diff --git a/book/_toc.yml b/book/_toc.yml index ffdb418..39a6e74 100644 --- a/book/_toc.yml +++ b/book/_toc.yml @@ -31,7 +31,7 @@ parts: - file: design_workflow/general_loads/variable_loads_2_wind - file: design_workflow/general_loads/variable_loads_3_rain_snow - file: design_workflow/general_loads/variable_loads_4_special - - file: design_workflow/general_loads/deflection_requirements + - file: design_workflow/general_loads/deformation limits - file: design_workflow/general_mechanics/general_mechanics sections: - file: design_workflow/general_mechanics/symbols diff --git a/book/design_workflow/general_design_guide.ipynb b/book/design_workflow/general_design_guide.ipynb index ae4df53..7e5cf09 100644 --- a/book/design_workflow/general_design_guide.ipynb +++ b/book/design_workflow/general_design_guide.ipynb @@ -14,6 +14,23 @@ "The terms ‘initiative’, ‘project definition’, ‘concepts’, ‘preliminary design’, \n", "and ‘verification of structural safety’ will be explained shortly below.\n", "\n", + "## Initiative\n", + "The client initiates a construction project or structure. The designer,\n", + "being advised by an architect, determines design goals. The design\n", + "goal is a general description of the desired result of the design and\n", + "execution process. After determining the design goal, the\n", + "designer can study different aspects of the project. For example: the\n", + "location, the budget and functional requirements. When all aspects are determined, \n", + "they are integrated and evaluated. The final step of this phase is to check whether \n", + "the project is financially and logisticallyfeasible. If this is not the case, \n", + "the design goals need to be adjusted. The concequence of this is that the whole \n", + "cycle starts again (aspects, integration, evaluation and check).\n", + "\n", + "`````{admonition} Result\n", + ":class: tip\n", + "A Program of Requirements (PoR) formulated by the client\n", + "`````\n", + "\n", "## Project definition\n", "\n", "To define the project, one first drafts a plan of action (strategy). This\n", @@ -23,6 +40,11 @@ "this leads to the formulation of a report containing all basic assumptions\n", "concerning the structural design. This forms a supplement to the PoR.\n", "\n", + "`````{admonition} Result\n", + ":class: tip\n", + "A Program of Requirements supplemented with structural assumptions\n", + "`````\n", + "\n", "## Concepts\n", "\n", "In this phase too several studies have to be performed. The designer makes several\n", @@ -44,6 +66,11 @@ "the different concepts based on a multi criteria analysis. The criteria are based\n", "on the PoR and structural assumptions.\n", "\n", + "`````{admonition} Result\n", + ":class: tip\n", + "Design sketches of the different concepts with a reasoned choice of a design\n", + "`````\n", + "\n", "## Preliminairy structural design\n", "\n", "Now all the dimensions of the chosen structure can be determined. Again the sections\n", @@ -53,6 +80,12 @@ "surprises in the final design stage. Also the building envelope deserves some\n", "attention. Use the different examples given in the later chapters.\n", "\n", + "`````{admonition} Result\n", + ":class: tip\n", + "General preliminary structural design, general dimensions of the main structure. Ideas on fabrication, erection,\n", + "foundation and façades.\n", + "`````\n", + "\n", "## Preliminary design\n", "\n", "In this phase a further analysis of the strength, behaviour of the structure\n", @@ -65,12 +98,24 @@ "possible façades, roof elements and other building finishes needs to be made. How\n", "are the building finishes connected to the load bearing structure?\n", "\n", + "`````{admonition} Result\n", + ":class: tip\n", + "A structure which retains its place and shape under loading with dimensioned structural parts. A conceptual design of\n", + "the foundation, building envelope, fabrication, erection and structural details.\n", + "`````\n", + "\n", "## Verification of the structural safety and servicability\n", "\n", "The final preliminairy design of which the final dimensions are now determined,\n", "has to be checked with a structural code. In Europe this is the Eurocode. The\n", "different sections on steel, timber, concrete and foundations contain the\n", - "necessary information to perform the check.\n" + "necessary information to perform the check.\n", + "\n", + "`````{admonition} Result\n", + ":class: tip\n", + "A structural design which not only meets the needs of the client and other stakeholders but also complies with the\n", + "applying structural code.\n", + "`````\n" ] }, { diff --git a/book/design_workflow/general_drawing/Images/Aliminium.png b/book/design_workflow/general_drawing/Images/Aliminium.png new file mode 100644 index 0000000..64194ce Binary files /dev/null and b/book/design_workflow/general_drawing/Images/Aliminium.png differ diff --git a/book/design_workflow/general_drawing/Images/Brick 1.png b/book/design_workflow/general_drawing/Images/Brick 1.png new file mode 100644 index 0000000..7b256dc Binary files /dev/null and b/book/design_workflow/general_drawing/Images/Brick 1.png differ diff --git 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b/book/design_workflow/general_drawing/Images/Water.png new file mode 100644 index 0000000..dc85d62 Binary files /dev/null and b/book/design_workflow/general_drawing/Images/Water.png differ diff --git a/book/design_workflow/general_drawing/Images/Zinc.png b/book/design_workflow/general_drawing/Images/Zinc.png new file mode 100644 index 0000000..6647593 Binary files /dev/null and b/book/design_workflow/general_drawing/Images/Zinc.png differ diff --git a/book/design_workflow/general_drawing/cross_section_indications.ipynb b/book/design_workflow/general_drawing/cross_section_indications.ipynb index 32b974c..cf97f9c 100644 --- a/book/design_workflow/general_drawing/cross_section_indications.ipynb +++ b/book/design_workflow/general_drawing/cross_section_indications.ipynb @@ -6,13 +6,103 @@ "source": [ "# Cross section indications\n", "\n", - "\n" + "For each material, a different hatch is used. Furthermore, the type of hatch can differ as the scale of the drawing\n", + "changes. This is done to make sure that at higher scales the hatches are not too complicated, as the areas to\n", + "hatch on the drawing decrease rapidly with increasing scale. In the tables below two markings appear: \n", + " \n", + ":black_circle: = Scale at which the hatch needs to be used \n", + ":white_circle: = Scale at which the hatch needs to be used with the material added in text\n", + " \n", + "The tables are based on the Dutch code NEN 47.