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The values\nEN 1991-1-5 gives:",[36,994,995,1020],{},[39,996,997],{},[42,998,999,1002],{},[45,1000,1001],{},"Material",[45,1003,1004,1019],{},[67,1005,1007],{"className":1006},[70],[67,1008,1010],{"className":1009,"ariaHidden":75},[74],[67,1011,1013,1016],{"className":1012},[79],[67,1014],{"className":1015,"style":111},[83],[67,1017,247],{"className":1018,"style":246},[88,93],", per °C",[58,1021,1022,1030,1038,1046,1054],{},[42,1023,1024,1027],{},[63,1025,1026],{},"Structural steel",[63,1028,1029],{},"12 × 10⁻⁶",[42,1031,1032,1035],{},[63,1033,1034],{},"Concrete",[63,1036,1037],{},"10 × 10⁻⁶",[42,1039,1040,1043],{},[63,1041,1042],{},"Aluminium",[63,1044,1045],{},"24 × 10⁻⁶",[42,1047,1048,1051],{},[63,1049,1050],{},"Timber, parallel to grain",[63,1052,1053],{},"5 × 10⁻⁶",[42,1055,1056,1059],{},[63,1057,1058],{},"Stainless steel",[63,1060,1061],{},"16 × 10⁻⁶",[11,1063,1064],{},"For composite steel–concrete structures EN 1994 permits 10 × 10⁻⁶ for both, so the two do\nnot fight over a value that is uncertain anyway.",[31,1066,1068],{"id":1067},"orders-of-magnitude","Orders of magnitude",[11,1070,1071],{},"Steel, 30 °C rise, a 20 m member fully restrained:",[67,1073,1075],{"className":1074},[208],[67,1076,1078],{"className":1077},[70],[67,1079,1081],{"className":1080,"ariaHidden":75},[74],[67,1082,1084,1088],{"className":1083},[79],[67,1085],{"className":1086,"style":1087},[83],"height:2.7482em;vertical-align:-1.1241em;",[67,1089,1091],{"className":1090},[88],[67,1092,1095,1147],{"className":1093},[1094],"mtable",[67,1096,1099],{"className":1097},[1098],"col-align-r",[67,1100,1102,1138],{"className":1101},[341,342],[67,1103,1105,1135],{"className":1104},[346],[67,1106,1109,1121],{"className":1107,"style":1108},[350],"height:1.6241em;",[67,1110,1112,1115],{"style":1111},"top:-3.76em;",[67,1113],{"className":1114,"style":539},[358],[67,1116,1118],{"className":1117},[88],[67,1119,115],{"className":1120},[88,93],[67,1122,1124,1127],{"style":1123},"top:-2.2359em;",[67,1125],{"className":1126,"style":539},[358],[67,1128,1130],{"className":1129},[88],[67,1131,1134],{"className":1132,"style":1133},[88,93],"margin-right:0.0359em;","σ",[67,1136,385],{"className":1137},[384],[67,1139,1141],{"className":1140},[346],[67,1142,1145],{"className":1143,"style":1144},[350],"height:1.1241em;",[67,1146],{},[67,1148,1151],{"className":1149},[1150],"col-align-l",[67,1152,1154,1406],{"className":1153},[341,342],[67,1155,1157,1403],{"className":1156},[346],[67,1158,1160,1274],{"className":1159,"style":1108},[350],[67,1161,1162,1165],{"style":1111},[67,1163],{"className":1164,"style":539},[358],[67,1166,1168,1171,1174,1177,1180,1184,1187,1191,1194,1198,1237,1240,1243,1246,1250,1253,1256,1259,1263,1267,1271],{"className":1167},[88],[67,1169],{"className":1170},[88],[67,1172],{"className":1173,"style":228},[227],[67,1175,233],{"className":1176},[232],[67,1178],{"className":1179,"style":228},[227],[67,1181,1183],{"className":1182},[88],"12",[67,1185],{"className":1186,"style":398},[227],[67,1188,1190],{"className":1189},[402],"×",[67,1192],{"className":1193,"style":398},[227],[67,1195,1197],{"className":1196},[88],"1",[67,1199,1201,1205],{"className":1200},[88],[67,1202,1204],{"className":1203},[88],"0",[67,1206,1208],{"className":1207},[337],[67,1209,1211],{"className":1210},[341],[67,1212,1214],{"className":1213},[346],[67,1215,1218],{"className":1216,"style":1217},[350],"height:0.8641em;",[67,1219,1221,1224],{"style":1220},"top:-3.113em;margin-right:0.05em;",[67,1222],{"className":1223,"style":359},[358],[67,1225,1227],{"className":1226},[363,364,365,366],[67,1228,1230,1233],{"className":1229},[88,366],[67,1231,284],{"className":1232},[88,366],[67,1234,1236],{"className":1235},[88,366],"6",[67,1238],{"className":1239,"style":398},[227],[67,1241,1190],{"className":1242},[402],[67,1244],{"className":1245,"style":398},[227],[67,1247,1249],{"className":1248},[88],"30",[67,1251],{"className":1252,"style":228},[227],[67,1254,233],{"className":1255},[232],[67,1257],{"className":1258,"style":228},[227],[67,1260,1262],{"className":1261},[88],"360",[67,1264,1266],{"className":1265},[227]," ",[67,1268,1270],{"className":1269},[88,93],"μ",[67,1272,115],{"className":1273},[88,93],[67,1275,1276,1279],{"style":1123},[67,1277],{"className":1278,"style":539},[358],[67,1280,1282,1285,1288,1291,1294