Bài giảng môn Sức bền vật liệu 1 tóm tắt nhưng đầy đủ các nội dung cơ bản và ví dụ trọng tâm. Sức bền vật liêu 1 là môn cơ sơ ngành quan trọng của khối nghành xây dựng. Vì vậy hy vọng với bài giảng này sẽ giúp các bạn sinh viên hệ thống lại được nhưng kiến thức cần nắm của môn học này
Chương 6 CHUYEÅN VÒ DAÀM CHÒU UOÁN 6.1. Chuyển vị của dầm chịu uốn (1) 1. Khái niệm chung Đường đàn hồi: Đường cong của trục dầm sau khi chịu uốn Trọng tâm mặt cắt ngang của dầm K - trước biến dạng K’ – sau biến dạng KK’ – chuyển vị của trọng tâm mặt cắt ngang Biến dạng bé: u(z)<<v(z) v(z) => độ võng: y(z)=> B F L K K’ K K’ z v(z) u(z) KK’ v(z) - chuyển vị đứng u(z) - chuyển vị ngang Độ võng của dầm chịu uốn là chuyển vị theo phương thẳng đứng của trọng tâm mặt cắt ngang University of Architechture [...]... xoay trên dầm thực University of Architechture Bài tập - Ví dụ 6. 1.1 (1) P Ví dụ 6. 2: Cho dầm có liên kết và chịu tải trọng như hình vẽ Xác định độ võng tạitiết diện đặt lực P A B L/2 L/2 Giải: Bước 1: Vẽ biểu đồ mô men uốn nội lực Bước 2: Xác định liên kết trên dầm giả tạo, tải trọng giả tạo, M>0 nên tải trọng giả tạo hướng xuống M PL qgt EI x 4 EI x Bước 3: Xác định nội lực trên dầm giả tạo.. .6. 1 Chuyển vị của dầm chịu uốn (10) Các bước thực hiện: Vẽ biểu đồ mô men uốn trên dầm thực Chia tung độ biểu đồ cho độ cứng EI để có trị số của tải trọng giả tạo Nếu Mx>0 thì qgt z = 3a => y1(z=a) = 0 y3(z=3a) = 0 Từ hai phương trình độ võng y1(z) và y3(z), áp dụng điều kiện biên: 5qa 4 yo 24EI x Từ đó tính được: qa 3 o 6EI x 7qa 4 y C y 2 (z 2a) 24EI x qa 3 D y'3 (z 3a) 6EI x University of Architechture 6. 2 Bài toán siêu tĩnh (1) July 2009 University of Architechture 6. 2 Bài toán siêu tĩnh (2) July 2009... z ) y0 0 z EI ' a ' i 1 ' i z2 z3 z4 z5 ' M 0 2! Q0 3! q0 4! q0 5! University of Architechture 6. 