[{"data":1,"prerenderedAt":1245},["ShallowReactive",2],{"kb-en-\u002Fkb\u002Fmodeling\u002Fplane-frames-in-3d":3,"kb-nav-en":855},{"page":4,"fallback":845},{"id":5,"title":6,"body":7,"description":843,"extension":844,"faq":845,"meta":846,"navigation":847,"ogImage":848,"order":849,"path":850,"raw":845,"robots":848,"schemaOrg":848,"seo":851,"sitemap":852,"stem":853,"__hash__":854},"content_en\u002Fkb\u002Fmodeling\u002Fplane-frames-in-3d.md","Plane frames in a 3D solver",{"type":8,"value":9,"toc":828},"minimark",[10,23,30,35,44,51,54,58,63,260,316,320,640,648,652,665,668,672,732,736,739,751,754,758,818,822,825],[11,12,13,14,18,19,22],"p",{},"A project's model type decides how many dimensions it has. ",[15,16,17],"strong",{},"2D Frame"," and ",[15,20,21],{},"2D Truss","\nkeep everything in the XZ plane, with three or two degrees of freedom per node, and a\nstructure in them cannot move out of plane. For a portal frame or a roof truss on its own,\nthat is the simplest correct model.",[11,24,25,26,29],{},"In a ",[15,27,28],{},"3D"," project every node has six degrees of freedom, and a portal frame drawn in the\nXZ plane is a 3D structure that happens to be flat. With nothing holding it out of plane it\nis a mechanism. The rest of this page is about that case: a plane structure inside a model\nthat needs the third dimension.",[31,32,34],"h2",{"id":33},"the-symptom","The symptom",[11,36,37,38,43],{},"A frame that is stable in the plane you drew it in stops with a\n",[39,40,42],"a",{"href":41},"\u002Fkb\u002Ftroubleshooting\u002Fsingular-stiffness-matrix","singular stiffness matrix",". The pre-solve\nmodel check names the free motion: translation in the out-of-plane direction, or rotation\nabout an in-plane axis, at nodes with nothing restraining them that way.",[11,45,46,47,50],{},"Pinned bases are the usual culprit. A pin restrains three translations, so the frame\ncannot slide out of plane at its feet. Nothing stops it ",[15,48,49],{},"rotating"," about the line\njoining the two bases and falling over sideways like a hinged gate. In a plane-frame\nprogram that motion does not exist. Here it does.",[52,53],"diagram-plane-frame",{},[31,55,57],{"id":56},"the-three-ways-to-restrain-it","The three ways to restrain it",[59,60,62],"h3",{"id":61},"_1-restrain-the-out-of-plane-degrees-of-freedom-at-the-supports","1. Restrain the out-of-plane degrees of freedom at the supports",[11,64,65,66,146,147,18,205,259],{},"For a portal frame in the global XZ plane, restrain ",[67,68,71],"span",{"className":69},[70],"katex",[67,72,76],{"className":73,"ariaHidden":75},[74],"katex-html","true",[67,77,80,85],{"className":78},[79],"base",[67,81],{"className":82,"style":84},[83],"strut","height:0.7167em;vertical-align:-0.2861em;",[67,86,89,94],{"className":87},[88],"mord",[67,90,93],{"className":91},[88,92],"mathnormal","u",[67,95,98],{"className":96},[97],"msupsub",[67,99,103,137],{"className":100},[101,102],"vlist-t","vlist-t2",[67,104,107,132],{"className":105},[106],"vlist-r",[67,108,112],{"className":109,"style":111},[110],"vlist","height:0.1514em;",[67,113,115,120],{"style":114},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[67,116],{"className":117,"style":119},[118],"pstrut","height:2.7em;",[67,121,127],{"className":122},[123,124,125,126],"sizing","reset-size6","size3","mtight",[67,128,131],{"className":129,"style":130},[88,92,126],"margin-right:0.0359em;","y",[67,133,136],{"className":134},[135],"vlist-s","​",[67,138,140],{"className":139},[106],[67,141,144],{"className":142,"style":143},[110],"height:0.2861em;",[67,145],{},", ",[67,148,150],{"className":149},[70],[67,151,153],{"className":152,"ariaHidden":75},[74],[67,154,156,160],{"className":155},[79],[67,157],{"className":158,"style":159},[83],"height:0.8444em;vertical-align:-0.15em;",[67,161,163,168],{"className":162},[88],[67,164,167],{"className":165,"style":166},[88,92],"margin-right:0.0278em;","θ",[67,169,171],{"className":170},[97],[67,172,174,196],{"className":173},[101,102],[67,175,177,193],{"className":176},[106],[67,178,180],{"className":179,"style":111},[110],[67,181,183,186],{"style":182},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