From 0c95bc4cb26c02604c168d1e9e9035ecbc91f150 Mon Sep 17 00:00:00 2001 From: Guus Date: Fri, 22 Mar 2024 10:43:38 +0100 Subject: [PATCH] Update loads and limit states --- .../general_loads/loads_limit_states.ipynb | 126 +++++++++++++++++- 1 file changed, 125 insertions(+), 1 deletion(-) 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": {