M-θ for notes (columns).ipynb

M-θ for notes (columns).ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Υπολογισμός διαγραμμάτων Μ-θ σύμφωνα με τον ΚΑΝ.ΕΠΕ."
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install numpy\n",
        "#!pip install pandas\n",
        "#!pip install sympy\n",
        "#!pip install matplotlib"
      ],
      "outputs": [],
      "execution_count": 1,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from sympy.solvers import solve\n",
        "from sympy import Symbol"
      ],
      "outputs": [],
      "execution_count": 1,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Δεδομένα παραδείγματος\n",
        "\n",
        "Δίνεται η διατομή του σχήματος που βρίσκεται στους ακραίους στύλους του ισογείου του φορέα των σημειώσεων.\n",
        "\n",
        "![Imgur](https://i.imgur.com/TyiAeHe.png)\n",
        "\n\n",
        "### Διαστάσεις της διατομής\n",
        "\n",
        "$b=0.45m$\n",
        "\n",
        "$h=0.45m$\n",
        "\n",
        "### Υλικά\n",
        "\n",
        "$f_c= 16MPa = 16000kPa$\n",
        "\n",
        "$E_c=25.3GPa=25300000kPa$\n",
        "\n",
        "$f_y= 500MPa = 500000kPa$\n",
        "\n",
        "$E_s= 200GPa = 200000000kPa$\n",
        "\n",
        "$f_{yw}= 500MPa=500000kPa$\n",
        "\n",
        "### Οπλισμός\n",
        "\n",
        "$c_{nom}=30mm = 0.03m$\n",
        "\n",
        "$\\emptyset_{L}=18mm = 0.018m$\n",
        "\n",
        "$A_s = 7.63cm^2$ για 3∅18\n",
        "\n",
        "$\\emptyset_{L}^{'}=18mm = 0.018m$\n",
        "\n",
        "$A_s = 7.63cm^2$ για 3∅18\n",
        "\n",
        "$\\emptyset_{Lv}=0mm = 0m$ Δεν υπάρχει ενδιάμεσος οπλισμός στη δοκό\n",
        "\n",
        "$A_{sv} = 5.09cm^2$ για 2∅18\n",
        "\n",
        "$\\emptyset_{d}=0mm = 0m$ Δεν υπάρχει δισδιαγώνιος οπλισμός στη δοκό\n",
        "\n",
        "$A_{sd} = 0cm^2$ \n",
        "\n",
        "$\\emptyset_{w}=8mm = 0.008m$\n",
        "\n",
        "$A_{sw} = 1.51cm^2$ για 3τμητους ∅8\n",
        "\n",
        "$s=120mm=0.12m$ Η απόσταση μεταξύ των συνδετήρων\n",
        "\n",
        "### Διαστάσεις του δομικού στοιχείου\n",
        "\n",
        "$L_s = 1.70m$ το μήκος διάτμησης\n",
        "\n\n"
      ],
      "metadata": {
        "nbpresent": {
          "id": "9e5a69e0-f4c0-40f3-a6fe-b9c46a89f1aa"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Δεδομένα χρήστη\n",
        "\nΣτο επόμενο κελί βάζετε τα δεδομένα σας. Προσοχή στις μονάδες"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Διαστάσεις της διατομής\n",
        "b = 0.45 # το πλάτος της θλιβόμενης ζώνης[m] \n",
        "h = 0.45 # το ύψος της διατομής[m]\n",
        "\n\n",
        "# Υλικά\n",
        "fc = 16000.0      # η θλιπτική αντοχή του σκυροδέματος[kPa] \n",
        "Ec = 25300000.0   # το μέτρο ελαστικότητας του σκυροδέματος [kPa] \n",
        "fy = 500000.0     # το όριο διαρροής του χάλυβα [kPa] \n",
        "Es = 200000000.0  # το μέτρο ελαστικότητας του χάλυβα [kPa] \n",
        "fyw = 500000.0    # το όριο διαρροής του χάλυβα των συνδετήρων [kPa]\n",
        "\n\n\n",
        "# Οπλισμός\n",
        "## Επικάλυψη\n",
        "cnom = 0.03       # [m] \n",
        "## Διαμήκης \n",
        "### Εφελκυόμενος\n",
        "nL = 3            # Ο αριθτμός των εφελκυόμενων ράβδων\n",
        "ΦL = 0.018        # Η διάμετρος των εφελκυόμενων ράβδων [m] \n",
        "### Θλιβόμενος\n",
        "nL2 = 3           # Ο αριθτμός των θλιβόμενων ράβδων\n",
        "ΦL2 = 0.018       # Η διάμετρος των θλιβόμενων ράβδων [m] \n",
        "### Ενδιάμεσος\n",
        "nLv = 2           # Ο αριθτμός των ενδιάμεσων ράβδων\n",
        "ΦLv = 0.018       # Η διάμετρος των ενδιάμεσων ράβδων [m] \n",
        "## Δισδιαγώνιος \n",
        "nd = 0            # Ο αριθτμός των δισδιαγώνιων ράβδων\n",
        "Φd = 0.           # Η διάμετρος των δισδιαγώνιων ράβδων [m] \n",
        "## Εγκάρσιος\n",
        "nw = 3            # Ο αριθμός των \"τμήσεων\" των συνδετήρων (πχ. 2 για 2τμητους)\n",