,1297,1300,1303,1306,1309,1313,1316,1320,1323,1326,1329,1332,1335,1338,1341,1344,1379,1382,1385,1388,1392,1395],{"className":1281},[88],[67,1283],{"className":1284},[88],[67,1286],{"className":1287,"style":228},[227],[67,1289,233],{"className":1290},[232],[67,1292],{"className":1293,"style":228},[227],[67,1295,289],{"className":1296,"style":288},[88,93],[67,1298,115],{"className":1299},[88,93],[67,1301],{"className":1302,"style":228},[227],[67,1304,233],{"className":1305},[232],[67,1307],{"className":1308,"style":228},[227],[67,1310,1312],{"className":1311},[88],"210",[67,1314],{"className":1315,"style":251},[227],[67,1317,1319],{"className":1318},[88],"000",[67,1321],{"className":1322,"style":398},[227],[67,1324,1190],{"className":1325},[402],[67,1327],{"className":1328,"style":398},[227],[67,1330,1262],{"className":1331},[88],[67,1333],{"className":1334,"style":398},[227],[67,1336,1190],{"className":1337},[402],[67,1339],{"className":1340,"style":398},[227],[67,1342,1197],{"className":1343},[88],[67,1345,1347,1350],{"className":1346},[88],[67,1348,1204],{"className":1349},[88],[67,1351,1353],{"className":1352},[337],[67,1354,1356],{"className":1355},[341],[67,1357,1359],{"className":1358},[346],[67,1360,1362],{"className":1361,"style":1217},[350],[67,1363,1364,1367],{"style":1220},[67,1365],{"className":1366,"style":359},[358],[67,1368,1370],{"className":1369},[363,364,365,366],[67,1371,1373,1376],{"className":1372},[88,366],[67,1374,284],{"className":1375},[88,366],[67,1377,1236],{"className":1378},[88,366],[67,1380],{"className":1381,"style":228},[227],[67,1383,233],{"className":1384},[232],[67,1386],{"className":1387,"style":228},[227],[67,1389,1391],{"className":1390},[88],"75.6",[67,1393,1266],{"className":1394},[227],[67,1396,1399],{"className":1397},[88,1398],"text",[67,1400,1402],{"className":1401},[88],"MPa",[67,1404,385],{"className":1405},[384],[67,1407,1409],{"className":1408},[346],[67,1410,1412],{"className":1411,"style":1144},[350],[67,1413],{},[11,1415,1416],{},"That is a third of the yield strength of S235, from a summer's afternoon, if nothing is\nallowed to move. It is why expansion joints exist, and why a model whose supports restrain\nthe structure more than the real bearings do reports thermal forces the structure will\nnever see.",[11,1418,1419,1420,1546],{},"The same member free at one end extends by ",[67,1421,1423],{"className":1422},[70],[67,1424,1426,1452,1470,1525],{"className":1425,"ariaHidden":75},[74],[67,1427,1429,1433,1437,1440,1443,1446,1449],{"className":1428},[79],[67,1430],{"className":1431,"style":1432},[83],"height:0.7278em;vertical-align:-0.0833em;",[67,1434,1436],{"className":1435},[88],"20",[67,1438],{"className":1439,"style":251},[227],[67,1441,1319],{"className":1442},[88],[67,1444],{"className":1445,"style":398},[227],[67,1447,1190],{"className":1448},[402],[67,1450],{"className":1451,"style":398},[227],[67,1453,1455,1458,1461,1464,1467],{"className":1454},[79],[67,1456],{"className":1457,"style":1432},[83],[67,1459,1262],{"className":1460},[88],[67,1462],{"className":1463,"style":398},[227],[67,1465,1190],{"className":1466},[402],[67,1468],{"className":1469,"style":398},[227],[67,1471,1473,1477,1480,1516,1519,1522],{"className":1472},[79],[67,1474],{"className":1475,"style":1476},[83],"height:0.8141em;",[67,1478,1197],{"className":1479},[88],[67,1481,1483,1486],{"className":1482},[88],[67,1484,1204],{"className":1485},[88],[67,1487,1489],{"className":1488},[337],[67,1490,1492],{"className":1491},[341],[67,1493,1495],{"className":1494},[346],[67,1496,1498],{"className":1497,"style":1476},[350],[67,1499,1501,1504],{"style":1500},"top:-3.063em;margin-right:0.05em;",[67,1502],{"className":1503,"style":359},[358],[67,1505,1507],{"className":1506},[363,364,365,366],[67,1508,1510,1513],{"className":1509},[88,366],[67,1511,284],{"className":1512},[88,366],[67,1514,1236],{"className":1515},[88,366],[67,1517],{"className":1518,"style":228},[227],[67,1520,233],{"className":1521},[232],[67,1523],{"className":1524,"style":228},[227],[67,1526,1528,1532,1536,1539],{"className":1527},[79],[67,1529],{"className":1530,"style":1531},[83],"height:0.6444em;",[67,1533,1535],{"className":1534},[88],"7.2",[67,1537,1266],{"className":1538},[227],[67,1540,1542],{"className":1541},[88,1398],[67,1543,1545],{"className":1544},[88],"mm","\nand carries no force at