AMAK1 Handbook

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ΔΗΜΟΣΘΕΝΗΣ ΤΑΛΑΣΛΙΔΗΣ ΗΛΙΑΣ ΜΠΟΥΓΑΪΔΗΣ ΙΩΑΝΝΗΣ ΝΤΙΝΟΠΟΥΛΟΣ ΑΡΙΘΜΗΤΙΚΕΣ ΜΕΘΟΔΟΙ ΑΝΑΛΥΣΗΣ ΚΑΤΑΣΚΕΥΩΝ Ι ΤΕΥΧΟΣ A Π Α Ν Ε Π Ι Σ Τ Η Μ Ι Α Κ Ε Σ Σ Η Μ Ε Ι Ω Σ Ε Ι Σ ΤΜΗΜΑ ΠΟΛΙΤΙΚΩΝ ΜΗΧΑΝΙΚΩΝ Α.Π.Θ. ΤΟΜΕΑΣ ΕΠΙΣΤΗΜΗΣ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΤΩΝ ΚΑΤΑΣΚΕΥΩΝ ΕΡΓΑΣΤΗΡΙΟ ΣΤΑΤΙΚΗΣ & ΔΥΝΑΜΙΚΗΣ ΤΩΝ ΚΑΤΑΣΚΕΥΩΝ ΘΕΣΣΑΛΟΝΙΚΗ 2011
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Transcript of AMAK1 Handbook

A ... & 2011 & A 2011 & : : - 1. 1 2. 16 3. 27 4. 39 5. 57 6. 63 : 67 : 1. 76 2. /81 3. 85 4. 89 5. 91 6. : / 95 7. 100 : 108 - 112 114 / 116 117 / 118 /124 :125 2008 & : : - 1. 1 2. 16 3. 27 4. 39 5. 57 6. 63 2011 : - - 1 1) 1 : P 1M2MT T1 1, EJ L2 2, EJ L . 1.1 :, P ,1M ,2M , T q1:) ------------------- (; ;) .. aabb M . 1.2 : - - 2 a ab b0 Q0 Q0 M02 F . 1.3 : :: : ; . 1.4 ) / 1 321 2 . 1.5 : - - 3 2:) (.. , ...) ) // iLk i - , ( ) L . : / . 1.6 a bi . 1.6 (. 1.7) a bi ; . 1.7 , . : 0iLiLiLiLp v k p + = (1.1) : - - 4 : iLk i - ) (L . iLv .. i - ( ) (..: ). 0iLp i - ( ) iLp i - ( ) (, ) : =2 22 234 6 2 66 12 6 122 6 4 66 12 6 12i i i ii ii i i ii iii iLLEJ k (1.2) 2 , 1 = i( ) : iLk , . .. 4 2 ( /=0): . 1.81 2) 1 (22 2 4= =yiLEJk 4 4 2) 1 (4kLEJyi= = iL1 2= y3 4 22) 1 (6kLEJyi= = 1 4 226kLEJyi= : - - 5 [ ]2 2 1 11y z y z LM Q M QT= p (1.3) [ ]3 3 2 22y z y z LM Q M QT= p (1.4) [ ]2 2 1 11y z y z Lu uT = v(1.5) [ ]3 3 2 22y z y z Lu uT = v (1.6) . 1.9 3: ( / ) 0iLp 0iLiLiLiLp v k p + = (1.7) : ) :, P ,1M2M( 7) 1 2 2 31 1,y yM 2 2,y yM 2 2,y yM 3 3,y yM 1 1,z zU Q2 2,z zU Q2 2,z zU Q3 3,z zU Q : - - 6 ):T =i T ii T iLd T EJd T EJ000ip (1.8) ) :q =12212222i0iiiiLqLqLqLqLp (1.9) : 0iLp : ): : . 1.10 Beton Kalender (.) . ): Beton Kalender . 1.6, ( a ) (-1.0), . 1.7. a a b bTi i : - - 7 4: : ( , X , Y ) ( ; ; ; . ) . 1.11 : ( , X , Y ) / . / . 1 22 3YXZ : - - 8 5:) ( ) T . 1.12 i : ,iGLi iLv T v = ,=iii 00 T 2 , 1 = i : . 5 (. ) :0 = = = =z x y xu u zUy =1 00 1yziu (1.11) i : a I T ==1 0 0 00 1 0 00 0 1 00 0 0 1bbyzyziuu(1.12) bYZ112 23zyxzUyUxUXyzxyuzuxu : - - 9 =bbyzyziLuuv( ) [ ]b by z y zTiGLU U = v) :( )i iLTi iGLT K T K = (1.14) : ( ) ( )iLiLT iGLK I K I K = = (1.15) :I T =i ) 0iLp( )0 0i iLTiGLp T p = (1.16) : =i T ii T iGLd T EJd T EJ000ip (1.17) . . :=12212222i0iiiiGLqLqLqLqLp (1.18) 6: : .