[67,184],{"className":185,"style":119},[118],[67,187,189],{"className":188},[123,124,125,126],[67,190,192],{"className":191},[88,92,126],"x",[67,194,136],{"className":195},[135],[67,197,199],{"className":198},[106],[67,200,203],{"className":201,"style":202},[110],"height:0.15em;",[67,204],{},[67,206,208],{"className":207},[70],[67,209,211],{"className":210,"ariaHidden":75},[74],[67,212,214,217],{"className":213},[79],[67,215],{"className":216,"style":159},[83],[67,218,220,223],{"className":219},[88],[67,221,167],{"className":222,"style":166},[88,92],[67,224,226],{"className":225},[97],[67,227,229,251],{"className":228},[101,102],[67,230,232,248],{"className":231},[106],[67,233,235],{"className":234,"style":111},[110],[67,236,237,240],{"style":182},[67,238],{"className":239,"style":119},[118],[67,241,243],{"className":242},[123,124,125,126],[67,244,247],{"className":245,"style":246},[88,92,126],"margin-right:0.044em;","z",[67,249,136],{"className":250},[135],[67,252,254],{"className":253},[106],[67,255,257],{"className":256,"style":202},[110],[67,258],{}," at\nevery base. The frame now cannot move in Y or rotate about X or Z at its feet. With the\nframe's own stiffness this is usually enough for a single frame.",[11,261,262,263,315],{},"It works because fixing ",[67,264,266],{"className":265},[70],[67,267,269],{"className":268,"ariaHidden":75},[74],[67,270,272,275],{"className":271},[79],[67,273],{"className":274,"style":159},[83],[67,276,278,281],{"className":277},[88],[67,279,167],{"className":280,"style":166},[88,92],[67,282,284],{"className":283},[97],[67,285,287,307],{"className":286},[101,102],[67,288,290,304],{"className":289},[106],[67,291,293],{"className":292,"style":111},[110],[67,294,295,298],{"style":182},[67,296],{"className":297,"style":119},[118],[67,299,301],{"className":300},[123,124,125,126],[67,302,192],{"className":303},[88,92,126],[67,305,136],{"className":306},[135],[67,308,310],{"className":309},[106],[67,311,313],{"className":312,"style":202},[110],[67,314],{}," at the bases stops the gate rotation: each column\nstands as an out-of-plane cantilever from its base, and the rafter ties the two together.\nThe real structure is held by purlins and bracing, not base fixity, so the out-of-plane\nresults (which you are not reading) are meaningless. If the model check still reports a\nfree motion, method 2 is more robust.",[59,317,319],{"id":318},"_2-restrain-the-out-of-plane-degrees-of-freedom-at-every-node","2. Restrain the out-of-plane degrees of freedom at every node",[11,321,322,323,146,375,18,427,479,480,533,534,146,586,639],{},"Fix ",[67,324,326],{"className":325},[70],[67,327,329],{"className":328,"ariaHidden":75},[74],[67,330,332,335],{"className":331},[79],[67,333],{"className":334,"style":84},[83],[67,336,338,341],{"className":337},[88],[67,339,93],{"className":340},[88,92],[67,342,344],{"className":343},[97],[67,345,347,367],{"className":346},[101,102],[67,348,350,364],{"className":349},[106],[67,351,353],{"className":352,"style":111},[110],[67,354,355,358],{"style":114},[67,356],{"className":357,"style":119},[118],[67,359,361],{"className":360},[123,124,125,126],[67,362,131],{"className":363,"style":130},[88,92,126],[67,365,136],{"className":366},[135],[67,368,370],{"className":369},[106],[67,371,373],{"className":372,"style":143},[110],[67,374],{},[67,376,378],{"className":377},[70],[67,379,381],{"className":380,"ariaHidden":75},[74],[67,382,384,387],{"className":383},[79],[67,385],{"className":386,"style":159},[83],[67,388,390,393],{"className":389},[88],[67,391,167],{"className":392,"style":166},[88,92],[67,394,396],{"className":395},[97],[67,397,399,419],{"className":398},[101,102],[67,400,402,416],{"className":401},[106],[67,403,405],{"className":404,"style":111},[110],[67,406,407,410],{"style":182},[67,408],{"className":409,"style":119},[118],[67,411,413],{"className":412},[123,124,125,126],[67,414,192],{"className":415},[88,92,126],[67,417,136],{"className":418},[135],[67,420,422],{"className":421},[106],[67,423,425],{"className":424,"style":202},[110],[67,426],{},[67,428,430],{"className":429},[70],[67,431,433],{"className":432,