        "Φw = 0.008        # Η διάμετρος των συνδετήρων [m] \n",
        "s = 0.12          # Η απόσταση μεταξύ των συνδετήρων [m] \n",
        "# Asw=1.01cm2Asw=1.01cm2 για 2τμητους ∅8\n",
        "\n",
        "# Αξονικό φορτίο\n",
        "N = 299.77            # Αξονικό φορτίο για το συνδυασμό G+0.3Q [kN] (ή 1.1G+0.3Q)\n",
        "\n",
        "# Μήκος διάτμησης\n",
        "Ls = 1.7        # [m]\n",
        "\n",
        "# Αποστάσεις bi περίσφιξης [m]\n",
        "# Υπολογίζονται με το χέρι (όχι αυτόματα)\n",
        "bi = np.array([0.191, 0.191, 0.191, 0.191, 0.191, 0.191, 0.191, 0.191]) "
      ],
      "outputs": [],
      "execution_count": 2,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Συναρτήσεις για τη δεδομένα της διατομής και τα ποσοστά οπλισμού\n",
        "\nΔεν απαιτείται να τις τροποποιήσετε"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Υπολογισμός As για n ράβδους διαμέτρου Φ. Δουλεύει και με numpy arrays\n",
        "def As_for_n_Φ(n, Φ):\n",
        "    if isinstance(n, np.ndarray):\n",
        "        return sum(n * Φ**2 * np.pi/4)\n",
        "    else:\n",
        "        return (n * Φ**2 * np.pi/4)\n",
        "\n",
        "# Υπολογισμός d1\n",
        "def d1calc(c, dL, dw):\n",
        "    return c + dw + 0.5 * dL\n",
        "\n",
        "# Ποσοστό οπλισμού\n",
        "def ρcalc(A, b, d):\n",
        "    return A / (b * d)\n",
        "\n",
        "# Μηχανικό ποσοστό οπλισμού\n",
        "def ωcalc(A: float, b: float, d: float, fy: float, fc: float):\n",
        "    return A / (b * d) * (fy / fc)\n",
        "\n",
        "# Ποσοστό εγκάρσιου οπλισμού ΚΑΝ.ΕΠΕ.\n",
        "def ρscalc(A, b, s):\n",
        "    return A / (b * s)\n",
        "\n",
        "# Ποσοστό εγκάρσιου οπλισμού EC2\n",
        "def ρwcalc(A, b, s, α):\n",
        "    return A / (b * s * np.sin(α))"
      ],
      "outputs": [],
      "execution_count": 3,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Συναρτήσεις για τον υπολογισμό της καμπυλότητας και της ροπής διαρροής"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "def ξycalc(α, A, B):\n",
        "    return (α**2 * A**2 + 2 * α * B)**0.5 - α*A \n",
        "    \n",
        "def Mycalc(b, d, φy, Ec, ξy, δ2, ρ1, ρ2, ρv, Es):\n",
        "    return b * d**3 * φy * (0.5 * Ec * ξy**2 * (0.5*(1 + δ2) -ξy/3) + ((1 - ξy) * ρ1 + (ξy - δ2) * ρ2 + ρv * (1 - δ2)/6)*(1-δ2)*Es/2)\n",
        "\n",
        "# (0.5*Ec*ξy**2)*(0.5*(1+δtonos)-ξy/3)+((1-ξy)*ρ1+(ξy-δtonos)* ρ2+ρv*(1-δtonos)/6)*(1-δtonos)*Es/2)  \n",
        "    \n",
        "def ABξφ_steel(ρ, ρ2, ρv, N, b, d, δ2, fy, α, Es):\n",
        "    A = ρ + ρ2 + ρv + N / (b * d * fy)\n",
        "    B = ρ + ρ2 * δ2 + 0.5 * ρv * (1 + δ2) + N / (b * d * fy)\n",
        "    ξy = ξycalc(α, A, B)\n",
        "    φy = fy / (Es * (1 - ξy) * d)\n",
        "    return A, B, ξy, φy\n",
        "\n",
        "def ABξφ_conc(ρ, ρ2, ρv, N, b, d, δ2, α, Ec, fc):\n",
        "    A = ρ + ρ2 + ρv - N / (1.8 * α * b * d * fc)\n",
        "    B = ρ + ρ2 * δ2 + 0.5 * ρv * (1+δ2)\n",
        "    ξy = ξycalc(α, A, B)\n",
        "    φy = 1.8 * fc / (Ec * ξy * d)\n",
        "    return A, B, ξy, φy"
      ],
      "outputs": [],
      "execution_count": 4,
      "metadata": {
        "nbpresent": {
          "id": "6e86f40d-c6fb-4740-9a3e-5771b7eb17a6"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Συναρτήσεις για τον υπολογισμό της στροφής διαρροής "
      ],
      "metadata": {
        "collapsed": true,
        "nbpresent": {
          "id": "ae1f40f9-048d-495a-bad8-3aa3871639e1"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def VRc(ρtot, b, d, fc, N, Ac):\n",
        "    # Ο ΚΑΝ.ΕΠΕ. μάλλον έχει λάθος σχέση. Πολύ μεγάλα νούμερα και μάλλον τάσεις. Πολλαπλασιασμό με b*d ίσως\n",
        "    # fc [MPa]\n",
        "    # N [kN] θετικ΄η η θλ΄ίψη\n",
        "    # διαστάσεις σε [m]\n",
        "    v1 = max(180. * (100. * ρtot)**(1./3.),\n",
        "             35. * (1. + (0.2/d)**0.5)**0.5 * fc**(1./6.)\n",
