{"id":{"repo_id":"aachen","oai_identifier":"oai:publications.rwth-aachen.de:59203"},"canonical_url":"https://search.dev.ndltd.org/etd/aachen/oai:publications.rwth-aachen.de:59203","repository":{"repo_id":"aachen","name":"RWTH Aachen University","base_url":"https://publications.rwth-aachen.de/oai2d"},"display":{"title":"Beitrag zur Bemessung sattelgelagerter Behälter unter vertikaler Belastung","abstract":"Saddle supported cylindrical vessels are often used to store or transport liquids or gaseous materials. The saddle support, especially rigid supports, lead to a concentrated loading at the saddle horn and this makes it necessary to determine the bending stresses in this area. The calculation of the internal forces can be based on precise shell theories, on approached theories by idealising the shell as a beam or by using the finite element method. A precise theoretical method based on the complete or simplified shell theory by Flügge is impracticable because the solution of the differential equations needs high calculation expenditure and in combination with flexible saddle supports additional theories are necessary. The semi-bending theory by Wlassow, which neglects the effect of moments in longitudinal direction and drilling moments is easier to handle but in the case of very thin vessels or a great distance between the saddle support and the vessel bottom inexactitudes have been determined. For rigid saddles in practice the design method developed by Zick in 1951 is used. The calculation of the internal forces is based on a circular curved beam which has a clamped support at the height of the saddle horn. The curved beam is charged by tangential orientated forces and the distribution of these forces is obtained by the bending theory of beams with a tube cross section. The resulting stress distribution is then calculated by considering an effective shell width dependant on the vessel diameter and length. The effective shell width is based on experiments but in comparison with later accomplished tests and calculations inexactitudes concerning short vessels and vessels with a great distance between support and bottom have been determined. Independant of the determined inaccuracies the design method of Zick is still used because it is very easy to handle and no alternative methods exist which are more precise but still easy to practice. The aim of this thesis is the development of a new design method in which the structural behaviour of a cylindrical shell is taken into account by employing a shell theory. Additional the new method should be able to consider different forms of saddles, the influence of ring stiffeners and the solution should be as simple as possible so that this method can be an alternative to the method of Zick. To realise this the new developed method is based on the principal procedure of the method of Zick by calculating the internal forces in a curved beam. Different saddle forms are represented by an elastic foundation along the curved beam in the region of the saddle angle. To avoid the inexactitudes in the method of Zick the loading of the beam is obtained from a separated calculation which is based on the shell theory in the generalised bending theory developed by Schardt. A comparison with other shell theories shows that the results obtained by the generalised bending theory are precise enough concerning the present conditions and the solution is reduced on a differential equation of fourth degree which can be solved in analogy to known problems in the classic theory of beams. Main problem is to guarantee the kinematic compatibility of the deformed shell and the saddle. This is solved indirectly by taking a saddle pressure distribution into account which has to be verified and improved by the calculation with the curved and elastic based beam. In general case this leads to an iterative procedure. For the case of a vessel on a rigid saddle it is shown by comparative calculations with results according to the FE method that the new method determines the structural behaviour realistically. It is also shown that by using known pressure distributions no iteration is necessary and the computation expenditure is minimised. In this form it is suitable for a practical application. With the presentation of the proceeding and the results for the case of vessels on a thin elastomer layer a possible extension of the new method is shown. The case of a thin layer requires an idealisation of non linear behaviour of elastomers. From investigations done by the FE-method a proposal results, how the non linear behaviour can be idealised by a linear elastic foundation. Determined formulas for the expected saddle pressure distribution, can be used, in order to reduce the computation expenditure as in the rigid case. On basis of a parameter study for this case, which was so far not yet the subject of an investigation, a simple design formula was developed. Finally it is shown, how by simple modifications the influence of stiffening rings can be considered. Thus a method is presented, with which different execution forms of saddle supported vessels can be designed without great mathematical difficulties and considering a realistic structural behaviour.","abstract_html":"Saddle supported cylindrical vessels are often used to store or transport liquids or gaseous materials. The saddle support, especially rigid supports, lead to a concentrated loading at the saddle horn and this makes it necessary to determine the bending stresses in this area. The calculation of the internal forces can be based on precise shell theories, on approached theories by idealising the shell as a beam or by using the finite element method. A precise theoretical method based on the complete or simplified shell theory by