[{"data":1,"prerenderedAt":4090},["ShallowReactive",2],{"kb-en-\u002Fkb\u002Ftheory\u002Fglossary":3,"kb-nav-en":3750},{"page":4,"fallback":3740},{"id":5,"title":6,"body":7,"description":3738,"extension":3739,"faq":3740,"meta":3741,"navigation":3742,"ogImage":3743,"order":3744,"path":3745,"raw":3740,"robots":3743,"schemaOrg":3743,"seo":3746,"sitemap":3747,"stem":3748,"__hash__":3749},"content_en\u002Fkb\u002Ftheory\u002Fglossary.md","Glossary",{"type":8,"value":9,"toc":3713},"minimark",[10,14,19,112,122,132,142,152,225,235,239,249,259,269,279,283,516,664,720,730,738,748,756,765,775,844,854,858,873,882,909,919,928,938,940,949,1236,1244,1254,1263,1273,1306,1316,1320,1471,1727,1729,1738,1798,1808,1812,1895,1897,1907,1915,1918,1972,2033,2043,2089,2098,2106,2165,2174,2238,2246,2249,2258,2268,2278,2287,2384,2393,2461,2521,2524,2534,2540,2544,2554,2557,2565,2573,2744,2753,2761,2770,2884,2887,3029,3032,3041,3049,3057,3066,3074,3082,3085,3093,3170,3286,3296,3304,3328,3337,3346,3354,3363,3373,3381,3389,3398,3401,3409,3412,3420,3428,3431,3440,3449,3457,3538,3541,3549],[11,12,13],"p",{},"Short definitions of the terms this knowledge base uses, in the sense it uses them.\nEach links to the page where the idea is worked through properly.",[15,16,18],"h2",{"id":17},"a","A",[11,20,21,25,26,106,107,111],{},[22,23,24],"strong",{},"Accompanying action."," In a load combination, a variable action present at its\nreduced ",[27,28,31],"span",{"className":29},[30],"katex",[27,32,36],{"className":33,"ariaHidden":35},[34],"katex-html","true",[27,37,40,45],{"className":38},[39],"base",[27,41],{"className":42,"style":44},[43],"strut","height:0.8889em;vertical-align:-0.1944em;",[27,46,49,55],{"className":47},[48],"mord",[27,50,54],{"className":51,"style":53},[48,52],"mathnormal","margin-right:0.0359em;","ψ",[27,56,59],{"className":57},[58],"msupsub",[27,60,64,97],{"className":61},[62,63],"vlist-t","vlist-t2",[27,65,68,92],{"className":66},[67],"vlist-r",[27,69,73],{"className":70,"style":72},[71],"vlist","height:0.3011em;",[27,74,76,81],{"style":75},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[27,77],{"className":78,"style":80},[79],"pstrut","height:2.7em;",[27,82,88],{"className":83},[84,85,86,87],"sizing","reset-size6","size3","mtight",[27,89,91],{"className":90},[48,87],"0",[27,93,96],{"className":94},[95],"vlist-s","​",[27,98,100],{"className":99},[67],[27,101,104],{"className":102,"style":103},[71],"height:0.15em;",[27,105],{}," value alongside the leading one. ",[17,108,110],{"href":109},"\u002Fkb\u002Floads\u002Fcombinations","Automatic combinations",".",[11,113,114,117,118,111],{},[22,115,116],{},"AISC 360."," The American steel specification. Elementarium's second design module\nchecks member strength to its Chapters D to H, compression buckling included. ",[17,119,121],{"href":120},"\u002Fkb\u002Fdesign-checks\u002Faisc","Steel — AISC 360",[11,123,124,127,128,111],{},[22,125,126],{},"All-quad mesh."," A surface mesh made entirely of quadrilaterals, with no triangles\nanywhere. What Elementarium's mesher guarantees, because the shell element is a\nfour-node quad. ",[17,129,131],{"href":130},"\u002Fkb\u002Fmeshing#the-mesher","Meshing",[11,133,134,137,138,111],{},[22,135,136],{},"Amplification factor."," The arbitrary scale applied to a deformed shape or mode shape\nso that it is visible. Never read a displacement off the picture.\n",[17,139,141],{"href":140},"\u002Fkb\u002Freports\u002Freading-diagrams#deformed-shape","Reading diagrams",[11,143,144,147,148,111],{},[22,145,146],{},"AMG — algebraic multigrid."," A preconditioner for the conjugate gradient solver that\nresolves long-wavelength error quickly. ",[17,149,151],{"href":150},"\u002Fkb\u002Fanalysis\u002Fsolvers","Choosing a linear solver",[11,153,154,157,158,220,221,111],{},[22,155,156],{},"ASD — allowable strength design."," The AISC method that compares nominal loads against\n",[27,159,161],{"className":160},[30],[27,162,164],{"className":163,"ariaHidden":35},[34],[27,165,167,171,216],{"className":166},[39],[27,168],{"className":169,"style":170},[43],"height:1em;vertical-align:-0.25em;",[27,172,174,179],{"className":173},[48],[27,175,178],{"className":176,"style":177},[48,52],"margin-right:0.0077em;","R",[27,180,182],{"className":181},[58],[27,183,185,208],{"className":184},[62,63],[27,186,188,205],{"className":187},[67],[27,189,192],{"className":190,"style":191},[71],"height:0.1514em;",[27,193,195,198],{"style":194},"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;",[27,196],{"className":197,"style":80},[79],[27,199,201],{"className":200},[84,85,86,87],[27,202,204],{"className":203},[48,52,87],"n",[27,206,96],{"className":207},[95],[27,209,211],{"className":210},[67],[27,212,214],{"className":213,"style":103},[71],[27,215],{},[27,217,219],{"className":218},[48],"\u002FΩ",". Paired with ASCE 7 §2.4 combinations. ",[17,222,224],{"href":223},"\u002Fkb\u002Floads\u002Fasce-7-combinations","ASCE 7 combinations",[11,226,227,230,231,111],{},[22,228,229],{},"Aspect ratio."," Longest side of an element over its shortest. Beyond about 3:1\nbending accuracy degrades; beyond 5:1 the result is not worth quoting.\n",[17,232,234],{"href":233},"\u002Fkb\u002Fmeshing\u002Fquality-checks","Mesh quality",[15,236,238],{"id":237},"b","B",[11,240,241,244,245,111],{},[22,242,243],{},"Bar."," A two-node element carrying axial force only, with three translational degrees\nof freedom per node. Cannot form a moment-release mechanism.\n",[17,246,248],{"href":247},"\u002Fkb\u002Fmodeling\u002Fbars-beams-and-trusses","Bars, beams and trusses",[11,250,251,254,255,111],{},[22,252,253],{},"Beam."," A two-node element with six degrees of freedom per node, carrying axial force,\ntwo shears, torsion and two bending moments. Exact for a prismatic member under end\nloads and uniform load. ",[17,256,258],{"href":257},"\u002Fkb\u002Ftheory\u002Felement-formulations#beam","Element formulations",[11,260,261,264,265,111],{},[22,262,263],{},"Bedding modulus."," See ",[266,267,268],"em",{},"modulus of subgrade reaction",[11,270,271,274,275,111],{},[22,272,273],{},"Buckling shape."," The eigenvector of a linear buckling analysis: the form the\nstructure takes at instability. Its amplitude is arbitrary. ",[17,276,278],{"href":277},"\u002Fkb\u002Fanalysis\u002Fbuckling","Linear buckling",[15,280,282],{"id":281},"c","C",[11,284,285,288,289,512,513,111],{},[22,286,287],{},"Characteristic combination."," The EN 1990 serviceability combination\n",[27,290,292],{"className":291},[30],[27,293,295,319,393],{"className":294,"ariaHidden":35},[34],[27,296,298,302,306,311,316],{"className":297},[39],[27,299],{"className":300,"style":301},[43],"height:0.7667em;vertical-align:-0.0833em;",[27,303,305],{"className":304},[48,52],"G",[27,307],{"className":308,"style":310},[309],"mspace","margin-right:0.2222em;",[27,312,315],{"className":313},[314],"mbin","+",[27,317],{"className":318,"style":310},[309],[27,320,322,326,384,387,390],{"className":321},[39],[27,323],{"className":324,"style":325},[43],"height:0.9694em;vertical-align:-0.2861em;",[27,327,329,333],{"className":328},[48],[27,330,332],{"className":331},[48,52],"Q",[27,334,336],{"className":335},[58],[27,337,339,375],{"className":338},[62,63],[27,340,342,372],{"className":341},[67],[27,343,346],{"className":344,"style":345},[71],"height:0.3361em;",[27,347,349,352],{"style":348},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[27,350],{"className":351,"style":80},[79],[27,353,355],{"className":354},[84,85,86,87],[27,356,358,363,368],{"className":357},[48,87],[27,359,362],{"className":360,"style":361},[48,52,87],"margin-right:0.0315em;","k",[27,364,367],{"className":365},[366,87],"mpunct",",",[27,369,371],{"className":370},[48,87],"1",[27,373,96],{"className":374},[95],[27,376,378],{"className":377},[67],[27,379,382],{"className":380,"style":381},[71],"height:0.2861em;",[27,383],{},[27,385],{"className":386,"style":310},[309],[27,388,315],{"className":389},[314],[27,391],{"className":392,"style":310},[309],[27,394,396,400,408,412,463],{"className":395},[39],[27,397],{"className":398,"style":399},[43],"height:1.0361em;vertical-align:-0.2861em;",[27,401,407],{"className":402,"style":406},[403,404,405],"mop","op-symbol","small-op","position:relative;top:0em;","∑",[27,409],{"className":410,"style":411},[309],"margin-right:0.1667em;",[27,413,415,418],{"className":414},[48],[27,416,54],{"className":417,"style":53},[48,52],[27,419,421],{"className":420},[58],[27,422,424,455],{"className":423},[62,63],[27,425,427,452],{"className":426},[67],[27,428,431],{"className":429,"style":430},[71],"height:0.3117em;",[27,432,433,436],{"style":75},[27,434],{"className":435,"style":80},[79],[27,437,439],{"className":438},[84,85,86,87],[27,440,442,445,448],{"className":441},[48,87],[27,443,91],{"className":444},[48,87],[27,446,367],{"className":447},[366,87],[27,449,451],{"className":450},[48,52,87],"i",[27,453,96],{"className":454},[95],[27,456,458],{"className":457},[67],[27,459,461],{"className":460,"style":381},[71],[27,462],{},[27,464,466,469],{"className":465},[48],[27,467,332],{"className":468},[48,52],[27,470,472],{"className":471},[58],[27,473,475,504],{"className":474},[62,63],[27,476,478,501],{"className":477},[67],[27,479,481],{"className":480,"style":345},[71],[27,482,483,486],{"style":348},[27,484],{"className":485,"style":80},[79],[27,487,489],{"className":488},[84,85,86,87],[27,490,492,495,498],{"className":491},[48,87],[27,493,362],{"className":494,"style":361},[48,52,87],[27,496,367],{"className":497},[366,87],[27,499,451],{"className":500},[48,52,87],[27,502,96],{"className":503},[95],[27,505,507],{"className":506},[67],[27,508,510],{"className":509,"style":381},[71],[27,511],{},", for irreversible effects. ",[17,514,110],{"href":515},"\u002Fkb\u002Floads\u002Fcombinations#serviceability",[11,517,518,521,522,659,660,111],{},[22,519,520],{},"Characteristic length."," ",[27,523,525],{"className":524},[30],[27,526,528,589],{"className":527,"ariaHidden":35},[34],[27,529,531,535,577,581,586],{"className":530},[39],[27,532],{"className":533,"style":534},[43],"height:0.8333em;vertical-align:-0.15em;",[27,536,538,542],{"className":537},[48],[27,539,541],{"className":540},[48,52],"L",[27,543,545],{"className":544},[58],[27,546,548,569],{"className":547},[62,63],[27,549,551,566],{"className":550},[67],[27,552,554],{"className":553,"style":191},[71],[27,555,556,559],{"style":348},[27,557],{"className":558,"style":80},[79],[27,560,562],{"className":561},[84,85,86,87],[27,563,565],{"className":564},[48,52,87],"e",[27,567,96],{"className":568},[95],[27,570,572],{"className":571},[67],[27,573,575],{"className":574,"style":103},[71],[27,576],{},[27,578],{"className":579,"style":580},[309],"margin-right:0.2778em;",[27,582,585],{"className":583},[584],"mrel","=",[27,587],{"className":588,"style":580},[309],[27,590,592,596,601,605,610,615,619,622],{"className":591},[39],[27,593],{"className":594,"style":595},[43],"height:1.138em;vertical-align:-0.25em;",[27,597,600],{"className":598},[599],"mopen","(",[27,602,604],{"className":603},[48],"4",[27,606,609],{"className":607,"style":608},[48,52],"margin-right:0.0576em;","E",[27,611,614],{"className":612,"style":613},[48,52],"margin-right:0.0785em;","I",[27,616,618],{"className":617},[48],"\u002F",[27,620,362],{"className":621,"style":361},[48,52],[27,623,626,630],{"className":624},[625],"mclose",[27,627,629],{"className":628},[625],")",[27,631,633],{"className":632},[58],[27,634,636],{"className":635},[62],[27,637,639],{"className":638},[67],[27,640,643],{"className":641,"style":642},[71],"height:0.888em;",[27,644,646,649],{"style":645},"top:-3.063em;margin-right:0.05em;",[27,647],{"className":648,"style":80},[79],[27,650,652],{"className":651},[84,85,86,87],[27,653,655],{"className":654},[48,87],[27,656,658],{"className":657},[48,87],"1\u002F4"," for a beam on Winkler bedding — the\ndistance over which a point load's effect spreads. ",[17,661,663],{"href":662},"\u002Fkb\u002Ftheory\u002Fwinkler-foundations#the-characteristic-length","Winkler foundations",[11,665,666,669,670,717,718,111],{},[22,667,668],{},"Cholesky factorisation."," The ",[27,671,673],{"className":672},[30],[27,674,676],{"className":675,"ariaHidden":35},[34],[27,677,679,683,686],{"className":678},[39],[27,680],{"className":681,"style":682},[43],"height:0.8491em;",[27,684,541],{"className":685},[48,52],[27,687,689,692],{"className":688},[48],[27,690,541],{"className":691},[48,52],[27,693,695],{"className":694},[58],[27,696,698],{"className":697},[62],[27,699,701],{"className":700},[67],[27,702,704],{"className":703,"style":682},[71],[27,705,706,709],{"style":645},[27,707],{"className":708,"style":80},[79],[27,710,712],{"className":711},[84,85,86,87],[27,713,716],{"className":714},[48,715,87],"mathsf","T"," direct solver, for symmetric positive definite\nsystems. ",[17,719,151],{"href":150},[11,721,722,725,726,111],{},[22,723,724],{},"Class (of a cross-section)."," EN 1993-1-1's four categories of steel section by\nsusceptibility to local buckling; decides plastic or elastic resistance.