.       -                                   (Fiber-reinforced polymer – FRP)      , 2016. UNIVERSITY OF NIŠ FACULTY OF CIVIL ENGINEERING AND ARCHITECTURE M.Sc. Žarko I. Petrovi Experimental - theoretical analysis of limit states of continuous beams made of self- compacting concrete strengthened with fiber reinforced polymer (FRP) DOCTORAL DISSERTATION Niš, 2016.          :    !"#$, # %&', #( ) ), *#'"-+"'" &")! '!#: "'%,!- '" !( -.+ '/ ,0'"+ ")!+ -  ',)-*) )$- 0  .+ #!", ,, %!,, (Fiber-reinforced polymer – FRP) (,:  '1  ') %"( ()! "'%,!-  ),."- '%#/ ,0'"+ ( 2) ")!+ -+ '. (*+  ',)-*) )$- 0  .+ ,),  #!", ,, %!,, (Fiber Reinforced Polymer - FRP).  .#/  (# )-/, 3 %"  '"!+  "0'"+ #!" ) (, '! ) 0 (  ,), "  !%4/, 3 "  )-4.+ #!"  (-) %# 0 (2 ,). '%  ' ")!+ '. (!5+ )1 ) "" - '."- %$/  !,, % .,) ') , #' )-0  !1  ) 0), .!.  3 ,).  .#/, -+ '. , '"!, (Ø10 mm)  "0'", (Ø8 mm) 3 %", %'-)  %#$/ '#' ) ')  "!) ( .)) -)  22%  82% ) (#''  #'  %!5  3  ./ "   .#/, -- '. 3 ", %'-) %#$/ '#'  50%. 3 *#/ -.- '/ '#', (#   %# -.- '/ )%04#', %$ ') %'" &,1 '" '/ '.  &,/ %!'.+ (-!0#. 3,,  (#  ,!/ '.  '%#  ),." ! !( "$/, %-, ANSYS. 0  ()! ),." !( ') %"(! 0 '!-/ ' ()!, "'%,!- '%#/.  '#) '%#- '5#/ ("4).   '  .#/, ")!+ -+ '. 3 ,), ,5 '# (.  %#$/ '#' 0( 0(  #') 3 ,)  ,)  ./, % .,)   ,  ./ , ( %' ) ')  2 ,)  ./. ). 0!': *#'# ). '1%!: +." ,+"    "')"1  4). .: ',)-*) )$ 0, #!", , %!,, ,0'" ")! '., "'%,! '%#/, ),." ! !(, , ".+ !, : 624.072.2(043.3) CERIF "!'&"1 :  002 *#'" +!-  % !11 # ( 1: CC BY-NC-ND Data on Doctoral Dissertation Doctoral Supervisor: D.Sc. Marina Mijalkovi6, full professor,University of Nis, Faculty of Civil Engineering and Architecture Title: Experimental - theoretical analysis of limit states of continuous beams made of self-compacting concrete strengthened with fiber reinforced polymer (FRP) Abstract: The paper presents the results of experimental and numerical investigations of the reinforced (RC) continuous beams made of self-compacting concrete strengthened with fiber reinforced polymer (FRP). Strengthening was performed by mounting glass and carbon FRP bars under the concrete surface (NSM method) as well as by glueing the FRP strips on the tensioned concrete surface (EB method). Six continuous beams were tested during which the deformations of beams and the strains in concrete, steel and FRP reinforcement were recorded until failure under monotonically incresed loading. By strengthening beams with additional glass (Ø10 mm) and carbon (Ø8 mm) FRP bars increasing in bearing capacity was achieved compared to control (unstrengthened) beam of 22% to 82% depending on the type and the position of FRP reinforcement while by strengthening beam with FRP strips increasing in bearing capacity was achieved of 50%. In addition to observed the ultimate strength state, the ultimate serviceability state was verified, while the stress-strain states of the beams and formation of plastic joints were monitored. By using FEM, continuous beams were modelled, and numerical non-linear analysis was conducted using the program ANSYS. The obtained results of numerical analysis correlated very well with the experimental results. Based on the carried out investigation it is concluded that a significant increase in capacity can be achieved by strengthening of continuous beams using reinforcement made of FRP materials, regardless of the type of FRP reinforcement and strengthening method, whereby the NSM method has many advantages compared to the EB method. Scientific Field: Civil Engineering Scientific Discipline: Technical mechanics and theory of structures Key Words: self-compacting concrete, fiber reinforced polymer, reinforced-concrete continuous beams, experimental research, numerical non-linear analysis, finite element method. UDC: 624.072.2(043.3) CERIF Classification:  002 Building technology Creative Commons License Type: CC BY-NC-ND iii                       ,              . ,                !           " ,               #         " . $      "      „%  &  "“ '               . #"       (%)*     +!%          &. %      ,   -  ,   .            "   ' ,         "      . /     "   "          "      .       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&   ....................................................48 4.1 3     ............................................................................48 4.2 %          ................................................................48 4.3 '     +!%       .............................49 4.3.1 %  (#         .................50 4.3.2 %  (#        .................50 4.3.3 %        (#   .................51 4.4 %  (# "        .............................53 4.5 2    +!%    – )#  (Externally Bonded - EB) ...........................................................................................................................56 4.5.1 2 ...............................................................................................................56 4.5.2 2   )# +!%  ............................................................................56 4.5.3 )# +!%    ............................................................................57 vi 4.5.4     )# +!%  ....................................................57 4.5.5 2    )# +!%    ........................................60 4.6    "  +!%         (     ) – '   (Near Surface Mounted - NSM) .................64 4.6.1 2 ...............................................................................................................64 4.6.2 2   '   ............................................................................65 4.6.3 %  "  +!%    ................................................................66 4.6.4 %   +!%    ................................................................71 4.6.5. 2    '  +!%    ........................................76 4.6.6 %     '        )#  ...........................................................................................................................80 4.7 2       &    +!%           ........................................................................................81 5 ' *'" * ) # 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.............................................................................................................202 7.2.2 1         ..................................................207 7.2.3 +!%    ......................................................................................208 7.3            ......................................210 7.3.1 (     ......................................................................................210 7.3.2 +!%    ......................................................................................211 7.3.3 1   ......................................................................................211 7.4 3          "      &      .............................................................................................................212 7.5 !      ..........................................................................214 8 + * .................................................................................................223 8.1 /      & ..............................................................224 8.2 %       & ..............................................................228 , ........................................................................................................................229 " ........................................................................................................................241 )#- ........................................................................................................................247 ix .  ./) c      "     "  cc      "   "   ct    " "   "   f      +!%    frp    +!%    (+!%   ) Afrp,b    +!%        "  m      +!%    As    "       As2            Cc         "   Ce          Cs2            0c       0f       +!%    0frp     +!%    (+!%   ) 0m       +!%    0s          & ()  0sp         & ()  11                      12                      M     Mcr        Mext      Mn    "        Mo           /u "        (    ) /y    "       Tc    "    "   Tfrp    +!%    Tg     "   TM            Ts1    "       Vm       +!%    x Vf       +!%    c         "  '   ag        '   b    "    " "   "   bg       '   d      db        " +!%  dfrp   +!%           d2                  fc5         fct        ff     +!%       ffrp   +!%    (+!%   )    fm     +!%       ft           fy(2v)        h   "    " "   "   hf    +!%             "  +!%  hg       '   k             "     " +!%  n    +!%    r             +!%    tfrp    +!%   ,             "  +!%  tf      +!%    x               xb                         " +!%    xo                   y         "      yCc          Cc yCs2          Cs2 yTc          Tc yTfrp          Tfrp yTs1          Ts1 31           4 "               xi 4t          41         "            5   5c    5cc          5cc,o         ,     5ct    "     5ct,o    "    ,     5cu "            5c1      "          fc' 5f,u "        +!%       5frp   +!%    5frp,ef   "      +!%       5frp,u "      +!%       5m,u "        +!%       5s    5su "          5s1   "       5s2           5y      "     (fy) θ "            6      6m       "      +!%       7         &    8s       "       8s2               8frp,b        +!%    8frp,b        +!%            ν %     2  2c     "      (6c) 2cc         2ct   "     2cu     "  "            (6cu) 2f9    +!%          2frp  +!%    2s   xii 2s1  "       2s2          2m9    +!%          :frp        "      +!%   .  1 ./ )      &             ;&            0      0)      +!%    /10       /    "  +!%         <<   "    &          <&             .  .1  1-1      "              "  "   (ISIS Educational module 2, 2006) ..................................2  1-2: # 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'      (De Lorenzis and Teng, 2007) ...................69  4-19 !  '     (Parretti and Nanni, 2004) ............................................70  4-20 %    '  +!%   : ()     &   ; ( )             &  ; ()              "   (De Lorenzis and Teng, 2007) ..........................................................................................................................73  4-21 2          '       (De Lorenzis and Teng, 2007) ......................................................................75  5-1 !        (# "    "  +!%     .............................................................................................................85  5-2       )#    (Bank, 2006) ...................86  5-3 0 "                   .............................................................................................................87  5-4 !     (# "     +!%    ...................88  5-5 0 "               .....89  5-6 0 "           +!%   ...................90 xv  5-7 0 "       ()     (8)   (# "     +!%    ...................................................................................91  5-8 %     ,         (# "     +!%    (       ) .....91  5-9 !  ,              : ()    "  , ( )   "  ......................................................................93  5-10 !  ,             : ()    "  , ( )   "  .........................................................94  5-11 !  ,            : ()    "  , ( )   "  .........................................................95  5-12 0 "                 .....98  5-13 0 "                -+!%   , Afrp=10 mm2 ...................................................................................98  5-14 0 "                -+!%   , Afrp=20 mm2 ...................................................................................98  5-15 0 "                -+!%   , Afrp=30 mm2 ...................................................................................99  5-16 0 "                -+!%   , Afrp=40 mm2 ...................................................................................99  5-17 0 "                -+!%   , Afrp=50 mm2 ...................................................................................99  5-18 0 "                -+!%   , Afrp=60 mm2 .................................................................................100  5-19 0 "                -+!%   , Afrp=70 mm2 .................................................................................100  5-20 0 "                -+!%   , Afrp=80 mm2 .................................................................................100  5-21 0 "                -+!%   , Afrp=90 mm2 .................................................................................101  5-22 0 "                -+!%   , Afrp=100 mm2 .................................................................................101  5-23 0 "                4+!%   , Afrp=10 mm2 .................................................................................101  5-24 0 "                4+!%   , Afrp=20 mm2 .................................................................................102  5-25 0 "                4+!%   , Afrp=30 mm2 .................................................................................102 xvi  5-26 0 "                4+!%   , Afrp=40 mm2 .................................................................................102  5-27 0 "                4+!%   , Afrp=50 mm2 .................................................................................103  5-28 0 "                4+!%   , Afrp=60 mm2 .................................................................................103  5-29 0 "                4+!%   , Afrp=70 mm2 .................................................................................103  5-30 0 "                4+!%   , Afrp=80 mm2 .................................................................................104  5-31 0 "                4+!%   , Afrp=90 mm2 .................................................................................104  5-32 0 "                4+!%   , Afrp=100 mm2 .................................................................................104  5-33 !  ,         (# "     +!%    ..............................................................................................108  5-34 (#     +!%   , fc5 = 20 MPa, 9s = 0,2 %: a)  "   "    , )   +!%    .................115  5-35 (#     +!%   , fc5 = 25 MPa, 9s = 0,2 %: a)  "   "    , )   +!%    .................116  5-36 (#     +!%   , fc5 = 30 MPa, 9s = 0,2 %: a)  "   "    , )   +!%    .................116  5-37 (#     +!%   , fc5 = 35 MPa, 9s = 0,2 %: a)  "   "    , )   +!%    .................117  5-38 (#     +!%   , fc5 = 40 MPa, 9s = 0,2 %: a)  "   "    , )   +!%    .................117  5-39 (#     +!%   , fc5 = 45 MPa, 9s = 0,2 %: a)  "   "    , )   +!%    .................118  5-40 (#     +!%   , fc5 = 50 MPa, 9s = 0,2 %: a)  "   "    , )   +!%    .................118  5-41 (#     +!%   , fc5 = 20 MPa, 9s = 0,5 %: a)  "   "    , )   +!%    .................119  5-42 (#     +!%   , fc5 = 25 MPa, 9s = 0,5 %: a)  "   "    , )   +!%    .................119 xvii  5-43 (#     +!%   , fc5 = 30 MPa, 9s = 0,5 %: a)  "   "    , )   +!%    .................120  5-44 (#     +!%   , fc5 = 35 MPa, 9s = 0,5 %: a)  "   "    , )   +!%    .................120  5-45 (#     +!%   , fc5 = 40 MPa, 9s = 0,5 %: a)  "   "    , )   +!%    .................121  5-46 (#     +!%   , fc5 = 45 MPa, 9s = 0,5 %: a)  "   "    , )   +!%    .................121  5-47 (#     +!%   , fc5 = 50 MPa, 9s = 0,5 %: a)  "   "    , )   +!%    .................122  5-48 (#     +!%   , fc5 = 20 MPa, 9s = 0,8 %: a)  "   "    , )   +!%    .................122  5-49 (#     +!%   , fc5 = 25 MPa, 9s = 0,8 %: a)  "   "    , )   +!%    .................123  5-50 (#     +!%   , fc5 = 30 MPa, 9s = 0,8 %: a)  "   "    , )   +!%    .................123  5-51 (#     +!%   , fc5 = 35 MPa, 9s = 0,8 %: a)  "   "    , )   +!%    .................124  5-52 (#     +!%   , fc5 = 40 MPa, 9s = 0,8 %: a)  "   "    , )   +!%    .................124  5-53 (#     +!%   , fc5 = 45 MPa, 9s = 0,8 %: a)  "   "    , )   +!%    .................125  5-54 (#     +!%   , fc5 = 50 MPa, 9s = 0,8 %: a)  "   "    , )   +!%    .................125  5-55 (#     +!%   , fc5 = 20 MPa, 9s = 1,1 %: a)  "   "    , )   +!%    .................126  5-56 (#     +!%   , fc5 = 25 MPa, 9s = 1,1 %: a)  "   "    , )   +!%    .................126  5-57 (#     +!%   , fc5 = 30 MPa, 9s = 1,1 %: a)  "   "    , )   +!%    .................127  5-58 (#     +!%   , fc5 = 35 MPa, 9s = 1,1 %: a)  "   "    , )   +!%    .................127 xviii  5-59 (#     +!%   , fc5 = 40 MPa, 9s = 1,1 %: a)  "   "    , )   +!%    .................128  5-60 (#     +!%   , fc5 = 45 MPa, 9s = 1,1 %: a)  "   "    , )   +!%    .................128  5-61 (#     +!%   , fc5 = 50 MPa, 9s = 1,1 %: a)  "   "    , )   +!%    .................129  5-62 (#     +!%   , fc5 = 20 MPa, 9s = 1,4 %: a)  "   "    , )   +!%    .................129  5-63 (#     +!%   , fc5 = 25 MPa, 9s = 1,4 %: a)  "   "    , )   +!%    .................130  5-64 (#     +!%   , fc5 = 30 MPa, 9s = 1,4 %: a)  "   "    , )   +!%    .................130  5-65 (#     +!%   , fc5 = 35 MPa, 9s = 1,4 %: a)  "   "    , )   +!%    .................131  5-66 (#     +!%   , fc5 = 40 MPa, 9s = 1,4 %: a)  "   "    , )   +!%    .................131  5-67 (#     +!%   , fc5 = 45 MPa, 9s = 1,4 %: a)  "   "    , )   +!%    .................132  5-68 (#     +!%   , fc5 = 50 MPa, 9s = 1,4 %: a)  "   "    , )   +!%    .................132  5-69 (#     -+!%   : () 9s = 0,2 %, ( ) 9s = 0,5 %, () 9s = 0,8 %, (") 9s = 1,1 %, () 9s = 1,4 % .................................................................................133  5-70 (#     4+!%   : () 9s = 0,2 %, ( ) 9s = 0,5 %, () 9s = 0,8 %, (") 9s = 1,1 %, () 9s = 1,4 % .................................................................................134  5-71 (#     -+!