[{"data":1,"prerenderedAt":1788},["ShallowReactive",2],{"kb-en-\u002Fkb\u002Fmodeling\u002Fsurfaces":3,"kb-nav-en":1403},{"page":4,"fallback":1393},{"id":5,"title":6,"body":7,"description":1391,"extension":1392,"faq":1393,"meta":1394,"navigation":1395,"ogImage":1396,"order":1397,"path":1398,"raw":1393,"robots":1396,"schemaOrg":1396,"seo":1399,"sitemap":1400,"stem":1401,"__hash__":1402},"content_en\u002Fkb\u002Fmodeling\u002Fsurfaces.md","Slabs, walls and shells",{"type":8,"value":9,"toc":1375},"minimark",[10,25,30,33,552,555,559,643,650,656,660,679,710,713,718,723,734,742,751,906,912,993,1008,1013,1017,1083,1284,1287,1290,1294,1305,1309,1348,1352],[11,12,13,14,19,20,24],"p",{},"A surface in Elementarium is an outline with a thickness and a material. You draw the\nslab, wall or shell as a shape, cut its openings, and the mesher turns it into\n",[15,16,18],"a",{"href":17},"\u002Fkb\u002Ftheory\u002Felement-formulations#shell-mitc4","four-node shell elements"," that solve with the\nframe around them. This page covers the modelling decisions; the mesh itself is in\n",[15,21,23],{"href":22},"\u002Fkb\u002Fmeshing","Meshing",".",[26,27,29],"h2",{"id":28},"one-element-three-names","One element, three names",[11,31,32],{},"Slabs, walls and shells are the same element under different loading. It carries\nout-of-plane bending (MITC4) and in-plane membrane action (an enhanced-strain membrane\nthat bends in plane without locking) at once, with a drilling degree of freedom so every\nnode has all six. The names describe what you expect\nthe surface to do, not what it can do:",[34,35,36,52],"table",{},[37,38,39],"thead",{},[40,41,42,46,49],"tr",{},[43,44,45],"th",{},"You call it",[43,47,48],{},"It mostly carries",[43,50,51],{},"Typical results to read",[53,54,55,367,541],"tbody",{},[40,56,57,61,64],{},[58,59,60],"td",{},"Slab, raft, flat plate",[58,62,63],{},"Out-of-plane bending and shear",[58,65,66,145,146,145,202,145,260,145,314,366],{},[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:0.5806em;vertical-align:-0.15em;",[67,86,89,94],{"className":87},[88],"mord",[67,90,93],{"className":91},[88,92],"mathnormal","m",[67,95,98],{"className":96},[97],"msupsub",[67,99,103,136],{"className":100},[101,102],"vlist-t","vlist-t2",[67,104,107,131],{"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",[67,128,130],{"className":129},[88,92,126],"x",[67,132,135],{"className":133},[134],"vlist-s","​",[67,137,139],{"className":138},[106],[67,140,143],{"className":141,"style":142},[110],"height:0.15em;",[67,144],{},", ",[67,147,149],{"className":148},[70],[67,150,152],{"className":151,"ariaHidden":75},[74],[67,153,155,159],{"className":154},[79],[67,156],{"className":157,"style":158},[83],"height:0.7167em;vertical-align:-0.2861em;",[67,160,162,165],{"className":161},[88],[67,163,93],{"className":164},[88,92],[67,166,168],{"className":167},[97],[67,169,171,193],{"className":170},[101,102],[67,172,174,190],{"className":173},[106],[67,175,177],{"className":176,"style":111},[110],[67,178,179,182],{"style":114},[67,180],{"className":181,"style":119},[118],[67,183,185],{"className":184},[123,124,125,126],[67,186,189],{"className":187,"style":188},[88,92,126],"margin-right:0.0359em;","y",[67,191,135],{"className":192},[134],[67,194,196],{"className":195},[106],[67,197,200],{"className":198,"style":199},[110],"height:0.2861em;",[67,201],{},[67,203,205],{"className":204},[70],[67,206,208],{"className":207,"ariaHidden":75},[74],[67,209,211,214],{"className":210},[79],[67,212],{"className":213,"style":158},[83],[67,215,217,220],{"className":216},[88],[67,218,93],{"className":219},[88,92],[67,221,223],{"className":222},[97],[67,224,226,252],{"className":225},[101,102],[67,227,229,249],{"className":228},[106],[67,230,232],{"className":231,"style":111},[110],[67,233,234,237],{"style":114},[67,235],{"className":236,"style":119},[118],[67,238,240],{"className":239},[123,124,125,126],[67,241,243,246],{"className":242},[88,126],[67,244,130],{"className":245},[88,92,126],[67,247,189],{"className":248,"style":188},[88,92,126],[67,250,135],{"className":251},[134],[67,253,255],{"className":254},[106],[67,256,258],{"className":257,"style":199},[110],[67,259],{},[67,261,263],{"className":262},[70],[67,264,266],{"className":265,"ariaHidden":75},[74],[67,267,269,272],{"className":268},[79],[67,270],{"className":271,"style":84},[83],[67,273,275,279],{"className":274},[88],[67,276,278],{"className":277,"style":188},[88,92],"v",[67,280,282],{"className":281},[97],[67,283,285,306],{"className":284},[101,102],[67,286,288,303],{"className":287},[106],[67,289,291],{"className":290,"style":111},[110],[67,292,294,297],{"style":293},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[67,295],{"className":296,"style":119},[118],[67,298,300],{"className":299},[123,124,125,126],[67