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168 lines
8.3 KiB
Text
168 lines
8.3 KiB
Text
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"source": [
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"# Loads and limit states"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Limits\n",
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"Every structure has to comply with two possible limit states which are directly\n",
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"related to the reliablity (strength) and usability of the structure. The Ultimate\n",
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"Limit State (ULS) is used to check structural safety. The Serviceability\n",
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"Limit State (SLS) is used to check usability."
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]
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},
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"metadata": {},
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"source": [
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"## Load combinations\n",
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"Load combinations consist of a combination of design values of\n",
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"the permanent and variable loads. Both characteristic and reduced\n",
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"characteristic loads are combined for the ULS or SLS. The determination\n",
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"of the critical combination of actions is left to the structural engineer.\n",
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"Important here is to keep in mind what kind of element you are designing: a\n",
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"beam, foundation, column or stability measures.\n",
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"\n",
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"Building structures and parts of building structures or their supports\n",
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"and connections must be sufficiently reliable during their service life. They\n",
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"must withstand the most unfavourable combination of loads that can act\n",
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"simultaneously. Exceptions:\n",
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"\n",
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"- The extreme value of a variable load does not have to be combined with the\n",
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"extreme value of other variable loads.\n",
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"- An accidental load does not have to be combined with the extreme value of\n",
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"other accidental loads or extreme variable loads.\n",
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"- For certain cases is its phyisically not possible for two loads to simultaneously\n",
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"act in their extreme or zero value in the same load combination. (e.g. snow and\n",
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"wind loads).\n",
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"\n",
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"A few basic rules according to the Eurocode (EN 1990) will be explained below."
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]
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"source": [
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"## Ultimate Limite State (ULS)\n",
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"$γ_G G_k + γ_{Q;1} Q_{1;k} + Σ(γ_{Q;i} Ψ_{0;i} Q_{i;k})$\n",
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"\n",
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"$γ_G$ = partial factor for permanent loads \n",
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"$G_k$ = total permanent load \n",
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"$γ_{Q;i}$ = partial factor for variable loads \n",
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"$Q_{1;lk}$ = characteristic value of the leading variable load \n",
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"$Ψ_{0;i}$ = factor for combination of variable load i with the leading variable load \n",
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"$Q_{i;k}$ = characteristic value of variable load i \n",
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"\n",
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"```{note}\n",
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"For a more complete explanation see: NEN-EN 1990.\n",
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"```"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Ultimate limit state: load factors ($γ$)\n",
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"\n",
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"| Design Situation | Permanent Loads | Variable Loads | Unfavourable | Favourable | Leading | Other |\n",
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"|------------------|-----------------|----------------|--------------|------------|---------|-------|\n",
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"| 1 | 1.35 | 0.9 | - | 1.5 | - | - |\n",
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"| 2 | 1.2 | 0.9 | 1.5 | 1.5 | - | - | \n",
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" \n",
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"```{note}\n",
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"A favourable load can for example be the dead load of a roof in combination with uplift forces due to wind.\n",
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"```"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Consequence classes\n",
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"\n",
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"| Concequence Class | Description | Examples | KFI |\n",
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"|-------------------|----------------------------------------------------------|-----------------------------------------------------------|-----|\n",
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"| 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",
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"| 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",
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"| 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",
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"\n",
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"```{note}\n",
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"To take the concequence class into account, the applicable load factors ($γ_G$ & $γ_{Q;1}$) have to be multiplied by $K_{FI}$\n",
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"```"
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]
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},
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"## Load categories with corresponding $Ψ$ factors for buildings\n",
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"\n",
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"| Action Category (General Loads) | Example | Ψ0 | Ψ1 | Ψ2 |\n",
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"|----------------------------------|-----------------------------------------------------------|-----|-----|-----|\n",
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"| Category A: Domestic, Residential Areas | - | 0.4 | 0.5 | 0.3 |\n",
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"| Category B: Office Areas | - | 0.5 | 0.5 | 0.3 |\n",
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"| Category C: Congregation Areas | C1: Areas with tables (school, restaurants) | 0.25| 0.7 | 0.6 |\n",
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"| | C2: Areas with fixed seats (theatres, churches, lecture halls) | - | - | - |\n",
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"| | C3: Areas without obstacles for people (museums, hospitals) | - | - | - |\n",
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"| | C4: Areas with physical activities (dance halls, gymnastic rooms) | - | - | - |\n",
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"| | C5: Areas susceptible to large crowds (stadiums, terraces, railway platforms) | - | - | - |\n",
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"| Category D: Shopping Areas | D1: General retail | 0.4 | 0.7 | 0.6 |\n",
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"| | D2: Department stores | - | - | - |\n",
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"| Category E: Storage Areas | E1: Areas susceptible to accumulation of goods | 1.0 | 0.9 | 0.8 |\n",
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"| | E2: Industrial use | - | - | - |\n",
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"| Category F: Traffic Area, Vehicle Weight ≤ 30 kN | - | 0.7 | 0.7 | 0.6 |\n",
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"| Category G: Traffic Area, 30 kN ≤ Vehicle Weight ≤ 160 kN | - | 0.7 | 0.5 | 0.3 |\n",
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"| Category H: Roofs | - | 0 | 0 | 0 |\n",
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"\n",
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" \n",
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" \n",
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"| Other Actions (Environmental Actions) | Example | Ψ0 | Ψ1 | Ψ2 |\n",
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"|----------------------------------------|------------------------------------------------|-----|-----|-----|\n",
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"| Snow Loads on Buildings | - | 0 | 0.2 | 0 |\n",
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"| Wind Loads on Buildings | - | 0 | 0.2 | 0 |\n",
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"| Temperature on Buildings (non-fire) | - | 0 | 0.5 | 0 |\n",
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"\n",
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" \n",
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" \n",
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"$Ψ_0$ = factor for combination value of a variable action\n",
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"$Ψ_1$ = factor for frequent value of a variable action (for example used in combination with accidental loading)\n",
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"$Ψ_2$ = factor for quasi-permanent value of a variable action (for example used in creep calculations)\n"
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