\n",[17,727,729],{"href":728},"\u002Fkb\u002Fdesign-checks\u002Fsection-classification","Section classification",[11,731,732,735,736,111],{},[22,733,734],{},"Combination."," A factored sum of load cases, one per code equation and leading action.\n",[17,737,110],{"href":109},[11,739,740,743,744,111],{},[22,741,742],{},"Completeness check."," A Sturm-sequence test that the modes returned by a modal or\nbuckling analysis are really the lowest ones, with none skipped.\n",[17,745,747],{"href":746},"\u002Fkb\u002Fanalysis\u002Fmodal","Modal analysis",[11,749,750,753,754,111],{},[22,751,752],{},"Conjugate gradients (CG)."," An iterative linear solver that converges towards the\nsolution to a tolerance you set, rather than factorising the matrix.\n",[17,755,151],{"href":150},[11,757,758,761,762,111],{},[22,759,760],{},"Consistent mass."," A mass matrix distributed with the element's own interpolation.\nBounds true frequencies from above; the default. ",[17,763,747],{"href":764},"\u002Fkb\u002Fanalysis\u002Fmodal#consistent-or-lumped",[11,766,767,770,771,111],{},[22,768,769],{},"Convergence (mesh)."," The property that a result stops changing as the mesh is\nrefined. Tested by halving the element size and comparing.\n",[17,772,774],{"href":773},"\u002Fkb\u002Fmeshing\u002Felement-size#convergence","Choosing element size",[11,776,777,841,842,111],{},[22,778,779,780,111],{},"Critical load factor — ",[27,781,783],{"className":782},[30],[27,784,786],{"className":785,"ariaHidden":35},[34],[27,787,789,793],{"className":788},[39],[27,790],{"className":791,"style":792},[43],"height:0.5806em;vertical-align:-0.15em;",[27,794,796,801],{"className":795},[48],[27,797,800],{"className":798,"style":799},[48,52],"margin-right:0.0037em;","α",[27,802,804],{"className":803},[58],[27,805,807,833],{"className":806},[62,63],[27,808,810,830],{"className":809},[67],[27,811,813],{"className":812,"style":191},[71],[27,814,816,819],{"style":815},"top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;",[27,817],{"className":818,"style":80},[79],[27,820,822],{"className":821},[84,85,86,87],[27,823,825],{"className":824},[48,87],[27,826,829],{"className":827,"style":828},[48,52,87],"margin-right:0.0278em;","cr",[27,831,96],{"className":832},[95],[27,834,836],{"className":835},[67],[27,837,839],{"className":838,"style":103},[71],[27,840],{}," The multiple of a reference loading at which the\nstructure buckles elastically. An upper bound, not a capacity.\n",[17,843,278],{"href":277},[11,845,846,849,850,111],{},[22,847,848],{},"Cross-origin isolation."," A browser security condition that lets a page share memory\nbetween threads. Where it is granted the solver runs on every core; where it is not, on\none. ",[17,851,853],{"href":852},"\u002Fkb\u002Fgetting-started\u002Fsystem-requirements","System requirements",[15,855,857],{"id":856},"d","D",[11,859,860,863,864,868,869,111],{},[22,861,862],{},"Degree of freedom (DoF)."," One independent way a node can move: three translations and\nthree rotations in a 3D model. The free plan caps the solved system at 500 of them.\n",[17,865,867],{"href":866},"\u002Fkb\u002Fmodeling\u002Fsupports-and-releases#degrees-of-freedom","Supports and releases",",\n",[17,870,872],{"href":871},"\u002Fkb\u002Faccount\u002Fplans","Plans and limits",[11,874,875,878,879,111],{},[22,876,877],{},"Design strip."," A width of slab over which a moment field is integrated to give the\nmoment reinforcement is designed for. A hand calculation from the contour today; a\nsection-cut tool is on the roadmap. ",[17,880,774],{"href":881},"\u002Fkb\u002Fmeshing\u002Felement-size",[11,883,884,887,888,906,907,111],{},[22,885,886],{},"Direct solver."," A linear solver that factorises ",[27,889,891],{"className":890},[30],[27,892,894],{"className":893,"ariaHidden":35},[34],[27,895,897,901],{"className":896},[39],[27,898],{"className":899,"style":900},[43],"height:0.6833em;",[27,902,905],{"className":903,"style":904},[48,52],"margin-right:0.0715em;","K"," once and resolves cheaply for\nevery load case. ",[17,908,151],{"href":150},[11,910,911,914,915,111],{},[22,912,913],{},"Direct stiffness method."," The procedure every finite element solver follows: element\nstiffness, transformation, assembly, constraints, solution, recovery.\n",[17,916,918],{"href":917},"\u002Fkb\u002Ftheory\u002Fdirect-stiffness-method","The direct stiffness method",[11,920,921,924,925,111],{},[22,922,923],{},"Drilling degree of freedom."," The in-plane rotation about a shell element's normal.\nWithout it a beam framing into a wall behaves as a pin. The shell element has one, tied\nto the membrane's own rotation (Hughes–Brezzi) rather than sprung to the ground.\n",[17,926,258],{"href":927},"\u002Fkb\u002Ftheory\u002Felement-formulations#drilling-degrees-of-freedom",[11,929,930,933,934,111],{},[22,931,932],{},"DXF."," A drawing exchange format. Imported as a reference underlay to snap against;\nnothing in it becomes a member. ",[17,935,937],{"href":936},"\u002Fkb\u002Fmodeling\u002Fdrawings-and-snapping","Drawings and snapping",[15,939,609],{"id":565},[11,941,942,945,946,111],{},[22,943,944],{},"Eccentricity."," An offset between a member's centreline and the node it connects to,\ncarried by the member itself rather than by a separate rigid arm.\n",[17,947,867],{"href":948},"\u002Fkb\u002Fmodeling\u002Fsupports-and-releases#rigid-arms",[11,950,951,521,954,1052,1053,1155,1156,1197,1198,1214,1215,1230,1231,1233,1234,111],{},[22,952,953],{},"Eigenvalue problem.",[27,955,957],{"className":956},[30],[27,958,960,982,1042],{"className":959,"ariaHidden":35},[34],[27,961,963,966,969,972,975,979],{"className":962},[39],[27,964],{"className":965,"style":170},[43],[27,967,600],{"className":968},[599],[27,970,905],{"className":971,"style":904},[48,52],[27,973],{"className":974,"style":310},[309],[27,976,978],{"className":977},[314],"−",[27,980],{"className":981,"style":310},[309],[27,983,985,989,1021,1026,1029,1033,1036,1039],{"className":984},[39],[27,986],{"className":987,"style":988},[43],"height:1.0641em;vertical-align:-0.25em;",[27,990,992,996],{"className":991},[48],[27,993,995],{"className":994,"style":53},[48,52],"ω",[27,997,999],{"className":998},[58],[27,1000,1002],{"className":1001},[62],[27,1003,1005],{"className":1004},[67],[27,1006,1009],{"className":1007,"style":1008},[71],"height:0.8141em;",[27,1010,1011,1014],{"style":645},[27,1012],{"className":1013,"style":80},[79],[27,1015,1017],{"className":1016},[84,85,86,87],[27,1018,1020],{"className":1019},[48,87],"2",[27,1022,1025],{"className":1023,"style":1024},[48,52],"margin-right:0.109em;","M",[27,1027,629],{"className":1028},[625],[27,1030,1032],{"className":1031},[48,52],"ϕ",[27,1034],{"className":1035,"style":580},[309],[27,1037,585],{"className":1038},[584],[27,1040],{"className":1041,"style":580},[309],[27,1043,1045,1049],{"className":1044},[39],[27,1046],{"className":1047,"style":1048},[43],"height:0.6444em;",[27,1050,91],{"className":1051},[48]," for modal analysis, ",[27,1054,1056],{"className":1055},[30],[27,1057,1059,1080,1146],{"className":1058,"ariaHidden":35},[34],[27,1060,1062,1065,1068,1071,1074,1077],{"className":1061},[39],[27,1063],{"className":1064,"style":170},[43],[27,1066,600],{"className":1067},[599],[27,1069,905],{"className":1070,"style":904},[48,52],[27,1072],{"className":1073,"style":310},[309],[27,1075,315],{"className":1076},[314],[27,1078],{"className":1079,"style":310},[309],[27,1081,1083,1086,1089,1131,1134,1137,1140,1143],{"className":1082},[39],[27,1084],{"className":1085,"style":399},[43],[27,1087,800],{"className":1088,"style":799},[48,52],[27,1090,1092,1095],{"className":1091},[48],[27,1093,905],{"className":1094,"style":904},[48,52],[27,1096,1098],{"className":1097},[58],[27,1099,1101,1123],{"className":1100},[62,63],[27,1102,1104,1120],{"className":1103},[67],[27,1105,1107],{"className":1106,"style":191},[71],[27,1108,1110,1113],{"style":1109},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[27,1111],{"className":1112,"style":80},[79],[27,1114,1116],{"className":1115},[84,85,86,87],[27,1117,1119],{"className":1118,"style":53},[48,52,87],"g",[27,1121,96],{"className":1122},[95],[27,1124,1126],{"className":1125},[67],[27,1127,1129],{"className":1128,"style":381},[71],[27,1130],{},[27,1132,629],{"className":1133},[625],[27,1135,1032],{"className":1136},[48,52],[27,1138],{"className":1139,"style":580},[309],[27,1141,585],{"className":1142},[584],[27,1144],{"className":1145,"style":580},[309],[27,1147,1149,1152],{"className":1148},[39],[27,1150],{"className":1151,"style":1048},[43],[27,1153,91],{"className":1154},[48]," for\nbuckling: solved for the values ",[27,1157,1159],{"className":1158},[30],[27,1160,1162],{"className":1161,"ariaHidden":35},[34],[27,1163,1165,1168],{"className":1164},[39],[27,1166],{"className":1167,"style":1008},[43],[27,1169,1171,1174],{"className":1170},[48],[27,1172,995],{"className":1173,"style":53},[48,52],[27,1175,1177],{"className":1176},[58],[27,1178,1180],{"className":1179},[62],[27,1181,1183],{"className":1182},[67],[27,1184,1186],{"className":1185,"style":1008},[71],[27,1187,1188,1191],{"style":645},[27,1189],{"className":1190,"style":80},[79],[27,1192,1194],{"className":1193},[84,85,86,87],[27,1195,1020],{"className":1196},[48,87]," or ",[27,1199,1201],{"className":1200},[30],[27,1202,1204],{"className":1203,"ariaHidden":35},[34],[27,1205,1207,1211],{"className":1206},[39],[27,1208],{"className":1209,"style":1210},[43],"height:0.4306em;",[27,1212,800],{"className":1213,"style":799},[48,52]," and the shapes ",[27,1216,1218],{"className":1217},[30],[27,1219,1221],{"className":1220,"ariaHidden":35},[34],[27,1222,1224,1227],{"className":1223},[39],[27,1225],{"className":1226,"style":44},[43],[27,1228,1032],{"className":1229},[48,52],".