,301,130],{"className":302},[88,92,126],[67,304,135],{"className":305},[134],[67,307,309],{"className":308},[106],[67,310,312],{"className":311,"style":142},[110],[67,313],{},[67,315,317],{"className":316},[70],[67,318,320],{"className":319,"ariaHidden":75},[74],[67,321,323,326],{"className":322},[79],[67,324],{"className":325,"style":158},[83],[67,327,329,332],{"className":328},[88],[67,330,278],{"className":331,"style":188},[88,92],[67,333,335],{"className":334},[97],[67,336,338,358],{"className":337},[101,102],[67,339,341,355],{"className":340},[106],[67,342,344],{"className":343,"style":111},[110],[67,345,346,349],{"style":293},[67,347],{"className":348,"style":119},[118],[67,350,352],{"className":351},[123,124,125,126],[67,353,189],{"className":354,"style":188},[88,92,126],[67,356,135],{"className":357},[134],[67,359,361],{"className":360},[106],[67,362,364],{"className":363,"style":199},[110],[67,365],{},", deflection",[40,368,369,372,375],{},[58,370,371],{},"Wall, core, deep beam",[58,373,374],{},"In-plane membrane forces",[58,376,377,145,430,145,482,540],{},[67,378,380],{"className":379},[70],[67,381,383],{"className":382,"ariaHidden":75},[74],[67,384,386,389],{"className":385},[79],[67,387],{"className":388,"style":84},[83],[67,390,392,396],{"className":391},[88],[67,393,395],{"className":394},[88,92],"n",[67,397,399],{"className":398},[97],[67,400,402,422],{"className":401},[101,102],[67,403,405,419],{"className":404},[106],[67,406,408],{"className":407,"style":111},[110],[67,409,410,413],{"style":114},[67,411],{"className":412,"style":119},[118],[67,414,416],{"className":415},[123,124,125,126],[67,417,130],{"className":418},[88,92,126],[67,420,135],{"className":421},[134],[67,423,425],{"className":424},[106],[67,426,428],{"className":427,"style":142},[110],[67,429],{},[67,431,433],{"className":432},[70],[67,434,436],{"className":435,"ariaHidden":75},[74],[67,437,439,442],{"className":438},[79],[67,440],{"className":441,"style":158},[83],[67,443,445,448],{"className":444},[88],[67,446,395],{"className":447},[88,92],[67,449,451],{"className":450},[97],[67,452,454,474],{"className":453},[101,102],[67,455,457,471],{"className":456},[106],[67,458,460],{"className":459,"style":111},[110],[67,461,462,465],{"style":114},[67,463],{"className":464,"style":119},[118],[67,466,468],{"className":467},[123,124,125,126],[67,469,189],{"className":470,"style":188},[88,92,126],[67,472,135],{"className":473},[134],[67,475,477],{"className":476},[106],[67,478,480],{"className":479,"style":199},[110],[67,481],{},[67,483,485],{"className":484},[70],[67,486,488],{"className":487,"ariaHidden":75},[74],[67,489,491,494],{"className":490},[79],[67,492],{"className":493,"style":158},[83],[67,495,497,500],{"className":496},[88],[67,498,395],{"className":499},[88,92],[67,501,503],{"className":502},[97],[67,504,506,532],{"className":505},[101,102],[67,507,509,529],{"className":508},[106],[67,510,512],{"className":511,"style":111},[110],[67,513,514,517],{"style":114},[67,515],{"className":516,"style":119},[118],[67,518,520],{"className":519},[123,124,125,126],[67,521,523,526],{"className":522},[88,126],[67,524,130],{"className":525},[88,92,126],[67,527,189],{"className":528,"style":188},[88,92,126],[67,530,135],{"className":531},[134],[67,533,535],{"className":534},[106],[67,536,538],{"className":537,"style":199},[110],[67,539],{},", principal forces",[40,542,543,546,549],{},[58,544,545],{},"Shell, tank, folded plate",[58,547,548],{},"Both together",[58,550,551],{},"Everything above",[11,553,554],{},"A floor slab that also acts as a diaphragm under wind, or a wall that also bends under\nsoil pressure, is the same surface with nothing extra to switch on.",[26,556,558],{"id":557},"drawing-a-surface","Drawing a surface",[560,561,562],"steps",{},[563,564,565,578,584,631,637],"ol",{},[566,567,568,572,573,577],"li",{},[569,570,571],"strong",{},"Outline it"," by its boundary, from coordinates or by snapping to a DXF underlay\n(",[15,574,576],{"href":575},"\u002Fkb\u002Fmodeling\u002Fdrawings-and-snapping","Drawings and snapping","). The outline is the\nsurface's mid-plane.",[566,579,580,583],{},[569,581,582],{},"Cut the openings."," A stair void, a service riser, a window in a wall: each is an\nopening in the surface, and the mesh goes round it.",[566,585,586,589,590,145,608,626,627,24],{},[569,587,588],{},"Set the thickness and the material."," Thickness is the one property the surface has\nthat a member gets from its section. Everything else (",[67,591,593],{"className":592},[70],[67,594,596],{"className":595,"ariaHidden":75},[74],[67,597,599,603],{"className":598},[79],[67,600],{"className":601,"style":602},[83],"height:0.6833em;",[67,604,607],{"className":605,"style":606},[88,92],"margin-right:0.0576em;","E",[67,609,611],{"className":610},[70],[67,612,614],{"className":613,"ariaHidden":75},[74],[67,615,617,621],{"className":616},[79],[67,618],{"className":619,"style":620},[83],"height:0.4306em;",[67,622,625],{"className":623,"style":624},[88,92],"margin-right:0.0637em;","ν",", density) comes