[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-232755-105":59,"doc-detail-232755-en":122},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":115,"head_meta":117,"extra_data":119,"updated_unix":121},105,"en","linearly-elastic-analysis-of-plane-frames-subjected-to-complex-loading-conditions-research-report-56-21-analytical-tool-and-computer-simulation-methods","Linearly Elastic Analysis of Plane Frames Subjected to Complex Loading Conditions - Research Report 56-21 - Analytical tool and computer simulation methods","","Analytical methods for the solution of plane-frame structures under complex loading conditions are presented using a computer program designed to reduce hand calculations. The approach is based on the linear elastic behavior exhibited by many plane frames, enabling efficient evaluation across multiple loading cases and combinations with only slightly higher computational cost than a single solution. The report is part of a broader research series supported by the Texas Highway Department and the U.S. Federal Highway Administration.",{"@graph":69,"@context":114},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/linearly-elastic-analysis-of-plane-frames-subjected-to-complex-loading-conditions-research-report-56-21-analytical-tool-and-computer-simulation-methods/232755/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/linearly-elastic-analysis-of-plane-frames-subjected-to-complex-loading-conditions-research-report-56-21-analytical-tool-and-computer-simulation-methods/232755.png","ImageObject",300,407,{"name":92,"@type":93},"Bintang","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-17","2026-09-10",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108],{"name":109,"@type":110,"acceptedAnswer":111},"Which organizations sponsored the development described in the report?","Question",{"text":112,"@type":113},"The work was conducted for the Texas Highway Department in cooperation with the U.S. Department of Transportation, Federal Highway Administration, by the Center for Highway Research at the University of Texas at Austin.","Answer","https://schema.org",{"og:url":83,"og:type":116,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":118,"canonical":83},"index,follow",{"doc_id":120,"site_id":62},232755,1789073494,{"code":4,"msg":5,"data":123},{"doc_id":120,"user_id":124,"nickname":92,"user_avatar":125,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":126,"file_id":127,"file_url":128,"file_type":129,"file_size":130,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":131,"language":132,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":133,"faqs":134,"seo_title":135,"seo_description":67,"update_tm":121,"read_time":136,"preview_page_count":4},962085564381,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","# LINEARLY ELASTIC ANALYSIS OF PLANE FRAMESSUBJECTED TO COMPLEX LOADING CONDITIONS\n\nby  \nClifford 0.Hays and Hudson Matlock  \nResearch Report Number 56-21  \n# Development of Methods for Computer Simulationof Beam-Columns and Grid-Beam and Slab SystemResearch Project 3-5-63-56\n\nconducted for  \nThe Texas Highway Department  \nin cooperation with theU.S.Department of TransportationFederal Highway Administration  \nby the  \nCENTER FOR HIGHWAY RESEARCHTHE UNIVERSITY OF TEXAS AT AUSTIN  \nJune 1971  \nThe opinions,findings,and conclusionsexpressed in this publication are thoseof the authors and not necessarily thoseof the Federal Highway Administration.  \n## PREFACE\n\nThis report presents an analytical tool for the solution of plane-framestructures.  The computer program developed for the solution is intended tobe well suited for solving complex structures with a minimum of hand calcula-tions.  \nThe solution techniques developed rely on the linear1y elastic behaviorthat many plane frames exhibit under design loads.  This linearity allows theuser to solve a structure for many loading cases and combinations of loadingcases at a cost only slight1y greater than that of a single solution.  \nThis is the twenty-first in a series of reports that describe work under  \nResearch Project No.3-5-63-56,'Development of Methods for Computer Simula-  \ntion of Beam-Columns and Grid-Beam and Slab Systems\".Reports No.56-1,56-3,  \n56-4,56-7,and 56-14 provide background information for this report.  \nDuplicate copies of the program deck and test data cards for the exampleproblems in this reporc may be obtained from the Center for Highway Research,The University of Texas at Austin.  \nThanks are due to the members of the staff of the Center for HighwayResearch for their assistance in producing this report.  \nClifford 0.Hays,Jr.Hudson Mat1ock  \nOctober 1970  \nThis page replaces an intentionally blank page in the original.--CTR Library Digitization Team  \nLIST OF REPORTS  \nReport No.56-1,\"A Finite-Element Method of Solution for Linearly Elastic  \nBeam-Columns\"by Hudson Matlock and T.Allan Haliburton,presents a finite-  \nelement solution for beam-columns that is a basic tool in subsequent reports.  \nReport No.56-2,\"A Computer Program to Analyze Bending of Bent Caps\"byHudson Matlock and Wayne B.Ingram,describes the application of the beam-columm solution to the particular problem of bent caps.  \nReport No.56-3,\"A Finite-Element Method of Solution for Structural Frames\"by Hudson Matlock and Berry Ray Grubbs,describes a solution for frames withno sway.  \nReport No.56-4,\"A Computer Program to Analyze Beam-Columns under MovableLoads\"by Hudson Matlock and Thomas P.Taylor,describes the application ofthe beam-columm solution to problems with any configuration of movable non-dynamic loads.  \nReport No.56-5,\"A Finite-Element Method for Bending Analysis of LayeredStructural Systems\"by Wayne B.Ingram and Hud son Matlock,describes analternating-direction iteration method for solving two-dimensional systemsof layered grids-over-beams and plates-over-beams.  \nReport No.56-6,\"Discontinuous Orthotropic Plates and Pavement Slabs\"byW.Ronald Hudson and Hudson Matlock,describes an alternating-directioniteration method for solving complex two-dimensional plate and slab problemswith emphasis on pavement slabs,  \nReport No.56-7,\"A Finite-Element Analysis of Structural Frames\"by T.AllanHaliburton and Hudson Matlock,describes a method of analysis for rectangularplane frames with three degrees of freedom at each joint.  \nReport No.56-8,\"A Finite-Element Method for Transverse Vibrations of Beamsand Plates\"by Harold Salani and Hudson Matlock,describes an 1mplicit pro-cedure for determining the transient and steady-state vibrations of beams andplates,including pavement slabs.  \nReport No.56-9,\"A Direct Computer Solution for Plates and Pavement Slabs\"by C.Fred Stelzer,Jr.,and W.Ronald Hudson,describes a direct method forsolving complex two-dimensional plate and slab problems.  \nReport No.56-10,","cbCaipBR5CQ1pem8","https://ap.wps.com/l/cbCaipBR5CQ1pem8","pdf",13519989,256,"English","# Preface\n## Linear elastic analytical approach\n## Computer program and loading-case efficiency\n## Report series context\n## Program deck and test data availability\n## Acknowledgments\n# List of Reports","[{\"question\":\"Which organizations sponsored the development described in the report?\",\"answer\":\"The work was conducted for the Texas Highway Department in cooperation with the U.S. Department of Transportation, Federal Highway Administration, by the Center for Highway Research at the University of Texas at Austin.\"}]","Linearly Elastic Analysis of Plane Frames Subjected to Complex Loading Conditions - Research Report 56-21 - Analytical tool and computer simulation methods | PDF",645]