\n", + "\n", + "## Stone-like materials\n", + "\n", + "| No. | Description | Hatch | Scale | | | | | |Remarks |\n", + "| --- | ----------------------- | ----- | ----- | ----- | ---- | ---- | ---- | ---- | --- |\n", + "| | | | 1:100 |1:50 |1:20 |1:10 |1:5 |1:1 | | \n", + "| 1 | Brick masonry |```{figure} Images/Brick 1.png``` |:black_circle:|:black_circle:| | | | | |\n", + "| | |```{figure} Images/Brick 2.png``` | |:black_circle:|:black_circle:|:black_circle:|:black_circle:|:black_circle:| |\n", + "| | |```{figure} Images/Brick 3.png``` | |:black_circle:|:black_circle:|:black_circle:|:black_circle:|:black_circle:| |\n", + "| 2 | Stone-like materials |```{figure} Images/Stone-like.png``` |:white_circle:| | | | | |e.g. fireproof material, roof tiles |\n", + "| 3 | Non-brick masonry |```{figure} Images/Non-brick.png``` | | | | | | |e.g. concrete masonry units |\n", + "| 4 | Non load carrying division walls |```{figure} Images/Non-load.png``` | | | | | | | |\n", + "| | |```{figure} Images/Non-load 2.png``` | | | | | | | |\n", + "| | |```{figure} Images/Non-load 3.png``` | | | | | | | |\n", + "| 5 | Reinforced concrete (cast in situ) |```{figure} Images/Reinforced concrete.png``` | | | | | | | |\n", + "| | |```{figure} Images/Reinforced concrete 2.png``` | | | | | | | |\n", + "| 6 | Reinforced concrete (precast) |```{figure} Images/Reinforced concrete precast.png```| | | | | | | |\n", + "| 7 | Plain concrete |```{figure} Images/Plain concrete.png``` | | | | | | |e.g. lightweight concrete |\n", + "| 8 | Decorative concrete |```{figure} Images/Decorative concrete.png``` | | | | | | | |\n", + "| 9 | Natural stone |```{figure} Images/Natural stone.png``` | | | | | | | |\n", + "| 10 | Single floor/wall finishing |```{figure} Images/Single floor wall.png``` | | | | | | | e.g. plaster |\n", + "| 11 | Composite floor/wall finishing |```{figure} Images/Composite.png``` | | | | | | | |\n" ] }, { "cell_type": "markdown", "metadata": {}, - "source": [] + "source": [ + "## Timber materials" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "|No.| Description | Hatch | Scale | | | | | |Remarks |\n", + "|---| ----------------------- | ----- | ----- | ----- | ---- | ---- | ---- | ---- | --- |\n", + "| | | | 1:100 |1:50 |1:20 |1:10 |1:5 |1:1 | | \n", + "|12 | Softwood |```{figure} Images/Softwood.png``` | | | | | | | |\n", + "|13 | Hardwood |```{figure} Images/Hardwood.png``` | | | | | | | |\n", + "|14 | Softwood/Hardwood (along the grain)|```{figure} Images/Soft-Hardwood along the grain.png``` | | | | | | | |\n", + "|15 | Glued seam |```{figure} Images/Glued seam.png``` | | | | | | | |\n", + "|16 | Cladding panel |```{figure} Images/Cladding panel.png``` | | | | | | | |\n", + "|17 | Isolation panel |```{figure} Images/Isolation panel.png``` | | | | | | | |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Metals" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "| No. | Description | Hatch | Scale | | | | | |Remarks |\n", + "| --- | ----------------------- | ----- | ----- | ----- | ---- | ---- | ---- | ---- | --- |\n", + "| | | | 1:100 |1:50 |1:20 |1:10 |1:5 |1:1 | | \n", + "| 18 | Steel |```{figure} Images/Steel.png```| | | | | | | |\n", + "| 19 | Aluminium, brass, copper etc. |```{figure} Images/Aluminium.png```| | | | | | | |\n", + "| 20 | Lead |```{figure} Images/Lead.png```| | | | | | | |\n", + "| 21 | Zinc |```{figure} Images/Zinc.png```| | | | | | | |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Miscellaneous" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "| No. | Description | Hatch | Scale | | | | | |Remarks |\n", + "| --- | -------------- | ----- | ----- | ----- | ---- | ---- | ---- | ---- | --- |\n", + "| | | | 1:100 |1:50 |1:20 |1:10 |1:5 |1:1 | | \n", + "| 22 | Synthetics |```{figure} Images/Synthetics.png``` | | | | | | | |\n", + "| 23 | Sealant |```{figure} Images/Sealant.png``` | | | | | | | |\n", + "| 24 | Foil, bitumen |```{figure} Images/Foil.png``` | | | | | | | |\n", + "| 25 | Ground level |```{figure} Images/Gorund level.png``` | | | | | | | |\n", + "| 26 | Sand |```{figure} Images/Sand.png``` | | | | | | | |\n", + "| 27 | Gravel |```{figure} Images/Gravel.png``` | | | | | | | |\n", + "| 28 | Water |```{figure} Images/Water.png``` | | | | | | | |\n", + "| 29 | Glass |```{figure} Images/Glass.png``` | | | | | | | |" + ] } ], "metadata": { diff --git a/book/design_workflow/general_drawing/technical_drawings.ipynb b/book/design_workflow/general_drawing/technical_drawings.ipynb index e2a3474..bcde8cd 100644 --- a/book/design_workflow/general_drawing/technical_drawings.ipynb +++ b/book/design_workflow/general_drawing/technical_drawings.ipynb @@ -6,8 +6,118 @@ "source": [ "# Technical drawings\n", "\n", - "\n" + "To make a clear technical drawing it is wise to follow the steps depicted below.\n", + "Every step discribes shortly what should be done. For more in formation\n", + "how it should be done reference is made to the lecture notes ‘Technical\n", + "Drawings’ (CT1052-09). The steps below are mainly applicable for handdrawings,\n", + "but are also useful for CADdrawings.\n", + "\n", + "## Size and header\n", + "Paper size can vary from A4 to A0. Most of the time A3 is chosen. Draw a\n", + "frame which does not touch the edges of the paper.\n", + "\n", + "```{figure} Images/General drawing 1.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "\n", + "## Header\n", + "The header contains information on the drawing, drawer, scale and units.\n", + "\n", + "```{figure} Images/General drawing 2.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "\n", + "## Layout\n", + "A technical drawing contains a minimum of three elevations or corsssections. The elevation containing most information is placed a the top left position. The other elevations are now determined with third angle projection (Dutch: Amerikaanse projectie). If\n", + "additional elevations, sections or detail drawings need to be added, they are placed at the bottom right corner of the paper.