1 Chuyển vị của dầm chịu uốn (13) ' y0 ,0 , M 0 , Q0 , q0 , q0 , gọi là các thông Các thông số số ban đầu và được xác định từ điều kiện biên Chú : Chiều dương của mô men tập trung, lực tập trung, tải trọng phân bố như hình vẽ Nếu liên kết giữa hai đoạn thứ (i) và (i+1)... tải phân bố, ta nhận được công thức truy hồi của hàm độ võng (hàm độ võng trên đoạn thứ i+1 được xác định khi biết hàm độ võng trên đoạn thứ i) University of Architechture 6. 1 Chuyển vị của dầm chịu uốn (12) Khi độ cứng của dầm EI=const trên cả chiều dài yi 1 ( z ) yi ( z ) ya a ( z a) 1 EI Với ( z a) 2 ( z a )3 ( z a) 4 ( z a)5 M a Qa qa q 'a 2! 3!... 0 Ví dụ University of Architechture Bài tập – Ví dụ 6. 4.2 (1) q Ví dụ 6. 4. 2: Dùng phương pháp thông A số ban đầu, xác định độ võng tại C và góc xoay tại D của dầm chịu tải trọng như hình vẽ 1 a 2 Lập bảng thông số ban đầu Tìm yC => hàm độ võng y2 Tìm D => hàm góc xoay y3’ D C B 2 3 VB a a VD 3a 1 Xác định phản lực 9 VD qa 4 2 M=qa 2a Bài giải: 11 VB qa 4 P=4qa z=0 z=a z = 2a y0 0 0 0 M0... M a 0 Qa P qa 0 , qa 0 University of Architechture Ví dụ 6. 1.2 (2) Công thức truy hồi: yi 1 ( z ) yi ( z ) ya a ( z a) 1 EI 5 ( z a)2 ( z a )3 ( z a)4 ' ( z a) M a 2! Qa 3! qa 4! q a 5! z=0 Xét đoạn 1(AB ): 0 ≤ z ≤ a qz 4 y1 (z) y o o z 24EI x Xét đoạn 2 (BC ): a ≤ z ≤ 2a z=a z = 2a y0 0 0 0 M0 0 Q0 0 q0 q , q0 0 ya . Chương 6 CHUYEÅN VÒ DAÀM CHÒU UOÁN 6. 1. Chuyển vị của dầm chịu uốn (1) 1. Khái niệm chung Đường đàn hồi: Đường cong của trục dầm sau khi chịu uốn Trọng tâm mặt cắt ngang của dầm K -. src="data:image/png;base64,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 56+ JUf+tff+y9bnzQdYACs4AACAyng9/1778r+Zfvz7L2dWtV5mPsC8WMEBAABUxkeaL933xI3Tj//ll//JcID5soIDAACopEzHd6ffXeWn/3Z7Q4MfxwLz4JQBAABU0sOPtE0/+A/PvmkywLwIHAAAQCV9ct1HmpdfOuXgtw/8i8kA8yJwAAAAFbblvtYpR74+cLxY/MBkgLkTOAAAgAr7oy2rph989eS/mgwwdwIHAABQYee8Kexzx94wGWDuBA4AAKDy7rhr5ZQjx18qGAswdwIHAABQeZ9c++EpR1 768 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 66+ 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 466 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 066 tzo6OiyZcumXJk4MTGRyWT0L4iltBRr+j/nZcuWhV6WJXAA8AtKW2ysWLGivb191i02ZmLrDahas27GUUZpk44VK1bYpKMOZbPZzs7Ocz6Uy+V27txpRBDIzp07Z1qW29nZmc1mg /65 BA4AUvr3LTY6OjpKW2wsrGuU2HoDqtwcN+OYycTERGmTjo6Ojmw2a5OOmlcsFvv6+rq7u8s8p7+/f3h42KwghOHh4fKLc7u7u/v6+iKuzBI4AOr9Zevo6GhXV1dpi425bB1anq03IIR5bcYxk1wu193dvXTp0vXr19uko4a/Tdx 666 29vb2zPnPjxo3j4+MmBlVufHx848aNsz6tt7f31ltvDXdiFzgA6tTY2NiOHTsaGxs7OzvP3i7ufLS0tOzdu9dsIYQFbMYxk5GRkdImHTt27LBJRy0p1Y05bi+9e/fuK6+80tCgyl155ZW7d++e47k9XOMQOADqSz6f7+vrK22xMd+tQ2d1+PDhpqYmQ4YQzmczjpn09/eXNuno6+vzw/zo5lU3jh49umvXLrsvQYiT /65 du44ePTqXJ4drHAIHQF0oFAqDg4OlLTYWvHVoeQMDA21tbUYNgZznZhwzmZiY6O3tXb16dUdHx+DgoE06Ipp73Whvbz916tS6desMDQJZt27dqVOn2tvbZ31mrBGCmDUAACAASURBVMaxZHJy0lcXIIqVl3z7zK+//3JmVetlF+Q/m8/np7wD2bp16xx/aleSyWSeeuopXyCIqKura17XqbW3tx86dOjsI01NTc3NzSa5aB7Pntz2hR+Wfn3HXSsfyX7iwv735143MpnMk08+aeEGBFV7/9it4AAgNTc3t55l375986obLS0tBw8eNEYIar6bceRyuX379p190lA36vMNz+7du9UNCK2hoeGpp56ay5YcUdZxCBwA/ILBwcG57JZ/NltvQPQXuPPdjKO3t7evr8/oas/c68bQ0JBNN6A27Nq1ay6XK4ZoHAIHAD83Ojra09Mzr99i6w2oAQvYjKO3t3d0dNToasyWLVvmUjeOHj3qjuBQS7q6uuay7ejIyMiWLVuq+Q8icABwWj6f7+zsnNdvyWQy27ZtMzqojVe3mUxmXr+ls7PTrVJqSV9f31x2Yzl69KgtRaH2rFu3bi6NY//+/dW8gk/gACCllAqFwlx20j6brTegxhw8eHBem3GklG 666 SY3SakNw8PDc7k+Ud2AGjbHxtHb25vNZqvzjyBwAJBSSnfeeed87x1r6w2oMU1NTYcPH57Xb5mYmLjzzjuNLrqxsbGNGzfO+jR1A2reHBtHd3d3dV6lKHAAkAYHB+d125Rk6w2oUW1tbQMDA/P6LSMjI4ODg0YXVz6f37Bhw6xPUzegTsyxcWzatCmfz1fbJy9wANS7sbGx+W4sausNqGHbtm2b72YcPT09Y2NjRhdRsVjs6uqadQWfugF1ZS6NY2Jioqurq9puqiJwANT7S9u5/ODubLbegJq3gM04NmzYYDOOiB 566 KFZV/CpG1CH5tI4RkZGdu7cWVWftsABUNe2bNlS/gd309/k2HoDat45N+Movw/xxMTE1q1bjS6W0dHRWTcWHRgYUDegPq1bt2737t3ln9Pf3z88PFw9n7PAAVDXL23L3xGwpaXlgQcemPJK19YbUA+mb8axdevW8ss69u/fX1UvcymvUChs2rSp/HN2797tgkSoZ7t27Zq1cdxzzz3Vs4KvwdcMoD4Vi8VZX9p +61 vfOnLkyJkPbb0BdWXbtm2HDh06c/3Ciy++ePjw4fLrOO65554TJ040NHiFGcDWrVvLr+DLZDL333+/QcVTKKQzWz++8kr66U9//tBLL6Uf/3iW3176yUdLS/rMZ2Z55u23/8KHbW3p8stP//rKK5PzQK24//77n3 766 TLXspVup/XUU09Vw2e7ZHJy0tcMIIqVl3z7zK+//3JmVetlC/5P7dixo7+/v8wTdu/evWvXrhUrVpReAbe0tLz00ksuToE6e6NUuPrqq8+cBF599dW+vr7yFzVs3779K1/5itFdVI9nT277wg9Lv77jrpWPZD8x3/9CNpvt7u4u8wTn/Oo1Pv4L5eLZZ0/njLJLMiumvT1df31KKV17bbr66pRSWrs2pZSam5O/XTG/F8xkaGioq6ur4p+qwAEQyYUKHOPj46tXry7zhEwm8+STT548efLM03K5nItToA6NjY2dWbWRy+XWrFlz 