{"id":3128,"date":"2026-03-06T14:33:37","date_gmt":"2026-03-06T13:33:37","guid":{"rendered":"https:\/\/solveredu.com\/?p=3128"},"modified":"2026-03-06T14:33:42","modified_gmt":"2026-03-06T13:33:42","slug":"kiris-sehim-hesaplama","status":"publish","type":"post","link":"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/","title":{"rendered":"Kiri\u015f sapmas\u0131n\u0131n hesaplanmas\u0131: Moment entegrasyonundan kullan\u0131ma haz\u0131r bir hesap makinesine"},"content":{"rendered":"<p class=\"has-text-align-left wp-block-paragraph\" id=\"foo\">Sapma \u00e7izgisinin belirlenmesi, yap\u0131sal tasar\u0131m\u0131n kilit ad\u0131mlar\u0131ndan biridir. \u0130ster malzeme dayan\u0131m\u0131 kolokyumuna haz\u0131rlanan bir \u00f6\u011frenci ister bir bile\u015fenin rijitli\u011fini do\u011frulayan bir m\u00fchendis olun, kiri\u015fin y\u00fck alt\u0131nda nas\u0131l \u201e\u00e7al\u0131\u015ft\u0131\u011f\u0131n\u0131\u201d bilmeniz gerekir.<\/p>\n\n\n\n<p class=\"has-text-align-left wp-block-paragraph\">Bu makalede, klasik teoriden ba\u015flayarak t\u00fcm yolu y\u00fcr\u00fcyece\u011fiz. <strong>sapma \u00e7izgisinin diferansiyel denkleminin entegrasyonu<\/strong>, d\u00f6nme a\u00e7\u0131s\u0131 diyagramlar\u0131n\u0131n pratik \u00e7izimi yoluyla \u00f6rneklere <strong>basit\u00e7e desteklenmi\u015f bir kiri\u015f<\/strong> ve <strong>braket<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-left wp-block-paragraph\" id=\"foo\">Ve e\u011fer zaman\u0131n\u0131za de\u011fer veriyorsan\u0131z ve s\u0131k\u0131c\u0131 el hesaplamalar\u0131ndan ka\u00e7\u0131nmak istiyorsan\u0131z, makalenin sonunda benim <strong>tescilli \u0131\u015f\u0131n hesaplay\u0131c\u0131<\/strong>, bu i\u015flemleri sizin i\u00e7in birka\u00e7 saniye i\u00e7inde ger\u00e7ekle\u015ftirecektir. Hadi ba\u015flayal\u0131m!<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong><a href=\"#Teoria-i-Metodyka\" data-type=\"internal\" data-id=\"#Teoria-i-Metodyka\">Teorik temel: Sapma \u00e7izgisinin diferansiyel denklemi<\/a><\/strong><\/li>\n\n\n\n<li><strong><a href=\"#calkowanie\">Analitik y\u00f6ntem: Ad\u0131m ad\u0131m entegrasyon<\/a><\/strong><\/li>\n\n\n\n<li><strong><a href=\"#Przyk\u0142ad1\">\u00d6rnek 1: Basit mesnetli kiri\u015f<\/a><\/strong><\/li>\n\n\n\n<li><strong><a href=\"#Przyk\u0142ad2\">\u00d6rnek 2: Konsol kiri\u015f<\/a><\/strong><\/li>\n\n\n\n<li><strong><a href=\"#Sprawd\u017a\">H\u0131zl\u0131 do\u011frulama: \u00c7evrimi\u00e7i kiri\u015f hesaplay\u0131c\u0131s\u0131n\u0131 kullan\u0131n<\/a><\/strong><\/li>\n<\/ol>\n\n\n\n<h2 id=\"Teoria-i-Metodyka\" class=\"wp-block-heading\" style=\"font-size:clamp(16.293px, 1.018rem + ((1vw - 3.2px) * 0.777), 25px);\">1. Teori ve Metodoloji: Sapma nereden kaynaklan\u0131yor?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Kiri\u015f sapmas\u0131n\u0131n hesaplanmas\u0131<\/strong> Servis Verilebilirlik S\u0131n\u0131r Durumunun (SGU) kontrol edilmesinin en \u00f6nemli unsurlar\u0131ndan biridir. Bu s\u00fcreci anlayabilmek i\u00e7in, SGU'nun temeline geri d\u00f6nmemiz gerekir. <strong>kiri\u015f sapma do\u011frusunun diferansiyel denklemi<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Birbirine ba\u011flayan temel ili\u015fki <strong>e\u011filme momentine kar\u015f\u0131 sapma<\/strong>, form\u00fcl\u00fc ile tan\u0131mlanmaktad\u0131r:<\/p>\n\n\n\n<div class=\"wp-block-math has-medium-font-size\"><math display=\"block\"><semantics><mrow><mi>E<\/mi><mi>I<\/mi><mo>\u22c5<\/mo><msup><mi>y<\/mi><mrow><mo lspace=\"0em\" rspace=\"0em\" class=\"tml-prime\">\u2032<\/mo><mo lspace=\"0em\" rspace=\"0em\" class=\"tml-prime\">\u2032<\/mo><\/mrow><\/msup><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mo form=\"prefix\" stretchy=\"false\">\u2212<\/mo><mi>M<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">EI \u0192cdot y\u201d(x) = -M(x)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Nerede?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"EI \"><semantics><mrow><mi>E<\/mi><mi>I<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">EI <\/annotation><\/semantics><\/math>- o <strong>kiri\u015fin e\u011filme rijitli\u011fi<\/strong> (E - Young mod\u00fcl\u00fc, I - kesitin eylemsizlik momenti).