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Recent Patents on Engineering

Editor-in-Chief

ISSN (Print): 1872-2121
ISSN (Online): 2212-4047

Recent Advances in the Dynamic Analysis of Stiffened Plates - Application to Concrete or to Composite Steel-Concrete Structures

Author(s): Evangelos J. Sapountzakis

Volume 3, Issue 1, 2009

Page: [39 - 59] Pages: 21

DOI: 10.2174/187221209787259956

Price: $65

Abstract

In this paper, an improved model for the dynamic analysis of reinforced concrete plates stiffened by arbitrarily placed parallel reinforced concrete or steel beams with deformable connection taking into account the influence of creep and shrinkage effects relative with the time of the casting and the time of the loading of the plate and the beams is presented. According to the proposed model, the stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, making the hypothesis that the plate and the beams can slip in all directions of the connection without separation (i.e. uplift neglected) and taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting two interface lines, along which the loading of the beams as well as the additional loading of the plate is defined. Their unknown distribution is established by applying continuity conditions in all directions at the interfaces taking into account their relation with the interface slip through the shear connector stiffness. The utilization of two interface lines for each beam enables the nonuniform distribution of the interface transverse shear forces and the nonuniform torsional response of the beams to be taken into account describing better in this way the actual response of the plate - beams system. The analysis of both the plate and the beams is accomplished on their deformed shape taking into account second-order effects. Six boundary value problems are formulated and solved using the Analog Equation Method (AEM), a BEM based method. The solution of the aforementioned plate and beam problems, which are nonlinearly coupled, is achieved using iterative numerical methods. The adopted model permits the evaluation of the shear forces at the interfaces in both directions, the knowledge of which is very important in the design of prefabricated ribbed plates. Both free and forced damped or undamped transverse vibrations are considered and numerical examples with great practical interest with patent discussion are presented.

Keywords: Elastic stiffened plate, reinforced plate with beams, bending, deformable connection, nonuniform torsion, warping, ribbed plate, boundary element method, slab-and-beam structure, creep