from\nthe ",[15,628,630],{"href":629},"\u002Fkb\u002Fmodeling\u002Fsections-and-materials","material",[566,632,633,636],{},[569,634,635],{},"Support it"," along edges or at points: a line support along a wall line, a nodal\nsupport at a column.",[566,638,639,642],{},[569,640,641],{},"Mesh and solve."," The mesh is generated from the outline at the project's target\nelement size, with a local override where the surface earns one.",[11,644,645,646,649],{},"Surfaces are modelled at their ",[569,647,648],{},"mid-plane",", as members are at their centreline. A 250 mm\nslab on a 600 mm downstand beam has its mid-plane 425 mm above the beam's centreline.\nWhere that offset matters, model it with an eccentricity (below).",[651,652],"kb-figure",{"alt":653,"caption":654,"src":655},"A wireframe viewport of the concrete floor example showing the slab mesh lines, the rectangular opening, the edge beams and the columns","The concrete floor in wireframe: the slab outline with its opening, the mesh the mesher produced from it, and the beams along the edges and across the middle sharing the mesh’s node lines.","\u002Fkb\u002Fviewport-floor-wireframe.webp",[26,657,659],{"id":658},"how-other-things-attach","How other things attach",[11,661,662,663,666,667,670,671,674,675,678],{},"The mesh is the connection, and the connection is stored, never guessed. When you draw a\nnode or member that lies on a plate, ",[569,664,665],{},"Connect to plate?"," asks whether it should be\nmeshed in; ",[569,668,669],{},"Not now"," leaves it separate, with its own nodes even where it lies on the\nplate's line. The plate's properties list what is connected, with ",[569,672,673],{},"Connect to the plate","\nand ",[569,676,677],{},"Disconnect from the plate"," to change it. Once connected, a curve is discretised\nexactly once, and every surface or member on it shares the chain of nodes along it:",[680,681,682,688,694,700],"ul",{},[566,683,684,687],{},[569,685,686],{},"Two slabs sharing an edge"," are continuous across it. A two-panel floor gives the same\nanswer as one surface or two.",[566,689,690,693],{},[569,691,692],{},"A wall meeting a slab"," shares the edge nodes, and because the element has a drilling\ndegree of freedom the moment transfers. A slab spanning onto a core wall is continuous\nwith it unless you release it deliberately.",[566,695,696,699],{},[569,697,698],{},"A beam along a slab edge, or a rib across a slab",", is embedded in the slab's mesh and\nshares one row of nodes with it. The beam and slab act together, and the finer of the\ntwo subdivisions wins, so the beam cannot be coarser than the slab it stiffens.",[566,701,702,705,706,24],{},[569,703,704],{},"A column under a slab"," meets it at a node. That node is a point support in a plate,\nand the moment there is a singularity: read the moment at the column face, or spread the\nsupport over its real bearing area. See\n",[15,707,709],{"href":708},"\u002Fkb\u002Fmeshing\u002Felement-size#singularities-where-refinement-never-helps","Choosing element size",[11,711,712],{},"A member that is not connected — skipped at the prompt, or merely passing near the\nsurface — shares no nodes with it and does not act with it. If a slab and its edge beam\ndeflect independently, check the plate's connections first.",[714,715],"try-example",{"id":716,"note":717},"concrete-floor","A 200 mm C30\u002F37 slab in two panels on a steel frame, with an opening, meshed at 1 m.",[719,720,722],"h3",{"id":721},"downstands-and-offsets","Downstands and offsets",[11,724,725,726,729,730,24],{},"A beam under a slab acts compositely with it, and the composite action comes from the\noffset between the two centrelines. Modelling both at the same level gives a T-beam its\nweb only. A member can carry its own ",[569,727,728],{},"eccentricity",": a downstand sits below the slab\nmid-plane by half the slab depth plus half the beam depth, and the solver adds the offset\nas a constraint without a separate node and rigid arm. See\n",[15,731,733],{"href":732},"\u002Fkb\u002Fmodeling\u002Fsupports-and-releases#rigid-arms","Supports and releases",[735,736,739],"callout",{"title":737,"type":738},"The offset changes the forces, correctly","note",[11,740,741],{},"The eccentric beam now carries an axial force, because bending of the composite section\nputs it in tension or compression. That force is real and the design check will see it.