An analytical algorithm for reasonable central tower stiffness in the three-tower suspension bridge with unequal-length main spans
•The three-tower suspension bridge with unequal-length main spans is discussed.•The reasonable range of the central tower stiffness is determined analytically.•Hanger tensile forces under the joint action of dead and live loads are calculated.•Cases of the live load acting on the shorter main span a...
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| Veröffentlicht in: | Engineering structures 2019-11, Vol.199, p.109595, Article 109595 |
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| creator | Zhang, Wen-ming Yang, Chao-yu Wang, Zhi-wei Liu, Zhao |
| description | •The three-tower suspension bridge with unequal-length main spans is discussed.•The reasonable range of the central tower stiffness is determined analytically.•Hanger tensile forces under the joint action of dead and live loads are calculated.•Cases of the live load acting on the shorter main span and longer one are considered.•Effects of the dead-to-live load ratio and the friction coefficient are discussed.
Three-tower suspension bridges with unequal-length main spans more easily adapt to different terrain features and therefore, have broader application prospects. However, due to the unique “central tower effect” of the three-tower suspension bridge, it is required that the lateral stiffness of the central tower in the longitudinal direction of the bridge girder should be neither too large nor too small. To calculate the reasonable range for the central tower stiffness in the three-tower suspension bridge with unequal-length main spans, this study proposes an analytical algorithm based on the segmental catenary theory. Firstly, hanger tensile forces under the joint action of dead and live loads are calculated. Next, the governing equations for the main cable shape of each span are constructed for the following conditions: closure of elevation difference, closure of span length, moment balance of splay saddle, and conservation of unstrained length of the main cable. The solutions of the derived set of simultaneous equations are obtained for (i) deflection-to-span ratio limit of the stiffening girder and (ii) anti-slip control between the main cable and saddle conditions, which yield the lower and upper limits of reasonable stiffness of the central tower, respectively. This study discusses a three-tower suspension bridge spanned as 248 m + 1060 m + 1360 m + 380 m. The calculation is performed for the two cases of the live load application: (i) to the longer main span and (ii) to the shorter main span. The results obtained proved the feasibility and effectiveness of the proposed algorithm. The following findings are reported: The upper and lower limits of reasonable central tower stiffness are derived from the above two cases, respectively. Therefore, it is not sufficient to consider only the former case when calculating the central tower stiffness of the three-tower suspension bridge with equal-length main spans. The dead-to-live load ratio and friction coefficient between the main cable and saddle also strongly influence the central tower stiffness: thei |
| doi_str_mv | 10.1016/j.engstruct.2019.109595 |
| format | Article |
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Three-tower suspension bridges with unequal-length main spans more easily adapt to different terrain features and therefore, have broader application prospects. However, due to the unique “central tower effect” of the three-tower suspension bridge, it is required that the lateral stiffness of the central tower in the longitudinal direction of the bridge girder should be neither too large nor too small. To calculate the reasonable range for the central tower stiffness in the three-tower suspension bridge with unequal-length main spans, this study proposes an analytical algorithm based on the segmental catenary theory. Firstly, hanger tensile forces under the joint action of dead and live loads are calculated. Next, the governing equations for the main cable shape of each span are constructed for the following conditions: closure of elevation difference, closure of span length, moment balance of splay saddle, and conservation of unstrained length of the main cable. The solutions of the derived set of simultaneous equations are obtained for (i) deflection-to-span ratio limit of the stiffening girder and (ii) anti-slip control between the main cable and saddle conditions, which yield the lower and upper limits of reasonable stiffness of the central tower, respectively. This study discusses a three-tower suspension bridge spanned as 248 m + 1060 m + 1360 m + 380 m. The calculation is performed for the two cases of the live load application: (i) to the longer main span and (ii) to the shorter main span. The results obtained proved the feasibility and effectiveness of the proposed algorithm. The following findings are reported: The upper and lower limits of reasonable central tower stiffness are derived from the above two cases, respectively. Therefore, it is not sufficient to consider only the former case when calculating the central tower stiffness of the three-tower suspension bridge with equal-length main spans. The dead-to-live load ratio and friction coefficient between the main cable and saddle also strongly influence the central tower stiffness: their increase can expand the reasonable range of the latter but if they are too small, no such optimization can be provided.</description><identifier>ISSN: 0141-0296</identifier><identifier>EISSN: 1873-7323</identifier><identifier>DOI: 10.1016/j.engstruct.2019.109595</identifier><language>eng</language><publisher>Kidlington: Elsevier Ltd</publisher><subject>Algorithms ; Analytical algorithm ; Bridge loads ; Bridge towers ; Central tower effect ; Central tower stiffness ; Coefficient of friction ; Dead loads ; Elevation ; Girder bridges ; GRG method ; Live loads ; Mathematical analysis ; Optimization ; Simultaneous equations ; Stiffening ; Stiffness ; Suspension bridges ; Telecommunications towers ; Three-tower suspension bridge ; Unequal-length main spans</subject><ispartof>Engineering structures, 2019-11, Vol.199, p.109595, Article 109595</ispartof><rights>2019 Elsevier Ltd</rights><rights>Copyright Elsevier BV Nov 15, 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c343t-19cf93c3bbc1aed44cdbec15ab1efed5375fc5bdb0f4954bb5f1eadbb7ac183</citedby><cites>FETCH-LOGICAL-c343t-19cf93c3bbc1aed44cdbec15ab1efed5375fc5bdb0f4954bb5f1eadbb7ac183</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.engstruct.2019.109595$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Zhang, Wen-ming</creatorcontrib><creatorcontrib>Yang, Chao-yu</creatorcontrib><creatorcontrib>Wang, Zhi-wei</creatorcontrib><creatorcontrib>Liu, Zhao</creatorcontrib><title>An analytical algorithm for reasonable central tower stiffness in the three-tower suspension bridge with unequal-length main spans</title><title>Engineering structures</title><description>•The three-tower suspension bridge with unequal-length main spans is discussed.•The reasonable range of the central tower stiffness is determined analytically.•Hanger tensile forces under the joint action of dead and live loads are calculated.•Cases of the live load acting on the shorter main span and longer one are considered.•Effects of the dead-to-live load ratio and the friction coefficient are discussed.
