{"id":1432,"date":"2022-07-18T11:45:00","date_gmt":"2022-07-18T09:45:00","guid":{"rendered":"https:\/\/technischemechanik.com\/?p=1432"},"modified":"2022-07-17T20:57:46","modified_gmt":"2022-07-17T18:57:46","slug":"statik-gleichgewicht-am-gerbertraeger","status":"publish","type":"post","link":"https:\/\/technischemechanik.com\/de\/2022\/07\/18\/statik-gleichgewicht-am-gerbertraeger\/","title":{"rendered":"Statik: Gleichgewicht am Gerbertr\u00e4ger"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Herzlich Willkommen!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Wir sehen uns heute an was eigentlich ein Gerbertr\u00e4ger ist und wie wir dessen Lagerreaktionen bestimmen k\u00f6nnen.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>Der zusammengesetzte Balken ist in C gelenkig gelagert und wird in A und B jeweils von einem Rollenlager gehalten. In D ist ein Scharniergelenk angebracht. Bestimme die Lagerkr\u00e4fte unter Vernachl\u00e4ssigung der Dicke des Balkens. <\/p><p>Geg.: F1=4kN, F2=8kN, F3=12kN, M=15kNm, l=2m, \u03b1=30\u00b0, tan\u03b2=4\/3<\/p><cite>Quelle: Aufgabe 6.73 (S. 351) aus Russell C. Hibbeler, Technische Mechanik 1 Statik, 12. Auflage, 2012 Pearson GmbH, M\u00fcnchen<\/cite><\/blockquote>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"712\" height=\"355\" data-attachment-id=\"1434\" data-permalink=\"https:\/\/technischemechanik.com\/de\/2022\/07\/18\/statik-gleichgewicht-am-gerbertraeger\/abb08\/\" data-orig-file=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/07\/Abb08.jpg?fit=894%2C446&amp;ssl=1\" data-orig-size=\"894,446\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Abb08\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/07\/Abb08.jpg?fit=712%2C355&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/07\/Abb08.jpg?resize=712%2C355&#038;ssl=1\" alt=\"\" class=\"wp-image-1434\" srcset=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/07\/Abb08.jpg?w=894&amp;ssl=1 894w, https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/07\/Abb08.jpg?resize=300%2C150&amp;ssl=1 300w, https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/07\/Abb08.jpg?resize=768%2C383&amp;ssl=1 768w\" sizes=\"auto, (max-width: 712px) 100vw, 712px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Beim Gerbertr\u00e4ger kommt es darauf an, dass wir ein im Grunde statisch unbestimmtes System durch zerlegen im Gerbergelenk zu einem statisch bestimmten System machen k\u00f6nnen. Wir erhalten dadurch im vorliegenden Beispiel zwei Teilsysteme. F\u00fcr beide Teilsysteme k\u00f6nnen wir unsere Gleichgewichtsbedingungen (Momenten-, und Kr\u00e4ftegleichgewicht) separat anschreiben und erhalten damit sechs Gleichungen f\u00fcr insgesamt sechs Unbekannte (vier Lagerreaktionen und zwei Gelenkskr\u00e4fte). Damit l\u00e4sst sich das System schlussendlich vollst\u00e4ndig berechnen. Wichtig hierbei ist, dass die Gelenkskr\u00e4fte innere Kr\u00e4fte sind und sich beim Zusammensetzen des Tr\u00e4gers wieder aufheben m\u00fcssen. Daher m\u00fcssen Sie an den beiden Teilsystemen in jeweils entgegengesetzte Richtung zeigen. Alle Details zur Rechnung und viele weitere Anmerkungen erfahrt ihr wieder im verlinkten Video. Viel Spa\u00df damit! <\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-rich is-provider-handler-einbetten wp-block-embed-handler-einbetten wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"712\" height=\"401\" src=\"https:\/\/www.youtube.com\/embed\/k_CN-_X2m9c?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=de-DE&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><figcaption class=\"wp-element-caption\"><br><\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Wenn Fragen oder Unklarheiten auftauchen, freue ich mich jederzeit auf eure Kommentare &#8211; entweder hier oder direkt auf YouTube. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bis bald,<br>Markus <\/p>\n\n\n<div class=\"crowdsignal-feedback-wrapper\" data-crowdsignal-feedback=\"{&quot;feedbackPlaceholder&quot;:&quot;Sag mir bitte was dir besonders gefallen hat und was ich verbessern soll! Vielen Dank!&quot;,&quot;submitText&quot;:&quot;Danke f\\u00fcr dein Feedback!&quot;,&quot;surveyId&quot;:2705235,&quot;title&quot;:&quot;Feedback&quot;,&quot;emailResponses&quot;:false,&quot;emailPlaceholder&quot;:&quot;Deine E-Mail-Adresse&quot;,&quot;emailRequired&quot;:false,&quot;header&quot;:&quot;\\ud83d\\udc4b Hallo!&quot;,&quot;hideBranding&quot;:false,&quot;hideTriggerShadow&quot;:false,&quot;submitButtonLabel&quot;:&quot;Senden&quot;,&quot;toggleOn&quot;:&quot;click&quot;,&quot;triggerLabel&quot;:&quot;Feedback&quot;,&quot;x&quot;:&quot;left&quot;,&quot;y&quot;:&quot;bottom&quot;,&quot;status&quot;:&quot;open&quot;,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true},&quot;nonce&quot;:&quot;bc2d822b24&quot;}\"><\/div>\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\"><div class=\"crowdsignal-vote-wrapper\" data-crowdsignal-vote=\"{&quot;pollId&quot;:&quot;29311620-3302-4a28-8c62-34c614948b60&quot;,&quot;title&quot;:&quot;Unbenannte Abstimmung 20&quot;,&quot;hideBranding&quot;:false,&quot;pollStatus&quot;:&quot;open&quot;,&quot;size&quot;:&quot;medium&quot;,&quot;borderWidth&quot;:1,&quot;borderRadius&quot;:5,&quot;hideResults&quot;:false,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true},&quot;apiPollData&quot;:{&quot;id&quot;:11160746,&quot;question&quot;:&quot;&quot;,&quot;note&quot;:&quot;&quot;,&quot;settings&quot;:{&quot;title&quot;:&quot;Unbenannte Abstimmung 20&quot;,&quot;after_vote&quot;:&quot;results&quot;,&quot;after_message&quot;:&quot;&quot;,&quot;randomize_answers&quot;:false,&quot;restrict_vote_repeat&quot;:false,&quot;captcha&quot;:false,&quot;multiple_choice&quot;:false,&quot;redirect_url&quot;:&quot;&quot;,&quot;close_status&quot;:&quot;open&quot;,&quot;close_after&quot;:false},&quot;answers&quot;:[{&quot;answer_text&quot;:&quot;up&quot;,&quot;id&quot;:51079852,&quot;client_id&quot;:&quot;4ae8e890-5309-41a3-bae2-719a23a5da36&quot;},{&quot;answer_text&quot;:&quot;down&quot;,&quot;id&quot;:51079853,&quot;client_id&quot;:&quot;b583d8b0-1c19-492c-a781-9f4dfba236ce&quot;}],&quot;source_link&quot;:&quot;https:\\\/\\\/technischemechanik.com&quot;,&quot;client_id&quot;:&quot;29311620-3302-4a28-8c62-34c614948b60&quot;}}\">\n<div data-crowdsignal-vote-item=\"{&quot;answerId&quot;:&quot;4ae8e890-5309-41a3-bae2-719a23a5da36&quot;,&quot;type&quot;:&quot;up&quot;,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true}}\"><\/div>\n\n<div data-crowdsignal-vote-item=\"{&quot;answerId&quot;:&quot;b583d8b0-1c19-492c-a781-9f4dfba236ce&quot;,&quot;type&quot;:&quot;down&quot;,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true}}\"><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\"><div class=\"crowdsignal-applause-wrapper\" data-crowdsignal-applause=\"{&quot;pollId&quot;:&quot;94052372-60ee-4246-bdb3-b44cfaeeec3b&quot;,&quot;title&quot;:&quot;Unbenannter Applaus&quot;,&quot;answerId&quot;:&quot;4951fcb8-b48f-428e-82e4-90330cd7aed6&quot;,&quot;hideBranding&quot;:false,&quot;size&quot;:&quot;medium&quot;,&quot;pollStatus&quot;:&quot;open&quot;,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true},&quot;apiPollData&quot;:{&quot;id&quot;:11160747,&quot;question&quot;:&quot;&quot;,&quot;note&quot;:&quot;&quot;,&quot;settings&quot;:{&quot;title&quot;:&quot;Unbenannter