\nThe slab's membrane forces near the beam are also non-zero for the same reason, which a\nslab-only model would not show.",[26,743,745,746,750],{"id":744},"local-axes-and-what-m_x-means","Local axes and what ",[747,748,749],"code",{},"m_x"," means",[11,752,753,754,769,770,786,787,804,805,857,858,873,874,889,890,905],{},"Every surface has a local ",[67,755,757],{"className":756},[70],[67,758,760],{"className":759,"ariaHidden":75},[74],[67,761,763,766],{"className":762},[79],[67,764],{"className":765,"style":620},[83],[67,767,130],{"className":768},[88,92]," and ",[67,771,773],{"className":772},[70],[67,774,776],{"className":775,"ariaHidden":75},[74],[67,777,779,783],{"className":778},[79],[67,780],{"className":781,"style":782},[83],"height:0.625em;vertical-align:-0.1944em;",[67,784,189],{"className":785,"style":188},[88,92]," in its plane and ",[67,788,790],{"className":789},[70],[67,791,793],{"className":792,"ariaHidden":75},[74],[67,794,796,799],{"className":795},[79],[67,797],{"className":798,"style":620},[83],[67,800,803],{"className":801,"style":802},[88,92],"margin-right:0.044em;","z"," normal to it. Results are\nreported in those axes, per unit width. ",[67,806,808],{"className":807},[70],[67,809,811],{"className":810,"ariaHidden":75},[74],[67,812,814,817],{"className":813},[79],[67,815],{"className":816,"style":84},[83],[67,818,820,823],{"className":819},[88],[67,821,93],{"className":822},[88,92],[67,824,826],{"className":825},[97],[67,827,829,849],{"className":828},[101,102],[67,830,832,846],{"className":831},[106],[67,833,835],{"className":834,"style":111},[110],[67,836,837,840],{"style":114},[67,838],{"className":839,"style":119},[118],[67,841,843],{"className":842},[123,124,125,126],[67,844,130],{"className":845},[88,92,126],[67,847,135],{"className":848},[134],[67,850,852],{"className":851},[106],[67,853,855],{"className":854,"style":142},[110],[67,856],{}," is the bending moment about the local ",[67,859,861],{"className":860},[70],[67,862,864],{"className":863,"ariaHidden":75},[74],[67,865,867,870],{"className":866},[79],[67,868],{"className":869,"style":782},[83],[67,871,189],{"className":872,"style":188},[88,92],"\naxis, producing stress in the local ",[67,875,877],{"className":876},[70],[67,878,880],{"className":879,"ariaHidden":75},[74],[67,881,883,886],{"className":882},[79],[67,884],{"className":885,"style":620},[83],[67,887,130],{"className":888},[88,92]," direction: the moment that reinforcement running\nin ",[67,891,893],{"className":892},[70],[67,894,896],{"className":895,"ariaHidden":75},[74],[67,897,899,902],{"className":898},[79],[67,900],{"className":901,"style":620},[83],[67,903,130],{"className":904},[88,92]," resists.",[651,907],{"alt":908,"caption":909,"src":910,"meta":911},"The editor with the concrete floor model on the left and the mx shell moment contour on the right, legend in kNm\u002Fm","The concrete floor with the model in one viewport and the mx contour in the other. The legend reads kNm\u002Fm: the moment is per metre width, and the reinforcement running in the slab’s local x is what it is sized for.","\u002Fkb\u002Ffloor-mx.webp","4 LCs · 198 ms · 294 DoF",[735,913,916],{"title":914,"type":915},"Check local axes on rotated slabs","warning",[11,917,918,919,971,972,987,988,992],{},"A slab rotated 30° in plan reports ",[67,920,922],{"className":921},[70],[67,923,925],{"className":924,"ariaHidden":75},[74],[67,926,928,931],{"className":927},[79],[67,929],{"className":930,"style":84},[83],[67,932,934,937],{"className":933},[88],[67,935,93],{"className":936},[88,92],[67,938,940],{"className":939},[97],[67,941,943,963],{"className":942},[101,102],[67,944,946,960],{"className":945},[106],[67,947,949],{"className":948,"style":111},[110],[67,950,951,954],{"style":114},[67,952],{"className":953,"style":119},[118],[67,955,957],{"className":956},[123,124,125,126],[67,958,130],{"className":959},[88,92,126],[67,961,135],{"className":962},[134],[67,964,966],{"className":965},[106],[67,967,969],{"className":968,"style":142},[110],[67,970],{}," in its own ",[67,973,975],{"className":974},[70],[67,976,978],{"className":977,"ariaHidden":75},[74],[67,979,981,984],{"className":980},[79],[67,982],{"className":983,"style":620},[83],[67,985,130],{"className":986},[88,92],", and reconciling that with the\nreinforcement direction is up to you. Check the local axes before reading any surface\nresult on a slab not aligned with the global system.