all.",[31,1548,1550],{"id":1549},"modelling-decisions","Modelling decisions",[11,1552,1553,1556],{},[18,1554,1555],{},"Supports decide everything."," A temperature load tests the support idealisation harder\nthan any gravity case. A row of pinned bases on a long building restrains the whole floor\nplate against expansion; real base plates on slotted holes, or real columns bending, do\nnot.",[1558,1559,1561],"callout",{"type":1560},"warning",[11,1562,1563],{},"Where thermal results look enormous, the question is whether the restraint is real, not\nwhether the load is.",[11,1565,1566,1569,1570,1627],{},[18,1567,1568],{},"Springs are the realistic middle."," A column that bends to let the floor expand is a\nlateral spring of stiffness ",[67,1571,1573],{"className":1572},[70],[67,1574,1576],{"className":1575,"ariaHidden":75},[74],[67,1577,1579,1583,1587,1590,1593,1597],{"className":1578},[79],[67,1580],{"className":1581,"style":1582},[83],"height:1.0641em;vertical-align:-0.25em;",[67,1584,1586],{"className":1585},[88],"3",[67,1588,289],{"className":1589,"style":288},[88,93],[67,1591,791],{"className":1592,"style":790},[88,93],[67,1594,1596],{"className":1595},[88],"\u002F",[67,1598,1600,1604],{"className":1599},[88],[67,1601,1603],{"className":1602},[88,93],"L",[67,1605,1607],{"className":1606},[337],[67,1608,1610],{"className":1609},[341],[67,1611,1613],{"className":1612},[346],[67,1614,1616],{"className":1615,"style":1476},[350],[67,1617,1618,1621],{"style":1500},[67,1619],{"className":1620,"style":359},[358],[67,1622,1624],{"className":1623},[363,364,365,366],[67,1625,1586],{"className":1626},[88,366],"; a bearing with a known shear stiffness is a spring\nof that stiffness. Replacing the pin with the spring turns an unbounded thermal force into\na finite one that can be checked.",[11,1629,1630,1633],{},[18,1631,1632],{},"Gradients on surfaces"," work the same way as on members: a slab warmer on top than below\ntries to bow, and the restraint against bowing (its own continuity over supports, or a wall\nalong its edge) is where the moment comes from.",[11,1635,1636,1639,1640,1644],{},[18,1637,1638],{},"One temperature per load case."," Summer and winter are two cases, in an exclusive group,\nso that the ",[988,1641,1643],{"href":1642},"\u002Fkb\u002Floads\u002Fcombinations","combination generator"," treats them as alternatives\ninstead of adding a rise to a fall.",[31,1646,1648],{"id":1647},"combining","Combining",[11,1650,1651,1652,1727,1728,1727,1799,1870],{},"Under EN 1990 thermal actions are variable actions with their own ψ factors\n(",[67,1653,1655],{"className":1654},[70],[67,1656,1658,1717],{"className":1657,"ariaHidden":75},[74],[67,1659,1661,1665,1708,1711,1714],{"className":1660},[79],[67,1662],{"className":1663,"style":1664},[83],"height:0.8889em;vertical-align:-0.1944em;",[67,1666,1668,1672],{"className":1667},[88],[67,1669,1671],{"className":1670,"style":1133},[88,93],"ψ",[67,1673,1675],{"className":1674},[337],[67,1676,1678,1700],{"className":1677},[341,342],[67,1679,1681,1697],{"className":1680},[346],[67,1682,1685],{"className":1683,"style":1684},[350],"height:0.3011em;",[67,1686,1688,1691],{"style":1687},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[67,1689],{"className":1690,"style":359},[358],[67,1692,1694],{"className":1693},[363,364,365,366],[67,1695,1204],{"className":1696},[88,366],[67,1698,385],{"className":1699},[384],[67,1701,1703],{"className":1702},[346],[67,1704,1706],{"className":1705,"style":473},[350],[67,1707],{},[67,1709],{"className":1710,"style":228},[227],[67,1712,233],{"className":1713},[232],[67,1715],{"className":1716,"style":228},[227],[67,1718,1720,1723],{"className":1719},[79],[67,1721],{"className":1722,"style":1531},[83],[67,1724,1726],{"className":1725},[88],"0.6",", ",[67,1729,1731],{"className":1730},[70],[67,1732,1734,1789],{"className":1733,"ariaHidden":75},[74],[67,1735,1737,1740,1780,1783,1786],{"className":1736},[79],[67,1738],{"className":1739,"style":1664},[83],[67,1741,1743,1746],{"className":1742},[88],[67,1744,1671],{"className":1745,"style":1133},[88,93],[67,1747,1749],{"className":1748},[337],[67,1750,1752,1772],{"className":1751},[341,342],[67,1753,1755,1769],{"className":1754},[346],[67,1756,1758],{"className":1757,"style":1684},[350],[67,1759,1760,1763],{"style":1687},[67,1761],{"className":1762,"style":359},[358],[67,1764,1766],{"className":1765},[363,364