"ariaHidden":75},[74],[67,434,436,439],{"className":435},[79],[67,437],{"className":438,"style":159},[83],[67,440,442,445],{"className":441},[88],[67,443,167],{"className":444,"style":166},[88,92],[67,446,448],{"className":447},[97],[67,449,451,471],{"className":450},[101,102],[67,452,454,468],{"className":453},[106],[67,455,457],{"className":456,"style":111},[110],[67,458,459,462],{"style":182},[67,460],{"className":461,"style":119},[118],[67,463,465],{"className":464},[123,124,125,126],[67,466,247],{"className":467,"style":246},[88,92,126],[67,469,136],{"className":470},[135],[67,472,474],{"className":473},[106],[67,475,477],{"className":476,"style":202},[110],[67,478],{}," at every node in the frame. This is exactly what a 2D\nprogram does implicitly, so it is the exact equivalent. The in-plane behaviour (",[67,481,483],{"className":482},[70],[67,484,486],{"className":485,"ariaHidden":75},[74],[67,487,489,493],{"className":488},[79],[67,490],{"className":491,"style":492},[83],"height:0.5806em;vertical-align:-0.15em;",[67,494,496,499],{"className":495},[88],[67,497,93],{"className":498},[88,92],[67,500,502],{"className":501},[97],[67,503,505,525],{"className":504},[101,102],[67,506,508,522],{"className":507},[106],[67,509,511],{"className":510,"style":111},[110],[67,512,513,516],{"style":114},[67,514],{"className":515,"style":119},[118],[67,517,519],{"className":518},[123,124,125,126],[67,520,192],{"className":521},[88,92,126],[67,523,136],{"className":524},[135],[67,526,528],{"className":527},[106],[67,529,531],{"className":530,"style":202},[110],[67,532],{},",\n",[67,535,537],{"className":536},[70],[67,538,540],{"className":539,"ariaHidden":75},[74],[67,541,543,546],{"className":542},[79],[67,544],{"className":545,"style":492},[83],[67,547,549,552],{"className":548},[88],[67,550,93],{"className":551},[88,92],[67,553,555],{"className":554},[97],[67,556,558,578],{"className":557},[101,102],[67,559,561,575],{"className":560},[106],[67,562,564],{"className":563,"style":111},[110],[67,565,566,569],{"style":114},[67,567],{"className":568,"style":119},[118],[67,570,572],{"className":571},[123,124,125,126],[67,573,247],{"className":574,"style":246},[88,92,126],[67,576,136],{"className":577},[135],[67,579,581],{"className":580},[106],[67,582,584],{"className":583,"style":202},[110],[67,585],{},[67,587,589],{"className":588},[70],[67,590,592],{"className":591,"ariaHidden":75},[74],[67,593,595,599],{"className":594},[79],[67,596],{"className":597,"style":598},[83],"height:0.9805em;vertical-align:-0.2861em;",[67,600,602,605],{"className":601},[88],[67,603,167],{"className":604,"style":166},[88,92],[67,606,608],{"className":607},[97],[67,609,611,631],{"className":610},[101,102],[67,612,614,628],{"className":613},[106],[67,615,617],{"className":616,"style":111},[110],[67,618,619,622],{"style":182},[67,620],{"className":621,"style":119},[118],[67,623,625],{"className":624},[123,124,125,126],[67,626,131],{"className":627,"style":130},[88,92,126],[67,629,136],{"className":630},[135],[67,632,634],{"className":633},[106],[67,635,637],{"className":636,"style":143},[110],[67,638],{},") is untouched, and the reactions in the restrained directions are zero\nunder in-plane loading: a useful check that the model really is planar.",[11,641,642,643,647],{},"The properties panel applies a support to the whole selection, so this is one operation on\nall the nodes. See ",[39,644,646],{"href":645},"\u002Fkb\u002Fmodeling\u002Fsupports-and-releases","Supports and releases",".",[59,649,651],{"id":650},"_3-model-what-actually-holds-it","3. Model what actually holds it",[11,653,654,655,659,660,664],{},"A real portal frame is one of a row, tied by purlins and side rails and braced in one or\ntwo bays. The out-of-plane restraint exists in the members you left out. Adding the\npurlins as beams and the bracing as bars, as the ",[39,656,658],{"href":657},"\u002Fexamples","steel hall"," example does,\ngives a model with no artificial restraint. The purlins' restraint of the rafter is then\nalso there for the ",[39,661,663],{"href":662},"\u002Fkb\u002Fanalysis\u002Fbuckling","stability analysis"," to see.",[11,666,667],{},"This