nine_arch_compressive_demand_from_spandrel_walls.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%store -r masonry_unit_weight_realisations\n",
    "%store -r convergence_simulation_number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# spandrel_walls_unit_weight_realisations = np.random.normal(0, 1, convergence_simulation_number)*spandrel_walls_unit_weight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "compressive_demand_from_spandrel_walls = {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def arch_compressive_demand_from_spandrel_walls(spandrel_walls_unit_weight):\n",
    "\n",
    "    import math\n",
    "    import numpy as np\n",
    "\n",
    "    pi=math.pi\n",
    "\n",
    "    h_sw = 0.6 #m\n",
    "    r_e = 3950/1000 #m\n",
    "    r_i = 3450/1000 #m\n",
    "    H_sw = h_sw + r_e #m\n",
    "    B_p = 1.80 #m\n",
    "    L = 9260/1000 #m -span length\n",
    "    t = 500/1000 #m\n",
    "    b = 1 #m -investigated arch barrel slice-\n",
    "    b_sw = 0.20 #m -spandrel wall's thickness -assumed from Forgacs et al. (2019)\n",
    "\n",
    "    A_sq = (L/2 + B_p/2) * H_sw #the spandrel wall located above the central pier is examined\n",
    "    A_e = (1/4)*(pi * math.pow(r_e, 2))\n",
    "    A_sw = A_sq - A_e\n",
    "\n",
    "    P_sw = spandrel_walls_unit_weight * A_sw * b_sw #kN\n",
    "\n",
    "    x_sq = (L/2 + B_p/2)/2\n",
    "    x_e = 4/(3*pi)*r_e\n",
    "\n",
    "    x_sw = (A_sq * x_sq - A_e * x_e)/A_sw\n",
    "    print('x_sw = ', f'{x_sw:.2f}')\n",
    "\n",
    "    alfa_hinges = 0\n",
    "    xp_sw = (1/2 * L + 1/3 * t * math.cos(alfa_hinges) - x_sw)\n",
    "    print('xp_sw = ', f'{xp_sw:.2f}')\n",
    "\n",
    "    V_a = P_sw #kN\n",
    "    H_c = ((1/2 * L + 1/3 * t * math.cos(alfa_hinges) - xp_sw) * P_sw)/(2/3 * t + r_i - 1/3 * t * math.sin(alfa_hinges)) #kN\n",
    "    print(H_c)\n",
    "    H_a = H_c\n",
    "\n",
    "    S_a = np.sqrt(np.power(H_a,2) + np.power(V_a,2))\n",
    "\n",
    "    compressive_demand_from_spandrel_walls[\"H_a\"]=H_a\n",
    "    compressive_demand_from_spandrel_walls[\"V_a\"]=V_a\n",
    "    compressive_demand_from_spandrel_walls[\"S_a\"]=S_a\n",
    "\n",
    "    %store compressive_demand_from_spandrel_walls\n",
    "\n",
    "    return compressive_demand_from_spandrel_walls\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_sw =  3.80\n",
      "xp_sw =  1.00\n",
      "[56.10087926 45.93299314 57.73130001 ... 55.8755468  54.15826241\n",
      " 63.44886473]\n",
      "Stored 'compressive_demand_from_spandrel_walls' (dict)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'H_a': array([56.10087926, 45.93299314, 57.73130001, ..., 55.8755468 ,\n",
       "        54.15826241, 63.44886473]),\n",
       " 'V_a': array([55.87712876, 45.74979583, 57.50104681, ..., 55.65269501,\n",
       "        53.94225977, 63.19580783]),\n",
       " 'S_a': array([79.18056688, 64.82965122, 81.48173652, ..., 78.86253351,\n",
       "        76.43876488, 89.55148554])}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arch_compressive_demand_from_spandrel_walls(masonry_unit_weight_realisations)"
   ]
  }
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