,365,366],[67,1767,1197],{"className":1768},[88,366],[67,1770,385],{"className":1771},[384],[67,1773,1775],{"className":1774},[346],[67,1776,1778],{"className":1777,"style":473},[350],[67,1779],{},[67,1781],{"className":1782,"style":228},[227],[67,1784,233],{"className":1785},[232],[67,1787],{"className":1788,"style":228},[227],[67,1790,1792,1795],{"className":1791},[79],[67,1793],{"className":1794,"style":1531},[83],[67,1796,1798],{"className":1797},[88],"0.5",[67,1800,1802],{"className":1801},[70],[67,1803,1805,1861],{"className":1804,"ariaHidden":75},[74],[67,1806,1808,1811,1852,1855,1858],{"className":1807},[79],[67,1809],{"className":1810,"style":1664},[83],[67,1812,1814,1817],{"className":1813},[88],[67,1815,1671],{"className":1816,"style":1133},[88,93],[67,1818,1820],{"className":1819},[337],[67,1821,1823,1844],{"className":1822},[341,342],[67,1824,1826,1841],{"className":1825},[346],[67,1827,1829],{"className":1828,"style":1684},[350],[67,1830,1831,1834],{"style":1687},[67,1832],{"className":1833,"style":359},[358],[67,1835,1837],{"className":1836},[363,364,365,366],[67,1838,1840],{"className":1839},[88,366],"2",[67,1842,385],{"className":1843},[384],[67,1845,1847],{"className":1846},[346],[67,1848,1850],{"className":1849,"style":473},[350],[67,1851],{},[67,1853],{"className":1854,"style":228},[227],[67,1856,233],{"className":1857},[232],[67,1859],{"className":1860,"style":228},[227],[67,1862,1864,1867],{"className":1863},[79],[67,1865],{"className":1866,"style":1531},[83],[67,1868,1204],{"className":1869},[88]," in the recommended values), and they appear\nin combinations as a leading or an accompanying action like any other. The generator\nhandles that once the case is in the right group; the values are editable fields on the\ncombination, and the national annex may change them.",[11,1872,1873],{},"Thermal actions usually govern nothing at ULS in a building frame and quite a lot at SLS:\nmovement at joints, cracking in a restrained slab, the force on a bearing. Read them under\nthe serviceability combinations first.",[31,1875,1877],{"id":1876},"checking-a-thermal-result","Checking a thermal result",[1558,1879,1881],{"type":1880},"check",[1882,1883,1884,1891,1897,1930],"ul",{},[1885,1886,1887,1890],"li",{},[18,1888,1889],{},"Sum of reactions is zero"," under a temperature case alone, in every direction: the\naction is self-equilibrating. Non-zero individual reactions mean a restraint is carrying\nit, which is correct, but the total across all restraints still balances to nothing.",[1885,1892,1893,1896],{},[18,1894,1895],{},"An unrestrained member reports displacement and no force."," Not a bug.",[1885,1898,1899,1929],{},[18,1900,1901,1902],{},"A fully restrained member reports ",[67,1903,1905],{"className":1904},[70],[67,1906,1908],{"className":1907,"ariaHidden":75},[74],[67,1909,1911,1914,1917,1920,1923,1926],{"className":1910},[79],[67,1912],{"className":1913,"style":84},[83],[67,1915,289],{"className":1916,"style":288},[88,93],[67,1918,293],{"className":1919},[88,93],[67,1921,247],{"className":1922,"style":246},[88,93],[67,1924,89],{"className":1925},[88],[67,1927,95],{"className":1928,"style":94},[88,93]," in axial force, to a hand\ncalculation.",[1885,1931,1932,1935],{},[18,1933,1934],{},"Deflected shape"," under a gradient bows the way the hot face expands: hot on top, the\nbeam hogs.",[31,1937,1939],{"id":1938},"what-is-not-modelled","What is not modelled",[1882,1941,1942,1948,1954],{},[1885,1943,1944,1947],{},[18,1945,1946],{},"Fire."," The stiffness and strength reductions at elevated temperature are not applied;\nthe material is linear elastic at any temperature you enter.",[1885,1949,1950,1953],{},[18,1951,1952],{},"Transient heat flow."," The temperature you enter is the temperature; nothing is\ncomputed from ambient conditions or exposure.",[1885,1955,1956,1959],{},[18,1957,1958],{},"Non-linear gradients"," through the depth. The gradient is linear, which is what\nEN 1991-1-5's simplified approach uses for buildings.",[31,1961,1963],{"id":1962},"related","Related",[11,1965,1966,1970,1971,1975,1976,1980],{},[988,1967,1969],{"href":1968},"\u002Fkb\u002Floads\u002Fload-cases","Load cases"," for the load types alongside temperature;\n",[988,1972,1974],{"href":1973},"\u002Fkb\u002Fmodeling\u002Fsupports-and-releases","Supports and releases"," for the springs that make\nthermal results