{"id":1244,"date":"2024-09-23T14:59:17","date_gmt":"2024-09-23T12:59:17","guid":{"rendered":"https:\/\/solveredu.com\/?p=1244"},"modified":"2026-02-03T00:09:12","modified_gmt":"2026-02-02T23:09:12","slug":"tension-and-compression","status":"publish","type":"post","link":"https:\/\/solveredu.com\/ja\/post\/rozciaganie-i-sciskanie\/","title":{"rendered":"\u5f35\u529b\u3068\u5727\u7e2e"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\" id=\"foo\">W tym wpisie:<\/p>\n\n\n\n<ol id=\"ds3f5qplhbyj7q6015689\" class=\"wp-block-list\">\n<li><a href=\"#1qctj\">Definicja napr\u0119\u017cenia<\/a><\/li>\n\n\n\n<li><a href=\"#ln95\">Wz\u00f3r na napr\u0119\u017cenia normalne od rozci\u0105gania\/\u015bciskania<\/a><\/li>\n\n\n\n<li><a href=\"#6nmi9\">Sztywno\u015b\u0107 na rozci\u0105ganie<\/a><\/li>\n\n\n\n<li><a href=\"#7ct95\">Przyk\u0142adowe rozwi\u0105zanie zadania z rozci\u0105gania\/\u015bciskania<\/a><\/li>\n<\/ol>\n\n\n\n<h1 id=\"1qctj\" class=\"wp-block-heading has-large-font-size\">Rozci\u0105ganie i \u015bciskanie osiowe<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"3jmka\">Zanim om\u00f3wimy rozci\u0105ganie i \u015bciskanie zdefiniujmy sobie co to jest napr\u0119\u017cenie.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Napr\u0119\u017cenie \u2013 wielko\u015b\u0107 definiowana jako si\u0142a przypadaj\u0105ca na jednostk\u0119 powierzchni. Jednostk\u0105 napr\u0119\u017cenia w uk\u0142adzie SI jest [Pa]<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<div class=\"wp-block-columns is-style-default has-small-font-size is-layout-flex wp-container-core-columns-is-layout-f1e56d78 wp-block-columns-is-layout-flex\" style=\"margin-top:0;margin-bottom:0;padding-top:0;padding-right:0;padding-bottom:0;padding-left:0\">\n<div class=\"wp-block-column has-theme-6-background-color has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"padding-right:0px;padding-left:0px\">\n<figure class=\"wp-block-table table { height: 400px; \/* Sta\u0142a wysoko\u015b\u0107 tabeli *\/ overflow-y: auto; Pionowy pasek przewijania }\"><table class=\"has-theme-2-color has-theme-1-background-color has-text-color has-background has-link-color has-fixed-layout\"><tbody><tr><td><strong>Jednostki SI<\/strong><\/td><\/tr><tr><td><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=1%5BPa%5D%3D1%5B%5Cfrac+%7BN%7D%7Bmm%5E2%7D%5D+&#038;bg=ffffff&#038;fg=000&#038;s=2&#038;c=20201002\" alt=\"1[Pa]=1[&#92;frac {N}{mm^2}] \" class=\"latex\" \/><br>Najcz\u0119\u015bciej spotkasz si\u0119 z jednostk\u0105:<br><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=1%5BMPa%5D%3D10%5E6+%5BPa%5D+&#038;bg=ffffff&#038;fg=000&#038;s=2&#038;c=20201002\" alt=\"1[MPa]=10^6 [Pa] \" class=\"latex\" \/><br>Praktyczny przelicznik<br><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=1%5B%5Cfrac+%7BkN%7D%7Bcm%5E2%7D%5D%3D10%5BMPa%5D++&#038;bg=ffffff&#038;fg=000&#038;s=2&#038;c=20201002\" alt=\"1[&#92;frac {kN}{cm^2}]=10[MPa]  \" class=\"latex\" \/> <br><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\">\n<figure class=\"wp-block-table is-style-regular\"><table class=\"has-theme-2-color has-theme-1-background-color has-text-color has-background has-link-color has-fixed-layout\"><tbody><tr><td><strong>Jednostki imperialne<\/strong><\/td><\/tr><tr><td><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=1%5Bpsi%5D%3D1%5B%5Cfrac+%7Blbf%7D%7Binch%5E2%7D%5D+&#038;bg=ffffff&#038;fg=000&#038;s=2&#038;c=20201002\" alt=\"1[psi]=1[&#92;frac {lbf}{inch^2}] \" class=\"latex\" \/><br>Najcz\u0119\u015bciej spotkasz si\u0119 z jednostk\u0105:<br><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=1%5Bksi%5D%3D10%5E3+%5Bpsi%5D+&#038;bg=ffffff&#038;fg=000&#038;s=2&#038;c=20201002\" alt=\"1[ksi]=10^3 [psi] \" class=\"latex\" \/><br><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"36qg0\">Rozci\u0105ganie i \u015bciskanie to najprostszy stan napr\u0119\u017cenia jaki spotkamy w wytrzyma\u0142o\u015bci materia\u0142\u00f3w. W podr\u0119cznikach to z regu\u0142y dzia\u0142 od kt\u00f3rego wszystko si\u0119 zaczyna.