\n",[17,1232,747],{"href":746},", ",[17,1235,278],{"href":277},[11,1237,1238,1241,1242,111],{},[22,1239,1240],{},"EN 1990."," The Eurocode basis of design, whose equations 6.10, 6.10a and 6.10b define\nthe ULS combinations. ",[17,1243,110],{"href":109},[11,1245,1246,1249,1250,111],{},[22,1247,1248],{},"EN 1993-1-1."," The Eurocode for steel structures. Elementarium's first design module\nchecks cross-section and member resistance to its §6.2 and §6.3. ",[17,1251,1253],{"href":1252},"\u002Fkb\u002Fdesign-checks\u002Fsteel","Steel — EN 1993-1-1",[11,1255,1256,1259,1260,111],{},[22,1257,1258],{},"Enhanced assumed strain (EAS)."," Extra strain modes added inside an element and\ncondensed out, which let a four-node membrane bend in its own plane without the parasitic\nshear that otherwise stiffens it. The shell element's membrane uses four.\n",[17,1261,258],{"href":1262},"\u002Fkb\u002Ftheory\u002Felement-formulations#walls-and-deep-beams-the-membrane",[11,1264,1265,1268,1269,111],{},[22,1266,1267],{},"Envelope."," The maximum and minimum of a result quantity across a set of combinations,\nposition by position, each with its governing combination. Not an equilibrium state.\n",[17,1270,1272],{"href":1271},"\u002Fkb\u002Floads\u002Fenvelopes","Envelopes",[11,1274,1275,1278,1279,1303,1304,111],{},[22,1276,1277],{},"Equivalent nodal forces."," The nodal loads a distributed load is converted to for\nassembly — ",[27,1280,1282],{"className":1281},[30],[27,1283,1285],{"className":1284,"ariaHidden":35},[34],[27,1286,1288,1291,1296,1299],{"className":1287},[39],[27,1289],{"className":1290,"style":170},[43],[27,1292,1295],{"className":1293,"style":1294},[48,52],"margin-right:0.0269em;","w",[27,1297,541],{"className":1298},[48,52],[27,1300,1302],{"className":1301},[48],"\u002F2"," at each end of a uniformly loaded beam, plus fixed-end moments.\n",[17,1305,918],{"href":917},[11,1307,1308,1311,1312,111],{},[22,1309,1310],{},"Exclusive group."," A load group whose cases can never act together — wind directions,\narrangements of one imposed load. ",[17,1313,1315],{"href":1314},"\u002Fkb\u002Floads\u002Fload-cases#grouping","Load cases",[15,1317,1319],{"id":1318},"f","F",[11,1321,1322,1325,1326,1396,1397,1467,1468,111],{},[22,1323,1324],{},"Favourable action."," A permanent action that relieves the effect being checked,\nfactored at ",[27,1327,1329],{"className":1328},[30],[27,1330,1332],{"className":1331,"ariaHidden":35},[34],[27,1333,1335,1339],{"className":1334},[39],[27,1336],{"className":1337,"style":1338},[43],"height:0.7167em;vertical-align:-0.2861em;",[27,1340,1342,1347],{"className":1341},[48],[27,1343,1346],{"className":1344,"style":1345},[48,52],"margin-right:0.0556em;","γ",[27,1348,1350],{"className":1349},[58],[27,1351,1353,1388],{"className":1352},[62,63],[27,1354,1356,1385],{"className":1355},[67],[27,1357,1359],{"className":1358,"style":345},[71],[27,1360,1362,1365],{"style":1361},"top:-2.55em;margin-left:-0.0556em;margin-right:0.05em;",[27,1363],{"className":1364,"style":80},[79],[27,1366,1368],{"className":1367},[84,85,86,87],[27,1369,1371,1374,1377,1381],{"className":1370},[48,87],[27,1372,305],{"className":1373},[48,52,87],[27,1375,367],{"className":1376},[366,87],[27,1378,1380],{"className":1379},[48,52,87],"in",[27,1382,1318],{"className":1383,"style":1384},[48,52,87],"margin-right:0.1076em;",[27,1386,96],{"className":1387},[95],[27,1389,1391],{"className":1390},[67],[27,1392,1394],{"className":1393,"style":381},[71],[27,1395],{}," rather than ",[27,1398,1400],{"className":1399},[30],[27,1401,1403],{"className":1402,"ariaHidden":35},[34],[27,1404,1406,1409],{"className":1405},[39],[27,1407],{"className":1408,"style":1338},[43],[27,1410,1412,1415],{"className":1411},[48],[27,1413,1346],{"className":1414,"style":1345},[48,52],[27,1416,1418],{"className":1417},[58],[27,1419,1421,1459],{"className":1420},[62,63],[27,1422,1424,1456],{"className":1423},[67],[27,1425,1428],{"className":1426,"style":1427},[71],"height:0.3283em;",[27,1429,1430,1433],{"style":1361},[27,1431],{"className":1432,"style":80},[79],[27,1434,1436],{"className":1435},[84,85,86,87],[27,1437,1439,1442,1445,1449,1453],{"className":1438},[48,87],[27,1440,305],{"className":1441},[48,52,87],[27,1443,367],{"className":1444},[366,87],[27,1446,1448],{"className":1447},[48,52,87],"s",[27,1450,1452],{"className":1451},[48,52,87],"u",[27,1454,11],{"className":1455},[48,52,87],[27,1457,96],{"className":1458},[95],[27,1460,1462],{"className":1461},[67],[27,1463,1465],{"className":1464,"style":381},[71],[27,1466],{},". Decides uplift and overturning.\n",[17,1469,110],{"href":1470},"\u002Fkb\u002Floads\u002Fcombinations#favourable-and-unfavourable",[11,1472,1473,288,1476,1724,1725,111],{},[22,1474,1475],{},"Frequent combination.",[27,1477,1479],{"className":1478},[30],[27,1480,1482,1500,1614],{"className":1481,"ariaHidden":35},[34],[27,1483,1485,1488,1491,1494,1497],{"className":1484},[39],[27,1486],{"className":1487,"style":301},[43],[27,1489,305],{"className":1490},[48,52],[27,1492],{"className":1493,"style":310},[309],[27,1495,315],{"className":1496},[314],[27,1498],{"className":1499,"style":310},[309],[27,1501,1503,1507,1556,1605,1608,1611],{"className":1502},[39],[27,1504],{"className":1505,"style":1506},[43],"height:0.9805em;vertical-align:-0.2861em;",[27,1508,1510,1513],{"className":1509},[48],[27,1511,54],{"className":1512,"style":53},[48,52],[27,1514,1516],{"className":1515},[58],[27,1517,1519,1548],{"className":1518},[62,63],[27,1520,1522,1545],{"className":1521},[67],[27,1523,1525],{"className":1524,"style":72},[71],[27,1526,1527,1530],{"style":75},[27,1528],{"className":1529,"style":80},[79],[27,1531,1533],{"className":1532},[84,85,86,87],[27,1534,1536,1539,1542],{"className":1535},[48,87],[27,1537,371],{"className":1538},[48,87],[27,1540,367],{"className":1541},[366,87],[27,1543,371],{"className":1544},[48,87],[27,1546,96],{"className":1547},[95],[27,1549,1551],{"className":1550},[67],[27,1552,1554],{"className":1553,"style":381},[71],[27,1555],{},[27,1557,1559,1562],{"className":1558},[48],[27,1560,332],{"className":1561},[48,52],[27,1563,1565],{"className":1564},[58],[27,1566,1568,1597],{"className":1567},[62,63],[27,1569,1571,1594],{"className":1570},[67],[27,1572,1574],{"className":1573,"style":345},[71],[27,1575,1576,1579],{"style":348},[27,1577],{"className":1578,"style":80},[79],[27,1580,1582],{"className":1581},[84,85,86,87],[27,1583,1585,1588,1591],{"className":1584},[48,87],[27,1586,362],{"className":1587,"style":361},[48,52,87],[27,1589,367],{"className":1590},[366,87],[27,1592,371],{"className":1593},[48,87],[27,1595,96],{"className":1596},[95],[27,1598,1600],{"className":1599},[67],[27,1601,1603],{"className":1602,"style":381},[71],[27,1604],{},[27,1606],{"className":1607,"style":310},[309],[27,1609,315],{"className":1610},[314],[27,1612],{"className":1613,"style":310},[309],[27,1615,1617,1620,1623,1626,1675],{"className":1616},[39],[27,1618],{"className":1619,"style":399},[43],[27,1621,407],{"className":1622,"style":406},[403,404,405],[27,1624],{"className":1625,"style":411},[309],[27,1627,1629,1632],{"className":1628},[48],[27,1630,54],{"className":1631,"style":53},[48,52],[27,1633,1635],{"className":1634},[58],[27,1636,1638,1667],{"className":1637},[62,63],[27,1639,1641,1664],{"className":1640},[67],[27,1642,1644],{"className":1643,"style":430},[71],[27,1645,1646,1649],{"style":75},[27,1647],{"className":1648,"style":80},[79],[27,1650,1652],{"className":1651},[84,85,86,87],[27,1653,1655,1658,1661],{"className":1654},[48,87],[27,1656,1020],{"className":1657},[48,87],[27,1659,367],{"className":1660},[366,87],[27,1662,451],{"className":1663},[48,52,87],[27,1665,96],{"className":1666},[95],[27,1668,1670],{"className":1669},[67],[27,1671,1673],{"className":1672,"style":381},[71],[27,1674],{},[27,1676,1678,1681],{"className":1677},[48],[27,1679,332],{"className":1680},[48,52],[27,1682,1684],{"className":1683},[58],[27,1685,1687,1716],{"className":1686},[62,63],[27,1688,1690,1713],{"className":1689},[67],[27,1691,1693],{"className":1692,"style":345},[71],[27,1694,1695,1698],{"style":348},[27,1696],{"className":1697,"style":80},[79],[27,1699,1701],{"className":1700},[84,85,86,87],[27,1702,1704,1707,1710],{"className":1703},[48,87],[27,1705,362],{"className":1706,"style":361},[48,52,87],[27,1708,367],{"className":1709},[366,87],[27,1711,451],{"className":1712},[48,52,87],[27,1714,96],{"className":1715},[95],[27,1717,1719],{"className":1718},[67],[27,1720,1722],{"className":1721,"style":381},[71],[27,1723],{},", for reversible effects.\n",[17,1726,110],{"href":515},[15,1728,305],{"id":1119},[11,1730,1731,1734,1735,111],{},[22,1732,1733],{},"Gauss point."," A numerical integration point inside an element, where stresses are\nmost accurate. Results are carried from there to the corners by a recovery method.\n",[17,1736,258],{"href":1737},"\u002Fkb\u002Ftheory\u002Felement-formulations#integration-and-result-recovery",[11,1739,1740,1795,1796,111],{},[22,1741,1742,1743,111],{},"Geometric stiffness — ",[27,1744,1746],{"className":1745},[30],[27,1747,1749],{"className":1748,"ariaHidden":35},[34],[27,1750,1752,1755],{"className":1751},[39],[27,1753],{"className":1754,"style":325},[43],[27,1756,1758,1761],{"className":1757},[48],[27,1759,905],{"className":1760,"style":904},[48,52],[27,1762,1764],{"className":1763},[58],[27,1765,1767,1787],{"className":1766},[62,63],[27,1768,1770,1784],{"className":1769},[67],[27,1771,1773],{"className":1772,"style":191},[71],[27,1774,1775,1778],{"style":1109},[27,1776],{"className":1777,"style":80},[79],[27,1779,1781],{"className":1780},[84,85,86,87],[27,1782,1119],{"className":1783,"style":53},[48,52,87],[27,1785,96],{"className":1786},[95],[27,1788,1790],{"className":1789},[67],[27,1791,1793],{"className":1792,"style":381},[71],[27,1794],{}," The stiffness contribution of axial force acting through\nlateral deflection. Assembled from a static solve for buckling; from the current state\nfor second-order. ",[17,1797,278],{"href":277},[11,1799,1800,1803,1804,111],{},[22,1801,1802],{},"Governing combination."," The combination that produced an extreme value or a\nutilisation. Every check and every table carries it.\n",[17,1805,1807],{"href":1806},"\u002Fkb\u002Fdesign-checks","Design checks",[15,1809,1811],{"id":1810},"h","H",[11,1813,1814,1817,1818,1872,1873,1890,1891,111],{},[22,1815,1816],{},"Hogging."," Bending that puts the top of a beam in tension — over a support, at the\neaves of a portal. Whether that is a positive or a negative ",[27,1819,1821],{"className":1820},[30],[27,1822,1824],{"className":1823,"ariaHidden":35},[34],[27,1825,1827,1830],{"className":1826},[39],[27,1828],{"className":1829,"style":325},[43],[27,1831,1833,1836],{"className":1832},[48],[27,1834,1025],{"className":1835,"style":1024},[48,52],[27,1837,1839],{"className":1838},[58],[27,1840,1842,1864],{"className":1841},[62,63],[27,1843,1845,1861],{"className":1844},[67],[27,1846,1848],{"className":1847,"style":191},[71],[27,1849,1851,1854],{"style":1850},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[27,1852],{"className":1853,"style":80},[79],[27,1855,1857],{"className":1856},[84,85,86,87],[27,1858,1860],{"className":1859,"style":53},[48,52,87],"y",[27,1862,96],{"className":1863},[95],[27,1865,1867],{"className":1866},[67],[27,1868,1870],{"className":1869,"style":381},[71],[27,1871],{}," depends on which way\nthe member's local ",[27,1874,1876],{"className":1875},[30],[27,1877,1879],{"className":1878,"ariaHidden":35},[34],[27,1880,1882,1885],{"className":1881},[39],[27,1883],{"className":1884,"style":1210},[43],[27,1886,1889],{"className":1887,"style":1888},[48,52],"margin-right:0.044em;","z"," axis points; the diagram is drawn on the tension side either way.