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      • 16. app/Models/Subject.php:220
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      • 19. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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      • 11. app/Models/Issue.php:298
      • 12. app/Http/Controllers/ArticleController.php:2068
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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      • 13. app/Models/Article.php:528
      • 14. app/Http/Controllers/ArticleController.php:2070
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select a.nid,a.publish_on, a.pmid,a.article_id,a.doi,j.journal_id,j.subtitle,v.volume_name,a.volume_id as volume_id, a.issue_id,a.title,first_page, last_page, page_count,abstract,ifnull(is_abstract,"y"),asec.title as article_section,at.type_name as article_type_name, a.article_id as ArticleID ,is_epub,epub_price,epub_type,a.created, y.year from `article` as `a` left join `article_section` as `asec` on `asec`.`art_sec_id` = `a`.`is_epub` left join `article_type` as `at` on `at`.`art_type_id` = `a`.`art_type` left join `journal` as `j` on `j`.`journal_id` = `a`.`journal_id` inner join `volume` as `v` on `a`.`volume_id` = `v`.`volume_id` inner join `year` as `y` on `v`.`year_id` = `y`.`id` where a.article_status != "W" and a.is_epub = 4 and a.journal_id = 78 and a.is_uploaded = 1 group by `a`.`article_id` order by `a`.`publish_on` desc
      4.3msalphaeurekaselec_live_10_06_2022Article.php#528
      Backtrace
      • 13. app/Models/Article.php:528
      • 14. app/Http/Controllers/ArticleController.php:2071
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select pdf, html, epub, prc from `article_metrics` where `article_id` = 38133 limit 1
      1.26msalphaeurekaselec_live_10_06_2022Article.php#744
      Bindings
      • 0: 38133
      Backtrace
      • 14. app/Models/Article.php:744
      • 15. app/Http/Controllers/ArticleController.php:2091
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select * from content_by_diseases where content_id = 38133 and content_type = 'article' order by status desc limit 1
      310μsalphaeurekaselec_live_10_06_2022Article.php#751
      Backtrace
      • 11. app/Models/Article.php:751
      • 12. app/Http/Controllers/ArticleController.php:2094
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select * from `node_meta` where `nid` = 93157 limit 1
      220μsalphaeurekaselec_live_10_06_2022Meta.php#30
      Bindings
      • 0: 93157
      Backtrace
      • 14. app/Models/Meta.php:30
      • 15. app/Http/Controllers/ArticleController.php:2101
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select `bo`.* from `bundle_offer` as `bo` where `bo`.`bundle_status` = 'A' order by `bo`.`bundle_id` desc
      250μsalphaeurekaselec_live_10_06_2022BundleOffer.php#57
      Bindings
      • 0: A
      Backtrace
      • 13. app/Models/BundleOffer.php:57
      • 14. app/Http/Controllers/ArticleController.php:2108
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select * from `tbl_ht_submission` as `h` where `h`.`subtitle` = 'ENG' and (h.proposal_closing_date = 0 OR TO_DAYS(FROM_UNIXTIME(h.proposal_closing_date)) >= TO_DAYS(NOW())) order by `h`.`manuscript` asc
      380μsalphaeurekaselec_live_10_06_2022Article.php#2025
      Bindings
      • 0: ENG
      Backtrace
      • 13. app/Models/Article.php:2025
      • 14. app/Http/Controllers/ArticleController.php:2112
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select count(*) as total_count, content_type_access_id as access_type from journal_access where content_type_id = '38133' and content_type = 'a' and ( (from_date <= CURDATE() and to_date >= CURDATE() and perpetual= 0) or (from_date is null and to_date is null and perpetual= 1) )
      490μsalphaeurekaselec_live_10_06_2022ContentAccess.php#647
      Backtrace
      • 11. app/Models/ContentAccess.php:647
      • 12. app/Http/Controllers/ArticleController.php:2186
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select count(*) as total_count, content_type_access_id as access_type from journal_access where content_type_id = '2913' and content_type = 'i' and ( (from_date <= CURDATE() and to_date >= CURDATE() and perpetual= 0) or (from_date is null and to_date is null and perpetual= 1) )
      300μsalphaeurekaselec_live_10_06_2022ContentAccess.php#647
      Backtrace
      • 11. app/Models/ContentAccess.php:647
      • 12. app/Http/Controllers/ArticleController.php:2207
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select count(*) as total_count, content_type_access_id as access_type from journal_access where content_type_id = '643' and content_type = 'v' and ( (from_date <= CURDATE() and to_date >= CURDATE() and perpetual= 0) or (from_date is null and to_date is null and perpetual= 1) )
      240μsalphaeurekaselec_live_10_06_2022ContentAccess.php#647
      Backtrace
      • 11. app/Models/ContentAccess.php:647
      • 12. app/Http/Controllers/ArticleController.php:2231
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"volume" as access_level,"" as issue_id,"" as article_id from `user_access_journal_volume_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59689235 and j.to_ip >=59689235 )) and ((j.from_date <= 1740513698 and j.to_date >= 1740513698 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.volume_id = 643) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"volume" as access_level,"" as issue_id,"" as article_id from `user_access_journal_volume_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59689235 and j.to_ip >=59689235 )) and ((j.from_date <= 1740513698 and j.to_date >= 1740513698 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.volume_id = 643) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"volume" as access_level,"" as issue_id,"" as article_id from `user_access_journal_volume_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59689235 and j.to_ip >=59689235 )) and ((j.from_date <= 1740513698 and j.to_date >= 1740513698 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.volume_id = 643)
