{"id":2177,"date":"2025-04-08T15:28:26","date_gmt":"2025-04-08T13:28:26","guid":{"rendered":"https:\/\/solveredu.com\/?p=2177"},"modified":"2025-10-12T13:47:03","modified_gmt":"2025-10-12T11:47:03","slug":"bir-cemberin-atalet-momenti","status":"publish","type":"post","link":"https:\/\/solveredu.com\/tr\/post\/moment-bezwladnosci-kola\/","title":{"rendered":"Bir tekerle\u011fin eylemsizlik momenti - teori, form\u00fcller ve hesaplama \u00f6rnekleri"},"content":{"rendered":"

Eylemsizlik momenti nedir?<\/strong><\/strong><\/h1>\n\n\n\n

Eylemsizlik momenti, bir k\u00fctlenin veya y\u00fczeyin bir d\u00f6nme ekseni etraf\u0131ndaki da\u011f\u0131l\u0131m\u0131n\u0131 tan\u0131mlayan temel geometrik b\u00fcy\u00fckl\u00fcklerden biridir. Yap\u0131sal mekanikte, bir y\u00fczeyin atalet momenti (di\u011fer ad\u0131yla ikinci alan momenti) bir kesitin e\u011filmeye kar\u015f\u0131 direncini tan\u0131mlar. Eylemsizlik momenti ne kadar b\u00fcy\u00fckse, eleman\u0131n sertli\u011fi de o kadar b\u00fcy\u00fck olur.<\/p>\n\n\n\n

Bir tekerle\u011fin eylemsizlik momenti - form\u00fcl<\/strong><\/strong><\/h2>\n\n\n\n

Yar\u0131\u00e7apl\u0131 bir daire (kat\u0131 disk) i\u00e7in, dairenin merkezinden ge\u00e7en ve dairenin y\u00fczeyine dik olan bir eksene g\u00f6re y\u00fczeyin eylemsizlik momenti :<\/p>\n\n\n\n

\"I_{x},I_{y}<\/p>\n\n\n\n

E\u011fer \u00e7ap\u0131 biliyorsan\u0131z, d\u00f6n\u00fc\u015ft\u00fcr\u00fclm\u00fc\u015f form\u00fcl\u00fc kullanabilirsiniz:<\/p>\n\n\n\n

\"I_{x},I_{y}<\/p>\n\n\n\n

Bir daire i\u00e7in hesaplama \u00f6rne\u011fi<\/strong><\/p>\n\n\n\n

A\u015fa\u011f\u0131da, online hesap makinemizde bir dairenin eylemsizlik momentinin nas\u0131l hesaplanaca\u011f\u0131na dair bir \u00f6rnek yer almaktad\u0131r. Basit\u00e7e \"daire\" \u015feklini se\u00e7in, yar\u0131\u00e7ap\u0131 girin ve hesap makinesi eylemsizlik momentinin de\u011ferini otomatik olarak hesaplayacakt\u0131r.<\/p>\n\n\n\n

\"Tekerle\u011fin<\/figure>\n\n\n\n

Yar\u0131m dairenin eylemsizlik momenti - simetri eksikli\u011fi<\/strong><\/strong><\/strong><\/h2>\n\n\n\n

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

Bir yar\u0131m daire i\u00e7in eylemsizlik momenti form\u00fcl\u00fc farkl\u0131d\u0131r \u00e7\u00fcnk\u00fc \u015fekil yatay eksen etraf\u0131nda simetrik de\u011fildir. Yar\u0131m dairenin a\u011f\u0131rl\u0131k merkezinden ge\u00e7en yatay eksene g\u00f6re yar\u0131m dairenin eylemsizlik momenti:<\/p>\n\n\n\n

\"I_{x}<\/p>\n\n\n\n

Yar\u0131m dairenin a\u011f\u0131rl\u0131k merkezinden ge\u00e7en dikey eksene g\u00f6re yar\u0131m dairenin eylemsizlik momenti:<\/p>\n\n\n\n

