-1\\\\\n",
    "-1&0&1&0\\\\\n",
    "0&-1&0&1\n",
    "\\end{bmatrix}\n",
    "\\begin{matrix}\n",
    "5\\\\\n",
    "6\\\\\n",
    "3\\\\\n",
    "4\n",
    "\\end{matrix}\n",
    "\\end{align}\n",
    "\\begin{matrix}\n",
    "&  & & & &1& &2& &5& &6\\\\\n",
    "\\end{matrix}\n",
    "\\begin{align}\n",
    "K_3 &= \\frac{29.5 *10^6}{50}\n",
    "\\begin{bmatrix}\n",
    ".64&.48&-.64&-.48\\\\\n",
    ".48&.36&-.48&-.36\\\\\n",
    ".48&-.36&.48&.36\\\\\n",
    "0&0&0&0\n",
    "\\end{bmatrix}\n",
    "\\begin{matrix}\n",
    "1\\\\\n",
    "2\\\\\n",
    "5\\\\\n",
    "6\n",
    "\\end{matrix}\n",
    "\\end{align}\n",
    "\\begin{matrix}\n",
    "& & & & & &7&8&5&6\\\\\n",
    "\\end{matrix}\n",
    "\\begin{align}\n",
    "K_4 &= \\frac{29.5* 10^6}{40}\n",
    "\\begin{bmatrix}\n",
    "1&0&-1&0\\\\\n",
    "0&0&0&0\\\\\n",
    "-1&0&1&0\\\\\n",
    "0&0&0&0\n",
    "\\end{bmatrix}\n",
    "\\begin{matrix}\n",
    "7\\\\\n",
    "8\\\\\n",
    "5\\\\\n",
    "6\n",
    "\\end{matrix}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "Perceba que cada linha e coluna estão numeradas conforme o seu grau de liberdade correspondente.\n",
    "\n",
    "As matrizes locais serão agora alocadas na matriz global(8x8) conforme os seus graus de liberdade. Caso haja a superposição de valores, esses devem ser somados.\n",
    "\\begin{matrix}\n",
    "& & & & &  &  1 \\qquad & 2\\quad  & 3\\qquad & 4\\quad  & 5\\quad  & 6\\qquad  & 7\\quad  & 8 \\\\\n",
    "\\end{matrix}\n",
    "\\begin{align}\n",
    "K = \\frac{29.5*10^6}{600}\n",
    "\\begin{bmatrix}\n",
    "22.68 & 5.76 & -15 & 0 & -7.68 & -5.76 & 0& 0 \\\\\n",
    "5.76 & 4.32 & 0 & 0 & -5.76 & -4.32 & 0 & 0\\\\\n",
    "-15 & 0 &15 & 0 &0 & 0& 0 & 0\\\\\n",
    "0& 0 & 0 & 20& 0 & -20 & 0 & 0\\\\\n",
    "-7.68 & -5.76 & 0 & 0 & 22.68 & 5.76 & -15&0 \\\\\n",
    "-5.76 & -4.32&0 & -20 & 5.76 & 24.32 & 0&0\\\\\n",
    "0 & 0 & 0 & 0 & -15 & 0 & 15 & 0\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0& 0& 0\n",
    "\\end{bmatrix}\n",
    "\\begin{matrix}\n",
    "1\\\\\n",
    "2\\\\\n",
    "3\\\\\n",
    "4\\\\\n",
    "5\\\\\n",
    "6\\\\\n",
    "7\\\\\n",
    "8\\\\\n",
    "\\end{matrix}\n",
    "\\end{align}\n",
    "\n",
    "De forma genérica, podemos acoplar as matrizes locais na matriz global na forma de quadrantes, ao invés de acopla-las termo a termo, visto que cada nó (quadrante) tem 2 gdls em sequencia.\n",
    "\\begin{align}\n",
    "K_l^G &= \n",
    "\\begin{bmatrix}\n",
    "k_{ii} & k_{ij}\\\\\n",
    "k_{ji} & k_{jj}\n",
    "\\end{bmatrix}\\\\\n",
    "K &= \n",
    "\\begin{bmatrix}\n",
    "k_{ii} &\\dots& k_{ij}\\\\\n",
    "\\vdots  & \\ddots & \\vdots \\\\\n",
    "k_{ji} &\\dots & k_{jj}\n",
    "\\end{bmatrix}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
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   "source": [
    "## Montagem do vetor de forças externas<a name=\"section_13\"></a>\n",
    "\n",
    "O vetor de forças externas deve possuir dimensões n x 1, em que n é a quantidade de graus de liberdade. Dessa forma a posição de um valor no vetor corresponde ao seu gdl (as linhas com numeração ímpar correspondem aos gdl horizontais, enquanto as linhas com numeração par estão relacionadas aos gdl verticais). Montando o vetor de forças para o exemplo acima, temos:\n",
    "\n",
    "\\begin{align}\n",
    "F^G =\n",
    "\\begin{bmatrix}\n",
    "0\\\\\n",
    "0\\\\\n",
    "20000\\\\\n",
    "0\\\\\n",
    "0\\\\\n",
    "-25000\\\\\n",
    "0\\\\\n",
    "0\\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{matrix}\n",
    "1\\\\\n",
    "2\\\\\n",
    "3\\\\\n",
    "4\\\\\n",
    "5\\\\\n",
    "6\\\\\n",
    "7\\\\\n",
    "8\\\\\n",
    "\\end{matrix}\n",
    "\\end{align}"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Aplicação das condições de contorno<a name=\"section_14\"></a>\n",
    "\n",
    "Para a aplicação das condições de contorno existem duas possibilidades: a remoção das linhas e as colunas dos graus de liberdade restritos ou a substituição dessas linhas e colunas por zeros, mantendo 1 na diagonal principal. A primeira metodologia apresenta vantagens em relação ao processamento da estrutura, reduzindo as dimensões da matriz, enquanto a implementação da segunda é de maior facilidade, sendo essa aqui abordada.  \n",
    "\n",
    "\\begin{align}\n",
    "K_R &= \\frac{29.5*10^6}{600}\n",
    "\\begin{bmatrix}\n",
    "1 & 0 & 0 & 0 & 0 & 0 & 0& 0 \\\\\n",
    "0 & 1 & 0 & 0 & 0 & 0 & 0& 0 \\\\\n",
    "0 & 0 &15 & 0 &0 & 0& 0 & 0\\\\\n",
    "0 & 0 & 0 & 1 & 0 & 0 & 0& 0 \\\\\n",
    "0 & 0 & 0 & 0 & 22.68 & 5.76 & 0 &0 \\\\\n",
    "0 & 0 &0 & 0 & 5.76 & 24.32 & 0\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 0& 0 \n",
    "\\end{bmatrix}\n",
    "\\begin{matrix}\n",
    "1\\\\\n",
    "2\\\\\n",
    "3\\\\\n",
    "4\\\\\n",
    "5\\\\\n",
    "6\\\\\n",
    "7\\\\\n",
    "8\\\\\n",
    "\\end{matrix}\n",
    "\\end{align}"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cálculo dos deslocamentos<a name=\"section_15\"></a>\n",
    "\n",
    "Para a realização do cálculo dos deslocamentos, basta resolver o sistema de equações:\n",
    "\n",
    "\\begin{align}\n",
    "K_R U = F^G\n",
    "\\end{align}\n",
    "\n",
    "## Determinação das reações de apoio<a name=\"section_16\"></a>\n",
    "\n",
    "Agora em posse dos deslocamentos (U), ao realizar o produto da matriz de rigidez sem restrições pelo vetor deslocamento ($KU$), o vetor de forças resultante($F^G$) possuirá valores referentes aos graus de liberdade restritos, sendo esses os valores das reações de apoio.\n",
    "\n",
    "## Determinação dos esforços em cada barra<a name=\"section_17\"></a>\n",
    "\n",
    "Para a determinação dos esforços atuantes em cada barra, devemos resolver a equação de equilíbrio local de cada barra. Para isso, será necessário a utilização da matriz de rigidez local da barra ($K_l^l$) e do deslocamento de cada nó da barra em coordenadas locais ($U^l$). Para realizar a conversão do deslocamento global para o local, utilizaremos novamente a expressão $ U^l = \\Theta U^G $. Portanto, para o cálculo dos esforços, basta resolver o sistema abaixo:\n",
    "\n",
    "\\begin{align}\n",
    "K_l^l U^l = F^l\n",
    "\\end{align}\n",
    "\n"
   ]
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   "cell_type": "markdown",
