diff --git a/book/design_workflow/general_loads/Images/Positive external pressure.png b/book/design_workflow/general_loads/Images/Positive external pressure.png new file mode 100644 index 0000000..77eb314 Binary files /dev/null and b/book/design_workflow/general_loads/Images/Positive external pressure.png differ diff --git a/book/design_workflow/general_loads/Images/Positive internal pressure.png b/book/design_workflow/general_loads/Images/Positive internal pressure.png new file mode 100644 index 0000000..3be1e03 Binary files /dev/null and b/book/design_workflow/general_loads/Images/Positive internal pressure.png differ diff --git a/book/design_workflow/general_loads/Images/Wind zones canopies 2.png b/book/design_workflow/general_loads/Images/Wind zones canopies 2.png new file mode 100644 index 0000000..5f2060a Binary files /dev/null and b/book/design_workflow/general_loads/Images/Wind zones canopies 2.png differ diff --git a/book/design_workflow/general_loads/Images/Wind zones canopies 3.png b/book/design_workflow/general_loads/Images/Wind zones canopies 3.png new file mode 100644 index 0000000..489aff4 Binary files /dev/null and b/book/design_workflow/general_loads/Images/Wind zones canopies 3.png differ diff --git a/book/design_workflow/general_loads/Images/Wind zones canopies.png b/book/design_workflow/general_loads/Images/Wind zones canopies.png new file mode 100644 index 0000000..9ee5975 Binary files /dev/null and b/book/design_workflow/general_loads/Images/Wind zones canopies.png differ diff --git a/book/design_workflow/general_loads/Images/Windbox.png b/book/design_workflow/general_loads/Images/Windbox.png new file mode 100644 index 0000000..2c807d6 Binary files /dev/null and b/book/design_workflow/general_loads/Images/Windbox.png differ diff --git a/book/design_workflow/general_loads/Images/Windzones 1.png b/book/design_workflow/general_loads/Images/Windzones 1.png new file mode 100644 index 0000000..0d8c63c Binary files /dev/null and b/book/design_workflow/general_loads/Images/Windzones 1.png differ diff --git a/book/design_workflow/general_loads/Images/Windzones 2.png b/book/design_workflow/general_loads/Images/Windzones 2.png new file mode 100644 index 0000000..1ea23f7 Binary files /dev/null and b/book/design_workflow/general_loads/Images/Windzones 2.png differ diff --git a/book/design_workflow/general_loads/Images/Windzones NL.png b/book/design_workflow/general_loads/Images/Windzones NL.png new file mode 100644 index 0000000..23c6dc6 Binary files /dev/null and b/book/design_workflow/general_loads/Images/Windzones NL.png differ diff --git a/book/design_workflow/general_loads/Images/Windzones roofs 1.png b/book/design_workflow/general_loads/Images/Windzones roofs 1.png new file mode 100644 index 0000000..2162e7f Binary files /dev/null and b/book/design_workflow/general_loads/Images/Windzones roofs 1.png differ diff --git a/book/design_workflow/general_loads/Images/Windzones roofs 2.png b/book/design_workflow/general_loads/Images/Windzones roofs 2.png new file mode 100644 index 0000000..9d7e49e Binary files /dev/null and b/book/design_workflow/general_loads/Images/Windzones roofs 2.png differ diff --git a/book/design_workflow/general_loads/Images/Windzones roofs 3.png b/book/design_workflow/general_loads/Images/Windzones roofs 3.png new file mode 100644 index 0000000..bcd6cdb Binary files /dev/null and b/book/design_workflow/general_loads/Images/Windzones roofs 3.png differ diff --git a/book/design_workflow/general_loads/variable_loads_2_wind.ipynb b/book/design_workflow/general_loads/variable_loads_2_wind.ipynb index cb2d86f..f364c61 100644 --- a/book/design_workflow/general_loads/variable_loads_2_wind.ipynb +++ b/book/design_workflow/general_loads/variable_loads_2_wind.ipynb @@ -10,7 +10,398 @@ { "cell_type": "markdown", "metadata": {}, - "source": [] + "source": [ + "Loads caused by wind can be considerable and therefore have to be\n", + "studied with care. For design purposes it is sometimes possible to use a\n", + "simplified version of the code such as the one below. \n", + "\n", + "```{note}\n", + "For a detailed analysis or for building with an irregular shape, always use NEN-EN 1991-1-4 General Actions - Wind Actions.