\n",[17,1892,1894],{"href":1893},"\u002Fkb\u002Ftheory\u002Fsign-conventions#bending-diagram-convention","Sign conventions",[15,1896,614],{"id":451},[11,1898,1899,1902,1903,111],{},[22,1900,1901],{},"Imperfection."," An initial out-of-straightness or out-of-plumb applied before a\nsecond-order analysis, to EN 1993-1-1 §5.3: global sway, member bow, or a scaled\nbuckling shape. ",[17,1904,1906],{"href":1905},"\u002Fkb\u002Fanalysis\u002Fsecond-order","Second-order analysis",[11,1908,1909,1912,1913,111],{},[22,1910,1911],{},"Incomplete Cholesky."," A preconditioner for conjugate gradients built from an\napproximate factorisation. ",[17,1914,151],{"href":150},[15,1916,541],{"id":1917},"l",[11,1919,1920,1969,1970,111],{},[22,1921,1922,111],{},[27,1923,1925],{"className":1924},[30],[27,1926,1928],{"className":1927,"ariaHidden":35},[34],[27,1929,1931,1934,1937,1940],{"className":1930},[39],[27,1932],{"className":1933,"style":682},[43],[27,1935,541],{"className":1936},[48,52],[27,1938,857],{"className":1939,"style":828},[48,52],[27,1941,1943,1946],{"className":1942},[48],[27,1944,541],{"className":1945},[48,52],[27,1947,1949],{"className":1948},[58],[27,1950,1952],{"className":1951},[62],[27,1953,1955],{"className":1954},[67],[27,1956,1958],{"className":1957,"style":682},[71],[27,1959,1960,1963],{"style":645},[27,1961],{"className":1962,"style":80},[79],[27,1964,1966],{"className":1965},[84,85,86,87],[27,1967,716],{"className":1968},[48,715,87]," A direct solver that factorises symmetric matrices including indefinite ones;\nits negative pivots are what second-order analysis watches for instability.\n",[17,1971,151],{"href":150},[11,1973,1974,1977,1978,1230,2030,111],{},[22,1975,1976],{},"Leading action."," The variable action taking its full characteristic value in a\ncombination, while the others accompany at ",[27,1979,1981],{"className":1980},[30],[27,1982,1984],{"className":1983,"ariaHidden":35},[34],[27,1985,1987,1990],{"className":1986},[39],[27,1988],{"className":1989,"style":44},[43],[27,1991,1993,1996],{"className":1992},[48],[27,1994,54],{"className":1995,"style":53},[48,52],[27,1997,1999],{"className":1998},[58],[27,2000,2002,2022],{"className":2001},[62,63],[27,2003,2005,2019],{"className":2004},[67],[27,2006,2008],{"className":2007,"style":72},[71],[27,2009,2010,2013],{"style":75},[27,2011],{"className":2012,"style":80},[79],[27,2014,2016],{"className":2015},[84,85,86,87],[27,2017,91],{"className":2018},[48,87],[27,2020,96],{"className":2021},[95],[27,2023,2025],{"className":2024},[67],[27,2026,2028],{"className":2027,"style":103},[71],[27,2029],{},[17,2031,110],{"href":2032},"\u002Fkb\u002Floads\u002Fcombinations#the-eurocode-equations",[11,2034,2035,2038,2039,111],{},[22,2036,2037],{},"Line support."," A support distributed along a member or a slab edge, with stiffness per\nunit length — the Winkler bed for a grade beam or a wall under a slab.\n",[17,2040,2042],{"href":2041},"\u002Fkb\u002Fmodeling\u002Felastic-foundations","Elastic foundations",[11,2044,2045,521,2048,2084,2085,111],{},[22,2046,2047],{},"Linear static analysis.",[27,2049,2051],{"className":2050},[30],[27,2052,2054,2075],{"className":2053,"ariaHidden":35},[34],[27,2055,2057,2060,2063,2066,2069,2072],{"className":2056},[39],[27,2058],{"className":2059,"style":900},[43],[27,2061,905],{"className":2062,"style":904},[48,52],[27,2064,1452],{"className":2065},[48,52],[27,2067],{"className":2068,"style":580},[309],[27,2070,585],{"className":2071},[584],[27,2073],{"className":2074,"style":580},[309],[27,2076,2078,2081],{"className":2077},[39],[27,2079],{"className":2080,"style":44},[43],[27,2082,1318],{"className":2083,"style":1384},[48,52]," on the undeformed geometry with elastic material;\nthe workhorse. ",[17,2086,2088],{"href":2087},"\u002Fkb\u002Fanalysis\u002Flinear-static","Linear static",[11,2090,2091,2094,2095,111],{},[22,2092,2093],{},"Load case."," One action, unfactored. ",[17,2096,1315],{"href":2097},"\u002Fkb\u002Floads\u002Fload-cases",[11,2099,2100,2103,2104,111],{},[22,2101,2102],{},"Load group."," Cases that share a factor and a relationship — permanent, variable\nexclusive, variable simultaneous, accidental. ",[17,2105,1315],{"href":1314},[11,2107,2108,2111,2112,2128,2129,2145,2146,2161,2162,111],{},[22,2109,2110],{},"Local axes."," A member's own ",[27,2113,2115],{"className":2114},[30],[27,2116,2118],{"className":2117,"ariaHidden":35},[34],[27,2119,2121,2124],{"className":2120},[39],[27,2122],{"className":2123,"style":1210},[43],[27,2125,2127],{"className":2126},[48,52],"x"," along its length, ",[27,2130,2132],{"className":2131},[30],[27,2133,2135],{"className":2134,"ariaHidden":35},[34],[27,2136,2138,2142],{"className":2137},[39],[27,2139],{"className":2140,"style":2141},[43],"height:0.625em;vertical-align:-0.1944em;",[27,2143,1860],{"className":2144,"style":53},[48,52]," and ",[27,2147,2149],{"className":2148},[30],[27,2150,2152],{"className":2151,"ariaHidden":35},[34],[27,2153,2155,2158],{"className":2154},[39],[27,2156],{"className":2157,"style":1210},[43],[27,2159,1889],{"className":2160,"style":1888},[48,52]," in the section, fixed\nby the direction it was drawn. ",[17,2163,1894],{"href":2164},"\u002Fkb\u002Ftheory\u002Fsign-conventions#local-member-axes",[11,2166,2167,2170,2171,111],{},[22,2168,2169],{},"Locking."," Spurious stiffness from a constraint the element cannot satisfy. Shear\nlocking stiffens a displacement-based plate element as it gets thin; in-plane bending\nlocking (parasitic shear) stiffens a plain four-node membrane in a wall or deep beam. The\nshell element locks in neither.\n",[17,2172,258],{"href":2173},"\u002Fkb\u002Ftheory\u002Felement-formulations#why-the-mixed-interpolation-matters",[11,2175,2176,2179,2180,2235,2236,111],{},[22,2177,2178],{},"LRFD — load and resistance factor design."," The AISC strength method that compares\nfactored loads against ",[27,2181,2183],{"className":2182},[30],[27,2184,2186],{"className":2185,"ariaHidden":35},[34],[27,2187,2189,2192,2195],{"className":2188},[39],[27,2190],{"className":2191,"style":44},[43],[27,2193,1032],{"className":2194},[48,52],[27,2196,2198,2201],{"className":2197},[48],[27,2199,178],{"className":2200,"style":177},[48,52],[27,2202,2204],{"className":2203},[58],[27,2205,2207,2227],{"className":2206},[62,63],[27,2208,2210,2224],{"className":2209},[67],[27,2211,2213],{"className":2212,"style":191},[71],[27,2214,2215,2218],{"style":194},[27,2216],{"className":2217,"style":80},[79],[27,2219,2221],{"className":2220},[84,85,86,87],[27,2222,204],{"className":2223},[48,52,87],[27,2225,96],{"className":2226},[95],[27,2228,2230],{"className":2229},[67],[27,2231,2233],{"className":2232,"style":103},[71],[27,2234],{},". Paired with ASCE 7 §2.3.1 combinations.\n",[17,2237,224],{"href":223},[11,2239,2240,2243,2244,111],{},[22,2241,2242],{},"Lumped mass."," A mass matrix concentrated on the diagonal. Usually gives frequencies\nbelow the true ones, though not as a guaranteed bound. ",[17,2245,747],{"href":764},[15,2247,1025],{"id":2248},"m",[11,2250,2251,2254,2255,111],{},[22,2252,2253],{},"Mass target."," A modal analysis setting: keep extracting modes until a fraction of the\nmass — 0.9, per EN 1998-1 — participates. ",[17,2256,747],{"href":2257},"\u002Fkb\u002Fanalysis\u002Fmodal#how-many-modes",[11,2259,2260,2263,2264,111],{},[22,2261,2262],{},"Mechanism."," A structure, or part of one, that can move without resistance. Produces a\nsingular stiffness matrix. ",[17,2265,2267],{"href":2266},"\u002Fkb\u002Ftroubleshooting\u002Fsingular-stiffness-matrix","Singular stiffness matrix",[11,2269,2270,2273,2274,111],{},[22,2271,2272],{},"Mid-plane."," The surface a slab or wall is modelled at, as a member is modelled at its\ncentreline. ",[17,2275,2277],{"href":2276},"\u002Fkb\u002Fmodeling\u002Fsurfaces","Slabs, walls and shells",[11,2279,2280,2283,2284,111],{},[22,2281,2282],{},"MITC4."," Mixed Interpolation of Tensorial Components, four nodes: the Reissner–Mindlin\nbending and transverse-shear formulation of the shell element every surface in\nElementarium uses, which samples the shear at the edge midpoints so that thin plates do\nnot lock. Its membrane is enhanced separately (EAS). ",[17,2285,258],{"href":2286},"\u002Fkb\u002Ftheory\u002Felement-formulations#shell-mitc4",[11,2288,2289,2292,2293,1230,2382,111],{},[22,2290,2291],{},"Modal analysis."," Natural frequencies and mode shapes from ",[27,2294,2296],{"className":2295},[30],[27,2297,2299,2320,2373],{"className":2298,"ariaHidden":35},[34],[27,2300,2302,2305,2308,2311,2314,2317],{"className":2301},[39],[27,2303],{"className":2304,"style":170},[43],[27,2306,600],{"className":2307},[599],[27,2309,905],{"className":2310,"style":904},[48,52],[27,2312],{"className":2313,"style":310},[309],[27,2315,978],{"className":2316},[314],[27,2318],{"className":2319,"style":310},[309],[27,2321,2323,2326,2355,2358,2361,2364,2367,2370],{"className":2322},[39],[27,2324],{"className":2325,"style":988},[43],[27,2327,2329,2332],{"className":2328},[48],[27,2330,995],{"className":2331,"style":53},[48,52],[27,2333,2335],{"className":2334},[58],[27,2336,2338],{"className":2337},[62],[27,2339,2341],{"className":2340},[67],[27,2342,2344],{"className":2343,"style":1008},[71],[27,2345,2346,2349],{"style":645},[27,2347],{"className":2348,"style":80},[79],[27,2350,2352],{"className":2351},[84,85,86,87],[27,2353,1020],{"className":2354},[48,87],[27,2356,1025],{"className":2357,"style":1024},[48,52],[27,2359,629],{"className":2360},[625],[27,2362,1032],{"className":2363},[48,52],[27,2365],{"className":2366,"style":580},[309],[27,2368,585],{"className":2369},[584],[27,2371],{"className":2372,"style":580},[309],[27,2374,2376,2379],{"className":2375},[39],[27,2377],{"className":2378,"style":1048},[43],[27,2380,91],{"className":2381},[48],[17,2383,747],{"href":746},[11,2385,2386,2389,2390,111],{},[22,2387,2388],{},"Mode shape."," The deflected form of a natural mode, normalised to unit modal mass. Only\nthe shape means anything. ",[17,2391,747],{"href":2392},"\u002Fkb\u002Fanalysis\u002Fmodal#reading-the-output",[11,2394,2395,2452,2453,2457,2458,111],{},[22,2396,2397,2398,111],{},"Modulus of subgrade reaction — ",[27,2399,2401],{"className":2400},[30],[27,2402,2404],{"className":2403,"ariaHidden":35},[34],[27,2405,2407,2411],{"className":2406},[39],[27,2408],{"className":2409,"style":2410},[43],"height:0.8444em;vertical-align:-0.15em;",[27,2412,2414,2417],{"className":2413},[48],[27,2415,362],{"className":2416,"style":361},[48,52],[27,2418,2420],{"className":2419},[58],[27,2421,2423,2444],{"className":2422},[62,63],[27,2424,2426,2441],{"className":2425},[67],[27,2427,2429],{"className":2428,"style":191},[71],[27,2430,2432,2435],{"style":2431},"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;",[27,2433],{"className":2434,"style":80},[79],[27,2436,2438],{"className":2437},[84,85,86,87],[27,2439,1448],{"className":2440},[48,52,87],[27,2442,96],{"className":2443},[95],[27,2445,2447],{"className":2446},[67],[27,2448,2450],{"className":2449,"style":103},[71],[27,2451],{}," Contact pressure per unit settlement,\n",[2454,2455,2456],"code",{},"kN\u002Fm³",". Not a soil property: it depends on the size of the loaded area.