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"3dk0f\">No w\u0142a\u015bnie rozci\u0105ganie lub \u015bciskanie to <strong>stan napr\u0119\u017cenia<\/strong> wywo\u0142any w prostym pr\u0119cie pryzmatycznym ( czyli w pr\u0119cie o sta\u0142ym przekroju) przez takie obci\u0105\u017cenie, kt\u00f3re powoduje jedynie napr\u0119\u017cenie normalne. Je\u015bli napr\u0119\u017cenia s\u0105 dodatnie to mamy <strong>rozci\u0105ganie<\/strong> je\u015bli natomiast s\u0105 ujemne to <strong>\u015bciskanie.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"557\" height=\"609\" data-attachment-id=\"1248\" data-permalink=\"https:\/\/solveredu.com\/ja\/post\/rozciaganie-i-sciskanie\/rozciag-rys\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/rozciag-rys.png?fit=557%2C609&amp;ssl=1\" data-orig-size=\"557,609\" 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=\"rozciag rys\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/rozciag-rys.png?fit=274%2C300&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/rozciag-rys.png?fit=557%2C609&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/rozciag-rys.png?resize=557%2C609&#038;ssl=1\" alt=\"\" class=\"wp-image-1248\" style=\"width:464px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/rozciag-rys.png?w=557&amp;ssl=1 557w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/rozciag-rys.png?resize=274%2C300&amp;ssl=1 274w\" sizes=\"auto, (max-width: 557px) 100vw, 557px\" \/><\/figure>\n\n\n\n<h2 id=\"ln95\" class=\"wp-block-heading has-medium-font-size\">Wz\u00f3r na napr\u0119\u017cenia normalne od rozci\u0105gania\/\u015bciskania<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"2n3gf\">Poni\u017cej znajdziesz wz\u00f3r na napr\u0119\u017cenie normalne:<\/p>\n\n\n\n<div class=\"wp-block-columns is-style-default has-small-font-size is-layout-flex wp-container-core-columns-is-layout-f1e56d78 wp-block-columns-is-layout-flex\" style=\"margin-top:0;margin-bottom:0;padding-top:0;padding-right:0;padding-bottom:0;padding-left:0\">\n<div class=\"wp-block-column has-theme-6-background-color has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"padding-right:0px;padding-left:0px\">\n<figure class=\"wp-block-table table { height: 400px; \/* Sta\u0142a wysoko\u015b\u0107 tabeli *\/ overflow-y: auto; Pionowy pasek przewijania } is-style-stripes\" style=\"font-size:clamp(14px, 0.875rem + ((1vw - 3.2px) * 0.536), 20px);\"><table class=\"has-theme-5-color has-text-color has-link-color has-fixed-layout\"><tbody><tr><td><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csigma+%3D+%5Cfrac+%7BN%7D%7BA%7D+&#038;bg=ffffff&#038;fg=000&#038;s=3&#038;c=20201002\" alt=\"&#92;sigma = &#92;frac {N}{A} \" class=\"latex\" \/><br>gdzie:<br>N-si\u0142a normalna<br>A-pole przekroju<br><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n<h3 id=\"6nmi9\" class=\"wp-block-heading\">Sztywno\u015b\u0107 na rozci\u0105ganie<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"864\" height=\"236\" data-attachment-id=\"1251\" data-permalink=\"https:\/\/solveredu.com\/ja\/post\/rozciaganie-i-sciskanie\/sztywnosc\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sztywnosc.png?fit=864%2C236&amp;ssl=1\" data-orig-size=\"864,236\" 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=\"sztywnosc\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sztywnosc.png?fit=300%2C82&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sztywnosc.png?fit=864%2C236&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sztywnosc.png?resize=864%2C236&#038;ssl=1\" alt=\"\" class=\"wp-image-1251\" style=\"width:520px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sztywnosc.png?w=864&amp;ssl=1 