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Determining the wind loading (simplified formula)\n", + "$F_i = c_s · c_d · c_f · q_p(z_e) · A_{ref}$\n", + "\n", + "$F_i$ = Wind force on a structure or structural component [$kN$] \n", + "$c_s * c_ d$ = Structural factor1 [-] \n", + "$c_f$ = Force coefficient for structure or structural component [-] \n", + "$q_p(z_e)$ = Peak velocity pressure at reference height2 ze [$kN/m^2$] \n", + "$A_{ref}$ = Reference area on structure or structural component [$m^2$] \n", + "\n", + "```{note}\n", + "1. The structural factor cscd can be taken as 1 for regular, low-rise buildings, for more information see NEN-EN 1991-1-4 \n", + "2. For high buildings (h>b) the velocity pressure may be assumed to decline towards ground level, for details see NEN-EN 1991-1-4\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Force coefficient for structures and strucural components: roofs and façades\n", + "In this section the force coefficients for a simple building will be pointed\n", + "out. As Eurocode is very extensive, the method for determining wind load\n", + "will be pointed out using a simple structure. For more complicated\n", + "shapes, use NEN-EN 1991-1-4. The directions of the different wind loads\n", + "first need to be determined:\n", + "\n", + "The force coefficients corresponding to the different wind zones depend on the\n", + "geometry of the building. For certain values the force coefficients are given.\n", + "For other values linear interpolation is allowed. In this section only the force\n", + "coefficients belonging to large surfaces are given (>10m2). For smaller surfaces see NEN-EN-1991-1-4.\n", + "\n", + "```{figure} Images/Positive external pressure.png\n", + "---\n", + "scale: 100%\n", + "align: right\n", + "---\n", + "Positive external pressure\n", + "```\n", + "\n", + "```{figure} Images/Positive internal pressure.png\n", + "---\n", + "scale: 100%\n", + "align: right\n", + "---\n", + "Positive internal pressure\n", + "```\n", + "\n", + "```{note}\n", + "Both these pressures need to be combined in the most unfavourable way.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Building parameters" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$h$ = highest point of building [$m$] \n", + "$d$ = dimension in wind direction [$m$] \n", + "$b$ = dimension in crosswind direction \n", + "$e$ = $b$ or $2h$, whichever is smaller \n", + "\n", + "```{Note}\n", + "For both wind directions a different set of parameters applies.\n", + "```\n", + "\n", + "```{figure} Images/Windbox.png\n", + "---\n", + "scale: 100%\n", + "align: right\n", + "---\n", + "Building parameters\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Windzones for façades" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The different windzones on the façades of a building are shown below.\n", + "Note that for different values of e and d the number of windzones on the\n", + "side façades differ from 1 to 3. For buildings with duopitch roofs the same\n", + "zones apply. The value h should then be taken as the height of the roof-ridge\n", + "above ground level.