From 618c34129b03470e6c277951be0b7f80ed38e4d8 Mon Sep 17 00:00:00 2001 From: Guus Date: Wed, 27 Mar 2024 12:45:26 +0100 Subject: [PATCH] Update beams on supports --- .../Images/Beams on multiple supports 2.png | Bin 0 -> 12852 bytes .../Images/Beams on multiple supports.png | Bin 0 -> 9046 bytes .../Images/Forgetmenots 1.jpg | Bin 0 -> 85754 bytes .../Images/Forgetmenots 2.jpg | Bin 0 -> 54128 bytes .../Images/Forgetmenots 3.jpg | Bin 0 -> 154631 bytes .../beams_with_multiple_supports.ipynb | 92 +++++++++++++++++- .../general_mechanics/forget_me_nots.ipynb | 15 ++- .../general_mechanics/mechanic_formulas.ipynb | 21 +++- 8 files changed, 125 insertions(+), 3 deletions(-) create mode 100644 book/design_workflow/general_mechanics/Images/Beams on multiple supports 2.png create mode 100644 book/design_workflow/general_mechanics/Images/Beams on multiple supports.png create mode 100644 book/design_workflow/general_mechanics/Images/Forgetmenots 1.jpg create mode 100644 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z%}%YFEJcZ?u6^(vjWM?dwR-pmErpP0Q!H^ico62R>WW&dYu}*A%f|PoPYOGO#-<!3Gz-j#N`P>3D~sU)4SMi znkcVC_G8&bP&XaLT<)dcGYGBTDYnO?5YmsDGIr|Esk5|I6iP zKtX2+q?vkubXcr^FK=|P0yv(i8YtP&>4Gc<%0&L)_k~m-Lkv+P{~vh?tU#X;O$*kr z&m*5Qyb7f*DJ@ zK(9_OAod~%{lR_@I4yy%25)It(4#;DT_uXrpFw{<)gyiaYzgeA$vXTXb1UG literal 0 HcmV?d00001 diff --git a/book/design_workflow/general_mechanics/beams_with_multiple_supports.ipynb b/book/design_workflow/general_mechanics/beams_with_multiple_supports.ipynb index 852d5a7..f7c65e6 100644 --- a/book/design_workflow/general_mechanics/beams_with_multiple_supports.ipynb +++ b/book/design_workflow/general_mechanics/beams_with_multiple_supports.ipynb @@ -12,7 +12,97 @@ { "cell_type": "markdown", "metadata": {}, - "source": [] + "source": [ + "## Beams on multiple supports (concentrated loads)\n", + "```{figure} Images/Beams on multiple supports.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "\n", + "| Type | M(1) | M2 | M(2) | M3 | M(3) | R1 | R2 | R3 | R4 |\n", + "|------|--------|--------|--------|--------|--------|--------|--------|--------|--------|\n", + "| a | 0.1562 | -0.1875| 0.1562 | || 0.3125 | 1.3750 | 0.3125 | | | |\n", + "| b | 0.2031 | -0.0938| -0.0469||| 0.4062 | 0.6876 | -0.0938| | | |\n", + "| c | 0.1750 | -0.1500| 0.1000 | -0.1500| 0.1750 | 0.3500 | 1.1500 | 1.1500 | 0.3500 |\n", + "| d | 0.2125 | -0.0750| -0.0750| -0.0750| 0.2125 | 0.4250 | 0.5750 | 0.5750 | 0.4250 |\n", + "| e | -0.0375| -0.0750| 0.1750 | -0.0750| -0.0375| -0.0750| 0.5750 | 0.5750 | -0.0750|\n", + "| f | 0.1625 | -0.0175| 0.1375 | -0.0500| -0.0250| 0.3250 | 1.3000 | 0.4250 | -0.0500|\n", + "| g | 0.2000 | -0.1000| -0.0375| 0.0250 | 0.0125 | 0.4000 | 0.7250 | -0.1500| 0.0250 |\n", + "\n", + "$M = factor * F * L$ \n", + "$R = factor *x* F$\n", + "\n", + "The numbers in the tables are related to the concentrated loads working on the structure. The bending moments and support reactions in the designated points are found by multiplying the factors in the table with F x L or F.\n", + "\n", + "For example:\n", + "- M(1) is the maximum bending in beam (1).\n", + "- M3 is the hogging moment located at support 3.\n", + "- R2 is the support reaction in support 2.\n", + "\n", + "For situation c:\n", + "- F = 30 kN\n", + "- L = 8 m\n", + "\n", + "The calculations are as follows:\n", + "- M(1) = 0.175 x 30 x 8 kNm\n", + "- M3 = -0.15 x 30 x 8 kNm\n", + "- R2 = 1.15 x 30 kN\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Beams on multiple supports (distributed load)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{figure} Images/Beams on multiple supports 1.