\n", + "\n", + "```{figure} Images/General drawing 3.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "\n", + "## Scale\n", + "Only scales 1:1, 1:2 and 1:5 or multiples of 10 of these are allowed. Always try to draw the object as large as possible on the chosen paper.\n", + "Remember however that also some space will be used for dimensions and text. If one or more elevations (details!) have a different scale, mention this in\n", + "the title below this particular elevation. \n", + "\n", + "```{figure} Images/General drawing 4.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "\n", + "## Contours\n", + "With a pencil grid lines, centre lines and datum lines can be drawn. After this, draw the contours of the object. If necessary, some changes to the layout\n", + "or scale of the drawing can be made.\n", + "\n", + "```{figure} Images/General drawing 5.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "\n", + "## Objects\n", + "The object is drawn in detail.\n", + "\n", + "```{figure} Images/General drawing 6.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "\n", + "## Dimensions\n", + "How? Dimensions are indicated by a dimension line and two auxilairy lines indicating the length to be dimensioned. The intersection\n", + "between the lines is indicated with a little diagonal line, dot or arrow. The auxilairy lines do not touch the object. The value of the\n", + "dimension is written in the middle of the dimension line, but can be placed on a leader if there is a lack of space. Heights are usually\n", + "measured in relation to a reference level and are indicated with an arrow. The units used depend on the size of the object, but can only\n", + "be: micrometers, millimeters, meters and kilometers. What? Only the dimensions necessary to understand and built\n", + "the object need to be shown. Where possible, use centre lines. Where? Place dimensions as much as possible to the right and below\n", + "the elevation which shows the important component the clearest. Deviations of this ‘general rule’ are only allowed if this clarifies the\n", + "drawing. If multiple dimensions are shown on one line, a summation must always be added, with an extra dimension line.\n", + "\n", + "```{figure} Images/General drawing 7.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "\n", + "```{figure} Images/General drawing 8.png\n", + "---\n", + "scale: 100%\n", + "---\n", + "\n", + "## Hatching\n", + "To indicate used materials cross sections are hatched. See gd|b for different types of hatches. Note that the hatch to be used depends\n", + "on the scale of the drawing. If two components meet which must be hatched in the same way, the hatch is rotated 90°. This is only applicable to\n", + "hatches consisting of diagonal lines.\n", + "\n", + "```{figure} Images/General drawing 9.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "\n", + "## Lines\n", + "Now the different lines in the drawing need to be given the correct thickness and type. For an overview of the different types and thicknesses and\n", + "their applications, see the lecture notes on Technical Drawing.\n", + "\n", + "```{figure} Images/General drawing 10.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "\n", + "## Text\n", + "Finally, if necessary with the aid of leaders, texts are added. Elevation titles need to be placed below the object, aligned to the left. If this\n", + "particular elevation differs in scale of the rest of the drawing mention this in the elevation title. Do not use abbreviations in titles.\n", + "\n", + "```{figure} Images/General drawing 11.jpg\n", + "---\n", + "scale: 100%\n", + "---" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] } ], "metadata": { diff --git a/book/design_workflow/general_loads/Images/Deformation.jpg b/book/design_workflow/general_loads/Images/Deformation.jpg new file mode 100644 index 0000000..31ff6fc Binary files /dev/null and b/book/design_workflow/general_loads/Images/Deformation.jpg differ diff --git a/book/design_workflow/general_loads/Images/Emergency overflow 2.jpg b/book/design_workflow/general_loads/Images/Emergency overflow 2.jpg new file mode 100644 index 0000000..18c69b8 Binary files /dev/null and b/book/design_workflow/general_loads/Images/Emergency overflow 2.jpg differ diff --git a/book/design_workflow/general_loads/Images/Emergency overflow.jpg b/book/design_workflow/general_loads/Images/Emergency overflow.jpg new file mode 100644 index 0000000..0b51638 Binary files 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b/book/design_workflow/general_loads/Images/Windzones roofs 3.png differ diff --git a/book/design_workflow/general_loads/deflection_requirements.ipynb b/book/design_workflow/general_loads/deflection_requirements.ipynb index 47eb913..3ff3cdd 100644 --- a/book/design_workflow/general_loads/deflection_requirements.ipynb +++ b/book/design_workflow/general_loads/deflection_requirements.ipynb @@ -4,7 +4,110 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Deflection requirements" + "# Deformation limits" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Vertical deformation\n", + "\n", + "$w_c$ = precamber \n", + "$w_1$ = initial deflection under permanent actions \n", + "$w_2$ = long term deflection under permanent actions (creep) \n", + "$w_3$ = deflection under variable actions \n", + "$w_{tot} = w_1 + w_2 + w_3$ \n", + "$w_{max}= w_{tot}-w_c$ \n", + "\n", + "```{figure} Images/Deformation.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "As Eurocode does not specify deformation limits, the old limits\n", + "originating in the Dutch code are used (NEN 6702 Belastingen en vervormingen TGB 1990).\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Floors in general $w_3 = 0,003 * l$ \n", + "Floors carrying non-flexible walls $w_3 = 0,002 * l$ \n", + "Roofs $w_3 = 0,004 * l$ \n", + "Maximum deflection $w_{max} = 0,004 * l$ " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Water accumulation\n", + "\n", + "Even if the drainage systems works properly there is a possibility of water accumulation.\n", + "To prevent this, the roof must be designed stiff enough to ensure the remaining slope of\n", + "the roof at the lowest support stays positive. It is therefore recommended to design for a minimum slope of 1,6%.