Flügge is impracticable because the solution of the differential equations needs high calculation expenditure and in combination with flexible saddle supports additional theories are necessary. The semi-bending theory by Wlassow, which neglects the effect of moments in longitudinal direction and drilling moments is easier to handle but in the case of very thin vessels or a great distance between the saddle support and the vessel bottom inexactitudes have been determined. For rigid saddles in practice the design method developed by Zick in 1951 is used. The calculation of the internal forces is based on a circular curved beam which has a clamped support at the height of the saddle horn. The curved beam is charged by tangential orientated forces and the distribution of these forces is obtained by the bending theory of beams with a tube cross section. The resulting stress distribution is then calculated by considering an effective shell width dependant on the vessel diameter and length. The effective shell width is based on experiments but in comparison with later accomplished tests and calculations inexactitudes concerning short vessels and vessels with a great distance between support and bottom have been determined. Independant of the determined inaccuracies the design method of Zick is still used because it is very easy to handle and no alternative methods exist which are more precise but still easy to practice. The aim of this thesis is the development of a new design method in which the structural behaviour of a cylindrical shell is taken into account by employing a shell theory. Additional the new method should be able to consider different forms of saddles, the influence of ring stiffeners and the solution should be as simple as possible so that this method can be an alternative to the method of Zick. To realise this the new developed method is based on the principal procedure of the method of Zick by calculating the internal forces in a curved beam. Different saddle forms are represented by an elastic foundation along the curved beam in the region of the saddle angle. To avoid the inexactitudes in the method of Zick the loading of the beam is obtained from a separated calculation which is based on the shell theory in the generalised bending theory developed by Schardt. A comparison with other shell theories shows that the results obtained by the generalised bending theory are precise enough concerning the present conditions and the solution is reduced on a differential equation of fourth degree which can be solved in analogy to known problems in the classic theory of beams. Main problem is to guarantee the kinematic compatibility of the deformed shell and the saddle. This is solved indirectly by taking a saddle pressure distribution into account which has to be verified and improved by the calculation with the curved and elastic based beam. In general case this leads to an iterative procedure. For the case of a vessel on a rigid saddle it is shown by comparative calculations with results according to the FE method that the new method determines the structural behaviour realistically. It is also shown that by using known pressure distributions no iteration is necessary and the computation expenditure is minimised. In this form it is suitable for a practical application. With the presentation of the proceeding and the results for the case of vessels on a thin elastomer layer a possible extension of the new method is shown. The case of a thin layer requires an idealisation of non linear behaviour of elastomers. From investigations done by the FE-method a proposal results, how the non linear behaviour can be idealised by a linear elastic foundation. Determined formulas for the expected saddle pressure distribution, can be used, in order to reduce the computation expenditure as in the rigid case. On basis of a parameter study for this case, which was so far not yet the subject of an investigation, a simple design formula was developed. Finally it is shown, how by simple modifications the influence of stiffening rings can be considered. Thus a method is presented, with which different execution forms of saddle supported vessels can be designed without great mathematical difficulties and considering a realistic structural behaviour.","abstract_has_math":false,"creators":["Keppler, Jan Alexander"],"institution":"Publikationsserver der RWTH Aachen University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Güldenpfennig, Jürgen"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2004,"date_issued":"2004","date_published":"2004","updated_at":"2026-07-30T19:42:39Z","subjects":["info:eu-repo/classification/ddc/620","Behälter","Sattellager","Vertikale Belastung","Tragverhalten","Bemessung","Finite-Elemente-Methode","Ingenieurwissenschaften","Schalentheorien","FEM","Sattelpressung","nichtlineare Bettung"],"languages":["ger"],"rights":["info:eu-repo/semantics/openAccess"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-121010%22"],"render_values":[{"text":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-121010%22","href":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-121010%22","code":true}]}]},"links":{"outbound_url":"https://publications.rwth-aachen.de/record/59203","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Güldenpfennig, Jürgen"]},{"key":"dc:creator","label":"Author","values":["Keppler, Jan Alexander"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:coverage","label":"Dc Coverage","values":["DE"]},{"key":"dc:date","label":"Dc Date","values":["2004"]},{"key":"dc:publisher","label":"Institution","values":["Publikationsserver der RWTH Aachen University"]},{"key":"dc:relation","label":"Dc