662 3lt+W8vjx 462 trUZ38Zxn4JjLexVfxAorFtPJk6crxhtvpGPHUj6f5nlD9wDOrBMpLQZZuzY1NaXmZl//KjTrS8eU0jvvvFPxKmrhEEA9uuOOO8o/IZvNNjQ0PPHEE6UPbb0Bdau0GUfpZtLf+9732trastnssmXLyp9hnn/+eaOrWrNenDI0NKRuLPJ7x9Mto7QcozrXYlwMExOn/7BT/sil8FFa9KF6VIfW1tahoaHyK7+2bt2azWYr+3lawQEQyQVZwTE6OtrZ2Vn+pW1pkWFHR0cul8tkMlVyXSVQKevXrx8ZGWlvby+Vi1kvcHBj0YvqfFZwnL0k55yc8y +68 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 /64 wFFZ5TdgeuSRR+p9QKWLUA4cSP39lfw0Si1j7dp01VXpuutqIWTM+B604fQak9L/lt4Dl+7gMz5+et1H6RKYilSPkZHTy3ba29PWrenzn1c6ypw9yizi+NKXvrT4gcMKDoBIFraCo/ziZJdeA+f99nCWKyDef/99J5kLaF4rOMbGxtrb22d+T13Hyzcq2zVKOeP220+vy7AHRJkv08mT6Uc/Ss89V7Hk0dKS7rsv/eEfJq12mvKLOBZ/BZ+7qADUvmeffbbMG48HHnjAGw/gfDQ0NDzwwAPlz0KmVClf+9rXyjz68MMP1+Mb5tHRtGNHamxMnZ2LVzc2b 067 d6fvfCcdP54mJ9Pzz6dsNnV1pXXr1I3y55fU2ppuuy3t2pWy2TQ5md55J+VyaWgobd+eZo53F9LEROrtTe3tqaMjDQ6e3mGEOZxDyp9/LgYrOAAiWdgKjq6urv0z/8Tj1KlTbg0InKd8Pr9s2bKZ39ltzpbWn3MhzH0FR7FYbGxsnOnRulvBNzaWvva1xSsamUy6+eZ0ww3puuskjIuotMTj2LH0xBOLt4lp6eqVu+9OTU11P/7qWsFnBQdA7X/jKVM3MpmMugGcv+bm5kwmM9Oj+/fvLxaLprT4Dh8+XObRelnBl8+nvr60YkVqb7+4daOlJW3enIaG0vHj6f3301NPpV270m23qRsXV2mJR1dXymbTq6+md95JR4+mgYE08xnpAsjlUk9PWro0rV+fRkdTHZ/fZl3BV/4sdMEJHAA1rvzK8D/5kz8xIuCCKH8+cZVKRXz5y18u8+jdd99dy3/4YjEND6eOjrRsWertvVg/2G9pSdu3p+98J506lV599fRVJ62tbjVaMU1Nad26tG1beuqp9P77KZe7uLFjZCR1dqbGxtTXd/qeuPWn/Jmk/FnoghM4AGrcgQMHyjz6e7/3e0YEXBAbNmxY8LmIi/MGvzhSuhnEuWQymaZaXV0/Pp 76+ 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 067 ae3uRuluztqnxS2Yz09G5015uZiYECxRmuplnWcPx+3bkWlEuVyFAr1+cpLSxtHrjT1vpUGqeATcAA0s7//+7+v9dAf/uEfGh+g7jLmFm049lN2vcxnPvOZVJ/Y+npMTsbRo/XcjVLNNVZXY2pKZw0iIjo7Y3g4btyoc9JR3bdSKjXleSsNUsEn4ABoWuvr65Xai7/Pfvazhgiouy9+8Yu1HlpaWlpvgb3oDSK7gi/JDtNrazE+HkePRn9/fc58LRY/lGvous3d7kg66uLixY3zVmZnm2moGqSCT8AB0LSuX7+e8ehjjz128N9itcYYaCK/8zu/s+t5iTpqqgq+tbUYHY3Dh2NwsA7RRqGw0V9jbk6uwXZVk4 469 