\n", + "\n", + "```{figure} Images/Water accumulation.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "```{figure} Images/Water accumulation 2.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "Too large deformations leading to water accumulation and eventually failure.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Horzintal deformations\n", + "\n", + "As Eurocode does not specify deformation limits, the old limits\n", + "originating in the Dutch code are used (NEN 6702 Belastingen en\n", + "vervormingen TGB 1990).\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Low rise\n", + "\n", + "$u <= 1/150*h$ for industrial buildings \n", + "$u <= 1/300*h$ for other buildings\n", + "\n", + "```{figure} Images/Low rise deformation.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "### High rise\n", + "\n", + "$u <= 1/300*h$ for storey height \n", + "$u <= 1/500*h$ for total height\n", + "\n", + "```{figure} Images/High rise deformation.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```" ] }, { diff --git a/book/design_workflow/general_loads/general_loads.md b/book/design_workflow/general_loads/general_loads.md index 6390da7..be2d6d4 100644 --- a/book/design_workflow/general_loads/general_loads.md +++ b/book/design_workflow/general_loads/general_loads.md @@ -1,4 +1,30 @@ # General loads +This section will explain what possible loads and load combinations can act +on a structure. Loads are part of the greater group of ‘actions’. ‘Actions’ +comprise all possible infuences on a structure (e.g. temperature +differences). In most cases the words ‘actions’ and ‘loads’ are synonyms. +Most information will be stated in tables and diagrams. From these the +actions can easily be determined. Before the design of a structure can +start, the designer must have a clear idea of the structure that needs to be +built. Or, put differently: what will be the functions of the structure? From +the functions of the structure the use of the structure can be determined. Once +the use of a structure is known, the possible actions can also be derived. + +1 Idea of the structure +2 Possible functions +3 Use +4 Loads + +First the loads, limit states and load combinations will be attended to. +After this introduction the different permanent and variable loads will be +adressed. + +`````{admonition} Caution +:class: warning +The information in this section is a simplified representation of the Eurocode, and therefore only fit for design +purposes. It cannot be used for the final strength verification! +```` + ```{tableofcontents} ``` \ No newline at end of file diff --git a/book/design_workflow/general_loads/loads_limit_states.ipynb b/book/design_workflow/general_loads/loads_limit_states.ipynb index 2b8ff78..6bdd927 100644 --- a/book/design_workflow/general_loads/loads_limit_states.ipynb +++ b/book/design_workflow/general_loads/loads_limit_states.ipynb @@ -10,7 +10,131 @@ { "cell_type": "markdown", "metadata": {}, - "source": [] + "source": [ + "## Limits\n", + "Every structure has to comply with two possible limit states which are directly\n", + "related to the reliablity (strength) and usability of the structure. The Ultimate\n", + "Limit State (ULS) is used to check structural safety. The Serviceability\n", + "Limit State (SLS) is used to check usability." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Load combinations\n", + "Load combinations consist of a combination of design values of\n", + "the permanent and variable loads. Both characteristic and reduced\n", + "characteristic loads are combined for the ULS or SLS. The determination\n", + "of the critical combination of actions is left to the structural engineer.\n", + "Important here is to keep in mind what kind of element you are designing: a\n", + "beam, foundation, column or stability measures.\n", + "\n", + "Building structures and parts of building structures or their supports\n", + "and connections must be sufficiently reliable during their service life. They\n", + "must withstand the most unfavourable combination of loads that can act\n", + "simultaneously. Exceptions:\n", + "\n", + "- The extreme value of a variable load does not have to be combined with the\n", + "extreme value of other variable loads.\n", + "- An accidental load does not have to be combined with the extreme value of\n", + "other accidental loads or extreme variable loads.\n", + "- For certain cases is its phyisically not possible for two loads to simultaneously\n", + "act in their extreme or zero value in the same load combination. (e.g. snow and\n", + "wind loads).\n", + "\n", + "A few basic rules according to the Eurocode (EN 1990) will be explained below." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ultimate Limite State (ULS)\n", + "$γ_G G_k + γ_{Q;1} Q_{1;k} + Σ(γ_{Q;i} Ψ_{0;i} Q_{i;k})$\n", + "\n", + "$γ_G$ = partial factor for permanent loads \n", + "$G_k$ = total permanent load \n", + "$γ_{Q;i}$ = partial factor for variable loads \n", + "$Q_{1;lk}$ = characteristic value of the leading variable load \n", + "$Ψ_{0;i}$ = factor for combination of variable load i with the leading variable load \n", + "$Q_{i;k}$ = characteristic value of variable load i \n", + "\n", + "```{note}\n", + "For a more complete explanation see: NEN-EN 1990.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ultimate limit state: load factors ($γ$)\n", + "\n", + "| Design Situation | Permanent Loads | Variable Loads | Unfavourable | Favourable | Leading | Other |\n", + "|------------------|-----------------|----------------|--------------|------------|---------|-------|\n", + "| 1 | 1.35 | 0.9 | - | 1.5 | - | - |\n", + "| 2 | 1.2 | 0.9 | 1.5 | 1.5 | - | - | \n", + " \n", + "```{note}\n", + "A favourable load can for example be the dead load of a roof in combination with uplift forces due to wind.