finite; ",[988,1977,1979],{"href":1978},"\u002Fkb\u002Floads\u002Fload-cases#load-types","Prescribed displacements"," are\nthe other self-equilibrating action, and settlement behaves in the same way.",{"title":1982,"searchDepth":1983,"depth":1983,"links":1984},"",2,[1985,1986,1987,1988,1989,1990,1991,1992],{"id":33,"depth":1983,"text":34},{"id":967,"depth":1983,"text":968},{"id":1067,"depth":1983,"text":1068},{"id":1549,"depth":1983,"text":1550},{"id":1647,"depth":1983,"text":1648},{"id":1876,"depth":1983,"text":1877},{"id":1938,"depth":1983,"text":1939},{"id":1962,"depth":1983,"text":1963},"Uniform temperature change and through-depth gradients — what each does to a free and a restrained structure, and the coefficients to use.","md",false,{},true,null,5,"\u002Fkb\u002Floads\u002Ftemperature-loads",{"title":6,"description":1993},{"loc":2000},"kb\u002Floads\u002Ftemperature-loads","CWzVRXxxN7j8ek3lC1EoKAeZU8lDVef81OWU5xkexQI",{"sections":2006,"extras":2312,"flat":2325},[2007,2042,2083,2102,2131,2162,2189,2220,2247,2274,2289],{"path":2008,"slug":2009,"title":2010,"description":2011,"icon":2012,"articles":2013},"\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",[2014,2018,2022,2026,2030,2034,2038],{"path":2015,"title":2016,"description":2017,"translated":1997},"\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":2019,"title":2020,"description":2021,"translated":1997},"\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":2023,"title":2024,"description":2025,"translated":1997},"\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":2027,"title":2028,"description":2029,"translated":1997},"\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":2031,"title":2032,"description":2033,"translated":1997},"\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":2035,"title":2036,"description":2037,"translated":1997},"\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":2039,"title":2040,"description":2041,"translated":1997},"\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":2043,"slug":2044,"title":2045,"description":2046,"icon":2047,"articles":2048},"\u002Fkb\u002Fmodeling","modeling","Modeling","Bars, beams, 3D frames, slabs and walls. Geometry, sections, supports and releases that behave like the real structure.","lucide:frame",[2049,2053,2057,2061,2065,2068,2072,2076,2079],{"path":2050,"title":2051,"description":2052,"translated":1997},"\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":2054,"title":2055,"description":2056,"translated":1997},"\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":2058,"title":2059,"description":2060,"translated":1997},"\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":2062,"title":2063,"description":2064,"translated":1997},"\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":990,"title":2066,"description":2067,"translated":1997},"Sections & materials","What a section and a material contribute to the stiffness matrix and the design checks, and the values worth checking twice.",{"path":2069,"title":2070,"description":2071,"translated":1997},"\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":2073,"title":2074,"description":2075,"translated":1997},"\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":1973,"title":2077,"description":2078,"translated":1997},"Supports & releases","Pins, fixities, springs and end releases — what each one does to the stiffness matrix, and when each is right.",{"path":2080,"title":2081,"description":2082,"translated":1997},"\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":2084,"slug":2085,"title":2086,"description":2087,"icon":2088,"articles":2089},"\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",[2090,2094,2098],{"path":2091,"title":2092,"description":2093,"translated":1997},"\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":2095,"title":2096,"description":2097,"translated":1997},"\u002Fkb\u002Fmeshing\u002Frefinement","Local refinement","Where to spend elements, where not to bother, and how to refine without wrecking element shape.",{"path":2099,"title":2100,"description":2101,"translated":1997},"\u002Fkb\u002Fmeshing\u002Fquality-checks","Mesh quality","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":2103,"slug":2104,"title":2105,"description":2106,"icon":2107,"articles":2108},"\u002Fkb\u002Floads","loads","Loads & combinations","Build load cases, generate code combinations