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   "source": [
    "# Introdução<a name=\"section_2\"></a>\n",
    "\n",
    "A análise matricial de treliças requer a criação de arrays que nos permitem modelar a estrutura de forma matemática. São necessárias:\n",
    "\n",
    "* array de coordendas nodais: coordenadas `X` e `Y`;\n",
    "* array de conectividade: contendo os nós que delimitam cada barra;\n",
    "* array de propriedades: contendo a área e o módulo de elasticidade longitudinal;\n",
    "* array de forças externas : contendo os valores de forças horizontais e verticais;\n",
    "* array de restrições : contendo os graus de liberdade que são restritos.\n",
    "\n",
    "Para criação dessas arrays os dados serão importados através do módulo `pandas` de planilha do Excel chamada `entrada.xlsx`. A planilha de entrada de dados deve ter duas abas, a primeira chamada de `Nós` contendo as coordenadas de cada nó e a segunda chamada `Barras` com as conectividades (nó inicial e final) e as propriedades de cada barra. \n",
    "\n",
    "\n",
    "## Estrutura em estudo<a name=\"section_21\"></a>\n",
    "\n",
    "A estrutura em estudo é uma treliça plana com 12 nós, 21 barras e 2 gdl por nó. As coordenadas dos nós e os elementos podem ser visualizadas na figura.\n",
    "\n",
    "![treliça](Resources/treliça.PNG)\n",
    "\n",
    "Todas as barras possuem a mesma área de seção transversal $ A = 0.01 m^2$ e o mesmo módulo de elasticidade $E = 21 * 10^{10} \\frac{N}{m^2}$.\n",
    "\n",
    "Vamos então importar os módulos necessários:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Entrada de dados<a name=\"section_3\"></a>\n",
    "Conforme apresentado anteriormente a entrada de dados é realizada através do arquivo `entrada.xlsx`. Vamos então importar cada aba separadamente especificando o `keyarg` `sheet_name`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "      <td>-9000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-15000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-8000.0</td>\n",
       "      <td>-9000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-8000.0</td>\n",
       "      <td>-9000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     X  Y   RX   RY      FX       FY\n",
       "1    0  0  1.0  1.0     0.0      0.0\n",
       "2    2  1  0.0  0.0  8000.0  -9000.0\n",
       "3    2  0  0.0  0.0     0.0      0.0\n",
       "4    4  2  0.0  0.0  8000.0  -9000.0\n",
       "5    4  0  0.0  0.0     0.0      0.0\n",
       "6    6  3  0.0  0.0     0.0 -15000.0\n",
       "7    6  0  0.0  0.0     0.0      0.0\n",
       "8    8  2  0.0  0.0 -8000.0  -9000.0\n",
       "9    8  0  0.0  0.0     0.0      0.0\n",
       "10  10  1  0.0  0.0 -8000.0  -9000.0\n",
       "11  10  0  0.0  0.0     0.0      0.0\n",
       "12  12  0  0.0  1.0     0.0      0.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nos = pd.read_excel('resources/entrada.xlsx', sheet_name='Nós')\n",
    "barras = pd.read_excel('resources/entrada.xlsx', sheet_name='Barras')\n",
    "\n",
    "# Acertando os números dos nós e das barras conforme a figura (iniciando em 1)\n",
    "nos.index += 1\n",
    "barras.index += 1\n",
    "\n",
    "# Trocando celulas vazias por zeros\n",
    "nos.fillna(0, inplace=True)\n",
    "\n",
    "# Printando os valores na tela\n",
    "nos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>N1</th>\n",
       "      <th>N2</th>\n",
       "      <th>A</th>\n",
       "      <th>E</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>6</td>\n",
       "      <td>8</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>9</td>\n",
       "      <td>11</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>10</td>\n",
       "      <td>12</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>11</td>\n",
       "      <td>12</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    N1  N2     A             E\n",
       "1    1   2  0.01  210000000000\n",
       "2    1   3  0.01  210000000000\n",
       "3    2   3  0.01  210000000000\n",
       "4    2   4  0.01  210000000000\n",
       "5    2   5  0.01  210000000000\n",
       "6    3   5  0.01  210000000000\n",
       "7    4   5  0.01  210000000000\n",
       "8    4   6  0.01  210000000000\n",
       "9    4   7  0.01  210000000000\n",
       "10   5   7  0.01  210000000000\n",
       "11   6   7  0.01  210000000000\n",
       "12   6   8  0.01  210000000000\n",
       "13   7   8  0.01  210000000000\n",
       "14   7   9  0.01  210000000000\n",
       "15   8   9  0.01  210000000000\n",
       "16   8  10  0.01  210000000000\n",
       "17   9  10  0.01  210000000000\n",
       "18   9  11  0.01  210000000000\n",
       "19  10  11  0.01  210000000000\n",
       "20  10  12  0.01  210000000000\n",
       "21  11  12  0.01  210000000000"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "barras"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotagem da estrutura<a name=\"section_4\"></a>\n",
    "\n",
    "O código abaixo permite a montagem da estrutura plotando elemento a elemento a partir das matrizes das barras e dos nós \n",
    "."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1,figsize=(12,4))\n",
    "plt.ylim(-1,5)\n",
    "\n",
    "# Plotagem dos apoios e das forças\n",
    "for no in nos.index:\n",
    "    X,Y,RX,RY,Fx,Fy = nos.loc[no]\n",
    "\n",
    "    # Se RX restrito aplica sobre gl de X\n",
    "    if RX == 1:\n",
    "        plt.scatter(X,Y,400,marker =5,zorder = -2,color ='gray')\n",
    "    if RY == 1:\n",
    "        plt.scatter(X,Y,400,marker =6,zorder = -2,color ='gray')\n",
    "\n",
    "    if Fx >0:\n",
    "        plt.arrow(X-1.5,Y,1,0,width =0.05,color='k')\n",
    "        plt.text(X-1.5,Y,'{}kN'.format(Fx/1000),va='bottom')\n",
    "    if Fx <0:\n",
    "       plt.arrow(X+1.5,Y,-1,0,width =0.05,color='k')\n",
    "       plt.text(X+.5,Y,'{}kN'.format(Fx/1000),va='bottom')\n",
    "    if Fy >0:\n",
    "        plt.arrow(X,Y-1.5,0,1,width =0.05,color='k')\n",
    "        plt.text(X,Y,'{}kN'.format(Fy/1000),va='bottom',rotation=90)\n",
    "    if Fy <0:\n",
    "       plt.arrow(X,Y+1.5,0,-1,width =0.05,color='k')\n",
    "       plt.text(X,Y+.5,'{}kN'.format(Fy/1000),ha='right',rotation=90)\n",
    "\n",
    "\n",
    "# Plotagem das barras\n",
