{"id":15390,"date":"2025-07-10T08:20:47","date_gmt":"2025-07-10T08:20:47","guid":{"rendered":"https:\/\/support.buildsoft.eu\/?post_type=ht_kb&p=15390"},"modified":"2025-10-03T08:50:07","modified_gmt":"2025-10-03T08:50:07","slug":"sll-10-stresses-in-l-section","status":"publish","type":"ht_kb","link":"https:\/\/support.buildsoft.eu\/nl\/knowledge-base\/sll-10-stresses-in-l-section\/","title":{"rendered":"SLL 10: elastic stresses in an L-section"},"content":{"rendered":"

Description<\/h2>\n

\"\"<\/p>\n

\n\n\n\n\n
Geometry<\/th>\nL shaped cross-section:<\/td>\n\"B=100mm\"
\n\"H=200mm\"
\n\"t=10mm\"
\n\"r_1=r_2=0mm\"<\/td>\n<\/tr>\n
Load<\/th>\nDesign forces:<\/td>\n\"M_{y'}=125 \text{kNm}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
<\/span>About the stresses in Diamonds<\/div>
\nBefore we get started, we’d like to point out a few (often forgotten) properties about the stresses in Diamonds:<\/p>\n
    \n
  • The stresses in Diamonds are always elastic stresses, calculated with \"W_{el}\".
    \nEven for concrete cross-sections! Even for steel cross-section of section classes 1,2 and 4!<\/li>\n
  • The stresses are calculated based in axial force \"N\" and bending moment \"M\".\n
      \n
    • Where the bounding box of the cross-section intersects with the principal axes, the stresses in those 4 points are either due to \"N+M_U\" or due to \"N+M_V\".
      \nThose 4 points are shown in red for different cross-section shapes:
      \n\"\"
      \nThe stresses in those 4 points, correspond to the 4 buttons allowing to show stresses in the global results \"\". Note that some of those points aren’t located on the cross-section!<\/li>\n
    • When looking at the stresses, you can also request a detailed view of them by selecting the beam and then clicking on the button \"\".
      \nIn the dialog that pops up, you can hoover the mouse over the cross-section. The stresses are shown at the bottom of the dialog. These are stresses due to \"N+M_U+M_V\". Stresses due to shear or torsion, or Von Mises stresses cannot be consulted in Diamonds.
      \n\"\"<\/li>\n
    • When the cross-section is double symmetric, the local axes will coincide with the principal axes, U and V can then be replaced by z’ and y’.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div><\/div><\/div>\nThe stresses are determined in points A until H.<\/p>\n
        \n
      • y’ and z’ are the local axes of the cross-section<\/li>\n
      • U and V are the principal axes of the cross-section<\/li>\n
      • COG is the centre of gravity of the cross-section<\/li>\n
      • The distances [mm] (shown in black in the image below) will be calculated further down this article.
        \n\"\"<\/li>\n<\/ul>\n

        Independent reference results<\/h2>\n
        <\/span>Open handcalculations<\/div>
        \n

        As loads always follow the path of greatest stiffness, they will follow the principle axes of the cross-section, not the path of the local axes. Since for this L-section, the principle (U and V) and local axes (y’ and z’) don’t coincide, we’ll transform all coordinates to the principle axes.<\/p>\n

        Points A until D have the following coordinates in relation the center of gravity:<\/p>\n

          <\/span>   <\/span>\"\begin{align*}<\/p>\n

        We transform these coordinates to the principal coordinate system:<\/p>\n

          <\/span>   <\/span>\"\begin{align*}<\/p>\n

        The coordinates of points E until H can easily be defined based on the coordinates of points A until D in the principal coordinate system:<\/p>\n

          <\/span>   <\/span>\"\begin{align*}<\/p>\n

        Also the applied bending moment should be transformed to the principal coordinate system:<\/p>\n

          <\/span>   <\/span>\"\begin{align*}<\/p>\n

        This results in the following stresses:<\/p>\n

          \n
        • In point A: \"M_V\" gives compression and \"M_U\" gives compression as well.
          \nCompression has a negative sign in Diamonds, tension a positive.<\/p>\n

            <\/span>   <\/span>\"\begin{align*}<\/p>\n

          The result is compression.<\/li>\n

        • In point B: \"M_V\" gives compression and \"M_U\" gives tension.\n

            <\/span>   <\/span>\"\begin{align*}<\/p>\n

          The result is compression.<\/li>\n

        • In point C: \"M_V\" gives tension and \"M_U\" gives tension as well.\n

            <\/span>   <\/span>\"\begin{align*}<\/p>\n

          The result is tension.<\/li>\n

        • In point D: \"M_V\" gives compression and \"M_U\" gives tension.\n

            <\/span>   <\/span>\"\begin{align*}<\/p>\n

          The result is compression.<\/li>\n

        • In point E: \"M_U\" gives compression and \"M_V\" does nothing because E is on the neutral line\n