+ =+ =+ =iGLiGLiGLGL GL GLGL GL GL GLv K pv K pp v K p. .......... ..........2 2 21 1 1 10 : - - 10 : / + =0P V K P(1.19) = 3 3 2 2 1 1 Y Z Y Z Y ZT U U U V . 1.13 K = (: ) P = ( ) ) K iGLK ; () : 1) N N = N ..*) V2) .. . 3) 1GLK K ( ) 4) 2GLK K ( ) 5) . ( !) 1 y2 y3 yYZX1 zU2 zU3 zU : - - 11 :K 1 ZU1 Y2 ZU2 Y3 ZU3 Y(1.21) 1 ZU1121 16 L 112 1 16 L 0 01 Y1 16 L 21 14 L 1 16 L 21 12 L 0 02 ZU112 1 16 L 211212+ 2 21 166LL 212 2 26 L 2 Y1 16 L 21 12 L 2 21 166LL 22 221 144LL+ 2 26 L 22 22 L 3 ZU 0 0212 2 26 L 2122 26 L 3 Y0 02 26 L 22 22 L 2 26 L 22 24 L : 3i i iL EJ = ) 0P ) : ++ + =12212 122 212200 0022222212 12112 22 2 1 11 10qLqL qL qLqL qLqLqLd T EJd T EJ d T EJd T EJPTT TT (1.22) T q*) ..: ) . =21332211000MMPUUUyzyzyzP (1.23) : - - 12 ) K) , . ) ( ). ), 0 det =totK . - : 0 > x K xtotT,x : ,0 x ,0 det totK4) ; 7: ( ) ; . 1.14 YZX12303 =zU 01 1= =y zU : - - 13 1: 6 5 4 3 2 1=x x xx x xx x x0 0 00 1 0 0 0 00 0 00 0 00 0 0 0 1 00 0 0 0 0 1654321K=xxx000P=xxx0000P: 1 xU .. .1: 1 1 (1,1) . :1) 0 1. 2) , . 2: . 1,25. rK : ( )( )+ +=222222 222 1212 2 2 2 1 1 2 14 .2 46 6 12 12 LL L LL L LrK (1.24) , (P , M ) T ( ) =2 22 2 1 1 00d J T Ed J d J T ETT P=21MMPP(1.25) T : - - 14 8: ( ) ( ) = + = 010P P K V P V K Pr r(1.26) 61 2 10 4 52 122 112 110 0 1 . 020 5 1010 / 10 1 . 2 1= = = == = = == = = =TM m d dT N P m J JNm M m N E m L L ( )6 3 5 112 110 1 . 2 1 10 10 1 . 2 = = = , rK, 0P , P =6 26 2 6 26 610 1 . 2 1 4 .10 1 . 2 1 2 10 1 . 2 1 2 410 1 . 2 1 6 0 10 1 . 2 2 12rK = 1 . 0 / 20 10 10 10 1 , 2006 5 110P(T )=1005P( )384 10 1 . 21192 48 4848 60 1248 12 2861 =rK ( ) M P P + : ( )611067859 . 2669643 . 0 768849 . 01005 ==rK V ( ) T P 0: ( )6110100252542000 ==rK V 0P P + : : - - 15 ( )611067857 . 102669643 . 25 768849 . 25420 1005 = =rK V[ ]3 2 2 y y zTU =V. 1.15 : Beton Kalender (a)mEJPLw63210 1736112 . 07687 = =(b); ( )mEJMLw63 2 2210 595238 . 04 == (c ):md T LwT 62210 254 == : ) (); ) (); ; 122 y3 y(a)(b)(c)TMP : - - 16 2. : .2.1 :P1:) ( 1 ) ) / *) ; . 2.2 : , ( ;), 1 1, F L3 3, F L2 2, F L045P123321 : - - 17 . . .. ()()() 2: : ( , X , Y ) ( x ) : . 2.4 : x b 1 :3 1 1 = ,3 = b2 :2 1 3 :3 2 2 = ,3 = b 1 710 11 12 13 14YZXaaabbb321 : - - 18 3:) (.. , , ...) ) iLk i - , ( ) L . i0LiLiLiLp v k p + = (2.1) 1 11 1iiLiEAL = k (2.2) :3 , 2 , 1 = i ( ) [ ]3 11x xTLN N = p (2.3) ) 1 2 (i0 = 0 pL[ ]2 12x xTLN N = p (2.4) [ ]3 23x xTLN N = p (2.5) [ ]3 11x xTLu u = v (2.6) [ ]2 12x xTLu u = v (2.7) [ ]3 23x xTLu u = v (2.8) . 2.5 12311xxuN11xxuN22xxuN22xxuN33xxuN33xxuN1 a1 a2 a3 b3 b2 b : - - 19 4: : LiLiLiLi0p v k p + = (2.9) ) 1 2 (i0 = 0 pL ( , . 6) 5:) ( ) T . 2.6 i : ,iGLi iLv T v = 3 , 2 , 1 = i ..:( ) [ ]3 2 3vx xTLu u =( ) [ ]3 3 2 2 3vZ X Z XTGLU U U U = X Z X Z =0 1 0 00 0 0 11xxT (2.10) a b =1 0 0 00 0 1 02T (2.11) 211 1 0 00 0 1 13= T (2.12) 333222111YZX : - - 20 ) : iLi iGLTT K T K = (2.14) 11 10 0 0 00 1 0 10 0 0 00 1 0 1LEAGL= K (2.15) 22 21 0 1 00 0 0 01 0 1 00 0 0 0LEAGL= K (2.16) 33 321 1 1 11 1 1 11 1 1 11 1 1 1LEAGL = K (2.17) : 0 >ijd . , , ( !). . o0 , 0 > . ) i0Lp i0i0 LiTGLp T p = (2.18) : - - 21 6: + =0P V K P (2.19) . 2.7 = 3 3 2 2 1 1 Z X Z X Z XTU U U U U U V : :K 1 XU1 ZU2 XU2 ZU3 XU3 ZU(2.20) 1 XU12* 10bb + 12* 00bb + 20 b 20 b 11 b 10 b 1 ZU12* 00bb + 12* 01bb + 20 b 21 b 10 b 10 b 2 XU20 b 20 b 32* 10bb + 32* 10bb + 3* 1 b 3* 1 b 2 ZU20 b 21 b 32* 10bb + 32* 11bb + 3* 1 b 3* 1 b 3 XU11 b 10 b 3* 1 b 3* 1 b 13* 11bb + 13* 01bb + 3 ZU10 b 10 b 3* 1 b 3* 1 b 13* 01bb + 13* 01bb + : iiiLE Ab = ,2 , 1 = i 3332LE Ab =3211 zU2 zU3 zU1 xU2 xU3 xU : - - 22 ) ( ) +=P00000P (2.21) ) K) ) ( ). ), 0 det =totK ( ) ( ) : =totK b : 0 > x K xtotT,x : ,0 x bb00 : - - 23 7: ( ) . 2.8 1: 6 5 4 3 2 1=x x xx x xx x x0 0 00 0 00 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1654321K=xxx000P: 1 XU 1: 1 1 (1,1) . : 1) 0 1. 2) , . 2: . 1, 2 3 . rK : YZX02 1 1= = =x z xU U U213 : - - 24 2 ZU3 XU3 ZU + +=3 3 33 3 1 33 3 3 2b b bb b b bb b b brK ,+=P00P (2.22), (2.23) 8: ( ) ( ) = + = 010P P K V P V K Pr r(2.24) N Pm N Em A m Lm A A m L L100/ 10 1 . 22 02 . 0 201 . 0 12 1123 322 1 2 1= = = == = = = ( )( ) ( )9 1139 112 110 1 . 2 2 2 2 02 . 0 10 1 . 210 1 . 2 1 01 . 0 10 1 . 2 = = = = =bb b (2.22), (2.23) 910 1 . 21 1 1 -1 2 11 1 2 =rK =10000P ( )9110 1 . 213 1 11 1 01 0 1 =rK P : ( )9110 1 . 2130010010010000 == rK V : - - 25 [ ]3 3 2 Z X ZrU U U =V231 . 2.9 9: i i i i iGL GL GL GL0p v K p + = (2.25) 8 ) (01000100300100000 0 0 00 1 0 10 0 0 00 1 0 133111NNNNNzxzxGL=== p) (100010001000001 0 1 00 0 0 01 0 1 00 0 0 022112NNNNNzxzxGL=== p) (10010010010030010010001 1 1 11 1 1 11 1 1 11 1 1 133223NNNNNzxzxGL= == p : - - 26 .2.10 :N S 1001 = N S 1002 = N S 2 1003 = : 0 10022: 0 FZ022S : 0 FX33 1= == =SS ( ): ,igi iL v T v = Li iLiLiL 0p v K p + =1001001001001001001001001S2S3SN 1003 : - - 27 3. . 3.1 : 7443 2 110 1 . 210 75 . 1 = = = = =EAEJ EJ EJ EJ 14 . 14 L 20 L 14 . 14 L 10 L1000 1000 1000 454 3 2 12 1o= = = == = = = = q M M P 1,2,3: : 1)q 2), P ,1M2M 3) o10 = 1:) ; ) , , . 3.2 21341234P 1M2M1L2L3L4L1EJ2EJ3EJEA4 : - - 28 2: , : . 3.3 3: , . ) : ( . 3 , 2 , 1 = i ) =2 22 2314 6 2 66 12 6 122 6 4 66 12 6 12i i i ii ii i i ii iii iLL L L LL LL L L LL LLEJk (3.1) 0 iLiLiLiLp v k p + = (3.2) [ ] [ ][ ] [ ][ ] [ ]4 4 3 3 4 4 3 33 3 2 2 3 3 2 22 2 1 1 2 2 1 13 32 21 1y z y z L y z y z Ly z y z L y z y z Ly z y z L y z y z Lu u M Q M Qu u M Q M Qu u M Q M QT TT TT T = == == =v pv pv p 1 a2 bxxxxzzzy2 a3 b2 a13244 b4 b3 a : - - 29 . 3.4 ) : 4 =1 11 144 4LEALk (3.3) [ ]442x x LN NT= p (3.4) [ ]4 24x x Lu uT= v (3.5) . 3.5 4:) : k) : k) : Beton Kalender 2 2,z zu Q2 2,z zu Q1 1,z zu Q3 3,z zu Q4 4,z zu Q2 2,y yM 2 2,y yM 1 1,y yM 3 3,y yM 3 3,y yM 4 4,y yM 12 3 3 3,z zu Q2 2,x xu N4 4,x xu N442 : - - 30 =12 2 12 221 121 10qL qL qL qLpTL : 1 =12 2 12 221 121 10qL qL qL qLpTL : 2 5: ( ) T GL Lv T v = (3.6) XUZUY =1 0 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 0 1yzu1T (3.7) =1 0 0 0 0 0021210 0 00 0 0 1 0 00 0 0 021212T (3.8) =1 0 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 0 13T (3.9) =21210 00 021214T (3.10) : - - 31 : ( : ) X Y Z = 00 Ti cos( , ) cos( , ) cos( , )cos( , ) cos( , ) cos( , )cos( , ) cos( , ) cos( , )x x X x Y x Zy y X y Y y Zz z X z Y z Z = (3.11) . 3.6 , ) , cos( j i z y i , =() ( 4T) 5) i iLT iGLiT K T K =