      2.86msalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ArticleController.php:2272
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"issue" as access_level,j.issue_id,"" as article_id from `user_access_issue_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59689235 and j.to_ip >=59689235 )) and ((j.from_date <= 1740513698 and j.to_date >= 1740513698 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.issue_id = 2913) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"issue" as access_level,j.issue_id,"" as article_id from `user_access_issue_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59689235 and j.to_ip >=59689235 )) and ((j.from_date <= 1740513698 and j.to_date >= 1740513698 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.issue_id = 2913) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"issue" as access_level,j.issue_id,"" as article_id from `user_access_issue_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59689235 and j.to_ip >=59689235 )) and ((j.from_date <= 1740513698 and j.to_date >= 1740513698 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.issue_id = 2913)
      570μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ArticleController.php:2297
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"article" as access_level, j.issue_id, j.article_id from `user_access_article_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59689235 and j.to_ip >=59689235 )) and ((j.from_date <= 1740513698 and j.to_date >= 1740513698 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.article_id = 38133) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"article" as access_level, j.issue_id, j.article_id from `user_access_article_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59689235 and j.to_ip >=59689235 )) and ((j.from_date <= 1740513698 and j.to_date >= 1740513698 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.article_id = 38133) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"article" as access_level, j.issue_id, j.article_id from `user_access_article_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59689235 and j.to_ip >=59689235 )) and ((j.from_date <= 1740513698 and j.to_date >= 1740513698 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.article_id = 38133)
      600μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ArticleController.php:2329
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select * from `article` where `first_page` < '39' and is_uploaded = 1 and issue_id = 2913 order by cast(first_page as SIGNED) desc limit 1
      450μsalphaeurekaselec_live_10_06_2022Article.php#1819
      Bindings
      • 0: 39
      Backtrace
      • 14. app/Models/Article.php:1819
      • 15. app/Http/Controllers/ArticleController.php:2470
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select * from `article` where `last_page` > '59' and is_uploaded = 1 and issue_id = 2913 order by cast(first_page as SIGNED) asc limit 1
      380μsalphaeurekaselec_live_10_06_2022Article.php#1831
      Bindings
      • 0: 59
      Backtrace
      • 14. app/Models/Article.php:1831
      • 15. app/Http/Controllers/ArticleController.php:2472
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select `language_id` from `multilanguage` where `short_code` = 'en'
      190μsalphaeurekaselec_live_10_06_2022ArticleController.php#2497
      Bindings
      • 0: en
      Backtrace
      • 14. app/Http/Controllers/ArticleController.php:2497
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:206
    • select `source_lang_label`, `target_lang_label` from `multilanguage_labels` where `target_lang_id` = 1
      190μsalphaeurekaselec_live_10_06_2022MultiLanguage.php#23
      Bindings
      • 0: 1
      Backtrace
      • 13. app/Models/MultiLanguage.php:23
      • 14. app/Http/Controllers/ArticleController.php:2498
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select `id` from `multilanguage_article` where `article_id` = 38133 limit 1
      2.95msalphaeurekaselec_live_10_06_2022ArticleController.php#2506
      Bindings
      • 0: 38133
      Backtrace
      • 16. app/Http/Controllers/ArticleController.php:2506
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:206
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` inner join `journal` as `j` on `j`.`journal_id` = `bd`.`content_id` where `b`.`banner_journal` = 1 and `bd`.`content_type` = 'J' and `bd`.`content_id` = 78 and `b`.`banner_from_date` <= 1740513698 and `b`.`banner_to_date` >= 1740513698 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.24msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: J
      • 2: 78
      • 3: 1740513698
      • 4: 1740513698
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` inner join `journal` as `j` on `j`.`journal_id` = `bd`.`content_id` where `b`.`banner_journal` = 1 and `bd`.`content_type` = 'J' and `bd`.`content_id` = 78 and `b`.`banner_from_date` <= 1740513698 and `b`.`banner_to_date` >= 1740513698 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.16msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: J
      • 2: 78
      • 3: 1740513698
      • 4: 1740513698
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='f06269ed0c0d1dcd9b27494ef9e31f50'
      240μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\MultiLanguage
    1MultiLanguage.php#?
        _token
        CykXgxwJmgwsQmIfTmNaTQTwBVj82f7RfErmd9DA
        uc_cart_id
        f06269ed0c0d1dcd9b27494ef9e31f50
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/article/38133" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /article/38133
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
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