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Consequence classes\n", + "\n", + "| Concequence Class | Description | Examples | KFI |\n", + "|-------------------|----------------------------------------------------------|-----------------------------------------------------------|-----|\n", + "| CC1 | Low consequence for loss of human life, and economic, social or environmental consequences small or negligible | Agricultural buildings where people do not normally enter (e.g. storage buildings), greenhouses | 0.9 |\n", + "| CC2 | Medium consequence for loss of human life, economic, social or environmental consequences considerable | Residential and office buildings, public buildings where consequences of failure are medium (e.g. an office building) | 1.0 |\n", + "| CC3 | High consequence for loss of human life, or economic, social or environmental consequences very great | Grandstands, public buildings where consequences of failure are high (e.g. a concert hall) | 1.1 |\n", + "\n", + "```{note}\n", + "To take the concequence class into account, the applicable load factors ($γ_G$ & $γ_{Q;1}$) have to be multiplied by $K_{FI}$\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Load categories with corresponding $Ψ$ factors for buildings\n", + "\n", + "| Action Category (General Loads) | Example | Ψ0 | Ψ1 | Ψ2 |\n", + "|----------------------------------|-----------------------------------------------------------|-----|-----|-----|\n", + "| Category A: Domestic, Residential Areas | - | 0.4 | 0.5 | 0.3 |\n", + "| Category B: Office Areas | - | 0.5 | 0.5 | 0.3 |\n", + "| Category C: Congregation Areas | C1: Areas with tables (school, restaurants) | 0.25| 0.7 | 0.6 |\n", + "| | C2: Areas with fixed seats (theatres, churches, lecture halls) | - | - | - |\n", + "| | C3: Areas without obstacles for people (museums, hospitals) | - | - | - |\n", + "| | C4: Areas with physical activities (dance halls, gymnastic rooms) | - | - | - |\n", + "| | C5: Areas susceptible to large crowds (stadiums, terraces, railway platforms) | - | - | - |\n", + "| Category D: Shopping Areas | D1: General retail | 0.4 | 0.7 | 0.6 |\n", + "| | D2: Department stores | - | - | - |\n", + "| Category E: Storage Areas | E1: Areas susceptible to accumulation of goods | 1.0 | 0.9 | 0.8 |\n", + "| | E2: Industrial use | - | - | - |\n", + "| Category F: Traffic Area, Vehicle Weight ≤ 30 kN | - | 0.7 | 0.7 | 0.6 |\n", + "| Category G: Traffic Area, 30 kN ≤ Vehicle Weight ≤ 160 kN | - | 0.7 | 0.5 | 0.3 |\n", + "| Category H: Roofs | - | 0 | 0 | 0 |\n", + "\n", + " \n", + " \n", + "| Other Actions (Environmental Actions) | Example | Ψ0 | Ψ1 | Ψ2 |\n", + "|----------------------------------------|------------------------------------------------|-----|-----|-----|\n", + "| Snow Loads on Buildings | - | 0 | 0.2 | 0 |\n", + "| Wind Loads on Buildings | - | 0 | 0.2 | 0 |\n", + "| Temperature on Buildings (non-fire) | - | 0 | 0.5 | 0 |\n", + "\n", + " \n", + " \n", + "$Ψ_0$ = factor for combination value of a variable action\n", + "$Ψ_1$ = factor for frequent value of a variable action (for example used in combination with accidental loading)\n", + "$Ψ_2$ = factor for quasi-permanent value of a variable action (for example used in creep calculations)\n" + ] } ], "metadata": { diff --git a/book/design_workflow/general_loads/permanent_loads.ipynb b/book/design_workflow/general_loads/permanent_loads.ipynb index 9f53b58..d7fbe96 100644 --- a/book/design_workflow/general_loads/permanent_loads.ipynb +++ b/book/design_workflow/general_loads/permanent_loads.ipynb @@ -12,7 +12,129 @@ { "cell_type": "markdown", "metadata": {}, - "source": [] + "source": [ + "Permanent loads on a structure consist of the dead weight of the considered\n", + "component and the dead weight of the other components resting on the\n", + "considered component. With the aid of the tables given below\n", + "the one can determine the permanent loads for a given building. Note that for\n", + "specific structural elements (I-beams or hollow core slabs) separate tables\n", + "may exist with information on dead weight." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Materials (structural)\n", + " \n", + "| Material | ρ [$kg/m^3$] | Material | ρ [$kg/m^3$] | Material | ρ [$kg/m^3$] |\n", + "|--------------------------|-----------|---------------------------|-----------|-------------------------------|------------|\n", + "| Primary Building Materials | | Secondary Building Materials | | Concrete Masonry Units | |\n", + "| Dunesand ash | 1000 | Light | 800-1500 | | |\n", + "| | | Dry | 1550 | Blast Furnace Slag | 1700 |\n", + "| | | Humid | 1700 | Medium | 1500-1900 |\n", + "| | | Heavy | 1900-2300 | | |\n", + "| | | Saturated | 1950 | Masonry Cellular Concrete | 500-800 |\n", + "| River- and Pebble-sand | | Clinker Brick | 2000 | Gypsum Blocks | 1100 |\n", + "| | Dry | 1650 | Ordinary Façade Stones | Tiles |\n", + "| | Humid | 1750 | Full (0% Perforation) | 1700 |\n", + "| | Saturated | 2000 | Porous | 1900 |\n", + "| Gravel | | Hollow (35%) | 1100 | Perforated (20%) | 1400 |\n", + "| | Dry | 1600 | Non Porous | 2300 |\n", + "| | Humid | 1700-2000 | | |\n", + "| | Saturated | 1922 | | |\n", + "| Soil and Clay | | | | | |\n", + "| | Dry | 1600 | Reinforced Concrete | 2400-2550 |\n", + "| | Wet | 2000 | Normal Concrete | 2300-2450 |\n", + "| Natural Stone | | | | | |\n", + "| Basalt, Granite | | 2850 | Foamed Concrete | 300-1400 |\n", + "| Limestone, Marble | | 2700 | | |\n", + "| Shale | | 2700 | | |\n", + "\n", + " \n", + " \n", + "```{note}\n", + "The values above are given in [$kg/m^3$], which is not the same as [$kN/m^3$]!\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Materials (all)\n", + "| Material | ρ [$kg/m^3$] | Material | ρ [$kg/m^3$] | Material | ρ [$kg/m^3$] |\n", + "|-----------------------------------|-----------|---------------------------------|-----------|-------------------------------|-----------|\n", + "| aluminium, cast | 2768 | glass, in crates | 960 | red lead, dry | 2112 |\n", + "| artificial stone | 2304 | glass, plate | 2787 | reinforced concrete 2% | 2401 |\n", + "| ashes, coal | 719 | glass, sheet | 2497 | reinforced concrete 3% | 2503 |\n", + "| asphalt, paving | 2308 | glycerine, in cases | 832 | rosin, in barrels | 769 |\n", + "| granite | 2722 | rubber | 960 | | |\n", + "| ballast, brick, gravel | 1788 | granite, dressed | 2642 | saltpetre | 1072 |\n", + "| barley, in bags | 576 | granite, rubble | 2477 | sand, dry | 1598 |\n", + "| barley, in bulk | 640 | gravel | 1918 | sand, wet | 1998 |\n", + "| bleach, in barrels | 512 | sandstone | 2403 | | |\n", + "| blockwork | 1305-2202 | hay, in bales, compressed | 384 | sandstone | 2403 |\n", + "| brass, cast | 8431 | hay, not compressed | 224 | screws, nails, in