            <\/span>   <\/span>\"\begin{align*}<\/p>\n

          The result is compression.<\/li>\n

        • In point F: \"M_V\" gives tension and \"M_U\" does nothing because F is on the neutral line\n

            <\/span>   <\/span>\"\begin{align*}<\/p>\n

          The result is tension.<\/li>\n

        • In point G: \"M_V\" gives compression and \"M_U\" does nothing because G is on the neutral line\n

            <\/span>   <\/span>\"\begin{align*}<\/p>\n

          The result is tension.<\/li>\n

        • In point H: \"M_U\" gives tension and \"M_V\" does nothing because H is on the neutral line\n

            <\/span>   <\/span>\"\begin{align*}<\/p>\n

          The result is tension.<\/li>\n<\/ul>\n<\/div><\/div><\/div>\n

          Diamonds results and comparison<\/h2>\n

          \"\"<\/p>\n

          The tensile stresses \"\sigma_t\" due to \"N+M_v\" calculated by Diamonds, which corresponds to the stress in point F of the cross-section
          \n<\/strong><\/p>\n

          \"\"<\/p>\n

          Elastic stresses due to \"N+M_U+M_V\" in point A calculated by Diamonds. The location of point A can be entered by clicking on x and y.
          \nThis is a detailed view of the stresses in the corss-section.
          \n<\/strong><\/p>\n

          \n\n\n\n\n\n\n\n\n\n\n\n
          Results<\/th>\nIndependent reference<\/th>\nDiamonds<\/th>\nDifference<\/th>\n<\/tr>\n
          \"\sigma_A\"<\/td>\n-1534.87 N\/mm\u00b2<\/td>\n-1534.87 N\/mm\u00b2<\/td>\n0%<\/td>\n<\/tr>\n
          \"\sigma_B\"<\/td>\n-561.22 N\/mm\u00b2<\/td>\n-561.22 N\/mm\u00b2<\/td>\n0%<\/td>\n<\/tr>\n
          \"\sigma_C\"<\/td>\n1484.07 N\/mm\u00b2<\/td>\n1484.07 N\/mm\u00b2<\/td>\n0%<\/td>\n<\/tr>\n
          \"\sigma_D\"<\/td>\n-712.17 N\/mm\u00b2<\/td>\n-712.17 N\/mm\u00b2<\/td>\n0%<\/td>\n<\/tr>\n
          \"\sigma_E\"<\/td>\n-1203.04 N\/mm\u00b2<\/td>\n-1203.04 N\/mm\u00b2<\/td>\n0%<\/td>\n<\/tr>\n
          \"\sigma_F\"<\/td>\n905.27 N\/mm\u00b2<\/td>\n905.27 N\/mm\u00b2<\/td>\n0%<\/td>\n<\/tr>\n
          \"\sigma_G\"<\/td>\n-1442.91 N\/mm\u00b2<\/td>\n-1442.91 N\/mm\u00b2<\/td>\n0%<\/td>\n<\/tr>\n
          \"\sigma_H\"<\/td>\n819.83 N\/mm\u00b2<\/td>\n819.83 N\/mm\u00b2<\/td>\n0%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

          References<\/h2>\n
            \n
          • HIBBELER, R.C. Sterkteleer, Tweede editie<\/em>.<\/li>\n<\/ul>\n
              \n
            • Tested in Diamonds 2026.<\/li>\n<\/ul>\n\n","protected":false},"excerpt":{"rendered":"

              Description The stresses are determined in points A until H. y’ and z’ are the local axes of the cross-section U and V are the principal axes of the cross-section COG is the centre of gravity of the cross-section The distances [mm] (shown in black in the image below) will…<\/p>\n","protected":false},"author":3,"comment_status":"closed","ping_status":"closed","template":"","format":"standard","meta":[],"ht-kb-category":[1213],"ht-kb-tag":[1331,386,1313,417,418],"_links":{"self":[{"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb\/15390"}],"collection":[{"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb"}],"about":[{"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/types\/ht_kb"}],"author":[{"embeddable":true,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/comments?post=15390"}],"version-history":[{"count":3,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb\/15390\/revisions"}],"predecessor-version":[{"id":18440,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb\/15390\/revisions\/18440"}],"wp:attachment":[{"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/media?parent=15390"}],"wp:term":[{"taxonomy":"ht_kb_category","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb-category?post=15390"},{"taxonomy":"ht_kb_tag","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb-tag?post=15390"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}