{"id":13130,"date":"2024-07-31T15:24:44","date_gmt":"2024-07-31T15:24:44","guid":{"rendered":"https:\/\/support.buildsoft.eu\/?post_type=ht_kb&p=13130"},"modified":"2025-11-26T14:00:00","modified_gmt":"2025-11-26T14:00:00","slug":"sll-08-axial-force-in-eccentric-beam","status":"publish","type":"ht_kb","link":"https:\/\/support.buildsoft.eu\/fr\/knowledge-base\/sll-08-axial-force-in-eccentric-beam\/","title":{"rendered":"SLL 08: axial force in eccentric beam"},"content":{"rendered":"

Description<\/h2>\n

\"\"<\/p>\n

\n\n\n\n\n\n\n
Material<\/th>\n<\/td>\nConcrete C25\/30<\/td>\n<\/tr>\n
Geometry<\/th>\nbeam<\/td>\n\"b=200mm\" & \"h=500mm\"<\/td>\n<\/tr>\n
one way plate<\/td>\n\"t=200mm\"<\/td>\n<\/tr>\n
Loads<\/th>\nSelf-weight beam & plate<\/td>\nresulting in a total line load \"q=23,6kN/m\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

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

The horizontal deformations of the beam at the bottom are zero:<\/p>\n

  <\/span>   <\/span>\"\[\Delta x_{at.the.bottom}=\Delta x_{.M_q}+\Delta x_{.M_H}+\Delta x_{.N_H}=0\]\"<\/p>\n

With \"\Delta x_{.M_q}\" the horizontal displacement at the bottom due to the bending moment in the beam:<\/p>\n

  <\/span>   <\/span>\"\[\Delta x_{.M_q}=\int_{0}^{L} \varepsilon _{x.M_q}dx=\int_{0}^{L} \frac{\sigma _{x.M_q}}{E}dx=\int_{0}^{L/2} \frac{M_{p(x)} \frac{h}{2}}{E}dx=\int_{0}^{L/2} \frac{\left ( \frac{qL}{2} x - \frac{qx^2}{2} \right )h}{E}dx\]\"<\/p>\n

  <\/span>   <\/span>\"\[=\int_{0}^{L/2} \frac{\left ( \frac{qL}{2} x - \frac{qx^2}{2} \right )h}{E}dx=\frac{h}{EI}\left [ \frac{qL^3}{16}-\frac{qL^3}{48} \right ]=\frac{qL^3h}{24EI}\]\"<\/p>\n

Because the horizontal reaction force is at the bottom of the beam, it causes a bending moment round the neutral axis. Also this bending moment will cause horizontal displacement:<\/p>\n

  <\/span>   <\/span>\"\[\Delta x_{.M_H}=\int_{0}^{L} \frac{\left ( -H \frac{h}{2} \right )\frac{h}{2}}{EI}dx=\frac{-Hh^2L}{4EI}\]\"<\/p>\n

With \"\Delta x_{.N_H}\" the prevented horizontal displacement at the bottom due to the axial force in the beam:<\/p>\n

  <\/span>   <\/span>\"\[\Delta x_{.N_H} =\int_{0}^{L}\frac{-H}{EA}dx=\frac{-HL}{EA}\]\"<\/p>\n

This results in:<\/p>\n

  <\/span>   <\/span>\"\[\frac{qL^3h}{24EI}-\frac{-Hh^2L}{4EI}-\frac{-HL}{EA}=0\]\"<\/p>\n

Of which H can be deducted:<\/p>\n

  <\/span>   <\/span>\"\[H=\frac{qL^3h}{24EI\left ( \frac{h^2L}{4EI}+ \frac{L}{EA}\right )}=147.6kN\]\"<\/p>\n<\/div><\/div><\/div>\n

Diamonds results and comparison<\/h2>\n

\"\"<\/p>\n

Axial force \"N\" in Diamonds<\/strong><\/p>\n

\n\n\n\n\n\n
Which result<\/th>\nIndependent reference<\/th>\nDiamonds<\/th>\nDifference<\/th>\n<\/tr>\n
Axial force \"N\" (plate model)<\/td>\n146,2kN<\/td>\n147,6kN<\/td>\n-1.0%<\/td>\n<\/tr>\n
Axial force \"N\" (beam model)<\/td>\n147,6kN<\/td>\n147,6kN<\/td>\n0.0%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

References<\/h2>\n
    \n
  • Minne, P. (2024, 26 maart). Structurele analyse van betonnen platen en wanden<\/em> [Presentatieslides 127-134; Pdf].<\/li>\n<\/ul>\n
      \n
    • Tested in Diamonds 2026.<\/li>\n<\/ul>\n\n","protected":false},"excerpt":{"rendered":"

      Description Independent reference results Diamonds results and comparison Axial force in Diamonds References Minne, P. (2024, 26 maart). Structurele analyse van betonnen platen en wanden [Presentatieslides 127-134; Pdf].<\/p>\n","protected":false},"author":3,"comment_status":"closed","ping_status":"closed","template":"","format":"standard","meta":[],"ht-kb-category":[1204],"ht-kb-tag":[],"_links":{"self":[{"href":"https:\/\/support.buildsoft.eu\/fr\/wp-json\/wp\/v2\/ht-kb\/13130"}],"collection":[{"href":"https:\/\/support.buildsoft.eu\/fr\/wp-json\/wp\/v2\/ht-kb"}],"about":[{"href":"https:\/\/support.buildsoft.eu\/fr\/wp-json\/wp\/v2\/types\/ht_kb"}],"author":[{"embeddable":true,"href":"https:\/\/support.buildsoft.eu\/fr\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/support.buildsoft.eu\/fr\/wp-json\/wp\/v2\/comments?post=13130"}],"version-history":[{"count":3,"href":"https:\/\/support.buildsoft.eu\/fr\/wp-json\/wp\/v2\/ht-kb\/13130\/revisions"}],"predecessor-version":[{"id":21283,"href":"https:\/\/support.buildsoft.eu\/fr\/wp-json\/wp\/v2\/ht-kb\/13130\/revisions\/21283"}],"wp:attachment":[{"href":"https:\/\/support.buildsoft.eu\/fr\/wp-json\/wp\/v2\/media?parent=13130"}],"wp:term":[{"taxonomy":"ht_kb_category","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/fr\/wp-json\/wp\/v2\/ht-kb-category?post=13130"},{"taxonomy":"ht_kb_tag","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/fr\/wp-json\/wp\/v2\/ht-kb-tag?post=13130"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}