864w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sztywnosc.png?resize=300%2C82&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/sztywnosc.png?resize=768%2C210&amp;ssl=1 768w\" sizes=\"auto, (max-width: 864px) 100vw, 864px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"5vkng\">Sztywno\u015b\u0107 na rozci\u0105ganie definiujemy jako iloczyn modu\u0142u Younga &#8222;E&#8221; oraz pola przekroju rozci\u0105ganego &#8222;A&#8221;. Czyli sztywno\u015b\u0107 ta zale\u017cy od dw\u00f3ch czynnik\u00f3w:<\/p>\n\n\n\n<ul id=\"klea3qplhbyj7q6015711\" class=\"wp-block-list\">\n<li>od tego z czego wykonany jest nasz rozci\u0105gany element. R\u00f3\u017cne materia\u0142y posiadaj\u0105 r\u00f3\u017cne modu\u0142y spr\u0119\u017cysto\u015bci pod\u0142u\u017cnej<\/li>\n\n\n\n<li>od wymiar\u00f3w przekroju, im wi\u0119ksze pole przekroju poprzecznego , tym wi\u0119ksza sztywno\u015b\u0107<\/li>\n<\/ul>\n\n\n\n<h3 id=\"1s3me\" class=\"wp-block-heading\">Wz\u00f3r na wyd\u0142u\u017cenie\/skr\u00f3cenie od rozci\u0105gania\/\u015bciskania<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"94a6o\">Poni\u017cej znajdziesz wz\u00f3r na wyd\u0142u\u017cenie lub skr\u00f3cenie elementu. Wyd\u0142u\u017cenie je\u015bli mamy do czynienia z rozci\u0105ganiem oraz skr\u00f3cenie je\u015bli m\u00f3wimy o \u015bciskaniu.<\/p>\n\n\n\n<div class=\"wp-block-columns is-style-default has-small-font-size is-layout-flex wp-container-core-columns-is-layout-f1e56d78 wp-block-columns-is-layout-flex\" style=\"margin-top:0;margin-bottom:0;padding-top:0;padding-right:0;padding-bottom:0;padding-left:0\">\n<div class=\"wp-block-column has-theme-6-background-color has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"padding-right:0px;padding-left:0px\">\n<figure class=\"wp-block-table table { height: 400px; \/* Sta\u0142a wysoko\u015b\u0107 tabeli *\/ overflow-y: auto; Pionowy pasek przewijania } is-style-stripes\" style=\"font-size:clamp(14px, 0.875rem + ((1vw - 3.2px) * 0.536), 20px);\"><table class=\"has-theme-5-color has-text-color has-link-color has-fixed-layout\"><tbody><tr><td><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+L+%3D+%5Cfrac+%7BN+%5Ccdot+L%7D%7BE+%5Ccdot+A%7D+&#038;bg=ffffff&#038;fg=000&#038;s=3&#038;c=20201002\" alt=\"&#92;Delta L = &#92;frac {N &#92;cdot L}{E &#92;cdot A} \" class=\"latex\" \/><br>gdzie:<br>N-si\u0142a normalna<br>L-d\u0142ugo\u015b\u0107 pocz\u0105tkowa<br>E-modu\u0142 Younga<br>A-pole przekroju<br><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"3v9jc\">Im wi\u0119ksza si\u0142a oraz d\u0142ugo\u015b\u0107 pocz\u0105tkowa elementu tym zmiana d\u0142ugo\u015bci b\u0119dzie wi\u0119ksza. Jednostk\u0105 wyd\u0142u\u017cenia jest [m]. Im wi\u0119ksza sztywno\u015b\u0107 na rozci\u0105ganie tym wyd\u0142u\u017cenie b\u0119dzie mniejsze.<\/p>\n\n\n\n<h3 id=\"7ct95\" class=\"wp-block-heading\">Przyk\u0142adowe rozwi\u0105zanie zadania z rozci\u0105gania\/\u015bciskania<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"440hd\">Poni\u017cej znajdziesz schemat pr\u0119ta obci\u0105\u017conego dwiema si\u0142ami normalnymi. Rozwi\u0105\u017cemy wsp\u00f3lnie to zadanie. Jest to pr\u0119 pryzmatyczny o przekroju o:<\/p>\n\n\n\n<ul id=\"yv2p3qplhbyj7q6015723\" class=\"wp-block-list\">\n<li>A=20 [mm^2]<\/li>\n\n\n\n<li>d\u0142ugo\u015bci L=8 [m]<\/li>\n\n\n\n<li>modu\u0142 Younga E=200 000 [MPa]<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1006\" height=\"221\" data-attachment-id=\"1254\" data-permalink=\"https:\/\/solveredu.com\/ja\/post\/rozciaganie-i-sciskanie\/pret_przyklad1\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/pret_przyklad1.png?fit=1006%2C221&amp;ssl=1\" data-orig-size=\"1006,221\" 