automatically and find out which one actually governs.","lucide:arrow-down-to-line",[2109,2113,2116,2120,2122,2126,2127],{"path":2110,"title":2111,"description":2112,"translated":1997},"\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":1642,"title":2114,"description":2115,"translated":1997},"Automatic combinations","Generating EN 1990 and ASCE 7 combinations, understanding the equations behind them, and reading the generated set critically.",{"path":2117,"title":2118,"description":2119,"translated":1997},"\u002Fkb\u002Floads\u002Fenvelopes","Envelopes","Extracting the governing value across dozens of combinations without reading every one — and the traps in doing so.",{"path":1968,"title":1969,"description":2121,"translated":1997},"Actions, self-weight, imposed loads and load arrangements — how to build cases that stay separable.",{"path":2123,"title":2124,"description":2125,"translated":1997},"\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":2000,"title":6,"description":1993,"translated":1997},{"path":2128,"title":2129,"description":2130,"translated":1997},"\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":2132,"slug":2133,"title":2134,"description":2135,"icon":2136,"articles":2137},"\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",[2138,2142,2146,2150,2154,2158],{"path":2139,"title":2140,"description":2141,"translated":1997},"\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":2143,"title":2144,"description":2145,"translated":1997},"\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":2147,"title":2148,"description":2149,"translated":1997},"\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":2151,"title":2152,"description":2153,"translated":1997},"\u002Fkb\u002Fanalysis\u002Fmodal","Modal analysis","Natural frequencies and mode shapes — mass modelling, participation factors and what the numbers are good for.",{"path":2155,"title":2156,"description":2157,"translated":1997},"\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":2159,"title":2160,"description":2161,"translated":1997},"\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":2163,"slug":2164,"title":2165,"description":2166,"icon":2167,"articles":2168},"\u002Fkb\u002Fdesign-checks","design-checks","Design checks","Utilisation ratios, governing cases and the clause behind every number a check reports.","lucide:clipboard-check",[2169,2173,2177,2181,2185],{"path":2170,"title":2171,"description":2172,"translated":1997},"\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":2174,"title":2175,"description":2176,"translated":1997},"\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":2178,"title":2179,"description":2180,"translated":1997},"\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":2182,"title":2183,"description":2184,"translated":1997},"\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":2186,"title":2187,"description":2188,"translated":1997},"\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":2190,"slug":2191,"title":2192,"description":2193,"icon":2194,"articles":2195},"\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",[2196,2200,2204,2208,2212,2216],{"path":2197,"title":2198,"description":2199,"translated":1997},"\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":2201,"title":2202,"description":2203,"translated":1997},"\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":2205,"title":2206,"description":2207,"translated":1997},"\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":2209,"title":2210,"description":2211,"translated":1997},"\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":2213,"title":2214,"description":2215,"translated":1997},"\u002Fkb\u002Freports\u002Fresult-tables","Result tables","Filtering, sorting and extracting numbers — getting the value you need out of a solved model without scrolling.",{"path":2217,"title":2218,"description":2219,"translated":1997},"\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":2221,"slug":2222,"title":2223,"description":2224,"icon":2225,"articles":2226},"\u002Fkb\u002Fcollaboration","collaboration","Collaboration & sync","Shared models, real-time editing, and offline edits that merge cleanly when you