=21 121 11 121 121 11 1311 14 0 6 2 0 60 0 0 0 0 06 0 12 6 0 122 0 6 4 0 60 0 0 0 0 06 0 12 6 0 12L L L LL LL L L LL LLEJGLK (3.12) XXZZYY2 1 1 : - - 32 =22 2 222 2 22 22 222 2 222 2 22 22 2322 24 2 3 2 3 2 2 3 2 32 3 6 6 2 3 6 62 3 6 6 2 3 6 62 2 3 2 3 4 2 3 2 32 3 6 6 2 3 6 62 3 6 6 2 3 6 6L L L L L LL LL LL L L L L LL LL LLEJGLK (3.13) =2323 33 323233 3333 333 34 0 6 2 0 60 0 0 0 0 06 0 12 6 0 122 0 6 4 0 60 0 0 0 0 06 0 12 6 0 12L L L LL LL L L LL LLEJGLK (3.14) =1 1 1 11 1 1 11 1 1 11 1 1 1244 4LEJGLK (3.15) : 2 1 4GLK 2 1 ) 45 cos(o= . 4GLK 4T, 21212121= : - - 33 5) i0i0 LiTGLp T p (3.16) ( ) [ ] 12 0 2 12 0 22121 1i01qL qL qL qLTGL p (3.17) . 3.7 / ( )2xu3xu2y2zu3zu2232xu2xu3xu2y3y2zu2zu3zu224411y1xu1zu4xu4xu4zu4zu14334y3y : - - 34

K 31 1L EJ32 2L EJ33 3L EJ4 42L EA1 XU1 ZU1 Y2 XU2 ZU2 Y3 XU3 ZU3 Y4 XU4 ZU4 Y112 0116 L 112 0116 L 0 0 0 0 0 01 16 L 01214 L116 L01212 L 112 0116 L421612++ 4260 ++ 2 21 12 36LL 26 26 2 22 3 L 4 4 0 0 0 4260 ++ 4260 ++ 2 22 30 L 26 26 2 22 3 L 4 4 1 16 L 01212 L2 21 12 36LL 2 22 30 L 22122144LL+ 2 22 3 L2 22 3 L2222 L 26 26 2 22 3 L32126+ 062 + 3 32 262 3LL+ 312 03 36 L 26 26 2 22 3 L062 + 062 + 02 32 2+ L 0 00 2 22 3 L 2 22 3 L 2222 L3 32 262 3LL 02 32 2+ L 32322244LL+ 3 36 L 03232 L 4 4 312 03 36 L 4312+ 40 + 3 36 L 4 4 0 0 040 + 40 + 0 3 36 L 03232 L 3 36 L 03234 L : - - 35 7: ( . 6) 1:01 1 1 Y Z XU U 4:04 4 4 Y Z XU U : 1, 2, 3, 10, 11, 12. (. [3.19]) 03 2 Z ZU U/ /(3.20) / / / / / // // // / / / // / u U UX X 3 21 4 : u U UX X 3 2; : + + + + + +k x xp x x xp x x xp x x x2 11 3 2 11 3 2 11 3 2 14 5 35 2 23 2 10 3 32 1 33 32 31 34 88 164 ) 5 3 () (5 ) 2 2 (3 ) 2 10 (p x kp p x kp x kp x kp x k +++ + ++ + + + + 3 3 , ( k x x2 1), ( ) 2 2 . (3.20) : : - - 36

K 3 2224 2 112 6666 12 + ++ + 2 22 2 1 12 32 3 6 LL L+ 3 32 22 262 32 3LLL++ (3.21) 2 22 2 1 12 32 3 6 LL L+ 22122 14 4 L L +2222 L3 32 22 262 32 3LLL++ 2222 L32223 24 4 L L +U2 Y3 Y : , P ,1M2M]]]]],,,,++

100010001000P : TOT 0p]]]]],,,,

02 10 10002 10 100020p : 10: + + + + + +10205 9 1 255 1 1 3105 2 3 513 2 13 2 13 2 1xx x xx x xx x x + +185 2 2055 9 125 3 55 1 11 3 21 3 2x x xx x x : : - - 37 ]]]]],,,,

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035001050010 210 6121 11LLP ( ) ( ) ( ) P - P - P K V P P V K P0tot1tot 0tot tot + + r r(3.22) : :00 194404 . 000 37968826 . 003 9046065 . 0,:00 187111 . 000 903654 . 002 551985 . 0,, , :00 194404 . 000 131107 . 002 146274 . 0,3232tot 02 132]]]]],,,,++ ]]]]],,,,+ + ]]]]],,,,++ EEE UpqEEE UpM M PEEE UpYYYYYYVVV i i i iP V K PGLGL GL GL 0+ (3.24) i i i iP V K PLL L L 0+ (3.25) : - - 38 : 2 1, , M M P80512075,8196739,95532,639,967266,4951946,775,840212010131013152815282431 : - - 39 4 : XZY 555 5006000 10 6 6 4 . 45000 10 5 5 3 . 30 . 0 400 4 2 . 23000 300 3 1 . 12000 200 2 2 . 01000 100 1 1 . 02 16106 6 25105 5 14 4 4 23 3 3 12 2 2 21 1 1 1 C CEI EA MEI EA MEI EA PEI EA PEI EA qEI EA q

o30o60 003 . 03 T ,3 . 03d , 010 T : ) K , P ,,0PK ( ), GLU) 1 M Q, 4 3 : 4 , 2,, 20, 104 43 222

Y ZZ ZYXUUU : - - 40 1) , , 122345134XxXXZzZZYa : 1) 2C; 2) 6665553 , 4 EICEIC ; (. BETON-KALENDER, 57, 48) 3) 1P ; 344535641P1Pa P cos1a P sin1]]],, ??P : - - 41 4):? ?b 5)4: ; 2) , i i i

p u p , ,o : ,EA EJy,:3 , 2 , 1i XuZuY bXubZubY]]]]]]]]]]],,,,,,,,,,

i i i i i i i ii i i i i ii ii i i i i i i ii i i i i ii iiL 2 22 24 6 0 2 6 06 12 0 6 12 00 0 0 02 6 0 4 6 06 12 0 6 12 00 0 0 0 k,iiiEA

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. 5112211 q M MB A ]]],, 12 2012 202111121111T o q q q qLp Beton-Kal.: 422 q Q QB A . 5422 2965 q M MB A: P?11 21qB b,2qA a, : - - 43 ]]],, + 22 22222 2222o9654096540

q q q qLpaxuazuaybxubzuby ___________________________________________________________ 1PBeton-Kal.:,21PQ QB A 831 P M MB A. 50T Beton-Kal.:, 0B AQ Q 33dT EJM MTB A . 58]]],, + ++ + + 33311333113o8020 08020 0dTEJ PPd TEJ PPTT iLp 1PT3ab : - - 44 4) iT(((,\,,,(j

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100ZE (. . 5) 1 Z Y XE E E1 z y xe e e ( ) ( ) j ij i, cos 1 1 E e iGLi iLv T v ,,XUYUZbXUbYUGLZ]]] ( ) ( )( ) ( )( )( ) 0E eE e E eE e E e]]]]]]]]]],,,,,,,,,

bZ yY z X zY x X xLbybzbxyzxuuuu3 30 0 0 0 00 0 0 00 0 0 0 i b ,b ; yExEzEXZYXZ Ybyexeze : - - 45 : XUbYUbXUbYU( ) ( )( ) ( )Y x X xY x X xbxxuuE e E eE e E e0 00 0= : i=Txe =Tye =Tze( )( )( )( )( )( )( )( )( )( )( )( ) 0 cos sin0 cos sin0 1 00 0 11 0 01 0 01 0 01 0 00 sin cos0 sin cos0 0 10 1 04321 1 0 00 0 10 1 01= 1 0 00 1 00 0 12 = 1 0 00 cos sin0 sin cos3 = sin cos 0 00 0 sin cos4= TT) (sin 0cos 00 sin0 cos4T = : - - 46 5),iGLKiGLp i iLiT iGLT k T K = = ) ( 4) ( 60) ( 2) ( 60) ( 6) ( 12) () ( 6) ( 12) () ( 6) ( 12) () ( 6) ( 12) () ( 2) ( 60) ( 4) ( 60) ( 6) ( 12) () ( 6) ( 12) () ( 6) ( 12) () ( 6) ( 12) (2222Z y i iZ y i iZ y i iZ y i iY z i iY z iY x iY z i iY z iY x iX z i iX z iX x iX z i iX z iX x iZ y i iZ y i iZ y i iZ y i iY z i iY z iY x iY z i iY z iY x iX z i iX z iX x ix z i iX z iX x ii iLE e E eE eE eE e E eE eE e E eE eE e E eE eE e E eE eE e E eE eE eE e E eE eE eE eE eE e E eE eE eE eE eT K