<\/li>\n\n\n\n<li><math data-latex=\"y''(x)\"><semantics><mrow><msup><mi>y<\/mi><mrow><mo lspace=\"0em\" rspace=\"0em\" class=\"tml-prime\">\u2032<\/mo><mo lspace=\"0em\" rspace=\"0em\" class=\"tml-prime\">\u2032<\/mo><\/mrow><\/msup><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">y\u201d(x)<\/annotation><\/semantics><\/math> - sapman\u0131n (e\u011frilik) ikinci t\u00fcrevidir.<\/li>\n\n\n\n<li><math data-latex=\"M(x)\"><semantics><mrow><mi>M<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">M(x)<\/annotation><\/semantics><\/math> - belirli bir kesitteki e\u011filme momentinin bir fonksiyonudur.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Bizim ba\u015fvurumuz <strong>sehi\u0307mleri\u0307n hesaplanmasi i\u0307\u00e7i\u0307n anali\u0307ti\u0307k y\u00f6ntem<\/strong> i\u00e7 kuvvetlerden bile\u015fenin ger\u00e7ek deformasyonuna ge\u00e7erek bu denklemi \u00e7ift skalal\u0131 hale getirmektir.<\/p>\n\n\n\n<h2 id=\"calkowanie\" class=\"wp-block-heading\" style=\"font-size:clamp(16.293px, 1.018rem + ((1vw - 3.2px) * 0.777), 25px);\">2. Sapma \u00e7izgisi denkleminin ad\u0131m ad\u0131m integre edilmesi<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Kiri\u015f sapmas\u0131 hesaplamas\u0131n\u0131n bu k\u0131sm\u0131, herkes taraf\u0131ndan sevilmeyen integraller nedeniyle genellikle en \u00e7ok soruna neden olur. Kiri\u015fler i\u00e7in moment denklemleri s\u00f6z konusu oldu\u011funda, bunlar genellikle entegre edilecek basit fonksiyonlard\u0131r, bu nedenle endi\u015felenecek bir \u015fey yoktur. <strong>Sapma \u00e7izgisi denkleminin entegrasyonu<\/strong> iki a\u015famada ger\u00e7ekle\u015ftirilir:<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\u0130lk entegrasyon:<\/strong> Kesitlerin d\u00f6n\u00fc\u015f a\u00e7\u0131lar\u0131n\u0131n fonksiyonunun elde edilmesini sa\u011flar <math data-latex=\"\\theta(x)\"><semantics><mrow><mi>\u03b8<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\theta(x)<\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li><strong>\u0130kinci entegrasyon:<\/strong> Sapma fonksiyonunun belirlenmesini sa\u011flar <math data-latex=\"y(x)\"><semantics><mrow><mi>y<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">y(x)<\/annotation><\/semantics><\/math>, Bu da aranan sapma \u00e7izgisidir.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Hesaplama s\u0131ras\u0131nda C1 ve C2 entegrasyon sabitleri ortaya \u00e7\u0131kar. Bunlar\u0131 belirlemek i\u00e7in \"entegrasyon sabitleri\" olarak adland\u0131r\u0131lan sabitleri tan\u0131mlamam\u0131z gerekir. <strong>ba\u015flang\u0131\u00e7 ko\u015fullar\u0131<\/strong>, Kiri\u015fin desteklenme \u015feklinden kaynaklan\u0131r (\u00f6rn. mesnette sapma olmamas\u0131).<\/p>\n\n\n\n<h2 id=\"Przyk\u0142ad1\" class=\"wp-block-heading\" style=\"font-size:clamp(16.293px, 1.018rem + ((1vw - 3.2px) * 0.777), 25px);\">3 \u00d6rnek 1: Basit mesnetli kiri\u015f - sehim ve hesaplamalar<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Bu, in\u015faat sekt\u00f6r\u00fcnde en s\u0131k kar\u015f\u0131la\u015f\u0131lan durumdur. <strong>Basit\u00e7e desteklenen kiri\u015f ve sehimi<\/strong> Konsantre veya \u00fcniform bir y\u00fck ile inceleme g\u00f6revlerinin bir klasi\u011fidir.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A\u015fa\u011f\u0131da bir kiri\u015fin sapmas\u0131n\u0131 hesaplamak i\u00e7in \u00f6rnek bir \u00e7\u00f6z\u00fcm bulacaks\u0131n\u0131z. \u00d6rnek \u00e7\u00f6z\u00fcmler i\u00e7in \u015funlar\u0131 kulland\u0131m <a href=\"https:\/\/solveredu.com\/tr\/kiris-hesaplayici\/\" data-type=\"page\" data-id=\"166\">\u0131\u015f\u0131n hesaplay\u0131c\u0131<\/a> Size de tavsiye ederim.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00d6rne\u011fimizde, iki ucundan desteklenen ve s\u00fcrekli bir q y\u00fck\u00fc ve bir F konsantre kuvveti ile y\u00fcklenen 2m uzunlu\u011funda bir kiri\u015f vard\u0131r. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"724\" height=\"668\" data-attachment-id=\"3143\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/1-5\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/1.jpg?fit=724%2C668&amp;ssl=1\" data-orig-size=\"724,668\" 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=\"1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/1.jpg?fit=724%2C668&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/1.jpg?resize=724%2C668&#038;ssl=1\" alt=\"Her iki ucundan desteklenen ve q s\u00fcrekli y\u00fck\u00fc ve F konsantre kuvveti ile y\u00fcklenen 2 m uzunlu\u011funda bir kiri\u015f, \u00e7\u00f6z\u00fcld\u00fc\" class=\"wp-image-3143\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/1.jpg?w=724&amp;ssl=1 724w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/1.jpg?resize=300%2C277&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/1.jpg?resize=13%2C12&amp;ssl=1 13w\" sizes=\"auto, (max-width: 724px) 100vw, 724px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Sapmay\u0131 hesaplamak i\u00e7in e\u011filme momentine ihtiyac\u0131m\u0131z olacakt\u0131r, bu nedenle \u00f6nce reaksiyon ve e\u011filme momenti denklemlerini belirleyerek kiri\u015fi \u00e7\u00f6zmemiz gerekir. Bu konuda daha fazla bilgiyi \u015furada bulabilirsiniz <a href=\"https:\/\/solveredu.com\/tr\/post\/internal-forces-in-beams\/\" data-type=\"post\" data-id=\"899\">Giri\u015f<\/a>. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Desteklerdeki reaksiyonlar\u0131n hesaplanmas\u0131. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"556\" height=\"273\" data-attachment-id=\"3144\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/2-5\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.jpg?fit=556%2C273&amp;ssl=1\" data-orig-size=\"556,273\" 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=\"2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.jpg?fit=556%2C273&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.jpg?resize=556%2C273&#038;ssl=1\" alt=\"\" class=\"wp-image-3144\" style=\"aspect-ratio:2.036689370957587;width:406px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.jpg?w=556&amp;ssl=1 556w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.jpg?resize=300%2C147&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.jpg?resize=18%2C9&amp;ssl=1 18w\" sizes=\"auto, (max-width: 556px) 100vw, 556px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">B\u00f6lmelerdeki e\u011filme momentinin hesaplanmas\u0131. <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"520\" data-attachment-id=\"3145\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/3-4\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/3.jpg?fit=1114%2C566&amp;ssl=1\" data-orig-size=\"1114,566\" 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=\"3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/3.jpg?fit=1024%2C520&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/3.jpg?resize=1024%2C520&#038;ssl=1\" alt=\"\" class=\"wp-image-3145\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/3.jpg?resize=1024%2C520&amp;ssl=1 1024w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/3.jpg?resize=300%2C152&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/3.jpg?resize=768%2C390&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/3.jpg?resize=18%2C9&amp;ssl=1 18w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/3.jpg?w=1114&amp;ssl=1 1114w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u00d6rnek kiri\u015fimiz i\u00e7in e\u011filme momenti denklemlerini belirledikten sonra, entegrasyona ve sapma \u00e7izgisini belirlemeye ge\u00e7ebiliriz. Bunu yapmak i\u00e7in, bir \u00f6nceki ad\u0131mda hesaplanan her bir b\u00f6lme i\u00e7in e\u011filme momenti denklemlerini kullan\u0131r ve bunlar\u0131 iki kez integre ederiz. \u0130lk denklem bize sapma a\u00e7\u0131s\u0131 i\u00e7in, ikincisi ise sapma i\u00e7in \u00e7\u00f6z\u00fcm verir. B\u00f6ylece C1, C2, C3, C4 olmak \u00fczere 4 entegrasyon sabiti elde ederiz. Her bir kompartman i\u00e7in iki sabit. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"718\" height=\"259\" data-attachment-id=\"3147\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/4-3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/4.jpg?fit=718%2C259&amp;ssl=1\" data-orig-size=\"718,259\" 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=\"4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/4.jpg?fit=718%2C259&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/4.jpg?resize=718%2C259&#038;ssl=1\" alt=\"kiri\u015f sapmas\u0131n\u0131n hesaplanmas\u0131, \u00e7\u00f6z\u00fclm\u00fc\u015f\" class=\"wp-image-3147\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/4.jpg?w=718&amp;ssl=1 718w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/4.jpg?resize=300%2C108&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/4.jpg?resize=18%2C6&amp;ssl=1 18w\" sizes=\"auto, (max-width: 718px) 100vw, 718px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Bir sonraki ad\u0131mda, entegrasyon sabitlerini hesaplamam\u0131z gerekiyor. Bunun i\u00e7in ba\u015flang\u0131\u00e7 ko\u015fullar\u0131n\u0131 kullanaca\u011f\u0131z.<strong> \u0130lke olarak, entegrasyon sabitleri kadar \u00e7ok say\u0131da ko\u015fula ihtiyac\u0131m\u0131z vard\u0131r<\/strong>- Bizim durumumuzda 4. Mesnetlerin bulundu\u011fu yerlerde kiri\u015fte herhangi bir sapma olmayaca\u011f\u0131ndan eminiz, bu nedenle mesnetlerin bulundu\u011fu yerlerdeki y(x) s\u0131f\u0131ra e\u015fit al\u0131n\u0131r. Buna ek olarak, iki b\u00f6lmenin birle\u015fiminde sapma ve sapma a\u00e7\u0131s\u0131n\u0131n s\u00fcreklili\u011fine sahip olmam\u0131z gerekti\u011fini biliyoruz, bu nedenle iki ek denklemimiz var.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"522\" height=\"193\" data-attachment-id=\"3149\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/5-3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/5.jpg?fit=522%2C193&amp;ssl=1\" data-orig-size=\"522,193\" 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=\"5\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/5.jpg?fit=522%2C193&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/5.jpg?resize=522%2C193&#038;ssl=1\" alt=\"\" class=\"wp-image-3149\" style=\"aspect-ratio:2.7048012306695814;width:439px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/5.jpg?w=522&amp;ssl=1 522w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/5.jpg?resize=300%2C111&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/5.jpg?resize=18%2C7&amp;ssl=1 18w\" sizes=\"auto, (max-width: 522px) 100vw, 522px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">S\u0131n\u0131r ko\u015fullar\u0131n\u0131 yerine getirdikten sonra, uygun de\u011ferleri denklemlerde yerine koyarak entegrasyon sabitlerini hesaplamaya devam ediyoruz. Bu art\u0131k saf matematiktir. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Entegrasyon sabitleri i\u00e7in elde edilen sonu\u00e7lar<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"477\" height=\"82\" data-attachment-id=\"3151\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/6-3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/6.jpg?fit=477%2C82&amp;ssl=1\" data-orig-size=\"477,82\" 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=\"6\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/6.jpg?fit=477%2C82&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/6.jpg?resize=477%2C82&#038;ssl=1\" alt=\"\" class=\"wp-image-3151\" style=\"aspect-ratio:5.817991233085572;width:414px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/6.jpg?w=477&amp;ssl=1 477w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/6.jpg?resize=300%2C52&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/6.jpg?resize=18%2C3&amp;ssl=1 18w\" sizes=\"auto, (max-width: 477px) 100vw, 477px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Entegrasyon sabitlerini denklemlerde yerine koyduktan sonra, denklemlerin son halini elde ederiz:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"752\" height=\"237\" data-attachment-id=\"3153\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/attachment\/7\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/7.jpg?fit=752%2C237&amp;ssl=1\" data-orig-size=\"752,237\" 