    "for barra in barras.index:\n",
    "    # Vamos passar os nós para as variáveis N1 e N2\n",
    "    N1 = barras.loc[barra, 'N1']\n",
    "    N2 = barras.loc[barra, 'N2']\n",
    "\n",
    "    # Agora vamos acessar as coordendas de cada um dos nós\n",
    "    x1, y1 = nos.loc[N1, ['X','Y']]\n",
    "    x2, y2 = nos.loc[N2, ['X','Y']]\n",
    "    y = [y1,y2]\n",
    "    x = [x1,x2]\n",
    "    \n",
    "    plt.plot(x,y,'black')\n",
    "    plt.scatter(x,y, s=80,marker ='o',color ='black')\n",
    "    #plt.grid(True)\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok! Podemos visualizar que os dados foram importados corretamente!\n",
    "\n",
    "# Comprimento das barras e cossenos diretores <a name=\"section_5\"></a>\n",
    "\n",
    "Vamos, então, determinar os comprimentos das barras e seus cossenos diretores. Para isso vamos percorrer DataFrame de barras e a cada passo acessar o DataFrame de nós para obter suas coordendas. Os valores cálculados serão armazenados em listas que serão inseridas no DataFrame ao fim do processo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>N1</th>\n",
       "      <th>N2</th>\n",
       "      <th>A</th>\n",
       "      <th>E</th>\n",
       "      <th>L</th>\n",
       "      <th>sen</th>\n",
       "      <th>cos</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.236068</td>\n",
       "      <td>0.447214</td>\n",
       "      <td>0.894427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.236068</td>\n",
       "      <td>0.447214</td>\n",
       "      <td>0.894427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.236068</td>\n",
       "      <td>-0.447214</td>\n",
       "      <td>0.894427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.236068</td>\n",
       "      <td>0.447214</td>\n",
       "      <td>0.894427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.828427</td>\n",
       "      <td>-0.707107</td>\n",
       "      <td>0.707107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>6</td>\n",
       "      <td>8</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.236068</td>\n",
       "      <td>-0.447214</td>\n",
       "      <td>0.894427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.828427</td>\n",
       "      <td>0.707107</td>\n",
       "      <td>0.707107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.236068</td>\n",
       "      <td>-0.447214</td>\n",
       "      <td>0.894427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.236068</td>\n",
       "      <td>0.447214</td>\n",
       "      <td>0.894427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>9</td>\n",
       "      <td>11</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>10</td>\n",
       "      <td>12</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.236068</td>\n",
       "      <td>-0.447214</td>\n",
       "      <td>0.894427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>11</td>\n",
       "      <td>12</td>\n",
       "      <td>0.01</td>\n",
       "      <td>210000000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    N1  N2     A             E         L       sen       cos\n",
       "1    1   2  0.01  210000000000  2.236068  0.447214  0.894427\n",
       "2    1   3  0.01  210000000000  2.000000  0.000000  1.000000\n",
       "3    2   3  0.01  210000000000  1.000000 -1.000000  0.000000\n",
       "4    2   4  0.01  210000000000  2.236068  0.447214  0.894427\n",
       "5    2   5  0.01  210000000000  2.236068 -0.447214  0.894427\n",
       "6    3   5  0.01  210000000000  2.000000  0.000000  1.000000\n",
       "7    4   5  0.01  210000000000  2.000000 -1.000000  0.000000\n",
       "8    4   6  0.01  210000000000  2.236068  0.447214  0.894427\n",
       "9    4   7  0.01  210000000000  2.828427 -0.707107  0.707107\n",
       "10   5   7  0.01  210000000000  2.000000  0.000000  1.000000\n",
       "11   6   7  0.01  210000000000  3.000000 -1.000000  0.000000\n",
       "12   6   8  0.01  210000000000  2.236068 -0.447214  0.894427\n",
       "13   7   8  0.01  210000000000  2.828427  0.707107  0.707107\n",
       "14   7   9  0.01  210000000000  2.000000  0.000000  1.000000\n",
       "15   8   9  0.01  210000000000  2.000000 -1.000000  0.000000\n",
       "16   8  10  0.01  210000000000  2.236068 -0.447214  0.894427\n",
       "17   9  10  0.01  210000000000  2.236068  0.447214  0.894427\n",
       "18   9  11  0.01  210000000000  2.000000  0.000000  1.000000\n",
       "19  10  11  0.01  210000000000  1.000000 -1.000000  0.000000\n",
       "20  10  12  0.01  210000000000  2.236068 -0.447214  0.894427\n",
       "21  11  12  0.01  210000000000  2.000000  0.000000  1.000000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Criação de listas vazias para armazenar as variáves\n",
    "Ls   = []\n",
    "sens = []\n",
    "coss = []\n",
    "\n",
    "for barra in barras.index:\n",
    "    # Vamos passar os nós para as variáveis N1 e N2\n",
    "    N1 = barras.loc[barra, 'N1']\n",
    "    N2 = barras.loc[barra, 'N2']\n",
    "\n",
    "    # Agora vamos acessar as coordendas de cada um dos nós\n",
    "    x1, y1 = nos.loc[N1, ['X','Y']]\n",
    "    x2, y2 = nos.loc[N2, ['X','Y']]\n",
    "\n",
    "    # O comprimento da barra é dado pelo teorema de Pitagoras\n",
    "    Lx = x2 - x1\n",
    "    Ly = y2 - y1\n",
    "    L = np.sqrt(Lx**2 + Ly**2)\n",
    "    \n",
    "    # Os cossenos diretores são então:\n",
    "    sen = Ly/L\n",
    "    cos = Lx/L\n",
    "\n",
    "    # Inserindo nas listas\n",
    "    Ls.append(L)\n",
    "    sens.append(sen)\n",
    "    coss.append(cos)\n",
    "\n",
    "# Agora que saimos do loop vamos inserir no DataFrame\n",
    "barras['L']   = Ls\n",
    "barras['sen'] = sens\n",
    "barras['cos'] = coss\n",
    "\n",
    "# Printando novo DataFrame\n",
    "barras"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Montagem da matriz de rigidez<a name=\"section_6\"></a>\n",
    "Em posse das propriedades das barras podemos agora montar as matrizes de rigidez locais e acoplalas na matriz de rigidez global. Por se tratar de barras de treliça plana cada nó possui 2 graus de liberdade (deslocamentos horizontal e vertical), portanto em treliças planas o números de graus de liberdade sempre será o dobro do número de nós. \n",
    "\n",