        "            )\n",
        "    \n",
        "    return (v1 * (1 + (0.2/d)**0.5) * fc**(1/3) + 0.15 * N / Ac)* b * d\n",
        "    \n",
        "def VRdcEC2(CRdc, Asl, fck, σcp, bw, d):\n",
        "    ρl = min(Asl / (bw * d), 0.02)\n",
        "    k = min(1 + (200.0 / d)**0.5, 2.0)\n",
        "    vmin = 0.035 * k**1.5 * fck**0.5\n",
        "    k1 = 0.15\n",
        "\n",
        "    VRdc1 = (CRdc * k * ((100 * ρl * fck)**(1/3)) + k1 * σcp) * bw * d\n",
        "    VRdc2 = (vmin + k1 * σcp) * bw * d\n",
        "\n",
        "    _VRdc = max(VRdc1, VRdc2)   \n",
        "    return ρl, k, vmin, k1, VRdc1, VRdc2, _VRdc\n",
        "\n",
        "def θycalc(φy, Ls, av, z, h, db, fy, fc):\n",
        "    # (fy και fc σε MPa)\n",
        "    fy /= 1000\n",
        "    fc /= 1000\n",
        "    return φy * (Ls + av*z) / 3 + 0.0014 * (1 + 1.5 * h/Ls) + φy*db*fy / (8 * fc**0.5)\n",
        "\n"
      ],
      "outputs": [],
      "execution_count": 5,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Συναρτήσεις για τον υπολογισμό της στροφής αστοχίας\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "def θumcalc(ν, ωtot, ω2, αs, α, ρs, ρd, fc, fyw):\n",
        "    part1 = (fc * max(0.01, ω2) / max(0.01, (ωtot-ω2)))**0.225\n",
        "    part2 = αs**0.35\n",
        "    part3 = 25.0**(α * ρs * fyw / fc)\n",
        "    part4 = 1.25**(100 * ρd)\n",
        "    return 0.016 * 0.3**ν * part1 * part2 * part3 * part4\n",
        "\n\n",
        "def αcalc(sh, bc, hc, Σbi2):\n",
        "    return (1-sh/(2*bc))*(1-sh/(2*hc))*(1-Σbi2/(6*bc*hc))"
      ],
      "outputs": [],
      "execution_count": 6,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Διατμητική αντοχή"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Τέμνουσα που παραλαμβάνουν οι συνδετήρες\n",
        "def Vwcalc(ρw, bw, z, fyw):\n",
        "    return ρw * bw * z * fyw\n",
        "\n",
        "# Τέμνουσα αντοχής\n",
        "def VRcalc(h, x, Ls , N, Ac, fc, μθpl, ρtot, αs, Vw):\n",
        "    # Η σχέση θέλει MN και m. Αποτέλεσμα σε MN\n",
        "    # Θετική η θλίψη, 0 ο εφελκυσμός\n",
        "    if N < 0: N = 0\n",
        "    part1 = ((h-x)/(2*Ls)) * min(N, 0.55 * Ac * fc)\n",
        "    part2 = 1.0 - 0.05 * min(5, μθpl)\n",
        "    part3 = 0.16 * max(0.5, 100 * ρtot)*(1 - 0.16 * min(5, αs)) * fc**0.5 * Ac + Vw\n",
        "    return part1 + part2 * part3"
      ],
      "outputs": [],
      "execution_count": 7,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Αποτελέσματα"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "αs = Ls / h\n",
        "print(f'Λόγος διάτμησης: αs = {αs:.2f}')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Λόγος διάτμησης: αs = 3.78\n"
          ]
        }
      ],
      "execution_count": 8,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Εμβαδά οπλισμού"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "As = As_for_n_Φ(nL, ΦL)\n",
        "print(f'Εμβαδό του εφελκυόμενου οπλισμού: As = {As:.6f}m2 = {10000*As:.2f}cm2')\n",
        "\n",
        "As2 = As_for_n_Φ(nL2, ΦL2)\n",
        "print(f'Εμβαδό του θλιβόμενου οπλισμού: As2 = {As2:.6f}m2 = {10000*As2:.2f}cm2')\n",
        "\n",
        "Asv = As_for_n_Φ(nLv, ΦLv)\n",
        "print(f'Εμβαδό του ενδιάμεσου οπλισμού: Asv = {Asv:.6f}m2 = {10000*Asv:.2f}cm2')\n",
        "\n",
        "Asd = As_for_n_Φ(nd, Φd)\n",
        "print(f'Εμβαδό του δισδιαγώνιου οπλισμού: Asd = {Asd:.6f}m2 = {10000*Asd:.2f}cm2')\n",
        "\n",
        "Asw = As_for_n_Φ(nw, Φw)\n",
        "print(f'Εμβαδό του εγκάρσιου οπλισμού: Asw = {Asw:.6f}m2 = {10000*Asw:.2f}cm2')\n",
        "\n",
        "Astot = As + As2 + Asv\n",
        "print(f'Συνολικό εμβαδό του διαμήκους οπλισμού: Astot = {Astot:.6f}m2 = {10000*Astot:.2f}cm2')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Εμβαδό του εφελκυόμενου οπλισμού: As = 0.000763m2 = 7.63cm2\n",
            "Εμβαδό του θλιβόμενου οπλισμού: As2 = 0.000763m2 = 7.63cm2\n",