%   : () fc5=20 MPa, ( ) fc5=25 MPa, () fc5=30 MPa, (") fc5=35 MPa ..............................................................................................135  5-72 (#     -+!%   : () fc5=40 MPa, ( ) fc5=45 MPa, () fc5=50 MPa ........................................................................................................................136  5-73 (#     4+!%   : () fc5=20 MPa, ( ) fc5=25 MPa, () fc5=30 MPa, (") fc5=35 MPa ..............................................................................................137  5-74 (#     4+!%   : () fc5=40 MPa, ( ) fc5=45 MPa, () fc5=50 MPa ,,,,,...................................................................................................................138 xix  5-75 % "   "     (u)         -+!%   : ) 9frp = 0,22 %, ) 9frp = 0,44 % .......................................................139  5-76              "   "  (#     " -+!%    ....................................................................142  5-77 %    "   "     (u)         4+!%   : ) 9frp = 0,22 %, ) 9frp = 0,44 % ..............................143  5-78              "   "  (#     " 4+!%    ....................................................................145  6-1 0      "    ..........................................147  6-2 %    –   .................................................................................148  6-3 %      ..............................................................................................148  6-4               "     " "     "    ....................................................................149  6-5 %               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........................................................................................................................159  6-18 0       "             "     ..............................160  6-19 0 "              "              ..............................160  6-20 0            (     ) ..............................................................................................161  6-21 $        "    ..........................................164 xx  6-22 0     " "  "         .165  6-23 !           "  .......................................................165  6-24 0 "        "    I (U1)    II (U2)     "  ..............................................................................................167  6-25 4    "      "      "   ........................................................................................................................167  6-26 0 "         e  (4)       (1)   I     "  .......................................................168  6-27 0 "         e  (D1)       (2)   II     "  ..........................................168  6-28 0 "         e  (5)       (3)   III     "  ..........................................169  6-29 !       "    #-41 ..........................................169  6-30 0 "        "    I (U1)    II (U2) "  #-41 ..............................................................................................170  6-31 4    "      "   "  #-41 ...170  6-32 0 "           (4)       (1)   I "  #-41 .......................................................171  6-33 0 "           (D1),      (2)  +!%    (6)   II "  #-41 .................171  6-34 0 "           (5)       (3)   III "  #-41 .......................................................172  6-35 !       "    #-42 ..........................................172  6-36 0 "        "    I (U1)    II (U2) "  #-42 ..............................................................................................173  6-37 4    "      "   "  #-42 ...173  6-38 0 "           (4),      (1)  +!%    (6)   I "  #-42 .................174  6-39 0 "           (D1)       (2)   II "  #-42 .......................................................174  6-40 0 "           (5),      (3)  +!%    (7)   III "  #-42 ................175  6-41 !       "    #-43 ..........................................175  6-42 0 "        "    I (U1)    II (U2) " e #-43...........................................................................................................176  6-43 4    "      "   " e #-43.......176 xxi  6-44 0 "           (4),      (1)  +!%    (6)   I "  #-43.........................177  6-45 0 "           (D1),      (2)  +!%    (7)   II "  #-43.......................177  6-46 0 "           (5),      (3)  +!%    (8)   III "  #-43....................178  6-47 !       "    #--....................................................178  6-48 0 "        "    I (U1)    II (U2) " e #--............................................................................................................179  6-49 4    "      "   " e #--.........179  6-50 0 "           (4),      (1)  +!%    (6)   I "  #--...........................180  6-51 0 "           (D1),      (2)  +!%    (7)   II "  #--.........................180  6-52 0 "           (5),      (3)  +!%    (8)   III "  #--.......................181  6-53 !       "    #-)-..................................................181  6-54 0 "        "    I (U1)    II (U2) "  #-)-..........................................................................................................182  6-55 4    "      "   "  #-)-......182  6-56 0 "           (4),      (1)  +!%    (6)   I "  #-)-.......................183  6-57 0 "           (D1),      (2)  +!%    (7)   II "  #-)-......................183  6-58 0 "           (5),      (3)  +!%    (8)   III "  #-)-.....................184  6-59 0 "  "             .............185  6-60 3    "         "     "     "  ..............................................................................................186  6-61 3        "          " .........................................................................................................186  6-62 0 "             "                "   .....188  6-63 0 "          "               "   .........................188  6-64 0 "             +!%             "   .......................................189 xxii  6-65 0 "          +!%            "   ...........................................................189  6-66 /                     "   ...........................................................190  6-67 /                 "   ........................................................................................190  6-68 0       "    ..................................................191  6-69 .           " ......................................................191  6-70 .          " ..........................................................191  6-71 0  "  #-41............................................................................................192  6-72 !          ................................................................192  6-73 !           .....................................................192  6-74           (" ").........................192  6-75 !        (    )......................................192  6-76 0   "  #-42   ............................................................193  6-77 2   4+!%     ..............................................................193  6-78 .     .......................................................................................193  6-79         .............................................................194  6-80 !              ("     )........................................................................................................................194  6-81 .        .......................................................194  6-82                        (    " )..............................................................194  6-83 2       "     (     ).195  6-84 2       "     (    )....195  6-85             ..............................195  6-86 !              ...........................195  6-87         ("     )...............................195  6-88 %                    "      ..............................................................................................195  6-89 . "  "  #--1  "    -+!%   ...........196  6-90             ..............................197  6-91              ......................... 197  6-92 2       "          ......... 197  6-93 %                        ...................................................................................................197 xxiii  6-94 -+!%     "     .............................................. 197  6-95 4         "       .. 197  6-96 2       "    ...............................................198  6-97 4         "   "     .198  7-1 %   &                       (Barrett, 2013) .......................................................200  7-2 2 "    "            - "  "    (! , 2010) ....................................................................202  7-3 0 "                     (Bangash, 1989) ....................................................................203  7-4 %     "                   .................................................................................205  7-5 %      (ANSYS, 2014) .......................................................206  7-6 0 "               ...207  7-7 0 "           +!%   .................208  7-8 4    &     "    65 (ANSYS, 2014)..210  7-9 4    &     "   .  180 (ANSYS, 2014)..211  7-10 4    &     "    46 (ANSYS, 2014)..211  7-11 4    &     "   45 (ANSYS, 2014)..212  7-12 %        (# "         ..212  7-13 %            "   2587, 19736  155968   ...........................................................................................................213  7-14 %        " "  "  ..........................................214  7-15 %    "      "         : ) P=50 kN; ) P=100 kN .................................................................................215  7-16 3    "        "    I (U1)    III (U2 )     "              MKE (Ansys) ........................................................................................................................216  7-17 %     "  "  #-41 .......................................................216  7-18 %    "      "         : ) P=40 kN; ) P=80 kN; ) P=120 kN ....................................................................217  7-19 3    "        "    I (U1)    II (U2 ) "  #-41             MKE (Ansys) ........................................................................................................................218  7-20 3    "    +!%      I "  #-41         (MT6)         ) (Ansys).....218 xxiv  7-21 %    "      "   e           : ) P=50 kN; ) P=100 kN; ) P=145 kN ..........................................219  7-22 3    "        "    I (U1)    II (U2 ) "  #-42             MKE (Ansys) ........................................................................................................................220  7-23 3    "    +!%      I "  #-42         (MT6)         ) (Ansys).....220  7-24 %    "      "   e           : ) P=50 kN; ) P=100 kN; ) P=165 kN ..........................................221  7-25 3    "        "    I (U1)    III (U2) "  #-43             MKE (Ansys) .......................................................................................................................222  7-26 3    "    +!%      I "  #-43         (MT6)         ) (Ansys)....222 .  )0   2-1 3           )     "    (EFNARC, 2006) ...................................................................................12   2-2 '            &     "  "   ...................................................................................13   2-3                          (Aslani and Nejadi, 2012) ...................17   3-1   "            +!%        ................................................................................................23   3-2 +!%     "  .........................................................24   3-3 %  &                ..........................................................................................................................28   3-4 %  &                 .............................................................................................................29   3-5 %  &                  ................................................................................................34   3-6             4+!%, -+!%, (+!%      ................................................................................................38   3-7 %         "        +!%    (fib bulletin 14, 2001) ......................................................................40 xxv   3-8 +           +!%      &    ACI 440.2R-08 ......................................................................45   6-1    +!%            ..150   6-2    ...........................................................................................................157   6-3 1        ....................................................................158   6-4 $              +!%   162   6-5 %               ..............................166   7-1    +!%    (Kachlakev and McCurry, 2000) .................209   7-2      "       "    &   .................213 1  1 1  1.1                                            ()           .      (Self-consolidating concrete - SCC)                    !    "   .                   ,       ,             ,           !   ,             .   ,   "        "                                              "          . #                   "       :  , ,    . $        ,                      "  .        ,  "               "       ,         "  1  2          .                                            . % ,  "          "            "              .         & ,       $   , '          !     !                       "       (ISIS, 2006).      "    ,   ,        "           ,        ( 1500    !                 " ) ,   ,     "                  . (                                 ,              ()  , 2010). *              !                   ( 1-1),         ,               "  (ISIS, 2006).  1-1:                            (ISIS Educational module 2,2006)   ,            !      "      "    !  ,     "   "       ,    !     1  3    ,     !     !    "       "   "  .             :     ! .      "      "                 "        ,     "   " , .     ,   ,     , !      " . '       /            ,                             "  ,                "  . (         "            :      "  ,       ,      .                      "                  ,                      . +        – ,) (Fiber Reinforced Polymer – FRP),                   ,                                    . '       ,       !          !       ". +       ,     "                  .                       ,          ,) (Aramid Fiber Reinforced Polymer), -,) (Carbon Fiber Reinforced Polymer) #,) (Glass Fiber Reinforced Polymer)     . .         ,)         50-70 %     25-35 %    (fib bulletin 14, 2001). /      ,)       "            "              "       ,                "             ,     (ISIS, 2006):  +        ;  /            ; 1  4  0     .   !     ;  &       ,          "     "   ;  %                           "     ;  /          ,       !  . ,)          "     (fib bulletin 14, 2001):  1       "     ,       "   . % ,    "  "      "   , !      ,)                            ;  1          - , ,)          -    (           "   ),          " ,         ;  1 ,)     ,          ,        "      "   ;  2         (     )                (           45-70°C). .   ,)                           "     "   ,           "         .                 !   !    – &   (EB - externally bonded)                       – 1%   (NSM - near surface mounting),    ,          "      . 1  5 1.2            /      ! " !        1%                      ,            (-,), #,)). *   " !          !  !  (&   )      !  (1%   )     .                 (&),          !  . 3-            (!  )   (-,))     (#,))         . (         ,      ,                    . )        (" ! )              !     ,)                     ,    !         . 1.2.1      - !                        ,)                  :        ,     "      (  )   ,        ,   . 1.2.2        - !           :  /       1%             ;  /     "       (1% &)               ;  /     "                                 ; 1  6  /     "       (-,) #,))             ;  +   "                                  (%'&). 1.2.3       1         " !    "                   (     " ,   ,   )           . '               ,    " !           "      ,)           . '  ,        !      (ANSYS),          :   ,   ,)  .                                                   . 1.3        3         !                 120/200 mm,    3200 mm,          ! ,           "  1500 mm. 1          "        ! ,              ,)  . %   "   "                 (   ,     , )            ,       ( )  . %    "    ,     ,)    "       .                    5 kN. 1                    65 (Solid 65), 0  180 (Link 180)   45 (Solid 45). /              . 1  7 $     "     8  !       "          1-2.            ,   " !    ,      .    !                  .    !               ,)      ,           ,)     .      !                        "  ,)  .     !                     & 1%  ,       "         :        ,               ,   .     !                  (     ),                     .    !       %'&                    .                    "             .     !         ,    !"      ,    "      . 1  8  1-2:          2.  !"#$%&! '( 3.  )# !(#*%+*! 4. %,- ' "# )# !(#*%+*! 6. . #*!(+O * *(*- ' .(*+*/  , %,*/ )# #!(#! 1.  7. !#*,. !+*#- #*!! !. 8. 0#1 ! 5. +*(*,.* ##, # . ' "# %, )# #!(#! 2       9 2      2.1                       ,              ,  , ,    ,             ,                   . !  ,    ,   ,              . "    ,       ,   ,     . #                 ,          – $$  (Self-Compacting Concrete – SCC)    (Self-Placing Concrete – SPC). !  ,                            %   .                               . &       ,         ,            (    2       10     ,          ,         ),                (' , 2007). (        ),     *   (Hajime Okamure)  ( (Kochi) +                  . ,        ,            ,    ,   -  (Ozawa, 1989; Okamura, 1993; Maekawa, 1999)  +    " . . 1988.              .          (High Performance Concrete-HPC),                   (Self-Compacting High Performance Concrete).      1980-,   ,               ),        , /     %  &. (           ,     ,          .                                    . !                   ,         ,        ,      . !                        ( ,   ,  ,     ),       .                              ,     ,      ,              . +                                           . ,            ,          ,         ,           . 2       11                ,              . +                        ,     ,    . !              (-  , 2016):  /                     .           ;  0              ,           ;  !            ,                      ;                          ;     ,       ,               %   . #                             %   . 2.2 !" #   " $               e      . ,                                      . (             ,    ,     ,        (-    ,, 2008; 1  , 2008; Uysal, 2012; Mnahoncakova et al., 2008). 2  2-1            . 2       12  2-1:               (Holschemacher and Yvette, 2002)                  ,                          . !           ,    :    (Okamura and Ozawa, 1995),    (Su et al., 2001),  (Bosiljkov, 2003)    (Sonebi, 2004). !             :      31,2 %   ,    34,8 %   ,    500 kg/m3,        0,34  ,         47,5 %   .   2-1:                  (EFNARC, 2006)   +       kg/m3 +        l/m3 !   380 - 600 ! 300 - 380 . 150 - 210 (   270 - 360    ( ) 48 - 55%       .  0,85 - 1,10         !       [ % ]     0/2   2/16   2       13 /        (EFNARC, 2002; EFNARC, 2006)        $$ ,     2-1,                 . 2.3 %"  " &   " $                      :     , ,           . &                          ,                   . &                (Luis, 2004). &                   ,         (High Range Water Reducing Admixture – HRWR),   ,         ,          ,      (' , 2007). &               ,      (Viscocity Modifying Agent – VMA),             ,                 . 2                                .   2-2:                    (   (         Slump–flow test . T500 Slump-flow ili V–funnel test    L – box test        "     2       14 2                       /        (EFNARC, 2002; EFNARC, 2006),      2-2. 2.4 %"  " '(    #           ,                 (0  3  , 2010). +               (Domone, 2007). +                         ,                    . 0,                              . 2.4.1 )    " &                         . (                                 ,                  (HU et al., 2008). (                        ,                    . (                 0,76,              0,80  1,0 (Domone, 2007). 2       "  0 *   (,                  0,84       (HU et al., 2008). 2       15 2.4.2 )    # (                        ,       ,        (Castel et al., 2010). (                 ,               . #                                  .                     ,                          / 2 (Domone, 2007). &        0     (Itterbeack et al., 2011). 2.4.3 * –+( , .                                 . %                          (HU et al., 2008; Suresh Babu , et al., 2008; Kumar et al., 2011; Prasad et al., 2009). 2 " 0 *   ( (HU et al., 2008)                     . 2       ( 2-2)                     .                  ,      %                  –. 2       16  2-2:                  (HU et al., 2008) 2.4.4 +( ( '  %                              . !   ,            ,         ,    ,         (1 #., 2011). (          ,     ,            . (                  ,       . #                       20 %          ,      . %  2  (Aslani and Nejadi, 2012)                (Ec)       (fc4),    ,              : 2Kc1c )f(KE ′= (2-1) %  (2-1),                    ,           ,                      .      0,000 0,001 0,002 0,003 0,004 0 10 20 30 40 50 60 2       17   2-3:  !                      (Aslani and Nejadi, 2012) (    (1 (2 .   4835 0,490      4150 0,525                  3995 0,533           6847 0,410                3655 0,548           9455 0,345        3202 0,587 2.4.5 !##    ( %                      . %                   %    (Karatas et al., 2010). !                       ,                     . .                ,      . %                         . #               %   . 2                          . (               ,                 . 2              , & (Domone, 2007).             ,       , 2       18        .                   ,          . 0                        (   (Karatas et al., 2010).                         . - ,           15 %,       . 3 O    a 19 3 O    MA 3.1 O           –  (Fiber Reinforced Polymer – FRP)                  .                                              .                            ,    ,      ,    ,    ,     !         . "          ,                 .  ,             ,                (ISIS, 2006). # $                           $   $. "       . %  ,                #               . "                        $    . 3 O    a 20 $   $      !        ,                    . %         !   #$   :   $           ,  ,      ( 3-1   3-2),   $             ( 3-3  3-4),          ( 3-5)         ( 3-6).  3-1:                     (ISIS Educational module 2, 2006)  3-2:                 (Bank, 2006)  3-3:              (ISIS Educational module 2, 2006) 3 O    a 21  3-4:                 (Bank, 2006)  3-5:     56          (Nijmegen)         !            3-6:              "  #     "     (Laroin Foot Bridge, 2002) 3 O    a 22 "            $       !  &   (Sika),   (Mapei, Sinit, Sireg), '()- (Hughes Brothers),  (Pultral), * ,                .              ,      $,            ,       ,             $ #               . +  $$     ,         ,      $     . (                   ,                           (  )      ,   !     (  , 2010). 3 O    a 23 3.2          ,            #$    !             ,     $               $      . +     #    $               . $  3-1:        %                  American Concrete Institute (ACI) ((     ) 440 – Composites for Concrete (440 –    ) American Society of Civil Engineers (ASCE) ((   #$ !   #$) Structural Composites and Plastics (      ) American Society of Testing and Materials (ASTM) ((   #$    $   ) ASTM D20.18.01 – FRP Materials for Concrete (ASTM D20.18.01 –     ) AASHTO Bridge Subcommittee (AASHTO      ) T-21 – FRP Composites (+-21 –    ) International Federation for Structural Concrete (fib) (-! #$  ) Task Group 9.3 FRP – Reinforcement for Concrete Structures (. 9.3 –       ) Canadian Society of Civil Engineers (CSCE) (  #$ !   #$) ACMBS – Advanced Composite Materials for Bridges and Structures (ACMBS – %        ) Japan society of Civil Engineers (*  #$ !   #$) Committee on Concrete Structures with Externally Bonded Continuous Fiber Reinforcing materials (                         ) Transportation Research Board ("    # $) A2C07 – FRP Composites (A2C07 –    ) National Research Council of Italy (     #  ) CNR – FRP Systems (CNR –    ) 3 O    a 24 $  3-2:            Code/  Reference/ Canadian Building Code (    ) Design and Construction of Building components with Fiber Reinforced Plastics (  $                 ) Canadian Highway Bidge Design Code (CHBDC) (       ) Fiber Reinforced Structures (section of code) (        –     ) International Conference of Building Officials (ICBO) (-!    # ) AC 125: Acceptance Criteria for Concrete and Unreinforce Masonry Strengthening Using Fiber-Reinforced Composite Systems (AC 125:                $            ) Japan Society of Civil Engineers (JSCE) Standard Specification for Design and Construction of Concrete Structures (*  #$ !   #$) Recommendation for Design and Construction for Reinforced Concrete Structures Using Continuous Fiber Reinforcing Materials (     $       $              ) National Research Council (CNR) – Italy Advisory Committee on technical recommendation for construction (%   #    ) Giudelines for design and construction of Externally Bonded FRP systems for Strengthening existing structures (,    $         $     ) International Federation for Structural Concrete (fib) (-! #$  ) Design and use of externally bonded fibre reinforced polymer reinforcement (FRP EBR) for reinforced concrete structures (   $          ( /0)   $    ) American Concrete Institute (ACI) ((     ) Guide for the Design and Construction of Structural Concrete Reinforced with FRP bars (,             ) 3 O    a 25 3.3     ! 3.3.1 "  ! )               ,       :     (fiber)     (polymer matrix). "       o                      .           ,               . %        ,   !                         ,  ,   ,           $    . ' ,    ,           (base polymer)     (neat resin),               ,              $    .                  ,    !   ,       $              (Sourcebook, 2006). 3.3.2   "!                                             (continuous). 1          , #  10  50 mm,          $        ,         (glass-reinforced cements – GRCs)        (fiber-reinforced cementitous – FRC).      ,     20  60%    ,       ,              (Bank, 2006). -                   # #              $. + !,                        ,          $             ,        . ,                              $          ,    3 O    a 26         . #                      ,           $ (ISIS, 2006). -                              . -! ,   $                     ,            .   #       .      $              $              !  ,              . "        #   $     $      (ISIS, 2006):    ,      $,        !       ,        $      . -                  ,      a  a     !   #$ :   (glass),   (carbon)   (aramid).  3-7: &  (SEM - scanning electron microscope)      #      '    (ISIS Educational module 2, 2006)              ,  ,  ,   ,    . ,                      ,   :  , ,  ,  $        . %  3-8        !    e      3 O    a 27    . "                    .  3-8: %     (                    ! "!               #$,       ,      ,        $  ,      . '      (SiO2)            ,        50  70%.       ,   # $ ,   ,  ,       .               ,            ,              (Bank, 2006). /-  (E-glass – electrical glass)  -   ,                 ,        $                 #$ (  90%).   ,          ,    ,  !       . (-  –     (A-glass – window glass). 2-  (C-glass – corrosion resistant),  !   (-  (alkali- resistant glass),    -            $           #$         #$          . )(MPaσ & –   1000 2000 3000 4000 5000 6000 0 1 2 3 4 5 % 49          %             %               )     *(‰) 3 O    a 28 '-  (S-structural (high-strength) glass)      $                  . "         ,         ,                  . 3       /  - ,   * +- .              3  24 4m.     17 4m              #$. '        .                      $  3-3. $  3-3:   !      +                      .  (g/cm3) -    (GPa) 3  $ (GPa) -    #$ (%) / 2,57 72,5 3400 2,5 ( 2,46 73 2760 2,5 2 2,46 74 2350 2,5 ' 2,47 88 4600 3           #        :    ,       . " $          $          . '            #,                     . '       !    $ $ (   )         (Bank et al., 1995). '                ,                     . '                    . # "!        #$           $,       $.    $       #             #$       $          . 3 O    a 29                    5  10 4m,                    . ,        ,            ,         #    . #                          $ (Bank, 2006).   #                     $  3-4. $  3-4:   !      +                    .  (g/cm3) -    (GPa) 3  $ (GPa) -    #$ (%) ' 1,7 250 3700 1,2    1,8 250 4800 1,4        1,9 500 3000 0,5         2,1 800 2400 0,2 '         ,           #,           . ,  $                         ,   $               .                 (     #      )  $       (           ).                  #         ,   !          # $   .                #  ,              . -! ,                                             $ !             . %  # $      #     3 O    a 30          (      )         (Alias and Brown, 1992; Torres-Acosta, 2002),         ,    .        ,    !   .  "!          .             ) (DuPont)     ,              . )       29,    # ,   49,         . "  !                ,    (  (Akzo)   +,  + #  (Teijin) +. (         $        $,  1980- ,  / *. -! ,      !              $,            $  $. 5       ,     $ ,       ,     $           ,        $       #$. 1          ,                    ,        ,   .      ,                   #     ,                ,       1,4 g/cm3. ,         ,   $           ! 3400 4100 MPa,   $                70  125 GPa. 3.3.3 ! ! +    (polymer)                           ,      !     .               $        ,   #       $     . +      (polymer resin),    ,                   3 O    a 31      !     . "        !     (matrix)   (binder).               ,                  (plastic),          !           (fiber reinforced plastic). (    (reinforced plastic)       ,    $                         (Bank, 2006). -               #        (ISIS, 2006):      ,               ,    !       ,     !       . .                ,   $      ,       #           . )    #       ,           !       .            $     !          . "  ,    !            $           . )      :     (thermosetting)    (thermoplastic)   . "  !        $             . +         ,     $                     #     . 5    $ ,           $         !         (Van der Waals)       (Schwartz, 1997),     $          . ,    ,         ,          ,  #  $          . '  ,              „ “      #        !$. 3 O    a 32 %        :   ,        ,  ,   ,        ,       :   ,   ,    ,     .                            .  ,         #               .                  . "        $              $ .          #      $ (White and Turnbull, 1994). +               180ºC,                         . +            ,   450ºC. -             ,                     :     ,    , $ $     ,          $. !  !         $         !    ,    $     . ,                ,       ,                   #      .               $  ,            $       ,    $   . %                  $               . ,          ,              ,      ,           ! 40 110ºC.   !                     !    . -       3 O    a 33        $           ,                   $      (      )     $  . /            $          ,               $  . /          $     $       ,   $     $      $,    $     ,              $    . /             ,    $  $             $,       $     $     $ . /                 ,     180ºC. -                               40˚  300ºC.     $  20-30  , "!  !                 !      $                (Blankenship et al., 1989.). )            $             ,       ,     $     $,          %'-  . "    #          $             #$ .             ! 40º 120ºC,           ,    . ! !            ,                  #$.               220  250ºC. ,                ,                 $    . 3 O    a 34 + !  !      #       ,    $     $                         . +                         $        (Connolly et al., 2005).                                      ,      . $  3-5:   !      +                           .  (g/cm3) -    (GPa) 3  $ (GPa) -    #$ (%)    1,2 4,0 65 2,5 /   1,2 3,0 90 8,0    1,12 3,5 82 6,0   1,24 2,5 40 1,8      2,9 71 5,9 3.3.4 $            #   .          $          ,     #  ,  ,   ,  ,   $,  ,          . '         ,   $      ,               . ! ( # )       $     :   ,  ,      ,        $$ $   ,       $,  $     .  ,  #      ,         . 3 O    a 35          $ !         . %         $        $$  $,   ,       , # ,    ,     ,        #   . 3.4   "% !     !        $            #$. %   #    $          (  )   ,         , :     (Pultrusion);    # $ (Hand r wet layup);  %$    (Filament winding).    ,          $,          ,   :  Resin Transfer Molding (RTM);  Vacuum Assisted Resin Transfer Molding (VARTM);  Compression Molding;  Injection Molding;  Reinforced Reaction Injection Molding (RRIM);  Centrifugal Casting;  Pull-winding. 3.4.1 !  (Pultrusion)      $       1950- ,                ,       .           $      ,     $                  $        . %  3-9                    #$. 3 O    a 36  3-9:           + (ISIS Educational module 2, 2006)       ,  Glastruder,    0 .  (Brandt Goldswrthy)    1950-  (Goldsworthy, 1954.). &             3-10.  3-10: ,    (Bank, 2006)        #  $                 .          ,              ,        .              #       # . "                #   ,             . 3.4.2 & ! "!'  "(% (Hand r Wet layup) "     ,             $ $.  $         ,                 ,   ,         . ,   ,                     (    '    $ +  $ " $ !     ,                 $ 3 O    a 37  )   . ,                         $    . ,    ,                       #  .    $           3-11.  3-11:         )-     #       " (ISIS Educational module 2, 2006) 3.4.3 ) "% "! (Filament Winding)            ,     3-12,                          . %$           ,                  , #   .  $      ,                          !   .  3-12:                                (ISIS Educational module 2, 2006) 3 O    a 38 3.5    !     ! "                    (ISIS, 2006):            ,          (  ,       ),       ,    $. %  3-13        !              ,     (fib bulletin 14, 2001). %           . (           $      $,   2       #              . + !                $        .  3:13: %     (       ., '  )      (fib bulletin 14, 2001) $  3-6: %          +       ., ', )      3 . 2 ( % $ (MPa) 276-517 - - - 3  $(MPa) 483-690 483-1600 600-3690 1720-2540 -    (MPa) 200 35-51 120-580 41-125 )   $ (‰) 0,14 - - - 2 ( . 3 6 7 (GPa) 3 O    a 39 3.5.1 ! ! &        ,               $      . ,    ,         (Efrp) #    #               ,  .        (Em)         (Ef),            (Vm Vf),          (rule of mixtures): mfmfffmmfrp EV)EE(VEVEE +−=+= , (3-1) 1VV mf =+ . (3-2) *  (3-1)  #                ,                $ .             -   $,    !           $ (fib bulletin 14, 2001). 5              #          ,   -   ,       ,   $   ,      ,           !     . ,                                      !. '  ,      $     ,     ,              #   ,                #   .      !                ,                   .   !           $    (fib bulletin 14, 2001). ,   $        ( )        !$     ,          !               .                      ,        $  !$        .  ,          $     $$   $           3 O    a 40 !$         . %             !                        . "                                     ($  3-7  3-14). $  3-7:       +                (fib bulletin 14, 2001)  : Af –     , Am –    , Afrp –      , ff –   $   , fm –   $  , ffrp –   $    . ,          ((f=70 mm2) $           $   $     (Am). 5    $      , $                    $.            : /f = 220 GPa ff = 4000 MPa Em = 3 GPa fm = 80MPa      "      "$  Af (mm2) Am (mm2) Afrp (mm2) Vf (%) Efrp ( . (3-1)) (MPa) ffrp ( . (3-2)) (MPa) .     (6u) (‰) (kN) (%) 70 0 70 100 220000 4000 1,818 280,0 100,0 70 30 100 70 154900 2824 1,823 282,4 100,9 70 70 140 50 111500 2040 1,830 285,6 102,0 ,           100 mm      100 mm       ( 0,7 mm, 1,0 mm 1,4 mm). 3 O    a 41  3-14: %     (                     Vf       $  3-4 (fib bulletin 14, 2001). )                    ! $ $            . ,                                       . -            $        $     50  80%      $,          . 3.5.2 *" + 3                   $      ,       $           . $      $                  . %  3-15  3-16                ,    #    $       (ISIS, 2006). ,             (6m,u) $         (6f,u)        3-15,           (Vf)  ($  0,10),            . , 7 (MPa) 4000 3000 2000 1000 (    ) 1 2 6 (‰) 100 % 0,7 mm 70 % 1,0 mm 50 % 1,4 mm    = 100 mm fV frpt 3 O    a 42           $ (ffrp)       #   (3-3): )V1(fVf fmfffrp −+σ′= , (3-3)  : 7f8 –            .  3-15: %     (                            -! ,            ,        $             . ,    , $        $      (6f,u). 3      $ (ffrp)       (3-4): fffrp Vff = . (3-4)  3-16: %     (                    #         : 7m8 –          . σ ε /    fσ′ mf u,mε u,fε ff σ ε   -  mσ′ mf u,mεu,fε ff 3 O    a 43 ,    ,          (6m,u)           (6f,u),        3-16,            ,              ,        $ (ffrp)     : )V1(ff fmfrp −= . (3-5) -! ,            ,    $                 ,          . 3      $ (ffrp)  #   : )V1(Vff fmfffrp −σ′+= . (3-6) ,          !   #$       ( fV )    0,10    . 3      $         $             ,         $                   !   #$. 3           $      $        ,        ,    ,     !      , #       -  $   ,   $     $. 3                       # 55%, 20% 78%   $  ,         . (              ,                         (ISIS, 2006). 3.5.3 ,              !   #$     !$        . -  # $ $     , #               . "       $            . +                 $  $,      3 O    a 44   !     ,        .   $    $        -                              . '         $               $  $         . " #                 .   . (           !                   $      .   ,        $             #       . 3.5.4 &% +$                 #$          $        .    ,                $         ,            -          „ “   $. +$ !                  ,            $.  , ,   #,        $    . -! ,               !   #$ $          $                 . 3.5.5 % &% (  ) %      (    )   #        $ $                $       . 5  #           .       ,            $,  $  20  25%       $. 3 O    a 45 3.5.6    !  !" '"   +                   $             ,   :  ,    ,     ,   , $         . -                $  ,     # $     #        .  $        #                       ,  #,  -  $,          $   . ,         (ACI 440.2R-08)       ($  3-8)   $             ,            # . ,                               !    . $  3-8:                   !     ACI 440.2R-08 ,   #         Ce 5   0,95 '  0,75 (  0,85 "  ( ,  ,  #)  0,85 '  0,65 (  0,75 (      (      )  0,85 '  0,50 (  0,70             $  $            .     ,       #,           . %                    ,     3 O    a 46           (  )         . ,               # $      . )$ # $                      $ $   $          (ISIS, 2006):       $    ;                         ;             !      !       (     $   ,   )       $     !               ;  +          ,    $       $      ,  #      /   . -!' : .    ,       #   ,            $.                                 . +    $ (ISIS, 2006)   $  #                          $,                .          $ $            $  #     . '  ,                (         $)              # . (               #               $   #   ,        $    $  . 5          $      # #        . 3 O    a 47 )              #                      $.      $     ,              ,                  # . .! (#&  &% #      . (        #       $,            .  ,                 $. )       $ #           ,                 $          . %  ,         $  $  $,              . !!  :           $              . " #$          (pH      ! 12 13,5)  #               ,     $       #$. 5   .          -       .                      ,                            . - : '         #     ,     #     #            .                         !       , ,      /    ,           #           $           .                             #  ,     #,     ,      . 4        48 4       4.1                      (ISIS, 2004):         !a,      "   " !      , !e " "    ",   !e #  ,    #       "  ;      ,    !    "       "   ;           "   "$  (     )    "       (    );   "            #   . 4.2   !  "#" %                "          "     !.               ! 4        49      "  !   "  / !. &             "        " .  !    !      " $  #  !   "      ! # $   "     .     !    !,     "              .             "  (ACI Committee 440, 2002),  #  !     :   "  ! ;  #,   "      !;  '  #  "    ;  '  #     ;  (      ;  % ,    " ,           " " .  !    !    "   #  "         ! !    !   "    !   !     !       )     !  !. 4.3 $%  !& &'  !(  (      $       $   !    " (ISIS, 2004):         ,         !,        . 4        50 4.3.1 ( ( (  '& ! )  ( '           "   $  "  /       "     ( 4-1). *$               4.4.  4-1:                     () fib bulletin 14, 2001; () Motavalli and Czaderski, 2007 4.3.2 ( ( (  '& ! )  & &          !,                "   4-2.           !.  4-2:    !      (Bank, 2006) &                   #   .                ( 4-3())    &- ( 4-3())     "        . () () 4        51  4-3:          !              &-        $                    $      .          ! #             . %$ "$             "       ! . '  #     "      ( )     ,         ".    ,       #       $           !. '   "         ! !      ,      "      15 mm (Bank, 2006). 4.3.3 ( ( ( "' !#)  #*(           $        $ "$   ()   ( 4-4). '    "#   ,     #      -    -    "-"    #-# $ $    $-$ () () () (!) ( ) 4        52   .    ""   ""     # (confine)     $     . '  !       ,       ! .  4-4: ()  %          ; () &        %  (http://cordis.europa.eu/documents/documentlibrary/116371391EN6.pdf) %$ "$    )      "              ( 4-5 ()). +),           ,      "            #     ( 4-5 ()).  4-5: ()         (Bank, 2006); () '    (   ! %     ,                 %$ "$      #   "    !   #           !    "         !.    - ()()           '%     σ ε () () 4        53 4.4 ( ( (  +, ! )  (   ()        #  $   "   "      (   )       ""  ,        ( ). &     ,           !   "", .     #    ( 4-6).  4-6:     )  !        "      #            "        "    ! $     "  "        ! #    " ")      .       "           "    4-7.  4-7:               (Alkhrdaji et al., 2000)                      "   "     . +),    ":         -      ,   "   $     (debonding, delamination)      "   .    - 4        54 "  #  !      $    !                                "        ! # . , "    ,           ""   2000 MPa       280 GPa,        #  " . ,            "  #  "         . &                       "  (  #$),    „ “            . -  ""    ,                 "       . ,       !                       "      .  4-8: '    (              !  ! (Alkhrdaji et al., 2000) '     " ")                   "    4-8 (Alkhrdaji et al., 2000). & (mm) .  (  )   (  ) .  ( )   ( ) '      '      + $  + $  !     ( k N ) 4        55 &        !                ""   . &      "     ,      #       "",              " ")     . *   ""       #   .   ,    )    "         "           (Alkhrdaji et al., 2000). " "          , "      "          "  (ACI 440.2R-02),      )    # "  (fib bulletin 14, 2001), "      !               !      #           .    #      "     ,      "  ")        "  " !.               !         "       . ,                    ,   !       20  40%   !       "   ,      ,       !.    ,   #         "  "    "$  " $           " "     . &                  ,  "      $       !             .             "     ,   " , ,      !.      "  $  (laminate)  "        (  ).      "           (bars)    (strips) $   #   ",  "  ,        "     !  (%+  ). 4        56 4.5 O%(e !-& '!-& &# –  &, (xternally Bonded – EB) 4.5.1 ! +   $ $        ,               $          .          $ # " "     !,            .       $ $   $   /#  !  ! (Fleming and King, 1967; Bresson, 1971).     "      #                ! (Baker and Chester, 1992; Mays and Hutchinson, 1992; Allan and Bird, 1986). &    $     $   ,       !     ,   :   " #$      $  ,          "  !     "         ", #      ,   "       #  . '                  (    )     $    "      "   $   )  . 4.5.2  !"'#  &, 0  "       "     %    * #    1930.  . +),  "   #       " $   !  1980-  " ! !    (National Science Foundation - NSF)        (Federal Highway Administration - FHWA). &       $   !    $  1978.     (Wolf and Miessler, 1989),       #  $   ! $      "$  /,   #     $ "$         !         80-     . 0 #  4        57 1! ,   "            $    , "    Swiss Federal Laboratories for Materials Testing and Research (EMPA) 1987.   (Meier, 1987; Rostasy, 1987).   " "        /  1980- (Fardis and Khalili, 1981; Katsumata et al., 1987)      "       "$  Hyogoken Nanbu 1995.   (Nanni, 1995). '            "              $    . %$ "$           " , , ,    !   #).    $    !   :  , , , " , " ( ), !,  , , , , !  . 4.5.3  & %               ") .  "      "  ,           "   . & "     ,              !  (wet lay-up, cured in-situ)      (prefab, precured). 4.5.4 )" %(  && .          !      " "       !.         "    "   !        "  "  !  "   . 1. ( )"                 !       $         " ")            4        58  (  ). .           !    "   4-1().        "     :    ,      . " !,'+        "             . '   "   14 (fib bulletin 14, 2001),    "           ,  ,  !,  ,       "      , #,      ,  .     ( )                !        $  .    !     "        #  "     $        . $   $    !             : ,  ,    #   ) .  ")      )  "                    . &                "    . &"   "    ,      "        . '       " $         "    ")  .   ")          0,3 mm       "              "           . 0    " (Resin injection or sealing)               "     . &  ,              $  "  !        (ACI Committee 440, 2002). !#" !(.% „/"“    "           (http://srb.sika.com/sr/solutions_products/02/02a013.html): 4        59           ,   !         0,5 mm.   "          . . !  2 m #   10 mm,  " 0,3 m #  4 mm.    !            . &  ,            (, " ,      ).        28 ,     " ""     $          2,0 N/mm2 ( 1,5 N/mm2).       " , ,   " ! ,  ,   , , $, "         "       " ! ( ).                " !    $,                 . !"        "  "  )   .     )     ")      "    . 2   " ")        .    ,  #              !   "       . &# & "       ,   #      (fib bulletin 14, 2001):     (prefab or pre-cured)    (strips)   (laminates)       ")    " ,    ,     .   $  1,0  1,5 mm,     " . '       # "  ")    .  .  (sheets)   (fabrics)     !  (wet lay-up or cured in situ),       ")    „ “,  "     "              4        60  "        . &   ,    $ "  "!. '      ,        " "     "   "   !  . 2. /!' )" "         ,  !   "     "     "    .       !               " (fib bulletin 14, 2001):    (Automated wrapping);       ;  "    !     ) " "  (In-situ fast curing using heating device);     ;  0  !     . 4.5.5 *' '& ",  & % !        $ $            : 1. !      # "           $         , 2. !     "             . 1. *' '& ! ,0& ,%"& ,'(# !    $    # "         :  . "         $     "          ;  . "                  !     $    ;  + $            $     !   .        #$. &  4        61  $      "    "   !      (" ). 2. *' '& # '#%# !" ,%"+ ,'(   " ")    "     "                !  " (bond failure)   "  "        . 2 "     "   "     $     $        ")         . , "   ",    (localised debonding) "    " " ")              " ")            ,  .   # "  2 mm  "        . 2             "         $ $    . '            "         $       "  ( . peeling-off). &           $ "$               "    . 2 "  #   "      ") ,      ,       (Szabó and Balázs, 2007) ( 4-9):  4-9:   !!       $  !    (Szabó and Balázs, 2007)       $   "     # $ , . #        ( 4-10),   "  ; 1)   2) ")    3)   4) ")   -    4        62  4-10:   !           (" )  #            ""         "",  .                ""  . (    ""      !            ""      !         $  ,       ( $   )      ;          ")           ( " )  $           ,  "    "         "  ;         (   !)  # )  ")    !. . "  #              ,         . 0,            $   "  ,      )   ".   $ ( )               #  .    " ") $           "   . & "     !  , "    ! " ( 4-11):    $ ( )     "    "  " !   $     (  1);    -      !           !   !%    4        63         " ,     #    ,  #     "    "     " (  2);    $ ( )     "     ( !)      $   "       #           (  3);       ( )    (  4).  4-11:       !  $  ! (Blaschko et al., 1998) & &&  "# &#   # (Oehlers and Moran, 1990; Jansze ,1997) "     $ "$    "   ! (      )      #        "$  ,    $ "       !.    , "     " ,    !      "    $     "        #    (% 4-12).       "    (concrete rip-off).  4-12: *                               1   2   4   3 L 4        64 4.6 , % #+,& &# # *"& & '# (# *' !() – $/ &, (Near Surface Mounted – NSM) 4.6.1 ! &         "       "      !   !   !         (Alkhrdaji et al., 1999; De Lorenzis et al., 2000),   "     "  (Tumialan et al., 2001).          "  "  –      !,  #        ,   "       (Porta et al., 2001).   4-14  "    %+     !  (Enmons et al., 2001)      "    (Warren, 1998).  4-13:     !  +,  ! (Tumialan et al., 2001)  4-14:      (Enmons et al, 2001)       (Warren, 1998) 4        65 %+            !  "    , "  #   !.         " "   $: "             !,      "   " ")      , "!  ! $,                  .    ! %+    " "    !  ,     "$    ,  "  (, 2010): 1. -      ; 2. +      " ) ; 3.       (     $); 4. -   "; 5.          "; 6. '       $; 7. (     ""  !; 8. '  #  ,    . %     ,     ,      ! . 4.6.2  !"'# $/ &, , "      "        ,           "          ,     "     .  !      $          "    !    . '   ,      !   "  "    ,          )     "         " (   !). %+                    "    "   :       "    (grouted reinforcement) (Apslund, 1949.)   )    (embedded reinforcement) (Warren, 1998.). 4        66 +         "    $  1948.  .  1  (Asplund, 1949)                    "  $   " .          "   !  !$        (Atkinsosn and Shuller, 1992),      "  "      (Garrity, 1995). &  "        )  " !  ,              ,      15       "  (Hassan and Rizkalla, 2003; Tälisten et al., 2003; Barros and Fortes 2005; Barros et al., 2006). %    , ! ,           , "    . ,  #           )     "   . 3  #           ",  ,     ,  "   -        . 4.6.3 #!" #+, &# %+      "     ( 4-15) (Taljsten et al., 2003): 1. 0!   "  "  ,  "    $  "  "       ; 2. #$    "   "             !      "; 3. &         "         . &    !           "   #        ; 4. & )      !  ; 5. & )         "         !  .                   "           !,                 .    , "     " "            "    . &   #,  "        4        67               " (Aidoo et al., 2006).  4-15:  !     !           +,  ! &# "  " # $/ &, &      ! %+        (4 )   ,    (3 )          %+    "     !. (    ""     4      "      3          !   "", 4     "   3  ,           " "   .  !        4    ,  "  #                ". -#   " "        !,      3  (  3  #),   "     " ,        )  4 .  4-16: )        +,  ! (http://mguadagnini.staff.shef.ac.uk/frp/frp.php) %   "       (   " ) $   '    " (a) () () ( )      4        68          %+              # ,           ( 4-16). " !      "      #         .    ,                           ",    #             !     ". '        ")             "       "   ,    $   "  . &     "    "  "          !,    $ "  ,   !         .     "   "          $,       ,  ,      $      ,              ,         .  4-17:     : )   , )      , )  )         !# ! 0   "  " ")         !. %   ! , #      "      ""      !. (    ""       $           $      "". 0   "  $            .   "       " ) ) ) ) 4        69   ,  "     #     ",           ",    "    !   .    #      #  "     !,   ",  !   !         ".         "       ")           (Warren, 1998). &  !'0 !   4-18  "o je   %+ ,   db       ,  tf  hf $ ( )          . 1      " (bg  hg),  ")      " (ag)      "      (c)    !           ",        . &   #,     "    #      (Sena Cruz and Barros, 2002),   #         (Hassan and Rizkalla, 2003) ( 4-18). '      "    $       "     " $.  4-18:  +,      (De Lorenzis and Teng, 2007) &      #    , "    "  "      " * 2 ! (De Lorenzis,          $ %+           "   "   "    $ %+              !    !    !  4        70 2002),   #      "    1,5               ,    2            .     (Parreti and Nanni, 2004)   #        "    1,5      ,              "            $  ,      "     1,5        ( 4-19).  (Blaschko, 2003)   #               "   "  3 mm   $         ,     $     1-2 mm.  4-19:  +,  (Parretti and Nanni, 2004) &                #            "  . +),               ")   (  "),       !      #     .    ")       "   "      . &      ,         "            " (Hassan and Rizkalla, 2003)         "    "        ")    .     "     $  #  (De Lorenzis, 2004)            "  !          ")       ", " "          "     $  ,     "    "   ". ,    ""  ,       "              . 