T iT iZ yY z Y xX z x xT iE eE e E eE e E e00T) 3 3 () 3 3 () ( 0 00 ) ( ) (0 ) ( ) (= ( ) ( )Yix Y xE e E e = =121 1 1 121 1 11 11 1 1 1 1 1121 1 1 121 1 11 11 1 1 1 1 114 0 6 2 0 60 0 0 06 0 12 6 0 122 0 6 4 0 60 0 0 06 0 12 6 0 12 GLk : - - 47 =222 2 2 222 2 22 2 2 2 2 22 2222 2 2 222 2 22 2 2 2 2 22 224 6 0 2 6 06 12 0 6 12 00 0 0 02 6 0 4 6 06 12 0 6 12 00 0 0 0 GLk ; cos3 = c ; sin3 = s3iyiiEJ

= 323 3 33 3 3323 3 36 3 3 33 3 323223 3 3 3 3 33 3 323225 3 3 3 3 3 33 3 33 3 3 3 3 323233 3 33 3 3 3 3 3423 323 3323 3 33 3 312 323 3 33 3 3 33 3 323233 3 3 3 3 33 3 323232 3 3 3 3 3 33 3 33 3 3 3 3 323233 3 33 3 3 3 3 3123 323 33333 33 33 3333 33 33 346626) ( 661212612) ( 1261212 612) ( 12266) ( 4 6) ( 661212612) ( 1261212612) ( 12

cscf sc c ss c s ccc sf s c c sss c c sc sss c s cf s ccsfcf scc ss c c scc sf s c s css c s cs css c c sf s cGL= + = + + ++ = == + + += + = += K sincos33==sc K=21 20 1820 19 17 `18 17 1615 11 614 10 513 9 415 14 1311 10 96 5 412 8 38 7 23 2 13f f ff f ff f ff f ff f ff f ff f ff f ff f ff f ff f ff f fGLK , cos4 = c , sin4 = s444

EA= 44 4 4 44 4 4 4 4 4 = s c s cs c s cL T K : - - 48 ( )4424 4 424 4 44 424 4 42424 4 424 4 44 424 4 4244 4GL LTs c s s c sc s c s c cs c s s c ss c c s c cK T K T = = 4) 4iiK ; _____________________________________________________________ iLT i iGLp T po o=333122 2213 1 223 1 11333122 2213 1 223 1 118 965122 402028 965122 4020211dTEJ P q qc Pqs PqdTEJ P q qc Pqs PqTT ++

1 oGLP2 oGLP3 oGLP6),GL K ,oGLPGLP,122112112111 1K KK KKTGL = ,233223223222 2K KK KKTGL = 344334334333 3K KK KKTGL =455445445444 4K KK KKTGL =:kijK ) 3 3 ( 3 , 2 , 1 = k) 2 2 ( 4 = k..: 24 4 44 424 445s s cs c cT= K121 111 1 111212 0 60 06 0 12

=TK : - - 49 244243331222:0 ::000::::0 :0 :MUP UUUMUUZYXZYXZYX+ + =P33313131333122 231223122 22112211i o8228 9652 420965124002dTEJ PcPsPdTEJ P qcP qsPq qqqTTGL + + + + ++ =

P ,2XU ,2YU2Z ,3XU ,3YU3Z,4XU ,4YU4Z 222122K K +1c + 223K 0 GL= K : " !"+ ; T 223K 333233K K +65cc++ 334K 0 T 334K 444344" " K K + : - - 50 2XU2YU2Z3Z4XU4YU4z2112+ 00+ 061 1+ 0 0 0 000+ 21 112++ c 2 260+ 2 26 0 0 0061 1+ 2 260+ 22122144

+ 2222 0 0 002 26 2222 6 5122224c c f+ ++ 13f14f15f0 0 013f2416cf+ 4 417s cf 18f0 0 014f4 417s cf 2419sf+ 20f0 0 0 15f18f20f21f

GLK m =K 2 112 + 01 16 0 n 12 112c ++ 2 26 2 26 022 122144

+ 2222 0 06 5 122224c c f + + + 13f14f15f24 16c f +4 4 17s c f 18f024 19s f +20f0 0 21f 0 0 0 : - - 51 A7) ( ) GLP P K Uo 1 1) , 102

XU , 202

YU , 24 Z44

YU 2Z3Z4XU22212144

+ 2222 0= ((,\,,(j+ 22 2211 196512

q q M2222 12 2226 54 fc c++ + 13f((,\,,(j + + TdJE P qT33122 28 9650

013f24 16c f + (,\,(j 231 2sP P ( ) 10 61 1 ( ) 20 62 2 + 4 0 2 0 10 0 ( ) 20 62 2 + 414 f 215 f10 0 20 0 [ ]44 4 17 s c f 218 f 3 2Z Z 4XU+ ]]]]]]]]]]],,,,,,,,,,

++ ++ +++||4220 4 424 16 1312 22213 6 5 222222222 121

c f fff c c : - - 52 4XU 22212 6 5 222222 222 121422 4 4

++ + ++ +f c c130 f + 13f24 16c f + 15 14 2 233 3 1 22 2 2 2 1 122 2211 12 4 1208 965120 6096512f fdT EJ Pq q q MT + +

4 4 17 1831 24 4 22s c f fsP P + + , 10001100031 , 250820002 111 . 1112730003, 400055000 45

c 300066000 36

c, 40002730009 4 4323 12 f , 5 . 03s 866 . 03c000 . 1 5 . 02730003 6 63 3 3 13 s f 3 . 408 75 3 . 333 75 . 033005 . 0 5 . 02730001216 + + f20002730009 2 2323 15 f1732 866 . 02730003 614 f03 . 534 866 . 0 5 . 0330012 866 . 0 5 . 027300017 f1000 5 . 02730003 618 f : - - 53

]]]]]]]],,,,,,,+ ++ + + + + + 25 . 0 3 . 408 10001000250 4 44000 3000 4000 250 4 2250 4 2 250 4 4 1000 1 4 ]]]]]]],,,,,, + + + + +

866 . 0 5 . 0 4 03 . 534 4 1000 2 5 . 021 . 12 . 21732 4 2000 2 250 2 12010 10 33 . 030008 3 1 . 1250 2 120 1000 601211 . 0 3 . 33 4XU]]],,

]]],,1361773696 . 408 10001000 27000 24 . 705 . 1827000 10001000 6 . 408det1341

]]]],,,

ZXUA 2405 . 18 24 . 700 24 . 72010000444333222111

ZYXZYXZYXZYXUUUUUUUU XZY : - - 54 2) 1 ,24 . 720100001

GLv]]]]]]]]]],,,,,,,,,

0083 . 0 005 . 00083 . 0 005 . 01 oGLp1 o 1 1GL GL GL GLp v k p + 4 0 6 2 0 60 1 . 0 0 0 1 . 0 06 0 12 6 0 122 0 6 4 0 60 1 . 0 0 0 1 . 0 06 0 12 6 0 1210001 GLk]]]]]]]]]],,,,,,,,,++

+ + + + + + +

9917 . 31039 000 . 205 . 7655945520000 . 205 . 0 5600 . 760083 . 0 005 . 00083 . 0 005 . 024 , 7 4 60 0 224 . 7 6 12024 . 7 2 20 0 10 624 . 7 0 20 1 . 0 10 024 . 7 6 20 0 12010001 o 1 1GL GLp v k XZY?2000200045520,008331039,991776559,952176560,05 : - - 55 1 1 o 1 1 1222111L L LyzxyzxLMQNMQNp v k p + ]]]]]]]]]],,,,,,,,,

