Nh� vaäy ta coù moät khaùi nieäm öùng suaát taïi 1 ñieåm ñöôïc ñaëc tröng bôûi

Nh? vaäy ta coù moät khaùi nieäm öùng suaát

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Nhö vaäy, ta coù moät khaùi nieäm: öùng suaát taïi 1 ñieåm ñöôïc ñaëc tröng bôûi 9 thaønh phaàn vaø chuùng ñöôïc vieát döôùi daïng 1 tensor. z zy zx yz y yx xz xy x T (2.4) 2. TRAÏNG THAÙI ÖÙNG SUAÁT: 2.1. Traïng thaùi öùng suaát taïi 1 ñieåm: Neáu cho qua M nhöõng maët caét khaùc nhau, thì töông öùng vôùi moãi vò trí cuûa ta ñöôïc 1 vector öùng suaát t . Taäp hôïp taát caû moïi t cuûa taát caû caùc maët qua M ñöôïc goïi laø traïng thaùi öùng suaát taïi M. Taäp hôïp ñoù khoâng laø moät taäp hôïp caùc vector ñoäc laäp. Thöïc vaäy ñeå khaûo saùt traïng thaùi öùng suaát taïi moät ñieåm M cuûa moâi tröôøng lieân tuïc, ta ñöa vaøo caùc truïc 0x, 0y, 0z vôùi 0 M cuûa moät heä toaï ñoä cartesian vaø taùch ra moät phaân toá töù dieän 0ABC, (hình 2.3a). Hình 2.3 Goïi: z y x n , n , n n laø phaùp tuyeán ñôn vò cuûa maët phaúng nghieâng x y z C 0 A ) b x y z C 0 B A ) a dA z dA y dA z dA p n n n B ' z z p ' y ' x ' 0 y p yz yx y zy z zx xz xy x
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Giaùo Trình CÔ CHÖÔNG 2: ÖÙNG SUAÁT VAØ BIEÁN DAÏNG 71 TS. Vuõ Coâng Hoøa Vaø: dA laø dieän tích cuûa tam giaùc ABC dA x laø dieän tích cuûa tam giaùc 0BC dA x = dA.n x dA y laø dieän tích cuûa tam giaùc 0AC dA y = dA.n y dA z laø dieän tích cuûa tam giaùc 0AB dA x = dA.n z z y x z y x p , p , p p & t , t , t laø öùng suaát treân caùc maët 0BC, 0AC, 0AB, ABC. k , j , i laø vector ñôn vò treân caùc truïc toaï ñoä. Theá thì: k . j . i . t k . j . i . t k . j . i . t z zy zx z yz y yx y xz xy x x (2.5) 2.1.1. Ñieàu kieän vector toång baèng khoâng (vector chính baèng khoâng): Töø ñieàu kieän caân baèng cuûa phaân toá: 0 p n . t n . t n . t 0 dA . p dA . t dA . t dA . t z z y y x x z z y y x x (2.6) Chieáu xuoáng caùc truïc: z z y yz x xz z z zy y y x xy y z zx y yx x x x n . n . n . p n . n . n . p n . n . n . p (2.7) i ij j n p (2.8) Vaø: j i ij z y yz z x xz y x xy z z y y x x n n n n n n n n n n n n 2 . 2 . 2 . . 2 2 2 (2.9)
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Giaùo Trình CÔ CHÖÔNG 2: ÖÙNG SUAÁT VAØ BIEÁN DAÏNG 72 TS. Vuõ Coâng Hoøa 2.1.2. Ñieàu kieän moment toång baèng 0 (vector moment chính baèng khoâng): Töø ñieàu kieän caân baèng cuûa phaân toá: Goïi 0 / : troïng taâm cuûa tam giaùc ABC.
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