            "Εμβαδό του ενδιάμεσου οπλισμού: Asv = 0.000509m2 = 5.09cm2\n",
            "Εμβαδό του δισδιαγώνιου οπλισμού: Asd = 0.000000m2 = 0.00cm2\n",
            "Εμβαδό του εγκάρσιου οπλισμού: Asw = 0.000151m2 = 1.51cm2\n",
            "Συνολικό εμβαδό του διαμήκους οπλισμού: Astot = 0.002036m2 = 20.36cm2\n"
          ]
        }
      ],
      "execution_count": 9,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Γεωμετρικά στοιχεία οπλισμού"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "d1 = d1calc(cnom, ΦL, Φw)\n",
        "print(f'Συνολική επικάλυψη εφελκυόμενου: d1={d1:.3f}m')\n",
        "\n",
        "d2 = d1calc(cnom, ΦL2, Φw)\n",
        "print(f'Συνολική επικάλυψη θλιβόμενου: d`=d2={d2:.3f}m')\n",
        "\n",
        "d = h - d1\n",
        "print(f'Στατικό ύψος: d={d:.3f}m')\n",
        "\n",
        "δ2 = d2/d\n",
        "print(f'Λόγος δ`={δ2:.3f}')\n",
        "\n",
        "sh = s  #- Φw\n",
        "print(f'Απόσταση των συνδετήρων: sh={sh:.3f}m')\n",
        "print('Παρατήρηση: Σε παλιότερες εκδόσεις του ΚΑΝ.ΕΠΕ. ως sh ορίζονταν η καθαρή απόσταση s-Φw')\n",
        "print('')\n",
        "z = d - d2\n",
        "print(f'Ο μοχλοβραχίονας εσωτερικών δυνάμεων: z={z:.3f}m')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Συνολική επικάλυψη εφελκυόμενου: d1=0.047m\n",
            "Συνολική επικάλυψη θλιβόμενου: d`=d2=0.047m\n",
            "Στατικό ύψος: d=0.403m\n",
            "Λόγος δ`=0.117\n",
            "Απόσταση των συνδετήρων: sh=0.120m\n",
            "Παρατήρηση: Σε παλιότερες εκδόσεις του ΚΑΝ.ΕΠΕ. ως sh ορίζονταν η καθαρή απόσταση s-Φw\n",
            "\n",
            "Ο μοχλοβραχίονας εσωτερικών δυνάμεων: z=0.356m\n"
          ]
        }
      ],
      "execution_count": 10,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Ποσοστά οπλισμού"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "ρ = ρcalc(As, b, d)\n",
        "ω = ωcalc(As, b, d, fy, fc)\n",
        "print(f'Ποσοστό του εφελκυόμενου οπλισμού: ρ = {ρ:.5f} = {1000*ρ:.2f}‰')\n",
        "print(f'Μηχανικό ποσοστό του εφελκυόμενου οπλισμού: ω = {ω:.3f}')\n",
        "print()\n",
        "\n",
        "ρ2 = ρcalc(As2, b, d)\n",
        "ω2 = ωcalc(As2, b, d, fy, fc)\n",
        "print(f'Ποσοστό του θλιβόμενου οπλισμού: ρ` = ρ2 = {ρ2:.5f} = {1000*ρ2:.2f}‰')\n",
        "print(f'Μηχανικό ποσοστό του θλιβόμενου οπλισμού: ω` = ω2 = {ω2:.3f}')\n",
        "print()\n",
        "\n",
        "ρv = ρcalc(Asv, b, d)\n",
        "ωv = ωcalc(Asv, b, d, fy, fc)\n",
        "print(f'Ποσοστό του ενδιάμεσου οπλισμού: ρv = {ρv:.5f} = {1000*ρv:.2f}‰')\n",
        "print(f'Μηχανικό ποσοστό του ενδιάμεσου οπλισμού: ωv = {ωv:.3f}')\n",
        "print()\n",
        "\n",
        "ρtot = ρ + ρ2 + ρv\n",
        "ωtot = ω + ω2 + ωv\n",
        "print(f'Συνολικό ποσοστό του διαμήκους οπλισμού: ρtot = {ρtot:.5f} = {1000*ρtot:.2f}‰')\n",
        "print(f'Συνολικό μηχανικό ποσοστό του διαμήκους οπλισμού: ωtot = {ωtot:.3f}')\n",
        "print()\n",
        "\n",
        "ρd = ρcalc(Asd, b, d)\n",
        "ωd = ωcalc(Asd, b, d, fy, fc)\n",
        "print(f'Ποσοστό του δισδιαγώνιου οπλισμού: ρd = {ρd:.5f} = {1000*ρd:.2f}‰')\n",
        "print(f'Μηχανικό ποσοστό του δισδιαγώνιου οπλισμού: ωd = {ωd:.3f}')\n",
        "print()\n",
        "\n",
        "ρs = ρscalc(Asw, b, sh)\n",
        "print(f'Ποσοστό του εγκάρσιου οπλισμού (σχέση ΚΑΝ.ΕΠΕ.): ρs = {ρs:.5f} = {1000*ρs:.2f}‰')\n",
        "\n",
        "ρw = ρwcalc(Asw, b, s, np.pi/2)\n",
        "print(f'Ποσοστό του εγκάρσιου οπλισμού (σχέση EC2): ρw = {ρw:.5f} = {1000*ρw:.2f}‰')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Ποσοστό του εφελκυόμενου οπλισμού: ρ = 0.00421 = 4.21‰\n",
            "Μηχανικό ποσοστό του εφελκυόμενου οπλισμού: ω = 0.132\n",
            "\n",
            "Ποσοστό του θλιβόμενου οπλισμού: ρ` = ρ2 = 0.00421 = 4.21‰\n",
            "Μηχανικό ποσοστό του θλιβόμενου οπλισμού: ω` = ω2 = 0.132\n",
            "\n",
            "Ποσοστό του ενδιάμεσου οπλισμού: ρv = 0.00281 = 2.81‰\n",