\n", + "\n", + "|Façades | | | | | |\n", + "|---------|---------|----------|----------|----------|----------|\n", + "| | A | B | C | D | E |\n", + "| h/d = 5 | -1.2 | -0.8 | -0.5 | +0.8 | -0.7 |\n", + "| h/d = 1 | -1.2 | -0.8 | -0.5 | +0.8 | -0.5 |\n", + "| h/d ≤ 0.25 | -1.2 | -0.8 | -0.5 | +0.7 | -0.3 |\n", + "\n", + "```{figure} Images/Windzones 1.png\n", + "---\n", + "scale: 100%\n", + "align: right\n", + "---\n", + "```\n", + "\n", + "```{figure} Images/Windzones 2.png\n", + "---\n", + "scale: 100%\n", + "align: right\n", + "---\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Windzones for flat roofs (closed buildings)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{figure} Images/Windzones roofs 1.png\n", + "---\n", + "scale: 100%\n", + "align: right\n", + "---\n", + "```\n", + " \n", + "| Type | F | G | H | I |\n", + "|-------------|-------|-------|-------|----------|\n", + "| Sharp eaves | -1.8 | -1.2 | -0.7 | +0.2/-0.2|\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Windzones for duopitch roofs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{figure} Images/Windzones roofs 2.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + " \n", + "```{figure} Images/Windzones roofs 3.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + " \n", + "| Roof Angle (α) | F | G | H | I | J |\n", + "|----------------|---------|---------|---------|---------|---------|\n", + "| 5º | -1.7 | -1.2 | -0.6 | -0.6 | +0.2 |\n", + "| | +0.0 | +0.0 | +0.0 | -0.6 | -0.6 |\n", + "|----------------|---------|---------|---------|---------|---------|\n", + "| 15º | -0.9 | -0.8 | -0.3 | -0.4 | -1.0 |\n", + "| | +0.2 | +0.2 | +0.2 | +0.0 | +0.0 |\n", + "|----------------|---------|---------|---------|---------|---------|\n", + "| 30º | -0.5 | -0.5 | -0.2 | -0.4 | -0.5 |\n", + "| | +0.7 | +0.7 | +0.4 | +0.0 | +0.0 |\n", + "|----------------|---------|---------|---------|---------|---------|\n", + "| 45º | 0.0 | 0.0 | 0.0 | -0.2 | -0.3 |\n", + "| | +0.7 | +0.7 | +0.6 | +0.0 | +0.0 |\n", + "|----------------|---------|---------|---------|---------|---------|\n", + "| 60º | +0.7 | +0.7 | +0.7 | -0.2 | -0.3 |\n", + "| 75º | +0.8 | +0.8 | +0.8 | -0.2 | -0.3 |\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "| Roof Angle (α) | F | G | H | I |\n", + "|----------------|---------|---------|---------|---------|\n", + "| 5º | -1.6 | -2.2 | -0.7 | -0.6 |\n", + "|----------------|---------|---------|---------|---------|\n", + "| 15º | -1.3 | -2.0 | -0.6 | -0.5 |\n", + "|----------------|---------|---------|---------|---------|\n", + "| 30º | -1.1 | -1.5 | -0.8 | -0.5 |\n", + "|----------------|---------|---------|---------|---------|\n", + "| 45º | -1.1 | -1.5 | -0.9 | -0.5 |\n", + "|----------------|---------|---------|---------|---------|\n", + "| 60º | -1.1 | -1.5 | -0.8 | -0.5 |\n", + "|----------------|---------|---------|---------|---------|\n", + "| 75º | -1.1 | -1.5 | -0.8 | -0.5 |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Windzones for canopies" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For canopies a resultant force can be determined (without the use of wind\n", + "zones). This force represents the effect of all windzones on the total structure.\n", + "The force acts on the points depicted below and is calculated with the same\n", + "formula as other windloads. The location where this force acts depends\n", + "on geometry and the sign of the overall force coefficient ($c_f$).\n", + "\n", + "```{figure} Images/Wind zones canopies.