\n",[17,2459,663],{"href":2460},"\u002Fkb\u002Ftheory\u002Fwinkler-foundations",[11,2462,2463,2518,2519,111],{},[22,2464,2465,2466,111],{},"Moment-gradient factor — ",[27,2467,2469],{"className":2468},[30],[27,2470,2472],{"className":2471,"ariaHidden":35},[34],[27,2473,2475,2478],{"className":2474},[39],[27,2476],{"className":2477,"style":534},[43],[27,2479,2481,2484],{"className":2480},[48],[27,2482,282],{"className":2483,"style":904},[48,52],[27,2485,2487],{"className":2486},[58],[27,2488,2490,2510],{"className":2489},[62,63],[27,2491,2493,2507],{"className":2492},[67],[27,2494,2496],{"className":2495,"style":345},[71],[27,2497,2498,2501],{"style":1109},[27,2499],{"className":2500,"style":80},[79],[27,2502,2504],{"className":2503},[84,85,86,87],[27,2505,237],{"className":2506},[48,52,87],[27,2508,96],{"className":2509},[95],[27,2511,2513],{"className":2512},[67],[27,2514,2516],{"className":2515,"style":103},[71],[27,2517],{}," AISC's allowance for the shape of the moment diagram\nin lateral-torsional buckling. Derived per combination from the sampled forces.\n",[17,2520,121],{"href":120},[15,2522,2523],{"id":204},"N",[11,2525,2526,2529,2530,111],{},[22,2527,2528],{},"National annex."," A country's published choices for the parameters a Eurocode leaves\nopen — partial factors, ψ values, permitted combination rules.\n",[17,2531,2533],{"href":2532},"\u002Fkb\u002Fdesign-checks\u002Fnational-annexes","National annexes",[11,2535,2536,2539],{},[22,2537,2538],{},"Nationally determined parameter (NDP)."," One of those choices.",[15,2541,2543],{"id":2542},"o","O",[11,2545,2546,2549,2550,111],{},[22,2547,2548],{},"OOFEM."," An open-source finite element code. Elementarium exports an OOFEM input deck\nfor reproducing a solve independently. ",[17,2551,2553],{"href":2552},"\u002Fkb\u002Freports\u002Fexchange","Import and export formats",[15,2555,2556],{"id":11},"P",[11,2558,2559,2562,2563,111],{},[22,2560,2561],{},"P-Δ, P-δ."," The second-order moments from gravity acting through frame sway (Δ) and\nthrough a member's own bow (δ). ",[17,2564,1906],{"href":1905},[11,2566,2567,2570,2571,111],{},[22,2568,2569],{},"Participating mass."," The share of the structure's mass that moves in a given\ndirection in a given mode; the 90% test. ",[17,2572,747],{"href":746},[11,2574,2575,521,2578,1233,2630,1233,2682,2740,2741,111],{},[22,2576,2577],{},"Partial factor.",[27,2579,2581],{"className":2580},[30],[27,2582,2584],{"className":2583,"ariaHidden":35},[34],[27,2585,2587,2590],{"className":2586},[39],[27,2588],{"className":2589,"style":2141},[43],[27,2591,2593,2596],{"className":2592},[48],[27,2594,1346],{"className":2595,"style":1345},[48,52],[27,2597,2599],{"className":2598},[58],[27,2600,2602,2622],{"className":2601},[62,63],[27,2603,2605,2619],{"className":2604},[67],[27,2606,2608],{"className":2607,"style":1427},[71],[27,2609,2610,2613],{"style":1361},[27,2611],{"className":2612,"style":80},[79],[27,2614,2616],{"className":2615},[84,85,86,87],[27,2617,305],{"className":2618},[48,52,87],[27,2620,96],{"className":2621},[95],[27,2623,2625],{"className":2624},[67],[27,2626,2628],{"className":2627,"style":103},[71],[27,2629],{},[27,2631,2633],{"className":2632},[30],[27,2634,2636],{"className":2635,"ariaHidden":35},[34],[27,2637,2639,2642],{"className":2638},[39],[27,2640],{"className":2641,"style":1338},[43],[27,2643,2645,2648],{"className":2644},[48],[27,2646,1346],{"className":2647,"style":1345},[48,52],[27,2649,2651],{"className":2650},[58],[27,2652,2654,2674],{"className":2653},[62,63],[27,2655,2657,2671],{"className":2656},[67],[27,2658,2660],{"className":2659,"style":1427},[71],[27,2661,2662,2665],{"style":1361},[27,2663],{"className":2664,"style":80},[79],[27,2666,2668],{"className":2667},[84,85,86,87],[27,2669,332],{"className":2670},[48,52,87],[27,2672,96],{"className":2673},[95],[27,2675,2677],{"className":2676},[67],[27,2678,2680],{"className":2679,"style":381},[71],[27,2681],{},[27,2683,2685],{"className":2684},[30],[27,2686,2688],{"className":2687,"ariaHidden":35},[34],[27,2689,2691,2694],{"className":2690},[39],[27,2692],{"className":2693,"style":2141},[43],[27,2695,2697,2700],{"className":2696},[48],[27,2698,1346],{"className":2699,"style":1345},[48,52],[27,2701,2703],{"className":2702},[58],[27,2704,2706,2732],{"className":2705},[62,63],[27,2707,2709,2729],{"className":2708},[67],[27,2710,2712],{"className":2711,"style":1427},[71],[27,2713,2714,2717],{"style":1361},[27,2715],{"className":2716,"style":80},[79],[27,2718,2720],{"className":2719},[84,85,86,87],[27,2721,2723,2726],{"className":2722},[48,87],[27,2724,1025],{"className":2725,"style":1024},[48,52,87],[27,2727,91],{"className":2728},[48,87],[27,2730,96],{"className":2731},[95],[27,2733,2735],{"className":2734},[67],[27,2736,2738],{"className":2737,"style":103},[71],[27,2739],{}," and the rest — the safety factors applied to\nactions and resistances. Editable fields in the combination and set by the national\nannex for the check. ",[17,2742,110],{"href":2743},"\u002Fkb\u002Floads\u002Fcombinations#partial-factors",[11,2745,2746,2749,2750,111],{},[22,2747,2748],{},"Patch test."," A test that an element reproduces a constant strain state exactly on an\narbitrary mesh. The shell element passes it in membrane and in bending. ",[17,2751,258],{"href":2752},"\u002Fkb\u002Ftheory\u002Felement-formulations",[11,2754,2755,2758,2759,111],{},[22,2756,2757],{},"Preconditioner."," A transformation that makes an iterative solver converge faster —\nJacobi, incomplete Cholesky or AMG. ",[17,2760,151],{"href":150},[11,2762,2763,2766,2767,111],{},[22,2764,2765],{},"Prescribed displacement."," A support that moves by a set amount — settlement — rather\nthan staying still. ",[17,2768,1315],{"href":2769},"\u002Fkb\u002Floads\u002Fload-cases#load-types",[11,2771,2772,2879,2880,111],{},[22,2773,2774,2775,1233,2827,111],{},"Principal moments — ",[27,2776,2778],{"className":2777},[30],[27,2779,2781],{"className":2780,"ariaHidden":35},[34],[27,2782,2784,2787],{"className":2783},[39],[27,2785],{"className":2786,"style":792},[43],[27,2788,2790,2793],{"className":2789},[48],[27,2791,2248],{"className":2792},[48,52],[27,2794,2796],{"className":2795},[58],[27,2797,2799,2819],{"className":2798},[62,63],[27,2800,2802,2816],{"className":2801},[67],[27,2803,2805],{"className":2804,"style":72},[71],[27,2806,2807,2810],{"style":348},[27,2808],{"className":2809,"style":80},[79],[27,2811,2813],{"className":2812},[84,85,86,87],[27,2814,371],{"className":2815},[48,87],[27,2817,96],{"className":2818},[95],[27,2820,2822],{"className":2821},[67],[27,2823,2825],{"className":2824,"style":103},[71],[27,2826],{},[27,2828,2830],{"className":2829},[30],[27,2831,2833],{"className":2832,"ariaHidden":35},[34],[27,2834,2836,2839],{"className":2835},[39],[27,2837],{"className":2838,"style":792},[43],[27,2840,2842,2845],{"className":2841},[48],[27,2843,2248],{"className":2844},[48,52],[27,2846,2848],{"className":2847},[58],[27,2849,2851,2871],{"className":2850},[62,63],[27,2852,2854,2868],{"className":2853},[67],[27,2855,2857],{"className":2856,"style":72},[71],[27,2858,2859,2862],{"style":348},[27,2860],{"className":2861,"style":80},[79],[27,2863,2865],{"className":2864},[84,85,86,87],[27,2866,1020],{"className":2867},[48,87],[27,2869,96],{"className":2870},[95],[27,2872,2874],{"className":2873},[67],[27,2875,2877],{"className":2876,"style":103},[71],[27,2878],{}," The extreme bending moments in a plate and the\ndirections they act in. ",[17,2881,2883],{"href":2882},"\u002Fkb\u002Freports","Results and reports",[15,2885,332],{"id":2886},"q",[11,2888,2889,288,2892,3026,3027,111],{},[22,2890,2891],{},"Quasi-permanent combination.",[27,2893,2895],{"className":2894},[30],[27,2896,2898,2916],{"className":2897,"ariaHidden":35},[34],[27,2899,2901,2904,2907,2910,2913],{"className":2900},[39],[27,2902],{"className":2903,"style":301},[43],[27,2905,305],{"className":2906},[48,52],[27,2908],{"className":2909,"style":310},[309],[27,2911,315],{"className":2912},[314],[27,2914],{"className":2915,"style":310},[309],[27,2917,2919,2922,2925,2928,2977],{"className":2918},[39],[27,2920],{"className":2921,"style":399},[43],[27,2923,407],{"className":2924,"style":406},[403,404,405],[27,2926],{"className":2927,"style":411},[309],[27,2929,2931,2934],{"className":2930},[48],[27,2932,54],{"className":2933,"style":53},[48,52],[27,2935,2937],{"className":2936},[58],[27,2938,2940,2969],{"className":2939},[62,63],[27,2941,2943,2966],{"className":2942},[67],[27,2944,2946],{"className":2945,"style":430},[71],[27,2947,2948,2951],{"style":75},[27,2949],{"className":2950,"style":80},[79],[27,2952,2954],{"className":2953},[84,85,86,87],[27,2955,2957,2960,2963],{"className":2956},[48,87],[27,2958,1020],{"className":2959},[48,87],[27,2961,367],{"className":2962},[366,87],[27,2964,451],{"className":2965},[48,52,87],[27,2967,96],{"className":2968},[95],[27,2970,2972],{"className":2971},[67],[27,2973,2975],{"className":2974,"style":381},[71],[27,2976],{},[27,2978,2980,2983],{"className":2979},[48],[27,2981,332],{"className":2982},[48,52],[27,2984,2986],{"className":2985},[58],[27,2987,2989,3018],{"className":2988},[62,63],[27,2990,2992,3015],{"className":2991},[67],[27,2993,2995],{"className":2994,"style":345},[71],[27,2996,2997,3000],{"style":348},[27,2998],{"className":2999,"style":80},[79],[27,3001,3003],{"className":3002},[84,85,86,87],[27,3004,3006,3009,3012],{"className":3005},[48,87],[27,3007,362],{"className":3008,"style":361},[48,52,87],[27,3010,367],{"className":3011},[366,87],[27,3013,451],{"className":3014},[48,52,87],[27,3016,96],{"className":3017},[95],[27,3019,3021],{"className":3020},[67],[27,3022,3024],{"className":3023,"style":381},[71],[27,3025],{},", for long-term effects.\n",[17,3028,110],{"href":515},[15,3030,178],{"id":3031},"r",[11,3033,3034,3037,3038,111],{},[22,3035,3036],{},"Reaction."," The force at a restrained degree of freedom, in global axes, acting on the\nstructure. Their sum equals the applied load. ",[17,3039,1894],{"href":3040},"\u002Fkb\u002Ftheory\u002Fsign-conventions#reactions",[11,3042,3043,3046,3047,111],{},[22,3044,3045],{},"Recovery."," Carrying stresses from Gauss points to element corners — Zienkiewicz–Zhu,\nnodal average, area-weighted average, or none.\n",[17,3048,258],{"href":1737},[11,3050,3051,3054,3055,111],{},[22,3052,3053],{},"Reissner–Mindlin."," Plate theory that includes transverse shear deformation, so one\nformulation serves thin and thick plates. ",[17,3056,258],{"href":2286},[11,3058,3059,3062,3063,111],{},[22,3060,3061],{},"Release."," Removal of continuity at one end of one member in one degree of freedom —\nfully, or partially with a stiffness. ",[17,3064,867],{"href":3065},"\u002Fkb\u002Fmodeling\u002Fsupports-and-releases#releases",[11,3067,3068,3071,3072,111],{},[22,3069,3070],{},"Rigid arm."," A constraint tying an offset node's degrees of freedom to a master node.\nNot a stiff member. ",[17,3073,867],{"href":948},[11,3075,3076,3079,3080,111],{},[22,3077,3078],{},"Rigid-body motion."," Movement of the whole structure, or part of it, without strain.\nThe pre-solve model check detects it and names the direction.\n",[17,3081,2267],{"href":2266},[15,3083,3084],{"id":1448},"S",[11,3086,3087,3090,3091,111],{},[22,3088,3089],{},"SAF."," The Structural Analysis Format — an open spreadsheet-based model exchange\nformat read and written by SCIA Engineer, RFEM and others. Elementarium imports and\nexports SAF 2.2. ",[17,3092,2553],{"href":2552},[11,3094,3095,3098,3099,3151,3152,3167,3168,111],{},[22,3096,3097],{},"Sagging."," Bending that puts the bottom of a beam in tension — mid-span under gravity.