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "\n", + "| Type | M(1) location rel. to 1* | M2 | M(2) location rel. to 2** | M3 | M(3) | R1 | R2 | R3 | R4 |\n", + "|------|---------------------------|--------|----------------------------|--------|------|--------|--------|--------|--------|\n", + "| h | 0.0703 | 0.3750 | -0.1250 | 0.0703 | 0.6250||| 0.3750 | 1.2500 | 0.3750 | |\n", + "| i | 0.0957 | 0.4375 | -0.0625 | -0.0313| || | 0.4375 | 0.6250 | -0.0625| |\n", + "| j | 0.0800 | 0.4000 | -0.1000 | 0.0250 | 0.5000| -0.1000| 0.0800 | 0.4000 | 1.1000 | 1.1000 | 0.4000 |\n", + "| k | 0.1013 | 0.4500 | -0.0500 | -0.0500| | -0.0500| 0.1013 | 0.4500 | 0.5500 | 0.5500 | 0.4500 |\n", + "| l | -0.025 | | -0.0500 | 0.0750 | 0.5000| -0.0500| | -0.0500| 0.5500 | 0.5500 | -0.0500|\n", + "| m | 0.0735 | 0.3833 | -0.1167 | 0.0535 | 0.5830| -0.0333| | 0.3833 | 1.2001 | 0.4499 | -0.0333|\n", + "| n | 0.0939 | 0.4333 | -0.0667 | -0.0250| | 0.0167 | | 0.4333 | 0.6501 | -0.1001| 0.0167 |\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$M = factor * q * L^2$ \n", + "$R = factor * q * L$\n", + "\n", + "The numbers in the tables are related to the concentrated loads\n", + "working on the structure. The bending moments and support reactions in\n", + "the designated points are found by multiplying the factors in the table with\n", + "$q * L^2$ or $q * L$.\n", + "\n", + "For example: M(1) is the maximum bending in beam\n", + "(1). M3 is the hogging moment located at\n", + "support 3. R2 is the support reaction in support 2. \n", + " \n", + "For situation m: \n", + "$F = 5 kN/m$\n", + "$L = 6 m$ \n", + "$M(1) = 0,0735 * 5 * 62 kNm$ \n", + "$M3 = -0,0333 * 5 * 62 kNm$ \n", + "$R2 = 1,2001 * 5 * 6 kN$ \n", + " \n", + "*) location of bending moment M(1) in relation to support 1 (distance = factor x L) \n", + "**) location of bending moment M(2) in relation to support 2 (distance = factor\n", + "x L) " + ] } ], "metadata": { diff --git a/book/design_workflow/general_mechanics/forget_me_nots.ipynb b/book/design_workflow/general_mechanics/forget_me_nots.ipynb index 46cbdfd..4c400bd 100644 --- a/book/design_workflow/general_mechanics/forget_me_nots.ipynb +++ b/book/design_workflow/general_mechanics/forget_me_nots.ipynb @@ -10,7 +10,20 @@ { "cell_type": "markdown", "metadata": {}, - "source": [] + "source": [ + "```{figure} Images/Forgetmenots 1.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```{figure} Images/Forgetmenots 2.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```{figure} Images/Forgetmenots 3.jpg\n", + "---\n", + "scale: 100%\n", + "---" + ] } ], "metadata": { diff --git a/book/design_workflow/general_mechanics/mechanic_formulas.ipynb b/book/design_workflow/general_mechanics/mechanic_formulas.ipynb index fa4cc33..e643cfb 100644 --- a/book/design_workflow/general_mechanics/mechanic_formulas.ipynb +++ b/book/design_workflow/general_mechanics/mechanic_formulas.ipynb @@ -12,7 +12,26 @@ { "cell_type": "markdown", "metadata": {}, - "source": [] + "source": [ + "| | Kinematic relations | Constitutive relations | Static relations | Differential equation |\n", + "|--------|-------------------------------------|--------------------------------------|-----------------------------------|---------------------------------|\n", + "| Extension | $\\epsilon = \\frac{du}{dx}$ | $ N = EA \\epsilon $ | $\\frac{dN}{dx} + q_x = 0$ | $EA \\frac{d^2u}{dx^2} + q_x = 0$ |\n", + "| Bending | $\\phi = -\\frac{dw}{dx}$; $\\kappa = \\frac{d\\phi}{dx}$; $\\kappa=-\\frac{d^2w}{dx^2}$ | $M=EI\\kappa$|$\\frac{dV}{dx}+q_z=0$; $\\frac{dM}{dx}-v=0$; $\\frac{d^2M}{dx^2}+q_z=0$ | $-EI\\frac{d^4w}{dx^4}+q_z=0$|\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$\\epsilon (z) = \\epsilon + \\kappa_z z$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$\\sigma(z)=\\sigma^N+\\sigma^N=\\frac{N}{A}+\\frac{M_z z}{I_zz}$" + ] } ], "metadata": {