diff --git a/book/design_workflow/general_mechanics/Images/Beams on multiple supports 2.png b/book/design_workflow/general_mechanics/Images/Beams on multiple supports 2.png new file mode 100644 index 0000000..be084ec Binary files /dev/null and b/book/design_workflow/general_mechanics/Images/Beams on multiple supports 2.png differ diff --git a/book/design_workflow/general_mechanics/Images/Beams on multiple supports.png b/book/design_workflow/general_mechanics/Images/Beams on multiple supports.png new file mode 100644 index 0000000..c0a67b1 Binary files /dev/null and b/book/design_workflow/general_mechanics/Images/Beams on multiple supports.png differ diff --git a/book/design_workflow/general_mechanics/Images/Forgetmenots 1.jpg b/book/design_workflow/general_mechanics/Images/Forgetmenots 1.jpg new file mode 100644 index 0000000..8ea134b Binary files /dev/null and b/book/design_workflow/general_mechanics/Images/Forgetmenots 1.jpg differ diff --git a/book/design_workflow/general_mechanics/Images/Forgetmenots 2.jpg b/book/design_workflow/general_mechanics/Images/Forgetmenots 2.jpg new file mode 100644 index 0000000..d8e36b7 Binary files /dev/null and b/book/design_workflow/general_mechanics/Images/Forgetmenots 2.jpg differ diff --git a/book/design_workflow/general_mechanics/Images/Forgetmenots 3.jpg b/book/design_workflow/general_mechanics/Images/Forgetmenots 3.jpg new file mode 100644 index 0000000..3ac23f8 Binary files /dev/null and b/book/design_workflow/general_mechanics/Images/Forgetmenots 3.jpg differ 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": {