\nThe sign of ",[27,3100,3102],{"className":3101},[30],[27,3103,3105],{"className":3104,"ariaHidden":35},[34],[27,3106,3108,3111],{"className":3107},[39],[27,3109],{"className":3110,"style":325},[43],[27,3112,3114,3117],{"className":3113},[48],[27,3115,1025],{"className":3116,"style":1024},[48,52],[27,3118,3120],{"className":3119},[58],[27,3121,3123,3143],{"className":3122},[62,63],[27,3124,3126,3140],{"className":3125},[67],[27,3127,3129],{"className":3128,"style":191},[71],[27,3130,3131,3134],{"style":1850},[27,3132],{"className":3133,"style":80},[79],[27,3135,3137],{"className":3136},[84,85,86,87],[27,3138,1860],{"className":3139,"style":53},[48,52,87],[27,3141,96],{"className":3142},[95],[27,3144,3146],{"className":3145},[67],[27,3147,3149],{"className":3148,"style":381},[71],[27,3150],{}," follows the member's local ",[27,3153,3155],{"className":3154},[30],[27,3156,3158],{"className":3157,"ariaHidden":35},[34],[27,3159,3161,3164],{"className":3160},[39],[27,3162],{"className":3163,"style":1210},[43],[27,3165,1889],{"className":3166,"style":1888},[48,52]," axis, so read the diagram side, not the\nsign. ",[17,3169,1894],{"href":1893},[11,3171,3172,521,3175,3283,3284,111],{},[22,3173,3174],{},"Second-order analysis.",[27,3176,3178],{"className":3177},[30],[27,3179,3181,3203,3274],{"className":3180,"ariaHidden":35},[34],[27,3182,3184,3187,3191,3194,3197,3200],{"className":3183},[39],[27,3185],{"className":3186,"style":170},[43],[27,3188,3190],{"className":3189},[599],"[",[27,3192,905],{"className":3193,"style":904},[48,52],[27,3195],{"className":3196,"style":310},[309],[27,3198,315],{"className":3199},[314],[27,3201],{"className":3202,"style":310},[309],[27,3204,3206,3209,3249,3252,3255,3259,3262,3265,3268,3271],{"className":3205},[39],[27,3207],{"className":3208,"style":399},[43],[27,3210,3212,3215],{"className":3211},[48],[27,3213,905],{"className":3214,"style":904},[48,52],[27,3216,3218],{"className":3217},[58],[27,3219,3221,3241],{"className":3220},[62,63],[27,3222,3224,3238],{"className":3223},[67],[27,3225,3227],{"className":3226,"style":191},[71],[27,3228,3229,3232],{"style":1109},[27,3230],{"className":3231,"style":80},[79],[27,3233,3235],{"className":3234},[84,85,86,87],[27,3236,1119],{"className":3237,"style":53},[48,52,87],[27,3239,96],{"className":3240},[95],[27,3242,3244],{"className":3243},[67],[27,3245,3247],{"className":3246,"style":381},[71],[27,3248],{},[27,3250,600],{"className":3251},[599],[27,3253,1452],{"className":3254},[48,52],[27,3256,3258],{"className":3257},[625],")]",[27,3260],{"className":3261,"style":411},[309],[27,3263,1452],{"className":3264},[48,52],[27,3266],{"className":3267,"style":580},[309],[27,3269,585],{"className":3270},[584],[27,3272],{"className":3273,"style":580},[309],[27,3275,3277,3280],{"className":3276},[39],[27,3278],{"className":3279,"style":44},[43],[27,3281,1318],{"className":3282,"style":1384},[48,52]," by iteration, on the deformed geometry.\nResults do not superpose. ",[17,3285,1906],{"href":1905},[11,3287,3288,3291,3292,111],{},[22,3289,3290],{},"Setup (analysis)."," A named analysis configuration — type, solver, mesh minimums, mass\nsources — stored with the project and keeping its own results.\n",[17,3293,3295],{"href":3294},"\u002Fkb\u002Fanalysis","Analysis types",[11,3297,3298,3301,3302,111],{},[22,3299,3300],{},"Shell."," A surface element carrying both bending and membrane action. In Elementarium,\nevery surface. ",[17,3303,2277],{"href":2276},[11,3305,3306,3309,3310,3325,3326,111],{},[22,3307,3308],{},"Singular stiffness matrix."," A ",[27,3311,3313],{"className":3312},[30],[27,3314,3316],{"className":3315,"ariaHidden":35},[34],[27,3317,3319,3322],{"className":3318},[39],[27,3320],{"className":3321,"style":900},[43],[27,3323,905],{"className":3324,"style":904},[48,52]," with no unique solution — the structure contains a\nmechanism. ",[17,3327,2267],{"href":2266},[11,3329,3330,3333,3334,111],{},[22,3331,3332],{},"Singularity (stress)."," A point where the elastic solution is infinite — a point\nsupport in a plate, a re-entrant corner. Refinement never converges there.\n",[17,3335,774],{"href":3336},"\u002Fkb\u002Fmeshing\u002Felement-size#singularities-where-refinement-never-helps",[11,3338,3339,3342,3343,111],{},[22,3340,3341],{},"Skew support."," A support whose restrained directions are expressed in axes you define\nrather than the global ones. ",[17,3344,867],{"href":3345},"\u002Fkb\u002Fmodeling\u002Fsupports-and-releases",[11,3347,3348,3351,3352,111],{},[22,3349,3350],{},"Sparse matrix."," One that is mostly zeros, as a stiffness matrix is. The solvers exploit\nit. ",[17,3353,151],{"href":150},[11,3355,3356,3359,3360,111],{},[22,3357,3358],{},"Spring."," A support with finite stiffness in a direction, in place of free or rigid.\nLinear in both directions — it resists tension. ",[17,3361,867],{"href":3362},"\u002Fkb\u002Fmodeling\u002Fsupports-and-releases#springs",[11,3364,3365,3368,3369,111],{},[22,3366,3367],{},"St. Venant torsion."," Uniform torsion, without warping restraint. What the beam element\ncarries. ",[17,3370,3372],{"href":3371},"\u002Fkb\u002Fmodeling\u002Fsections-and-materials#torsion","Sections and materials",[11,3374,3375,3378,3379,111],{},[22,3376,3377],{},"Station."," One of the positions along a member at which internal forces are sampled\nand checks evaluated — eleven per member. ",[17,3380,121],{"href":120},[11,3382,3383,264,3386,111],{},[22,3384,3385],{},"Sturm sequence.",[266,3387,3388],{},"completeness check",[11,3390,3391,3394,3395,111],{},[22,3392,3393],{},"Superposition."," The property of a linear system that the response to a combination is\nthe factored sum of the responses to its cases. Lost in second-order analysis.\n",[17,3396,2088],{"href":3397},"\u002Fkb\u002Fanalysis\u002Flinear-static#superposition",[15,3399,716],{"id":3400},"t",[11,3402,3403,3406,3407,111],{},[22,3404,3405],{},"Tributary length."," The length of a line support attributed to each analysis node\nalong it, by which its stiffness per unit length is lumped.\n",[17,3408,2042],{"href":2041},[15,3410,3411],{"id":1452},"U",[11,3413,3414,3417,3418,111],{},[22,3415,3416],{},"ULS \u002F SLS."," Ultimate and serviceability limit states — strength and stability against\ndeflection, vibration and cracking. Different combinations for each.\n",[17,3419,110],{"href":109},[11,3421,3422,3425,3426,111],{},[22,3423,3424],{},"Utilisation ratio."," Design effect over design resistance for a clause; above 1.0 the\nmember fails it. Every one names its combination, position, clause and substituted\nformula. ",[17,3427,1807],{"href":1806},[15,3429,3430],{"id":1295},"W",[11,3432,3433,3436,3437,111],{},[22,3434,3435],{},"Warping (element)."," Out-of-plane twist of a quadrilateral's four nodes, on curved\nsurfaces. The shell element corrects for it, so a rigid motion strains nothing, but the\nfacet stays flat: beyond about 10° it is too coarse to quote.\n",[17,3438,234],{"href":3439},"\u002Fkb\u002Fmeshing\u002Fquality-checks#warping",[11,3441,3442,3445,3446,111],{},[22,3443,3444],{},"Warping (torsion)."," The out-of-plane distortion of an open section under torsion, and\nthe restraint of it. Not modelled by the beam element.\n",[17,3447,1253],{"href":3448},"\u002Fkb\u002Fdesign-checks\u002Fsteel#not-covered",[11,3450,3451,3454,3455,111],{},[22,3452,3453],{},"WebAssembly."," The binary format the C++ solver is compiled to so that it runs at\nnative speed in a browser. ",[17,3456,853],{"href":852},[11,3458,3459,3462,3463,1230,3536,111],{},[22,3460,3461],{},"Winkler bed."," Soil idealised as independent linear springs, ",[27,3464,3466],{"className":3465},[30],[27,3467,3469,3487],{"className":3468,"ariaHidden":35},[34],[27,3470,3472,3475,3478,3481,3484],{"className":3471},[39],[27,3473],{"className":3474,"style":2141},[43],[27,3476,11],{"className":3477},[48,52],[27,3479],{"className":3480,"style":580},[309],[27,3482,585],{"className":3483},[584],[27,3485],{"className":3486,"style":580},[309],[27,3488,3490,3493,3533],{"className":3489},[39],[27,3491],{"className":3492,"style":2410},[43],[27,3494,3496,3499],{"className":3495},[48],[27,3497,362],{"className":3498,"style":361},[48,52],[27,3500,3502],{"className":3501},[58],[27,3503,3505,3525],{"className":3504},[62,63],[27,3506,3508,3522],{"className":3507},[67],[27,3509,3511],{"className":3510,"style":191},[71],[27,3512,3513,3516],{"style":2431},[27,3514],{"className":3515,"style":80},[79],[27,3517,3519],{"className":3518},[84,85,86,87],[27,3520,1448],{"className":3521},[48,52,87],[27,3523,96],{"className":3524},[95],[27,3526,3528],{"className":3527},[67],[27,3529,3531],{"className":3530,"style":103},[71],[27,3532],{},[27,3534,1295],{"className":3535,"style":1294},[48,52],[17,3537,663],{"href":2460},[15,3539,3540],{"id":1889},"Z",[11,3542,3543,3546,3547,111],{},[22,3544,3545],{},"Zienkiewicz–Zhu."," An L² projection used to recover nodal stresses from element values,\nbounded by the element values, so it cannot invent a peak the elements do not carry.\n",[17,3548,258],{"href":1737},[11,3550,3551,521,3554,1233,3606,1233,3658,3710,3711,111],{},[22,3552,3553],{},"ψ factors.",[27,3555,3557],{"className":3556},[30],[27,3558,3560],{"className":3559,"ariaHidden":35},[34],[27,3561,3563,3566],{"className":3562},[39],[27,3564],{"className":3565,"style":44},[43],[27,3567,3569,3572],{"className":3568},[48],[27,3570,54],{"className":3571,"style":53},[48,52],[27,3573,3575],{"className":3574},[58],[27,3576,3578,3598],{"className":3577},[62,63],[27,3579,3581,3595],{"className":3580},[67],[27,3582,3584],{"className":3583,"style":72},[71],[27,3585,3586,3589],{"style":75},[27,3587],{"className":3588,"style":80},[79],[27,3590,3592],{"className":3591},[84,85,86,87],[27,3593,91],{"className":3594},[48,87],[27,3596,96],{"className":3597},[95],[27,3599,3601],{"className":3600},[67],[27,3602,3604],{"className":3603,"style":103},[71],[27,3605],{},[27,3607,3609],{"className":3608},[30],[27,3610,3612],{"className":3611,"ariaHidden":35},[34],[27,3613,3615,3618],{"className":3614},[39],[27,3616],{"className":3617,"style":44},[43],[27,3619,3621,3624],{"className":3620},[48],[27,3622,54],{"className":3623,"style":53},[48,52],[27,3625,3627],{"className":3626},[58],[27,3628,3630,3650],{"className":3629},[62,63],[27,3631,3633,3647],{"className":3632},[67],[27,3634,3636],{"className":3635,"style":72},[71],[27,3637,3638,3641],{"style":75},[27,3639],{"className":3640,"style":80},[79],[27,3642,3644],{"className":3643},[84,85,86,87],[27,3645,371],{"className":3646},[48,87],[27,3648,96],{"className":3649},[95],[27,3651,3653],{"className":3652},[67],[27,3654,3656],{"className":3655,"style":103},[71],[27,3657],{},[27,3659,3661],{"className":3660},[30],[27,3662,3664],{"className":3663,"ariaHidden":35},[34],[27,3665,3667,3670],{"className":3666},[39],[27,3668],{"className":3669,"style":44},[43],[27,3671,3673,3676],{"className":3672},[48],[27,3674,54],{"className":3675,"style":53},[48,52],[27,3677,3679],{"className":3678},[58],[27,3680,3682,3702],{"className":3681},[62,63],[27,3683,3685,3699],{"className":3684},[67],[27,3686,3688],{"className":3687,"style":72},[71],[27,3689,3690,3693],{"style":75},[27,3691],{"className":3692,"style":80},[79],[27,3694,3696],{"className":3695},[84,85,86,87],[27,3697,1020],{"className":3698},[48,87],[27,3700,96],{"className":3701},[95],[27,3703,3705],{"className":3704},[67],[27,3706,3708],{"className":3707,"style":103},[71],[27,3709],{}," — the reductions applied to accompanying variable\nactions in EN 1990 combinations, by action category.