Relation","values":["info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-7676"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["info:eu-repo/classification/ddc/620","Behälter","Sattellager","Vertikale Belastung","Tragverhalten","Bemessung","Finite-Elemente-Methode","Ingenieurwissenschaften","Schalentheorien","FEM","Sattelpressung","nichtlineare Bettung"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["ger"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/record/59203","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-121010%22"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Saddle supported cylindrical vessels are often used to store or transport liquids or gaseous materials. The saddle support, especially rigid supports, lead to a concentrated loading at the saddle horn and this makes it necessary to determine the bending stresses in this area. The calculation of the internal forces can be based on precise shell theories, on approached theories by idealising the shell as a beam or by using the finite element method. A precise theoretical method based on the complete or simplified shell theory by Flügge is impracticable because the solution of the differential equations needs high calculation expenditure and in combination with flexible saddle supports additional theories are necessary. The semi-bending theory by Wlassow, which neglects the effect of moments in longitudinal direction and drilling moments is easier to handle but in the case of very thin vessels or a great distance between the saddle support and the vessel bottom inexactitudes have been determined. For rigid saddles in practice the design method developed by Zick in 1951 is used. The calculation of the internal forces is based on a circular curved beam which has a clamped support at the height of the saddle horn. The curved beam is charged by tangential orientated forces and the distribution of these forces is obtained by the bending theory of beams with a tube cross section. The resulting stress distribution is then calculated by considering an effective shell width dependant on the vessel diameter and length. The effective shell width is based on experiments but in comparison with later accomplished tests and calculations inexactitudes concerning short vessels and vessels with a great distance between support and bottom have been determined. Independant of the determined inaccuracies the design method of Zick is still used because it is very easy to handle and no alternative methods exist which are more precise but still easy to practice. The aim of this thesis is the development of a new design method in which the structural behaviour of a cylindrical shell is taken into account by employing a shell theory. Additional the new method should be able to consider different forms of saddles, the influence of ring stiffeners and the solution should be as simple as possible so that this method can be an alternative to the method of Zick. To realise this the new developed method is based on the principal procedure of the method of Zick by calculating the internal forces in a curved beam. Different saddle forms are represented by an elastic foundation along the curved beam in the region of the saddle angle. To avoid the inexactitudes in the method of Zick the loading of the beam is obtained from a separated calculation which is based on the shell theory in the generalised bending theory developed by Schardt. A comparison with other shell theories shows that the results obtained by the generalised bending theory are precise enough concerning the present conditions and the solution is reduced on a differential equation of fourth degree which can be solved in analogy to known problems in the classic theory of beams. Main problem is to guarantee the kinematic compatibility of the deformed shell and the saddle. This is solved indirectly by taking a saddle pressure distribution into account which has to be verified and improved by the calculation with the curved and elastic based beam. In general case this leads to an iterative procedure. For the case of a vessel on a rigid saddle it is shown by comparative calculations with results according to the FE method that the new method determines the structural behaviour realistically. It is also shown that by using known pressure distributions no iteration is necessary and the computation expenditure is minimised. In this form it is suitable for a practical application. With the presentation of the proceeding and the results for the case of vessels on a thin elastomer layer a possible extension of the new method is shown. The case of a thin layer requires an idealisation of non linear behaviour of elastomers. From investigations done by the FE-method a proposal results, how the non linear behaviour can be idealised by a linear elastic foundation. Determined formulas for the expected saddle pressure distribution, can be used, in order to reduce the computation expenditure as in the rigid case. On basis of a parameter study for this case, which was so far not yet the subject of an investigation, a simple design formula was developed. Finally it is shown, how by simple modifications the influence of stiffening rings can be considered. Thus a method is presented, with which different execution forms of saddle supported vessels can be designed without great mathematical difficulties and considering a realistic structural behaviour."]