panagop/M-θ for notes (beams).ipynb

## M-θ for notes (beams).ipynb
{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Υπολογισμός διαγραμμάτων Μ-θ σύμφωνα με τον ΚΑΝ.ΕΠΕ."
      ],
      "metadata": {
        "slideshow": {
          "slide_type": "-"
        }
      }
    },
    {
      "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": 137,
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Δεδομένα παραδείγματος\n",
        "\n",
        "Δίνεται η διατομή του σχήματος που βρίσκεται στις κρίσιμες περιοχές της εσωτερικής δοκού του ισογείου του φορέα των σημειώσεων.\n",
        "\n",
        "![Imgur](https://i.imgur.com/VtnieT0.png)\n",
        "\n\n",
        "### Διαστάσεις της διατομής\n",
        "\n",
        "$b=0.25m$\n",
        "\n",
        "$h=0.65m$\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",
        "$A_s = 12.72cm^2$ για 5∅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",
        "$A_{sv} = 0cm^2$ \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",
        "$A_{sw} = 1.01cm^2$ για 2τμητους ∅8\n",
        "\n",
        "$s=150mm=0.15m$ Η απόσταση μεταξύ των συνδετήρων\n",
        "\n",
        "### Διαστάσεις του δομικού στοιχείου\n",
        "\n",
        "$L_s = 2.525m$ το μήκος διάτμησης\n",
        "\n\n"
      ],
      "metadata": {
        "nbpresent": {
          "id": "9e5a69e0-f4c0-40f3-a6fe-b9c46a89f1aa"
        },
        "slideshow": {
          "slide_type": "-"
        }
      }
    },
    {
      "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 = 0.25 # το πλάτος της θλιβόμενης ζώνης[m] \n",
        "h = 0.60 # 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",
        "# Οπλισμός\n",
        "## Επικάλυψη\n",
        "cnom = 0.03       # [m] \n",
        "## Διαμήκης \n",
        "### Εφελκυόμενος\n",
        "nL = 5            # 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 = 0           # Ο αριθτμός των ενδιάμεσων ράβδων\n",
        "ΦLv = 0.          # 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 = 2            # Ο αριθμός των \"τμήσεων\" των συνδετήρων (πχ. 2 για 2τμητους)\n",
        "Φw = 0.008        # Η διάμετρος των συνδετήρων [m] \n",
        "s = 0.15          # Η απόσταση μεταξύ των συνδετήρων [m] \n",
        "# Asw=1.01cm2Asw=1.01cm2 για 2τμητους ∅8\n",
        "\n",
        "# Οπλισμός\n",
        "N = 0.            # Αξονικό φορτίο [kN]\n",
        "\n",
        "# Μήκος διάτμησης\n",
        "Ls = 2.525        # [m]\n",
        "\n",
        "# Αποστάσεις bi περίσφιξης [m]\n",
        "bi = np.array([0.0, 0.0]) "
      ],
      "outputs": [],
      "execution_count": 138,
      "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": 139,
      "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": 140,
      "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": 141,
      "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": 142,
      "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": 143,
      "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 = 4.21\n"
          ]
        }
      ],
      "execution_count": 144,
      "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 = 0.001272m2 = 12.72cm2\n",
            "Εμβαδό του θλιβόμενου οπλισμού: As2 = 0.000763m2 = 7.63cm2\n",
            "Εμβαδό του ενδιάμεσου οπλισμού: Asv = 0.000000m2 = 0.00cm2\n",
            "Εμβαδό του δισδιαγώνιου οπλισμού: Asd = 0.000000m2 = 0.00cm2\n",
            "Εμβαδό του εγκάρσιου οπλισμού: Asw = 0.000101m2 = 1.01cm2\n",
            "Συνολικό εμβαδό του διαμήκους οπλισμού: Astot = 0.002036m2 = 20.36cm2\n"
          ]
        }
      ],
      "execution_count": 145,
      "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=0.553m\n",
            "Λόγος δ`=0.085\n",
            "Απόσταση των συνδετήρων: sh=0.150m\n",
            "Παρατήρηση: Σε παλιότερες εκδόσεις του ΚΑΝ.ΕΠΕ. ως sh ορίζονταν η καθαρή απόσταση s-Φw\n",
            "\n",
            "Ο μοχλοβραχίονας εσωτερικών δυνάμεων: z=0.506m\n"
          ]
        }
      ],
      "execution_count": 146,
      "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 = 0.00920 = 9.20‰\n",
            "Μηχανικό ποσοστό του εφελκυόμενου οπλισμού: ω = 0.288\n",
            "\n",
            "Ποσοστό του θλιβόμενου οπλισμού: ρ` = ρ2 = 0.00552 = 5.52‰\n",
            "Μηχανικό ποσοστό του θλιβόμενου οπλισμού: ω` = ω2 = 0.173\n",
            "\n",
            "Ποσοστό του ενδιάμεσου οπλισμού: ρv = 0.00000 = 0.00‰\n",
            "Μηχανικό ποσοστό του ενδιάμεσου οπλισμού: ωv = 0.000\n",
            "\n",
            "Συνολικό ποσοστό του διαμήκους οπλισμού: ρtot = 0.01473 = 14.73‰\n",
            "Συνολικό μηχανικό ποσοστό του διαμήκους οπλισμού: ωtot = 0.460\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 = 0.00268 = 2.68‰\n",