1 124 . 7102000024 . 72010000*1 0 00 0 10 1 01 0 00 0 10 1 0L Lv00v

]]]]]]]]]],,,,,,,,,

, 1000 *4 6 0 2 6 06 12 0 6 12 00 0 1 . 0 0 0 1 . 02 6 0 4 6 06 12 0 6 12 00 0 1 . 0 0 0 1 . 01

Lk0083 . 005 . 000083 . 005 . 001 o

Lp]]]]]]]]]],,,,,,,,,

]]]]]]]]]],,,,,,,,,

]]]]]]]]]],,,,,,,,,+]]]]]]]]]],,,,,,,,, +2221110083 . 3104095 . 76559000 . 20083 . 4552005 . 76560000 . 20083 . 005 . 000083 . 005 . 00100004 . 31 56 . 76252 . 45 56 . 7621 o 1 1yzxyzxL L LMQNMQNp v k : - - 56 B3) 4 4,y zM Q 3 [ ] 2 4 05 . 18 24 . 7 0 03 TGLv,3 3 3GL Lv T v L L L Lp v k po+ 2025 . 763 . 17 24 . 7002cos 4 sin 05 . 18sin 4 cos 05 . 1824 . 7003

+

Lv[ ] (,\,(j + 26 12 0 6 12 01 33 3 3 3 3 34PQL zv ((,\,,(j + ]]],, 33313323 3 3 323 3 3484 6 0 2 6 0dTEJ P MT L y

v 2000200045520,008331039,991776559,9576560,05+8211 q : - - 57 5. GL LV T V =T K T KLTGL =LTGL0 0p T p = ! ; xauzauyaxbuzbuyb / EA 0 0/ EA 0 0 0 12 6 0 12 6 :iLK0 6 240 622 / EA 0 0/ EA 0 0 0 12 6 0 12 60 6 220 624 3

yEJ = : - - 58 1 = = =z y xe e e , 1 = = =iZiYiXE E E , b a i , =0 = = = z y z x y xe e e e e e , 0 = = = iZiYiZiXiYiXE E E E E E..) , cos( 1 1i iZ xZ x = E e iZiZiYiYiXiX ziz yiyL xixiGL GL GL L LU U U u u u V E E E e e e + + = + + =( ) ( ) ( )( ) ( ) ( )iZ ziZiY ziYiX ziXiziziZ xiZiY xiYiX xiXixixGL GL GL LGL GL GL LU U U u VU U U u VE e E e E e eE e E e E e e + + = = + + = = A: iZiZiYiYiXiX ziL yiy xixiGL GL GL z L LE E E e e e + + = + + = ( ) ( ) ( )iZ xiZiY xiYiX xiXixixGL GL GL LE e E e E e e + + = = ayEaxEazEaXaYaZ byexezebyEbxEbzEbXbYbZaVabVbyxz : - - 59 aXGLUaYGLUaZGLUaXGLaYGLaZGLbXGLUbYGLUbzGLU( )TbGLaxLuayLuazLu ax xE e ax yE e ax zE e ay xE e ay yE e ay zE e az xE e az yE e az zE e 3 303 301 30axLayLazL 3x3 : a 0 a 0 0bxLubyLubzLu0a0bbxLbyLbzL 00 T GL LTV V = ,1 = T TT,( )i iY xY x, cos = E e b a : ;( ) =bZbYbXTbGLGL GL GLb : a( bZbYbXaZaYaXE E E E E E , , , , ) : - - 60 [ ][ ][ ] [ ][ ] [ ] 1 0 0 , 1 0 00 1 0 , 0 1 00 0 10 0 1= == ===TZTzTYTyTXTxE eE eEe 1 0 00 1 00 0 12 1 = = : = aXGLUaZGLUGLaYbXGLUbZGLUbYGL axLu10 02 20 0 azLu 01 0 ayL 0 01 0 0 bxLu 0 0 010 0 bzLu 0 0 0 01 0 byL00 0 0 01 T ( ) azLu 1 00ayL 01 bzLu 01 0byL 01 yexeze1 2yExEzEX : - - 61 (. 3) ) :,zuy 2134xxxxXZY 1 :[ ] 1 0 0 =Txe ,[ ] 0 1 0 =Tye , [ ] 0 0 1 =Tze2 :[ ] a aTxsin 0 cos = e ,[ ] 0 1 0 =Tye , [ ] a aTzcos 0 sin = e3 :[ ] 1 0 0 =Txe ,[ ] 0 1 0 =Tye , [ ] 0 0 1 =Tze4 :[ ] sin 0 cos =Txe ,[ ] 0 1 0 =Tye , [ ] cos 0 sin =Tze 045 = a = aXGLUaZGLUaYGLbXGLUbZGLUbYLGazLu X z E e Z z E e 00ayL 0 0Y y E e bzLu0X z E e Z z E e 0byL0 0Y y E e =1T1 0 00 0 10 =2T1 0 00 cos sin a a001 0 00 0 1 01 0 00 cos sin a a =3T1 0 00 0 1 001 0 00 0 1 : - - 62 =4TaXGLUaZGLUbXGLUbZGLUX x E e Z x E e 00X x E e Z x E e = cos sin0 00 0 cos sin b) : ixu , izu , iy aXGLUaZGLUaYGLbXGLUbZGLUbYGLaxLuX x E e Z x E e 0 0azLuX z E e Z z E e 0ayL 0 0Y y E e bxLu 0 bzLubyL T 1 0 00 0 10 1 01= 1 0 00 cos sin0 sin cos2a aa a = 1 0 00 0 10 1 03 = : - - 63 6. 6.1 ( 2) (6.1) . 6.1 6.2 ( ) . 6.2 1 11 1xa xaxb xbN uEAN u L = (6.2) 6.3 () . 6.3 =xbxaTxbxaLGJMM1 11 1[6.3] ayuayayMaxuaxaxNazuazazQazMbbxubxNbxbxMbybyMbyubyQbzubzQbzMbyaxNaxubxubxNbbaxMaxbxbxM : - - 64 6.1 : ( y zM Q , z x ) . 6.4 =ybzbyazayybzbyazauuL L L LL LL L L LL LLEJMQMQ2 22 234 6 2 66 12 6 122 6 4 66 12 6 12(6.4) LK 6.2 : ( z yM Q , y x ) . 6.5 =zbybzayazzbybzayauuL L L LL LL L L LL LLEJMQMQ2 22 234 6 2 66 12 6 122 6 4 66 12 6 12(6.5) ayMaybybyMbazuazQbzubzQbayQayubyubyQazazMbzbzM : - - 65 6.3 ( y x zM M Q , x z ,y z ) . 6.6 =ybxbzbyaxazaybxbzbyaxazauua L La a L Lab bLa a La aa L La a L Lab bLa a La aMMQMMQ2 22 24 0 6 2 0 60 0 0 06 0 12 6 0 122 0 6 4 0 60 0 0 06 0 12 6 0 12(6.6) : 3LEJay=LGJbT= baxMaxbxbxMbybyMbzubzQazuazQayayM : - - 66 xauyauzauxayazaxbuybuzbuxbybzb xaN L EA0 0 0 0 0L EA - 0 0 0 0 0yaQ0312 L EJz0 0 026 L EJz0312 L EJz 0 0 026 L EJz zaQ 0 0312 L EJy026 L EJy 0 0 0312 L EJy 026 L EJy 0xaM 0 0 0 L GJT0 0 0 0 0 L GJT 0 0yaM0 026 L EJy 0 L EJy40 0 026 L EJy0 L EJy20zaM =026 L EJz0 0 0 L EJz4 026 L EJz 0 0 0 L EJz2xbNL EA - 0 0 0 0 0 L EA 0 0 0 0 0ybQ0312 L EJz 0 0 026 L EJz 0312 L EJz0 0 026 L EJzzbQ 0 0312 L EJy 026 L EJy0 0 0312 L EJy026 L EJy0xbM 0 0 0 L GJT 0 0 0 0 0 L GJT0 0ybM0 026 L EJy 0 L EJy20 0 026 L EJy0 L EJy40zbM 026 L EJz0 0 0 L EJz2 026 L EJz 0 0 0 L EJz4 (6.1) & : : 67 2011 : - - 67 1 : 1)? = P 1 = 2),BQ BM : = =2 1EJ EJ 104 3= = EJ EJ1 2 3 4" " EA EA EA EA = = = =610, EA= 520 2 EA=, 60 = q , 100 = = t t Tu 210=T, 1 = d 1 = 52 22 2 ( 2 ) 2 2EA EAC= = 1y2zu2y =K322 143 4 ++EJ EJ 36 322 = 1106020 36 6 53 42 212 12EA EA ++ + 3466