Three-tower suspension bridges with unequal-length main spans more easily adapt to different terrain features and therefore, have broader application prospects. However, due to the unique “central tower effect” of the three-tower suspension bridge, it is required that the lateral stiffness of the central tower in the longitudinal direction of the bridge girder should be neither too large nor too small. To calculate the reasonable range for the central tower stiffness in the three-tower suspension bridge with unequal-length main spans, this study proposes an analytical algorithm based on the segmental catenary theory. Firstly, hanger tensile forces under the joint action of dead and live loads are calculated. Next, the governing equations for the main cable shape of each span are constructed for the following conditions: closure of elevation difference, closure of span length, moment balance of splay saddle, and conservation of unstrained length of the main cable. The solutions of the derived set of simultaneous equations are obtained for (i) deflection-to-span ratio limit of the stiffening girder and (ii) anti-slip control between the main cable and saddle conditions, which yield the lower and upper limits of reasonable stiffness of the central tower, respectively. This study discusses a three-tower suspension bridge spanned as 248 m + 1060 m + 1360 m + 380 m. The calculation is performed for the two cases of the live load application: (i) to the longer main span and (ii) to the shorter main span. The results obtained proved the feasibility and effectiveness of the proposed algorithm. The following findings are reported: The upper and lower limits of reasonable central tower stiffness are derived from the above two cases, respectively. Therefore, it is not sufficient to consider only the former case when calculating the central tower stiffness of the three-tower suspension bridge with equal-length main spans. The dead-to-live load ratio and friction coefficient between the main cable and saddle also strongly influence the central tower stiffness: their increase can expand the reasonable range of the latter but if they are too small, no such optimization can be provided.</description><subject>Algorithms</subject><subject>Analytical algorithm</subject><subject>Bridge loads</subject><subject>Bridge towers</subject><subject>Central tower effect</subject><subject>Central tower stiffness</subject><subject>Coefficient of friction</subject><subject>Dead loads</subject><subject>Elevation</subject><subject>Girder bridges</subject><subject>GRG method</subject><subject>Live loads</subject><subject>Mathematical analysis</subject><subject>Optimization</subject><subject>Simultaneous equations</subject><subject>Stiffening</subject><subject>Stiffness</subject><subject>Suspension bridges</subject><subject>Telecommunications towers</subject><subject>Three-tower suspension bridge</subject><subject>Unequal-length main spans</subject><issn>0141-0296</issn><issn>1873-7323</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNqFkEtPAyEUhYnRxPr4DZK4ngrD4HSWTeMrMXGhewLMpdJMoeUyNm795dK0ceuCEC7nnNzzEXLD2ZQzfn-3mkJYYk6jzdOa8a5MO9nJEzLhs1ZUrajFKZkw3vCK1d39OblAXDHG6tmMTcjPPFAd9PCdvdUD1cMyJp8_19TFRBNojEGbAaiFkFMR5LiDRDF75wIgUh9o_oRyEkB1_BxxAwF9DNQk3y-B7koiHQNsRz1UQ1m3PNe6WHGjA16RM6cHhOvjfUneHx8-Fs_V69vTy2L-WlnRiFzxzrpOWGGM5Rr6prG9AculNhwc9FK00llpesNc08nGGOk46N6YVls-E5fk9pC6SXE7Ama1imMqzVHVgktZULK9qj2obIqICZzaJL_W6Vtxpva41Ur94VZ73OqAuzjnByeUCl8ekkLrIVjofYKi7aP_N-MXogqS_w</recordid><startdate>20191115</startdate><enddate>20191115</enddate><creator>Zhang, Wen-ming</creator><creator>Yang, Chao-yu</creator><creator>Wang, Zhi-wei</creator><creator>Liu, Zhao</creator><general>Elsevier Ltd</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SR</scope><scope>7ST</scope><scope>8BQ</scope><scope>8FD</scope><scope>C1K</scope><scope>FR3</scope><scope>JG9</scope><scope>KR7</scope><scope>SOI</scope></search><sort><creationdate>20191115</creationdate><title>An analytical algorithm for reasonable central tower stiffness in the three-tower suspension bridge with unequal-length main spans</title><author>Zhang, Wen-ming ; Yang, Chao-yu ; Wang, Zhi-wei ; Liu, Zhao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c343t-19cf93c3bbc1aed44cdbec15ab1efed5375fc5bdb0f4954bb5f1eadbb7ac183</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algorithms</topic><topic>Analytical algorithm</topic><topic>Bridge loads</topic><topic>Bridge towers</topic><topic>Central tower effect</topic><topic>Central tower stiffness</topic><topic>Coefficient of friction</topic><topic>Dead loads</topic><topic>Elevation</topic><topic>Girder bridges</topic><topic>GRG method</topic><topic>Live loads</topic><topic>Mathematical analysis</topic><topic>Optimization</topic><topic>Simultaneous