packages | 1600 |\n", + "| brass, rolled | 8546 | slate | 2877 | | |\n", + "| brickwork | 1549-2365 | iron, cast | 7203 | snow, freshly fallen | 96 |\n", + "| bronze | 8386 | iron, wrought | 7682 | snow, wet, compact | 320 |\n", + "| ironmongery, in packages | 896 | soda ash, in barrels | 992 | | |\n", + "| cement, in bags | 1345 | soda, caustic, in drums | 1409 | starch, in barrels | 401 |\n", + "| cement, in barrels | 1168 | lead, cast | 11328 | steel, cast | 8002 |\n", + "| cement, mortar | 1678 | lead, sheet | 11358 | steel, rolled | 8002 |\n", + "| cement, Portland loose | 1438 | leather, hides, compress. | 368 | | |\n", + "| clay, china, kaolin | 2209 | leather, in bundles | 256 | straw, in bales, compress | 304 |\n", + "| clay, damp, plastic | 1788 | lime mortar | 1648 | sulphuric acid | 960 |\n", + "| clay, potters, dry | 1920 | lime, in barrels | 800 | | |\n", + "| coal, loose | 896 | limestone | 2562 | tar | 1024 |\n", + "| coke, loose | 480 | terracotta | 1794 | | |\n", + "| concrete, breeze | 1538 | macadam | 2403 | timber, pine, spruce | 481 |\n", + "| concrete, brick | 1918 | marble | 2642 | timber, pitch pine | 673 |\n", + "| concrete, stone | 2308 | timber, redwood | 561 | | |\n", + "| copper, cast | 8801 | nickel, monel metal | 8896 | timber, teak, oak | 721 |\n", + "| copper, rolled | 8930 | tin, cast | 7282 | | |\n", + "| crockery, in crates | 640 | oats, in bags | 432 | tin, rolled | 7392 |\n", + "| oats, in bulk | 512 | tin, sheet, in boxes | 4450 | | |\n", + "| earth, dry, loose | 1152 | oil, in barrels | 576 | water, fresh | 1000 |\n", + "| earth, dry, rammed | 1788 | oil, in bulk | 896 | water, sea | 1024 |\n", + "| earth, moist, packed | 1538 | oil, in drums | 721 | | |\n", + "| wheat, in bags | 624 | | | | |\n", + "| flint | 2640 | paper, printing | 640 | wheat, in bulk | 721 |\n", + "| flour, in bags | 721 | paper, writing | 960 | white lead, paste | 2785 |\n", + "| freestone, dressed | 2398 | petrol | 672 | white-lead, dry | 138 |\n", + "| freestone, rubble | 2238 | pitch | 1119 | wire, in coils | 1185 |\n", + "| plaster | 1538 | plaster of Paris, set | 1278 | zinc | 6993 |\n", + "| plaster, in barrels | 848 | potash | 3276 | | |\n", + "| potatoes, piled | 721 | | | | |\n", + "\n", + "\n", + " \n", + " \n", + "```{note}\n", + "The values above are given in [$kg/m^3$], which is not the same as [$kN/m^3$]!\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Action per unit surface area for composed structures\n", + "\n", + "| Material | [$kN/m^2$] | Material | [$kN/m^2$] |\n", + "|--------------------------------------|---------|-------------------------------------------------|---------|\n", + "| steel façade elements | 0.05-0.13 | polymer foils | 0.02 |\n", + "| façade insulation | 0.015-0.05 | corrugated sheet - fibre reinforced cement | |\n", + "| timber floor + beams | 0.3 | plate only | 0.15 |\n", + "| steel roof sheeting | 0.05-0.18 | plate + connections and purlins | 0.25 |\n", + "| - e.g. steel roof sheet (t=0.75 mm) | 0.11 | corrugated sheet - polymers | 0.02 |\n", + "| insulation and roofing | 0.10-0.20 | corrugated steet - galvanized | |\n", + "| bitumenlayers + connectons and purlins | 0.15 | | |\n", + "| glass fabric 2 layers | 0.07 | roof tiles + underlay and purlins | 0.65 |\n", + "| glass fabric 3 layers | 0.1 | flat roof + beams and underlay (no gravel) | 0.36 |\n", + "| shingles | 0.07 | | |\n" + ] } ], "metadata": { diff --git a/book/design_workflow/general_loads/variable_loads_1_buildings.ipynb b/book/design_workflow/general_loads/variable_loads_1_buildings.ipynb index 04464ed..025f29b 100644 --- a/book/design_workflow/general_loads/variable_loads_1_buildings.ipynb +++ b/book/design_workflow/general_loads/variable_loads_1_buildings.ipynb @@ -12,7 +12,77 @@ { "cell_type": "markdown", "metadata": {}, - "source": [] + "source": [ + "Variable loads are loads which are not present during the whole lifetime\n", + "of the structure, or have variations in time which are not negligible.Examples\n", + "of variable loads are persons, goods, vehicles, wind, accumulating water,\n", + "earthquakes, collisions, loads during erection etcetera." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Verticle and variable loads on floors and roofs\n", + "| Category | Distributed [$kN/m^2$] | Concentrated [$kN$] | Remarks |\n", + "|---------------------------------------|---------------------|-------------------|------------------|\n", + "| Category A: residential areas | | | |\n", + "| A - floors | 1.75 | 3 | |\n", + "| A - stairs | 2 | 3 | |\n", + "| A - balconies | 2.5 | 3 | |\n", + "| A - access routes | 2 | 3 | d |\n", + "| Category B: office areas | | | |\n", + "| B - floors | 2.5 | 3 | |\n", + "| B - access routes | 3 | 3 | |\n", + "| Category C: congregation areas | | | |\n", + "| C1 - floors | 4 | 7 | |\n", + "| C2 - floors | 4 | 7 | |\n", + "| C3 - floors | 5 | 7 | |\n", + "| C4 - floors | 5 | 7 | |\n", + "| C5 - floors | 5 | 7 | |\n", + "| C - access routes | 5 | 7 | |\n", + "| Category D: shopping areas | | | |\n", + "| D1 - floors | 4 | 7 | |\n", + "| D2 - floors | 4 | 7 | |\n", + "| D - access routes | 4 | 4 | |\n", + "| Category E: storage areas | | | |\n", + "| E1 - floors - shops | ≥5 | ≥7 | e |\n", + "| E1 - floors - libraries | ≥2.5 | ≥3 | a,e |\n", + "| E1 - floors - other | ≥5 | ≥10 | e |\n", + "| E2 - floors | depends on use, | depends on use, | |\n", + "| | but ≥3 | but ≥7 | |\n", + "| E1 - access routes - libraries | 3 | 3 | |\n", + "| E1 - access routes - other | 4 | 4 | |\n", + "| E2 - access routes | 4 | 4 | |\n", + "| Category F: traffic area (light) | | | |\n", + "| F - floors | 2 | 10 | e |\n", + "| Category G: traffic area (heavy) | | | |\n", + "| G - floors | 5 | 40 | e |\n", + "| Category H: roofs | | | |\n", + "| dependend of roof angle | | | a: |\n", + "| - 0 ≤ a ≤ 15 | 1 | 1.5 | b,c,f |\n", + "| - 15 ≤ a ≤ 20 | 4 - 0.2a | 1.5 | b,c,f |\n", + "| - 20 ≤ a | 0 | 1.5 | b,c,f |\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "a The given value needs to be applied between the shelves. Underneath the shelves the following formula needs to be applied: \n", + "   $q_k = (A_1*γ_{bk}*h+A_2*p_0)/(A_1+A_2)$ \n", + "   Where: \n", + "   $A_1$: Area beneath the shelves [$m^2$] \n", + "   $A_2$: Remaining area [$m^2$] \n", + "   $γ_{bk}$: Dead weight of books: 6 [$kg/m^3$] \n", + "   $p_0$: Action on floors between shelves: 2,5 [$kN/m^2$] \n", + "   $h$: Height of the shelves \n", + "b The concentrated load is applied on a surface of $0,1 * 0,1 m^2$ \n", + "c The distributed load acts on a maximum area of $10 m^2$ \n", + "d Applied over an area of $0,5* 0,5 m^2$ \n", + "e Take impact loads into account \n", + "f Take water accumulation into account\n" + ] } ], "metadata": { 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": { diff --git a/book/design_workflow/general_loads/variable_loads_3_rain_snow.ipynb b/book/design_workflow/general_loads/variable_loads_3_rain_snow.ipynb index 1081cf9..21f8a7f 100644 --- a/book/design_workflow/general_loads/variable_loads_3_rain_snow.ipynb +++ b/book/design_workflow/general_loads/variable_loads_3_rain_snow.ipynb @@ -4,9 +4,66 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Variable loads 3: rain and snow\n", + "# Variable loads 3: rain and snow" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Loading by rainwater\n", + "Loads by rainwater are the result of accumulating water due to for example\n", + "hogging of adjacent roof parts or clogging of the drainage systems.\n", + "The most practical way of dealing with these actions is converting the snow\n", + "load to a layer of water (e.g.: 0,56 kN/ m2 equals 56 mm water on the roof)\n", + "and preventing the water from rising above this amount by designing for\n", + "emergency overflow. Furthermore, always design a roof with a small pitch (general loads, general)\n", "\n", - "\n" + "```{figure} Images/Emergency overflow.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "Emergency overflow by means of a so called \"mailbox\"\n", + "```\n", + "\n", + "```{figure} Images/Emergency overflow 2.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Snow loads\n", + "Snow can cause considerable loads, as it doesn’t run off like rain. It is therefore important to check whether a load combination containing snow\n", + "loads is leading. For different parts of Europe the value of the snow load can differ greatly (e.g.: compare the Mediterranean Coast to the Alps). In\n", + "the Dutch National Annex of NEN-EN 1991-1-3 the complex calculations are substituted by one value for the whole country (sk = 0,7 kN/m2). For other areas NEN-EN 1991-1-3 must be consulted." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Determining the snow loading\n", + "\n", + "$s = μ_i · C_e · C_t · s_k$\n", + " \n", + "$s$ = Characteristic value of the snow load on the ground [$kN/m^2$] ($0,7 kN/m^2$ in\n", + "the Netherlands) \n", + "$μ_i$ = Shape coefficient, dependend on roof angle α \n", + "$C_e$ = Exposure coefficient (1,0 for most cases) \n", + "$C_t$ = Thermal coefficient (1,0 for most cases) \n", + " \n", + "The shape coefficient can be determined with the shown diagram. Note that μ2 is only applicable where snow accumulation can occur. For complex roof shapes and more information, see NEN-EN 1991-1-3.\n", + "\n", + "```{figure} Images/Snow loading.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```" ] }, { diff --git a/book/design_workflow/general_loads/variable_loads_4_special.ipynb b/book/design_workflow/general_loads/variable_loads_4_special.ipynb index c26c1f5..15cdcd8 100644 --- a/book/design_workflow/general_loads/variable_loads_4_special.ipynb +++ b/book/design_workflow/general_loads/variable_loads_4_special.ipynb @@ -10,7 +10,19 @@ { "cell_type": "markdown", "metadata": {}, - "source": [] + "source": [ + "Accidental loads are typical high loads, with great effects on the structure.\n", + "These loads must therefore be accounted for in the design. Not all loads have to be withstood (e.g.: a\n", + "buffer can prevent ship collisions at a lock gate). Examples of accidental loads are: \n", + "- Fire \n", + "- (Gas)explosion \n", + "- Collision by vehicles \n", + "- Impact loads on roofs and guard rails, \n", + "- High groundwater tables (flooding) \n", + "- Earthquakes \n", + " \n", + "For a complete list and determination of the accidental loads see NEN-EN1991-1-7." + ] } ], "metadata": { 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 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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/cross_sectional_quantities.ipynb b/book/design_workflow/general_mechanics/cross_sectional_quantities.ipynb index 566dcd5..2b806d2 100644 --- a/book/design_workflow/general_mechanics/cross_sectional_quantities.ipynb +++ b/book/design_workflow/general_mechanics/cross_sectional_quantities.ipynb @@ -7,6 +7,173 @@ "# Cross sectional quantitites" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Definition section parameters\n", + "| Surface |Static moment of area| Moment of Inertia | Polar moment of inertia | Steiner's rule |\n", + "|--------------|---------------------|------------------------------|-----------------------------------------|----------------|\n", + "|$A=\\int_A\\,dA$|$S_y = \\int_A y\\, dA$|$I_{yy}=I_z=\\int_A y^2\\,dA$ |$I_p = \\int_A r^2\\, dA = I_{yy} + I_{zz}$|$I_{\\overline{yy}}=I_{yy(own)}+\\bar{y}_c^2 \\cdot A$| \n", + "| |$S_z = \\int_A z\\, dA$|$I_{yz}=I_{zy}=\\int_A y*z\\,dA$| |$I_{\\overline{yz}}=I_{\\overline{zy}}=I_{yz(own)}+\\bar{y}_c \\cdot \\bar{z}_c \\ A$|\n", + "| | |$I_{zz}=I_{y}=\\int_A z^2\\,dA$ | |$I_{\\overline{zz}}=I_{zz(own)}+\\bar{z}_c^2 \\cdot A$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Section parameters\n", + "\n", + "```{figure} Images/Rectangle shape.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "### Square\n", + "|Area, centre of gravity| Moments of intertia own | other |\n", + "|-----------------------|-------------------------|-----------------------------|\n", + "|$A=bh$ |$I_{yy}=\\frac{1}{12}*b^3*h$ |$I_{\\overline{yy}}=1/3b^3h$ | \n", + "|$\\bar{y}_C=\\frac{1}{2}b$ |$I_{zz}=\\frac{1}{12}bh^3$ |$I_{\\overline{zz}}=\\frac{1}{3}bh^3$ |\n", + "|$\\bar{z}_C=\\frac{1}{2}b$ |$I_{yz}=\\frac{1}{12}bh^3$ |$I_{\\overline{yz}}=\\frac{1}{4}b^2h^2$|\n", + "\n", + "```{figure} Images/Parallelogram shape.