+ 20+120 +120 0 322 3466

+ 324244

+ . sym 40 +40 333

EJ= 344

EJ= : - - 68 o3p 2211222020 73020 3:MQMQqqqqBK

2020 73020 322 o3

qqqq= p 4oT p dTEJdTEJBKTT00:=dTEJdTEJTTT004op = +=+= 2 1 32122020 730220PdTEJ qP qqT

P P 1)1!2 = =zu ) 60 2 ( 62 20 1102 1 = = +y y 2 80 202 1= +y y 5952 . 01 =y1738 . 02=y3 , 203 = P2)0p ku p + =+1000174 . 01406060120206060120 52 . 57 1 174 . 0 20 6056 . 109 174 . 0 60 120 = + = = + =BBMQ : - - 69 2 000 . 10 =REI000 . 12 =stEI , 105 =t, 5 . 0 =Rd4 . 0 =Std

0t: .K B

ut dTEJ M MT B A = = ;0 = = B A 0t t Tu = ; , 0 = w 94 . 00 3010 000 . 1265 . 00 3010 000 . 1055 = = = =tSRMM RRREIk

=000 . 10 4 =RktttSSSEIk

= 000 . 16 4 =tSk REIt SEIRdt Sd030 =iT0a0 = T3 h42 134333366669999+fixed : - - 70 1234 3333442442 04402244=++++ttttttSRRSRSSRSRSRkksymkkkkkkkkkk

4!3 =2!1 = 13000 . 101 . 2 8 . 01 . 2 8 . 08 . 0 1 . 28 . 0 1 . 233336 . 2 5 . 0 8 . 0 05 . 0 6 . 2 0 8 . 08 . 0 0 6 . 2 5 . 00 8 . 0 5 . 0 6 . 2000 . 10 = 133!166000 . 102 . 4 6 . 16 . 1 2 . 4 = = 1 = 666 . 26 . 2000 . 10 = 000 . 10122 . 51 0002307 . 01 = 6 153846 . 16 ) 000 . 5 000 . 10 (153846 . 74 3 3+ == + + = RM : - - 71 3 :,1RM, SM, StM 41 110 559 .833 . 265 . 15 . 1345343 (,\,(j+ + EI 5808 . 2 3 41925 . 0430 1 + +MEIMR2453 . 2 5 . 1 74533 . 0340 1 +MEIMSt3354 . 05311 EIMS 5 . 1 q3 h2 W4123" "1EF 3 , 2 , 1 iSMStMRM341EIC432EIC ) 5 (333

EIC384 5 12

5 . 1123 0 22

1.51.52.24530.3354i = : - - 72 4 10P 199M1 2 5" " EA EA EA = = = , 103

iEI, 10 4

T 12 1d d out t 100 3 4200 2 EA EA = = : ) P K , ) 4N: 42 22 2 (2 ) 2 2EA EAC= =

1zu 1y 2y )

K 2 212EF+ 6 6

P ]]]]]]]]],,,,,,,,+MdEJdEJTT110 24 + 22 + , 22444

++EI 3LEJa . :Ta10!1 y10 P0t t Tu 113322445199 M1 32XYZEJC4 ~3 : - - 73 ) 0!1 y 1 zu2y ]]],,

]]],,20001200 6060 22 19298 .2y52632 .1 zu 14.52632 5.26312 2zEAN u C = = =

72157 . 3222631 . 54 N 10!1 y72157 . 3222631 . 54 N2631 . 52 252632 .~4 1 EFC u NzEA : - - 74 5 000 . 10EJ1000 TGJ : ), ) ~22!

b by x 1 1 200102 2 10EA = = 200 EFABCD(0, 0, 10)(10, 0, 10)(0, 10, 10)(0, 0, 0)AABCC102EFxy000 bzbxfreeEA = 200 EA : - - 75 bzubx by( ) 24 0 1006 0 10 12

sym

+ = 120 22

qq 103

yEJ100101000

TGI zu ~ 4100600 130sym= 106 075 . 1 zu132925 . 0~ ~45 cosx ~45 siny ]]]]]]],,,,,,+]]]]]]]]]],,,,,,,,,]]]]],,,,

... 2133 . 0 133 . 0075 . 1 000200 0 600 ....0 100 0 ....600 0 120 .... qMMQyxz & : : 1. 76 2. /81 3. 85 4. 89 5. 91 6. : / 95 7. 100 2011 : - 76 - 1. i 1P ;; j 2P ;; (.. SAP) j ;

1): 0 byM bbbbaayzyzyzyzuuMQMQ2 22 24 6 2 66 12 6 122 6 4 66 12 6 12 (1) 3 EJ ( ) 0 4 6 2 6!2 2 + + + b b by z y z yu u M ( )b bz y z yu u

6 2 64122 (2) 0 jM0 aM0 kQ0 N1P2P iakj

a b : - 77 - (2) (1) azuayb zu

(,\,(j((,\,,(j(,\,(j+ (,\,(j((,\,,(j(,\,(j+ (,\,(j+ ((,\,,(j+ (,\,(j

64612 6426466 122466 2424462 664612 6426466 122 222222222222 222b zaya zQMQ 0 yM ( )( )( ) ( ) 5 5 6 63 34 4 L LLLkkk k 3 3 33 3 33 3 32) 3 3 (

L k .. ..:,23dEJQ QT B A

dEJ MT A23 T : - 78 - 2):0 yM [ ] 0 2 6 4 6!2 2 + + + b z y z ybu u M [ ]22412 6 6

b by z z yu u ( )]]],, b z y z z z zb b bu u u u Q

6 12 2 6 6461222

bzQ 23 3 33 3 33 3 3

k 3): 0 zQ 2 22 200 0 00 ! a b : - 79 - - 6 6 b aLK b a (L: ) bzx : ayazbxayazaxu u u u , , , , ,- 5 5b aLKa b aLKb ayM 0 byM 0, ( ay by , ) bb b aLKa b aLKb i : i : - 80 - / (, ,/, SAP): 1) jikl j iLK , k iLK , iLKi ixU , izU , iy 2) kji 2a) j iLKi, k iLKi, ixU , izU , iy2b) j iLK , k iLKi, ixU , izU , iy : iyM 0; 2c) j iLKi, k iLKi, ixU , izU 3) M 4)

0000 0 0 0 000 +kiy iy 0k 1010 k ; : - 81 - 2. / 1: 01 1 1 w u ,, 02u, 02w03 3 3 w u 02

]]]]]]],,,,,,

x x x xx x x xx x L xx x x xLEJk2324

LEJC42 2: 1-2-3 2P /k1 1223LEJC42 2C" " , EF LL112 2 3xuyzuH1P2Ph" " : A E

LkH : - 82 - 1: 1-2-3. +2k k " "1 2xu2zu2y3xu3zu3y222 2222 2 2 2222 12 22 2 12 2 2 21 14 6 0 2 6 06 12 0 6 12 00 0 0 02 6 0 4 4 6 6 06 12 0 6 12 00 0 6 0 0 12 + + + +EA EAh hEAhEA ,31h EJ 32 EJ 2: ( 1-2-3) , ... : 0031 1 13 2

zy z xx xuu uu u 1122 3,1Ph

kH : - 83 - 3xu2y3y,4 2 024460 6 122222221222111

hhh+

12122121

ppH P ,2 1 h]]]]],,,,

2 22 234 0 22 6 80 12 6

EJK 12122121

PPH 3: ( )2y( GAUSS) 2y3xu3y]]]]],,,,

2 22 234 0 22 6 80 12 6

EJK( )( ) 4 14 312124 0 20 12 62 6 821212 22 23332 ]]]]]],,,,,

]]]]],,,,]]]]]],,,,,

p HpuEJyxy ]]]]]]]]],,,,,,,,++]]]]]]]],,,,,,, 48 1212 4312214460 2 24602912 6 62 6 821211212 2 2 22 23

P PP HpEJ : - 84 - ]]]]]]],,,,,,+

]]]]]],,,,,]]]]]],,,,, 48 516125 . 3 5 . 1 05 . 1 5 . 7 02 6 8211_2133222 23

pppuEJHyxy 3 3C ) (Ck L : ]]],,

235 . 3 5 . 15 . 1 5 . 7L LLLEJCk , 3 k4821 P21PkC(,\,(j+161 P H2P : - 85 - 3. ; - Rigid offsets: :

b k3 EJ2 2224 6 2 66 12 6 122 6 4 66 12 6 12 b :cdk?

