{"id":1093,"date":"2024-09-23T14:59:28","date_gmt":"2024-09-23T12:59:28","guid":{"rendered":"https:\/\/solveredu.com\/?p=1093"},"modified":"2026-01-27T23:34:47","modified_gmt":"2026-01-27T22:34:47","slug":"static-equilibrium-equations","status":"publish","type":"post","link":"https:\/\/solveredu.com\/tr\/post\/rownania-rownowagi\/","title":{"rendered":"Denge denklemleri"},"content":{"rendered":"

Bu yaz\u0131da \u015fu konularda bilgi bulacaks\u0131n\u0131z:<\/p>\n\n\n\n

    \n
  1. Denge denklemleri nelerdir?<\/a><\/li>\n\n\n\n
  2. Bir d\u00fczlem kuvvet sistemi i\u00e7in denge denklemleri (2D)<\/a><\/li>\n\n\n\n
  3. Uzamsal bir kuvvet sistemi i\u00e7in denge denklemleri (3D)<\/a><\/li>\n<\/ol>\n\n\n\n
    Denge denklemleri, dengede olan bir cismin durumunu tan\u0131mlamak i\u00e7in kullan\u0131l\u0131r. B\u00f6yle bir cisim konumunu de\u011fi\u015ftirmez, yani hareketsizdir.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Hareketsiz bir cisme etki eden t\u00fcm kuvvet ve momentlerin toplam\u0131 dengede olmal\u0131d\u0131r, bunu matematiksel olarak a\u015fa\u011f\u0131daki gibi tan\u0131mlar\u0131z:<\/p>\n\n\n\n

    \"\\F_{ix} - kuvvetlerin x ekseni \u00fczerindeki izd\u00fc\u015f\u00fcmlerinin toplam\u0131<\/p>\n\n\n\n

    \"\\F_{iy} - kuvvetlerin y eksenindeki izd\u00fc\u015f\u00fcmlerinin toplam\u0131<\/p>\n\n\n\n

    \"\\M_{i} - bir noktadaki momentlerin toplam\u0131<\/p>\n\n\n\n

    D\u00fczlem sistem (2D) - denge denklemleri<\/h1>\n\n\n\n

    Yukar\u0131daki denklemler \u015fu durumlarda ge\u00e7erlidir d\u00fcz g\u00fc\u00e7 sistemi<\/strong>. Bunlar\u0131 kiri\u015flerin, \u00e7er\u00e7evelerin ve kafes kiri\u015flerin reaksiyonlar\u0131n\u0131 belirlemek i\u00e7in kullan\u0131r\u0131z. Bu t\u00fcr elemanlar stati\u011fin temel sorular\u0131d\u0131r. Bu t\u00fcr g\u00f6revlerde, elemanlar\u0131n hareketsiz kalmas\u0131n\u0131 isteriz. E\u011fer cisimler hareket ediyorsa, kinematik veya dinamik gibi mekani\u011fin di\u011fer dallar\u0131ndan bahsediyoruz demektir.<\/p>\n\n\n\n

    \"2B<\/figure>\n\n\n\n

    Bir d\u00fczlem sisteminde, bir cisim x ve y y\u00f6nlerinde hareket edebilir ve bize bakan z ekseni etraf\u0131nda d\u00f6nebilir. D\u00fczlem sistemde bir cismin 3 serbestlik derecesi vard\u0131r. Ve bir cismin hareketsiz kalabilmesi i\u00e7in bu 3 serbestlik derecesini dengelememiz gerekir. \u0130\u015fte bu ama\u00e7la denge denklemlerini kullan\u0131r\u0131z. E\u011fer x ve y kuvvetlerinin dengesi ve momentlerin toplam\u0131 s\u0131f\u0131ra e\u015fitse, bu cismin hareket etmedi\u011fi veya d\u00f6nmedi\u011fi anlam\u0131na gelir.<\/p>\n\n\n\n

    Belirli bir d\u00fcz sistem t\u00fcr\u00fc d\u00fcz yak\u0131nsak kuvvet sistemi<\/strong> (merkezi sistem olarak da adland\u0131r\u0131l\u0131r). Bu, kuvvetlerin tek bir noktada kesi\u015fti\u011fi bir sistemdir. Bu noktada birle\u015firler. B\u00f6yle bir sistem i\u00e7in denge ko\u015fulu sadece iki denklemdir:<\/p>\n\n\n\n