            "Μηχανικό ποσοστό του ενδιάμεσου οπλισμού: ωv = 0.088\n",
            "\n",
            "Συνολικό ποσοστό του διαμήκους οπλισμού: ρtot = 0.01123 = 11.23‰\n",
            "Συνολικό μηχανικό ποσοστό του διαμήκους οπλισμού: ωtot = 0.351\n",
            "\n",
            "Ποσοστό του δισδιαγώνιου οπλισμού: ρd = 0.00000 = 0.00‰\n",
            "Μηχανικό ποσοστό του δισδιαγώνιου οπλισμού: ωd = 0.000\n",
            "\n",
            "Ποσοστό του εγκάρσιου οπλισμού (σχέση ΚΑΝ.ΕΠΕ.): ρs = 0.00279 = 2.79‰\n",
            "Ποσοστό του εγκάρσιου οπλισμού (σχέση EC2): ρw = 0.00279 = 2.79‰\n"
          ]
        }
      ],
      "execution_count": 11,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Υπολογισμός της καμπυλότητας και της ροπής διαρροής"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "α = Es/Ec\n",
        "print(f'α = {α:.3f}')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "α = 7.905\n"
          ]
        }
      ],
      "execution_count": 12,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Διαρροή λόγω χάλυβα"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "A_steel, B_steel, ξy_steel, φy_steel = ABξφ_steel(ρ, ρ2, ρv, N, b, d, δ2, fy, α, Es)\n",
        "print(f'A = {A_steel:.5f}')\n",
        "print(f'B = {B_steel:.5f}')\n",
        "print(f'ξy = {ξy_steel:.3f}')\n",
        "print(f'φy = {φy_steel:.5f}m-1')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "A = 0.01453\n",
            "B = 0.00957\n",
            "ξy = 0.291\n",
            "φy = 0.00875m-1\n"
          ]
        }
      ],
      "execution_count": 13,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Διαρροή λόγω μη-γραμμικότητας των παραμορφώσεων του θλιβόµενου σκυροδέματος"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "A_conc, B_conc, ξy_conc, φy_conc = ABξφ_conc(ρ, ρ2, ρv, N, b, d, δ2, α, Ec, fc)\n",
        "print(f'A = {A_conc:.5f}')\n",
        "print(f'B = {B_conc:.5f}')\n",
        "print(f'ξy = {ξy_conc:.3f}')\n",
        "print(f'φy = {φy_conc:.5f}m-1')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "A = 0.00397\n",
            "B = 0.00627\n",
            "ξy = 0.285\n",
            "φy = 0.00991m-1\n"
          ]
        }
      ],
      "execution_count": 14,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Τελικές τιμές στη διαρροή"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "if φy_steel<φy_conc:\n",
        "    ξy = ξy_steel\n",
        "    φy = φy_steel\n",
        "    verdict = 'χάλυβα'\n",
        "else:\n",
        "    ξy = ξy_conc\n",
        "    φy = φy_conc\n",
        "    verdict = 'μη-γραμμικότητας των παραμορφώσεων του θλιβόµενου σκυροδέματος'\n",
        "\n",
        "My = Mycalc(b, d, φy, Ec, ξy, δ2, ρ, ρ2, ρv, Es)\n",
        "    \n",
        "xy = ξy * d\n",
        "\n",
        "print(f'Παρατηρείται ότι προηγείται η διαρροή λόγω {verdict}, οπότε τελικά:')\n",
        "print(f'ξy = {ξy:.3f}')\n",
        "print(f'xy = {xy:.3f}m (Το ύψος της θλιβόμενης ζώνης στη διαρροή)')\n",
        "print(f'φy = {φy:.5f}m-1')\n",
        "print(f'My = {My:.2f}kNm')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Παρατηρείται ότι προηγείται η διαρροή λόγω χάλυβα, οπότε τελικά:\n",
            "ξy = 0.291\n",
            "xy = 0.117m (Το ύψος της θλιβόμενης ζώνης στη διαρροή)\n",
            "φy = 0.00875m-1\n",
            "My = 221.16kNm\n"
          ]
        }
      ],
      "execution_count": 15,
      "metadata": {
        "scrolled": true
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Προσεγγιστικές σχέσεις ΚΑΝ.ΕΠΕ. (δε χρησιμοποιούνται στη συνέχεια)\n",
        "print(f'φy = {1.73* fy /(Es *h):.5f}m-1')\n",
        "print(f'φy = {1.52* fy /(Es *d):.5f}m-1')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "φy = 0.00961m-1\n",
            "φy = 0.00943m-1\n"
          ]
        }
      ],