\n",[15,989,991],{"href":990},"\u002Fkb\u002Ftheory\u002Fsign-conventions#surface-results","Sign conventions"," has the full convention,\nincluding which face is \"bottom\".",[11,994,995,996,145,999,1002,1003,1007],{},"Units are per unit width: ",[747,997,998],{},"kNm\u002Fm",[747,1000,1001],{},"kN\u002Fm",". ",[15,1004,1006],{"href":1005},"\u002Fkb\u002Fgetting-started\u002Funits","Units"," explains why\nthis is the most common silent error in slab design.",[651,1009],{"alt":1010,"caption":1011,"src":1012},"Slab with a triangular opening, supported on two columns and an edge beam, shown as a total displacement contour with a legend","Meshed slab with a triangular opening on two columns and an edge beam · total displacement under live load","\u002Fplate1.png",[26,1014,1016],{"id":1015},"thickness-and-what-it-buys","Thickness and what it buys",[11,1018,1019,1020,1037,1038,1082],{},"The element does not shear-lock, so a thin slab and a thick raft use the same formulation\nwith no thin-versus-thick switch. Thickness enters the membrane stiffness as ",[67,1021,1023],{"className":1022},[70],[67,1024,1026],{"className":1025,"ariaHidden":75},[74],[67,1027,1029,1033],{"className":1028},[79],[67,1030],{"className":1031,"style":1032},[83],"height:0.6151em;",[67,1034,1036],{"className":1035},[88,92],"t"," and the\nbending stiffness as ",[67,1039,1041],{"className":1040},[70],[67,1042,1044],{"className":1043,"ariaHidden":75},[74],[67,1045,1047,1051],{"className":1046},[79],[67,1048],{"className":1049,"style":1050},[83],"height:0.8141em;",[67,1052,1054,1057],{"className":1053},[88],[67,1055,1036],{"className":1056},[88,92],[67,1058,1060],{"className":1059},[97],[67,1061,1063],{"className":1062},[101],[67,1064,1066],{"className":1065},[106],[67,1067,1069],{"className":1068,"style":1050},[110],[67,1070,1072,1075],{"style":1071},"top:-3.063em;margin-right:0.05em;",[67,1073],{"className":1074,"style":119},[118],[67,1076,1078],{"className":1077},[123,124,125,126],[67,1079,1081],{"className":1080},[88,126],"3",":",[67,1084,1087],{"className":1085},[1086],"katex-display",[67,1088,1090],{"className":1089},[70],[67,1091,1093,1117],{"className":1092,"ariaHidden":75},[74],[67,1094,1096,1099,1104,1109,1114],{"className":1095},[79],[67,1097],{"className":1098,"style":602},[83],[67,1100,1103],{"className":1101,"style":1102},[88,92],"margin-right:0.0278em;","D",[67,1105],{"className":1106,"style":1108},[1107],"mspace","margin-right:0.2778em;",[67,1110,1113],{"className":1111},[1112],"mrel","=",[67,1115],{"className":1116,"style":1108},[1107],[67,1118,1120,1124],{"className":1119},[79],[67,1121],{"className":1122,"style":1123},[83],"height:2.4271em;vertical-align:-0.936em;",[67,1125,1127,1132,1281],{"className":1126},[88],[67,1128],{"className":1129},[1130,1131],"mopen","nulldelimiter",[67,1133,1136],{"className":1134},[1135],"mfrac",[67,1137,1139,1272],{"className":1138},[101,102],[67,1140,1142,1269],{"className":1141},[106],[67,1143,1146,1217,1228],{"className":1144,"style":1145},[110],"height:1.4911em;",[67,1147,1149,1153],{"style":1148},"top:-2.314em;",[67,1150],{"className":1151,"style":1152},[118],"height:3em;",[67,1154,1156,1160,1164,1168,1172,1177,1180,1212],{"className":1155},[88],[67,1157,1159],{"className":1158},[88],"12",[67,1161,1163],{"className":1162},[1130],"(",[67,1165,1167],{"className":1166},[88],"1",[67,1169],{"className":1170,"style":1171},[1107],"margin-right:0.2222em;",[67,1173,1176],{"className":1174},[1175],"mbin","−",[67,1178],{"className":1179,"style":1171},[1107],[67,1181,1183,1186],{"className":1182},[88],[67,1184,625],{"className":1185,"style":624},[88,92],[67,1187,1189],{"className":1188},[97],[67,1190,1192],{"className":1191},[101],[67,1193,1195],{"className":1194},[106],[67,1196,1199],{"className":1197,"style":1198},[110],"height:0.7401em;",[67,1200,1202,1205],{"style":1201},"top:-2.989em;margin-right:0.05em;",[67,1203],{"className":1204,"style":119},[118],[67,1206,1208],{"className":1207},[123,124,125,126],[67,1209,1211],{"className":1210},[88,126],"2",[67,1213,1216],{"className":1214},[1215],"mclose",")",[67,1218,1220,1223],{"style":1219},"top:-3.23em;",[67,1221],{"className":1222,"style":1152},[118],[67,1224],{"className":1225,"style":1227},[1226],"frac-line","border-bottom-width:0.04em;",[67,1229,1231,1234],{"style":1230},"top:-3.677em;",[67,1232],{"className":1233,"style":1152},[118],[67,1235,1237,1240],{"className":1236},[88],[67,1238,607],{"className":1239,"style":606},[88,92],[67,1241,1243,1246],{"className":1242},[88],[67,1244,1036],{"className":1245},[88,92],[67,1247,1249],{"className":1248},[97],[67,1250,1252],{"className":1251},[101],[67,1253,1255],{"className":1254},[106],[67,1256,1258],{"className":1257,"style":1050},[110],[67,1259,1260,1263],{"style":1071},[67,1261],{"className":1262,"style":119},[118],[67,1264,1266],{"className":1265},[123,124,125,126],[67,1267,1081],{"className":1268},[88,126],[67,1270,135],{"className":1271},[134],[67,1273,1275],{"className":1274},[106],[67,1276,1279],{"className":1277,"style":1278},[110],"height:0.936em;",[67,1280],{},[67,1282],{"className":1283},[1215,1131],[11,1285,1286],{},"Doubling a slab's thickness makes it eight times stiffer in bending and only twice as\nstiff in-plane. That is why a deflection problem is solved with depth and a diaphragm\nproblem is not.",[11,1288,1289],{},"Mass