    "Neste nosso exemplo teremos então 24 graus de liberdade, esses são numerados em função do número do nó conforme as expressões a seguir:\n",
    "$$gdl_h=2n-1$$\n",
    "$$gdl_v=2n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nossa matriz de rigidez global será então uma matriz de ordem `24x24`, em que os graus de liberdade ímpares correspondem aos deslocamentos horizontais e pares aos verticais.\n",
    "\n",
    "A matriz de rigidez global é a obtida pela superposição das matrizes de rigidez locais nos respectivos graus de liberdade. Inicialmente a matriz global `K` deve ser pré alocada como uma matriz de zeros."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "maxgl = 2*len(nos)\n",
    "K = np.zeros([maxgl,maxgl])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A alocação é realizada percorrendo todas as barras novamente, cálculando suas matrizes de rigidez local e alocando suas componentes na matriz global."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "for barra in barras.index:\n",
    "    # Vamos importar as propriedades necessárias para construção da matriz local e da matriz de rotação\n",
    "    L   = barras.loc[barra, 'L']\n",
    "    sen = barras.loc[barra, 'sen']\n",
    "    cos = barras.loc[barra, 'cos']\n",
    "    A   = barras.loc[barra, 'A']\n",
    "    E   = barras.loc[barra, 'E']\n",
    "    N1  = barras.loc[barra, 'N1']\n",
    "    N2  = barras.loc[barra, 'N2']\n",
    "\n",
    "    # Matriz de rigidez no sistema local \n",
    "    Kl = E*A/L*np.array([[ 1, 0,-1, 0],\n",
    "                         [ 0, 0, 0, 0], \n",
    "                         [-1, 0, 1, 0],\n",
    "                         [ 0, 0, 0, 0]])\n",
    "\n",
    "    # Matriz de rotação\n",
    "    Mrot = np.array([[ cos,  sen,    0,   0],\n",
    "                     [-sen,  cos,    0,   0],\n",
    "                     [    0,   0,  cos, sen],\n",
    "                     [    0,   0, -sen, cos]])\n",
    "\n",
    "    # Rotação da matriz de coordenadas locais para globais\n",
    "    Klr = np.dot(np.dot(Mrot.T, Kl), Mrot)\n",
    "\n",
    "    # Cálculo dos graus de liberdade\n",
    "    gl1 = 2*N1 - 1\n",
    "    gl2 = 2*N1 \n",
    "    gl3 = 2*N2 - 1\n",
    "    gl4 = 2*N2\n",
    "\n",
    "    # Aloca a matriz local na matriz global\n",
    "    # Lembrando as propriedades das listas do Python!\n",
    "    K[gl1-1:gl2, gl1-1:gl2] += Klr[0:2, 0:2]\n",
    "    K[gl3-1:gl4, gl1-1:gl2] += Klr[2:4, 0:2]\n",
    "    K[gl1-1:gl2, gl3-1:gl4] += Klr[0:2, 2:4]\n",
    "    K[gl3-1:gl4, gl3-1:gl4] += Klr[2:4, 2:4]\n",
    "\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Aplicação das condições de contorno<a name=\"section_7\"></a>\n",
    "Agora, para solução do problema, a matriz de rigidez global é clonada e as restrições de apoio são impostas zerando as respectivas linhas e colunas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Aplicando restrição horizontal no nó 1.\n",
      "Aplicando restrição vertical no nó 1.\n",
      "Aplicando restrição vertical no nó 12.\n"
     ]
    }
   ],
   "source": [
    "Kcompleta = K.copy()    # Alocando a matriz em outro espaço de memória\n",
    "\n",
    "for no in nos.index:\n",
    "    RX, RY = nos.loc[no, ['RX','RY']]\n",
    "    # Se RX restrito aplica sobre gl de X\n",
    "    if RX == 1:\n",
    "        gl = 2*no - 1\n",
    "        K[:,    gl-1] = 0\n",
    "        K[gl-1,    :] = 0\n",
    "        K[gl-1, gl-1] = 1\n",
    "        print('Aplicando restrição horizontal no nó {:d}.'.format(no))\n",
    "    \n",
    "    if RY == 1:\n",
    "        gl = 2*no\n",
    "        K[:,    gl-1] = 0\n",
    "        K[gl-1,    :] = 0\n",
    "        K[gl-1, gl-1] = 1\n",
    "        print('Aplicando restrição vertical no nó {:d}.'.format(no))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Montagem do vetor de forças<a name=\"section_8\"></a>\n",
    "Com a matriz global restringida vamos montar o vetor de forças aplicadas. Este vetor tem como dimensão o número de graus de liberdade."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "F = np.zeros(maxgl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "for no in nos.index:\n",
    "    FX, FY = nos.loc[no, ['FX','FY']]\n",
    "    gl1 = 2*no - 1\n",
    "    gl2 = 2*no \n",
    "    F[gl1-1] = FX\n",
    "    F[gl2-1] = FY"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Resolução da equação de equilíbrio<a name=\"section_9\"></a>\n",
    "Resolvendo o sistema pelo `numpy.linalg.solve()` obtemos os deslocamentos nodais."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "U = np.linalg.solve(K, F)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotagem da treliça deformada<a name=\"section_10\"></a>\n",
    "Em posse dos valores de deslocamento, é possível realizar a plotagem da treliça deslocada, junto com suas reações de apoio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "e = 1000\n",
    "for barra in barras.index:\n",
    "    # Vamos passar os nós para as variáveis N1 e N2\n",
    "    N1 = barras.loc[barra, 'N1']\n",
    "    N2 = barras.loc[barra, 'N2']\n",
    "\n",
    "    # Agora vamos acessar as coordendas de cada um dos nós\n",
    "    x1, y1  = nos.loc[N1, ['X','Y']]\n",
    "    x2, y2  = nos.loc[N2, ['X','Y']]\n",
    "\n",
    "    dx = np.array([U[2*N1-2],U[2*N2-2]])\n",
    "    dy = np.array([U[2*N1-1],U[2*N2-1]])\n",
    "    y = [y1,y2]\n",
    "    x = [x1,x2]\n",
    "    plt.figure(1,figsize=(12,4))\n",
    "    plt.plot(x,y,'g:')\n",
    "    plt.plot(x+dx*e,y+dy*e,'black')\n",
    "    plt.scatter(x+dx*e,y+dy*e, s=80,marker ='o',color ='black')\n",
    "    #plt.grid(True)\n",
    "\n",
    "_=plt.title('Treliça deformada')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotagem das reações de apoio<a name=\"section_111\"></a>\n",
    "\n",
    "Como comentado na fundamentação teórica, o cálculo das reações de apoio é feito a partir do produto da matriz de rigidez pelos deslocamentos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 7.27595761e-12  2.55000000e+04  8.00000000e+03 -9.00000000e+03\n",
      "  0.00000000e+00  0.00000000e+00  8.00000000e+03 -9.00000000e+03\n",
      "  5.82076609e-11  2.32830644e-10  5.82076609e-11 -1.50000000e+04\n",
      "  0.00000000e+00  0.00000000e+00 -8.00000000e+03 -9.00000000e+03\n",