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=\"pret_przyklad1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/pret_przyklad1.png?fit=300%2C66&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/pret_przyklad1.png?fit=1006%2C221&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/pret_przyklad1.png?resize=1006%2C221&#038;ssl=1\" alt=\"\" class=\"wp-image-1254\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/pret_przyklad1.png?w=1006&amp;ssl=1 1006w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/pret_przyklad1.png?resize=300%2C66&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/pret_przyklad1.png?resize=768%2C169&amp;ssl=1 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<figure style=\"font-size:clamp(14px, 0.875rem + ((1vw - 3.2px) * 0.536), 20px);\" class=\"wp-block-table\"><table class=\"has-theme-5-background-color has-text-color has-background has-link-color has-fixed-layout\" style=\"color:#fefefe\"><tbody><tr><td>Wszystkie przyk\u0142ady u\u017cyte w tym wpisie zosta\u0142y utworzone w <a href=\"\/kalkulator-sil-normalnych-rozciaganie-sciskanie\/\" target=\"_blank\" rel=\"noreferrer noopener\">Kalkulatorze Si\u0142 Normalnych<\/a>. Zapraszam do wypr\u00f3bowania. W tej aplikacji wyznaczysz si\u0142y normalne, napr\u0119\u017cenie normalne oraz wyd\u0142u\u017cenie lub skr\u00f3cenie pr\u0119ta.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"25mlb\">W pierwszej kolejno\u015bci wyznaczymy reakcj\u0119 &#8222;R&#8221; w utwierdzeniu.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"383\" height=\"127\" data-attachment-id=\"1257\" data-permalink=\"https:\/\/solveredu.com\/ja\/post\/rozciaganie-i-sciskanie\/reakcje1-2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje1-1.png?fit=383%2C127&amp;ssl=1\" data-orig-size=\"383,127\" 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=\"reakcje1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje1-1.png?fit=300%2C99&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje1-1.png?fit=383%2C127&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje1-1.png?resize=383%2C127&#038;ssl=1\" alt=\"\" class=\"wp-image-1257\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje1-1.png?w=383&amp;ssl=1 383w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/reakcje1-1.png?resize=300%2C99&amp;ssl=1 300w\" sizes=\"auto, (max-width: 383px) 100vw, 383px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"6ohv2\">Do wyznaczenia reakcji wystarczy nam jedno r\u00f3wnanie r\u00f3wnowagi. Suma si\u0142 w kierunku poziomym musi by\u0107 r\u00f3wna zero.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"8hovo\">W kolejnym etapie wyliczymy si\u0142y osiowe, napr\u0119\u017cenie normalne oraz wyd\u0142u\u017cenie w poszczeg\u00f3lnych przedzia\u0142ach. Przedzia\u0142y wyznaczamy tam gdzie zmienia si\u0119 si\u0142a normalna. W naszym przyk\u0142adzie mamy dwa przedzia\u0142y.<\/p>\n\n\n\n<h4 id=\"79jc\" class=\"wp-block-heading\">Przedzia\u0142 pierwszy<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"337\" height=\"358\" data-attachment-id=\"1259\" data-permalink=\"https:\/\/solveredu.com\/ja\/post\/rozciaganie-i-sciskanie\/przedzial1-3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial1-1.png?fit=337%2C358&amp;ssl=1\" data-orig-size=\"337,358\" 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=\"przedzial1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial1-1.png?fit=282%2C300&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial1-1.png?fit=337%2C358&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial1-1.png?resize=337%2C358&#038;ssl=1\" alt=\"\" class=\"wp-image-1259\" style=\"width:307px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial1-1.png?w=337&amp;ssl=1 337w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial1-1.png?resize=282%2C300&amp;ssl=1 282w\" sizes=\"auto, (max-width: 337px) 100vw, 337px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"nmba\">Dla ka\u017cdego przedzia\u0142u wyznaczymy si\u0142\u0119 normaln\u0105 &#8222;N&#8221;, pisz\u0105c r\u00f3wnanie r\u00f3wnowagi si\u0142 osiowych. W pierwszym fragmencie pr\u0119ta si\u0142a ta jest r\u00f3wna reakcji utwierdzenia R=50 [N].