and self-weight are also generated from thickness, so a slab whose thickness is in\nthe wrong unit is both weightless and floppy, or the reverse.",[26,1291,1293],{"id":1292},"curved-surfaces","Curved surfaces",[11,1295,1296,1297,1300,1301,24],{},"A shell is meshed into ",[569,1298,1299],{},"flat facets",", so a curved surface (a tank wall, a dome, a barrel\nroof) is approximated by planar elements, and the accuracy of the curvature depends on the\nmesh in a way a flat slab's does not. The element corrects for warping, so a four-node\nelement whose corners leave its plane is not strained by a rigid motion and a twisted\nsurface does not lock, but each facet is still flat: keep warping across the curvature\nbelow about 10° where you quote results, and refine until each element spans less\ncurvature. See ",[15,1302,1304],{"href":1303},"\u002Fkb\u002Fmeshing\u002Fquality-checks#warping","Mesh quality",[26,1306,1308],{"id":1307},"what-a-surface-will-not-do","What a surface will not do",[680,1310,1311,1317,1327,1333,1339],{},[566,1312,1313,1316],{},[569,1314,1315],{},"Crack, creep or yield."," The result is linear elastic and uncracked. Service\ndeflections of a concrete slab are several times the linear value; apply the code's\ncracked-section methods to the linear result.",[566,1318,1319,1322,1323,24],{},[569,1320,1321],{},"Lift off a support."," A line support along a wall resists tension. Where a combination\nlifts an edge, look at the reactions and interpret. See\n",[15,1324,1326],{"href":1325},"\u002Fkb\u002Fmodeling\u002Felastic-foundations#where-the-model-breaks","Elastic foundations",[566,1328,1329,1332],{},[569,1330,1331],{},"Buckle locally."," The analysis reports the elastic response. Plate buckling of a thin\nwall is a design question, and neither steel module covers it.",[566,1334,1335,1338],{},[569,1336,1337],{},"Give you a design strip moment."," The contour is the element field, and the peak over\na column is a singularity. Integrating across a strip is a hand calculation from the\ncontour or the element table today; a section-cut tool is on the roadmap.",[566,1340,1341,1344,1345,24],{},[569,1342,1343],{},"Sit on a Winkler bed under its face."," A line support along an edge is available; the\narea case is not switched on yet. See the note on\n",[15,1346,1326],{"href":1347},"\u002Fkb\u002Fmodeling\u002Felastic-foundations",[26,1349,1351],{"id":1350},"before-you-solve","Before you solve",[680,1353,1354,1357,1360,1363,1366,1369],{},[566,1355,1356],{},"The outline is closed, and openings lie inside it.",[566,1358,1359],{},"Thickness and material are set, in the right units.",[566,1361,1362],{},"Every member meant to attach lies on the outline or across the surface, not near it.",[566,1364,1365],{},"Local axes point where the reinforcement will run.",[566,1367,1368],{},"Supports restrain the surface in plane as well as out of plane. A slab on vertical-only\nsupports is free to slide.",[566,1370,1371,1372,24],{},"The mesh is fine enough for the quantity you will quote, and you have checked that by\nrefining once. See ",[15,1373,709],{"href":1374},"\u002Fkb\u002Fmeshing\u002Felement-size#convergence",{"title":1376,"searchDepth":1377,"depth":1377,"links":1378},"",2,[1379,1380,1381,1385,1387,1388,1389,1390],{"id":28,"depth":1377,"text":29},{"id":557,"depth":1377,"text":558},{"id":658,"depth":1377,"text":659,"children":1382},[1383],{"id":721,"depth":1384,"text":722},3,{"id":744,"depth":1377,"text":1386},"Local axes and what m_x means",{"id":1015,"depth":1377,"text":1016},{"id":1292,"depth":1377,"text":1293},{"id":1307,"depth":1377,"text":1308},{"id":1350,"depth":1377,"text":1351},"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.","md",false,{},true,null,8,"\u002Fkb\u002Fmodeling\u002Fsurfaces",{"title":6,"description":1391},{"loc":1398},"kb\u002Fmodeling\u002Fsurfaces","1tJCYQK6xyjv5fN9zgieGe-5-ornEpWX75KSHBDuFfM",{"sections":1404,"extras":1704,"flat":1717},[1405,1438,1474,1489,1524,1555,1582,1613,1640,1666,1681],{"path":1406,"slug":1407,"title":1408,"description":1409,"icon":1410,"articles":1411},"\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",[1412,1416,1420,1424,1428,1432,1434],{"path":1413,"title":1414,"description":1415,"translated":1395},"\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":1417,"title":1418,"description":1419,"translated":1395},"\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":1421,"title":1422,"description":1423,"translated":1395},"\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":1425,"title":1426,"description":1427,"translated":1395},"\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":1429,"title":1430,"description":1431,"translated":1395},"\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":1005,"title":1006,"description":1433,"translated":1395},"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":1435,"title":1436,"description":1437,"translated":1395},"\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":1439,"slug":1440,"title":1441,"description":1442,"icon":1443,"articles":1444},"\u002Fkb\u002Fmodeling","modeling","Modeling","Bars, beams, 