      "  0.00000000e+00 -1.16415322e-10 -8.00000000e+03 -9.00000000e+03\n",
      " -5.82076609e-11  0.00000000e+00 -5.82076609e-11  2.55000000e+04]\n"
     ]
    }
   ],
   "source": [
    "R = np.dot(Kcompleta,U)\n",
    "print(R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora, para a realização da plotagem, é necessário escolher apenas os graus de liberdade que sãoo restritos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vmjRpgilTpkBPTw8eHh64fv263BGJiACwCCaiF4iPj4epqSkaNmwIU1NTxMfHP9MmNzcXX331FXR0dPDll1/CxMQEhw4dwrlz5zB8+HBUq1ZNhuRUEaipqWHQoEE4efIkoqKiYG1tjUWLFkFXVxeTJ09GRkbGc5crzX5HRKQMkhydF6ysrERsbGy5b5eIXq2wsBCNGjV67hiw2trauHr1KtLS0rBixQrs2LEDRUVF+Oijj/Dll1/CyspKhsQVU48ePQAAx44dkzVHRZKUlPTC/aY0+52GhoYMqYmospMkKU4I8cwJ6q2LYEmSdABsB9AYQDEAfyHEypctwyKYqOKqX7/+SydBqFatGgoKCqCpqYnPPvsMM2bMQPPmzcsxYeXAIvjFcnNzsWrVKqxduxb37t2DnZ0dYmJikJeX98JltLW1cfPmzXJMSURVxYuKYGXcDlEIwF0IYQagM4DJkiS1VMJ6iaicxcfHv3IWsIKCAkyYMAHZ2dklY8QSvY73338fXl5eyMnJgbe3NxITE19aAAPArVu3cP78+XJKSESq4K2LYCHEFSFE/N//vg8gCUDTt10vEZW/oUOHlqrd8ePH0bBhwzJOQ1VdnTp1MHPmTNSrV69U7V1dXcs4ERGpEqV2jJMkSR9AWwBnnvO7cZIkxUqSFMvewUQVU2n/3MzPMCnTq/768A/ud0SkTEorgiVJqgXgJwBfCCHu/ff3Qgh/IYSVEMKKV5CIKp6cnBwUFRWVqi0/w6RM9evXL1W7OnXqlHESIlIlSimCJUmqhr8K4J1CiGBlrJOIyseFCxcwcuRIGBoa4t69Z76/PldgYGAZpyJVsnLlS/tSl8jMzISTkxNOnz5dxomISBW8dREsSZIEYBOAJCHEt28fiYjKmhACx44dQ79+/WBhYYGgoKCSsVu1tbVfuqwkSaW+Ykz0KhkZGZg0adIr29WrVw9z587F0aNH0aVLF9jY2GD//v0oLi4uh5REVBUp40qwNYBPAfSUJCnh70c/JayXiJSsqKgIQUFB6NSpE+zs7BAbG4vFixdDoVDA19cXenp6uHr16gsL4bp160JHRwe2trYc+ove2rlz52BtbY07d+4gOjr6hfudtrY2rl+/jiVLliAnJwe+vr7Izs6Go6MjWrdujS1btiA/P7+c0xNRZaeM0SGihBCSEMJCCGH59+OgMsIRkXI8evQIa9euhYmJCVxcXHD79m2sW7cO2dnZmD9//lP3ZGpoaODmzZuIi4uDlpYWNDQ0YGZmhnPnzpUUK82aNYODgwP27dsn46uiyiwyMhK2traoVq0aoqKi0LVr1xfudzdv3iyZKKNWrVqYNm0a0tPTERAQgGrVqsHNzQ2GhoZYvnw57t69K/MrI6LKgtMmE1VhN2/exOLFi6Gnp4dJkyahfv36CAoKQnJyMsaPHw9NTc0XLtuuXTt06NAB1tbWuHjxIiwsLAAAzZo1Q2RkJCwtLeHs7IwtW7aU18uhKuLAgQPo06cPGjdujOjoaJiZmZX87kX73X9Vq1YNw4YNQ0JCAsLCwmBmZobZs2dDR0cHs2bNwuXLl8vr5RBRJcUimKgKysrKwtSpU6Grq4sFCxagY8eOOH78OE6fPg1nZ2eoq6u/1frr16+PI0eOoHfv3nBzc4O3t7eSklNVt337dgwaNAitW7dGZGQkdHV132p9kiShT58+OHLkCGJjY9GvXz/4+PjAwMAAbm5uuHjxopKSE1FVwyKYqAr57bffMHToUBgZGWHdunVwcXHBhQsXcODAAdjY2OCvfqzKUatWLezfvx8ff/wxZs2ahVmzZuFtp2Gnqs3X1xcjR46Era0tIiIilD7UXvv27REYGIi0tDSMHz8egYGBaNWqFQYOHIjIyEjun0T0FBbBRJWcEALh4eGwt7dHu3btcODAAUyfPh2XLl3C1q1b0bp16zLbdvXq1bFz505MnDgR3t7eGDNmDAoLC8tse1Q5CSEwb948TJ8+HU5OTjh48CBq165dZtszNDTE999/D4VCAQ8PD5w6dQo2Njbo2rUrgoODOboJEQFgEUxUaRUWFmLXrl1o164d+vTpg8TERHh5eUGhUMDb2xvNmjUrlxzq6urw8/PDggULsHnzZri4uODx48flsm2q+IqKijBhwgR4enpi7Nix2LNnD2rUqFEu227QoAEWLlwIhUIBPz8/XLt2Dc7OzjAzM4O/vz/3UyIVxyKYqJJ58OABVq1aBWNjYwwdOhSPHz/Gpk2bkJmZidmzZ6NevXrlnkmSJCxatAgrV67Evn370Ldv31JPvEFVV35+PlxdXeHv7485c+Zg/fr1b30/+pvQ0tLCpEmTkJKSgt27d6NOnToYP3489PX14enpidu3b5d7JiKSH4tgokri2rVrWLBgAXR1dTFt2jQ0bdoUISEhSExMhJubW7ldXXuZqVOnIiAgAFFRUbCzs8O1a9fkjkQyuX//Pvr374+goCD4+PjA09NTqfekvwkNDQ0MGTIEMTExiIiIQNu2bTFv3jzo6Ohg+vTpUCgUsuYjovLFIpiogktPT8fEiROhp6eHJUuWwMbGBtHR0YiKioKjoyPU1CrWx3jYsGEICQlBUlISunXrhqysLLkjUTm7ceMGevXqhWPHjmHbtm2YMWOG3JGeIkkS7OzscOjQIZw7dw6DBw/G6tWrYWhoiE8//RTnz5+XOyIRlYOKdfYkohIxMTFwcXFBixYtsHnzZgwfPhwXL17E3r170bVrV7njvVS/fv0QHh6O69evw9raGomJiXJHonKiUCjQrVs3XLhwAXv37sWIESPkjvRSFhYW2LFjBzIyMjB16lTs3bsXbdq0gYODAyIiIjiiBFEVxiKYqAIRQuDgwYOws7NDx44dER4ejq+++gpZWVnYsGEDTE1N5Y5YatbW1jhx4gSEEOjevTtOnToldyQqY0lJSbC2tsaVK1cQFhaGgQMHyh2p1HR1dfHtt98iJycHS5cuRUJCAnr16oUOHTpg9+7dHPWEqApiEUxUATx58gTbt2+HhYUF+vfvj/T0dPj4+CAnJweenp5o0qSJ3BHfiLm5OaKjo6GtrY3evXsjLCxM7khURmJiYtC9e3cUFBTg+PHjsLGxkTvSG3n33Xcxd+5cZGVlwd/fH/fv34erqytatGgBPz8/PHz4UO6IRKQkLIKJZHTv3j34+PigefPmGDlyJIC/ZtTKyMjAjBkzynQs1fJiYGCA6OhoGBsbY+DAgQgMDJQ7EinZkSNHYGdnhzp16iA6OhqWlpZyR3prNWvWxNixY3Hx4kUEBwejUaNG+Pzzz6GrqwsPDw/cuHFD7ohE9JZYBBPJ4MqVK5gzZw50dXUxc+ZMGBkZ4eDBgzh//jw+/fRTVK9eXe6IStWoUSMcP34cXbp0wdChQ+Hn5yd3JFKSoKAg9O/fH4aGhoiOjkbz5s3ljqRU6urqGDx4ME6ePInIyEh07doVixYtgq6uLj7//HNcunRJ7ohE9IZYBBOVo+TkZIwZMwb6+vpYvnw5+vTpg7Nnz+Lo0aPo27ev7ENIlaW6devil19+wcCBA/H5559j0aJF7HRUya1fvx5DhgyBlZUVjh8/Xmlv2ykNSZLQrVs3/Pzzz0hMTMQnn3wCf39/GBsbw9XVFXFxcXJHJKLXxCKYqBycPHkSgwYNgpmZGXbu3InRo0cjJSUFe/bsQYcOHeSOV240NTXx008/YeTIkfDw8MDUqVNRXFwsdyx6TUIIeHp6YsKECejbty/Cw8Px7rvvyh2r3LRs2bJkgpqZM2fi0KFDsLKyQq9evRAWFsYvd0SVBItgojJSXFyMkJAQdOvWDdbW1oiMjMSCBQuQnZ2NNWvWwMjISO6IstDQ0MDmzZvh7u6O1atXY/jw4Xjy5IncsaiUiouL4e7ujnnz5mH48OHYt28ftLS05I4li6ZNm+Kbb76BQqHA8uXLkZycDAcHB1haWiIgIAAFBQVyRySil2ARTKRk+fn52LRpE1q2bIlBgwbhjz/+wKpVq6BQKLBo0SK89957ckeUnZqaGry9veHl5YVdu3bhww8/xIMHD+SORa9QUFCAUaNG4bvvvsPUqVOxbds2VKtWTe5Ysqtbty6+/PJLZGZmYsuWLSgsLMSnn36K5s2bw9fXF3l5eXJHJKLnYBFMpCR37tyBl5cX9PX1MWbMGGhpaWHXrl1IT0/HlClT8M4778gdsUKRJAmzZ8/Ghg0bcPjwYdjb2+PWrVtyx6IXePjwIQYPHowdO3Zg8eLF8PX1rXCzFcqtevXqGDVqFC5cuID9+/fDwMAA06dPh66uLubNm4erV6/KHZGI/oVHMKK39Mcff2DmzJnQ0dHBnDlzYG5ujvDwcMTFxcHV1RUaGhpyR6zQxowZgx9//BFxcXGwsbHB5cuX5Y5E/3Hnzh188MEHOHjwINasWYP58+dX6U6cb0tNTQ0DBgzA8ePHcerUKdjZ2WHZsmXQ09PD+PHjkZqaKndEIgKLYKI39vvvv2PkyJEwMDCAr68vHB0dER8fj8OHD6N3794sEl6Dk5MTDh06hOzsbFhbWyMtLU3uSPS3P//8E7a2tjhz5gwCAwMxceJEuSNVKp07d8ZPP/2E5ORkjBo1Ctu2bYOpqSmcnZ1x+vRpueMRqTQWwUSvQQiB48ePo3///jA3N0dQUBAmTZqE9PR07Ny5E23btpU7YqXVs2dPHD16FA8ePIC1tTV+++03uSOpvIyMDFhbWyMjIwOhoaEYMmSI3JEqrRYtWmDdunXIzs7G3LlzERERgS5dusDGxgYHDhzgKClEMmARXIkIITj0jkyKiooQFBSETp06oUePHoiJicHixYuhUCiwcuVK6Ovryx2xSrCyskJUVBQ0NTVha2uLY8eOyR1JZZ07dw7W1ta4c+cOfv31V9jb28sdqUpo1KgRlixZgpycHPj6+iI7OxsDBw6Eubk5tmzZgvz8fLkjqiSeX1UTi+BKoqCgANra2tiyZYvcUVTKo0ePsG7dOpiYmMDFxQW3bt3C2rVrkZ2djfnz56N+/fpyR6xyTExMEB0djWbNmsHBwQEhISFyR1I5UVFRsLW1hYaGBiIjI9GpUye5I1U5tWrVwrRp05Ceno6AgABoaGjAzc0NhoaG8Pb2xt27d+WOqFLCw8NRo0YN3L59W+4oVI5YBFcShw8fxr1797BmzRq5o6iEmzdvYvHixdDT08PEiROhra2NoKAgpKSkYMKECdDU1JQ7YpXWrFkzREZGwtLSEk5OTvzyV45CQ0Nhb2+PRo0aITo6Gi1btpQ7UpVWrVo1DBs2DAkJCQgLC4OZmRlmzZoFXV1dzJo1ix1Fy4m/vz8KCwuxZ88euaNQOWIRXEmsW7cOxcXFSExMRE5OjtxxqqysrCxMmzYNurq6WLBgATp06IBjx47hzJkzcHZ2hrq6utwRVUb9+vVx5MgR9OrVC25ubvD29pY7UpW3Y8cOfPjhh2jVqhWioqKgp6cndySVIUkS+vTpgyNHjiA2NhZ9+/aFj48PDAwM4ObmhosXL8odscp68OABQkNDIYTghSYVwyK4Erh37x6OHDlS8vOOHTtkTFP5xMfHw9TUFA0bNoSpqSni4+OfafPbb79h6NChMDIywpo1a+Di4oILFy4gNDQUtra2HOlBJrVq1cL+/fsxZMgQzJo1C7Nnz+Z9e2XE19cXI0aMgK2tLY4ePYqGDRvKHUlltW/fHoGBgUhLS8P48eMRGBiIVq1aYeDAgYiMjHzhZ6A0xzp6VnBwcMlQlqmpqcjMzJQ5EZWbf24GL89H+/btBZXepk2bxDvvvCMACABCV1dXFBcXyx2rwisoKBDa2tol79u/H9ra2uLJkyciPDxc2NvbCwCiVq1awt3dXSgUCrmjVxi2trbC1tZW7hiisLBQTJw4UQAQo0ePFgUFBXJHeqWK8t69SnFxsZg3b54AIJycnMSjR4/kjlRp3rvycv36deHh4SHq168vAIjOnTuL4OBgUVhYKIR49bGuMnxe5NSlS5eS96tGjRpiwYIFckciJQMQK55TjyrlSrAkSZslSbomSdLvylgfPW3NmjVPTSl78+ZNJCQkyJiocmjUqNELZyC7desWNDU1YW9vjwsXLsDLyws5OTlYsWIFdHR0yjkpvYq6ulXsr84AACAASURBVDr8/PywYMECbNq0CS4uLnj8+LHcsSq9oqIiTJw4EUuXLsWYMWOwZ88e1KxZU+5Y9B8NGjTAwoULoVAosHr1aly9ehVOTk5o2bIl/P398d577730WNeoUaNyTlx5XLly5akr5vn5+di4cSP/4qQilHU7xFYADkpaF/1LTk4OEhMTn3ru8ePH2Lhx4wvb29nZwczMDK1atcLKlSsBAB4eHmjatCksLS1haWmJgwcPPnd5fX19mJubw9LSElZWViXP37p1C/b29jA2Noa9vX1JD9qtW7fi888/f2Y9Hh4e0NLSwrVr10qeq1Wr1uu9+LcQHx//yil4i4qKsHDhQmRlZWH27NmoV69eOaWjNyFJEhYtWoSVK1di37596Nu3L+7duyd3rEorPz8frq6uWL9+PebMmQN/f3/e817BaWlpYfLkyUhNTcXu3btRu3ZtjB8//pUjGty6dQvnz58vp5SVS0BAwDPTf9+9excxMTHPbc9zbNWilCJYCHECwMsrDnoj27dvf2YQ9aKiIgQEBKCwsPCZ9hoaGvDx8UFSUhJOnz4NPz+/kg4V06dPR0JCAhISEtCvX78XbvPo0aNISEhAbGxsyXNeXl7o1asX0tLS0KtXL3h5eb0ye4MGDeDj41Pal6pUQ4cOLVW7PXv2oEaNGmWchpRp6tSpCAgIQFRUFOzs7J46CVDp3L9/HwMGDEBQUBBWrFgBT09P3vdeiWhoaGDIkCGIiYlBs2bNSrWMq6trGaeqnNavX49Hjx499dzDhw+xYcOG57bnObZqKbeOcZIkjZMkKVaSpNjr16+X12YrvZo1a6Jx48aoVq0agL++6TVu3BhGRkYoKCh4pn2TJk3Qrl07AEDt2rVhZmamlCF2QkJCMHLkSADAyJEjsW/fvmfahIaGokuXLrhx4wYAwM3NDbt3737lFdmycPPmzVK1475YOQ0bNgwhISFISkpCt27dkJ2dLXekSuPGjRvo1asXjh49iq1bt8Ld3V3uSPSGJEkq9W1BPNY9SwgBXV1dNG3aFFpaWgD+KnJ1dHRQp06d5y7Dc2zVUm5FsBDCXwhhJYSwYq/j0nN3d0d2djZMTU0B/HVvZEhICOLi4l45Vm1WVhZ+++23koHuV69eDQsLC7i5ub3wz2f/DNPTvn17+Pv7lzx/9epVNGnSBMBfB4H/Xn3bu3cvvLy8cPDgQTRo0ADAXwW7m5tbyZ+LysvZs2dLfWLgvlh59evXD+Hh4bh+/Tq6du36zG1D9KycnBx0794dFy5cQHBwcMlJlyqnxMREPHnypFRt/zku0/+TJAkRERGIiYkpuQe4Xr16yM7OLtUVVlU9x1YlHCKtisrLy4OzszN8fX1Rp04dTJw4ERkZGUhISECTJk1eePUnOjoa8fHxOHToEPz8/HDixIlXbuvo0aP45ptvEBoainffffep302dOhXbtm0r83s3hRA4ePAgevTo8VqzW73zzjs4ePAgO0FUUtbW1jhx4gSEEOjevTtOnTold6QKKzk5GdbW1sjNzUVYWBgcHR3ljkRvQAiByMhIDBw4EK1bty71NMtqamrYvXv3c2+jo9enaufYqopFcBVUUFAAZ2dnDBs2DE5OTgD+GilBXV0dampqGDt2LM6ePfvcZd9//30AwHvvvYfBgweXtGvUqBGuXLkC4K/etO+9917JMoaGhrh//z5SU1OfWV+9evUwdOjQMhuA/MmTJ9i+fTssLCzQv39/ZGRkwMfHB7m5udDW1n7pspqamvjzzz/Rv39/WFhYYPv27aW+qkIVh7m5OaKjo6GtrY3evXsjLCxM7kgVTkxMDLp164b8/HwcP34cNjY2ckei11RUVITg4GB07doVNjY2OH36NDw8PPDHH3+88linpaWFwsJCuLq6okWLFvDz88PDhw/LKXnVo0rn2KpOWUOk7QJwCoCJJEl/SJI0WhnrpdcnhMDo0aNhZmaGGTNmlDz/z4cL+OvPKq1bt35m2QcPHuD+/fsl/z58+HBJO0dHR2zbtg0AsG3bNnz44Ycly+np6SE4OBgjRox47p+kZ8yYgfXr1yv1CsS9e/fg4+OD5s2bl/xJd/v27bh06RJmzJiB2rVr4+rVqy88OWhra+PevXu4dOkStm/fDuCv+7AMDQ3h4+PDb9WVjIGBAaKjo2FsbIyBAwciMDBQ7kgVxpEjR2BnZ4fatWsjOjoalpaWckei1/D48WP4+/vDzMwMzs7OuHbtGvz8/JCdnY2FCxeiQYMGrzzW3b17FxcvXkRwcDAaNWqEzz//HLq6uvDw8Ci5v5RKR1XOsSrjeYMHl/WDk2W8PnNzcwFA1K1bV5w5c+aF7SIjIwUAYW5uLtq0aSPatGkjQkNDxfDhw0Xr1q2Fubm5GDhwoMjNzRVCCHH58mXRt29fIYQQGRkZwsLCQlhYWIiWLVuKJUuWlKz3xo0bomfPnsLIyEj07NlT3Lx5UwghxJYtW8TkyZOFEELEx8cLMzMzkZ6eLhYuXCi8vb1Llp8+fbr4a3d7O7m5ueKrr74SdevWFQCEnZ2dOHjw4EsnD4mLixNaWlpCQ0NDmJmZiXPnzj3Tpri4WBw8eFDY2dmVvM9fffVVyfukqirbpAV37twRNjY2QpIk4efnJ2uWivDe/fjjj6J69eqidevW4vLly7JmeR0V4b2T282bN8WSJUvEe++9JwCI9u3bi927d7904ovSHusiIyPFwIEDBQChqakpJk+eLDIyMsry5VRoubm5QlNTUwAQDRo0eGnbqn6OrarwgskyWARXEqUtgquqpKQkMXr0aFG9enWhpqYmXFxcxNmzZ0u9/OucVM+ePStcXFyEmpqaqF69uhg9erRISkp6w+SVW2UsRh4+fFhygvfw8JBtdkW537v169cLSZJE165dxa1bt2TL8Sbkfu/klJ2dLb744ouSWUIdHBxEREREqffj13nvEhMThZubm6hWrZpQU1MTH3/8sYiNjX2L9JXT6xTBVDm9qAjmPcFUoZ08eRKDBg2CmZkZdu7cidGjRyMlJQV79uxBhw4dymSbHTp0wJ49e5CSkoLRo0dj586dMDMzw6BBgxAdHV0m2yTl0dTULBn5wMPDA1OnTn1mrO2qTAgBT09PjB8/Hg4ODggPD3+mMw1VPOfOncPw4cNhaGiI1atXw8nJCefOncOhQ4dgZ2dXJuM4t2zZEps2bUJmZiZmzpyJQ4cOwcrKCr169UJYWBg7DFOVxyKYKpzi4mKEhISgW7dusLa2RmRkJBYsWACFQoE1a9bAyMioXHIYGRlhzZo1UCgUWLBgASIjI0syhYSEqFRhVdloaGhg8+bNcHd3x+rVqzF8+HCV6PRYXFwMd3d3zJs3r2Qs5X/GP6WKRwiBiIgIODg4wNLSEvv27cPUqVORkZFR0uG3PDRt2hTffPMNFAoFli9fjuTk5JJMAQEBzx2TnqgqYBFMFUZ+fj42bdqEli1bYtCgQbh8+TJWrVoFhUKBRYsWyTamb8OGDbFo0SIoFAqsWrUKubm5GDRoEFq2bImNGzeWeogiKl9qamrw9vaGl5cXdu3ahQ8//BAPHjyQO1aZKSgowKhRo/Ddd99hypQp2L59e8kkO1SxFBYWYvfu3SVXXRMSEuDp6YmcnBx8++230NXVlSVX3bp18eWXXyIzMxNbtmxBYWEhPv30UzRv3hy+vr7Iy8uTJRdRWWERTLK7c+cOvLy8oK+vjzFjxkBLSwu7du1CWloapkyZgnfeeUfuiAD+GlN4ypQpSEtLw65du6ClpYWxY8dCX18fXl5euHPnjtwR6T8kScLs2bPh7++Pw4cPw97evkrOrvTo0SM4OTlhx44d+Prrr7Fy5UqoqfHwXtE8fPgQfn5+aNGiBVxdXZGXlwd/f39kZWVhzpw5Fea2lerVq2PUqFG4cOEC9u/fDwMDA0yfPh26urqYN28erl69KndEIqXgUZJk88cff2DmzJnQ0dHBnDlzYG5ujvDwcMTFxcHV1RUaGhpyR3wuDQ0NuLq6Ii4uDuHh4bCwsMCcOXOgo6MDd3d35OTkyB2R/mPs2LH48ccfERcXBxsbG6VMc1pR3LlzBx988AFCQ0OxZs0a/O9//yuT+0fpzd24cQMeHh7Q1dXF559/jkaNGiE4OBgXL17E2LFjUbNmTbkjPpeamhoGDBiA48eP49SpU7Czs8OyZcugp6eH8ePHP3fcWqLKhEUwlbvff/8dI0eOhIGBAXx9feHo6Ij4+HgcPnwYvXv3rjQncEmSSiZn+O233+Do6IiVK1fC0NAQI0eOxO+//y53RPoXJycnHDp0CNnZ2ejWrRvS0tLkjvTW/vzzT/To0QOnT59GYGAgJk6cKHck+pdLly6VjMm7aNEidO3aFZGRkTh58iQGDx4MdXV1uSOWWufOnfHTTz8hOTkZo0aNwrZt22BqagpnZ2ecOXNG7nhEb4RFMJULIQSOHz+O/v37w9zcHEFBQZg0aRLS09Oxc+dOtG3bVu6Ib8XS0hI7d+5Eeno6Jk+ejKCgIJibm6N///44duwYe1lXED179sTRo0eRl5eHbt264bfffpM70hu7dOkSrK2tkZaWhgMHDmDIkCFyR6K/xcXF4eOPP4axsTH8/f3xySefIDExET///DO6detWab7oP0+LFi2wbt06ZGdnY+7cuYiIiEDnzp1hY2ODAwcOsMMwVSosgqlMFRUVISgoCJ06dUKPHj0QExODxYsXQ6FQYOXKldDX15c7olLp6+vD19cXCoUCixcvRkxMDOzs7NCpUycEBQWhqKhI7ogqz8rKClFRUahRowZsbW1x7NgxuSO9tvPnz8Pa2hp37txBREQE+vTpI3cklSeEQFhYGHr16gUrKyv88ssvmDlzJrKysko6/FYljRo1wpIlS5CTkwNfX19kZ2dj4MCBMDc3x9atW1ViNBaq/FgEU5l49OgR1q1bBxMTE7i4uOD27dtYu3YtsrOzMX/+fNSvX1/uiGWqfv36mD9/PrKzs7F27Vrcvn0bLi4uMDExwdq1a/Ho0SO5I6o0ExMTnDx5Es2aNYODgwNCQkLkjlRqUVFRsLGxgbq6OiIjI9GpUye5I6m0goICBAQEwNLSEg4ODkhOToa3tzcUCgW++eYbvP/++3JHLFO1atXCtGnTkJ6ejoCAAGhoaOCzzz6DgYEBvL29cffuXbkjEr0Qi2BSqps3b2Lx4sXQ09PDxIkToa2tjaCgICQnJ2PChAnQ1NSUO2K50tTUxIQJE5CcnIygoCBoa2tj0qRJ0NPTw+LFi3Hz5k25I6qsZs2aITIyEpaWlnBycsKWLVvkjvRKoaGhsLe3R6NGjRAdHV3lri5WJnl5efD19UXz5s3x6aeforCwEFu2bCmZeKJu3bpyRyxX1apVw7Bhw5CQkICwsDCYmZlh1qxZ0NXVxezZs5Gbmyt3RKJnsAgmpcjKysK0adOgq6uLBQsWoEOHDjh27BjOnDkDZ2fnStUBpCyoq6uXdCA5duwYOnbsiAULFkBXVxfTpk1DVlaW3BFVUv369XHkyBH06tULbm5u8Pb2ljvSC+3YsQMffvghWrVqhaioKOjp6ckdSSVdvXoV8+bNg46ODqZPnw4DAwPs378fFy5cwKhRo1C9enW5I8pKkiT06dMHR44cQWxsLPr27YsVK1ZAX18fbm5uuHjxotwRiUqwCKa38ttvv2Ho0KEls6u5uLjgwoULCA0Nha2tbaXuAFIWJEmCra0tDhw4gAsXLsDFxaVkFryhQ4dW6o5alVWtWrWwf/9+DBkyBLNmzcLs2bMrXEfGlStXYsSIEbC1tUVERIRsE8eostTUVIwfPx56enpYtmwZevbsiVOnTuH48eMYMGAAx2V+jvbt2yMwMBBpaWkYP348AgMD0apVKzg6OiIqKqrCfc5I9fBTS69NCIEjR46gT58+aNeuHQ4cOIAvvvgCmZmZ2Lp1K1q3bi13xEqhdevW2Lp1KzIzMzF9+nQcOHAA7dq1Q58+fRAeHs4TRDmqUaMGfvjhB0yYMAHLly/H2LFjUVhYKHcsCCHwv//9D1988QWcnJwQGhqKOnXqyB1LpZw+fRpOTk4wNTXFtm3bMGrUKCQnJ+Onn35C586d5Y5XKRgaGuL777+HQqGAh4cHTp48ie7du6Nr