is the right answer when out-of-plane behaviour matters: wind on the gable, the\nbuckling length of the rafter, a crane surge. For a quick in-plane check of one frame it\nis more model than the question needs.",[31,669,671],{"id":670},"which-one-to-use","Which one to use",[673,674,675,688],"table",{},[676,677,678],"thead",{},[679,680,681,685],"tr",{},[682,683,684],"th",{},"Question",[682,686,687],{},"Method",[689,690,691,700,708,716,724],"tbody",{},[679,692,693,697],{},[694,695,696],"td",{},"In-plane forces and moments in one frame",[694,698,699],{},"2 — restrain every node, it cannot go wrong",[679,701,702,705],{},[694,703,704],{},"Quick check, supports only",[694,706,707],{},"1 — and read the model check's answer",[679,709,710,713],{},[694,711,712],{},"Sway and buckling of the rafter",[694,714,715],{},"3 — the purlins are the restraint, model them",[679,717,718,721],{},[694,719,720],{},"Wind on the gable, or any out-of-plane load",[694,722,723],{},"3 — nothing else carries it",[679,725,726,729],{},[694,727,728],{},"Modal analysis of the frame",[694,730,731],{},"3, or 2 if only in-plane modes are wanted — the first mode of an unrestrained plane frame is out of plane",[31,733,735],{"id":734},"what-the-artificial-restraints-do-to-the-results","What the artificial restraints do to the results",[11,737,738],{},"In the plane, nothing, provided every load is in the plane too. A load with an\nout-of-plane component is carried by the restraints instead of the structure, and its\nreaction appears at whichever nodes you restrained.",[740,741,744],"callout",{"title":742,"type":743},"Out-of-plane reactions should be zero","check",[11,745,746,747,647],{},"Look at the reactions in the restrained directions under a planar load. If they are not\nzero, a load points somewhere you did not intend, usually a local-versus-global direction\nmistake on a sloping member. See\n",[39,748,750],{"href":749},"\u002Fkb\u002Floads\u002Fload-cases#local-versus-global-direction","Load cases",[11,752,753],{},"State in the report that the frame was analysed in its plane with out-of-plane motion\nrestrained. It is the first assumption a reviewer will look for.",[31,755,757],{"id":756},"trusses","Trusses",[11,759,760,761,813,814,647],{},"A planar truss modelled in 3D can move out of plane: restrain ",[67,762,764],{"className":763},[70],[67,765,767],{"className":766,"ariaHidden":75},[74],[67,768,770,773],{"className":769},[79],[67,771],{"className":772,"style":84},[83],[67,774,776,779],{"className":775},[88],[67,777,93],{"className":778},[88,92],[67,780,782],{"className":781},[97],[67,783,785,805],{"className":784},[101,102],[67,786,788,802],{"className":787},[106],[67,789,791],{"className":790,"style":111},[110],[67,792,793,796],{"style":114},[67,794],{"className":795,"style":119},[118],[67,797,799],{"className":798},[123,124,125,126],[67,800,131],{"className":801,"style":130},[88,92,126],[67,803,136],{"className":804},[135],[67,806,808],{"className":807},[106],[67,809,811],{"className":810,"style":143},[110],[67,812],{}," at its nodes, or use\nthe 2D Truss model type, which has no out-of-plane freedom to restrain. Its rotations need\nnothing: bars carry no rotational stiffness, and the solver locks rotations no member\nholds. See\n",[39,815,817],{"href":816},"\u002Fkb\u002Fmodeling\u002Fbars-beams-and-trusses","Bars, beams and trusses",[31,819,821],{"id":820},"grillages-and-floor-plates","Grillages and floor plates",[11,823,824],{},"The other flat structure is horizontal: a grillage of beams, or a slab, in the XY plane.