1x 2x cyMayMbyMdyMczQa zQbzQ d zQ : - 86 - cdk b k1X z y yQ M Mc 2 2 - 1 1x z zQ Q c 1 1 b dz zQ Q3 3 2 X z y yb b dQ M M +4 4 + 3 2x ( ) 222 222121 1216 4 12 6 6 2 12 66 12 6 126 2 12 6 6 4 12 66 12 6 12x x x xx x x x + + + + + + + , k k cd 3 EJ2222222 1 21222 12 1 2121 211 1212 1) ( 1266 412 612 66 212 612 61212 61212 66 212 6) ( 126 6 412 612 61212 612xxxxx x xxxx xx x xxxxx xxx x + + + + + + + + + + + + + + + +

k : - 87 - : y z zx u u c + 1 y yc

cyzcyzuxuV V T

1 011 2x y z zb b du u b dy y

byzdyzuxu 1 012 b b dV T V : bb bbbk kk kk ; Tba abk k ,1c a av T v,1d b bv T v( ) TaTcTa1 T v v ( ) TbTdTb1 T v v : [ ]!

]]],,]]],,

baab TbTa iAvvk v v : b [ ]]]],,]]],,dc cd TdTcvvk v v : d b b c + + c ab d1x 2x c zua zub zudzu : - 88 - ,TvTbv: ( ) ( ) [ ]!111 1

]]],,]]],, d bc abb baab aa TbTdTaTcv Tv Tk kk kT v T v [ ]]]],,dc cd TdTcvvk v v [ ]( ) ( ) ( ) ( )( ) ( )!1 11 1 1 1

]]],, dcb bbTbb abTa a aaTa TdTcsymvvT k TT k T T k Tv v [ ]]]],,dc cd TdTcvvk v v ( ) ( ) ( ) ( )( ) ( )1 11 1 1 1

b bbTbb abTa a aaTa cdsym T k TT k T T k Tk cdk : 3.1 ,1 d x ,2 b x c 3) (cEJcd k 12 ( ) c d 6 12 -12 ( ) c b 6 12 ( ) dc c d 12 4 122 2 2+ +( ) c d 6 12 + ( ) [ ] d b c c db + + + 6 2 122 2

sym 12 ( ) c b 6 12 + ( )2 2 24 12 12 c cb b + + : - 89 - 4 - ; - ; -Floating point arithmetic; digit; Fractional part a * 10b, 0.1| a | > w w f Mw w f Q 0 00 0 w ww w puOO 0 w0w wuO0 0 p` uO p0 " 0 " " " 0p uO + : - 92 - : : ( ) M W p w EIz : , , ... : 0+a iA A / u u u0 = . [ ] 0+ babazbaw P M dx w p dx EI [ ] 0+ babazbaw P M dx w p dx w w EI :. .. x : - 93 - [ ] 0+ babazbaw P M dx w p dx w EI w M w w EI M ;[ ] ( ) [ ]babababauv uv d uv vdu v u + ( ) [ ]babaw EI w dx w EI w ( ) ( )bababaw EI w dx w EI w w EI w + ( ) ( )bababaw EI w dx w EI w w EI w + [ ]babaw EI w w EI w dx w EI w + [ ] [ ]bababaw EI w w EI w w EI w dx w EI w + [ ] [ ] [ ] [ ] 0 + + babababazbaw P w EI w M w EI w dx w p w EI w 00 0 0

+ p 0u ( u u u0 ) : - 94 - [ ] ( ) [ ] ( ) [ ] 0) 0 ( ) 0 ( + + + pbaba zbaP EI w w M EI w dx p EI w wp 0ab ;b 0 a 0 zp EI w0u u000 + + P EI wM EI w p0

DuE : ... EI w 0A : zp EI w , () ( ) u u; .. : 2m : ) 2 () 1 (

mmp w I Ep u A Ezx : m w EI w , dx u A E u :) 1 ( m ( ) w w ,. m ( ) Q M w w , , . 0w w : - 95 - 6. : 6.1 ) ( 2 2 ) ( 1 1 s sh u h u u + () ( ) s h 1211 ( ) s h +1212 ,D sA s A A + ( ),212 1A A As+ ( )1 221A A AD ( ), 12s x +

2

ds dx

2dsdudxdsdsdudxdu [ ] ( )1 2 2 1 2 2 1 121 221 221) ( ) ( u u u u s h u s h udxdu (,\,(j+(,\,(j+ ( )( )( ) ds sA A u u u u E dx u EA uD s + 1 2111 2212

( )( )1 2 1 2u u u u EAs [ ]]]],,]]],,

212 11 11 1uuEAu us

k () 2u1u1A2Axs = -1s = 1s : - 96 - 6.2 6.2.1 ( ) ( ) [ ]1 2 2 121p p s p p p + + ( ) ds dx s x212 + :) ( 3 3 ) ( 2 2 ) ( 1 1 ) ( s s s sh u h u h u u + + ( ),2121s s h ( ),2122s s h + 231 s h ;ih( Lagrange) : dx u p s

0) ( ( ) ( ) [ ] ( ) ( ) ( ) ds s u s s u s s u p p s p p21212121232221 1 2 2 111

]]],, + + + + + sp dp ]]],,(,\,(j +(,\,(j+ +(,\,(j s D s D sp u p p u p p u3423232323283 2 1

( )(,\,(j+ +(,\,(j+(,\,(j

2 1 3 2 2 1 13 6 6p p u p u p u

[ ]( ) ]]]]],,,,+

3662 1213 2 1

p p ppu u u 2u1uxs = -1s = 1ss3u1 3 21p2p) (xp1 3 261p 62p32 1p p+ : - 97 - 6.2.2 () :) ( 4 ) ( 3 ) ( 2 ) ( 1 ) ( x b x b x a x a xH H w H H w w + + + ;iH(Hermite:w w , ) dx w pz( ) ( )a a zw p 3 2103 22 2 3 1 + + + ( ) ( ) d wa b

3 2 3 22 3 + + [ ]z b b a ap w w12212222

zpabx, : - 98 - 6.3 / / : P u u u (1) :,6 5 35 4 23 2 1]]]]],,,,

K K KK K KK K KK[ ] ,2 2 1 u u u [ ]1 2 1M P P P (1) [ ]+ + +2 3 2 2 1 1 1 k u k u k u[ ]+ + +2 5 2 4 1 2 2 k u k u k u[ ]1 2 2 2 1 1 2 6 2 5 1 3 2M P u P u k u k u k + ++ + (2) 1 :22u u 0!2u (;) (2) : ( ) ( )+ + +2 6 3 1 2 2 3 1 1 1 k k u k u k u( ) ( )2 2 5 1 2 2 1 1u k M u k P u + 1u225 122 16 33 1u k Mu k Pk kk k

: - 99 - 2 : u u2!1uu u u 2 1 (2) ( ) ( ) [ ]2 6 3 4 2 2 1 k k u k k k k u + + + + +( ) [ ] ( )1 2 2 1 2 6 5 3 2M P P u k u k k + ++ + + u212 16 5 35 3 4 2 12M P PK k kk k k k k+

++ + + : - 100 - 7. (Constraints) 7.1 k : 221x k ( ) ( )3 3 2 2 1 122 3 321 2 221 1212121:u P u P u Pu u k u u k u kp + +