167Yu3cvOwyTbFgEU6kVFhZi165daNeuHezt7XHhwgV4eXlBoVBgxYoVaNasmdwRK6VmzZqVdKTx8vLChQsXSr5g7Nq1q0IUY6pAXV29ZLKJTZs2YciQIXj8+LFseYqKijBx4kQsWbIEY8aMwZ49eyrspApVTXFxMfbv3w8bGxt06dIFR48exdy5c5GdnY1169ahRYsWckeslBo0aICFCxdCoVDAz88PV69ehZOTE1q2bIkNGzbI+nkj1cQimF7pwYMH+P7772FsbIyhQ4fi8ePH2LhxI7KysjB79mzUq1dP7ohVQr169TB79uySIZUeP36MoUOHwtjYGKtWrcKDBw/kjljlSZJUMu3w3r170a9fP9y7d6/cc+Tn58PV1RXr16/HV199BX9/f5W/r7485OfnY8uWLWjdujUcHR2RnZ0NX19f5OTkYMmSJWjUqJHcEasELS0tTJo0Campqdi9ezdq166NcePGQV9fH56enrh9+7bcEUlFsAimF7p27VpJ562pU6eiadOmCAkJQWJiIkaPHo0aNWrIHbFKqlGjBtzc3JCYmIiQkBA0bdr0qU6H165dkztilTd16lQEBAQgMjISdnZ25fqe5+XlYcCAAQgKCsKKFSuwbNky3ltfxu7evQtvb28YGhrCzc0N1apVQ0BAANLT0zFt2jTUqlVL7ohVkoaGBoYMGYKYmBhERESgbdu2JZ0OZ8yYAYVCIXdEquJYBNMz0tPTnxrGq3v37oiKikJUVBQcHR3ZAaScqKmplXQgiY6Oho2NDZYsWVIy/Fx6errcEau0YcOGISQkBElJSejWrRuys7PLfJs3btxAr169cPToUWzZsgXu7u5lvk1VdvnyZcyaNQs6OjqYNWsWzMzMEBYWhoSEBAwbNgzVqlWTO6JKkCQJdnZ2OHToEBISEjB48GB8//33JcPPnT9/Xu6IVEWxmqESMTExJRM6bNq0CcOHD0dSUhL27dsHa2trueOptH86kFy8eBHDhw/H5s2b0aJFC7i4uCAmJkbueFVWv379EB4ejuvXr8Pa2hqJiYlltq2cnBx0794d586dQ3BwMEaNGlVm21J1Fy9ehJubGwwMDODj44N+/fohNja2pMMvr7zLp02bNtixYwcyMjIwZcoU7N27F23atEHfvn1x9OhRdhgmpWIRrOKEEDh06BDs7OzQsWNHhIeHY9asWcjKysKGDRtgamoqd0T6F1NTU2zYsAFZWVn46quvEB4ejo4dO5ZcReEJQvmsra1x4sQJFBcXo3v37jh9+rTSt5GcnAxra2vk5uYiLCwMjo6OSt+GqhNCIDIyEgMHDkSrVq0QGBiI8ePHIy0tDYGBgWjfvr3cEelfdHV18e233yInJwdLly5FfHw8evbsiQ4dOmDPnj3sMExKwSJYRT158gTbt2+HhYUF+vXrh/T0dPj4+CAnJwfLli1DkyZN5I5IL9GkSRN4enoiJycHPj4+SE9PR79+/WBhYYHt27fjyZMnckesUszNzREVFQVtbW306tULYWFhSlt3TEwMunXrhvz8fBw7dgy2trZKWzf9NcpGcHAwunbtChsbG5w6dQoeHh5QKBT4/vvvYWhoKHdEeol33323ZGQOf39/3Lt3Dx9//DFMTEywZs0aPHz4UO6IVIlVmSL4l19+gYmJCYyMjODl5fXM74UQmDp1KoyMjGBhYYH4+PhXLtujRw/ExsY+sy59fX04OzuX/BwUFFRp/nR5//59fPvtt2jevDlGjhwJANi2bRsyMjIwY8YM1K5dW+aE9Dpq166NGTNmICMjA9u3bwcAjBw5Es2bN8e3336L+/fvy5yw6jA0NERUVBSMjY0xcOBABAYGvvU6f/31V/Ts2RO1a9dGVFQU2rZtq4SkBACPHz+Gv78/zMzM4OzsjKtXr8LPzw8KhQILFy5EgwYN5I5Ir6FmzZoYO3YskpKSEBwcjIYNG2Ly5MnQ09PDokWLcOPGDbkjUiVUJYrgoqIiTJ48GYcOHcLFixexa9euZ6ZmPHToENLS0pCWlgZ/f39MnDix1Ms+T2xsbJneH6hsV65cwZw5c6CjowN3d3cYGRnh4MGDOH/+PEaMGKHyU31WdtWrVy/pQHLw4EEYGRnB3d0dOjo6mDNnDq5cuSJ3xCqhcePGOHbsGDp37oyhQ4dizZo1b7yun376Cf369YO+vj6io6NhbGysxKSq6/bt2/D09IS+vj7Gjx+POnXqYPfu3UhNTcWkSZOgpaUld0R6C+rq6hg8eDBOnTqFEydOoEuXLvDw8ICuri6mTJmCzMxMuSNSJVIliuCzZ8/CyMgIhoaGqF69OlxdXRESEvJUm5CQEIwYMQKSJKFz5864c+cOrly5Uqpli4uLMXLkSMyfP7/kuZkzZ8LT07NcXt/bSElJwdixY6Gvr4/ly5fD3t4eZ86cwdGjR9G3b192AKliJEkq6UBy9uxZ9OnTB8uXL4e+vj7Gjh2LlJQUuSNWevXq1UNYWBgGDBiAyZMnY9GiRa99L/aGDRswZMgQWFlZ4cSJE3j//ffLKK3qUCgUmD59OnR0dDBv3jy0bdsWERERiImJwZAhQ6ChoSF3RFIiSZLQvXt3/Pzzz0hMTCwZV9vIyAiurq6Ii4uTOyJVAlWiCL58+TJ0dHRKfm7WrBkuX75cqjavWrawsBDDhg1DixYtsGTJkpLnhwwZgvj4+Ao7TNXJkycxaNAgmJmZISAgAKNHj0ZKSgp+/PFHdOzYUe54VA7+6UCSkpKC0aNHIyAgAGZmZhg0aBBOnjwpd7xKTVNTE8HBwRg5ciQ8PDwwdepUFBcXv3I5IQSWLVuGcePG4YMPPsDhw4fx7rvvlkPiquv8+fP49NNPYWhoiNWrV2Pw4MFISEgo6fDLL/pVX8uWLbF582ZkZmbC3d0dhw4dgpWVFXr37o2wsDB2GKYXqhJF8PN28P8e+F7U5lXLjh8/Hq1bt8a8efOeaqOuro4vv/wSy5Yte9PYSldcXIyff/4Z3bp1g7W1NSIjIzF//nxkZ2djzZo1MDIykjsiycDIyAhr1qxBdnY2/ve//yEyMhLW1tbo1q0bfv7551IVb/QsDQ0NbN68GTNmzMDq1asxfPjwl3ZILC4uhru7O+bOnYuhQ4ciJCQE77zzTjkmrjqEEIiIiICDgwPatGmDvXv3YurUqcjIyMCOHTvQpk0buSOSDJo2bYrly5dDoVBg+fLlSEpKgoODA9q2bYudO3eioKBA7ohU0Qghyv3Rvn17oUwnT54Uffr0KfnZ09NTeHp6PtVm3Lhx4ocffij5uUWLFiI3N/ely9ra2ooJEyaIXr16iUePHpW00dPTE9evXxdPnjwRRkZGwsfHR4wcOVKpr+m/TE1NBQChoaEhPvzwQ3H58uWS3z1+/Fhs3LixpI2enp5YtWqVyMvLK9NMlUVKSoqoW7eu0NTUFLa2tiIlJUXuSLLKy8sTq1atEnp6egKAMDU1FRs3bhSPHz9+ql1cXJzQ1NQUGhoawsTERMTFxcmUuGIrLi4Wy5YtEwCEg4ODyMvLEydOnBDVqlUTampqonHjxiIiIkKMGDFCABBTpkwRRUVFcseusF623xUUFIjAwEDRvn17AUC89957YunSpeLWrVsyJq44eKx72uPHj8XmzZtFy5YtBQChq6srfH19xf37959qFx8fL9TV1QUAUbNmzafOr1Q1AIgVz6lHlVLUAnAAkAIgHcBXr2qv7CK4oKBAGBgYiEuXLon8/HxhYWEhfv/996faHDhwQDg4OIji4mJx6tQp0aFDh1cua2trK2JiYoSPj48YMGCAKCgoEEL8fxEshBB+fn5CR0fnuUVwUlKSmDlzpoiMjBSFhYVv9NqKiopEnz59BIBnHnZ2dmLZsmWicePGAoCwtLQUP/zwQ0lOVVdYWCiMjIye+94ZGRm98f+TqqKgoEDs2rVLtG3bVgAQjRs3Fl5eXuL69etCW1v7ue+btrY2968X8Pf3F2pqakJNTe257x0AsXDhQlFcXCx31AqpoKDghfvdu+++K1auXCkMDAwEAGFsbCz8/f2fujihynise7mioiKxf/9+0b1795L9ad68eSI3N/eF59c+ffrwy2oVUmZFMAB1ABkADAFUB3AOQMuXLaPsIlgIIUJDQ4WxsbEwNDQUS5YsEUIIsXbtWrF27VohxF9XayZNmiQMDQ1F69atRUxMzEuXFeL/i2AhhFiwYIFwdXUVRUVFTxXBjx8/Fk2aNHluEbxs2TKhpqYmateuLWrXri2GDBki9u7d+1pXaF/0Af33w97eXhw+fJgn1/940Unh3ycH+uuzER4eLuzt7V+5r/1TCNPzVa9e/aXvnaamptwRK6wXFcD/fnTu3FkEBwerfFH3XzzWld6pU6eEk5OTkCTppV9Y/ymEqWp4UREsibe8YVySpC4APIQQH/z98xwAEEK88GZZKysr8bzxd9/EJ598guPHjytlXcp2//59PHz48Kl7LuvUqYP8/Hx06tQJw4YNg6OjIxo3bvzc5XNzc9G0adNXbufKlSsvXIeqSk1NhYmJySvbpaeno3nz5uWQqHL44YcfMGzYsFe2O3fuHCwsLMohUeURGRkJGxubV7Y7deoUOnfuXA6JKo/4+PhSzdiWkJDA+33/g8e6N1PazyvPr1WDJElxQgirZ55XQhH8EQAHIcSYv3/+FEAnIcTnL1pGmUVw48aNcfXqVaWsSy55eXnP7SAzbtw4bNiw4ZXLN2nSBC1atCiLaJVWQkIC7t69+8p29erV40n1X86ePYtHjx69sp2WlhY6dOhQDokqj5MnT5aq40316tXRpUuXYcf98QAACQxJREFUckhUeXC/e3M81r2Z1NTUUo2fPn78eKxbt64cElFZelERrIyBE583/swzlbUkSeMAjAP+mhNcWUxMTHDz5k2lrU+ZiouL/33bCIC/hlYSQqBx48ZwdXWFs7PzCwdv/+OPP0q1nfz8fKXkrUpKO20w37unlbb3NKdlflZRUVGp2hUWFpZxksqH+92b47HuzZT2/VAoFGWchOSkjCL4DwA6//q5GYDc/zYSQvgD8Af+uhKshO0CQIW9FQIAvLy8MHfuXNSuXRv5+fmwsLDA8OHD4ejoCAMDg1cu36xZs1Jtx8XFhd9U/6NHjx6l2jc6d+6MiIiIckhUOZiampZqQg1jY2McO3as7ANVIk2aNMGff/75ynb/zDpH/4/73Zvjse7NlPYvrcq8aEcVjzJuh9AAkAqgF4DLAGIADBVCvHBOYWXeDlGRnT17FkuXLsXHH/9fe/cfWtddh3H8eZpElkzHTMt0aYudS40ZQ90YY3MgxG6hmaNVQVRQCgrLH/6YouhGwf+UgaITFKVss4OVidTJhi7edVPIP1W0dd06k3qDwpYY25liFQOOsY9/3DMIbdLce5Lc7/32vF9Qmntv0jx8enLOk3u/95yPa2xsrOWT4rMmuDzWyZXT7NpM1gRfiDXB5bHdlce+rhyOr9WyYWuCi3/8TkkPqHGmiIcj4psX+/yqlOD18MZVpVYyOjqqWq3WxkT52Llz50Wv6Dc4OKh6vd7GRHnYvHmzzp49u+Lj/f39HbsEKbW+vr6Lrm3t7e3V4uJiGxPlg+2uPPZ15XB8rY6VSvC6XDEuIp6KiHdFxLWrFWC0ZmJiQqOjo8s+Njo6qomJiTYnysf09PSKV8kbHBzU9PR0mxPl4fTp0+rv71/2sf7+/uzfiLqRzp07p97e3mUf6+3tbeoNTFXFdlce+7pyOL7ikrhs8qVs06ZNqtVqmpub0/j4uMbGxjQ+Pq75+XnVajVt2sR/4Uq6urpUr9d16tQpjYyMaGhoSCMjI5qZmVG9XldXV1fqiB2pu7tbCwsLOnbsmIaHh7VlyxYNDw/rxIkTWlhYUHf3eryV4NLU09OjxcVFTU5OamBgQH19fRoYGNDRo0e1uLionp6e1BE7FttdeezryuH4inVZDtEqlkMAAACgHTZ0OQQAAACQE0owAAAAKocSDAAAgMqhBAMAAKByKMEAAACoHEowAAAAKocSDAAAgMqhBAMAAKByKMEAAACoHEowAAAAKocSDAAAgMqhBAMAAKByKMEAAACoHEowAAAAKocSDAAAgMqhBAMAAKByKMEAAACoHEowAAAAKocSDAAAgMqhBAMAAKByKMEAAACoHEowAAAAKocSDAAAgMqhBAMAAKByKMEAAACoHEowAAAAKmdNJdj2x2y/aPt12zetVygAAABgI631meCTkj4qaXIdsgAAAABt0b2WL46IKUmyvT5pAAAAgDZYUwluhe27Jd1d3Pyf7ZPt+t6XmC2S/pk6RKaYXTnMrTxmVx6zK4/ZlcPcyuv02b1juTtXLcG