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=\"7\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/7.jpg?fit=752%2C237&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/7.jpg?resize=752%2C237&#038;ssl=1\" alt=\"\" class=\"wp-image-3153\" style=\"aspect-ratio:3.1733845169545747;width:606px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/7.jpg?w=752&amp;ssl=1 752w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/7.jpg?resize=300%2C95&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/7.jpg?resize=18%2C6&amp;ssl=1 18w\" sizes=\"auto, (max-width: 752px) 100vw, 752px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Denklemleri bu \u015fekilde elde ettikten sonra, x yerine 0 ile 2 m aras\u0131ndaki say\u0131lar\u0131 koymak bize kiri\u015fimizin uzunlu\u011fu boyunca sapma okunu ve sapma a\u00e7\u0131s\u0131n\u0131 verecektir ve bunlar\u0131 bir grafik olarak \u00e7izebiliriz. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"759\" height=\"737\" data-attachment-id=\"3155\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/attachment\/8\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/8.jpg?fit=759%2C737&amp;ssl=1\" data-orig-size=\"759,737\" 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=\"8\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/8.jpg?fit=759%2C737&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/8.jpg?resize=759%2C737&#038;ssl=1\" alt=\"basit mesnetli bir kiri\u015f \u00f6rne\u011finin sapmas\u0131 ve sapma a\u00e7\u0131s\u0131, \u00e7\u00f6z\u00fclm\u00fc\u015f\" class=\"wp-image-3155\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/8.jpg?w=759&amp;ssl=1 759w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/8.jpg?resize=300%2C291&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/8.jpg?resize=12%2C12&amp;ssl=1 12w\" sizes=\"auto, (max-width: 759px) 100vw, 759px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h2 id=\"Przyk\u0142ad2\" class=\"wp-block-heading\" style=\"font-size:clamp(16.293px, 1.018rem + ((1vw - 3.2px) * 0.777), 25px);\">\u00d6rnek 2: Konsol kiri\u015f - sapma ve hesaplamalar<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Bu durumda <strong>braket, sapma hesaplamalar\u0131<\/strong> k\u0131s\u0131tlama nedeniyle biraz farkl\u0131 g\u00f6r\u00fcn\u00fcyor. W <strong>konsol kiri\u015f<\/strong> en b\u00fcy\u00fck sapma ve en b\u00fcy\u00fck d\u00f6nme a\u00e7\u0131s\u0131 serbest ucun kendisinde meydana gelir.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A\u015fa\u011f\u0131da bir kiri\u015fin sapmas\u0131n\u0131 hesaplamak i\u00e7in \u00f6rnek bir \u00e7\u00f6z\u00fcm bulacaks\u0131n\u0131z. \u00d6rnek \u00e7\u00f6z\u00fcmler i\u00e7in \u015funlar\u0131 kulland\u0131m <a href=\"https:\/\/solveredu.com\/tr\/kiris-hesaplayici\/\" data-type=\"page\" data-id=\"166\">\u0131\u015f\u0131n hesaplay\u0131c\u0131<\/a> Size de tavsiye ederim.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00d6rne\u011fimizde, sol ucunda A noktas\u0131nda k\u0131s\u0131tlanm\u0131\u015f ve di\u011fer ucunda F=5qL konsantre kuvveti ile y\u00fcklenmi\u015f L uzunlu\u011funda bir kiri\u015f bulunmaktad\u0131r.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"695\" height=\"666\" data-attachment-id=\"3158\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/2-1\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.1.jpg?fit=695%2C666&amp;ssl=1\" data-orig-size=\"695,666\" 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=\"2.1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.1.jpg?fit=695%2C666&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.1.jpg?resize=695%2C666&#038;ssl=1\" alt=\"konsol kiri\u015f uzunlu\u011fu L, e\u011filme momenti , solveredu\" class=\"wp-image-3158\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.1.jpg?w=695&amp;ssl=1 695w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.1.jpg?resize=300%2C287&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.1.jpg?resize=13%2C12&amp;ssl=1 13w\" sizes=\"auto, (max-width: 695px) 100vw, 695px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Sapmay\u0131 hesaplamak i\u00e7in e\u011filme momentine ihtiyac\u0131m\u0131z olacakt\u0131r, bu nedenle \u00f6nce reaksiyon ve e\u011filme momenti denklemlerini belirleyerek kiri\u015fi \u00e7\u00f6zmemiz gerekir. Bu konuda daha fazla bilgiyi \u015furada bulabilirsiniz <a href=\"https:\/\/solveredu.com\/tr\/post\/internal-forces-in-beams\/\" data-type=\"post\" data-id=\"899\">Giri\u015f<\/a>. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Desteklerdeki reaksiyonlar\u0131n hesaplanmas\u0131. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"366\" height=\"270\" data-attachment-id=\"3160\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/2-3-3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.3-1.jpg?fit=366%2C270&amp;ssl=1\" data-orig-size=\"366,270\" 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=\"2.3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.3-1.jpg?fit=366%2C270&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.3-1.jpg?resize=366%2C270&#038;ssl=1\" alt=\"\" class=\"wp-image-3160\" style=\"aspect-ratio:1.3556545896515801;width:283px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.3-1.jpg?w=366&amp;ssl=1 366w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.3-1.jpg?resize=300%2C221&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.3-1.jpg?resize=16%2C12&amp;ssl=1 16w\" sizes=\"auto, (max-width: 366px) 100vw, 366px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">B\u00f6lmelerdeki e\u011filme momentinin hesaplanmas\u0131. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"466\" height=\"263\" data-attachment-id=\"3161\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/2-4-2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.4.jpg?fit=466%2C263&amp;ssl=1\" data-orig-size=\"466,263\" 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=\"2.4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.4.jpg?fit=466%2C263&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.4.jpg?resize=466%2C263&#038;ssl=1\" alt=\"\" class=\"wp-image-3161\" style=\"aspect-ratio:1.7719089774820271;width:346px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.4.jpg?w=466&amp;ssl=1 466w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.4.jpg?resize=300%2C169&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.4.jpg?resize=18%2C10&amp;ssl=1 18w\" sizes=\"auto, (max-width: 466px) 100vw, 466px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u00d6rnek kiri\u015fimiz i\u00e7in e\u011filme momenti denklemlerini belirledikten sonra, entegrasyona ve sapma \u00e7izgisini belirlemeye ge\u00e7ebiliriz. Bunu yapmak i\u00e7in e\u011filme momenti denklemini kullan\u0131r ve iki kez integralini al\u0131r\u0131z. \u0130lk denklem bize sapma a\u00e7\u0131s\u0131 i\u00e7in, ikincisi ise sapma i\u00e7in \u00e7\u00f6z\u00fcm verir. B\u00f6ylece C1 ve C2 olmak \u00fczere 2 entegrasyon sabiti elde ederiz.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"594\" height=\"165\" data-attachment-id=\"3162\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/2-5-2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.5.jpg?fit=594%2C165&amp;ssl=1\" data-orig-size=\"594,165\" 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=\"2.5\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.5.jpg?fit=594%2C165&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.5.jpg?resize=594%2C165&#038;ssl=1\" alt=\"\" class=\"wp-image-3162\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.5.jpg?w=594&amp;ssl=1 594w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.5.jpg?resize=300%2C83&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.5.jpg?resize=18%2C5&amp;ssl=1 18w\" sizes=\"auto, (max-width: 594px) 100vw, 594px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Bir sonraki ad\u0131mda, entegrasyon sabitlerini hesaplamam\u0131z gerekir. Bu \u015fema i\u00e7in \u00f6nemli olan, k\u0131s\u0131tlama noktas\u0131nda hem sapman\u0131n hem de d\u00f6nme a\u00e7\u0131s\u0131n\u0131n s\u0131f\u0131r olmas\u0131d\u0131r. Bununla birlikte <strong>d\u00f6nme ve sapma a\u00e7\u0131s\u0131 diyagram\u0131<\/strong> duvarda s\u0131f\u0131r de\u011ferinden ba\u015flar ve kiri\u015fin ucuna do\u011fru h\u0131zla artar.