4        71    "  %+   (Blaschko, 2001, 2003),    #         !        20 mm    "   ! ! ,     #         30 mm,      ,     "      30 mm           .        "  $   #     5  ! (Hassan and Rizkalla, 2004)   #    ")    "         ,      "  !             " "       ". +),    "   %+   (De Lorenzis, 2002)             #         ,      " ,    $      #         ,  "     $    "   ! ")    ! .       (      ",           )  "   " "        .     ,     "  $ $       " $ $ "   "       "      . 4.6.4 -( &#     %+        , "   " $  $ ")      .  $              $    "   !     . % "   "       ,    "      $ "        "     ,            (, 2010). +#       $  #           ()        #  %+   "         "$     " " . * 2 !   (De Lorenzis and Nanni, 2002), * 2 !  . (De Lorenzis and Teng, 2007)  #   $       4        72   "  ,              "  %+      . 1. & (  ,, !( &.# !"  !",     $          –   - 0 (BE-I – bar-epoxy interfacial)   "  !    " (  BE-C – bar-epoxy cohesive). (                    , .          $   #  " ")      ",   "      "   " ")   . '   #                " $   "   !    ",    "       . * 2 !   (De Lorenzis and Nanni, 2002)    "$    !             k=bg/db   1,5. '"  !         $   (Blaschko, 2001, 2003)   !        !  . &   !      ,     ,    . %!             ,           "       ,     # (De Lorenzis and Nanni, 2002)           "   #      ". 2. & (  ,, !( &.# !",  * 2 "       ")     #           –   4-0 (EC-I – epoxy-concrete interfacial),   "  !   –   4-4 (EC-C – epoxy-concrete cohesive). (             "  $    ,   !   " (De Lorenzis et al., 2002). '             ,       " "         "  ), "       k. '                    k   4        73     ( # 2,0),   "     k  !    . '"  !       "           "  (De Lorenzis, 2002),       (Hassan and Rizkalla, 2003). 3. 1! – ,( !",+ '  # !    " /    #   ,   " !       (epoxy cover splitting), $         $ (       )   #    . +"         %+              .              #    ""      #  "      #     .      "  ) "#  ""  #                "",     $     . *                         "  "       ""   .  4-20:   ! +,   : ()      !%  ; ()         ! %  ; ( )         !     (De Lorenzis and Teng, 2007). () () ()   - 4        74 (      ""          "",  $       $ "  ,   "         ()      %+  .   4-20  "     #  ,   "  " " ")   #        . &    ,                "         . "   !     %+   "    4-21. '     k   (1,12-1,18),          $      –   %- (SP- – splitting epoxy). '       k,  $ !  # !         #   –   %-4- 1 (SP-C-1 – splitting concrete 1). 2         !          "" (De Lorenzis et al., 2004). &            6   30°      "  ! ( 4-21). '     " /              "" ,    #         )       –   %-4-2 (SP-C-2 – splitting concrete 2). !  "                  $ !         ,        " !  . &     " !   ,   #   ! !  –   %- * (SP-ED – splitting edge distance). &      $          $  !    (a'e)   20 mm (Blaschko, 2001)    6',    4-21  !  45°  70°. (  "  %-       "        "",    "    %-4-1  %-4-2 "       "". 0      "   $   ,               ",       "    #       .     %-4-2   . (  "    %-         " # (De Lorenzis et al., 2004). 4        75  4-21:    !     +,  !        (De Lorenzis and Teng, 2007) -0:   -       -4: "  !    4-0:    -      4-4: "  !   %- : !    " !  %-41: !     !   #    %- *: ! !  %-42: "  $ !   , !   #    4        76 4.6.5 *' '& ", $/ & % 1. *' '& ", !" &      # %+    $   #  "                  .                  :  " (bond tests)    (member tests) (Burke, 2008). *   #  "      %+   „ $     ",  "            ")             "  “ (De Lorenzis, 2000). 0"  "          #  " "  " ")    ,           )  $    . *    : 1.     (the direct pull-out test)  2.      (the beam pull-out test),      "  " . +           " "    "             " "  "    ! (De Lorenzis, 2001). &  # * 2 !    (De Lorenzis et al., 2000, 2001, 2002) "        .        # ",      ,            "   ". .  "       :   , !       . &         $    $    ",    " $    , " "             $ "  "    . 0  ) "     # "       "    "   ",      "      ,     "     $ "  !  (Burke, 2008). 4        77 &  $  # * 2 ! (De Lorenzis, 2002, 2004)      #  " %+  . &    #    :  , # ", "   "       . &    #, " 2002.  ,   "                        ". &    , %+   "    ,   #       ". 3      "       "       -,        #    ,       #   "   !, "   "       -. & $  # (2004.  )   #          "       $   "     " ". 0  "     "  "     " !  , #     "     ,    ! #     "" ! . .)        !  $  #       "       $     ". & ,    "" " "    # ".    " #    4  ,     3  .    "   "      "    "   !       .  !    "   "   "     "   ".        .    ,      , 5    (Hassan et al., 2004),  #  ! # "           4  . 0  "          . '    ""     # ",      "           -.        # ",            "    # ". '  # ",     6%     "",     # "   40–45%     "". &"  "  "    "$        „   " "   #        4        78 “(Hassan et al., 2004). 0  ) "  #             80               "      "     . &   ,      "       "   „“  ")   "             ""       -.   ""  $        "  $   " "    #   ". %    ,   ) "     "               -.           "  !            ,       "         . * 2 !    (De Lorenzis et al., 2000)      " 2000.   "        .    %+   . &     # !    (3   4    ), !          ( $   )  !  $   ,     . "   "      4   "            !  #     . '    3     "          "    . 0  "     %+     "   . &       25,7 %  44,3 %               . 2. *' '& ", $/ " *        #       %+        ! "  $     #    ,     #                    (Burke, 2008).    "          " #$ " "  !        "  . &           ,     "            #  "       "   "    4        79  #   (Blaschko, 2003). '  ,    "  ""      ,      ,        "  ""  #  "    " "  , "   "     " ".    ,              "           ,        ""   (Teng et al., 2006). &  # 5    " 2003.   (Hasan et al., 2003)   ! # "    ",  " "     # " "           -    "  "      "   )    " . '  "            (  15 %). %    , "             # "     $          !        # "        15 %  92 %. '     # ", "        ,  "             "".  "  "            " "        " $    " "   # ". &  # .     (Teng et al., 2006)    # "     . " "           -        # " " 17,5 %    ,        " " 6 %. 0  "            ,        $ "$     . &  # % !    (Seracino et al., 2007)   "       ,         ")       . 0 #  "              "          !     ,          " 100 %    "    !  118-157 %. "   !     " $  "    "   $ ". &     $       !       !    ",   # "    ",            # ". 4        80 &  #      (Barros et al., 2005)              . &    #    :  !          !       . '       , "      .  "                        "    .       ()  78 %  96 %   )     ,   !      62 %  91 %   ! ""  ,       !        . &  # .     (Teng et al., 2006)      # 3000 mm,      " # %+ 4    (500, 1200, 1800  2900 mm). '   # "  1200  1800 mm        30 %  90 %,        )      . "          "          . '     # "      106 %   )     . *      $ ,       "  ,           -    . 4.6.6 ,  , $/ &, % # !.#   &,& &  )   , %+          (De Lorenzis and Teng, 2007)   :  '      #  ,  "         !   "    (           ,        );                  "        )  "     )  $ "$   ;      )  "    #              !   ,   4        81                ",      $    ;  %+      #        ;      )    "  "       "#  !   ,     ",         "   "        ;  0"    !   . ,     ,            "                $ $      #     !   ,     "     $         " #$ . +    "     "       ,         1,5        ,       "   %+  .    ,     " (   )  "      ,      !  %+   ,    "         "  "       "  ". 4.7  #'& !),) 0( !& &'  %( *") '& &            #   %+   (Alkhrdaji et al., 1999)  )              " ,    $ "$ 4        %+   4  .         # . "        "           $ ,            !. 2   %+           ,                    . &             27 %    %+  ,   17 %     .     "          "    4        82  !        %+       4     " "      .            # " 2004.   (El-Hacha et al., 2004). /               %+ 4  , %+ 4     " ",  " "   ",  %+ 3      . "   "            ,                     ,      . &     %+ 4  , "  !    ,    "                %+  . '    %+ 4      "       ,  "      ,       %+ 3          . '  %+     ,          "        !  . %    $ "$      "        #         %+     "   4       ,   %+     # 4,8         . &  # " 2005.   (Quattkebaum et al., 2005)  )   $ "$ 4   , %+ 4        /    )  "      .               #    . "  #  "    " $ "$            %+       "   $ ,     %+            "    . &  # " 2006.   (Harrison et al., 2006)  )     $ "$ 4   , %+ 4   , $ "$        %+  )     .  #,       "   $        "   ,           ,     46 %  51 %,   )      . &  #      " 2006.   (idoo et al., 2006)       "   !       4        83 (Quattkebaum et al., 2005). * "     $ "$ 4        , "     %+       $        " ,           $   "  "    "  .      # " 2010.   (, 2010)  )          ,     $      „“  .      ) %+    4   3    ,                   %+  .     4       " 89 %         .     3      " 73 %           .           " 51 %         . * "      !        4         3    . *    # "   %+  ,     ,                $ "$   ,        "   %+   (Rizkalla et al., 2002; Quattlebaum et al., 2005; Aidoo et al., 2006; Rosenboom et al., 2007). 3     %+     "     " !   ",            "    "   !   #  %+   $   )   . +),       "   !    %+  ,      , "      ",             . %    #      ",    %+  , #  "       ",     !         . .),   !   !       # "  !  .   ,  "         " %+   ,  ! %+          # " (Burke, 2008). 5              84 5                                            ,      ,          :    ,          (  )            ,   . 5.1                    (Vasseur, Matthys and Taerwe, 2006; Akbarzadeh and Maghsoudi, 2009).                               .              ,      !             ,       . "      ,                !  #           ,                   (Teng et al., 2002).                          (Akbarzadeh, and Maghsoudi, 2009): 5              85 1.            –     (Bernoulli)      ; 2. $    #            ; 3. $    #      ; 4. %                            . 5.2                          .                       (& )            . '     (& )          (Mcr),             . (      (& )      (Mcr),                  (fib bulletin 14, 2001).               ( 5-1):  5-1:                       : As –  !        , As2 –  !       , b – !     , d –                (   ), h –     , xo –            , Mo xo )cc,o )ct,o As2 As b h d 5              86 )cc,o –        , , )ct,o –         , . *                                   ( 5-2),  5-2:            (Bank, 2006)   : )cc –        , )ct –         , )frp –     , )s1 –           .      : 1.  –  ! ,       ,         ()(1))               , + 5-2(); 2.   ,        ,         ()(2))                  (    ), + 5-2( ); 3.  ,                ()(final))                           , + 5-2(). '                      ,            (Bank, 2006). )frp(2)=)ct(2) )frp(final)=)frp(2) )frp(1)=0 )cc(1) )ct(1) )s1(1) )s1(2) )cc(2) )ct(final)=)ct(1)+)ct(2) )s1(final)=)s1(1)+)s1(2) )cc(final)=)cc(1)+)cc(2) ()     ( ) +  () '   5              87 5.3 "  #$! %#& #' ! 5.3.1 $! ( (                        #        ( 5-3). &  ,            (5-2)-(5-4) (Collins and Mitchell, 1987):  5-3:                        ε ε − ε ε ′=σ 2 1c c 1c c cc )( 2 f , (5-2) c c 1c E f2 ′ =ε , (5-3) cc f4500E ′= , (5-4)   : Ec –       , fc ' –        , )c –    , )cu –        (     ), )c1 –                fc', -c –     , -cu –                ()cu).                     5-4   '   &  (Collins and Mitchell, 1987). fc ' - ) )c )c1 )cu -c 1 .c -cu 5              88  5-4:                  : Afrp –  !    , x –            , /1 –  ,          , 01 –  ,                , -s1 –            , -s2 –           , -frp –      . ' ,         a    (/1  01)  #        : 2 0 cc 0 cc 11 )(3 1 ε ε − ε ε =βα , (5-5) ) 2 (6 )(4 0 cc 0 cc 1 ε ε − ε ε − =β , (5-6)   : )cc –        , ) –        . +    (Cc)             (yCc)        (Collins and Mitchell, 1987): bxfC c11c ′βα= , (5-7) h d As2 As x b /1fc' 01x     Afrp +         -frp -s1 -s2                  5              89 x 2 1 xy 1Cc β−= . (5-8) '            (-ct)           (fct),         (Tc)             (yTc)    : )xh(b 2 1 T ctc −σ= , (5-9) )xh( 3 2 y Tc −= , (5-10) cct f6,0f ′λ= , (5-11)   : fct –         , 1 – ,         . 5.3.2 $! !% (                        #           (   ! )  1 %    ( 5-5). &  ,            (5-12)  (5-13):  5-5:                    ε≥εε−ε+ ε≤εε =σ ysysspy ysss s )(Ef E , (5-12) ssp E01,0E = , (5-13)   : Es –             (  )  , Esp –              (  )  , ) fy )y 1 .s 1 .sp ft -s -s )s )s )su 5              90 ft –         , fy –        (  )  , )s –    , )su –         , )y –               , -s –     . 5.3.3 $!   '#)' (                     -     #         ,     5-6. &  ,             (5-14):  5-6:                 frpfrpfrp Eε=σ , (5-14)   : Efrp –         , ffrp –          , )frp –     , )frp,u –          (     ), -frp –      . 5.4 % $*'# %  '%  +'$     '#)'# $   5-7        #    (&)    (2)          ,         . 3                       : -frp )frp,u 1 .frp ) - ffrp )frp 5              91     ,                             .  5-7:           (!)   (")              : Mcr –     , &y –              , &u –       (       ). (           ,       ,               (  )             (Badawi, 2007).                5-8 (ISIS, 2004 –  #   $+&    ):  5-8:    #      ,     $%             (       %   )   : &y & 2 &u &cr        -      * $  (  !  h d x )ct b )s2 )s1 )frp Cs2 )cc -s2 -cc Cc Ts1 Tfrp -ct Tc dfrp d2 -s1 -frp 5              92 Cs2 –          , Tfrp –     , Ts1 –           , dfrp –           , d2 –              , )s1 –           , )s2 –          , -cc –         , -ct –          , -s1 –            , -s2 –           . "           !              !        (4X=0): 0dAdAdAdAdA frp1sct2scc A frpfrp A 1s1s A ctc A 2s2s A ccc =σ−σ−σ−σ+σ , (5-15)   : 0TTTCC frp1sc2sc =−−−+ , (5-16)          !     !      (4M=Mext): ext A frpfrp A 1s1s A ctc A 2s2s A cc MdAydAydAydAydAy frp1sct2scc =σ−σ−σ−σ+σ , (5-17)   : extTfrpT1sTcC2sCc MyTyTyTyCyC frp1sc2sc =−−−+ , (5-18)   : Acc –  !          , Act –  !           , Mext –  !    , y –             , yCs2 –         Cs2, yTfrp –         Tfrp, yTs1 –         Ts1. 5              93 5.4.1 % $*'# %  '  " '! (pre-cracking stage)                                    !    . 3                    (Ig).  5-9:    ,      $%      : ()      , ()    3           !  (4X=0  4M=Mext)           : 0A2/)xh(bA2/xb 1s1sct2s2scc =σ−σ−−σ+σ , (5-19) ext1s1sct 2 22s2scc 2 M)xd(A)xh(b 3 1 )dx(Axb 3 1 =−σ−σ−−−σ+σ , (5-20)       ,   : 0AA2/)xh(bA2/xb frpfrp1s1sct2s2scc =σ−σ−σ−−σ+σ , (5-21) extfrpfrpfrp 1s1sct 2 22s2scc 2 M)xd(A )xd(A)xh(b 3 1 )dx(Axb 3 1 =−σ− −−σ−σ−−−σ+σ , (5-22)     .     * $  (  !  ( ) h d x )ct b )s2 )s1 )frp Cs2 )cc -s2 -cc Cc Ts1 Tfrp -ct Tc dfrp d2 -s1 -frp     * $  (  !  () h d x )ct b )s2 )s1 Cs2 )cc -s2 -cc Cc Ts1 -ct Tc d2 -s1 -frp 5              94 5.4.2 % $*'# %  '  "  '#)' (pre- yielding stage) '                       ,       ,                .             5-10:  5-10:     ,     $%   &      : ()      , ()    5       !  (4X=0  4M=Mext)     (    )        : 0AAfxb 1s1s2s2sc11 =σ−σ+′βα , (5-23) ext1s1s22s2s1c 2 11 M)xd(A)dx(A)2 1 x(fxb =−σ−−σ+β−⋅′βα , (5-24)       ,   : 0AAAfxb frpfrp1s1s2s2sc11 =σ−σ−σ+′βα , (5-25) extfrpfrpfrp1s1s22s2s1c 2 11 M)xd(fA)xd(A)dx(A)2 1 x(fxb =−−−σ−−σ+β−′βα (5-26)     .     * $  h d x b )s2 )s1 )frp Cs2 )cc Cc Ts1 Tfrp d2 -s2 -cc -s1 dfrp (  !  ( )     * $  h d x b )s2 )s1 Cs2 )cc Cc Ts1 d2 -s2 -cc -s1 (  !  () 5              95 5.4.3 % $*'# %  !  "  '#)' (post-yielding stage)        (    )   ( )            5-11:  5-11:     ,     $%   &       : ()      , ()    (           !      : [ ] 0)(E01,0fAAfxb y1sspy1s2s2sc11 =ε−ε+−σ+′βα , (5-27) [ ] exty1sspy1s22s2s1c211 M)xd()(E01,0fA)dx(A)2 1 x(fxb =−ε−ε+−−σ+β−′βα ,(5-28)       ,   : [ ] 0A)(E01,0fAAfxb frpfrpy1sspy1s2s2sc11 =σ−ε−ε+−σ+′βα , (5-29) [ ] extfrpfrpfrp y1sspy1s22s2s1c 2 11 M)xd(A )xd()(E01,0fA)dx(fA) 2 1 x(fxb =−σ− −−ε−ε+−−+β−′βα , (5-30)     .     * $  (  !  ( ) h d x b )s2 )s1 )frp Cs2 )cc Cc Ts1 Tfrp d2 -s2 -cc -s1 dfrp -frp     * $  h d x b )s2 )s1 Cs2 )cc Cc Ts1 d2 -s2 -cc -s1 (  !  () 5              96 5.5 !, ," ,#-) ##  %'" ) '%)  +'$     '#)'# "      -                  !      (, 1985). "   #                !            . $           ()cc)              :          ()s2),           ()s1),     ()frp)          ()ct)       ( 5-11 ()): x dx 2 cc2s − ε=ε , (5-31) x xd cc1s − ε=ε , (5-32) x xd frp ccfrp − ε=ε , (5-33) x xh ccct − ε=ε . (5-34) 3     (5-31)-(5-34)      (5-16),                  (x),             (5-18),          (&)              ()cc). '          ,       (2)                   ()cc)            (x): x ccε=κ . (5-35) $         #        (&-2)          . '     #                                     : 1.                    , 2.             . (                    &_.m & (MATLAB R2014a).          5              97      #    #                ,      . 6 !        #        #            5.5.1,                    10   (0,00001 mm/mm). 5.5.1  +'# ," ,#-) ##  %'" ) '%)  +'$     '#)'# 7 !                     120/200 mm. "   #     #           fc8=40 MPa,                     2Ø8 (s = 100 mm2, 9s : 0,5%),      fy=400 MPa       Es=210 GPa. (   ,      6,    : 1.   ,    , 2.       ,       ffrp,u=2000 MPa,      Efrp=150 GPa     )frp,u=0,0133  3.    ;   ,       ffrp,u=760 MPa,      Efrp=40,8 GPa     )frp,u=0,0186. *    !              (Mcr),       (My)         (Mu),     M_.m          #       :      –     ( 5-12),             ( (5-13) – (5-22) ),          ;   ( (5-23) – ( 5-32)). 