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "Locally the wind pressure or suction on the canopy can of course be\n", + "larger than the average. For the design of roofing elements and fixings\n", + "these local loads must be taken into account. To calculate the local\n", + "wind actions the canopy is divided in different windzones as shown below.\n", + "\n", + "```{figure} Images/Wind zones canopies 2.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "Both the local and resultant force coefficient depents on the blockage\n", + "(φ) under the canopy. The blockage is defined as the ratio of the area of the\n", + "feasible, actual obstructions under the canopy divided by the cross\n", + "sectional area under the canopy.\n", + "\n", + "```{figure} Images/Wind zones canopies 3.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "| Roof Angle (α) | Blockage Factor (φ) | Overall Force cf | A | B | C |\n", + "|----------------|----------------------|------------------|---------|---------|---------|\n", + "| 0º | Maximum all φ | +0.2 | +0.5 | +1.8 | +1.1 |\n", + "| | Minimum φ=0 | -0.5 | -0.6 | -1.3 | -1.4 |\n", + "| | Minimum φ=1 | -1.3 | -1.5 | -1.8 | -2.2 |\n", + "| 5º | Maximum all φ | +0.4 | +0.8 | +2.1 | +1.3 |\n", + "| | Minimum φ=0 | -0.7 | -1.1 | -1.7 | -1.8 |\n", + "| | Minimum φ=1 | -1.4 | -1.6 | -2.2 | -2.5 |\n", + "| 10º | Maximum all φ | +0.5 | +1.2 | +2.4 | +1.6 |\n", + "| | Minimum φ=0 | -0.9 | -1.5 | -2.0 | -2.1 |\n", + "| | Minimum φ=1 | -1.4 | -2.1 | -2.6 | -2.7 |\n", + "| 15º | Maximum all φ | +0.7 | +1.4 | +2.7 | +1.8 |\n", + "| | Minimum φ=0 | -1.1 | -1.8 | -2.4 | -2.5 |\n", + "| | Minimum φ=1 | +1.4 | -1.6 | -2.9 | -3.0 |\n", + "| 20º | Maximum all φ | +0.8 | +1.7 | +2.9 | +2.1 |\n", + "| | Minimum φ=0 | -1.3 | -2.2 | -2.8 | -2.9 |\n", + "| | Minimum φ=1 | -1.4 | -1.6 | -2.9 | -3.0 |\n", + "| 25º | Maximum all φ | +1.0 | +2.0 | +3.1 | +2.3 |\n", + "| | Minimum φ=0 | -1.6 | -2.6 | -3.2 | -3.2 |\n", + "| | Minimum φ=1 | -1.4 | -1.5 | -2.5 | -2.8 |\n", + "| 30º | Maximum all φ | +1.2 | +2.2 | +3.2 | +2.4 |\n", + "| | Minimum φ=0 | -1.8 | -3.0 | -3.8 | -3.6 |\n", + "| | Minimum φ=1 | -1.4 | -1.5 | -2.2 | -2.7 |\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1 For other edges lower force coefficients may be applicable, see NEN-EN-1991-1-4 \n", + "2 For $θ=0$, between $α = 0º$ and $45º$ the pressure changes rapidly between positive and negative values. For those roofs, four cases should be considered where the largest or smallest values of all areas F, G, and H are combined with the largest or smallest values in areas I and J. No mixing of positive and negative values is allowed on the same face." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Force coefficients for friction\n", + "On faces parallel to the wind a friction force is acting. For design purposes it\n", + "may be assumed that this force acts along all faces parallel to the wind\n", + "direction. According NEN-EN-1991-1-4 this area can be reduced dependent\n", + "on geometry.\n", + " \n", + "| Surface | Friction Coefficient ($c_{fr}$) |\n", + "|--------------------------------------|----------------------------|\n", + "| Smooth (e.g.: smooth concrete, steel)| 0.01 |\n", + "| Rough (e.g.: rough concrete, tar-boards)| 0.02 |\n", + "| Very rough (e.g.: ripples, folds, ribs)| 0.04 |\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Force coefficients for internal pressure\n", + "The force coefficients for internal pressure depend on the amount of\n", + "openings in the façades and the geometry of the building. To avoid too\n", + "complicated calculations, for design a note is stated in NEN-EN-1991-1-4:\n", + "‘Where it is not possible, or not considered justified, to estimate $μ$\n", + "[dependend on geometry] then cpi should be taken as the more onerous\n", + "(unfavourable red.) of +0,2 and -0,3.’ However, if the total amount of\n", + "openings on two façades exeeds 30% of the area of those façades, the rules\n", + "for canopies should be applied." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Windregions in the Netherlands" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{figure} Images/Windzones NL.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Peak velocity pressure\n", + "| | Coastal Area I | Rural Area I | Urban Area I | Coastal Area II | Rural Area II | Urban Area II | Coastal Area III | Rural Area III | Urban Area III |\n", + "|---|----------------|--------------|--------------|----------------|---------------|---------------|-----------------|----------------|----------------|\n", + "| 1 | 0.93 | 0.71 | 0.69 | 0.78 | 0.60 | 0.58 | 0.49 | 0.48 | 0.48 |\n", + "| 2 | 1.11 | 0.71 | 0.69 | 0.93 | 0.60 | 0.58 | 0.49 | 0.48 | 0.48 |\n", + "| 3 | 1.22 | 0.71 | 0.69 | 1.02 | 0.60 | 0.58 | 0.49 | 0.48 | 0.48 |\n", + "| 4 | 1.30 | 0.71 | 0.69 | 1.09 | 0.60 | 0.58 | 0.49 | 0.49 | 0.48 |\n", + "| 5 | 1.37 | 0.78 | 0.69 | 1.14 | 0.66 | 0.58 | 0.54 | 0.48 | 0.48 |\n", + "| 6 | 1.42 | 0.84 | 0.69 | 1.19 | 0.71 | 0.58 | 0.58 | 0.48 | 0.48 |\n", + "| 7 | 1.47 | 0.89 | 0.69 | 1.23 | 0.75 | 0.58 | 0.62 | 0.48 | 0.48 |\n", + "| 8 | 1.51 | 0.94 | 0.73 | 1.26 | 0.79 | 0.62 | 0.65 | 0.51 | 0.48 |\n", + "| 9 | 1.55 | 0.98 | 0.77 | 1.29 | 0.82 | 0.65 | 0.68 | 0.53 | 0.48 |\n", + "| 10| 1.58 | 1.02 | 0.81 | 1.32 | 0.85 | 0.68 | 0.70 | 0.56 | 0.48 |\n", + "| 15| 1.71 | 1.16 | 0.96 | 1.43 | 0.98 | 0.80 | 0.80 | 0.66 | 0.66 |\n", + "| 20| 1.80 | 1.27 | 1.07 | 1.51 | 1.07 | 0.90 | 0.88 | 0.74 | 0.74 |\n", + "| 25| 1.88 | 1.36 | 1.16 | 1.57 | 1.14 | 0.97 | 0.94 | 0.80 | 0.80 |\n", + "| 30| 1.94 | 1.43 | 1.23 | 1.63 | 1.20 | 1.03 | 0.99 | 0.85 | 0.85 |\n", + "| 35| 2.00 | 1.50 | 1.30 | 1.67 | 1.25 | 1.09 | 1.03 | 0.89 | 0.89 |\n", + "| 40| 2.04 | 1.55 | 1.35 | 1.71 | 1.30 | 1.13 | 1.07 | 0.93 | 0.93 |\n", + "| 45| 2.09 | 1.60 | 1.40 | 1.75 | 1.34 | 1.17 | 1.11 | 0.97 | 0.97 |\n", + "| 50| 2.12 | 1.65 | 1.45 | 1.78 | 1.38 | 1.21 | 1.14 | 1.00 | 1.00 |\n", + "| 55| 2.16 | 1.69 | 1.49 | 1.81 | 1.42 | 1.25 | 1.17 | 1.03 | 1.03 |\n", + "| 60| 2.19 | 1.73 | 1.53 | 1.83 | 1.45 | 1.28 | 1.19 | 1.05 | 1.05 |\n", + "| 65| 2.22 | 1.76 | 1.57 | 1.86 | 1.48 | 1.31 | 1.22 | 1.08 | 1.08 |\n", + "| 70| 2.25 | 1.80 | 1.60 | 1.88 | 1.50 | 1.34 | 1.24 | 1.10 | 1.10 |\n", + "| 75| 2.27 | 1.83 | 1.63 | 1.90 | 1.53 | 1.37 | 1.26 | 1.13 | 1.13 |\n", + "| 80| 2.30 | 1.86 | 1.66 | 1.92 | 1.55 | 1.39 | 1.28 | 1.15 | 1.15 |\n", + "| 85| 2.32 | 1.88 | 1.69 | 1.94 | 1.58 | 1.42 | 1.30 | 1.17 | 1.17 |\n", + "| 90| 2.34 | 1.91 | 1.72 | 1.96 | 1.60 | 1.44 | 1.32 | 1.18 | 1.18 |\n", + "| 95| 2.36 | 1.93 | 1.74 | 1.98 | 1.62 | 1.46 | 1.33 | 1.20 | 1.20 |\n", + "|100| 2.38 | 1.96 | 1.77 | 1.99 | 1.64 | 1.48 | 1.35 | 1.22 | 1.22 |\n", + "|110| 2.42 | 2.00 | 1.81 | 2.03 | 1.68 | 1.52 | 1.38 | 1.25 | 1.25 |\n", + "|120| 2.45 | 2.04 | 1.85 | 2.05 | 1.71 | 1.55 | 1.41 | 1.28 | 1.28 |\n", + "|130| 2.48 | 2.08 | 1.89 | 2.08 | 1.74 | 1.59 | 1.44 | 1.31 | 1.31 |\n", + "|140| 2.51 | 2.12 | 1.93 | 2.10 | 1.77 | 1.62 | 1.46 | 1.33 | 1.33 |\n", + "|150| 2.54 | 2.15 | 1.96 | 2.13 | 1.80 | 1.65 | 1.48 | 1.35 | 1.35 |\n", + "|160| 2.56 | 2.18 | 2.00 | 2.15 | 1.83 | 1.67 | 1.50 | 1.38 | 1.38 |\n", + "|170| 2.59 | 2.21 | 2.03 | 2.17 | 1.85 | 1.70 | 1.52 | 1.40 | 1.40 |\n", + "|180| 2.61 | 2.24 | 2.06 | 2.19 | 1.88 | 1.72 | 1.54 | 1.42 | 1.42 |\n", + "|190| 2.63 | 2.27 | 2.08 | 2.20 | 1.90 | 1.75 | 1.56 | 1.44 | 1.44 |\n", + "|200| 2.65 | 2.29 | 2.11 | 2.22 | 1.92 | 1.77 | 1.58 | 1.46 | 1.46 |\n", + "\n" + ] } ], "metadata": {