3D frames, slabs and walls. Geometry, sections, supports and releases that behave like the real structure.","lucide:frame",[1445,1449,1452,1454,1458,1461,1462,1466,1470],{"path":1446,"title":1447,"description":1448,"translated":1395},"\u002Fkb\u002Fmodeling\u002Fbars-beams-and-trusses","Bars, beams and trusses","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":575,"title":1450,"description":1451,"translated":1395},"Drawings & snapping","Importing a DXF as a reference underlay, choosing its units and plane, and snapping model geometry onto it accurately.",{"path":1347,"title":1326,"description":1453,"translated":1395},"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":1455,"title":1456,"description":1457,"translated":1395},"\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":629,"title":1459,"description":1460,"translated":1395},"Sections & materials","What a section and a material contribute to the stiffness matrix and the design checks, and the values worth checking twice.",{"path":1398,"title":6,"description":1391,"translated":1395},{"path":1463,"title":1464,"description":1465,"translated":1395},"\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":1467,"title":1468,"description":1469,"translated":1395},"\u002Fkb\u002Fmodeling\u002Fsupports-and-releases","Supports & releases","Pins, fixities, springs and end releases — what each one does to the stiffness matrix, and when each is right.",{"path":1471,"title":1472,"description":1473,"translated":1395},"\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":22,"slug":1475,"title":23,"description":1476,"icon":1477,"articles":1478},"meshing","Mesh density, local refinement and the quality checks that tell you when a mesh is fine enough to trust.","lucide:grid-3x3",[1479,1482,1486],{"path":1480,"title":709,"description":1481,"translated":1395},"\u002Fkb\u002Fmeshing\u002Felement-size","Starting mesh densities for slabs, walls and rafts, and the convergence test that decides whether a mesh is fine enough.",{"path":1483,"title":1484,"description":1485,"translated":1395},"\u002Fkb\u002Fmeshing\u002Frefinement","Local refinement","Where to spend elements, where not to bother, and how to refine without wrecking element shape.",{"path":1487,"title":1304,"description":1488,"translated":1395},"\u002Fkb\u002Fmeshing\u002Fquality-checks","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":1490,"slug":1491,"title":1492,"description":1493,"icon":1494,"articles":1495},"\u002Fkb\u002Floads","loads","Loads & combinations","Build load cases, generate code combinations automatically and find out which one actually governs.","lucide:arrow-down-to-line",[1496,1500,1504,1508,1512,1516,1520],{"path":1497,"title":1498,"description":1499,"translated":1395},"\u002Fkb\u002Floads\u002Fasce-7-combinations","ASCE 7 combinations","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":1501,"title":1502,"description":1503,"translated":1395},"\u002Fkb\u002Floads\u002Fcombinations","Automatic combinations","Generating EN 1990 and ASCE 7 combinations, understanding the equations behind them, and reading the generated set critically.",{"path":1505,"title":1506,"description":1507,"translated":1395},"\u002Fkb\u002Floads\u002Fenvelopes","Envelopes","Extracting the governing value across dozens of combinations without reading every one — and the traps in doing so.",{"path":1509,"title":1510,"description":1511,"translated":1395},"\u002Fkb\u002Floads\u002Fload-cases","Load cases","Actions, self-weight, imposed loads and load arrangements — how to build cases that stay separable.",{"path":1513,"title":1514,"description":1515,"translated":1395},"\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":1517,"title":1518,"description":1519,"translated":1395},"\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":1521,"title":1522,"description":1523,"translated":1395},"\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":1525,"slug":1526,"title":1527,"description":1528,"icon":1529,"articles":1530},"\u002Fkb\u002Fanalysis","analysis","Analysis types","Linear static, modal, linear buckling and second-order — what each analysis assumes, what it returns and how to read the result.","lucide:activity",[1531,1535,1539,1543,1547,1551],{"path":1532,"title":1533,"description":1534,"translated":1395},"\u002Fkb\u002Fanalysis\u002Fsolvers","Choosing a linear solver","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":1536,"title":1537,"description":1538,"translated":1395},"\u002Fkb\u002Fanalysis\u002Fbuckling","Linear