      "execution_count": 16,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Υπολογισμός της στροφής διαρροής"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Έλεγχος τέμνουσας λοξής ρηγμάτωσης - Υπολογισμός αv"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# def VRc(ρtot, d, fc, N, Ac):\n",
        "# print(VRc(ρtot, d, fc/1000, N, b*d))\n",
        "\n",
        "# Χρησιμοποιείται η σχέση του EC2. Προσοχή στις μονάδες, θέλει [N], [mm]\n",
        "V_EC2 = VRdcEC2(0.18, As*10**6, fc/1000, 0.001*N/(b*h), 1000*b, 1000*d)\n",
        "V_kanepe = VRc(ρtot, b, d, fc/1000, N, b*h)\n",
        "\n",
        "# VRc = V_EC2[6]/1000.\n",
        "VRc = V_kanepe\n",
        "\n",
        "print(f'ρl = {V_EC2[0]:.5f}')\n",
        "print(f'k = {V_EC2[1]:.3f}')\n",
        "print(f'vmin = {V_EC2[2]:.3f}')\n",
        "print(f'VRdc (1η σχέση EC2) = {V_EC2[4]:.1f}N')\n",
        "print(f'VRdc (2η σχέση EC2) = {V_EC2[5]:.1f}N')\n",
        "\n",
        "print(f'V_kanepe = {V_kanepe:.2f}kN')\n",
        "\nprint(f'Vdc = {VRc:.2f}kN')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "ρl = 0.00421\n",
            "k = 1.704\n",
            "vmin = 0.312\n",
            "VRdc (1η σχέση EC2) = 145344.0N\n",
            "VRdc (2η σχέση EC2) = 96766.7N\n",
            "V_kanepe = 185.98kN\n",
            "Vdc = 185.98kN\n"
          ]
        }
      ],
      "execution_count": 17,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "VMu = My / Ls\n",
        "print(f'VMu = {VMu:.2f}kN')\n",
        "\n",
        "if VRc<VMu:\n",
        "    αv = 1.\n",
        "else:\n",
        "    αv = 0.   \n",
        "    \n",
        "print(f'αv = {αv:.1f}')  "
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "VMu = 130.10kN\n",
            "αv = 0.0\n"
          ]
        }
      ],
      "execution_count": 18,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Υπολογισμός θy"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "θy = θycalc(φy, Ls, αv, z, h, ΦL, fy, fc)\n",
        "print(f'θy = {θy:.4f}') "
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "θy = 0.0094\n"
          ]
        }
      ],
      "execution_count": 19,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Υπολογισμός της στροφής αστοχίας"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "ν = N / (b*h*fc)\n",
        "print(f'ν={ν:.3f}')\n",
        "\n",
        "bo = b - 2 * (cnom + 0.5*Φw)\n",
        "ho = h - 2 * (cnom + 0.5*Φw)\n",
        "print(f'bo={bo:.3f}m')\n",
        "print(f'ho={ho:.3f}m')\n",
        "\n",
        "if ho/bo > 2.0:\n",
        "    ho = xy - (cnom + 0.5*Φw)\n",
        "    print('hc/bc > 2.0 οπότε χρησιμοποιείται, αντί του ho, το ύψος της θλιβόµενης ζώνης εντός του περισφιγμένου πυρήνα')\n",
        "    print(f'ho={ho:.3f}m')\n",
        "\n",
        "if bi[0] == 0.0:  \n",
        "    bi = np.array([bo, ho, bo, ho])  # Για 2τμητους συνδετήρες\n",
        "\n",
        "Σbi2 = sum(bi**2)\n",
        "print(f'Σbi2={Σbi2:.4f}m2')\n",
        "\n",
        "απερ = αcalc(s, bo, ho, Σbi2)\n",
        "if απερ<0: απερ =0.\n",
        "print(\"Συντελεστής αποδοτικότητας περίσφιξης: α=\" + \"{0:.4f}\".format(απερ)+\"\")\n",
        "\n",
        "θu = θumcalc(ν, ωtot, ω2, αs, απερ, ρs, ρd, fc/1000, fyw/1000)\n",
        "print(f'θu={θu:.4f}')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "ν=0.093\n",
            "bo=0.382m\n",
            "ho=0.382m\n",
            "Σbi2=0.2918m2\n",
            "Συντελεστής αποδοτικότητας περίσφιξης: α=0.4737\n",
            "θu=0.0433\n"
          ]
        }
      ],
      "execution_count": 20,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Αρχικό διάγραμμα Μ-θ (χωρίς τον έλεγχο για τις τέμνουσες)"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "xMθs = [0, θy, θu]\n",
        "yMθs = [0, My, My]\n",
        "\n",
        "plt.figure(figsize=(8, 5))\n",
        "plt.plot(xMθs, yMθs, lw=2)\n",
        "plt.axis([0, 1.2*θu, 0, 1.2*My])\n",
        "\n",
        "plt.ylabel('M (kN)') \n",
        "plt.xlabel('θ')   \n",
        "plt.title('Αρχικό διάγραμμα Μ-θ (χωρίς τον έλεγχο για τις τέμνουσες)')\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": [