3213213 33 3 2 22 2 100PPPuuuk kk k k kk k k

+ +

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1 2 2 1 12 2 3 3 2 23 3 3 300k k k u Pk k k a k a u Pk a k a u P + + + = + 4 , 01u 6 , 02u2 3102uau ++ 6 , 01023++ au 59998 , 0 :5998 , 0 :5980 , 0 :5818 , 0 :5 , 0 :4182 , 0 :000 . 100000 . 10000 . 1100101333333

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]]],,]]],, +3 21212 22 2 1P PPuuk kk k k 4 , 01u3 26 , 0 u u1 : 1 , 0 01 , 0 2 , 0 01 , 0 3 , 0 000 . 000 . 11 2 1 1A J A J v E : - 105 - 100 KN4 m3 m 1 ( 2) 100 4 3 [1] [1][2]1 42 3123456yx 1 4u u = ( - ) : - 106 - : Lagrange 23 ( assign joint constraint equal translation xu ) : 100 [1] [1][2]50 5030,37 30,37 ( [2]) . 2. 100 50yxN=02 : - 107 - (constraintforce); P B KuT + (xxx.out) 50 0 50 50 100 + N Fx : (xxx.out) : Analyze > Set Options > Generate Output > Select Output Results > : Reaction / Spring forces & : : 108 - 112 114 / 116 117 / 118 /124 2011 : - E - 108 - ( ) / / / (.0.) vs. , : - E - 109 : - E - 110 : - E - 111 : - E - 112 *) 21BLvGk = 312sBLk k= = (;) G : v : Poisson ) 35 . 0 (B : // L : sk : Winkler ( ) *)*)*)BL k Cs=k BL (, L) : - E - 113 ) , ( y x u k qs =q :] [ ,] [ O ks , u : ] [ME : O:, M : ; (Soil-Structure Interaction) : --- q kC + : rigid offset : - E - 114 ( ) ; ( , , ) ; , . ____________ , (,slave,dependent) (master): : slave, dependent ( s ): m (master) : ,j mm m sj + = r U Umsj =j mzyxmzyxmzyxszyxrrruuuuuuj + = ,m s xx x rj = ,m s yy y rj = ,m s zz z rj = mmUmj mrjSzuyuxuzyx : - E - 115 ( ) ( )y z z y x s xr r u um j + = ( ) ( )x z z x ysyr r u umj + + = ( ) ( )x y y x z s zr r u um j + = ( z ): =zm00 ( )y z x s xr u um j = ( )x z ysyr u umj + = ( )m jz s z = SAP ; :constraints restraints ; () :" " A () " " I ( ) " " A () 415 3267ddd dBB : - E - 116 : 0b d b + =0b d b + =_____________________________________________________ ,, _______________________________________________________ n , ; ( )+ +++++bd0b : - E - 117 ( ) ( ) ( L B, ) ( j i )+ ( k i i ,): 3 3 , 12 , 126 5 , 6 5 ,:3 3 3 3LB B L I L B I B L IA A A A B L AH Lz y xy x= = == = =< , , . BLHzyxjik ;;f : - E - 118 : - E - 119 :) . + ) x 2yyJ (. . 110) , 3yy4(. . 109) KB y 3x 2(. . 99, 100, 101)1 1, A I2 2, A I3 3, A Iy 4yyJJ2.15 2.15k1.04k12xxII12 : - E - 120 x : (KB K ) : () 4 . : K // : x,yyIx sA . : 4 , 3 // : y,21xxJy sA21 . : KB : A : . zzJ( ) . : - E - 121 (;) . " " ; ; (St. Venant); I ( 5-6 6-7) GEHbs t I(,\,(j

2 24 : H ,: t ,: b , : SKB ,E: G () 2 zz xx syI I A A KB , , , : yy x sI A K , : : zzI KB K : ,

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: ) 2 1 ( 2221+ hI dGEIzz I : : - E - 122 h : 1 : ( , 121 3 5 . 11 ) :GA h EI22 , 7 ( A: ) G : () 5, 7: ( ;) TJ( 5-7): ( )]]]],,,(,\,(j 1211 21 . 03143hth t ht JT h : TJ ; " " TJ ; . ..., , , x yJ J.. .., , , x y xJ J , (( 3)x536 74tyyx : - E - 123 :: : ::KB : (): T , ,.KB (): T , ,kKB () () KB .KBA.AAxAAxAyA0yAxxI0xxIyyI.yyIyyIzI 0zIA0. A TxA0.xAyA. A.yAxxI.xxI.xxIy yI0.yyIzI.zI.zI yyyxxTKBkKB : - E - 124 : , , ; (, ) / ; . / : RAM; ; ; ; : / ; ; 30.000 ; & : :125 2011 : - 125 - 125 1. 3 ():[ ] [ ] 4 . 0 , 2 . 1 , 8 . 0 , 2 . 134 33 32 31k k k k . 32k ; ( m ) 2. GLk(z x ) b a . ; ! 3. 14. ! ( ) z x . 4. ( ). . . 5. . . a bzxzx1 234PM =11243342 : - 126 - 126 6. ; 7. ( 1P ) / ( 2P ) . P1 P1P2P2P2P2P1 P1 8. 1P 2P ; 9. : P1P2 : - 127 - 127 10.:, 1000EF 000 . 10EI ,, 12q , 10o45: ),xuzu ), Q M Z X .

/2/2BZXaEFEFEI 11. : . ( \ ) 12. Gauss: + 1 1002 122 1x xx x +01 102 12 12x xx x 2 ; ( : 101 1002 1x x ) : - 128 - 128 13.: ( ) ( ) ( ) ( )b b a aw w w 2 3 3 2 2 3 3 22 3 2 2 3 1 + + + + + ) ) :, T k T kLTGL LTGLP T P 14.: 510 8 RI ,4cm 1800 RA ,2cm710 3E2m kN410 24 REI2m kN410 6 SEI2m kN [ ]5 5 5 3 3 3 2 2 2 w u w u w u2102100042002105 . 3,81 . 367 . 8 . 1849 . 0 0 3 . 1533 . 1 67 . 0 5 . 667 . 0 22 . 0 0 0 02 . 190 0 15 49 . 0 0 3 . 300 0 0 33 . 1 67 . 0 0 8 . 30 0 0 67 . 0 22 . 0 0 67 . 0 8 . 180 0 0 0 0 15 49 . 0 0311PP symkEI kS : )?,11k ?3P( + ) ) ( ): , 492u, 3 . 92w, 1 . 582, 1 . 435u, 7 . 95w3 . 535, 7 . 453u, 2 . 263w, 5 . 23,i Siu EI u i Siw EI w p=x=waawbbm kN q 20 m kN q 70 4 510 2 cm Is 21300 cm As R RA I , R RA I ,s sA I ,s sA I ,q3.5 m6.0 m 6.0 muw : - 129 - 129 3-5 ) k( ) n m ?,m ?,n?, mnA?,21A?13A ) k " " SEA " " REA_________________________________________________________ 15. 1GLk 2GLk . ; 16. : , T k T kLTGL ;oLTGLp T P 17. : [ ]Z Y X Z Y X Z Y XTGLU U U U U U V 1 2 3 [ ] 3 , 10 , 0 5 , 0 , 0 5 , 0 , 0 + + : 18. ). 1 , 2; ; 1a21 2 3ZYX1 240o : - 130 - 130 ) . ; 19. : : k( ) ,33k ,35k13k; ; 20. ( , Q , M N ) : ; ____________________________________________________________ 21. :P u u K uT T [ ]6 4 4 1 1 1 w u w uT u[ ]6 4 4 1 1 1 w u w uT u[ ]6 5 4 3 2 1P P P P P PT P ]]]]]]]]]],,,,,,,,,

6656 5546 45 4436 35 34 3326 25 24 23 2216 15 14 13 12 11kk kk k k symk k k kk k k k kk k k k k kK10010020k=k33PPMq : - 131 - 131 : ), 01w ?1w ), 56 ?6 ! 22. 23. ? cabK 24. ,sxu ,syu ( ) ? ,m mzu fs T=?T=?30oa byxyxsm : - 132 - 132 25. ?K 26. ____________________________________________________________ 27. .. ; 28. ; 29. ; 30. ; ; 31. ; ; 32. , , ; 33. ; ; 34. ; K=?iiK =?abab