Update loads and limit states

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": {