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"536\" height=\"227\" data-attachment-id=\"3163\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/2-6\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.6.jpg?fit=536%2C227&amp;ssl=1\" data-orig-size=\"536,227\" 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=\"2.6\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.6.jpg?fit=536%2C227&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.6.jpg?resize=536%2C227&#038;ssl=1\" alt=\"\" class=\"wp-image-3163\" style=\"aspect-ratio:2.361489742530635;width:505px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.6.jpg?w=536&amp;ssl=1 536w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.6.jpg?resize=300%2C127&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.6.jpg?resize=18%2C8&amp;ssl=1 18w\" sizes=\"auto, (max-width: 536px) 100vw, 536px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Entegrasyon sabitlerini denklemlerde yerine koyduktan sonra, denklemlerin son halini elde ederiz:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"582\" height=\"136\" data-attachment-id=\"3165\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/2-7\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.7.jpg?fit=582%2C136&amp;ssl=1\" data-orig-size=\"582,136\" 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=\"2.7\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.7.jpg?fit=582%2C136&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.7.jpg?resize=582%2C136&#038;ssl=1\" alt=\"\" class=\"wp-image-3165\" style=\"aspect-ratio:4.279551337359793;width:533px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.7.jpg?w=582&amp;ssl=1 582w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.7.jpg?resize=300%2C70&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.7.jpg?resize=18%2C4&amp;ssl=1 18w\" sizes=\"auto, (max-width: 582px) 100vw, 582px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Denklemleri bu \u015fekilde elde ettikten sonra, x yerine 0'dan L'ye kadar say\u0131lar koymak bize kiri\u015fimizin uzunlu\u011fu boyunca sapma okunu ve sapma a\u00e7\u0131s\u0131n\u0131 verecektir ve bir grafik olarak \u00e7izilebilir.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"641\" height=\"618\" data-attachment-id=\"3166\" data-permalink=\"https:\/\/solveredu.com\/tr\/post\/obliczanie-ugiecia-belki\/2-2-2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.2.jpg?fit=641%2C618&amp;ssl=1\" data-orig-size=\"641,618\" 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=\"2.2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.2.jpg?fit=641%2C618&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.2.jpg?resize=641%2C618&#038;ssl=1\" alt=\"\" class=\"wp-image-3166\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.2.jpg?w=641&amp;ssl=1 641w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.2.jpg?resize=300%2C289&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.2.jpg?resize=12%2C12&amp;ssl=1 12w\" sizes=\"auto, (max-width: 641px) 100vw, 641px\" \/><\/figure>\n\n\n\n<h2 id=\"Sprawd\u017a\" class=\"wp-block-heading\" style=\"font-size:clamp(16.293px, 1.018rem + ((1vw - 3.2px) * 0.777), 25px);\">5 Sonu\u00e7lar\u0131n\u0131z\u0131 kontrol edin: \u00c7evrimi\u00e7i \u0131\u015f\u0131n hesaplay\u0131c\u0131<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">E\u011filme momentini elle entegre etmek, malzemelerin mukavemetini incelemede en \u00f6nemli becerilerden biridir. Bir kiri\u015fin nas\u0131l \u00e7al\u0131\u015ft\u0131\u011f\u0131n\u0131 ger\u00e7ekten bu \u015fekilde anlamaya ba\u015flars\u0131n\u0131z. Sorun \u015fu ki, daha karma\u015f\u0131k g\u00f6revlerde k\u00fc\u00e7\u00fck bir hata yapmak \u00e7ok kolayd\u0131r - momentte bir i\u015faret, k\u00f6t\u00fc yaz\u0131lm\u0131\u015f bir s\u0131n\u0131r ko\u015fulu veya entegrasyonda bir hata.