2n5H09mUe2h8RTzT73SPigKQDxb/5x4hgDXEJzK48ZlcOcyuP2ZXH7MpjduUwt/Jynd2qJTgibm9HEAAAAKBdOEUaAAAAKmetp0j7iO1ZSbdK+pXtWpNfemAt37fimF15zK4c5lYesyuP2ZXH7MphbuVlOTtHROoMAAAAQFuxHAIAAACVQwkGAABA5SQrwba/bXva9vO2f2H7ylRZcmB7t+1Ttmds35s6Ty5sb7f9W9tTxSW+70mdKTe2u2z/yfYvU2fJie0rbR8u9nNTtm9NnSkHtr9c/KyetP2Y7ctSZ+pUth+2fWbpefdt99s+Yrte/P3WlBk71Qqzo5c0YbnZLXnsq7bD9pYU2VqV8pngI5Kuj4j3SPqLpPsSZulotrsk/VDSmKTrJH3S9nVpU2XjNUlfiYhhSbdI+hyza9k9kqZSh8jQ9yX9OiLeLem9Yoarsr1V0hcl3RQR10vqkvSJtKk62kFJu8+7715Jz0bETknPFrdxoYO6cHb0kuYc1IWzk+3tku6Q9FK7A5WVrARHxNMR8Vpx83eStqXKkoGbJc1ExF8j4lVJP5W0N3GmLETEfEQcLz7+jxpFZGvaVPmwvU3ShyQ9mDpLTmxfIekDkh6SpIh4NSL+lTZVNrol9drultQn6e+J83SsiJiUdPa8u/dKeqT4+BFJH25rqEwsNzt6SXNW2O4k6XuSviYpmzMudMqa4M9ImkgdooNtlfTyktuzosi1zPYOSTdI+n3aJFl5QI2d2uupg2TmnZJekfSTYinJg7YvTx2q00XEnKTvqPFM0rykcxHxdNpU2XlbRMxLjScBJF2VOE+u6CUtsL1H0lxEnEidpRUbWoJtP1Os6zr/z94ln7NfjZesD21klsx5mfuy+U2rE9h+s6SfS/pSRPw7dZ4c2L5L0pmIOJY6S4a6Jd0o6UcRcYOk/4qXpVdVrF/dK+kaSQOSLrf9qbSpUDX0ktbY7pO0X9I3Umdp1aqXTV6L1S65bHufpLsk7QpOWHwxs5K2L7m9TbxE2DTbPWoU4EMR8XjqPBm5TdIe23dKukzSFbYfjQhKyepmJc1GxBuvOhwWJbgZt0v6W0S8Ikm2H5f0fkmPJk2Vl9O2r46IedtXSzqTOlBO6CWlXKvGL64nbEuNjnLc9s0R8Y+kyVaR8uwQuyV9XdKeiFhMlSMTf5C00/Y1tt+kxhtFnkycKQtu/EQ+JGkqIr6bOk9OIuK+iNgWETvU2OZ+QwFuTrHjf9n2UHHXLkl/ThgpFy9JusV2X/Gzu0u8obBVT0raV3y8T9ITCbNkhV5STkS8EBFXRcSO4ngxK+nGTi/AUto1wT+Q9BZJR2w/Z/vHCbN0tGKh/ucl1dQ4IPwsIl5Mmyobt0n6tKQPFtvZc8Uzm8BG+4KkQ7afl/Q+Sd9KnKfjFc+cH5Z0XNILahyjsrwcazvYfkzSUUlDtmdtf1bS/ZLusF1X453696fM2KlWmB29pAkrzC5LXDYZAAAAldMpZ4cAAAAA2oYSDAAAgMqhBAMAAKByKMEAAACoHEowAAAAKocSDAAAgMqhBAMAAKBy/g8+q70cDmmRvgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1,figsize=(12,4))\n",
    "plt.xlim(-2,15)\n",
    "plt.ylim(-1,5)\n",
    "\n",
    "# Plotagem dos apoios e das forças\n",
    "for no in nos.index:\n",
    "    X,Y,RX,RY= nos.loc[no,['X','Y','RX','RY']]\n",
    "\n",
    "    gl1 = 2*no - 1\n",
    "    gl2 = 2*no \n",
    "    Fx = R[gl1-1]\n",
    "    Fy = R[gl2-1]\n",
    "\n",
    "    # Se RX restrito aplica sobre gl de X\n",
    "    if RX == 1:\n",
    "        plt.arrow(X-1.5,Y,1,0,width =0.05,color='k')\n",
    "        plt.text(X-1.5,Y,'{:.2f}kN'.format(Fx/1000),va='bottom')\n",
    "    if RY == 1:\n",
    "        plt.arrow(X,Y,0,1,width =0.05,color='k')\n",
    "        plt.text(X+0.2,Y+0.8,'{:.2f}kN'.format(Fy/1000),va='bottom')\n",
    "\n",
    "# Plotagem das barras\n",
    "for barra in barras.index:\n",
    "    # Vamos passar os nós para as variáveis N1 e N2\n",
    "    N1 = barras.loc[barra, 'N1']\n",
    "    N2 = barras.loc[barra, 'N2']\n",
    "\n",
    "    # Agora vamos acessar as coordendas de cada um dos nós\n",
    "    x1, y1 = nos.loc[N1, ['X','Y']]\n",
    "    x2, y2 = nos.loc[N2, ['X','Y']]\n",
    "    y = [y1,y2]\n",
    "    x = [x1,x2]\n",
    "    \n",
    "    plt.plot(x,y,'black')\n",
    "    plt.scatter(x,y, s=80,marker ='o',color ='black')\n",
    "    #plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Determinação dos esforços<a name=\"section_112\"></a>\n",
    "Para finalizar a análise, é interessante o cálculo dos esforços atuantes em cada elemento, para isso, realiza-se o script abaixo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "Esf = []\n",
    "\n",
    "for barra in barras.index:\n",
    "    # Vamos importar as propriedades necessárias para construção da matriz local e da matriz de rotação\n",
    "    L   = barras.loc[barra, 'L']\n",
    "    sen = barras.loc[barra, 'sen']\n",
    "    cos = barras.loc[barra, 'cos']\n",
    "    A   = barras.loc[barra, 'A']\n",
    "    E   = barras.loc[barra, 'E']\n",
    "    N1  = barras.loc[barra, 'N1']\n",
    "    N2  = barras.loc[barra, 'N2']\n",
    "\n",
    "    # Matriz de rigidez no sistema local \n",
    "    Kl = E*A/L*np.array([[ 1, 0,-1, 0],\n",
    "                         [ 0, 0, 0, 0], \n",
    "                         [-1, 0, 1, 0],\n",
    "                         [ 0, 0, 0, 0]])\n",
    "\n",
    "    # Matriz de rotação\n",
    "    Mrot = np.array([[ cos,  sen,    0,   0],\n",
    "                     [-sen,  cos,    0,   0],\n",
    "                     [    0,   0,  cos, sen],\n",
    "                     [    0,   0, -sen, cos]])\n",
    "    # Recebendo os deslocamentos referentes ao elemento em análise\n",
    "    Ul = np.zeros(4)\n",
    "    Ul[0] = U[2*N1-2]\n",
    "    Ul[1] = U[2*N1-1]\n",
    "    Ul[2] = U[2*N2-2]\n",
    "    Ul[3] = U[2*N2-1]\n",
    "\n",
    "    # Realizando o equilíbrio local\n",
    "\n",
    "    F = np.dot(Kl,np.dot(Mrot,Ul))\n",
    "\n",
    "    # Salvando o terceiro valor do vetor de forças por convenção de sinais.\n",
    "    Esf.append(F[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora, vamos plotar os esforços, sinalizando as barras comprimidas pela cor azul e as tracionadas pela cor vermelha."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-18-beab2f44fc6e>:8: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  tg  = sen/cos\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for barra in barras.index:\n",
    "    # Vamos passar os nós para as variáveis N1 e N2\n",
    "    N1 = barras.loc[barra, 'N1']\n",
    "    N2 = barras.loc[barra, 'N2']\n",
    "    ax = Esf[barra-1]\n",
    "    cos = barras.loc[barra, 'cos']\n",
    "    sen = barras.loc[barra, 'sen']\n",
    "    tg  = sen/cos\n",
    "    # Agora vamos acessar as coordendas de cada um dos nós\n",
    "    x1, y1  = nos.loc[N1, ['X','Y']]\n",
    "    x2, y2  = nos.loc[N2, ['X','Y']]\n",
    "    y = [y1,y2]\n",
    "    x = [x1,x2]\n",
    "\n",
    "    plt.figure(1,figsize=(18,4.5))\n",
    "    if ax>0:\n",
    "        cor = 'r'\n",
    "    elif ax == 0:\n",
    "        cor = 'k'\n",
    "    else:\n",
    "        cor = 'b'\n",
    "    plt.plot(x,y,cor,zorder = -1)\n",
    "\n",
    "    plt.text(np.mean(x),np.mean(y),'{:.2f}kN'.format(ax/1000),rotation =180*np.arctan(tg)/np.pi,\n",
    "            horizontalalignment='center',\n",
    "            verticalalignment='center',\n",
    "            size = 16,\n",
    "            weight = 'bold')\n",
    "\n",
    "    plt.scatter(x,y, s=80,marker ='o',color ='black')\n",
    "    \n",
    "\n",
    "_=plt.title('Esforços atuantes')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Algumas coisas interessantes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}