reconnect.","lucide:users-round",[2227,2231,2235,2239,2243],{"path":2228,"title":2229,"description":2230,"translated":1997},"\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":2232,"title":2233,"description":2234,"translated":1997},"\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":2236,"title":2237,"description":2238,"translated":1997},"\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":2240,"title":2241,"description":2242,"translated":1997},"\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":2244,"title":2245,"description":2246,"translated":1997},"\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":2248,"slug":2249,"title":2250,"description":2251,"icon":2252,"articles":2253},"\u002Fkb\u002Ftheory","theory","Theory notes","The mechanics inside the solver — element formulations, sign conventions, numerical assumptions and their limits.","lucide:sigma",[2254,2258,2262,2266,2270],{"path":2255,"title":2256,"description":2257,"translated":1997},"\u002Fkb\u002Ftheory\u002Felement-formulations","Element formulations","Degrees of freedom, interpolation and limits for every element type in the solver — what each one can represent and what it cannot.",{"path":2259,"title":2260,"description":2261,"translated":1997},"\u002Fkb\u002Ftheory\u002Fglossary","Glossary","Finite element and structural terms as Elementarium uses them, from degrees of freedom to MITC4 and utilisation, each linked to its page.",{"path":2263,"title":2264,"description":2265,"translated":1997},"\u002Fkb\u002Ftheory\u002Fsign-conventions","Sign conventions","Axes, positive directions and how to read a diagram without guessing — the page that prevents most result confusion.",{"path":2267,"title":2268,"description":2269,"translated":1997},"\u002Fkb\u002Ftheory\u002Fdirect-stiffness-method","The direct stiffness method","How a finite element solver turns a model into K u = f and back — stiffness, transformation, assembly, constraints, solution and recovery.",{"path":2271,"title":2272,"description":2273,"translated":1997},"\u002Fkb\u002Ftheory\u002Fwinkler-foundations","Winkler foundations","The bedding model behind elastic foundations — what it assumes, how to choose a modulus, and precisely where the idealisation stops being true.",{"path":2275,"slug":2276,"title":2277,"description":2278,"icon":2279,"articles":2280},"\u002Fkb\u002Ftroubleshooting","troubleshooting","Troubleshooting","Solver errors, unstable models and results that look wrong — with the usual causes listed first.","lucide:life-buoy",[2281,2285],{"path":2282,"title":2283,"description":2284,"translated":1997},"\u002Fkb\u002Ftroubleshooting\u002Fsolver-errors","Solver errors","What each class of solver message means, what usually causes it, and what to do next.",{"path":2286,"title":2287,"description":2288,"translated":1997},"\u002Fkb\u002Ftroubleshooting\u002Fsingular-stiffness-matrix","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":2290,"slug":2291,"title":2292,"description":2293,"icon":2294,"articles":2295},"\u002Fkb\u002Faccount","account","Account & billing","Plans, limits, invoices, and what happens to your projects when a subscription ends.","lucide:credit-card",[2296,2300,2304,2308],{"path":2297,"title":2298,"description":2299,"translated":1997},"\u002Fkb\u002Faccount\u002Finvoices","Invoices & VAT","Billing details, receipts, VAT handling and how to get an invoice your accounts department will accept.",{"path":2301,"title":2302,"description":2303,"translated":1997},"\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":2305,"title":2306,"description":2307,"translated":1997},"\u002Fkb\u002Faccount\u002Fplans","Plans & limits","What the free plan includes, what Pro adds, and how the caps are actually measured.",{"path":2309,"title":2310,"description":2311,"translated":1997},"\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.",[2313,2317,2321],{"path":2314,"title":2315,"description":2316,"translated":1997},"\u002Fkb\u002Ffaq","Frequently asked questions","The questions engineers ask before they trust a new finite element package — answered directly.",{"path":2318,"title":2319,"description":2320,"translated":1997},"\u002Fkb\u002Frelease-notes","Release notes","What shipped in the tab, and what it changes in your models.",{"path":2322,"title":2323,"description":2324,"translated":1997},"\u002Fkb\u002Fall","All articles","Every article in the Elementarium knowledge base, grouped by