              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\n"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 21,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "μθ = θu/θy\n",
        "print(f'Αρχική τιμή πλαστιμότητας στροφών μθ={μθ:.2f}')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Αρχική τιμή πλαστιμότητας στροφών μθ=4.62\n"
          ]
        }
      ],
      "execution_count": 22,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Υπολογισμός διατμητικής αντοχής"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Τέμνουσα που παραλαμβάνουν οι συνδετήρες\n",
        "Vw = Vwcalc(ρw, b, z, fyw)\n",
        "print(f'Vw={Vw:.2f}kN={Vw/1000:.5f}MN')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Vw=223.68kN=0.22368MN\n"
          ]
        }
      ],
      "execution_count": 23,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "xs = np.linspace(0., 1.5*θu, 100)\n",
        "yVRs = list()\n",
        "yMs = list()\n",
        "\n",
        "for x in xs:\n",
        "    μθpl=max(0, (x/θy)-1)\n",
        "    VRi=VRcalc(h, xy, Ls , N/1000, b*d, fc/1000, μθpl, ρtot, αs, Vw/1000)*1000\n",
        "    MVRi = VRi * Ls\n",
        "    \n",
        "    yVRs.append(VRi)\n",
        "    yMs.append(MVRi)\n",
        "\n# print(xs)"
      ],
      "outputs": [],
      "execution_count": 24,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "xsy=[θy, θy]\n",
        "ysy=[0, 1.2*max(yVRs)]\n",
        "\n",
        "xsu=[θu, θu]\n",
        "ysu=[0, 1.2*max(yVRs)]\n",
        "\n",
        "plt.figure(figsize=(8, 5))\n",
        "plt.plot(xs, yVRs, label=\"Τέμνουσα αντοχής VR\", lw=2)\n",
        "plt.axis([0, 1.5*θu, 0, 1.2*max(yVRs)])\n",
        "# plt.axis([0, 8, 0, 1.2*max(VR0*Ls, My)])\n",
        "plt.plot(xsy, ysy, label=\"Διαρροή\", linestyle='--')\n",
        "plt.plot(xsu, ysu, label=\"Καμπτική αστοχία\", linestyle='--')\n",
        "plt.ylabel('VR (kN)') \n",
        "plt.xlabel('θ')   \n",
        "plt.title('Μείωση της τέμνουσας αντοχής με την ανελαστική παραμόρφωση')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": [
              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\n"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 25,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Έλεγχος πρόωρης αστοχίας από διάτμηση"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "ymax = max(max(yMs), My)\n",
        "\n",
        "xsy=[θy, θy]\n",
        "ysy=[0, 1.2*ymax]\n",
        "\n",
        "xsu=[θu, θu]\n",
        "ysu=[0, 1.2*ymax]\n",
        "\n",
        "xMθs = [0, θy, θu]\n",
        "yMθs = [0, My, My]\n",
        "\n",
        "plt.figure(figsize=(8, 5))\n",
        "plt.plot(xs, yMs, label=\"Ροπή τέμνουσας αντοχής (VR*Ls)\", lw=2)\n",
        "plt.axis([0, 1.5*θu, 0, 1.2*ymax])\n",
        "# plt.axis([0, 8, 0, 1.2*max(VR0*Ls, My)])\n",
        "plt.plot(xsy, ysy, label=\"Διαρροή\", linestyle='--')\n",
        "plt.plot(xsu, ysu, label=\"Αστοχία\", linestyle='--')\n",
        "plt.plot(xMθs, yMθs, label=\"Αρχικό διάγραμμα Μ-θ\")\n",
        "\n",
        "plt.ylabel('M (kN)') \n",
        "plt.xlabel('θ')   \n",
        "plt.title('Έλεγχος πρόωρης αστοχίας από διάτμηση')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": [
              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\n"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 26,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "υ = Symbol('υ')\n",
        "μθsol=solve((((h-xy)/(2*Ls))*min(N/1000, 0.55*b*d*fc/1000) + (1-0.05*υ) * (0.16*max(0.5, 100*ρtot)*(1-0.16*min(5,αs))*((fc/1000)**0.5)*b*d + Vw/1000)*1000-My/Ls),υ)[0]\n",
        "θsol = θy * (μθsol+1)\n",
        "# print(μθsol)\n",
        "# print(θsol)"
      ],
      "outputs": [],
      "execution_count": 27,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "VR0 = yVRs[0]\n",
        "if VR0 < My/Ls:\n",
        "    θu = 1.4 * θy\n",
        "    θy = θy * VR0 * Ls / My     \n",