5              98  5-12:                    5-13:                  '   , Afrp=10 mm2  5-14:                  '   , Afrp=20 mm2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 x 10 -4 0 2 4 6 8 k (mm/mm) M ( kN m ) 0 0.2 0.4 0.6 0.8 1 x 10 -4 0 2 4 6 8 10 12 k (mm/mm) M ( kN m ) 0 0.2 0.4 0.6 0.8 1 x 10 -4 0 2 4 6 8 10 12 14 k (mm/mm) M ( kN m ) My = 6 kNm Mu = 6,78 kNm My = 6,58 kNm Mu = 10,19 kNm My = 7,17 kNm Mu = 13,47 kNm 5              99  5-15:                  '   , Afrp=30 mm2  5-16:                  '   , Afrp=40 mm2  5-17:                  '   , Afrp=50 mm2 0 0.2 0.4 0.6 0.8 1 x 10 -4 0 2 4 6 8 10 12 14 16 18 k (mm/mm) M ( kN m ) 0 0.2 0.4 0.6 0.8 1 x 10 -4 0 2 4 6 8 10 12 14 16 18 20 k (mm/mm) M ( kN m ) 0 1 2 3 4 5 6 7 8 x 10 -5 0 4 8 12 16 20 24 k (mm/mm) M ( kN m ) My = 7,75 kNm Mu = 16,72 kNm My = 8,34 kNm Mu = 19,29 kNm My = 8,93 kNm Mu = 21,05 kNm 5              100  5-18:                  '   , Afrp=60 mm2  5-19:                  '   , Afrp=70 mm2  5-20:                  '   , Afrp=80 mm2 0 1 2 3 4 5 6 7 8 x 10 -5 0 4 8 12 16 20 24 k (mm/mm) M ( kN m ) 0 1 2 3 4 5 6 7 8 x 10 -5 0 4 8 12 16 20 24 k (mm/mm) M ( kN m ) 0 1 2 3 4 5 6 7 x 10 -5 0 4 8 12 16 20 24 28 k (mm/mm) M ( kN m ) 2 /mm) My = 9,52 kNm Mu = 22,58 kNm My = 10 kNm Mu = 23,95 kNm My = 10,60 kNm Mu = 25,17 kNm 5              101  5-21:                  '   , Afrp=90 mm2  5-22:                  '   , Afrp=100 mm2  5-23:                  (   , Afrp=10 mm2 0 1 2 3 4 5 6 7 x 10 -5 0 4 8 12 16 20 24 28 k (mm/mm) M ( kN m ) 0 1 2 3 4 5 6 7 x 10 -5 0 4 8 12 16 20 24 28 k (mm/mm) M ( kN m ) 0 0.2 0.4 0.6 0.8 1 1.2 x 10 -4 0 2 4 6 8 10 k (mm/mm) M ( kN m ) My = 11,19 kNm Mu = 26,29 kNm My = 11,78 kNm Mu = 27,31 kNm My = 6,18 kNm Mu = 8,44 kNm 5              102  5-24:                  (   , Afrp=20 mm2  5-25:                  (   , Afrp=30 mm2  5-26:                  (   , Afrp=40 mm2 0 0.2 0.4 0.6 0.8 1 1.2 x 10 -4 0 2 4 6 8 10 k (mm/mm) M ( kN m ) 0 0.2 0.4 0.6 0.8 1 1.2 x 10 -4 0 2 4 6 8 10 12 14 k (mm/mm) M ( kN m ) 0 0.2 0.4 0.6 0.8 1 1.2 x 10 -4 0 2 4 6 8 10 12 14 k (mm/mm) M ( kN m ) My = 6,35 kNm Mu = 9,69 kNm My = 6,53 kNm Mu = 10,93 kNm My = 6,70 kNm Mu = 11,95 kNm 5              103  5-27:                  (   , Afrp=50 mm2  5-28:                  (   , Afrp=60 mm2  5-29:                  (   , Afrp=70 mm2 0 0.2 0.4 0.6 0.8 1 1.2 x 10 -4 0 2 4 6 8 10 12 14 k (mm/mm) M ( kN m ) 0 0.2 0.4 0.6 0.8 1 1.2 x 10 -4 0 2 4 6 8 10 12 14 k (mm/mm) M ( kN m ) 0 0.2 0.4 0.6 0.8 1 1.2 x 10 -4 0 2 4 6 8 10 12 14 16 k (mm/mm) M ( kN m ) My = 6,79 kNm Mu = 12,86 kNm My = 6,96 kNm Mu = 13,71 kNm My = 7,14 kNm Mu = 14,50 kNm 5              104  5-30:                  (   , Afrp=80 mm2  5-31:                  (   , Afrp=90 mm2  5-32:                  (   , Afrp=100 mm2 0 0.2 0.4 0.6 0.8 1 x 10 -4 0 2 4 6 8 10 12 14 16 k (mm/mm) M ( kN m ) 0 0.2 0.4 0.6 0.8 1 x 10 -4 0 2 4 6 8 10 12 14 16 18 k (mm/mm) M ( kN m ) 0 0.2 0.4 0.6 0.8 1 x 10 -4 0 2 4 6 8 10 12 14 16 18 k (mm/mm) M ( kN m ) My = 7,31 kNm Mu = 15,24 kNm My = 7,49 kNm Mu = 15,94 kNm My = 7,68 kNm Mu = 18,50 kNm 5              105 $           #       ( 5- 12, 5-13  5-14),             (Mcr),       (&y)                  (2y),        (&u)           (2u),               : 1. + !                 ,            :          ,        (Mcr)    4,41 %,           !               !       ,       ;           (Mcr)    0,24 %,           !               !       . 2. + !               ,           :                   (My)    96,33 %,                        77,56 %,       ;            (My)    26,17 %,                        22,30 %. 3. + !             ,           :                    (Mu)    302,8 %,                      298,07 %,       ;             (Mu)    144,84 %,                      64,70 %. 5              106 5.6 !, +'+  " '%  +'$     '#)'# 5.6.1                         !            (ACI 440.2R-02). '   #          (Mu)                  . $ !                :        ,       (     )          (Arduini and Nanni, 1997; Spadea et al., 1998). +                       . $                                . & # ,                      ( #     )     , ,                     !      .      #         !                     # . (   ,          ,              ,         . .,           ()frp,ef)             ()frp,u)        ,   (2m),                           :   >≤ ε ≤≤− ε =κ in/lb1000000tEn90,0) tEn 500000 ( 60 1 in/lb1000000tEn90,0) 2000000 tEn 1( 60 1 frpfrp frpfrpu,frp frpfrp frpfrp u,frp m , (5-36)   : n –          , Efrp –                        , tfrp –           . 5              107 'o  ,    (2m)       0,90,                ()frp,u),                  . 6    ,                  :         (    1)        (    2).    #          (Mu),                      ,           ,          . %              (    1)  (    1 )                  !        . "                  . %             (    2)  (    2 )             ,                  (-cc < fc8),                    ()cc < )cu; )cu = 0,003).                                      !           . "                 . 5.6.2 $'-" (!% !#  +' "'$ ## "   !         !                 (x)               (&u). "             #                  !             .     ,                      . ' !     ,       ,          : 5              108  (!% !# 1: &                  ;  (!% !# 1(: &                 ;  (!% !# 2: %                  ;  (!% !# 2(: %                 . +                             ,  !                                    ((! !# 1  2). (  ,   !            ,    ()s)                        ()y). & # ,              ,           ,                  ((! !# 1(  2().    ,    ,       ,     ,                  (     ,                          ). 7 # ,             ,             ,                       .  5-33:     ,     $%                 * $  h d x b )s2 )s1 )cc Cc Ts1 Tfrp /1 fc8 -s1 dfrp (  !  -frp )bi )frp 01 fc8 As2 As Afrp 5              109 '  (!% !# 1                   ,                     ()frp < )frp,u). 3                             (-s1 = fy)        e,  01  /1   ,             ( 5-15). "            (x)           : [ ] 0x)xh(EAxfAx)bf85,0( bicufrpfrpy1s 2 1 ' c =ε−−ε−−β , (5-37)   : )bi –               . '                ,                 ,                           ,         ,           : ycu1s x xd ε≥ − ε=ε , (5-38) ef,frpbicufrp x xh ε≤ε− − ε=ε . (5-39) (     (5-38)  (5-39)    ,                       (-s1 = fy),           #     : frpfrpfrp E ε=σ . (5-40) $        (Mn)       : ) 2 x h(A) 2 x d(fAM 1frpfrpfrp 1 y1sn β −σψ+ β −= , (5-41)   :         : 1.   !    (Afrp) (     ,  !        0  100 mm2,       10 mm2. 2. >     (  ;) )    ,       ffrp,u = 2000 MPa,      Efrp = 150 GPa     )frp,u = 0,0133  ) ;   ,       ffrp,u = 760 MPa,      Efrp = 40,8 GPa     )frp,u = 0,0186. 3. '         (µ s) ) µ s = 0,2 %, ) µ s = 0,5 %, ) µ s = 0,8 %, ) µ s = 1,1 %, ) µ s = 1,4 %. 4. ?       (fc´) ) fc´ = 20 MPa, ) fc´ = 25 MPa, ) fc´ = 30 MPa, ) fc´ = 35 MPa, ) fc´ = 40 Mpa, #) fc´ = 45 MPa, ) fc´ = 50 Mpa. *    !                (Mu),  !     &_.m   & (MATLAB R2014a),      5.5. (     &_.m                               :   (    ),        (     )     (    !)       ,  . 5              115          ,  !       5.6,  #                       (ACI 440.2R-02).                 ;    ,   !        (5-34)  (5- 68). >         &_.m       - &_  ;-&_                         -6  ;-6.    ,            !               ,       #                   . *     #          !    ,         (fc´)      5-69  ,      5-70  ;   . *     #          !    ,             (µ s)     5-71  5-72  ,     5-73  5-74  ;   .  5-34:         , fc* = 20 MPa, +s = 0,2 %: a)   ,       , )  $,     0 5 10 15 20 25 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    2    1 5              116  5-35:         , fc* = 25 MPa, +s = 0,2 %: a)   ,       , )  $,      5-36:         , fc* = 30 MPa, +s = 0,2 %: a)   ,       , )  $,     0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    2    2    1 5              117  5-37:         , fc* = 35 MPa, +s = 0,2 %: a)   ,       , )  $,      5-38:         , fc* = 40 MPa, +s = 0,2 %: a)   ,       , )  $,     0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    2    1 5              118  5-39:         , fc* = 45 MPa, +s = 0,2 %: a)   ,       , )  $,      5-40:         , fc* = 50 MPa, +s = 0,2 %: a)   ,       , )  $,     0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 10 20 30 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    2    1    2    1 5              119  5-41:         , fc* = 20 MPa, +s = 0,5 %: a)   ,       , )  $,      5-42:         , fc* = 25 MPa, +s = 0,5 %: a)   ,       , )  $,     0 5 10 15 20 25 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    1    2    1 5              120  5-43:         , fc* = 30 MPa, +s = 0,5 %: a)   ,       , )  $,      5-44:         , fc* = 35 MPa, +s = 0,5 %: a)   ,       , )  $,     0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    2    1 5              121  5-45:         , fc* = 40 MPa, +s = 0,5 %: a)   ,       , )  $,      5-46:         , fc* = 45 MPa, +s = 0,5 %: a)   ,       , )  $,     0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    2    2 5              122  5-47:         , fc* = 50 MPa, +s = 0,5 %: a)   ,       , )  $,      5-48:         , fc* = 20 MPa, +s = 0,8 %: a)   ,       , )  $,     0 10 20 30 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    1    1 5              123  5-49:         , fc* = 25 MPa, +s = 0,8 %: a)   ,       , )  $,      5-50:         , fc* = 30 MPa, +s = 0,8 %: a)   ,       , )  $,     0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) frp (mm2)  ; ( ) 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    2    2    1 5              124  5-51:         , fc* = 35 MPa, +s = 0,8 %: a)   ,       , )  $,      5-52:         , fc* = 40 MPa, +s = 0,8 %: a)   ,       , )  $,     0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    2    1 5              125  5-53:         , fc* = 45 MPa, +s = 0,8 %: a)   ,       , )  $,      5-54:         , fc* = 50 MPa, +s = 0,8 %: a)   ,       , )  $,     0 10 20 30 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 10 20 30 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_' -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    2    1 5              126  5-55:         , fc* = 20 MPa, +s = 1,1 %: a)   ,       , )  $,      5-56:         , fc* = 25 MPa, +s = 1,1 %: a)   ,       , )  $,     0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    1 5              127  5-57:         , fc* = 30 MPa, +s = 1,1 %: a)   ,       , )  $,      5-58:         , fc* = 35 MPa, +s = 1,1 %: a)   ,       , )  $,     0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    1    2 5              128  5-59:         , fc* = 40 MPa, +s = 1,1 %: a)   ,       , )  $,      5-60:         , fc* = 45 MPa, +s = 1,1 %: a)   ,       , )  $,     0 10 20 30 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 10 20 30 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    1    2 5              129  5-61:         , fc* = 50 MPa, +s = 1,1 %: a)   ,       , )  $,      5-62:         , fc* = 20 MPa, +s = 1,4 %: a)   ,       , )  $,     0 10 20 30 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    1 5              130  5-63:         , fc* = 25 MPa, +s = 1,4 %: a)   ,       , )  $,      5-64:         , fc* = 30 MPa, +s = 1,4%: a)   ,       , )  $,     0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    1 5              131  5-65:         , fc* = 35 MPa, +s = 1,4 %: a)   ,       , )  $,      5-66:         , fc* = 40 MPa, +s = 1,4 %: a)   ,       , )  $,     0 10 20 30 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 10 20 30 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    1 5              132  5-67:         , fc* = 45 MPa, +s = 1,4 %: a)   ,       , )  $,      5-68:         , fc* = 50 MPa, +s = 1,4 %: (a)   ,       , ()  $,     0 10 20 30 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( ) 0 10 20 30 40 50 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) Afrp (mm2) -&_ ;-&_ -6 ;-6 () 0 20 40 60 80 100 120 0 10 20 30 40 50 60 70 80 90 100  % ' .     ' # )'  (% ) Afrp (mm2)  ; ( )    1    2 5              133  5-69:      '   : () +s = 0,2 %, () +s = 0,5 %, () +s = 0,8 %, () +s = 1,1 %, ( ) +s = 1,4 % 0 10 20 30 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) fc=20 MPa fc=25 MPa fc=30 MPa fc=35 MPa fc=40 MPa fc=45 MPa fc=50 MPa () 0 10 20 30 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) fc=20 MPa fc=25 MPa fc=30 MPa fc=35 MPa fc=40 MPa fc=45 MPa fc=50 MPa ( ) 0 10 20 30 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) fc=20 MPa fc=25 MPa fc=30 MPa fc=35 MPa fc=40 MPa fc=45 MPa fc=50 MPa () 0 10 20 30 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) fc=20 MPa fc=25 MPa fc=30 MPa fc=35 MPa fc=40 MPa fc=45 MPa fc=50 MPa () 0 10 20 30 40 50 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) fc=20 MPa fc=25 MPa fc=30 MPa fc=35 MPa fc=40 MPa fc=45 MPa fc=50 MPa () Afrp (mm2) 5              134  5-70:      (   : () +s = 0,2 %, () +s = 0,5 %, () +s = 0,8 %, () +s = 1,1 %, ( ) +s = 1,4 % 0 5 10 15 20 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) fc=20 MPa fc=25 MPa fc=30 MPa fc=35 MPa fc=40 MPa fc=45 MPa fc=50 MPa () 0 5 10 15 20 25 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) fc=20 MPa fc=25 MPa fc=30 MPa fc=35 MPa fc=40 MPa fc=45 MPa fc=50 MPa ( ) 0 5 10 15 20 25 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) fc=20 MPa fc=25 MPa fc=30 MPa fc=35 MPa fc=40 MPa fc=45 MPa fc=50 MPa () 0 10 20 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) fc=20 MPa fc=25 MPa fc=30 MPa fc=35 MPa fc=40 MPa fc=45 MPa fc=50 MPa () 0 10 20 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) fc=20 MPa fc=25 MPa fc=30 MPa fc=35 MPa fc=40 MPa fc=45 MPa fc=50 MPa () Afrp (mm2) 5              135  5-71:      '   : () fc*=20 MPa, () fc*=25 MPa, () fc*=30 MPa, () fc*=35 MPa 0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) 9s=0,20 % 9s=0,50 % 9s=0,80 % 9s=1,10 % 9s=1,40 % () 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) 9s=0,20 % 9s=0,50 % 9s=0,80 % 9s=1,10 % 9s=1,40 % ( ) 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) 9s=0,20 % 9s=0,50 % 9s=0,80 % 9s=1,10 % 9s=1,40 % () 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) 9s=0,20 % 9s=0,50 % 9s=0,80 % 9s=1,10 % 9s=1,40 % () Afrp (mm2) 5              136  5-72:      '   : () fc*=40 MPa, () fc*=45 MPa, () fc*=50 MPa 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) 9s=0,20 % 9s=0,50 % 9s=0,80 % 9s=1,10 % 9s=1,40 % () 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) 9s=0,20 % 9s=0,50 % 9s=0,80 % 9s=1,10 % 9s=1,40 % ( ) 0 10 20 30 40 50 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) 9s=0,20 % 9s=0,50 % 9s=0,80 % 9s=1,10 % 9s=1,40 % () Afrp (mm2) 5              137  5-73:      (   : () fc*=20 MPa, () fc*=25 MPa, () fc*=30 MPa, () fc*=35 MPa 0 5 10 15 20 25 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) 9s=0,20 % 9s=0,50 % 9s=0,80 % 9s=1,10 % 9s=1,40 % () 0 5 10 15 20 25 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) 9s=0,20 % 9s=0,50 % 9s=0,80 % 9s=1,10 % 9s=1,40 % ( ) 0 5 10 15 20 25 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) 9s=0,20 % 9s=0,50 % 9s=0,80 % 9s=1,10 % 9s=1,40 % () 0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) 9s=0,20 % 9s=0,50 % 9s=0,80 % 9s=1,10 % 9s=1,40 % () Afrp (mm2) 5              138  5-74:      (   : () fc*=40 MPa, () fc*=45 MPa, () fc*=50 MPa 0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) 9s=0,20 % 9s=0,50 % 9s=0,80 % 9s=1,10 % 9s=1,40 % () 0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) 9s=0,20 % 9s=0,50 % 9s=0,80 % 9s=1,10 % 9s=1,40 % ( ) 0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 80 90 100 M u ( kN m ) 9s=0,20 % 9s=0,50 % 9s=0,80 % 9s=1,10 % 9s=1,40 % () Afrp (mm2) 5              139 5.7.1 !, $( & "'$ /  '#)' – +' ## "            (&u)                      5-75.      :             (9frp) 0,22 %, !        !    8 mm (frp = 50 mm2),  5-75 ()              0,44 %, !       !   8 mm (frp = 100 mm2),  5-75 ().  5-75:   ,        (!u)       '   : ) +frp = 0,22 %, ) +frp = 0,44 % 0 100 200 300 400 500 600 15 20 25 30 35 40 45 50 55  ".   + '   + # #   "    ( % ) fc (Pa) 9s=0,2 % 9s=0,5 % 9s=0,8 % 9s=1,1 % 9s=1,4 % 0 100 200 300 400 500 600 700 800 900 15 20 25 30 35 40 45 50 55  ".   + '   + # #   "    ( % ) fc (MPa) 9s=0,2 % 9s=0,5 % 9s=0,8 % 9s=1,1 % 9s=1,4 % (a) ( ) 5              140           ( 5-75()),            0,22 %   :  449,04  507,16 %              (9s) 0,2 %,  176,86  238,57 %              0,5 %,  103,55  158,40 %              0,8 %,  60,70  100,89 %              1,1 %,  43,72  76,53 %              1,4 %.          ( 5-75()),            0,44 %   :  628,05  845, 67 %              0,2 %,  252,51  378,50 %              0,5 %,  150,96  233,81 %              0,8 %,  90,94  151,26 %              1,1 %,  66,71  116,38 %              1,4 %. /  '#)' – (! !# (                0,2 %      1  2 ( (5-34) (5-40)).                           . &                  (    1)                 0,114 %,         (fc8)  20 MPa. +                            ,    fc8 = 50 MPa,           9frp > 0,337 %.                 !  ( (5-34) (5-40)). '                              (    2)                !           ,             ! . 3             0,5 %      1  2 ( (5-41) (5-47)). &                             0,061 %,         5              141  20 MPa,             fc8 = 50 MPa,          (9frp > 0,284 %). '             0,8 %      1  2 ( (5-48) (5-54)). &                             0,011 %,         20 MPa,             fc8 = 50 MPa,     9frp > 0,234 %. (                1,1 %      1  2 ( (5-55) (5-61)). &                                 20  25 MPa. 3        30 MPa,                         0,025 %,             fc8 = 50 MPa,          (9frp > 0,174 %). '             1,4 %      1  2 ( (5-62) (5-68)). &                        ,          20-30 MPa. '                       fc8 > 30 MPa,                  0,129 %          50 MPa. '       5.6  #           ,    #        ,                                 . 7      #                    #                  5-76. "    1                     ,                       . "    2                      ,                       . 5              142  5-76: -       &                 '      '#)' – +' ## "                         ;        5-77.      :             (9frp) 0,22 %, !        !    8 mm (frp = 50 mm2),  5-77 ()              0,44 %, !       !   8 mm (frp = 100 mm2),  5-77 ().           ( 5-59()),        ;    0,22 %   :  197,41  206,57 %              0,2 %,  76,13  98,02 %              0,5 %,  41,95  65,81 %              0,8 %,  23,08  40,97 %              1,1 %,  16,06  30,39 %              1,4 %.           ( 5-59()),        ;    0,44 %   :  315,53  397,91 %              0,2 %,  124,17  179,46 %              0,5 %, 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 15 20 25 30 35 40 45 50 55 0 fr p (% ) fc (MPa) 9s=0,2 % 9s=0,5 % 9s=0,8 % 9s=1,1 % 9s=1,4 % (!% !# 1 (!% !# 2 5              143  69,91  107,88 %              0,8 %,  39,88  67,35 %              1,1 %,  28,26  50,51 %              1,4 %.  5-77:     ,        (!u)       (   : ) +frp = 0,22 %, ) +frp = 0,44 %   '#)' – (! !# (                (9s) 0,2 %      1  2 ( (5-34) (5-40)).                     1      # 0,192 %          20 MPa,  0,653 %          50 MPa. '                0 50 100 150 200 250 15 20 25 30 35 40 45 50 55  ".   + '   + # #   "    ( % ) fc (MPa) 9s=0,2 % 9s=0,5 % 9s=0,8 % 9s=1,1 % 9s=1,4 % 0 50 100 150 200 250 300 350 400 450 15 20 25 30 35 40 45 50 55  ".   + '   + # #   "    ( % ) fc (MPa) 9s=0,2 % 9s=0,5 % 9s=0,8 % 9s=1,1 % 9s=1,4 % (a) ( ) 5              144 0,44 %,                  40 MPa       2. K             0,5 %      1  2 ( (5-41) (5-47)). &                                  0,067 %,         20 MPa,      0,514%          50 MPa. +                   0,44 %,                      45 MPa. (              !                       . 3             0,8 %      1  2 ( (5-48) (5-54)). &                                  0,01 %,         25 MPa,      0,382 %          50 MPa. (                1,1 %      1  2 ( (5-55) (5-61)). '          20  35 MPa,                          . 3         40 MPa      2.              0,074 %,             50 MPa                  0,22 %. '             1,4 %      1  2 ( (5-62) (5-68)). &                  (    1)  ,          ,           20  40 MPa. '                 (    2)                0,031 %         45 MPa,                0,105 %         50 MPa. '       5.6  #           ,    #        ,                            5              145      . 7      #                    #                  5-78. "    1                     ,                       . "    2                      ,                       .  5-78: -       &                 (    0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 15 20 25 30 35 40 45 50 55 0 fr p (% ) fc (MPa) 9s=0,2 % 9s=0,5 % 9s=0,8 % 9s=1,1 % 9s=1,4 % (!% !# 1 (!% !# 2 6                   146 6  O                6.1                    ,       ,              ,        !   "     .                 #  !        ,     !     $              . %"     "  !    $   ,  !          (" ,     ,       )                  ,  !  ! " !      #  . &#           !        (    !   ). 6.2   !"!# ! !!$%          !        #  "      !        "   ,           ,                    . '         ((  )),      (  *+,)  !    .  !     !    6                   147        , !            !   "       ,       .          ,                 " ,    !                 "       !   . 6.2.1 &!' ! !!$!# (!# "   !         !  „  # “  *.           #             !   6-1.  #   3200 mm,       !  120×200 mm.    "   "      A 400/500-2,   !    ( 6-1),           "  M 30. %  "              "   !      !   !  " ( "   ) "       .  6-1:             6.2.2 ! " -  ! !               ,         ( 6-2). 3200 2Ø8 mm Ø6/75 mm Ø6/150 mm 2Ø8 mm 120 20 0 20 0 25 25 2Ø8 mm 2Ø8 mm Ø6/150/75 mm A A 1500 1500 6                   148  6-2:       –  6.2.3 ! ) .     !    6-1. % !          "    A 400/500-2   Ø8 mm  !       )A 240/360   Ø6 mm ( 6-3).    #         "    .  6-3:         6.2.4 !% (!# "      !  !        !   " # 1 m3.   !   $ " "     ! „  # “,       M 30. 6                   149  6-4:                                  6.2.5 *( )$ (+!# ") ! %!#$  &   "   !    "    "    ( 150 mm)     (Ø150/300 mm). + "!                   "     !        " !  !   !      .  6-5:                      6.3 ,!! ',$% ! !!$!#  ( /     !     ,     ! . -          $ ,  (MAPEI)     $ + (SIKA)            !    . -   !,  ,                  "  ( 6-1). 6                   150  6-1:                 !  -   ! '        (mm)    (mm2) 0 ! !  (MPa) ,       (GPa) G-rod ) Ø10 71,29 760 40,8 C-rod ( Ø8 50,24 2000 155 Carboplate E 170/50/1,4 ( 34×1,4 48 3100 170      Adesilex PG1 / / 30 MPa – ! ! 40 MPa –    >3 MPa – ! 4000 MPa    8000 MPa    -   ! )  !# - $  (m/m/ 1C) +  (MPa) &    + #    G-rod 2 % 6÷10×10-6 / >51C 75 % C-rod 1,5 % 6÷10×10-6 / >51C 71 % Carboplate E 170/50/1,4 2 % 0,6×10-6 77 >51C 68 %  6-6: " #     (G-rod)  $     (C-rod  Carboplate E)     %!  6-7: &   (Adesilex PG1) 6.3.1  ( ',% –  ) )(%  ) ) *! "') +           *+,            . *   $   ! " #    !  !             !  !      . *          !    "    !     !.        6                   151   "  ! "               . -  )   "  ! 25×25 mm,      (  !  20×20 mm         !          .  6-8: "     '(   ! )*                !       !  !        . +                     "   ! .        !       !         .           !      ! ,       , !       ( 6-9).  6-9:           )*   6                   152 &             !  ,                         ,      !   !     . %      " !        !      $       . &"           !      +5  +25°C,   !       !       . %           "      #       !   .           !   ,    $  „   “ 50 mm,                       "     . 6.3.2  ( ',% – ',$%  ( "-%  "!  $!! + /                     !     #    . /  "     ! ,        "!"    !    !        *+,     , !              . 2     "    ((  )         : *           „CarboDur S512“,   $ "   ! 50×1,2 mm,  "       !          (   Ø8 mm (E1A1=E2A2). -  , ! "    1,2 mm     !   34 mm. %                     "   " # 1 mm ( 6-10). * " #               , "!  "  "     " ( 6-10).  6-10:             &(   !  6                   153 2           ,           !   ,      ! "    . '     "         .     !   ,     #        7  . &        !                            *+,  . 6.4  $  ! !  ! !!$%   ,  6-11: !     '(  (experimental setup) 3        ! #     !      "   !    ,    $    *. +   "        !    2 "   !       )   -     $    *.       "           #  3200 mm,      „   “    . /     !   !   1500 mm. 6.4.1 .() % /% /         ,                        ,        "        !   1500 mm ( 6-11). %       6                   154                  #  2 m,                    100 mm        Ø30 mm     ! . /                        100 mm !            # . *       „   “,        "  $     . !     !   0,02 mm/s (1,2 mm/min). 6.4.2 % &           "  $     ("),    " ,       ,      !    ,   $        .           "  "          $ „   “ 50 mm       ,   5 kN !                      .  !    #  " !    (100 mm)          .       $    ,     " #  !             . 6.4.3   1. $,! % (LVDT)         "  : 3           LVDT (Linear Variable Displacement Transducers) W50      "  LVDT W20            !     !    !  " . 4          #  " !  100 mm  !    !    ( 6-12).  6-12:+!    U1 (LVDT)      (D1  D2) 6                   155 2. " !  *! ( ) ,      (    ),             " ,           !   ,  !   „   “ – ,& („strain gauge“). %     #       ,&  !  „Hottinger“ (HBM)       120 5,   !   #  " !. *      " !  " 6 mm, (   , )    (   6 mm "  50 mm ( 6-13).  6-13: *     , !       + "!    ,&   (    ), !     ,     "    , "   !        . 2     !   (    ) !    Z70 a "    X60  !  6  . *     !           (  )    !    ! .     ,&             !    ! .                 ,             (" ) (p=1/100  p=1/1000) !        ,     (ZDI-VDA  p=0,05 mm),              0,05 mm. %    (    )             (HBM U2A)     100 kN,    0,5%. 3. -$!*!.!' ! !  %          !           ,   !     (" )    $   (  ),               !   „Hottinger“ (HBM),    - !   MGC-plus  SPIDER 8 ( 6-14). 6                   156  6-14: * -!    MGC-plus  SPIDER 8 -         !    !     ,    "     ,           . /               1   ( !  ),     "      "    $     CATMAN (s/n 70341313408)   $ „Hottinger“. 6.5  !!$% #!,!# ! ! !/!# !'" (/ ! !!$% !'") 6.5.1 )0)')/! +                           "                 !                       !   . +     "       , 30 !       $ " "     ! „  # “     !    6-2. %    "      CEM I 42.5 R  !   HOLCIM,   "   "     $    2,692 g/cm3    MC PowerFlow 1102,    $      EN 934-2,          $     "  . . !   a !   0,5 %              (    "  ). 6                   157  6-2:     SCC kg/m3 ( : CEMI 42,5R 320,00  : Omya Ven7ac 100,00 0 – 4 mm (46%) 807,50 4 – 8 mm (22%) 380,00 8 – 16 mm (32%) 553,00  : MC Powerflow 2,2 '  210,00          , !   " # 1 m3,  "    !   !     (12    150 mm  6     Ø150/300 mm).          2, 7, 14, 28           . 3       (++ 3+/ 4012:2000),  ! !    (++ 3+/ 4108:2000)         " (++ 3+/ 6784:2000). 1. (0!$% ,$ / ! !! ) /            !  Controls,   Automax 5, !            0,5 MPa/s ( 6-15),  "  !     "    6-3   "     ( 6-16).  6-15:   Controls - Automax 5     !    6                   158  6-3: ,           +   " +     fsr [MPa] +     $       fb [MPa] 2 12,06 0,63 11,43 7 18,15 0,92 17,23 14 24,93 1,15 23,78 28 28,82 1,24 27,58 3    33,82 1,52 32,30  6-16: # %      !           %!    %                   , !   "   ,           fb =32,30 MPa. &     !   "                "       ,   !"         " ! . 2. (0!$% (!'  – (!".!' ) +) ! '( !'" !! ) )$ ! (0!$% ,$ / ! !! )  .!"!(!,! )$ %"                         ,                 "!     ,    (   )                       " . 3!  "           6                   159           !      !     .   $            .  6-17: !     -    !   !!    *    "     !          ",              . &          E&       ! 15  27 MPa, !         . 3. (0!$% !, ()" " !, ! ! !! ) ( ! ()") +                #    (++ 3+/ 6784:2000),       Ø150×300 mm,   !   6-18.             W20               120°,            .  !  !   100 mm  !         . 3       HPM 3000                "  (        ),  !       .        !          (      )      8b=0,5 MPa  8a=1/3·fc',                9b  9 .  !             . 6                   160  6-18: !        !      -    !   -         3!                      : ba ba cE ε−ε σ−σ = ε∆ σ∆ = , (6-1)       9  9b  "        !        . -          -  (8-9)                      6-19.  6-19: !     -    !               !    6                   161 '           $           #             :  1: 23,56 MPa  1: 27,72 MPa  1: 24,77 MPa 4. (0!$% ,$ / + ! **%) .% 0 "  ! !          Ø150×300 mm     SRPS ISO 4108:2000,      !     !   6-21.  6-20: !                   (        ) /        0,06 N/(mm2s)    ,    ! " #     240 kN. 2         ( 6-20). 0 ! !     fct (N/mm2)     : dl F2 f ct pi = , (6-2) MPa44,3 150300 2400002 fct = ⋅⋅pi ⋅ = , (6-3) 6.5.2 )   (   )                    "       !      !       6                   162       "      2 "       $    * (   , 2010).           $ "    !   .  6-4: .                    * !     ,       [MPa] )    9×10-6 )   [MPa] )    [MPa]  "    E fu     Ø8 205000 - 400 500 205000 500 C-rod Ø8 148100 13434 - 1940 150000 2000 G-rod Ø10 47000 15635 - 735 40800 760 S 512 CarboDur 165000 17000 - 3100 165000 3100 6                   163 6.6 *)"!  !"!# ! !!$% ! %!#$ "!* 6.6.1   .           #  ! !  !   "                             . '       (      $   ),           ,      !   (   ), !   "      (Excel)  -   (Catman). 3! !  !   !    "     , !                    $       ("   ). !         !      , !             ! . 6.6.2 *, (-! ! $!' ',% ! !!$!# !)"!# (!#  , %     ! "                 : 1. -- (B-Con – Beam Control): -  (    )  ; 2. -)1 (B-G1 – Beam Glass 1): )   )      Ø 10     !      ( 6-21 ()); 3. -)2 (B-G2 – Beam Glass 2): )   )      Ø 10     !  "     ( 6-21 ()); 4. -)3 (B-G3 – Beam Glass 3): )   )      Ø 10     !           !  "     ( 6-21 ()); 5. -( (B-C – Beam Carbon): )   (      Ø 8     !           !  "     ( 6-21 ()); 6. -( (B-EC – Beam External Carbon): )   (   dfrp=1,4 mm     !           !  "     ( 6-21 ()). 6                   164  6-21: . !  !       1500 1500 1400 1400 1400 1400 1400 1400 1400 1400 1400 1400 1400 1400 - -&1 -&2 -&3 -11 -1 6                   165 6.6.3 *)"! ! !!$% "! (!  , (-) -  (    )     !      !   6-22,             !  6-23.  6-22: !                     6-23:         !   U1 U2 U3 U4 MT1 MT3 MT4 MT5 D1 D2 P P/2 P/2 MT2 750 750 750 750 MT1 MT4 D1 D2 MT2 MT3 (: U – "  ,& –    D –    I  II  III MT5  I  III  II 6                   166  6-5:              ,   ,     /!      #     .# " !                + .    Din L/2 100 kN (0,5 %) " LVDT – W50 U1, U2 L/4 50 mm 1/1000 mm " LVDT – W50 U3, U4 /  5 mm 1/1000 mm .  .  D1 L/2 100 mm 10×10-6 .  .  D2 L/2 100 mm 10×10-6 .  ,   MT1, MT3 L/4 ( ) 6 1×10-6 .  ,   MT2 L/2 ( ) 6 1×10-6 .  ,   MT4, MT5 L/4 (" ) 50 1×10-6   ! /      !. „    “,  "!     "  0,02 mm/s  !      5 kN       ,  !          " #   !   "             $  "      .          !   6-23. %   "              W50 (LVDT)        "   .         "         1/100 mm. .          "    "              " !   50 mm. .                       ( 6-23). .   " !   100 mm         ,     ,         " . ,  "     !    $     ,             5 kN,        ,         . 6                   167  6-24: !     -           I (U1)    II (U2)     *    !    !     " ( 6-24)              "  :        ,          ,                            . *  6-25    $  ! "  !         .  6-25: # %                   6                   168 .   !    !        "               6-26 ( I), 6-27 ( II)  6-28 ( III). *        #               !           ,          .                 ,      75 kN ( 6-27).                      " # 90 kN ( 6-26  6-28).           !   "         100 kN.  6-26: !     -        !e    (*4)  !     (*1)    I      6-27: !     -        !e    (D1)  !     (*2)    II     6                   169  6-28: !     -        !e    (*5)  !     (*3)    III     !)"! (!  , -&1  6-29:           (-#1 U1 U2 U3 U4 MT6 MT1 MT4 MT5 D1 D2 P P/2 P/2 MT2 750 750 750 750  I  II  III MT3 MT1 MT4 D1 D2 MT2 MT3 (: U – "  ,& –    D –   MT5  I  III  II MT6 6                   170 3    !    !     "     )     !       ( 6-30)  "           ,    ,         (22 %)             "     !  "      .  6-30: !     -           I (U1)    II (U2)   (-#1 *  6-31    $  ! "     -)1,  !          .  6-31: # %                 (-#1 .   !    !        "        -)1      6-32 ( I), 6-33 ( II)  6-34 6                   171 ( III).                 "   ,      " # 80 kN ( 6-27  6-29).        (  )                 " # 100 kN,       ! !     )   ( 6- 33).      122 kN  !   "     ,              #  .  6-32: !     -        !    (*4)  !     (*1)    I   (-#1  6-33: !     -        !    (D1), !     (*2)       (*6)    II   (-#1 6                   172  6-34: !     -        !    (*5)  !     (*3)   III   (-#1 !)"! (!  , -&2  6-35:           (-#2 U1 U2 U3 U4 MT3 MT4 MT5 D1 D2 P P/2 P/2 MT2 MT7 750 750 750 750  I  II  III MT1 MT6 MT1 MT4 D1 D2 MT2 MT3 (: U – "  ,& –    D –   MT5  I  III  II MT7MT6 6                   173 *    !    !     "          !   !     (-)2)             "        : 1)        , 2)                    3)             ( 6-36). ,         !     (48 %),  !         " ,   !  "              .  6-36: !     -           I (U1)    II (U2)   (-#2 *  6-37    $  ! "     -)2    )   ,  !          .  6-37: # %                 (-#2 6                   174 .   !    !        " ,         "        -)2      6-38 ( I), 6-39 ( II)  6-40 ( III).                   ,      " # 110 kN ( 6-38  6-40),       ! !        .                     " # 120 kN ( 6-39).      140 kN  !   "     .  6-38: !     -        !    (*4), !     (*1)       (*6)    I   (-#2  6-39: !     -        !    (D1)  !     (*2)    II   (-#2 6                   175  6-40: !     -        !    (*5), !     (*3)       (*7)    III   (-#2 !)"! (!  , -&3  6-41:           (-#3 - !    !     "         -)3  "             ( 6-42). ,     (Pu = U1 U2 U3 U4 MT1 MT3 MT4 MT5 D1 D2 P P/2 P/2 MT2 MT6 MT8 MT7 750 750 750 750  I  II  III MT1 MT4 D1 D2 MT2 MT3 (: U – "  ,& –    D –   MT5  I  III  II MT8MT6 MT7 6                   176 167 kN)                     )    (-)1  -)2). %  !      ,       "           -)1  -)2   !           .  6-42: !     -           I (U1)    II (U2)  e (-#3 *  6-43    $  ! "     -)3    )   ,  !          .  6-43: # %                e (-#3 6                   177 .   !    !        " ,         "           -)3      6- 44 ( I), 6-45 ( II)  6-46 ( III).                " # 130 kN ( 6-44  6-46),       ! !        . .                 " ,              .  6-44: !     -        !    (*4), !     (*1)       (*6)    I   (-#3  6-45: !     -        !    (D1), !     (*2)       (*7)    II   (-#3 6                   178  6-46: !     -        !    (*5), !     (*3)       (*8)    III   (-#3 !)"! (!  , -1  6-47:           (-$ - !    !     "        (     !              )    ( U1 U2 U3 U4 MT1 MT3 MT4 MT5 D1 D2 P P/2 P/2 MT2 MT6 MT8 MT7 750 750 750 750  I  II  III MT1 MT4 D1 D2 MT2 MT3 (: U – "  ,& –    D –   MT5  I  III  II MT8MT6 MT7 6                   179 6-48). ,                 ! , !                                . ,               ! 82 %          "     !             .  6-48: !     -           I (U1)    II (U2)  e (-$ *  6-31    $  ! "  -)1,  !          .  6-49: # %                e (-$ 6                   180 .   !    !        " ,         "           -(      6-50 ( I), 6-51 ( II)  6-52 ( III). &              " # 150 kN ( 6-50  6-52)       ! !    !      . + o"!        !       182 kN,    (       !   70% ( 6-50  6-52).  6-50: !     -        !    (*4), !     (*1)       (*6)   I   (-$  6-51: !     -        !    (D1), !     (*2)       (*7)    II   (-$ 6                   181  6-52: !     -        !    (*5), !     (*3)       (*8)    III   (-$ !)"! (!  , -1  6-53:           (-&$ - !    !     "        (    " #           ! (failure) ( 6-54). U1 U2 U3 U4 MT1 MT3 MT4 MT5 D1 D2 P P/2 P/2 MT2 MT6 MT8 MT7 750 750 750 750  I  II  III MT1 MT4 D1 D2 MT2 MT3 (: U – "  ,& –    D –   MT5  I  III  II MT8MT6 MT7 6                   182 ,      ! 50 %                   "          .  6-54: !     -           I (U1)    II (U2)   (-&$ *  6-31    $  ! "  -(,  !          .  