{"id":10850,"date":"2023-11-13T13:06:58","date_gmt":"2023-11-13T13:06:58","guid":{"rendered":"https:\/\/support.buildsoft.eu\/?post_type=ht_kb&p=10850"},"modified":"2026-07-16T14:48:55","modified_gmt":"2026-07-16T14:48:55","slug":"sls-09-four-sides-simply-supported-plate-under-uniform-load","status":"publish","type":"ht_kb","link":"https:\/\/support.buildsoft.eu\/nl\/knowledge-base\/sls-09-four-sides-simply-supported-plate-under-uniform-load\/","title":{"rendered":"SLS 09: Four-sides simply supported plate under uniform load"},"content":{"rendered":"

Description<\/h2>\n

\"\"<\/p>\n

Length a =1m. Different ratio’s b\/a are tested by changing the length of b in each model.<\/p>\n

\n\n\n\n\n\n\n\n\n\n
Material<\/th>\n<\/td>\nModulus of elasticity<\/td>\n\"E = 100 N/mm^2\"<\/td>\n<\/tr>\n
Poisson’s ratio<\/td>\n\"\nu= 0,3\"<\/td>\n<\/tr>\n
Geometry<\/th>\nCross-section<\/td>\nThickness<\/td>\n\"e=10 mm\"<\/td>\n<\/tr>\n
Boundary conditions<\/td>\nAlong all edges<\/td>\nSimply supported<\/td>\n<\/tr>\n
Loads<\/th>\n<\/td>\nOn the entire surface<\/td>\n\"p=0.01 N/m^2\"<\/td>\n<\/tr>\n
Mesh<\/th>\n<\/td>\nMaximum element size<\/td>\n\"0.10m\"<\/td>\n<\/tr>\n
<\/td>\nMinimum element size<\/td>\n\"0.00m\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Independent reference results<\/h2>\n
<\/span>Open handcalculations<\/div>
\n
\n\n\n\n\n\n\n
b\/a<\/th>\n<\/th>\n<\/th>\n<\/th>\n<\/tr>\n
1.0<\/td>\n\"\alpha= 0.0443\"<\/td>\n\"\beta= 0.0479\"<\/td>\n\"\beta_1= 0.0479\"<\/td>\n<\/tr>\n
2.0<\/td>\n\"\alpha= 0.0443\"<\/td>\n\"\beta= 0.1017\"<\/td>\n\"\beta_1= 0.0464\"<\/td>\n<\/tr>\n
5.0<\/td>\n\"\alpha= 0.0443\"<\/td>\n\"\beta= 0.1246\"<\/td>\n\"\beta_1= 0.0375\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

  <\/span>   <\/span>\"\[\delta_y=\frac{\alpha \cdot p \cdot a^{4}}{E \cdot e^3}\]\"<\/p>\n

  <\/span>   <\/span>\"\[M_{xx,max}=\beta \cdot p \cdot a^{4}\]\"<\/p>\n

  <\/span>   <\/span>\"\[M_{zz,max}=\beta_1 \cdot p \cdot a^{4}\]\"<\/p>\n<\/div><\/div><\/div>\n

Diamonds results and comparison<\/h2>\n

\"\"<\/p>\n

Deformation \"\delta_y\" in Diamonds<\/strong><\/p>\n

\n\n\n\n\n\n\n\n\n\n\n\n\n
Case<\/th>\nWhich result<\/th>\nIndependent reference<\/th>\nDiamonds<\/th>\nDifference<\/th>\n<\/tr>\n
b=1m<\/td>\nDeformation \"\delta_y\"<\/td>\n4.43mm<\/td>\n0,163mm<\/td>\n-0.77%<\/td>\n<\/tr>\n
<\/td>\nBending moment \"M_{xx}\"<\/td>\n0.479N\/m\/m<\/td>\n0.4818N\/m\/m<\/td>\n0.58%<\/td>\n<\/tr>\n
<\/td>\nBending moment \"M_{zz}\"<\/td>\n0.479N\/m\/m<\/td>\n0.4818N\/m\/m<\/td>\n0.58%<\/td>\n<\/tr>\n
b=2m<\/td>\nDeformation \"\delta_y\"<\/td>\n11.06mm<\/td>\n10.993mm<\/td>\n-0.61%<\/td>\n<\/tr>\n
<\/td>\nBending moment \"M_{xx}\"<\/td>\n0.464N\/m\/m<\/td>\n0.4697N\/m\/m<\/td>\n1.23%<\/td>\n<\/tr>\n
<\/td>\nBending moment \"M_{zz}\"<\/td>\n1.017\/m\/m<\/td>\n1.0214N\/m\/m<\/td>\n0.43%<\/td>\n<\/tr>\n
b=5m<\/td>\nDeformation \"\delta_y\"<\/td>\n14.1632mm<\/td>\n14.081mm<\/td>\n-0.58%<\/td>\n<\/tr>\n
<\/td>\nBending moment \"M_{xx}\"<\/td>\n0.375N\/m\/m<\/td>\n0.3794N\/m\/m<\/td>\n1.17%<\/td>\n<\/tr>\n
<\/td>\nBending moment \"M_{zz}\"<\/td>\n1.246N\/m\/m<\/td>\n1.2451N\/m\/m<\/td>\n-0.07%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

References<\/h2>\n
\n
    \n
  • M\u00e9caniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SSLS 24: plaque rectangulaire sur appuis simples avec chargement uniforme.
    \n<\/i>Note: the modulus of elasticity and load imposed in the Afnor-example, felt outside the boundaries of Diamonds. As a work around, both parameters were multiplied by 10 and the results were recalculated accordingly.<\/li>\n
  • Timoshenko, S., & Woinowsky-Krieger, S. (1959). Theory of plates and shells<\/i>. McGraw-Hill Publishing Company.<\/li>\n<\/ul>\n
      \n
    • Tested in Diamonds 2026.<\/li>\n<\/ul>\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"

      Description Length a =1m. Different ratio’s b\/a are tested by changing the length of b in each model. Independent reference results Diamonds results and comparison Deformation in Diamonds References M\u00e9caniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SSLS 24: plaque rectangulaire sur appuis simples…<\/p>\n","protected":false},"author":3,"comment_status":"closed","ping_status":"closed","template":"","format":"standard","meta":[],"ht-kb-category":[1205],"ht-kb-tag":[],"_links":{"self":[{"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb\/10850"}],"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=10850"}],"version-history":[{"count":3,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb\/10850\/revisions"}],"predecessor-version":[{"id":30579,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb\/10850\/revisions\/30579"}],"wp:attachment":[{"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/media?parent=10850"}],"wp:term":[{"taxonomy":"ht_kb_category","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb-category?post=10850"},{"taxonomy":"ht_kb_tag","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb-tag?post=10850"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}