            "Ποσοστό του εγκάρσιου οπλισμού (σχέση EC2): ρw = 0.00268 = 2.68‰\n"
          ]
        }
      ],
      "execution_count": 147,
      "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": 148,
      "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 = 0.01473\n",
            "B = 0.00967\n",
            "ξy = 0.292\n",
            "φy = 0.00638m-1\n"
          ]
        }
      ],
      "execution_count": 149,
      "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 = 0.01473\n",
            "B = 0.00967\n",
            "ξy = 0.292\n",
            "φy = 0.00706m-1\n"
          ]
        }
      ],
      "execution_count": 150,
      "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 = 0.292\n",
            "xy = 0.161m (Το ύψος της θλιβόμενης ζώνης στη διαρροή)\n",
            "φy = 0.00638m-1\n",
            "My = 318.36kNm\n"
          ]
        }
      ],
      "execution_count": 151,
      "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 = 0.00721m-1\n",
            "φy = 0.00687m-1\n"
          ]
        }
      ],
      "execution_count": 152,
      "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",
        "# def VRc(ρtot, d, fc, N, Ac):\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 = 0.00920\n",
            "k = 1.601\n",
            "vmin = 0.284\n",
            "VRdc (1η σχέση EC2) = 97675.7N\n",
            "VRdc (2η σχέση EC2) = 39222.6N\n",
            "V_kanepe = 114.24kN\n",
            "Vdc = 114.24kN\n"
          ]
        }
      ],
      "execution_count": 153,
      "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 = 126.08kN\n",
            "αv = 1.0\n"
          ]
        }
      ],
      "execution_count": 154,
      "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 = 0.0101\n"
          ]
        }
      ],
      "execution_count": 155,
      "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=0.000\n",
            "bo=0.182m\n",
            "ho=0.532m\n",
            "hc/bc > 2.0 οπότε χρησιμοποιείται, αντί του ho, το ύψος της θλιβόµενης ζώνης εντός του περισφιγμένου πυρήνα\n",
            "ho=0.127m\n",
            "Σbi2=0.0986m2\n",
            "Συντελεστής αποδοτικότητας περίσφιξης: α=0.0701\n",
            "θu=0.0449\n"
          ]
        }
      ],
      "execution_count": 156,
      "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": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 157,
      "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=4.42\n"
          ]
        }
      ],
      "execution_count": 158,
      "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=169.56kN=0.16956MN\n"
          ]
        }
      ],
      "execution_count": 159,
      "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": 160,
      "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": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 161,
      "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": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 162,
      "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": 163,
      "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=318.36kNm\n",
            "θy=0.0101\n",
            "θu=0.0449\n"
          ]
        }
      ],
      "execution_count": 164,
      "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": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 165,
      "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=0.0347\n"
          ]
        }
      ],
      "execution_count": 166,
      "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": 167,
          "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>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>318.36</td>\n",
              "      <td>0.0000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>C</th>\n",
              "      <td>318.36</td>\n",
              "      <td>0.0347</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>D</th>\n",
              "      <td>63.67</td>\n",
              "      <td>0.0347</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>E</th>\n",
              "      <td>63.67</td>\n",
              "      <td>0.1735</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        M       θ\n",
              "A    0.00  0.0000\n",
              "B  318.36  0.0000\n",
              "C  318.36  0.0347\n",
              "D   63.67  0.0347\n",
              "E   63.67  0.1735"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 167,
      "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=26421.0kNm2\n",
            "K0=113850.0kNm2\n",
            "Modification Factor for SAP=0.232\n"
          ]
        }
      ],
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