umoVKK7u8lijoy5JWNGqi8BB0DTevfddzMebW9vP/hv8YUX4tSpOHaspY5Sg92bnIxSqcG/x+zmPtnzEnWUUcGXUWXTcDajjbr0EB0aikolbtzQX4Nd2uzTsboaly/X4ZTZ5oo5MuaWSn2PN6pNwAHQtH71q1/Veqin7seh7cK1a3HhwsbdvaMjxsdD7TrUsrAQx45Ff39cvNj 46+ 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 +6/ 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 861 dYDP/lJdHWlNQBvv/32LuYlWsI3vrHF77wWM7S4XC5KpVhdzWpS9s1vqmyqRcAB0LQ+/elPJ/l9t7XtqefWppGR6OiIkyftW2H/VHejHD 26+ 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 96+ o6qFKviABpA9q5w8eXJ/vg0BB0CTy35R8c477zT58+/s3CjoqG+HjtstLd0ZdkxO2sZy8NbW9inUqBoaikolbtxo1rNRtiN7PhFw7LNWrOADDk7GrLKfFXwCDoAml10T+Jd/+ZctMQptbRsdOpaX63nkyt2qYUd//8Y2lmrPjtlZxR37YX09FhZicjLOno1jx+Lw4fseasSvD0a5eTPOn4/Ozhb/CWTPJ5/5zGf8ku6zFq3gAw7gDtwoFXwCDoAml8vlenp6aj 168 eLF1tqJnc/HwEDcuBGVSpTL9zHpqKr27OjujiNH4oEHolSSd9R3PbWRaIyObpRpdHREf39cuBC1twHXR7EYly/H6urGwSjNe+br9q2trV2sffRMT09PW6sWthyg7BcVV69eNURAXWTPJ/sZcLgfAzS/P/uzP5uu/Sb2X/3VXw0MDLTcoHR2RmdnDA/HtWvx2mvx3e/Wv83k3S5e/NDhoz098Xu/F488Ek88Efl8ePm3pYWF+OUv4xe/iNdfj5/+9L6nGHcrFuO55+JrX/PDutvf/M3fZM9Chmj/ZVfwvfjii729vUYJ2LsXX3xx13NRfT1w69YtPw+AVDz8G/9r8+N/+Leeo+0f3c5nra+vHzp0qNajhUJhcXEx5y3o/Uw6aunri9/93XjkkejsjAcfbJGDRWv91sb 16/ Huu/GrXx1YnLGppye+9rU4eTIcAlLbQw89tFT7b2d1dVUFRx29Nnl94Kv/VP346T 96+ DuTj9e6slQqZVTWLC8vO9oG2KOVlZUjR47UXtr0TU5O7ts3o4IDoPnlcrmhoaFaeyOXlpbeeeedrtY78eFOt9d0vPVWvPzyAbyivvt1SKEQX/jCRurxyU/Gww9HW1uzvcyuNmR9++2IiNdfj5WV+9s1Y/v6+uKrX43Pf 169 xpZmZ2cz0o2hoSHpxkH50z/904yA4/vf/34rVvABdfX9738/exbaz29GBQdASnZXwRER 165 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 169 epV6UZjTv7f+973MkpvpqenJycnS6VSW1tbsVisVCruBUB1zi8Wi9V0Y3JycjrzHZfvfe97B3gLcO8BaEWdnZ19fX0XL17ccplrrBrtBcpG8FGr2cTCwsYHv/xl/OIXGx9v5iBVdSwG2Sy72FRNLqqeeGLjA7UYTWTLpW1fX599DQ2rt7e3mlzUuqC/v//kyZP5fP65554bHBycnp4eHx8f2MxYgRYzPj5enfOfe +65 2EZ76WKxeLDbnG1RAUhJXbaoVFUrkLOv2dyPTStaX9ftgjtsue86IlZXV21quN92t0WlqrqXPuOCnp6eN9544/r 165 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. – chuyển vị của trọng tâm mặt cắt ngang Biến dạng b : u(z)<<v(z) v(z) => độ võng: y(z)=> B F L K K’ K K’ z v(z) u(z) KK’ v(z) - chuyển vị đứng u(z) - chuyển vị ngang Độ võng của dầm