\n",[17,3712,110],{"href":2743},{"title":3714,"searchDepth":3715,"depth":3715,"links":3716},"",2,[3717,3718,3719,3720,3721,3722,3723,3724,3725,3726,3727,3728,3729,3730,3731,3732,3733,3734,3735,3736,3737],{"id":17,"depth":3715,"text":18},{"id":237,"depth":3715,"text":238},{"id":281,"depth":3715,"text":282},{"id":856,"depth":3715,"text":857},{"id":565,"depth":3715,"text":609},{"id":1318,"depth":3715,"text":1319},{"id":1119,"depth":3715,"text":305},{"id":1810,"depth":3715,"text":1811},{"id":451,"depth":3715,"text":614},{"id":1917,"depth":3715,"text":541},{"id":2248,"depth":3715,"text":1025},{"id":204,"depth":3715,"text":2523},{"id":2542,"depth":3715,"text":2543},{"id":11,"depth":3715,"text":2556},{"id":2886,"depth":3715,"text":332},{"id":3031,"depth":3715,"text":178},{"id":1448,"depth":3715,"text":3084},{"id":3400,"depth":3715,"text":716},{"id":1452,"depth":3715,"text":3411},{"id":1295,"depth":3715,"text":3430},{"id":1889,"depth":3715,"text":3540},"Finite element and structural terms as Elementarium uses them, from degrees of freedom to MITC4 and utilisation, each linked to its page.","md",false,{},true,null,5,"\u002Fkb\u002Ftheory\u002Fglossary",{"title":6,"description":3738},{"loc":3745},"kb\u002Ftheory\u002Fglossary","oG3MgrRBUS2i1t6QN8FcA1Kd4r9FSLqbFRgFLr-CN_E",{"sections":3751,"extras":4006,"flat":4019},[3752,3785,3820,3834,3861,3881,3898,3926,3953,3970,3984],{"path":3753,"slug":3754,"title":3755,"description":3756,"icon":3757,"articles":3758},"\u002Fkb\u002Fgetting-started","getting-started","Getting started","From an empty tab to a solved, checked structure — the three guides that get you productive in Elementarium.","lucide:rocket",[3759,3763,3767,3771,3773,3777,3781],{"path":3760,"title":3761,"description":3762,"translated":3742},"\u002Fkb\u002Fgetting-started\u002Fkeyboard-shortcuts","Keyboard shortcuts","Every key binding in the workspace, the pointer gestures in the viewports, what the number fields accept, and what the command palette understands.",{"path":3764,"title":3765,"description":3766,"translated":3742},"\u002Fkb\u002Fgetting-started\u002Fquickstart","Quickstart","Build a portal frame, load it, solve it and read the bending moment diagram — about ten minutes from an empty tab.",{"path":3768,"title":3769,"description":3770,"translated":3742},"\u002Fkb\u002Fgetting-started\u002Fscope-and-limits","Scope and limits","What Elementarium models, solves and checks today, and what it does not — on one page, before you commit a job to it.",{"path":852,"title":853,"description":3772,"translated":3742},"Which browsers and devices run Elementarium, how threading affects solve speed, and where the practical ceiling on model size comes from.",{"path":3774,"title":3775,"description":3776,"translated":3742},"\u002Fkb\u002Fgetting-started\u002Finterface-tour","Tour of the workspace","The ribbon, properties panel, dockable viewports, table dock, command palette and status bar — what each part of the editor is for.",{"path":3778,"title":3779,"description":3780,"translated":3742},"\u002Fkb\u002Fgetting-started\u002Funits","Units","How units work in Elementarium — SI inside, your unit system on screen — and the handful of conversions that cause most wrong answers in structural models.",{"path":3782,"title":3783,"description":3784,"translated":3742},"\u002Fkb\u002Fgetting-started\u002Ffirst-analysis","Your first analysis","Load cases, combinations and a linear static solve — then how to decide whether the answer is trustworthy.",{"path":3786,"slug":3787,"title":3788,"description":3789,"icon":3790,"articles":3791},"\u002Fkb\u002Fmodeling","modeling","Modeling","Bars, beams, 3D frames, slabs and walls. Geometry, sections, supports and releases that behave like the real structure.","lucide:frame",[3792,3794,3797,3799,3803,3807,3809,3813,3816],{"path":247,"title":248,"description":3793,"translated":3742},"When a member should be a bar and when a beam, how to model trusses and bracing, and what to do about members that only work in tension.",{"path":936,"title":3795,"description":3796,"translated":3742},"Drawings & snapping","Importing a DXF as a reference underlay, choosing its units and plane, and snapping model geometry onto it accurately.",{"path":2041,"title":2042,"description":3798,"translated":3742},"Grade beams, strip footings and walls on ground as line supports on springs — choosing a subgrade modulus, and where the model stops being true.",{"path":3800,"title":3801,"description":3802,"translated":3742},"\u002Fkb\u002Fmodeling\u002Fplane-frames-in-3d","Plane frames in a 3D solver","When to use the 2D Frame and 2D Truss model types, why a flat structure in a 3D model is a mechanism, and how to restrain it.",{"path":3804,"title":3805,"description":3806,"translated":3742},"\u002Fkb\u002Fmodeling\u002Fsections-and-materials","Sections & materials","What a section and a material contribute to the stiffness matrix and the design checks, and the values worth checking twice.",{"path":2276,"title":2277,"description":3808,"translated":3742},"Modelling surfaces in Elementarium — outlines, openings and thickness, how a beam or a wall attaches to a slab, local axes, and what a surface result means.",{"path":3810,"title":3811,"description":3812,"translated":3742},"\u002Fkb\u002Fmodeling\u002Fstructure-generators","Structure generators","Thirty-five parametric structures — trusses, frames, arches, towers, domes and shells — generated from a few dimensions, with supports and loads.",{"path":3345,"title":3814,"description":3815,"translated":3742},"Supports & releases","Pins, fixities, springs and end releases — what each one does to the stiffness matrix, and when each is right.",{"path":3817,"title":3818,"description":3819,"translated":3742},"\u002Fkb\u002Fmodeling\u002Ffirst-model","Your first model","The modeling loop end to end — geometry, sections, supports and releases — on a structure small enough to check by hand.",{"path":3821,"slug":3822,"title":131,"description":3823,"icon":3824,"articles":3825},"\u002Fkb\u002Fmeshing","meshing","Mesh density, local refinement and the quality checks that tell you when a mesh is fine enough to trust.","lucide:grid-3x3",[3826,3828,3832],{"path":881,"title":774,"description":3827,"translated":3742},"Starting mesh densities for slabs, walls and rafts, and the convergence test that decides whether a mesh is fine enough.",{"path":3829,"title":3830,"description":3831,"translated":3742},"\u002Fkb\u002Fmeshing\u002Frefinement","Local refinement","Where to spend elements, where not to bother, and how to refine without wrecking element shape.",{"path":233,"title":234,"description":3833,"translated":3742},"Aspect ratio, skew and warping — what degrades a result, what the mesher reports, and how to tell whether the elements you are worried about matter.",{"path":3835,"slug":3836,"title":3837,"description":3838,"icon":3839,"articles":3840},"\u002Fkb\u002Floads","loads","Loads & combinations","Build load cases, generate code combinations automatically and find out which one actually governs.","lucide:arrow-down-to-line",[3841,3843,3845,3847,3849,3853,3857],{"path":223,"title":224,"description":3842,"translated":3742},"LRFD and ASD combinations to ASCE 7-22 — how the generator maps your load groups onto D, L, Lr, S, W and E, and pairing them with the AISC check.",{"path":109,"title":110,"description":3844,"translated":3742},"Generating EN 1990 and ASCE 7 combinations, understanding the equations behind them, and reading the generated set critically.",{"path":1271,"title":1272,"description":3846,"translated":3742},"Extracting the governing value across dozens of combinations without reading every one — and the traps in doing so.",{"path":2097,"title":1315,"description":3848,"translated":3742},"Actions, self-weight, imposed loads and load arrangements — how to build cases that stay separable.",{"path":3850,"title":3851,"description":3852,"translated":3742},"\u002Fkb\u002Floads\u002Fload-panels","Load panels","Areas that hand a floor, roof or wall pressure to the members around them as line loads, one way or two way, without meshing a slab.",{"path":3854,"title":3855,"description":3856,"translated":3742},"\u002Fkb\u002Floads\u002Ftemperature-loads","Temperature loads","Uniform temperature change and through-depth gradients — what each does to a free and a restrained structure, and the coefficients to use.",{"path":3858,"title":3859,"description":3860,"translated":3742},"\u002Fkb\u002Floads\u002Fwind-and-snow","Wind and snow","Wind to EN 1991-1-4 and snow to EN 1991-1-3, generated on a building envelope — site inputs, recognised roof shapes, the cases produced, and the limits.",{"path":3294,"slug":3862,"title":3295,"description":3863,"icon":3864,"articles":3865},"analysis","Linear static, modal, linear buckling and second-order — what each analysis assumes, what it returns and how to read the result.","lucide:activity",[3866,3868,3870,3873,3875,3877],{"path":150,"title":151,"description":3867,"translated":3742},"Conjugate gradients with Jacobi, incomplete Cholesky or multigrid, or a direct factorisation — what each does, how to watch it, and when the choice matters.",{"path":277,"title":278,"description":3869,"translated":3742},"Critical load factors and buckling shapes — what α_cr means, why it is an upper bound, and how to use it for second-order effects.",{"path":2087,"title":3871,"description":3872,"translated":3742},"Linear static analysis","The workhorse analysis — what K u = f actually assumes, what it returns, and where linearity stops being a reasonable model.",{"path":746,"title":747,"description":3874,"translated":3742},"Natural frequencies and mode shapes — mass modelling, participation factors and what the numbers are good for.",{"path":1905,"title":1906,"description":3876,"translated":3742},"P-Δ and P-δ solved by iteration, geometric imperfections to EN 1993-1-1 §5.3, and why a second-order result cannot be superposed.",{"path":3878,"title":3879,"description":3880,"translated":3742},"\u002Fkb\u002Fanalysis\u002Fverification","Verifying the solver","Closed-form cases you can build in ten minutes to test the solver — beams, frames, columns, plates, frequencies — with the expected error of each.",{"path":1806,"slug":3882,"title":1807,"description":3883,"icon":3884,"articles":3885},"design-checks","Utilisation ratios, governing cases and the clause behind every number a check reports.","lucide:clipboard-check",[3886,3888,3890,3894,3896],{"path":2532,"title":2533,"description":3887,"translated":3742},"Where nationally determined parameters change the answer, how to select the right annex, and what to state in the report.",{"path":728,"title":729,"description":3889,"translated":3742},"How EN 1993-1-1 Table 5.2 classifies a steel section, why the class depends on the combination, and what the check does with shapes it cannot classify.",{"path":3891,"title":3892,"description":3893,"translated":3742},"\u002Fkb\u002Fdesign-checks\u002Fserviceability","Serviceability checks","Deflection, drift and floor frequency checked member by member at SLS, to the national annexes, EN 1990:2023, IBC, AISC or EN 1995-1-1.",{"path":120,"title":121,"description":3895,"translated":3742},"Member strength to Chapters D to H, LRFD or ASD — compression buckling, lateral-torsional buckling and every C_b option written down.",{"path":1252,"title":1253,"description":3897,"translated":3742},"Member resistance to §6.2 and §6.3 — what is checked at every station, where buckling lengths come from, and the clauses left to you.",{"path":2882,"slug":3899,"title":3900,"description":3901,"icon":3902,"articles":3903},"reports","Results & reports","Diagrams, contours and tables in the viewport, and the calculation package you hand to a