{"id":1023,"date":"2024-09-23T14:59:06","date_gmt":"2024-09-23T12:59:06","guid":{"rendered":"https:\/\/solveredu.com\/?p=1023"},"modified":"2026-01-27T23:49:50","modified_gmt":"2026-01-27T22:49:50","slug":"statyczna-wyznaczalnosc","status":"publish","type":"post","link":"https:\/\/solveredu.com\/tr\/post\/statyczna-wyznaczalnosc\/","title":{"rendered":"Statik belirlenebilirlik"},"content":{"rendered":"

Bu yaz\u0131da statik belirsizli\u011fin derecesinin ne oldu\u011funu \u00f6\u011freneceksiniz. Bir sistemin (kiri\u015f, \u00e7er\u00e7eve, kafes kiri\u015f) statik olarak belirli olup olmad\u0131\u011f\u0131 nas\u0131l belirlenir? Ayr\u0131ca, mekanikte kar\u015f\u0131la\u015ft\u0131\u011f\u0131m\u0131z olas\u0131 destek durumlar\u0131 hakk\u0131nda bilgi edineceksiniz.<\/p>\n\n\n\n

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

Statik bir sistem, dura\u011fan olan bir sistem olarak adland\u0131r\u0131l\u0131r. Yani, d\u0131\u015f kuvvetlerin etkisi alt\u0131nda hareket edemez. E\u011fer hareket ederse o zaman bir mekanizmad\u0131r.<\/p>\n\n\n\n

Cisimlerin hareketi ile ilgilenece\u011fimiz mekanik dal\u0131 kinematik ve dinamiktir. Statik<\/strong> mekani\u011fin bile\u015fenlerin hareketsiz oldu\u011fu k\u0131sm\u0131d\u0131r, bunun b\u00f6yle olmas\u0131 i\u00e7in birka\u00e7 ko\u015fulun kar\u015f\u0131lanmas\u0131 gerekir.<\/p>\n\n\n\n

Bu giri\u015fte:<\/p>\n\n\n\n

    \n
  1. Destekler. T\u00fcrler ve semboller<\/a><\/li>\n\n\n\n
  2. Statik belirlenmemi\u015flik derecesi<\/a><\/li>\n\n\n\n
  3. Statik olarak belirlenebilir sistemler<\/a><\/li>\n\n\n\n
  4. Statik olarak belirsiz sistemler<\/a><\/li>\n\n\n\n
  5. Mekanizmalar<\/a><\/li>\n<\/ol>\n\n\n\n

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

    Destekler. T\u00fcrler ve semboller<\/strong><\/h1>\n\n\n\n

    Sistemi sabit tutmak i\u00e7in onu desteklememiz gerekir. Mekanik \u00f6devlerinde \u00e7o\u011funlukla a\u015fa\u011f\u0131daki gibi desteklerle kar\u015f\u0131la\u015f\u0131rs\u0131n\u0131z. Diyagramlarda bunlar i\u015faretlenmi\u015ftir destek reaksiyonlar\u0131<\/strong> bireysel destekler i\u00e7in:<\/p>\n\n\n\n

    \"kaymayan
    Sabit mesnet<\/figcaption><\/figure>\n\n\n\n
    \"\"
    Hareketli (Kay\u0131c\u0131) Mesnet<\/figcaption><\/figure>\n\n\n\n
    \"\"
    K\u0131s\u0131tlama<\/figcaption><\/figure>\n\n\n\n
    \"\"
    Ara mafsal<\/figcaption><\/figure>\n\n\n\n
    Yukar\u0131da bahsedilen t\u00fcm destekler uygulamada bulunabilir Kiri\u015f hesaplay\u0131c\u0131<\/u><\/a> kiri\u015f sistemlerini destekleme yollar\u0131n\u0131 test edebilece\u011finiz bir yer.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Statik sistemleri iki t\u00fcre ay\u0131rabiliriz:<\/p>\n\n\n\n

      \n
    1. Statik olarak belirlenebilir sistemler - b\u00f6yle bir sistemin statik belirlenemezlik derecesi s\u0131f\u0131rd\u0131r.<\/li>\n\n\n\n
    2. Statik olarak belirsiz sistemler - b\u00f6yle bir sistemin statik belirsizlik derecesi s\u0131f\u0131rdan b\u00fcy\u00fckt\u00fcr.<\/li>\n<\/ol>\n\n\n\n