Applaus&quot;,&quot;after_vote&quot;:&quot;results&quot;,&quot;after_message&quot;:&quot;&quot;,&quot;randomize_answers&quot;:false,&quot;restrict_vote_repeat&quot;:false,&quot;captcha&quot;:false,&quot;multiple_choice&quot;:false,&quot;redirect_url&quot;:&quot;&quot;,&quot;close_status&quot;:&quot;open&quot;,&quot;close_after&quot;:false},&quot;answers&quot;:[{&quot;answer_text&quot;:&quot;clap&quot;,&quot;id&quot;:51079854,&quot;client_id&quot;:&quot;4951fcb8-b48f-428e-82e4-90330cd7aed6&quot;}],&quot;source_link&quot;:&quot;https:\\\/\\\/technischemechanik.com&quot;,&quot;client_id&quot;:&quot;94052372-60ee-4246-bdb3-b44cfaeeec3b&quot;}}\"><\/div><\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Herzlich Willkommen! Wir sehen uns heute an was eigentlich ein Gerbertr\u00e4ger ist und wie wir dessen Lagerreaktionen bestimmen k\u00f6nnen. Der zusammengesetzte Balken ist in C gelenkig gelagert und wird in A und B jeweils von einem Rollenlager gehalten. In D ist ein Scharniergelenk angebracht. Bestimme die Lagerkr\u00e4fte unter Vernachl\u00e4ssigung der Dicke des Balkens. Geg.: F1=4kN, &hellip; <a href=\"https:\/\/technischemechanik.com\/de\/2022\/07\/18\/statik-gleichgewicht-am-gerbertraeger\/\" class=\"more-link\"><span class=\"screen-reader-text\">Statik: Gleichgewicht am Gerbertr\u00e4ger<\/span> weiterlesen<\/a><\/p>\n","protected":false},"author":110396568,"featured_media":1419,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_crdt_document":"","advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[2602546,1584145,172484],"tags":[25466,729611524,100678,414019,35890,5167337,750913306,727961753,350894,166867,113216,290680250,163250810,2517859,8207,662707,720191,1213491,143003,10126,73726871,750913302,161115,750913295,2411,1121513,727213064,729611525,2326513,2722,1268153,271082537,727961757,729611523],"class_list":["post-1432","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ubungsaufgaben","category-gleichgewicht","category-statik","tag-beispiel","tag-ebenes-zentrales-kraftesystem","tag-einfuhrung","tag-erklart","tag-featured","tag-festigkeitslehre","tag-freikorperbild","tag-gleichgewicht","tag-grundlagen","tag-hochschule","tag-kraft","tag-kraftsystem","tag-kraftvektor","tag-krafte","tag-lernen","tag-maschinenbau","tag-mechanik","tag-nachhilfe","tag-newton","tag-physik","tag-physik-nachhilfe","tag-reduktion","tag-screencast","tag-statik","tag-studium","tag-technische-mechanik","tag-technische-mechanik-1","tag-technische-mechanik-grundlagen","tag-tm-1","tag-uni","tag-verstehen","tag-zentrales-kraftsystem","tag-zentrales-kraftesystem","tag-zentralkraftsystem"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/07\/YouTube-Thumbnail-Gleichgewicht-512-%C3%97-512-px.png?fit=512%2C512&ssl=1","jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7UJuu-n6","jetpack-related-posts":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/posts\/1432","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/users\/110396568"}],"replies":[{"embeddable":true,"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/comments?post=1432"}],"version-history":[{"count":4,"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/posts\/1432\/revisions"}],"predecessor-version":[{"id":1437,"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/posts\/1432\/revisions\/1437"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/media\/1419"}],"wp:attachment":[{"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/media?parent=1432"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/categories?post=1432"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/technischemechanik.com\/de\/wp-json\/wp\/v2\/tags?post=1432"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}