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "### Parallelogram\n", + "|Area, centre of gravity | Moments of intertia own | other |\n", + "|---------------------------|-------------------------------|-------------------------------|\n", + "|$A=bh$ |$I_{yy}=\\frac{1}{12}(a^2+b^2)$|$I_{\\overline{yy}}=1/3bh^3$ | \n", + "|$\\bar{y}_C=\\frac{1}{2}(a+b)$ |$I_{zz}=\\frac{1}{12}bh^3$ | |\n", + "|$\\bar{z_C}=\\frac{1}{2}h$ |$I_{yz}=\\frac{1}{12}abh^2$ | |\n", + "\n", + "```{figure} Images/Triangle shape.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "### Triangle\n", + "|Area, centre of gravity | Moments of intertia own | other |\n", + "|------------------------------|----------------------------------|---------------------------------|\n", + "|$A=\\frac{1}{2}bh$ |$I_{yy}=\\frac{1}{36}*(a^2-ab+b^2)$|$I_{\\overline{zz}}=\\frac{1}{3}bh^3$ | \n", + "|$\\bar{y}_C=\\frac{1}{3}(2a-b)$ |$I_{zz}=\\frac{1}{36}bh^3$ |$I_{\\overline{yz}}=\\frac{1}{8}(2a-b)bh^2$|\n", + "|$\\bar{z}_C=\\frac{2}{3}h$ |$I_{yz}=\\frac{1}{72}abh^2$ |$I_{\\overline{\\overline{zz}}}=\\frac{1}{12}bh^3$ |\n", + "\n", + "```{figure} Images/Trapezoid shape.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "### Trapezoid\n", + "|Area, centre of gravity | Moments of intertia own | other | \n", + "|-----------------------------------------|-----------------------------------------------|----------------------------------------------------|\n", + "|$A=\\frac{1}{2}(a+b)h$ |$I_{zz}=\\frac{1}{36}\\frac{a^2+4ab+b^2}{a+b}h^3$|$I_{\\overline{zz}}=\\frac{1}{3}bh^3$ | \n", + "|$\\bar{y}_C=\\frac{1}{3}\\frac{a+2b}{a+b}h$ | |$I_{\\overline{\\overline{zz}}}=\\frac{1}{12}(a+3b)h^3$|\n", + "|$\\bar{z}_C=\\frac{2}{3}h$ | | |\n", + "\n", + "```{figure} Images/Circle shape.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "### Circle\n", + "|Area, centre of gravity | Moments of intertia own | other | \n", + "|------------------------|------------------------------|-----------------------------------------------------|\n", + "|$A=πR^2$ |$I_{yy}=I_{zz}=\\frac{1}{4}R^4$|$I_{\\overline{yy}}=I_{\\overline{zz}}=\\frac{5}{4}πR^4$| \n", + "| |$I_{yz}=0$ |$I_{\\overline{\\overline{yz}}}=πR^4$ |\n", + "| |$I_p=\\frac{1}{2}πR^4$ | |\n", + "\n", + "```{figure} Image/Thick walled ring shape.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "### Thick-walled ring\n", + "|Area, centre of gravity | Moments of intertia own | other | \n", + "|------------------------|-----------------------------------------|-----------------|\n", + "|$A=πR_0^2R_i^2$ |$I_{yy}=I_{zz}=\\frac{1}{4}π(R_0^4-R_i^4)$| | \n", + "| |$I_{yz}=0$ | |\n", + "| |$I_p=\\frac{1}{2}π(R_0^4-R_i^4)$ | |\n", + "\n", + "```{figure} Images/Thin walled ring shape.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "### Thin-walled ring\n", + "|Area, centre of gravity | Moments of intertia own | other | \n", + "|------------------------|------------------------------|--------------------------------------------|\n", + "|$A=2πRt$ |$I_{yy}=I_{zz}=πR^3t$ |$I_{\\overline{yy}}=I_{\\overline{zz}}=3πR^3t$| \n", + "| |$I_{yz}=0$ | |\n", + "| |$I_p=\\frac{1}{2}πR^3t$ | |\n", + "\n", + "```{figure} Images/Half circle shape.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "### Half circle\n", + "|Area, centre of gravity | Moments of intertia own | other | \n", + "|--------------------------|--------------------------------------|-----------------------------------------------------|\n", + "|$A=\\frac{1}{2}πR^2$ |$I_{yy}=\\frac{1}{8}πR^4$ |$I_{\\overline{yy}}=I_{\\overline{zz}}=\\frac{1}{8}πR^4$| \n", + "|$\\bar{y}_C=0$ |$I_{zz}=(\\frac{π}{8}-\\frac{8}{9π})R^4$|$I_{\\overline{\\overline{yz}}}=0$ |\n", + "|$\\bar{z}_C=\\frac{4}{3π}R$ |$I_{yz}=0$ | |\n", + "\n", + "```{figure} Images/Half thin walled ring shape.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "### Half thin-walled ring\n", + "|Area, centre of gravity | Moments of intertia own | other | \n", + "|------------------------|-------------------------------|------------------------------------------------------|\n", + "|$A=πRt$ |$I_{yy}=I_{zz}=\\frac{1}{2}R^3t$|$I_{\\overline{yy}}=I_{\\overline{zz}}=\\frac{1}{2}πR^3t$| \n", + "|$\\bar{y}_C=0$ |$I_{zz}=0$ |$I_{\\overline{yz}}=0$ |\n", + "|$\\bar{z}_C=0$ |$I_{yz}=0$ | |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Centre of gravity for moment diagrams\n", + "\n", + "```{figure} Images/Centre of gravity 1.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "```{figure} Images/Centre of gravity 2.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "```{figure} Images/Centre of gravity 3.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```\n", + "\n", + "```{figure} Images/Centre of gravity 4.jpg\n", + "---\n", + "scale: 100%\n", + "---\n", + "```" + ] + }, { "cell_type": "markdown", "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": { diff --git a/book/design_workflow/general_mechanics/symbols.ipynb b/book/design_workflow/general_mechanics/symbols.ipynb index 0c6cb53..b667742 100644 --- a/book/design_workflow/general_mechanics/symbols.ipynb +++ b/book/design_workflow/general_mechanics/symbols.ipynb @@ -4,7 +4,41 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Symbols" + "# Symbols, quantities and units" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "| Symbol | Name | Symbol | \n", + "|--------|-------------------------------------|--------| \n", + "| qy | Distributed load in y direction | N/m | \n", + "| qz | Distributed load in z direction | N/m | \n", + "| s | Distributed shear force | N/m | \n", + "| t | Thickness | m | \n", + "| tf | Flange thickness | m | \n", + "| tw | Web thickness | m | \n", + "| yC | Y-coordinate of the center of gravity | m | \n", + "| zC | Z-coordinate of the center of gravity | m | \n", + "| yNC | Y-coordinate of the center of axial force | m | \n", + "| zNC | Z-coordinate of the center of axial force | m | \n", + "| I | Second moment of area | m^4 | \n", + "| i | Radius of gyration | m | \n", + "| W | Section modulus | m^3 | \n", + "| α | Thermal expansion coefficient | K^-1 | \n", + "| ε | Strain | - | \n", + "| εt | Breaking strain (tension) | - | \n", + "| εu | Ultimate strain | - | \n", + "| εy | Yield strain | - | \n", + "| κ | Curvature | m^-1 | \n", + "| γ | Load factor | - | \n", + "| γ | Shear strain | rad | \n", + "| γG | Load factor for permanent loads | - | \n", + "| γQ | Load factor for variable loads | - | \n", + "| θ | Angle of rotation | rad | \n", + "| σ | Normal stress | N/m^2 | \n", + "| τ | Shear stress | N/m^2 | \n" ] }, {