},{"key":"dc:source","label":"Dc Source","values":["Aachen : Publikationsserver der RWTH Aachen University 185 S. : graph. Darst. (2004). = Aachen, Techn. Hochsch., Diss., 2003"]},{"key":"dc:title","label":"Title","values":["Beitrag zur Bemessung sattelgelagerter Behälter unter vertikaler Belastung"]}]}],"canonical_facts":{"dc:contributor":["Güldenpfennig, Jürgen"],"dc:coverage":["DE"],"dc:creator":["Keppler, Jan Alexander"],"dc:date":["2004"],"dc:description":["Saddle supported cylindrical vessels are often used to store or transport liquids or gaseous materials. The saddle support, especially rigid supports, lead to a concentrated loading at the saddle horn and this makes it necessary to determine the bending stresses in this area. The calculation of the internal forces can be based on precise shell theories, on approached theories by idealising the shell as a beam or by using the finite element method. A precise theoretical method based on the complete or simplified shell theory by Flügge is impracticable because the solution of the differential equations needs high calculation expenditure and in combination with flexible saddle supports additional theories are necessary. The semi-bending theory by Wlassow, which neglects the effect of moments in longitudinal direction and drilling moments is easier to handle but in the case of very thin vessels or a great distance between the saddle support and the vessel bottom inexactitudes have been determined. For rigid saddles in practice the design method developed by Zick in 1951 is used. The calculation of the internal forces is based on a circular curved beam which has a clamped support at the height of the saddle horn. The curved beam is charged by tangential orientated forces and the distribution of these forces is obtained by the bending theory of beams with a tube cross section. The resulting stress distribution is then calculated by considering an effective shell width dependant on the vessel diameter and length. The effective shell width is based on experiments but in comparison with later accomplished tests and calculations inexactitudes concerning short vessels and vessels with a great distance between support and bottom have been determined. Independant of the determined inaccuracies the design method of Zick is still used because it is very easy to handle and no alternative methods exist which are more precise but still easy to practice. The aim of this thesis is the development of a new design method in which the structural behaviour of a cylindrical shell is taken into account by employing a shell theory. Additional the new method should be able to consider different forms of saddles, the influence of ring stiffeners and the solution should be as simple as possible so that this method can be an alternative to the method of Zick. To realise this the new developed method is based on the principal procedure of the method of Zick by calculating the internal forces in a curved beam. Different saddle forms are represented by an elastic foundation along the curved beam in the region of the saddle angle. To avoid the inexactitudes in the method of Zick the loading of the beam is obtained from a separated calculation which is based on the shell theory in the generalised bending theory developed by Schardt. A comparison with other shell theories shows that the results obtained by the generalised bending theory are precise enough concerning the present conditions and the solution is reduced on a differential equation of fourth degree which can be solved in analogy to known problems in the classic theory of beams. Main problem is to guarantee the kinematic compatibility of the deformed shell and the saddle. This is solved indirectly by taking a saddle pressure distribution into account which has to be verified and improved by the calculation with the curved and elastic based beam. In general case this leads to an iterative procedure. For the case of a vessel on a rigid saddle it is shown by comparative calculations with results according to the FE method that the new method determines the structural behaviour realistically. It is also shown that by using known pressure distributions no iteration is necessary and the computation expenditure is minimised. In this form it is suitable for a practical application. With the presentation of the proceeding and the results for the case of vessels on a thin elastomer layer a possible extension of the new method is shown. The case of a thin layer requires an idealisation of non linear behaviour of elastomers. From investigations done by the FE-method a proposal results, how the non linear behaviour can be idealised by a linear elastic foundation. Determined formulas for the expected saddle pressure distribution, can be used, in order to reduce the computation expenditure as in the rigid case. On basis of a parameter study for this case, which was so far not yet the subject of an investigation, a simple design formula was developed. Finally it is shown, how by simple modifications the influence of stiffening rings can be considered. Thus a method is presented, with which different execution forms of saddle supported vessels can be designed without great mathematical difficulties and considering a realistic structural behaviour."],"dc:identifier":["https://publications.rwth-aachen.de/record/59203","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-121010%22"],"dc:language":["ger"],"dc:publisher":["Publikationsserver der RWTH Aachen University"],"dc:relation":["info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-7676"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:source":["Aachen : Publikationsserver der RWTH Aachen University 185 S. : graph. Darst. (2004). = Aachen, Techn. Hochsch., Diss., 2003"],"dc:subject":["info:eu-repo/classification/ddc/620","Behälter","Sattellager","Vertikale Belastung","Tragverhalten","Bemessung","Finite-Elemente-Methode","Ingenieurwissenschaften","Schalentheorien","FEM","Sattelpressung","nichtlineare Bettung"],"dc:title":["Beitrag zur Bemessung sattelgelagerter Behälter unter vertikaler Belastung"],"dc:type":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]},"updated_at":"2026-07-30T19:42:39Z"}