    \"\\F_{ix} - kuvvetlerin x ekseni \u00fczerindeki izd\u00fc\u015f\u00fcmlerinin toplam\u0131<\/p>\n\n\n\n

    \"\\F_{iy} - kuvvetlerin y eksenindeki izd\u00fc\u015f\u00fcmlerinin toplam\u0131<\/p>\n\n\n\n

    Mekansal sistem (3D) - denge denklemleri<\/h2>\n\n\n\n

    Mek\u00e2nsal d\u00fczenleme biraz daha fazla serbestlik derecesine sahiptir. Alt\u0131 kadar serbestlik derecesi vard\u0131r. Her bir serbestlik derecesi i\u00e7in denge denklemini tan\u0131mlayan bir denklemimiz var. B\u00f6ylece alt\u0131 denklem elde ederiz. Uzamsal sistemlerde destek reaksiyonlar\u0131n\u0131 belirledi\u011fimiz g\u00f6revlerde, alt\u0131 denklem oldu\u011fu i\u00e7in \u00e7\u00f6z\u00fcm\u00fc bulmak daha zordur.<\/p>\n\n\n\n

    \"\\F_{ix} - kuvvetlerin x ekseni \u00fczerindeki izd\u00fc\u015f\u00fcmlerinin toplam\u0131<\/p>\n\n\n\n

    \"\\F_{iy} - kuvvetlerin y eksenindeki izd\u00fc\u015f\u00fcmlerinin toplam\u0131<\/p>\n\n\n\n

    \"\\F_{iz} - kuvvetlerin z ekseni \u00fczerindeki izd\u00fc\u015f\u00fcmlerinin toplam\u0131<\/p>\n\n\n\n

    \"\\\u25a0Sigma - x ekseni etraf\u0131ndaki momentlerin toplam\u0131<\/p>\n\n\n\n

    \"\\M_{iy} - y ekseni etraf\u0131ndaki momentlerin toplam\u0131<\/p>\n\n\n\n

    \"\\M_{iz} - z ekseni etraf\u0131ndaki momentlerin toplam\u0131<\/p>\n\n\n\n

    Maksimum bilinmeyen say\u0131s\u0131 kadar denklemi hat\u0131rlay\u0131n. 6 denklem = maksimum 6 bilinmeyen.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Bu, uzaydaki bir cismin \u00fc\u00e7 y\u00f6nde hareket edebilece\u011fi ve \u00fc\u00e7 eksen etraf\u0131nda d\u00f6nebilece\u011fi anlam\u0131na gelir.<\/p>\n\n\n\n

    \"3B<\/figure>\n\n\n\n

    Statikteki denge denklemleri konusunda benden bu kadar.<\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>","protected":false},"excerpt":{"rendered":"

    W tym wpisie znajdziesz informacj\u0119 na temat: R\u00f3wnania r\u00f3wnowagi s\u0142u\u017c\u0105 do opisania stanu cia\u0142a kt\u00f3re, jest w r\u00f3wnowadze. Takie cia\u0142o nie zmienia swojej pozycji, czyli jest w spoczynku. Suma wszystkich si\u0142 i moment\u00f3w dzia\u0142aj\u0105cych na cia\u0142o w stanie spoczynku musi si\u0119 r\u00f3wnowa\u017cy\u0107, opisujemy to matematycznie w nast\u0119puj\u0105cy spos\u00f3b: – suma rzut\u00f3w si\u0142 na o\u015b x […]<\/p>\n","protected":false},"author":255930052,"featured_media":1637,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_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":true},"categories":[14815],"tags":[14823,14822,14820],"class_list":["post-1093","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanika","tag-przestrzenny-uklad-sil","tag-plaski-uklad-sil-2","tag-rownania-rownowagi"],"jetpack_publicize_connections":[],"jetpack_shortlink":"https:\/\/wp.me\/pg3flK-hD","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/stopnie-swobody_3D_eng.png?fit=947%2C556&ssl=1","_links":{"self":[{"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts\/1093","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/users\/255930052"}],"replies":[{"embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/comments?post=1093"}],"version-history":[{"count":17,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts\/1093\/revisions"}],"predecessor-version":[{"id":3067,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts\/1093\/revisions\/3067"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/media\/1637"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/media?parent=1093"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/categories?post=1093"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/tags?post=1093"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}