\"I_{y}<\/p>\n\n\n\n

Yani, tam bir tekerle\u011fin atalet momentinin yar\u0131s\u0131 kadar.<\/p>\n\n\n\n

Yar\u0131m daire i\u00e7in hesaplama \u00f6rne\u011fi<\/strong><\/p>\n\n\n\n

A\u015fa\u011f\u0131da, online hesap makinemizde bir yar\u0131m dairenin eylemsizlik momentinin nas\u0131l hesaplanaca\u011f\u0131na dair bir \u00f6rnek yer almaktad\u0131r. Basit\u00e7e \"yar\u0131m daire\" \u015feklini se\u00e7in, d\u00fczlem \u00fczerindeki oryantasyonu se\u00e7in, yar\u0131\u00e7ap\u0131 ve yar\u0131m dairenin merkezinin konumunu girin ve hesap makinesi atalet momentinin de\u011ferini otomatik olarak hesaplayacakt\u0131r.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

Boru profil - hafif ve g\u00fc\u00e7l\u00fc<\/strong><\/h2>\n\n\n\n

Boru \u015feklindeki kesitler (yani halkalar) \u00e7ok elveri\u015fli bir atalet-a\u011f\u0131rl\u0131k oran\u0131na sahiptir. \u0130\u00e7i bo\u015f olmalar\u0131 sayesinde, \u00f6nemli \u00f6l\u00e7\u00fcde daha az malzeme t\u00fcketimiyle y\u00fcksek bir rijitlik sa\u011flarlar. D\u0131\u015f ve i\u00e7 yar\u0131\u00e7ap\u0131 olan bir halkan\u0131n (t\u00fcp) atalet momenti i\u00e7in form\u00fcl:<\/p>\n\n\n\n

\"I_{x},I_{y}<\/p>\n\n\n\n

Bir boru profili i\u00e7in hesaplama \u00f6rne\u011fi<\/strong><\/p>\n\n\n\n

A\u015fa\u011f\u0131da, \u00e7evrimi\u00e7i hesaplay\u0131c\u0131m\u0131zda bir boru kesitinin atalet momentinin nas\u0131l hesaplanaca\u011f\u0131na dair bir \u00f6rnek yer almaktad\u0131r. Basit\u00e7e 'daire' \u015feklini se\u00e7in, yar\u0131\u00e7ap\u0131 girin, ard\u0131ndan delik i\u00e7in tekrar 'daire'yi se\u00e7in, \u00e7ap\u0131 girin ve deli\u011fi kesmek i\u00e7in 'kes' se\u00e7ene\u011fini se\u00e7in. Ard\u0131ndan \u00e7\u00f6z d\u00fc\u011fmesine bas\u0131n ve hesap makinesi atalet momentinin de\u011ferini otomatik olarak hesaplayacakt\u0131r.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

G\u00f6r\u00fclebilece\u011fi gibi, boru \u015feklindeki kesitin atalet momenti kesik sayesinde azalmaktad\u0131r. Bununla birlikte, kesit k\u00fctle merkezine yak\u0131n oldu\u011fundan, e\u011filmeye kar\u015f\u0131 diren\u00e7 \u00fczerindeki etkisi minimum d\u00fczeydedir ve bu durumda malzeme kullan\u0131m\u0131n\u0131 verimsiz hale getirmektedir. Sonu\u00e7 olarak, kesitin bu k\u0131sm\u0131n\u0131n \u00e7\u0131kar\u0131lmas\u0131, kesitin sertli\u011fi \u00fczerinde daha b\u00fcy\u00fck bir etkiye sahip olan alanlarda daha iyi bir malzeme da\u011f\u0131l\u0131m\u0131na izin verdi\u011fi i\u00e7in yap\u0131n\u0131n verimlili\u011finde bir iyile\u015fmeye yol a\u00e7ar.<\/p>\n\n\n\n