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bu nedenle, h\u0131zl\u0131 bir \u015fekilde kiri\u015f sapmas\u0131 hesaplaman\u0131za olanak tan\u0131yan bir kiri\u015f sapma hesaplay\u0131c\u0131s\u0131 olu\u015fturdum <strong>hesaplamalar\u0131n\u0131z\u0131 do\u011frulay\u0131n<\/strong> - \u00f6zellikle de daha zor \u00f6rneklerle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bu ara\u00e7 size yard\u0131mc\u0131 olabilir:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Sonu\u00e7lar\u0131n\u0131z\u0131 kontrol edin<\/strong><br>Elle hesaplanan \u00e7\u00f6z\u00fcm\u00fc hesaplama modelinden elde edilen sonu\u00e7la kar\u015f\u0131la\u015ft\u0131r\u0131n ve integrallerinizin ve s\u0131n\u0131r ko\u015fullar\u0131n\u0131z\u0131n do\u011fru oldu\u011fundan emin olun.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Kiri\u015f davran\u0131\u015f\u0131n\u0131n daha iyi anla\u015f\u0131lmas\u0131<\/strong><br>Kesme kuvvetleri, e\u011filme momentleri ve sapma \u00e7izgilerinin otomatik olarak olu\u015fturulan grafikleri, yap\u0131da ger\u00e7ekten neler olup bitti\u011fini g\u00f6rmeye yard\u0131mc\u0131 olur.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Daha zor g\u00f6revlerle ba\u015fa \u00e7\u0131k\u0131n<\/strong><br>\u00c7e\u015fitli y\u00fck ve destek \u015femalar\u0131 i\u00e7in destek, arac\u0131 ev \u00f6devi veya projelerden daha zorlu \u00f6rnekler i\u00e7in ideal hale getirir.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hesaplamalar\u0131n\u0131z\u0131n do\u011fru oldu\u011fundan emin olmak istiyorsan\u0131z - <strong>saniyeler i\u00e7inde kontrol edin.<\/strong><\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-69bbf988 wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-text-align-center wp-element-button\" href=\"https:\/\/solveredu.com\/tr\/kiris-hesaplayici\/\" style=\"border-top-left-radius:8px;border-top-right-radius:8px;border-bottom-left-radius:8px;border-bottom-right-radius:8px\">\u00dccretsiz Dene<\/a><\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Entegrasyondaki k\u00fc\u00e7\u00fck bir hatan\u0131n t\u00fcm \u00f6devinizi mahvetmesine izin vermeyin. Hesaplamalar\u0131n\u0131z\u0131 do\u011frulay\u0131n ve malzeme dayan\u0131m\u0131n\u0131 \u00e7ok daha h\u0131zl\u0131 \u00f6\u011frenin.<\/p>","protected":false},"excerpt":{"rendered":"<p>Wyznaczanie linii ugi\u0119cia to jeden z kluczowych etap\u00f3w projektowania konstrukcji. Niezale\u017cnie od tego, czy jeste\u015b studentem przygotowuj\u0105cym si\u0119 do kolokwium z wytrzyma\u0142o\u015bci materia\u0142\u00f3w, czy in\u017cynierem weryfikuj\u0105cym sztywno\u015b\u0107 elementu, musisz wiedzie\u0107, jak \u201epracuje\u201d belka pod obci\u0105\u017ceniem. W tym artykule przejdziemy pe\u0142n\u0105 \u015bcie\u017ck\u0119: od klasycznej teorii ca\u0142kowania r\u00f3wnania r\u00f3\u017cniczkowego linii ugi\u0119cia, przez praktyczne rysowanie wykres\u00f3w k\u0105t\u00f3w obrotu, [&hellip;]<\/p>\n","protected":false},"author":255930052,"featured_media":3166,"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":[14815,14816],"tags":[14846,14820,14845,14847],"class_list":["post-3128","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanika","category-wytrzymalosc-materialow","tag-belka-swobodnie-podparta","tag-rownania-rownowagi","tag-reakcje-podporowe","tag-stateczna-wyznaczalnosc"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2026\/03\/2.2.jpg?fit=641%2C618&ssl=1","jetpack_shortlink":"https:\/\/wp.me\/pg3flK-Os","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts\/3128","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=3128"}],"version-history":[{"count":31,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts\/3128\/revisions"}],"predecessor-version":[{"id":3175,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts\/3128\/revisions\/3175"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/media\/3166"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/media?parent=3128"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/categories?post=3128"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/tags?post=3128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}