      Statik belirlenmemi\u015flik derecesi<\/strong><\/h2>\n\n\n\n

      Belirli bir sistemin statik ay\u0131rt edilemezlik derecesini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131labilir. Bu form\u00fcl en iyi \u015fu hesaplamalar\u0131 yaparken kullan\u0131l\u0131r Kiri\u015fler<\/strong> i ram<\/strong>.<\/p>\n\n\n\n

      N=R-J-3<\/em>
      Nerede?
      N - statik derecesi sonu\u00e7suz
      R - destek reaksiyonlar\u0131n\u0131n say\u0131s\u0131. Yani, desteklerimiz i\u00e7in t\u00fcm reaksiyonlar\u0131n toplam\u0131
      J - i\u00e7 ba\u011flant\u0131lar\u0131n say\u0131s\u0131 - mevcut de\u011filse P=0
      3 - denge denklemlerinin say\u0131s\u0131. Statik sistemlerde bu say\u0131 3't\u00fcr<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

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

      \u0130\u00e7in makas<\/strong> form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibi kullanaca\u011f\u0131z:<\/p>\n\n\n\n

      2n = m + r<\/em>
      Nerede?
      n - kafes kiri\u015f d\u00fc\u011f\u00fcm say\u0131s\u0131
      m - kafes kiri\u015f elemanlar\u0131n\u0131n say\u0131s\u0131 (elemanlar)
      r - destek reaksiyonlar\u0131n\u0131n say\u0131s\u0131<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

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

      Yukar\u0131daki ili\u015fki sa\u011flan\u0131yorsa bir kafes kiri\u015f belirlenebilirdir. Yani, iki kat\u0131na \u00e7\u0131kar\u0131lan d\u00fc\u011f\u00fcm say\u0131s\u0131, \u00e7ubuklar\u0131n toplam\u0131na ve reaksiyon say\u0131s\u0131na e\u015fit olmal\u0131d\u0131r.<\/p>\n\n\n\n

      Statik olarak belirlenebilir sistem<\/strong><\/h3>\n\n\n\n

      Peki bu statik belirlenebilirlik nedir? Statik olarak belirlenebilir bir sistem, destek reaksiyonlar\u0131n\u0131 hesaplayabildi\u011fimiz bir sistemdir. \u00d6rne\u011fin, kiri\u015fimiz veya \u00fc\u00e7 denge denklemini kullanarak t\u00fcm reaksiyonlar\u0131 hesaplayabiliyorsak statik olarak belirlenebilir olacakt\u0131r. Bu t\u00fcr sistemlerde statik belirsizli\u011fin derecesi s\u0131f\u0131rd\u0131r.<\/p>\n\n\n\n

      N=0<\/p>\n\n\n\n

      Yukar\u0131daki form\u00fcl\u00fc kullanarak<\/p>\n\n\n\n

      N=R-J-3 => N=3 - 0 - 3 = 0<\/p>\n\n\n\n

      Nerede?<\/p>\n\n\n\n

      R=3 - desteklerimiz i\u00e7in t\u00fcm reaksiyonlar\u0131n toplam\u0131<\/p>\n\n\n\n

      J=0 i\u00e7 eklem say\u0131s\u0131, mevcut de\u011fil<\/p>\n\n\n\n

      3 - denge denklemlerinin say\u0131s\u0131<\/p>\n\n\n\n

      Basit bir kafes kiri\u015f i\u00e7in hesaplama \u015fu \u015fekilde olacakt\u0131r:<\/p>\n\n\n\n

