{"id":10162,"date":"2023-10-26T20:45:04","date_gmt":"2023-10-26T20:45:04","guid":{"rendered":"https:\/\/support.buildsoft.eu\/?post_type=ht_kb&p=10162"},"modified":"2024-09-09T13:34:27","modified_gmt":"2024-09-09T13:34:27","slug":"sll-04-torsion-on-a-stepped-cantilever","status":"publish","type":"ht_kb","link":"https:\/\/support.buildsoft.eu\/es\/knowledge-base\/sll-04-torsion-on-a-stepped-cantilever\/","title":{"rendered":"SLL 04: torsion on a stepped cantilever"},"content":{"rendered":"

Description<\/h2>\n

\"\"<\/p>\n

\n\n\n\n\n\n\n\n\n\n\n\n
Material<\/th>\n<\/td>\nModulus of elasticity<\/td>\n\"G=80 000 N/mm^2\"<\/td>\n<\/tr>\n
Geometry<\/th>\nCross-section<\/td>\nFor bar AB<\/td>\n\u2300 80mm<\/td>\n<\/tr>\n
<\/td>\nFor bar BC<\/td>\n\u2300 60mm<\/td>\n<\/tr>\n
<\/td>\nFor bar CD<\/td>\n\u2300 40mm<\/td>\n<\/tr>\n
Boundary conditions<\/td>\nPoint A<\/td>\nFixed support<\/td>\n<\/tr>\n
Loads<\/th>\n<\/td>\nIn point B<\/td>\n\"M_x=3 kNm\"<\/td>\n<\/tr>\n
<\/th>\n<\/td>\nIn point C<\/td>\n\"M_x=2 kNm\"<\/td>\n<\/tr>\n
<\/th>\n<\/td>\nIn point D<\/td>\n\"M_x=0.8 kNm\"<\/td>\n<\/tr>\n
Mesh<\/th>\n<\/td>\nNo. of divisions<\/td>\n8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

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

  <\/span>   <\/span>\"\[I_{t.AB}=\frac{\pi \cdot D^4}{32}=\frac{\pi \cdot (80mm)^4}{32}=4.021 \cdot 10^6mm^4\]\"<\/p>\n

  <\/span>   <\/span>\"\[I_{t.BC}=\frac{\pi \cdot D^4}{32}=\frac{\pi \cdot (60mm)^4}{32}=1.272 \cdot 10^6mm^4\]\"<\/p>\n

  <\/span>   <\/span>\"\[I_{t.CD}=\frac{\pi \cdot D^4}{32}=\frac{\pi \cdot (40mm)^4}{32}=0.251 \cdot 10^6mm^4\]\"<\/p>\n

  <\/span>   <\/span>\"\[\varphi_{x.B}=\frac{L \cdot (M_{x.B}+M_{x.C}+M_{x.D})}{I_{t.AB} \cdot G}=\frac{0.5m \cdot (5.8kNm)}{4.021 \cdot 10^6mm^4 \cdot 80000N/mm^2}=0.000009rad\]\"<\/p>\n

  <\/span>   <\/span>\"\[\varphi_{x.C}=\varphi_{x.B}+\frac{L \cdot (M_{x.C}+M_{x.D})}{I_{t.BC} \cdot G}=0.000009rad+\frac{0.5m \cdot (3.8kNm)}{1.272 \cdot 10^6mm^4 \cdot 80000N/mm^2}=0.000023rad\]\"<\/p>\n

  <\/span>   <\/span>\"\[\varphi_{x.D}=\varphi_{x.B}+\varphi_{x.C}+\frac{L \cdot M_{x.D}}{I_{t.CD} \cdot G}=0.000009rad+0.000023rad+\frac{0.5m \cdot (3.8kNm)}{0.251 \cdot 10^6mm^4 \cdot 80000N/mm^2}=0.000043rad\]\"<\/p>\n<\/div><\/div><\/div>\n

Diamonds results and comparison<\/h2>\n

\"\"<\/p>\n

Angle of twist \"\varphi_x\" in Diamonds<\/strong><\/p>\n

\n\n\n\n\n\n\n
Point<\/th>\nWhich result<\/th>\nIndependent reference<\/th>\nDiamonds<\/th>\nDifference<\/th>\n<\/tr>\n
B<\/td>\nAngle of twist \"\varphi_x\"<\/td>\n0.000009rad<\/td>\n0.000009rad<\/td>\n0%<\/td>\n<\/tr>\n
C<\/td>\nAngle of twist \"\varphi_x\"<\/td>\n0.000023rad<\/td>\n0.000023rad<\/td>\n0%<\/td>\n<\/tr>\n
D<\/td>\nAngle of twist \"\varphi_x\"<\/td>\n0.000043rad<\/td>\n0.000043rad<\/td>\n0%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

References<\/h2>\n
    \n
  • Hibbeler, R. (2006). Sterkteleer, 2\/e<\/i>. Pearson Education.<\/li>\n
  • Gere J. M., and Timoshenko, S. P., Mechanics of Materials,<\/cite> 2nd Edition, PWS Engineering, Page 171, Problem 3.3 – 1<\/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 Angle of twist in Diamonds References Hibbeler, R. (2006). Sterkteleer, 2\/e. Pearson Education. Gere J. M., and Timoshenko, S. P., Mechanics of Materials, 2nd Edition, PWS Engineering, Page 171, Problem 3.3 – 1<\/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\/es\/wp-json\/wp\/v2\/ht-kb\/10162"}],"collection":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb"}],"about":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/types\/ht_kb"}],"author":[{"embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/comments?post=10162"}],"version-history":[{"count":3,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb\/10162\/revisions"}],"predecessor-version":[{"id":13515,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb\/10162\/revisions\/13515"}],"wp:attachment":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/media?parent=10162"}],"wp:term":[{"taxonomy":"ht_kb_category","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb-category?post=10162"},{"taxonomy":"ht_kb_tag","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb-tag?post=10162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}