buckling","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":1540,"title":1541,"description":1542,"translated":1395},"\u002Fkb\u002Fanalysis\u002Flinear-static","Linear static analysis","The workhorse analysis — what K u = f actually assumes, what it returns, and where linearity stops being a reasonable model.",{"path":1544,"title":1545,"description":1546,"translated":1395},"\u002Fkb\u002Fanalysis\u002Fmodal","Modal analysis","Natural frequencies and mode shapes — mass modelling, participation factors and what the numbers are good for.",{"path":1548,"title":1549,"description":1550,"translated":1395},"\u002Fkb\u002Fanalysis\u002Fsecond-order","Second-order analysis","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":1552,"title":1553,"description":1554,"translated":1395},"\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":1556,"slug":1557,"title":1558,"description":1559,"icon":1560,"articles":1561},"\u002Fkb\u002Fdesign-checks","design-checks","Design checks","Utilisation ratios, governing cases and the clause behind every number a check reports.","lucide:clipboard-check",[1562,1566,1570,1574,1578],{"path":1563,"title":1564,"description":1565,"translated":1395},"\u002Fkb\u002Fdesign-checks\u002Fnational-annexes","National annexes","Where nationally determined parameters change the answer, how to select the right annex, and what to state in the report.",{"path":1567,"title":1568,"description":1569,"translated":1395},"\u002Fkb\u002Fdesign-checks\u002Fsection-classification","Section classification","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":1571,"title":1572,"description":1573,"translated":1395},"\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":1575,"title":1576,"description":1577,"translated":1395},"\u002Fkb\u002Fdesign-checks\u002Faisc","Steel — AISC 360","Member strength to Chapters D to H, LRFD or ASD — compression buckling, lateral-torsional buckling and every C_b option written down.",{"path":1579,"title":1580,"description":1581,"translated":1395},"\u002Fkb\u002Fdesign-checks\u002Fsteel","Steel — EN 1993-1-1","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":1583,"slug":1584,"title":1585,"description":1586,"icon":1587,"articles":1588},"\u002Fkb\u002Freports","reports","Results & reports","Diagrams, contours and tables in the viewport, and the calculation package you hand to a reviewer.","lucide:file-chart-column",[1589,1593,1597,1601,1605,1609],{"path":1590,"title":1591,"description":1592,"translated":1395},"\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":1594,"title":1595,"description":1596,"translated":1395},"\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":1598,"title":1599,"description":1600,"translated":1395},"\u002Fkb\u002Freports\u002Fexchange","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":1602,"title":1603,"description":1604,"translated":1395},"\u002Fkb\u002Freports\u002Freading-diagrams","Reading diagrams","Bending, shear and axial diagrams, contour plots and deformed shapes — the conventions behind what you are looking at.",{"path":1606,"title":1607,"description":1608,"translated":1395},"\u002Fkb\u002Freports\u002Fresult-tables","Result tables","Filtering, sorting and extracting numbers — getting the value you need out of a solved model without scrolling.",{"path":1610,"title":1611,"description":1612,"translated":1395},"\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":1614,"slug":1615,"title":1616,"description":1617,"icon":1618,"articles":1619},"\u002Fkb\u002Fcollaboration","collaboration","Collaboration & sync","Shared models, real-time editing, and offline edits that merge cleanly when you reconnect.","lucide:users-round",[1620,1624,1628,1632,1636],{"path":1621,"title":1622,"description":1623,"translated":1395},"\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":1625,"title":1626,"description":1627,"translated":1395},"\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":1629,"title":1630,"description":1631,"translated":1395},"\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":1633,"title":1634,"description":1635,"translated":1395},"\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":1637,"title":1638,"description":1639,"translated":1395},"\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":1641,"slug":1642,"title":1643,"description":1644,"icon":1645,"articles":1646},"\u002Fkb\u002Ftheory","theory","Theory notes","The mechanics inside the solver — element formulations, sign conventions, numerical assumptions and their limits.","lucide:sigma",[1647,1651,1655,1658,1662],{"path":1648,"title":1649,"description":1650,"translated":1395},"\u002Fkb\u002Ftheory\u002Felement-formulations","Element formulations","Degrees of freedom, interpolation and limits for every 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