<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"5qln2\">Napr\u0119\u017cenie normalne 2.5 [MPa]. Mamy do czynienia z rozci\u0105ganiem wi\u0119c napr\u0119\u017cenie jest dodatnie.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"fe1v7\">W ostatnim kroku obliczymy zmian\u0119 d\u0142ugo\u015bci pierwszego fragmentu. Skorzystamy tu z <a href=\"#1s3me\">wzoru na wyd\u0142u\u017cenie<\/a>. Element zostanie wyd\u0142u\u017cony o 0.05 [mm].<\/p>\n\n\n\n<h4 id=\"56def\" class=\"wp-block-heading\">Przedzia\u0142 drugi<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"388\" height=\"354\" data-attachment-id=\"1260\" data-permalink=\"https:\/\/solveredu.com\/ja\/post\/rozciaganie-i-sciskanie\/przedzial2-3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial2-1.png?fit=388%2C354&amp;ssl=1\" data-orig-size=\"388,354\" 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=\"przedzial2\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial2-1.png?fit=300%2C274&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial2-1.png?fit=388%2C354&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial2-1.png?resize=388%2C354&#038;ssl=1\" alt=\"\" class=\"wp-image-1260\" style=\"width:326px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial2-1.png?w=388&amp;ssl=1 388w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przedzial2-1.png?resize=300%2C274&amp;ssl=1 300w\" sizes=\"auto, (max-width: 388px) 100vw, 388px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"d8cje\">W kolejnym fragmencie pr\u0119ta si\u0142a normalna r\u00f3wna jest sumie R + F1 = 100 [N].<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"7vau9\">Napr\u0119\u017cenie normalne wynosi 5 [MPa]. I podobnie jak w pierwszym przedziale mamy do czynienia z rozci\u0105ganiem wi\u0119c napr\u0119\u017cenie jest dodatnie.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"9bbtd\">Co do zmiany d\u0142ugo\u015bci mamy wyd\u0142u\u017cenie o 0.10 [mm].<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"9goka\">Na koniec wyznaczmy jeszcze wyd\u0142u\u017cenie ca\u0142kowite jako sum\u0119 wyd\u0142u\u017cenia poszczeg\u00f3lnych fragment\u00f3w.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"650\" height=\"47\" data-attachment-id=\"1261\" data-permalink=\"https:\/\/solveredu.com\/ja\/post\/rozciaganie-i-sciskanie\/wydluzenie-calkowite\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wydluzenie-calkowite.png?fit=650%2C47&amp;ssl=1\" data-orig-size=\"650,47\" 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=\"wydluzenie calkowite\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wydluzenie-calkowite.png?fit=300%2C22&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wydluzenie-calkowite.png?fit=650%2C47&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wydluzenie-calkowite.png?resize=650%2C47&#038;ssl=1\" alt=\"\" class=\"wp-image-1261\" style=\"width:575px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wydluzenie-calkowite.png?w=650&amp;ssl=1 650w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wydluzenie-calkowite.png?resize=300%2C22&amp;ssl=1 300w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"et0dp\">W ostatnim kroku wyznaczone warto\u015bci si\u0142 normalnych, napr\u0119\u017ce\u0144 normalnych oraz zmian\u0119 d\u0142ugo\u015bci przedstawimy na wykresach.