section.",[2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395],{"path":2008,"title":2010,"description":2011,"translated":1997},{"path":2015,"title":2016,"description":2017,"translated":1997},{"path":2019,"title":2020,"description":2021,"translated":1997},{"path":2023,"title":2024,"description":2025,"translated":1997},{"path":2027,"title":2028,"description":2029,"translated":1997},{"path":2031,"title":2032,"description":2033,"translated":1997},{"path":2035,"title":2036,"description":2037,"translated":1997},{"path":2039,"title":2040,"description":2041,"translated":1997},{"path":2043,"title":2045,"description":2046,"translated":1997},{"path":2050,"title":2051,"description":2052,"translated":1997},{"path":2054,"title":2055,"description":2056,"translated":1997},{"path":2058,"title":2059,"description":2060,"translated":1997},{"path":2062,"title":2063,"description":2064,"translated":1997},{"path":990,"title":2066,"description":2067,"translated":1997},{"path":2069,"title":2070,"description":2071,"translated":1997},{"path":2073,"title":2074,"description":2075,"translated":1997},{"path":1973,"title":2077,"description":2078,"translated":1997},{"path":2080,"title":2081,"description":2082,"translated":1997},{"path":2084,"title":2086,"description":2087,"translated":1997},{"path":2091,"title":2092,"description":2093,"translated":1997},{"path":2095,"title":2096,"description":2097,"translated":1997},{"path":2099,"title":2100,"description":2101,"translated":1997},{"path":2103,"title":2105,"description":2106,"translated":1997},{"path":2110,"title":2111,"description":2112,"translated":1997},{"path":1642,"title":2114,"description":2115,"translated":1997},{"path":2117,"title":2118,"description":2119,"translated":1997},{"path":1968,"title":1969,"description":2121,"translated":1997},{"path":2123,"title":2124,"description":2125,"translated":1997},{"path":2000,"title":6,"description":1993,"translated":1997},{"path":2128,"title":2129,"description":2130,"translated":1997},{"path":2132,"title":2134,"description":2135,"translated":1997},{"path":2139,"title":2140,"description":2141,"translated":1997},{"path":2143,"title":2144,"description":2145,"translated":1997},{"path":2147,"title":2148,"description":2149,"translated":1997},{"path":2151,"title":2152,"description":2153,"translated":1997},{"path":2155,"title":2156,"description":2157,"translated":1997},{"path":2159,"title":2160,"description":2161,"translated":1997},{"path":2163,"title":2165,"description":2166,"translated":1997},{"path":2170,"title":2171,"description":2172,"translated":1997},{"path":2174,"title":2175,"description":2176,"translated":1997},{"path":2178,"title":2179,"description":2180,"translated":1997},{"path":2182,"title":2183,"description":2184,"translated":1997},{"path":2186,"title":2187,"description":2188,"translated":1997},{"path":2190,"title":2192,"description":2193,"translated":1997},{"path":2197,"title":2198,"description":2199,"translated":1997},{"path":2201,"title":2202,"description":2203,"translated":1997},{"path":2205,"title":2206,"description":2207,"translated":1997},{"path":2209,"title":2210,"description":2211,"translated":1997},{"path":2213,"title":2214,"description":2215,"translated":1997},{"path":2217,"title":2218,"description":2219,"translated":1997},{"path":2221,"title":2223,"description":2224,"translated":1997},{"path":2228,"title":2229,"description":2230,"translated":1997},{"path":2232,"title":2233,"description":2234,"translated":1997},{"path":2236,"title":2237,"description":2238,"translated":1997},{"path":2240,"title":2241,"description":2242,"translated":1997},{"path":2244,"title":2245,"description":2246,"translated":1997},{"path":2248,"title":2250,"description":2251,"translated":1997},{"path":2255,"title":2256,"description":2257,"translated":1997},{"path":2259,"title":2260,"description":2261,"translated":1997},{"path":2263,"title":2264,"description":2265,"translated":1997},{"path":2267,"title":2268,"description":2269,"translated":1997},{"path":2271,"title":2272,"description":2273,"translated":1997},{"path":2275,"title":2277,"description":2278,"translated":1997},{"path":2282,"title":2283,"description":2284,"translated":1997},{"path":2286,"title":2287,"description":2288,"translated":1997},{"path":2290,"title":2292,"description":2293,"translated":1997},{"path":2297,"title":2298,"description":2299,"translated":1997},{"path":2301,"title":2302,"description":2303,"translated":1997},{"path":2305,"title":2306,"description":2307,"translated":1997},{"path":2309,"title":2310,"description":2311,"translated":1997},1792160761677]