reviewer.","lucide:file-chart-column",[3904,3908,3912,3915,3918,3922],{"path":3905,"title":3906,"description":3907,"translated":3742},"\u002Fkb\u002Freports\u002Fexporting","Exporting a report","Assembling a calculation package a reviewer can follow — inputs, model, results and checks, in the order a calc package should be.",{"path":3909,"title":3910,"description":3911,"translated":3742},"\u002Fkb\u002Freports\u002Fifc","IFC structural models","The IFC structural analysis view in and out — what IFC2X3, IFC4 and IFC4X3 files bring, what an export carries, and what IFC cannot say.",{"path":2552,"title":3913,"description":3914,"translated":3742},"Import & export formats","IFC structural models and SAF workbooks in and out, DXF as a reference drawing, result tables as CSV or xlsx, and an OOFEM input deck.",{"path":3916,"title":141,"description":3917,"translated":3742},"\u002Fkb\u002Freports\u002Freading-diagrams","Bending, shear and axial diagrams, contour plots and deformed shapes — the conventions behind what you are looking at.",{"path":3919,"title":3920,"description":3921,"translated":3742},"\u002Fkb\u002Freports\u002Fresult-tables","Result tables","Filtering, sorting and extracting numbers — getting the value you need out of a solved model without scrolling.",{"path":3923,"title":3924,"description":3925,"translated":3742},"\u002Fkb\u002Freports\u002Freviewing","Reviewing a calculation","For the checking engineer — how to interrogate a model you did not build, what the report guarantees, and the questions to ask first.",{"path":3927,"slug":3928,"title":3929,"description":3930,"icon":3931,"articles":3932},"\u002Fkb\u002Fcollaboration","collaboration","Collaboration & sync","Shared models, real-time editing, and offline edits that merge cleanly when you reconnect.","lucide:users-round",[3933,3937,3941,3945,3949],{"path":3934,"title":3935,"description":3936,"translated":3742},"\u002Fkb\u002Fcollaboration\u002Fcomments","Comments","Threads pinned to nodes, members, plates or points, @mentions, blocking comments that hold up a report, and the notifications they send.",{"path":3938,"title":3939,"description":3940,"translated":3742},"\u002Fkb\u002Fcollaboration\u002Fsharing-projects","Sharing a project","Inviting people to a model, what each role can do, and how to coordinate two engineers in the same structure.",{"path":3942,"title":3943,"description":3944,"translated":3742},"\u002Fkb\u002Fcollaboration\u002Fversion-history","Version history","Automatic checkpoints and named versions — how long they are kept, previewing an earlier state, and restoring it in place or as a new project.",{"path":3946,"title":3947,"description":3948,"translated":3742},"\u002Fkb\u002Fcollaboration\u002Fdevices","Working across devices","One account on every device — how a project follows you from desk to laptop, tablet or phone, and what changes on a small screen.",{"path":3950,"title":3951,"description":3952,"translated":3742},"\u002Fkb\u002Fcollaboration\u002Fworking-offline","Working offline","What keeps working with no connection, what does not, and how offline edits merge when you come back.",{"path":3954,"slug":3955,"title":3956,"description":3957,"icon":3958,"articles":3959},"\u002Fkb\u002Ftheory","theory","Theory notes","The mechanics inside the solver — element formulations, sign conventions, numerical assumptions and their limits.","lucide:sigma",[3960,3962,3963,3966,3968],{"path":2752,"title":258,"description":3961,"translated":3742},"Degrees of freedom, interpolation and limits for every element type in the solver — what each one can represent and what it cannot.",{"path":3745,"title":6,"description":3738,"translated":3742},{"path":3964,"title":1894,"description":3965,"translated":3742},"\u002Fkb\u002Ftheory\u002Fsign-conventions","Axes, positive directions and how to read a diagram without guessing — the page that prevents most result confusion.",{"path":917,"title":918,"description":3967,"translated":3742},"How a finite element solver turns a model into K u = f and back — stiffness, transformation, assembly, constraints, solution and recovery.",{"path":2460,"title":663,"description":3969,"translated":3742},"The bedding model behind elastic foundations — what it assumes, how to choose a modulus, and precisely where the idealisation stops being true.",{"path":3971,"slug":3972,"title":3973,"description":3974,"icon":3975,"articles":3976},"\u002Fkb\u002Ftroubleshooting","troubleshooting","Troubleshooting","Solver errors, unstable models and results that look wrong — with the usual causes listed first.","lucide:life-buoy",[3977,3981],{"path":3978,"title":3979,"description":3980,"translated":3742},"\u002Fkb\u002Ftroubleshooting\u002Fsolver-errors","Solver errors","What each class of solver message means, what usually causes it, and what to do next.",{"path":2266,"title":3982,"description":3983,"translated":3742},"Why the solver reports a singular stiffness matrix","The most common solver failure — what singularity means mechanically, the six causes in order of frequency, and how to find yours in minutes.",{"path":3985,"slug":3986,"title":3987,"description":3988,"icon":3989,"articles":3990},"\u002Fkb\u002Faccount","account","Account & billing","Plans, limits, invoices, and what happens to your projects when a subscription ends.","lucide:credit-card",[3991,3995,3999,4002],{"path":3992,"title":3993,"description":3994,"translated":3742},"\u002Fkb\u002Faccount\u002Finvoices","Invoices & VAT","Billing details, receipts, VAT handling and how to get an invoice your accounts department will accept.",{"path":3996,"title":3997,"description":3998,"translated":3742},"\u002Fkb\u002Faccount\u002Fcancelling","Pausing or cancelling","How to stop paying without losing your work — what happens to projects, reports and history when a subscription ends.",{"path":871,"title":4000,"description":4001,"translated":3742},"Plans & limits","What the free plan includes, what Pro adds, and how the caps are actually measured.",{"path":4003,"title":4004,"description":4005,"translated":3742},"\u002Fkb\u002Faccount\u002Fstudent","Student accounts","A larger free tier for students and researchers — verify an academic email address, what it unlocks, and why it is re-confirmed every year.",[4007,4011,4015],{"path":4008,"title":4009,"description":4010,"translated":3742},"\u002Fkb\u002Ffaq","Frequently asked questions","The questions engineers ask before they trust a new finite element package — answered directly.",{"path":4012,"title":4013,"description":4014,"translated":3742},"\u002Fkb\u002Frelease-notes","Release notes","What shipped in the tab, and what it changes in your models.",{"path":4016,"title":4017,"description":4018,"translated":3742},"\u002Fkb\u002Fall","All articles","Every article in the Elementarium knowledge base, grouped by section.",[4020,4021,4022,4023,4024,4025,4026,4027,4028,4029,4030,4031,4032,4033,4034,4035,4036,4037,4038,4039,4040,4041,4042,4043,4044,4045,4046,4047,4048,4049,4050,4051,4052,4053,4054,4055,4056,4057,4058,4059,4060,4061,4062,4063,4064,4065,4066,4067,4068,4069,4070,4071,4072,4073,4074,4075,4076,4077,4078,4079,4080,4081,4082,4083,4084,4085,4086,4087,4088,4089],{"path":3753,"title":3755,"description":3756,"translated":3742},{"path":3760,"title":3761,"description":3762,"translated":3742},{"path":3764,"title":3765,"description":3766,"translated":3742},{"path":3768,"title":3769,"description":3770,"translated":3742},{"path":852,"title":853,"description":3772,"translated":3742},{"path":3774,"title":3775,"description":3776,"translated":3742},{"path":3778,"title":3779,"description":3780,"translated":3742},{"path":3782,"title":3783,"description":3784,"translated":3742},{"path":3786,"title":3788,"description":3789,"translated":3742},{"path":247,"title":248,"description":3793,"translated":3742},{"path":936,"title":3795,"description":3796,"translated":3742},{"path":2041,"title":2042,"description":3798,"translated":3742},{"path":3800,"title":3801,"description":3802,"translated":3742},{"path":3804,"title":3805,"description":3806,"translated":3742},{"path":2276,"title":2277,"description":3808,"translated":3742},{"path":3810,"title":3811,"description":3812,"translated":3742},{"path":3345,"title":3814,"description":3815,"translated":3742},{"path":3817,"title":3818,"description":3819,"translated":3742},{"path":3821,"title":131,"description":3823,"translated":3742},{"path":881,"title":774,"description":3827,"translated":3742},{"path":3829,"title":3830,"description":3831,"translated":3742},{"path":233,"title":234,"description":3833,"translated":3742},{"path":3835,"title":3837,"description":3838,"translated":3742},{"path":223,"title":224,"description":3842,"translated":3742},{"path":109,"title":110,"description":3844,"translated":3742},{"path":1271,"title":1272,"description":3846,"translated":3742},{"path":2097,"title":1315,"description":3848,"translated":3742},{"path":3850,"title":3851,"description":3852,"translated":3742},{"path":3854,"title":3855,"description":3856,"translated":3742},{"path":3858,"title":3859,"description":3860,"translated":3742},{"path":3294,"title":3295,"description":3863,"translated":3742},{"path":150,"title":151,"description":3867,"translated":3742},{"path":277,"title":278,"description":3869,"translated":3742},{"path":2087,"title":3871,"description":3872,"translated":3742},{"path":746,"title":747,"description":3874,"translated":3742},{"path":1905,"title":1906,"description":3876,"translated":3742},{"path":3878,"title":3879,"description":3880,"translated":3742},{"path":1806,"title":1807,"description":3883,"translated":3742},{"path":2532,"title":2533,"description":3887,"translated":3742},{"path":728,"title":729,"description":3889,"translated":3742},{"path":3891,"title":3892,"description":3893,"translated":3742},{"path":120,"title":121,"description":3895,"translated":3742},{"path":1252,"title":1253,"description":3897,"translated":3742},{"path":2882,"title":3900,"description":3901,"translated":3742},{"path":3905,"title":3906,"description":3907,"translated":3742},{"path":3909,"title":3910,"description":3911,"translated":3742},{"path":2552,"title":3913,"description":3914,"translated":3742},{"path":3916,"title":141,"description":3917,"translated":3742},{"path":3919,"title":3920,"description":3921,"translated":3742},{"path":3923,"title":3924,"description":3925,"translated":3742},{"path":3927,"title":3929,"description":3930,"translated":3742},{"path":3934,"title":3935,"description":3936,"translated":3742},{"path":3938,"title":3939,"description":3940,"translated":3742},{"path":3942,"title":3943,"description":3944,"translated":3742},{"path":3946,"title":3947,"description":3948,"translated":3742},{"path":3950,"title":3951,"description":3952,"translated":3742},{"path":3954,"title":3956,"description":3957,"translated":3742},{"path":2752,"title":258,"description":3961,"translated":3742},{"path":3745,"title":6,"description":3738,"translated":3742},{"path":3964,"title":1894,"description":3965,"translated":3742},{"path":917,"title":918,"description":3967,"translated":3742},{"path":2460,"title":663,"description":3969,"translated":3742},{"path":3971,"title":3973,"description":3974,"translated":3742},{"path":3978,"title":3979,"description":3980,"translated":3742},{"path":2266,"title":3982,"description":3983,"translated":3742},{"path":3985,"title":3987,"description":3988,"translated":3742},{"path":3992,"title":3993,"description":3994,"translated":3742},{"path":3996,"title":3997,"description":3998,"translated":3742},{"path":871,"title":4000,"description":4001,"translated":3742},{"path":4003,"title":4004,"description":4005,"translated":3742},1792160743275]