equations</topic><topic>Stiffening</topic><topic>Stiffness</topic><topic>Suspension bridges</topic><topic>Telecommunications towers</topic><topic>Three-tower suspension bridge</topic><topic>Unequal-length main spans</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, Wen-ming</creatorcontrib><creatorcontrib>Yang, Chao-yu</creatorcontrib><creatorcontrib>Wang, Zhi-wei</creatorcontrib><creatorcontrib>Liu, Zhao</creatorcontrib><collection>CrossRef</collection><collection>Engineered Materials Abstracts</collection><collection>Environment Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Environmental Sciences and Pollution Management</collection><collection>Engineering Research Database</collection><collection>Materials Research Database</collection><collection>Civil Engineering Abstracts</collection><collection>Environment Abstracts</collection><jtitle>Engineering structures</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhang, Wen-ming</au><au>Yang, Chao-yu</au><au>Wang, Zhi-wei</au><au>Liu, Zhao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An analytical algorithm for reasonable central tower stiffness in the three-tower suspension bridge with unequal-length main spans</atitle><jtitle>Engineering structures</jtitle><date>2019-11-15</date><risdate>2019</risdate><volume>199</volume><spage>109595</spage><pages>109595-</pages><artnum>109595</artnum><issn>0141-0296</issn><eissn>1873-7323</eissn><abstract>•The three-tower suspension bridge with unequal-length main spans is discussed.•The reasonable range of the central tower stiffness is determined analytically.•Hanger tensile forces under the joint action of dead and live loads are calculated.•Cases of the live load acting on the shorter main span and longer one are considered.•Effects of the dead-to-live load ratio and the friction coefficient are discussed.
Three-tower suspension bridges with unequal-length main spans more easily adapt to different terrain features and therefore, have broader application prospects. However, due to the unique “central tower effect” of the three-tower suspension bridge, it is required that the lateral stiffness of the central tower in the longitudinal direction of the bridge girder should be neither too large nor too small. To calculate the reasonable range for the central tower stiffness in the three-tower suspension bridge with unequal-length main spans, this study proposes an analytical algorithm based on the segmental catenary theory. Firstly, hanger tensile forces under the joint action of dead and live loads are calculated. Next, the governing equations for the main cable shape of each span are constructed for the following conditions: closure of elevation difference, closure of span length, moment balance of splay saddle, and conservation of unstrained length of the main cable. The solutions of the derived set of simultaneous equations are obtained for (i) deflection-to-span ratio limit of the stiffening girder and (ii) anti-slip control between the main cable and saddle conditions, which yield the lower and upper limits of reasonable stiffness of the central tower, respectively. This study discusses a three-tower suspension bridge spanned as 248 m + 1060 m + 1360 m + 380 m. The calculation is performed for the two cases of the live load application: (i) to the longer main span and (ii) to the shorter main span. The results obtained proved the feasibility and effectiveness of the proposed algorithm. The following findings are reported: The upper and lower limits of reasonable central tower stiffness are derived from the above two cases, respectively. Therefore, it is not sufficient to consider only the former case when calculating the central tower stiffness of the three-tower suspension bridge with equal-length main spans. The dead-to-live load ratio and friction coefficient between the main cable and saddle also strongly influence the central tower stiffness: their increase can expand the reasonable range of the latter but if they are too small, no such optimization can be provided.</abstract><cop>Kidlington</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.engstruct.2019.109595</doi></addata></record> |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Algorithms Analytical algorithm Bridge loads Bridge towers Central tower effect Central tower stiffness Coefficient of friction Dead loads Elevation Girder bridges GRG method Live loads Mathematical analysis Optimization Simultaneous equations Stiffening Stiffness Suspension bridges Telecommunications towers Three-tower suspension bridge Unequal-length main spans |
| title | An analytical algorithm for reasonable central tower stiffness in the three-tower suspension bridge with unequal-length main spans |
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