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"771\" height=\"893\" data-attachment-id=\"1263\" data-permalink=\"https:\/\/solveredu.com\/ja\/post\/rozciaganie-i-sciskanie\/wykresy-2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy-1.png?fit=771%2C893&amp;ssl=1\" data-orig-size=\"771,893\" 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=\"wykresy\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy-1.png?fit=259%2C300&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy-1.png?fit=771%2C893&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy-1.png?resize=771%2C893&#038;ssl=1\" alt=\"\" class=\"wp-image-1263\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy-1.png?w=771&amp;ssl=1 771w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy-1.png?resize=259%2C300&amp;ssl=1 259w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/wykresy-1.png?resize=768%2C890&amp;ssl=1 768w\" sizes=\"auto, (max-width: 771px) 100vw, 771px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"2tum7\">Na tym zako\u0144czymy rozwi\u0105zywanie naszego przyk\u0142adu. Kolejne przyk\u0142ady bardziej z\u0142o\u017cone w kolejnym wpisie.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>W tym wpisie: Rozci\u0105ganie i \u015bciskanie osiowe Zanim om\u00f3wimy rozci\u0105ganie i \u015bciskanie zdefiniujmy sobie co to jest napr\u0119\u017cenie. Napr\u0119\u017cenie \u2013 wielko\u015b\u0107 definiowana jako si\u0142a przypadaj\u0105ca na jednostk\u0119 powierzchni. Jednostk\u0105 napr\u0119\u017cenia w uk\u0142adzie SI jest [Pa] Jednostki SI Najcz\u0119\u015bciej spotkasz si\u0119 z jednostk\u0105:Praktyczny przelicznik Jednostki imperialne Najcz\u0119\u015bciej spotkasz si\u0119 z jednostk\u0105: Rozci\u0105ganie i \u015bciskanie to najprostszy stan napr\u0119\u017cenia jaki spotkamy w wytrzyma\u0142o\u015bci materia\u0142\u00f3w. W podr\u0119cznikach to z regu\u0142y dzia\u0142 od kt\u00f3rego wszystko si\u0119 zaczyna. No w\u0142a\u015bnie rozci\u0105ganie lub \u015bciskanie to stan napr\u0119\u017cenia wywo\u0142any w prostym pr\u0119cie pryzmatycznym ( czyli w pr\u0119cie o sta\u0142ym przekroju) przez takie obci\u0105\u017cenie, kt\u00f3re powoduje jedynie napr\u0119\u017cenie normalne. Je\u015bli napr\u0119\u017cenia s\u0105 dodatnie to mamy rozci\u0105ganie je\u015bli natomiast [&hellip;]<\/p>\n","protected":false},"author":255930052,"featured_media":1265,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","jetpack_post_was_ever_published":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},"_wpas_customize_per_network":false},"categories":[14816,14815],"tags":[14836,14834,14837,14839,14838,14835],"class_list":["post-1244","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-wytrzymalosc-materialow","category-mechanika","tag-naprezenie-normalne","tag-rozciaganie","tag-sila-normalna","tag-sztywnosc-na-rozciaganie","tag-wydluzenie-preta","tag-sciskanie"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/rozciag-rys-1.png?fit=557%2C609&ssl=1","jetpack_shortlink":"https:\/\/wp.me\/pg3flK-k4","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/posts\/1244","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/users\/255930052"}],"replies":[{"embeddable":true,"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/comments?post=1244"}],"version-history":[{"count":27,"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/posts\/1244\/revisions"}],"predecessor-version":[{"id":3096,"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/posts\/1244\/revisions\/3096"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/media\/1265"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/media?parent=1244"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/categories?post=1244"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/ja\/wp-json\/wp\/v2\/tags?post=1244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}