\u00d6zet<\/strong> <\/h2>\n\n\n\n

Eylemsizlik momenti hem e\u011filme hem de deformasyon kuvvetleri i\u00e7in \u00f6nemlidir. Bu, eylemsizlik momentinin paydada yer ald\u0131\u011f\u0131 form\u00fcllerinde g\u00f6r\u00fclebilir:<\/p>\n\n\n\n

E\u011filme gerilmesi i\u00e7in form\u00fcl:<\/p>\n\n\n\n

\"\\\u25a0sigma<\/p>\n\n\n\n

U\u00e7tan kuvvetle y\u00fcklenmi\u015f dirsekli bir balyan\u0131n sapmas\u0131 i\u00e7in form\u00fcl:<\/p>\n\n\n\n

\"f=<\/p>\n\n\n\n

Dairesel kesitlerdeki eylemsizlik momenti her iki eksende de ayn\u0131 olmas\u0131yla karakterize edilir. Bu mant\u0131kl\u0131d\u0131r \u00e7\u00fcnk\u00fc kesit hem X hem de Y eksenleri etraf\u0131nda simetriktir. Bunu, atalet momentinin eksenden eksene de\u011fi\u015febildi\u011fi bir I-kiri\u015f ile kar\u015f\u0131la\u015ft\u0131rarak analiz edece\u011fiz. Bu simetriyi kullanmak, y\u00fck her zaman eleman\u0131n daha g\u00fc\u00e7l\u00fc ekseni boyunca hareket etmedi\u011finde avantajl\u0131d\u0131r, \u00e7\u00fcnk\u00fc y\u00fck\u00fcn y\u00f6n\u00fcnden ba\u011f\u0131ms\u0131z olarak eleman\u0131n g\u00fcc\u00fcn\u00fc tahmin ederiz.<\/p>\n\n\n\n

Di\u011fer temel \u015fekiller i\u00e7in eylemsizlik momentleri \u015furada bulunabilir Giri\u015f<\/a><\/p>\n\n\n\n

Atalet momenti, yap\u0131sal mukavemet analizinde \u00f6nemli bir niceliktir. Art\u0131k bir daire, yar\u0131m daire ve boru profil i\u00e7in form\u00fclleri biliyorsunuz ve hesap makinemiz gerekli hesaplamalar\u0131 h\u0131zl\u0131 ve do\u011fru bir \u015fekilde yapman\u0131z\u0131 sa\u011fl\u0131yor.
Yukar\u0131daki hesaplamalar\u0131 kendiniz test etmek i\u00e7in atalet momenti hesaplama arac\u0131m\u0131z\u0131 deneyin.<\/p>\n\n\n\n

\n
\u00dccretsiz Dene<\/a><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"

Czym jest moment bezw\u0142adno\u015bci? Moment bezw\u0142adno\u015bci to jedna z podstawowych wielko\u015bci geometrycznych opisuj\u0105cych rozk\u0142ad masy lub powierzchni wok\u00f3\u0142 osi obrotu. W mechanice konstrukcji moment bezw\u0142adno\u015bci powierzchni (inaczej: drugi moment powierzchni) opisuje odporno\u015b\u0107 przekroju poprzecznego na zginanie. Im wi\u0119kszy moment bezw\u0142adno\u015bci, tym wi\u0119ksza sztywno\u015b\u0107 elementu konstrukcyjnego. Moment bezw\u0142adno\u015bci ko\u0142a – wz\u00f3r Dla ko\u0142a (pe\u0142nego dysku) o […]<\/p>\n","protected":false},"author":255930052,"featured_media":2199,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_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},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[14815],"tags":[14867,14852],"class_list":["post-2177","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanika","tag-moment-bezwladnosci","tag-srodek-ciezkosci"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/04\/kolo-e1760269513848.jpg?fit=620%2C277&ssl=1","jetpack_shortlink":"https:\/\/wp.me\/pg3flK-z7","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts\/2177","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=2177"}],"version-history":[{"count":39,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts\/2177\/revisions"}],"predecessor-version":[{"id":2904,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts\/2177\/revisions\/2904"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/media\/2199"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/media?parent=2177"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/categories?post=2177"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/tags?post=2177"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}