        "    My = VR0 * Ls   \n",
        "\n",
        "elif θsol<θu:\n",
        "    θu = θsol    \n",
        "\n",
        "print('Τελικές τιμές')\n",
        "print(f'My=Mu={My:.2f}kNm')\n",
        "print(f'θy={θy:.4f}')\n",
        "print(f'θu={θu:.4f}')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Τελικές τιμές\n",
            "My=Mu=221.16kNm\n",
            "θy=0.0094\n",
            "θu=0.0433\n"
          ]
        }
      ],
      "execution_count": 28,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Τελικό διάγραμμα Μ-θ"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "xMθs = [0, θy, θu]\n",
        "yMθs = [0, My, My]\n",
        "\n",
        "plt.figure(figsize=(8, 5))\n",
        "plt.plot(xMθs, yMθs, lw=2)\n",
        "# plt.axis([0, 1.2*θu, 0, 1.2*My])\n",
        "\n",
        "plt.ylabel('M (kN)') \n",
        "plt.xlabel('θ')   \n",
        "plt.title('Τελικό διάγραμμα Μ-θ')\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": [
              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            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 29,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Αποτελέσματα για το SAP2000\n",
        "\n",
        "### Δεδομένα πλαστικής άρθρωσης (*Hinge Property*)\n",
        "\n",
        "Στις ιδιότητες των πλαστικών αρθρώσεων του SAP2000 δίνεται η τιμή της πλαστικής στροφής $θ_{pl}=θ_{u}-θ_{y}$\n",
        "\nΣτο σημείο της θεωρητικής αστοχίας λαμβάνεται πτώση αντοχής στο 20% της My και στη συνέχεια δίνεται η δυνατότητα παραμόρφωσης με την ίδια αντοχή έως το $5\\cdotθ_{pl}$"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "θpl = θu - θy\n",
        "print(f'θpl={θpl:.4f}')"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "θpl=0.0339\n"
          ]
        }
      ],
      "execution_count": 30,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "da = {'M': [0, My, My, 0.2*My, 0.2*My], 'θ': [0, 0, θpl, θpl, 5*θpl]}\n",
        "df = pd.DataFrame(data=da, index=['A', 'B', 'C', 'D', 'E'])\n",
        "df.round({'M': 2, 'θ': 4})"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 31,
          "data": {
            "text/plain": [
              "        M       θ\n",
              "A    0.00  0.0000\n",
              "B  221.16  0.0000\n",
              "C  221.16  0.0339\n",
              "D   44.23  0.0339\n",
              "E   44.23  0.1697"
            ],
            "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>M</th>\n",
              "      <th>θ</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>A</th>\n",
              "      <td>0.00</td>\n",
              "      <td>0.0000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>B</th>\n",
              "      <td>221.16</td>\n",
              "      <td>0.0000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>C</th>\n",
              "      <td>221.16</td>\n",
              "      <td>0.0339</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>D</th>\n",
              "      <td>44.23</td>\n",
              "      <td>0.0339</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>E</th>\n",
              "      <td>44.23</td>\n",
              "      <td>0.1697</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 31,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Ενεργός δυσκαμψία. Συντελεστής για SAP"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "K = My * Ls / (3 * θy)\n",
        "print(f'K={K:.1f}kNm2')\n",
        "\n",
        "I = b * h**3 / 12.0\n",
        "K0 = Ec * I\n",
        "print(f'K0={K0:.1f}kNm2')\n",
        "\n",
        "ModFactor = K / K0\n",
        "\nprint(\"Modification Factor for SAP=\" + \"{0:.3f}\".format(ModFactor))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "K=13371.6kNm2\n",
            "K0=86454.8kNm2\n",
            "Modification Factor for SAP=0.155\n"
          ]
        }
      ],
      "execution_count": 32,
      "metadata": {}
    }
  ],
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