      2n = m + r => 2*5 = 7 + 3 => 10 = 10<\/em><\/p>\n\n\n\n

      Nerede?<\/p>\n\n\n\n

      n = 5 - d\u00fc\u011f\u00fcm say\u0131s\u0131<\/p>\n\n\n\n

      m = 7 - kafes kiri\u015f elemanlar\u0131n\u0131n say\u0131s\u0131<\/p>\n\n\n\n

      r = 3 - destek reaksiyonlar\u0131n\u0131n say\u0131s\u0131<\/p>\n\n\n\n

      Statik olarak belirsiz sistemler<\/strong><\/h3>\n\n\n\n

      Statik olarak belirsiz bir sistem, destek reaksiyonlar\u0131n\u0131 hesaplayamad\u0131\u011f\u0131m\u0131z bir sistemdir. Bu t\u00fcr sistemlerde statik belirsizlik derecesi s\u0131f\u0131rdan b\u00fcy\u00fckt\u00fcr. Destek reaksiyonlar\u0131n\u0131n bilinmeyen say\u0131s\u0131 denge denklemlerinin say\u0131s\u0131ndan daha fazlad\u0131r.<\/p>\n\n\n\n

      N > 0<\/p>\n\n\n\n

      Nerede?<\/p>\n\n\n\n

      R=5 - desteklerimiz i\u00e7in t\u00fcm reaksiyonlar\u0131n toplam\u0131<\/p>\n\n\n\n

      J=0 - i\u00e7 eklem say\u0131s\u0131, mevcut de\u011fil<\/p>\n\n\n\n

      3 - denge denklemlerinin say\u0131s\u0131<\/p>\n\n\n\n

      Kiri\u015f iki kez statik olarak belirlenemez - (sonu\u00e7 N=2)<\/p>\n\n\n\n

      B\u00f6yle bir sistem kat\u0131d\u0131r ve \u00e7al\u0131\u015fma olas\u0131l\u0131\u011f\u0131 yoktur. Y\u00fck veya s\u0131cakl\u0131k de\u011fi\u015fimi alt\u0131ndaki bir kiri\u015fin yer de\u011fi\u015ftirme olas\u0131l\u0131\u011f\u0131, ba\u015fka bir deyi\u015fle \u00e7al\u0131\u015fma olas\u0131l\u0131\u011f\u0131 yoktur.<\/p>\n\n\n\n

      Mekanizmalar<\/strong><\/h3>\n\n\n\n

      Tart\u0131\u015faca\u011f\u0131m son sistem t\u00fcr\u00fc, hareket olas\u0131l\u0131\u011f\u0131 olan sistemlerdir - mekanizmalar. Bu t\u00fcr sistemler i\u00e7in statik belirsizlik derecesi negatiftir.<\/p>\n\n\n\n

      N < 0<\/p>\n\n\n\n

      N=R-J-3 => N=2-0- 3 = -1<\/p>\n\n\n\n

      Statik d\u0131\u015fb\u00fckey olmama konusunun sonuna geldik, te\u015fekk\u00fcrler ve di\u011fer g\u00f6nderilere g\u00f6z atmaktan \u00e7ekinmeyin \ud83d\ude0a<\/p>","protected":false},"excerpt":{"rendered":"

      W tym wpisie dowiesz si\u0119 co to jest stopie\u0144 statycznej niewyznaczalno\u015bci? W jaki spos\u00f3b wyznaczy\u0107 czy uk\u0142ad (belka, rama, kratownica) jest statycznie wyznaczalna. Dodatkowo poznasz mo\u017cliwe przypadki podp\u00f3r z kt\u00f3rymi spotykamy si\u0119 w zadaniach z mechaniki. Uk\u0142adem statycznym nazywamy taki uk\u0142ad, kt\u00f3ry jest nieruchomy. To znaczy, \u017ce nie mo\u017ce si\u0119 porusza\u0107 pod wp\u0142ywem dzia\u0142ania si\u0142 […]<\/p>\n","protected":false},"author":255930052,"featured_media":1040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_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","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":true},"categories":[14815],"tags":[14842,14844,14843],"class_list":["post-1023","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanika","tag-statyczna-wyznaczalnosc","tag-uklad-statycznie-niewyznaczalny","tag-uklad-statycznie-wyznaczalny"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Reakcja-przegubowa-przesuwna-blad.png?fit=753%2C589&ssl=1","jetpack_shortlink":"https:\/\/wp.me\/pg3flK-gv","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts\/1023","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=1023"}],"version-history":[{"count":14,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts\/1023\/revisions"}],"predecessor-version":[{"id":3080,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts\/1023\/revisions\/3080"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/media\/1040"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/media?parent=1023"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/categories?post=1023"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/tags?post=1023"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}