\nIts rigid-body motions are translation in X and Y and rotation about Z, and a model whose\nsupports are all vertical-only has all three free. Restrain the in-plane translations\nsomewhere: at one column base in both directions and at another in one, for a statically\ndeterminate set that attracts no thermal or in-plane force, or at every support if the\nreal structure is held that way.",[11,826,827],{},"The rule is the same as for frames. Six global directions; each must be restrained\nsomewhere; the pre-solve check tells you which one is not.",{"title":829,"searchDepth":830,"depth":830,"links":831},"",2,[832,833,839,840,841,842],{"id":33,"depth":830,"text":34},{"id":56,"depth":830,"text":57,"children":834},[835,837,838],{"id":61,"depth":836,"text":62},3,{"id":318,"depth":836,"text":319},{"id":650,"depth":836,"text":651},{"id":670,"depth":830,"text":671},{"id":734,"depth":830,"text":735},{"id":756,"depth":830,"text":757},{"id":820,"depth":830,"text":821},"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.","md",false,{},true,null,7,"\u002Fkb\u002Fmodeling\u002Fplane-frames-in-3d",{"title":6,"description":843},{"loc":850},"kb\u002Fmodeling\u002Fplane-frames-in-3d","L6XFN_zqBwESPdp9Q4fajLU0q292mDCHeJIPOHjXexM",{"sections":856,"extras":1161,"flat":1174},[857,892,929,948,982,1012,1039,1070,1097,1124,1138],{"path":858,"slug":859,"title":860,"description":861,"icon":862,"articles":863},"\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",[864,868,872,876,880,884,888],{"path":865,"title":866,"description":867,"translated":847},"\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":869,"title":870,"description":871,"translated":847},"\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":873,"title":874,"description":875,"translated":847},"\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":877,"title":878,"description":879,"translated":847},"\u002Fkb\u002Fgetting-started\u002Fsystem-requirements","System requirements","Which browsers and devices run Elementarium, how threading affects solve speed, and where the practical ceiling on model size comes from.",{"path":881,"title":882,"description":883,"translated":847},"\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":885,"title":886,"description":887,"translated":847},"\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":889,"title":890,"description":891,"translated":847},"\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":893,"slug":894,"title":895,"description":896,"icon":897,"articles":898},"\u002Fkb\u002Fmodeling","modeling","Modeling","Bars, beams, 3D frames, slabs and walls. Geometry, sections, supports and releases that behave like the real structure.","lucide:frame",[899,901,905,909,910,914,918,922,925],{"path":816,"title":817,"description":900,"translated":847},"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":902,"title":903,"description":904,"translated":847},"\u002Fkb\u002Fmodeling\u002Fdrawings-and-snapping","Drawings & snapping","Importing a DXF as a reference underlay, choosing its units and plane, and snapping model geometry onto it accurately.",{"path":906,"title":907,"description":908,"translated":847},"\u002Fkb\u002Fmodeling\u002Felastic-foundations","Elastic foundations","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":850,"title":6,"description":843,"translated":847},{"path":911,"title":912,"description":913,"translated":847},"\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":915,"title":916,"description":917,"translated":847},"\u002Fkb\u002Fmodeling\u002Fsurfaces","Slabs, walls and shells","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":919,"title":920,"description":921,"translated":847},"\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":645,"title":923,"description":924,"translated":847},"Supports & releases","Pins, fixities, springs and end releases — what each one does to the stiffness matrix, and when each is right.",{"path":926,"title":927,"description":928,"translated":847},"\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":930,"slug":931,"title":932,"description":933,"icon":934,"articles":935},"\u002Fkb\u002Fmeshing","meshing","Meshing","Mesh density, local refinement and the quality checks that tell you when a mesh is fine enough to trust.","lucide:grid-3x3",[936,940,944],{"path":937,"title":938,"description":939,"translated":847},"\u002Fkb\u002Fmeshing\u002Felement-size","Choosing element size","Starting mesh densities for slabs, walls and rafts, and the convergence test that decides whether a mesh is fine enough.",{"path":941,"title":942,"description":943,"translated":847},"\u002Fkb\u002Fmeshing\u002Frefinement","Local refinement","Where to spend elements, where not 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