6-55: # %                 (-&$ .   !    !        " ,         "           -(      6- 6                   183 56 ( I), 6-57 ( II)  6-58 ( III). %  !            ,                    "         "            .  6-56: !     -        !    (*4), !     (*1)       (*6)    I   (-&$  6-57: !     -        !    (D1), !     (*2)       (*7)    II   (-&$ 6                   184  6-58: !     -        !    (*5), !     (*3)       (*8)    III   (-&$ 6.7 "!*  !"!# *)" 6.7.1   !   "  ! !         "              !    ,     .   !  "                   : 1.       "    !      " (*+,   )  2.          " (   ).    #             "     ((   )           ()   ). 6.7.1 "!* )!+ :  "    !                  ", !"         #   "  #       !. '  "        "   ,   ,      ,       !           6                   185   . , "              (LVDT)          !    (MGC plus), !         $  (CATMAN).   ! "     !       ,     ,                "   ( 6-1). - !    !     "                 !    6-59. *                !       :  !       ,  !                  !             .                     ,            !          .  6-59: !          !  !  *  6-60  !          "            .     :  ,   "          *+,    )      !  32 mm      -)2   ! 50 %   "    "     ;  ,   "        *+,    (      (-() !  14 mm   ! 33 %          ; 6                   186  ,   "        (   (-() !  7 mm   ! 67 %      "     .  6-60: / -        !           *  6-61  !                .  6-61: / -      !           *                  *+,    )            -)3   ! 37 %        !+ ( m m )   / % ( k N m ) 6                   187 -)1,   ! 13 %       -)2. *          *+,    (        ! 9 %        *+,    )              . *       *+,                   .            ,       *+,      ! 21 %               . + "!     #   )      (  ,              !   ,   "   )  . 3            )    (-)1, -)2  -)3)  !          (3. = 4 ÷ 5),         (           (3. = 1,5). )   (   (-()    !            "             ( 6-61). 6.7.2 "!* (!".!' ) ,"!,' )! .   !    !        !         !         !    6-62 (      )   6-63 (   ). 3!      #         !         !             " ,                      .    $ !         o  !    ! #       . +      6-62  6-63     :  /         *+,    )                   !         14 %       -)1, 70 %       -)2  86 %       - )3;  /         *+,    (    ( -()                !         100 %        ;  -              (   ( -(),            . 6                   188  6-62: !     -          !    ! !                    6-63: !     -        !    ! !                6.7.3 "!* (!".!' )  )! .   !    !           !         !    6-64 (      )   6-65 (   ).                      )  (    ! !         6                   189    )         -)1  -)2. -                               (         " # 40 %.  6-64: !     -          !                      6-65: !     -        !                  6.7.4 "!* (!".!' ) +) .   !    !        "  !         !    6-66 (      )   6-67 (   ). 6                   190 3!  !       #         "    "     !                 " .            ,         ! #           .  6-66: 0   -          !                   6-67: 0   -        !               6                   191 6.7.5 +"!.! o* (")  , " (',) (  6-68: % !            6-69: 1             6-70: 1         *   6-68  6-70  !  "      (    )     . %  #         !             ! !       !     . &  !  $       ! "    $    !    . ,      !   100 kN,      $      "!     . 6                   192 !)"! (!  , -&1  6-71: !   (-#1  6-72:             6-74:           ( )  6-73:            6-75:       (    ) 6                   193 *   6-72  6-75  !  "       -)1      )     !          . %  #       ,   !                  " ( 6-72).     !           ( 6-73  6-75)     !    " , "!       !   . *          122 kN,    !! $  "    ! "!         . !)"! (!  , -&2  6-76: % !   (-#2        6-77: 2!   #         6-78: 1     6                   194  6-79: *             6-81: 1        !     6-80:              (    )  6-82:             !  !       (     ) *   6-76  6-82  !  "          )     !   !     (      )           "        .               !             ! !  ( 6-78  6-80).     !                   "     #       ( 6-81).     "  !       ( 6-79).        "            !       ( 6-82). *        148 kN, $  "    " ,    ! !        ( 6-81). 6                   195 !)"! (!  , -&3  6-83: 2!         !   (     )  6-85:                6-87:          (    )  6-84: 2!         !   (    )  6-86:                  6-88:      !  !     !       !    6                   196 *   6-83  6-88  !  "          )     !           (      )   !   !     (      )           "        . %  #              "     !     "    !      ( 6-83  6-84). *            (Pu=167 kN),    !   !  #     !        .     "  !       ( 6-79).        "                    !       ( 6-82). .$  "                     !    )  . !)"! (!  , -1  6-89: 1    (-$1         $     *   6-89  6-93  !  "          (     !           (      )   !   !     (      )           "        . %  #    !           "     !     "    !      ( 6-89). *                        (Pu=182 kN),  $  "   !!       ! !   !        . 6                   197  6-90:                6-92: 2!         !         6-91:                   6-93:      !  !     !           !)"! (!  , -1  6-94: $       !     6-95: #    !        !    6                   198  6-96: 2!         !    6-97: #    !        !                 (   )                          !      " (*+,   ). /  !   !"          "  !   "      ( 6-95  6-97)      !     "    !      ( 6-96). %  #     !        *+,  ,    $      . ,      150 kN $  "     !        ,   ! je                . 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 199 7 ɇɍɆȿɊɂЧɄɈ ɆɈȾȿɅɂɊȺЊȿ ɉɊɂɆȿɇɈɆ ɆȿɌɈȾȿ ɄɈɇȺЧɇɂɏ ȿɅȿɆȿɇȺɌȺ ɐɢʂ ɧɭɦɟɪɢɱɤɢɯ ɢɫɬɪɚɠɢɜɚʃɚ ʁɟ ɜɟɪɢɮɢɤɚɰɢʁɚ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨ ɞɨɛɢʁɟɧɢɯ ɪɟɡɭɥɬɚɬɚ ɨɫɧɨɜɧɢɯ ɦɟɪɟɧɢɯ ɩɚɪɚɦɟɬɚɪɚ (ɥɨɤɚɥɧɟ ɢ ɝɥɨɛɚɥɧɟ ɞɟɮɨɪɦɚɰɢʁɟ, ɤɪɭɬɨɫɬɢ, ɧɨɫɢɜɨɫɬɢ), ɧɚ ɢɫɩɢɬɢɜɚɧɢɦ ɝɪɟɞɧɢɦ ɧɨɫɚɱɢɦɚ. Ʉɚɤɨ ɫɭ ɦɨɝɭʄɧɨɫɬɢ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨɝ ɪɚɞɚ ɧɚʁɱɟɲʄɟ ɨɝɪɚɧɢɱɟɧɟ, ʁɟɞɚɧ ɨɞ ɰɢʂɟɜɚ ɛɢɨ ʁɟ ɩɪɨɜɟɪɢɬɢ ɦɨɝɭʄɧɨɫɬ ɦɨɞɟɥɢɪɚʃɚ ȺȻ ɤɨɧɬɢɧɭɚɥɧɢɯ ɝɪɟɞɚ ɨʁɚɱɚɧɢɯ ɎɊɉ ɚɪɦɚɬɭɪɨɦ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ – MKE. Ʉɨɪɢɲʄɟɧ ʁɟ, ɭ ɧɚɭɱɧɟ ɫɜɪɯɟ ɱɟɫɬɨ ɩɪɢɦɟʃɢɜɚɧ ɫɨɮɬɜɟɪ Ⱥɧɫɢɫ (ANSВS), ɭ ɤɨɦɟ ɫɭ ɦɨɞɟɥɢɪɚɧɢ ɤɨɧɬɢɧɭɚɥɧɢ ɝɪɟɞɧɢ ɧɨɫɚɱɢ ɢɫɩɢɬɢɜɚɧɢ ɭ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨɦ ɞɟɥɭ ɪɚɞɚ. ɋɩɪɨɜɟɞɟɧɚ ʁɟ ɧɟɥɢɧɟɚɪɧɚ ɚɧɚɥɢɡɚ ɢ ɞɚɬɨ ʁɟ ɭɩɨɪɟђɟʃɟ ɞɨɛɢʁɟɧɢɯ ɪɟɡɭɥɬɚɬɚ ɫɚ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɦ ɪɟɡɭɥɬɚɬɢɦɚ ɡɚ ɪɚɡɥɢɱɢɬɟ ɫɬɟɩɟɧɟ ɨɩɬɟɪɟʄɟʃɚ. 7.1 Ɉɩɲɬɟ ɧɚɩɨɦɟɧɟ ɉɨɱɟɰɢ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ – ɆКȿ (FТЧТtО ElОmОЧt MОtСoН – FEM) ɜɟɡɭʁɭ ɫɟ ɡɚ 1940-ɬɟ ɚɥɢ ɩɪɜɚ ɩɪɚɤɬɢɱɧɚ ɩɪɢɦɟɧɚ ɡɚ ɦɨɞɟɥɢɪɚʃɟ ɛɟɬɨɧɫɤɢɯ ɤɨɧɫɬɪɭɤɰɢʁɚ ʁɚɜʂɚ ɫɟ ɞɜɚɞɟɫɟɬɚɤ ɝɨɞɢɧɚ ɤɚɫɧɢʁɟ, ɤɚɞɚ ʁɟ ɩɪɨɮɟɫɨɪ Ɋɚʁɦɨɧɞ Кɥɨ (Raymond Clough) ɫɚ Ȼɟɪɤɥɢ ɭɧɢɜɟɪɡɢɬɟɬɚ (UC Berkly) ɢɡɜɪɲɢɨ ɧɭɦɟɪɢɱɤɭ ɚɧɚɥɢɡɭ ɛɟɬɨɧɫɤɟ ɛɪɚɧɟ ɩɪɢɤɚɡɚɧɟ ɧɚ ɋɥɢɰɢ 7-1 (Barrett, 2013). 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 200 ɋɥɢɤɚ 7-1: ɉɪɜɚ ɦɪɟɠɚ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ ɤɨɪɢɲʄɟɧɚ ɩɪɢ ɚɧɚɥɢɡɢ ɛɟɬɨɧɫɤɟ ɛɪɚɧɟ ɦɟɬɨɞɨɦ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ (Barrett, 2013) ɂɚɤɨ ʁɟ ɨɞ ɬɚɞɚ ɩɪɨɲɥɨ ɜɢɲɟ ɨɞ 50 ɝɨɞɢɧɚ ʁɨɲ ɭɜɟɤ ɧɟ ɩɨɫɬɨʁɢ ʁɟɞɢɧɫɬɜɟɧɨ ɦɢɲʂɟʃɟ ɨ ɧɚʁɛɨʂɟɦ ɧɚɱɢɧɭ ɦɨɞɟɥɢɪɚʃɚ ɛɟɬɨɧɫɤɢɯ ɤɨɧɫɬɪɭɤɰɢʁɚ ɤɨɧɚɱɧɢɦ ɟɥɟɦɟɧɬɢɦɚ. Ʉɚɤɨ ʁɟ ɛɟɬɨɧ ʁɟɞɚɧ ɨɞ ɧɚʁɤɨɦɩɥɢɤɨɜɚɧɢʁɢɯ ɦɚɬɟɪɢʁɚɥɚ ɡɚ ɦɨɞɟɥɢɪɚʃɟ, ɩɪɟɩɨɪɭɤɚ ɜɨɞɟʄɢɯ ɢɫɬɪɚɠɢɜɚɱɚ ɭ ɨɜɨʁ ɨɛɥɚɫɬɢ ʁɟ ɞɚ ɫɟ ɦɚɬɟɪɢʁɚɥɧɢ ɦɨɞɟɥ ɢɡɚɛɟɪɟ ɭ ɡɚɜɢɫɧɨɫɬɢ ɨɞ ɰɢʂɚ ɚɧɚɥɢɡɟ. ɇɚʁɱɟɲʄɟ ɦɟɬɨɞɟ ɡɚ ɚɧɚɥɢɡɭ ɛɟɬɨɧɫɤɢɯ ɤɨɧɫɬɪɭɤɰɢʁɚ ɤɨɧɚɱɧɢɦ ɟɥɟɦɟɧɬɢɦɚ ɫɭ (Barrett, 2013): ɥɢɧɟɚɪɧɨ ɦɨɞɟɥɢɪɚʃɟ ɛɟɬɨɧɚ ɩɪɢ ɩɪɨʁɟɤɬɨɜɚʃɭ ɤɨɧɫɬɪɭɤɰɢʁɚ ɢ ɧɟɥɢɧɟɚɪɧɨ ɦɨɞɟɥɢɪɚʃɟ ɛɟɬɨɧɚ. 7.1.1 Ʌɢɧɟɚɪɧɨ ɦɨɞɟɥɢɪɚʃɟ ɛɟɬɨɧɚ ɩɪɢ ɩɪɨјɟɤɬɨɜɚʃɭ ɤɨɧɫɬɪɭɤɰɢјɚ Ʉɚɞɚ ʁɟ ɰɢʂ ɦɨɞɟɥɢɪɚʃɚ ȺȻ ɟɥɟɦɟɧɚɬɚ ɩɪɨʁɟɤɬɨɜɚʃɟ ɤɨɧɫɬɪɭɤɰɢʁɚ, ɨɛɢɱɧɨ ɫɟ ɩɪɢɦɟʃɭʁɟ ɥɢɧɟɚɪɧɨ-ɟɥɚɫɬɢɱɧɢ ɦɨɞɟɥ, ɩɪɢ ɱɟɦɭ ɫɟ ɦɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ ɡɚ ɛɟɬɨɧ ɧɨɪɦɚɥɧɟ ɱɜɪɫɬɨʄɟ ɦɨɠɟ ɩɪɢɛɥɢɠɧɨ ɨɞɪɟɞɢɬɢ ɩɪɟɦɚ ɩɪɟɩɨɪɭɰɢ ɚɦɟɪɢɱɤɨɝ ɢɧɫɬɢɬɭɬɚ ɡɚ ɛɟɬɨɧ (ACI, 1999): cc f4730E  (7-1) ɝɞɟ ʁɟ: Ec – ɦɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ ɛɟɬɨɧɚ, fc΄ – ɱɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ. ɍ ɫɥɭɱɚʁɭ ɥɢɧɟɚɪɧɨɝ ɦɨɞɟɥɢɪɚʃɚ ɛɟɬɨɧɚ, ɰɢʂ ɚɧɚɥɢɡɟ ɧɚʁɱɟɲʄɟ ɧɢʁɟ ɞɟɬɚʂɧɚ ɚɧɚɥɢɡɚ ɧɚɩɨɧɚ ɜɟʄ ɩɪɨɪɚɱɭɧ ɫɢɥɚ ɭ ɩɪɟɫɟɰɢɦɚ. Ʉɨɪɢɫɬɟʄɢ ɫɪɚɱɭɧɚɬɟ ɫɢɥɟ ɭ ɩɪɟɫɟɰɢɦɚ ɨɞɪɟђɭʁɟ ɫɟ ɩɨɬɪɟɛɧɚ ɤɨɥɢɱɢɧɚ ɱɟɥɢɱɧɟ ɚɪɦɚɬɭɪɟ ɤɨʁɚ ʄɟ ɧɨɫɢɬɢ ɫɢɥɭ ɡɚɬɟɡɚʃɚ, ɩɪɢ 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 201 ɱɟɦɭ ɬɪɟɛɚ ɨɛɟɡɛɟɞɢɬɢ ɞɚ ɛɟɬɨɧ ɦɨɠɟ ɧɨɫɢɬɢ ɫɢɥɭ ɩɪɢɬɢɫɤɚ ɭ ɩɪɟɫɟɤɭ. Ʉɚɤɨ ʁɟ ɩɨɜɪɲɢɧɚ ɱɟɥɢɱɧɟ ɚɪɦɚɬɭɪɟ ɡɧɚɬɧɨ ɦɚʃɚ ɨɞ ɩɨɜɪɲɢɧɟ ɩɨɩɪɟɱɧɨɝ ɩɪɟɫɟɤɚ ɛɟɬɨɧɚ, ɧɟ ɩɨɫɬɨʁɢ ɩɨɬɪɟɛɚ ɡɚ ʃɟɧɢɦ ɩɨɫɟɛɧɢɦ ɦɨɞɟɥɢɪɚʃɟɦ. 7.1.2 ɇɟɥɢɧɟɚɪɧɨ ɦɨɞɟɥɢɪɚʃɟ ɤɨɧɫɬɪɭɤɰɢјɚ Ⱥɤɨ ɫɭ ɧɚɩɨɧɢ ɢ ɞɟɮɨɪɦɚɰɢʁɟ ɭ ɛɟɬɨɧɭ ɦɚɥɢ, ɨɧ ɫɟ ɩɨɧɚɲɚ ɤɚɨ ɥɢɧɟɚɪɧɨ ɟɥɚɫɬɢɱɚɧ ɦɚɬɟɪɢʁɚɥ. Ɇɟђɭɬɢɦ, ɤɚɞɚ ɧɚɩɨɧ ɧɚ ɡɚɬɟɝɧɭɬɨʁ ɢɜɢɰɢ ɛɟɬɨɧɫɤɨɝ ɩɪɟɫɟɤɚ ɞɨɫɬɢɝɧɟ ɜɪɟɞɧɨɫɬ ɞɨɡɜɨʂɟɧɨɝ ɧɚɩɨɧɚ ɩɪɢ ɡɚɬɟɡɚʃɭ, ɛɟɬɨɧ ɩɭɰɚ ɭɫɥɟɞ ɱɟɝɚ ɫɟ ɫɦɚʃɭʁɟ ɤɪɭɬɨɫɬ ɩɪɟɫɟɤɚ. ɋɦɚʃɟʃɟ ɤɪɭɬɨɫɬɢ ɩɪɨɭɡɪɨɤɭʁɟ „ɦɟɤɲɢ“ ɨɞɝɨɜɨɪ ɤɨɧɫɬɪɭɤɰɢʁɟ ɩɪɢ ɞɚʂɟɦ ɩɨɜɟʄɚʃɭ ɨɩɬɟɪɟʄɟʃɚ, ɭɫɥɟɞ ɱɟɝɚ ɞɨɥɚɡɢ ɞɨ ɦɪɜʂɟʃɚ ɛɟɬɨɧɚ ɭ ɩɪɢɬɢɫɧɭɬɨɦ ɞɟɥɭ ɛɟɬɨɧɫɤɨɝ ɩɪɟɫɟɤɚ. ɋɢɦɭɥɢɪɚʃɟ ɨɜɨɝ ɤɨɦɩɥɟɤɫɧɨɝ ɩɨɧɚɲɚʃɚ ɫɟ ɧɚʁɱɟɲʄɟ ɫɩɪɨɜɨɞɢ ɭ ɫɥɭɱɚʁɭ ɨɞɪɟђɢɜɚʃɚ ɝɪɚɧɢɱɧɨɝ ɨɩɬɟɪɟʄɟʃɚ, ɚɧɚɥɢɡɟ ɭɬɢɰɚʁɚ ɡɟɦʂɨɬɪɟɫɚ ɢɥɢ ɧɟɤɢɯ ɞɪɭɝɢɯ ɢɡɧɟɧɚɞɧɢɯ ɭɬɢɰɚʁɚ. Ⱦɚ ɛɢ ɫɟ ɩɪɢɤɚɡɚɥɨ ɫɬɜɚɪɧɨ ɩɨɧɚɲɚʃɟ ɛɟɬɨɧɚ, ɦɨɠɟ ɫɟ ɩɪɢɦɟɧɢɬɢ ɦɢɤɪɨɤɨɧɫɬɪɭɤɬɢɜɧɨ ɦɨɞɟɥɢɪɚʃɟ, ɲɬɨ ɧɢʁɟ ɩɪɚɤɬɢɱɧɨ ɡɚ ɚɧɚɥɢɡɭ ɪɟɚɥɧɢɯ ɝɪɚђɟɜɢɧɫɤɢɯ ɤɨɧɫɬɪɭɤɰɢʁɚ ɭ ɩɭɧɨʁ ɜɟɥɢɱɢɧɢ. Ɂɛɨɝ ɬɨɝɚ ɫɟ ɩɪɟɩɨɪɭɱɭʁɟ ɞɪɭɝɚɱɢʁɢ, ɮɟɧɨɦɟɧɨɥɨɲɤɢ ɩɪɢɫɬɭɩ ɛɚɡɢɪɚɧ ɧɚ ɧɟɥɢɧɟɚɪɧɨɦ ɨɞɧɨɫɭ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɟ ɢ ɧɟɥɢɧɟɚɪɧɨʁ ɩɨɜɪɲɢ ɥɨɦɚ. ɂɡɚɡɨɜ ɤɨʁɢ ɫɟ ʁɚɜʂɚ ɩɪɢ ɦɨɞɟɥɢɪɚʃɭ ɧɟ ɱɢɧɢ ɫɚɦɨ ɤɪɟɢɪɚʃɟ ɦɨɞɟɥɚ ɤɨʁɢ ɚɞɟɤɜɚɬɧɨ ɩɪɟɞɫɬɚɜʂɚ ɤɨɧɫɬɪɭɤɰɢʁɭ, ɜɟʄ ɢ ɦɨɞɟɥɚ ɤɨʁɢ ʁɟ ɩɨɭɡɞɚɧ ɢ ɟɮɢɤɚɫɚɧ, ɨɛɡɢɪɨɦ ɞɚ ɫɭ ɩɨʁɚɜɚ ɩɪɫɥɢɧɚ, ɦɪɜʂɟʃɟ ɢ ɨɦɟɤɲɚɜɚʃɟ ɛɟɬɨɧɚ ɭ ɩɨɬɩɭɧɨɫɬɢ ɧɟɥɢɧɟɚɪɧɟ ɤɚɪɚɤɬɟɪɢɫɬɢɤɟ (Barret, 2013). ɉɪɢɫɬɭɩ ɛɚɡɢɪɚɧ ɧɚ ɦɨɞɟɥɭ „ɪɚɡɦɚɡɚɧɟ“ ɩɪɫɥɢɧɟ ɤɨʁɢ ʁɟ ɩɪɜɢ ɩɪɟɞɫɬɚɜɢɨ Ɋɚɲɢɞ 1968. ɝɨɞɢɧɟ (Rashid, 1968), ʁɨɲ ɭɜɟɤ ʁɟ ʁɟɞɚɧ ɨɞ ɧɚʁɛɨʂɢɯ. Ɏɨɪɦɢɪɚʃɟ ɩɪɫɥɢɧɚ ɫɟ ɫɢɦɭɥɢɪɚ ɦɟʃɚʃɟɦ ɢɡɨɬɪɨɩɧɟ ɦɚɬɪɢɰɟ ɤɪɭɬɨɫɬɢ ɟɥɟɦɟɧɬɚ ɨɪɬɨɬɪɨɩɧɨɦ ɦɚɬɪɢɰɨɦ ɩɨɫɥɟ ɮɨɪɦɢɪɚʃɚ ɩɪɫɥɢɧɚ. ȼɪɟɞɧɨɫɬ ɧɚɩɨɧɚ ɭɩɪɚɜɧɢɯ ɧɚ ɩɪɚɜɚɰ ɩɪɫɥɢɧɟ ɨɩɚɞɚ ɫɜɟ ɞɨɤ ɧɟ ɞɨђɟ ɞɨ ɧɭɥɟ. Јɟɞɧɨɦ ɤɚɞɚ ɫɟ ɩɪɫɥɢɧɟ ɮɨɪɦɢɪɚʁɭ, ɨɧɟ ɫɟ ɦɨɝɭ ɨɬɜɚɪɚɬɢ ɢ ɡɚɬɜɚɪɚɬɢ, ɚɥɢ ʃɢɯɨɜ ɩɪɚɜɚɰ ɨɫɬɚʁɟ ɧɟɩɪɨɦɟʃɟɧ. Ⱥɪɦɚɬɭɪɧɢ ɟɥɟɦɟɧɬ ɫɟ ɦɨɠɟ ɢɥɢ „ɪɚɡɦɚɡɚɬɢ“ ɩɪɟɤɨ ɛɟɬɨɧɫɤɨɝ ɟɥɟɦɟɧɟɬɚ, ɤɚɨ ɲɬɨ ʁɟ ɋɨɥɢɞ 65 (Solid 65) ɟɥɟɦɟɧɬ ɭ Ⱥɧɫɢɫɭ, ɢɥɢ ɫɟ ɦɨɞɟɥɢɪɚɬɢ ɫɩɨʂɚ, ɩɪɢ ɱɟɦɭ ɢɦɚ ɡɚʁɟɞɧɢɱɤɟ ɱɜɨɪɨɜɟ ɫɚ ɛɟɬɨɧɫɤɢɦ ɟɥɟɦɟɧɬɨɦ. Ɉɜɢɦ ɧɚɱɢɧɨɦ ɦɨɞɟɥɢɪɚʃɚ ɦɨɝɭ ɫɟ ɚɧɚɥɢɡɢɪɚɬɢ ɩɨʁɚɜɚ ɥɨɤɚɥɧɢɯ ɩɪɫɥɢɧɚ, ɞɟɥɨɜɚʃɟ ɭɞɚɪɧɨɝ ɨɩɬɟɪɟʄɟʃɚ, ɤɚɨ ɢ ɚɧɚɥɢɡɚ ɩɪɨɝɪɟɫɢɜɧɨɝ ɥɨɦɚ ɤɨɞ ɪɟɚɥɧɢɯ ɝɪɚђɟɜɢɧɫɤɢɯ ɤɨɧɫɬɪɭɤɰɢʁɚ. ɍ ɫɥɭɱɚʁɟɜɢɦɚ ɤɚɞɚ ɫɟ ɤɨɪɢɫɬɢ ɦɨɞɟɥ „ɪɚɡɦɚɡɚɧɟ“ ɩɪɫɥɢɧɟ ɧɟɨɩɯɨɞɧɨ ʁɟ ɢɡɜɪɲɢɬɢ ɚɧɚɥɢɡɭ ɤɨɧɜɟɪɝɟɧɰɢʁɟ ɪɟɡɭɥɬɚɬɚ. ɉɨɪɟɞ ɬɨɝɚ, ɩɪɟɩɨɪɭɱɭʁɟ ɫɟ ɢ ɟɤɫɩɥɢɰɢɬɧɢʁɢ ɩɪɢɫɬɭɩ ɤɨɞ ɡɚɞɚɜɚʃɚ ɨɩɬɟɪɟʄɟʃɚ ɭ ɨɜɚɤɜɢɦ, ɟɤɫɬɪɟɦɧɨ ɧɟɥɢɧɟɚɪɧɢɦ ɫɥɭɱɚʁɟɜɢɦɚ, ɝɞɟ ɜɟɥɢɤɢ 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 202 ɛɪɨʁ ɦɟђɭɤɨɪɚɤɚ ɭ ɪɟɲɚɜɚʃɭ ʁɟɞɧɚɱɢɧɚ ɪɚɜɧɨɬɟɠɟ, ɡɚʁɟɞɧɨ ɫɚ ɭɫɥɨɜɢɦɚ ɤɨɧɜɟɪɝɟɧɰɢʁɟ ɛɚɡɢɪɚɧɢɦ ɧɚ ɩɨɦɟɪɚʃɢɦɚ, ɦɨɠɟ ɞɨɜɟɫɬɢ ɞɨ ɟɮɢɤɚɫɧɢʁɟ ɤɨɧɜɟɪɝɟɧɰɢʁɟ ɩɪɨɛɥɟɦɚ. ɉɨɦɟɧɭɬɢ ɩɪɨɝɪɚɦ Ⱥɧɫɢɫ ʁɟ ɫɜɟɬɫɤɢ ɩɪɢɡɧɚɬ ɫɨɮɬɜɟɪ ɡɚ ɚɧɚɥɢɡɭ ɤɨɧɫɬɪɭɤɰɢʁɚ, ɤɨʁɢ ɫɟ ɜɪɥɨ ɱɟɫɬɨ ɤɨɪɢɫɬɢ ɭ ɧɚɭɱɧɟ ɫɜɪɯɟ. Ɉɧ ɫɟ ɤɨɪɢɫɬɢ ɤɚɤɨ ɡɚ ɫɬɚɬɢɱɤɭ, ɬɚɤɨ ɢ ɡɚ ɞɢɧɚɦɢɱɤɭ ɥɢɧɟɚɪɧɭ ɢɥɢ ɧɟɥɢɧɟɚɪɧɭ ɚɧɚɥɢɡɭ ɤɨɧɫɬɪɭɤɰɢʁɚ. Ⱥɧɚɥɢɡɚ ɫɟ ɫɚɫɬɨʁɢ ɭ ɞɢɫɤɪɟɬɢɡɚɰɢʁɢ ɤɨɧɫɬɪɭɤɰɢʁɟ ɧɚ ɟɥɟɦɟɧɬɚɪɧɟ ɞɟɥɨɜɟ ɡɚ ɤɨʁɟ ɫɭ ɩɨɡɧɚɬɟ ɦɟɯɚɧɢɱɤɟ ɢ ɮɢɡɢɱɤɟ ɤɚɪɚɤɬɟɪɢɫɬɢɤɟ. ɍ ɦɧɨɝɢɦ ɢɫɬɪɚɠɢɜɚʃɢɦɚ ɭ ɤɨʁɢɦɚ ɫɭ ɚɧɚɥɢɡɢɪɚɧɢ ȺȻ ɝɪɟɞɧɢ ɧɨɫɚɱɢ ɨʁɚɱɚɧɢ ɎɊɉ ɚɪɦɚɬɭɪɨɦ, ɤɨɪɢɲʄɟɧ ʁɟ ɫɨɮɬɜɟɪ Ⱥɧɫɢɫ, ɚ ɞɨɛɢʁɟɧɢ ɪɟɡɭɥɬɚɬɢ ɫɭ ɫɟ ɞɨɛɪɨ ɫɥɚɝɚɥɢ ɫɚ ɪɟɡɭɥɬɚɬɢɦɚ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɯ ɢɫɩɢɬɢɜɚʃɚ (Ɋɚɧɤɨɜɢʄ, 2010). ɋɥɢɤɚ 7-2: Ɉɪɢɝɢɧɚɥɧɢ ɞɢʁɚɝɪɚɦ ɦɟɪɟɧɢɯ ɢ ɪɚɱɭɧɫɤɢɯ ɜɪɟɞɧɨɫɬɢ ɨɩɬɟɪɟʄɟʃɟ-ɭɝɢɛ ɡɚ ɝɪɟɞɧɢ ɧɨɫɚɱ (Ɋɚɧɤɨɜɢʄ, 2010) 7.2 Ɇɨɞɟɥɢ ɦɚɬɟɪɢјɚɥɚ ɭɫɜɨјɟɧɢ ɭ ɚɧɚɥɢɡɢ 7.2.1 Ȼɟɬɨɧ Ȼɟɬɨɧ ʁɟ ɤɜɚɡɢ-ɤɪɬ ɦɚɬɟɪɢʁɚɥ, ɤɨʁɢ ɫɟ ɪɚɡɥɢɱɢɬɨ ɩɨɧɚɲɚ ɩɪɢ ɩɪɢɬɢɫɤɭ ɢ ɡɚɬɟɡɚʃɭ, ɩɚ ʁɟ ɬɚɤɨ ɱɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɡɚɬɟɡɚʃɭ (fct) ɨɬɩɪɢɥɢɤɟ 8-15 % ɨɞ ɱɜɪɫɬɨʄɟ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ (П΄c) (Shah et al., 1995.). ɇɚ ɋɥɢɰɢ 7-3 ʁɟ ɩɪɢɤɚɡɚɧ ɞɢʁɚɝɪɚɦ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɟ ɩɪɢ ɚɤɫɢʁɚɥɧɨɦ ɧɚɩɪɟɡɚʃɭ ɛɟɬɨɧɚ (Bangash, 1989). ɍɝɢɛ (mm) ȿɤɫɩɟɪɢɦɟɧɬ ɆɄȿ Ɉɩ ɬɟɪ ɟʄɟ ʃɟ (Н КN ) 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 203 Ⱦɢʁɚɝɪɚɦ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɟ ɡɚ ɚɤɫɢʁɚɥɧɨ ɩɪɢɬɢɫɧɭɬ ɛɟɬɨɧ ʁɟ ɥɢɧɟɚɪɚɧ ɞɨ ɩɪɢɛɥɢɠɧɨ 30 % ɨɞ ɱɜɪɫɬɨʄɟ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ, ɩɨɫɥɟ ɱɟɝɚ ʁɟ ɡɚɜɢɫɧɨɫɬ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɟ ɧɟɥɢɧɟɚɪɧɚ. ɉɨɫɥɟ ɞɨɫɬɢɡɚʃɚ ɱɜɪɫɬɨʄɟ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ, ɤɪɢɜɚ ɨɩɚɞɚ (ɨɛɥɚɫɬ ɨɦɟɤɲɚɜɚʃɚ) ɫɜɟ ɞɨ ɟɜɟɧɬɭɚɥɧɨɝ ɥɨɦɚ ɦɪɜʂɟʃɟɦ ɤɨʁɢ ɫɟ ʁɚɜʂɚ ɩɪɢ ɝɪɚɧɢɱɧɨʁ ɞɢɥɚɬɚɰɢʁɢ (εcu). ɉɪɢ ɡɚɬɟɡɚʃɭ, ɞɢʁɚɝɪɚɦ ɡɚɜɢɫɧɨɫɬɢ ɡɚ ɛɟɬɨɧ ʁɟ ɩɪɢɛɥɢɠɧɨ ɥɢɧɟɚɪɚɧ ɫɜɟ ɞɨ ɞɨɫɬɢɡɚʃɚ ɱɜɪɫɬɨʄɟ ɛɟɬɨɧɚ ɩɪɢ ɡɚɬɟɡɚʃɭ. ɉɨɫɥɟ ɞɨɫɬɢɡɚʃɚ ɱɜɪɫɬɨʄɟ ɛɟɬɨɧɚ ɩɪɢ ɡɚɬɟɡɚʃɭ, ʁɚɜʂɚ ɫɟ ɩɭɰɚʃɟ ɛɟɬɨɧɚ ɢ ɨɩɚɞɚʃɟ ɱɜɪɫɬɨʄО ɩɨɫɬɟɩɟɧɨ ɞɨ ɧɭɥɟ (BКЧРКsС, 1989). ɋɥɢɤɚ 7-3: Ⱦɢʁɚɝɪɚɦ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɟ ɩɪɢ ɚɤɫɢʁɚɥɧɨɦ ɧɚɩɪɟɡɚʃɭ ɛɟɬɨɧɚ (Bangash, 1989) ɉɨɬɪɟɛɧɢ ɭɥɚɡɧɢ ɩɨɞɚɰɢ ɡɚ ɦɨɞɟɥɢɪɚʃɟ ɛɟɬɨɧɚ ɭ Ⱥɧɫɢɫɭ ɫɭ:  ɦɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ ɛɟɬɨɧɚ (Ec),  ɱɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ (fc΄),  ɱɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɡɚɬɟɡɚʃɭ (fct),  ɉɨɚɫɨɧɨɜ ɤɨɟɮɢɰɢʁɟɧɬ (ν),  ɤɨɟɮɢɰɢʁɟɧɬ ɩɪɟɧɨɫɚ ɧɚɩɨɧɚ ɫɦɢɰɚʃɚ (βt),  ɡɚɜɢɫɧɨɫɬ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɟ ɡɚ ɛɟɬɨɧ ɩɪɢ ɚɤɫɢʁɚɥɧɨɦ ɩɪɢɬɢɫɤɭ. ɇɚ ɨɫɧɨɜɭ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɯ ɪɟɡɭɥɬɚɬɚ ɞɨɛɢʁɟɧɢɯ ɫɨɩɫɬɜɟɧɢɦ ɥɚɛɨɪɚɬɨɪɢʁɫɤɢɦ ɢɫɩɢɬɢɜɚʃɟɦ ɧɚ ɟɩɪɭɜɟɬɚɦɚ ɭɫɜɨʁɟɧɟ ɫɭ ɫɥɟɞɟʄɟ ɜɪɟɞɧɨɫɬɢ ɩɨɬɪɟɛɧɢɯ ɩɚɪɚɦɟɬɚɪɚ. Ɇɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ: Ec = 25200 MPa; ɑɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ: fc΄ = 32,3 MPa; ɑɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɡɚɬɟɡɚʃɭ: fct = 3,40 MPa; ɉɨɚɫɨɧɨɜ ɤɨɟɮɢɰɢʁɟɧɬ: ν = 0,20. Ɂɚɬɟɡɚʃɟ ɱɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ ɨɦɟɤɲɚɜɚʃɟ ɉɪɢɬɢɫɚɤ cu cf  ctf 1c    cE 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 204 Ʉɨɟɮɢɰɢʁɟɧɬ ɩɪɟɧɨɫɚ ɧɚɩɨɧɚ ɫɦɢɰɚʃɚ (βt) ɩɪɟɞɫɬɚɜʂɚ ɫɬɚʃɟ ɩɨɜɪɲɢɧɟ ɩɪɫɥɢɧɟ. ȼɪɟɞɧɨɫɬ ɨɜɨɝ ɤɨɟɮɢɰɢʁɟɧɬɚ ʁɟ ɢɡɦɟђɭ 0 ɢ 1, ɝɞɟ 0 ɩɪɟɞɫɬɚɜʂɚ ɝɥɚɬɤɭ ɩɪɫɥɢɧɭ (ɤɨɦɩɥɟɬɚɧ ɝɭɛɢɬɚɤ ɩɪɟɧɨɫɚ ɧɚɩɨɧɚ ɫɦɢɰɚʃɚ), ɞɨɤ 1 ɩɪɟɞɫɬɚɜʂɚ ɝɪɭɛɭ ɩɪɫɥɢɧɭ (ɛɟɡ ɝɭɛɢɬɤɚ ɩɪɟɧɨɫɚ ɧɚɩɨɧɚ ɫɦɢɰɚʃɚ). ȼɪɟɞɧɨɫɬ βt, ɤɨɪɢɲʄɟɧɚ ɭ ɜɟʄɢɧɢ ɧɭɦɟɪɢɱɤɢɯ ɢɫɬɪɚɠɢɜɚʃɚ ɩɨɧɚɲɚʃɚ ȺȻ ɤɨɧɫɬɪɭɤɰɢʁɚ, ɜɚɪɢɪɚ ɢɡɦɟђɭ 0,05 ɢ 0,25 (Bangash, 1989; Huyse et al., 1994; Hemmaty, 1998). ɇɨɜɢʁɟ ɚɧɚɥɢɡɟ ɭɪɚђɟɧɟ ɫɚ ɪɚɡɥɢɱɢɬɢɦ ɜɪɟɞɧɨɫɬɢɦɚ ɤɨɟɮɢɰɢʁɟɧɬɚ ɩɪɟɧɨɫɚ ɧɚɩɨɧɚ ɫɦɢɰɚʃɚ ɭ ɨɜɢɦ ɝɪɚɧɢɰɚɦɚ, ɭɤɚɡɭʁɭ ɧɚ ɩɪɨɛɥɟɦ ɤɨɧɜɟɪɝɟɧɰɢʁɟ ɩɪɢ ɧɢɫɤɢɦ ɨɩɬɟɪɟʄɟʃɢɦɚ ɫɚ ɤɨɟɮɢɰɢʁɟɧɬɨɦ ɩɪɟɧɨɫɚ ɧɚɩɨɧɚ ɫɦɢɰɚʃɚ ɦɚʃɢɦ ɨɞ 0,20. Ɂɛɨɝ ɬɨɝɚ ʁɟ ɭ ɨɜɨɦ ɢɫɬɪɚɠɢɜɚʃɭ ɭɫɜɨʁɟɧ ɤɨɟɮɢɰɢʁɟɧɬ ɩɪɟɧɨɫɚ ɧɚɩɨɧɚ ɫɦɢɰɚʃɚ ɨɞ 0,20. Ɂɚɜɢɫɧɨɫɬ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢјɟ ɡɚ ɛɟɬɨɧ ɩɪɢ ɚɤɫɢјɚɥɧɨɦ ɩɪɢɬɢɫɤɭ Ɋɚɞɢ ɤɨɧɫɬɪɭɤɰɢʁɟ ɤɪɢɜɟ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɟ ɩɪɢ ɚɤɫɢʁɚɥɧɨɦ ɩɪɢɬɢɫɤɭ ɤɨʁɢ ʁɟ ɧɟɨɩɯɨɞɚɧ ɩɪɢ ɦɨɞɟɥɢɪɚʃɭ ɛɟɬɨɧɚ ɭ ɩɪɨɝɪɚɦɭ Ⱥɧɫɢɫ ɤɨɪɢɲʄɟɧɢ ɫɭ ɢɡɪɚɡɢ (7-2) ɢ (7-3) (DОsКвТ КЧН KrТsСЧКЧ, 1964), ɤɚɨ ɢ ɢɡɪɚɡ (7-4) (Gere and Timoshenko, 1997): 2 1c c cc c )(1 E    , (7-2) c c 1c E f2  , (7-3) c c cE   , (7-4) ɝɞɟ ʁɟ: Ec – ɦɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ ɛɟɬɨɧɚ, fc' –ɱɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ, εc – ɞɢɥɚɬɚɰɢʁɚ ɭ ɛɟɬɨɧɭ, εcu – ɝɪɚɧɢɱɧɚ ɞɢɥɚɬɚɰɢʁɚ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ (ɞɢɥɚɬɚɰɢʁɚ ɦɪɜʂɟʃɚ ɛɟɬɨɧɚ), εc1 – ɞɢɥɚɬɚɰɢʁɚ ɭ ɛɟɬɨɧɭ ɤɨʁɚ ɨɞɝɨɜɚɪɚ ɱɜɪɫɬɨʄɢ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ fc', σc – ɧɚɩɨɧ ɭ ɛɟɬɨɧɭ. ɇɚ ɋɥɢɰɢ 7-4 ɩɪɢɤɚɡɚɧ ʁɟ ɩɨʁɟɞɧɨɫɬɚɜʂɟɧɢ (ɦɭɥɬɢɥɢɧɟɚɪɧɢ) ɞɢʁɚɝɪɚɦ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɟ ɩɪɢ ɚɤɫɢʁɚɥɧɨɦ ɩɪɢɬɢɫɤɭ ɤɨʁɢ ʁɟ ɤɨɪɢɲʄɟɧ ɭ ɪɚɞɭ. 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 205 ɉɨʁɟɞɧɨɫɬɚɜʂɟɧɢ ɞɢʁɚɝɪɚɦ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɚ ɤɨɧɫɬɪɭɢɫɚɧ ʁɟ ɫɚ ɲɟɫɬ ɬɚɱɚɤɚ ɤɨʁɟ ɫɭ ɩɨɜɟɡɚɧɟ ɩɪɚɜɢɦ ɥɢɧɢʁɚɦɚ. Ⱦɢʁɚɝɪɚɦ ɩɨɱɢʃɟ ɨɞ ɧɭɥɬɨɝ ɫɬɚʃɚ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɚ. Ɍɚɱɤɚ 1 ɨɞɝɨɜɚɪɚ ɜɪɟɞɧɨɫɬɢ ɧɚɩɨɧɚ ɭ ɛɟɬɨɧɭ (σc = 0,3fc΄) ɢ ɫɪɚɱɭɧɚɬɚ ʁɟ ɩɪɟɦɚ ɨɞɧɨɫɭ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɚ ɡɚ ɛɟɬɨɧ ɭ ɟɥɚɫɬɢɱɧɨʁ ɨɛɥɚɫɬɢ (7-4). Ɍɚɱɤɟ 2, 3 ɢ 4 ɫɭ ɞɨɛɢʁɟɧɟ ɧɚ ɨɫɧɨɜɭ ɢɡɪɚɡɚ (7-2), ɩɪɢ ɱɟɦɭ ʁɟ ɞɢɥɚɬɚɰɢʁɚ (εc1) ɫɪɚɱɭɧɚɬК ɢɡ ɢɡɪɚɡɚ (7-3). Ɍɚɱɤɚ 5 ɨɞɝɨɜɚɪɚ ɞɢɥɚɬɚɰɢʁɢ (εc1) ɢ ɱɜɪɫɬɨʄɢ ɩɪɢ ɩɪɢɬɢɫɤɭ ɛɟɬɨɧɚ (fc΄). ɉɨɫɥɟ ɞɨɫɬɢɡɚʃɚ ɱɜɪɫɬɨʄɟ ɩɪɢ ɩɪɢɬɢɫɤɭ ɩɪɟɬɩɨɫɬɚɜʂɟɧɨ ʁɟ ɢɞɟɚɥɧɨ ɩɥɚɫɬɢɱɧɨ ɩɨɧɚɲɚʃɟ. ɋɥɢɤɚ 7-4: ɉɨʁɟɞɧɨɫɬɚɜʂɟɧɢ ɞɢʁɚɝɪɚɦ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɟ ɩɪɢ ɚɤɫɢʁɚɥɧɨɦ ɩɪɢɬɢɫɤɭ ɛɟɬɨɧɚ ɉɪɢɦɟɧɨɦ ɢɡɪɚɡɚ (7-2) ɢ (7-3) ɫɪɚɱɭɧɚɬ ʁɟ ɩɨɥɨɠɚʁ ɬɚɱɚɤɚ ɢ ɧɚɰɪɬɚɧ ɞɢʁɚɝɪɚɦ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɟ ɤɨʁɢ ʁɟ ɤɨɪɢɲʄɟɧ ɭ ɪɚɞɭ. 002563,025200 3,322 E f2 c c 1c  mm/mm Ɍɚɱɤɚ 1: 000385,0MPa69,9f3,0 1c  Ɍɚɱɤɚ 2: ɡɚ MPa37,180008,0 c2  Ɍɚɱɤɚ 3: ɡɚ MPa06,260013,0 c3  Ɍɚɱɤɚ 4: ɡɚ MPa90,300019,0 c4  Ɍɚɱɤɚ 5: ɡɚ MPa30,32002563,0 c5  Ʉɪɢɬɟɪɢјɭɦ ɥɨɦɚ ɡɚ ɛɟɬɨɧ ɍɩɨɬɪɟɛʂɟɧ ɦɚɬɟɪɢʁɚɥɧɢ ɦɨɞɟɥ ɢɦɚ ɨɩɰɢʁɭ ɥɨɦɚ, ɤɚɤɨ ɭɫɥɟɞ ɞɨɫɬɢɡɚʃɚ ɱɜɪɫɬɨʄɟ ɩɪɢ ɡɚɬɟɡɚʃɭ ɛɟɬɨɧɚ, ɬɚɤɨ ɢ ɥɨɦɚ ɦɪɜʂɟʃɟɦ ɛɟɬɨɧɚ (ɞɨɫɬɢɡɚʃɚ ɱɜɪɫɬɨʄɟ ɩɪɢ ɩɪɢɬɢɫɤɭ ɛɟɬɨɧɚ). Ⱦɚ ɛɢ ɫɟ ɞɟɮɢɧɢɫɚɥɚ ɩɨɜɪɲɢɧɚ ɥɨɦɚ ɛɟɬɨɧɚ, ɤɚɨ ɢ ɤɪɢɬɟɪɢʁɭɦ ɥɨɦɚ ɛɟɬɨɧɚ ɩɪɢ ɱɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ cf  1c     cE 1 2 3 4 5 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 206 ɩɪɨɫɬɨɪɧɨɦ ɧɚɩɨɧɫɤɨɦ ɫɬɚʃɭ, ɩɨɬɪɟɛɧɚ ɫɭ ɞɜɚ ɭɥɚɡɧɚ ɩɚɪɚɦɟɬɪɚ: ɱɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ ɢ ɱɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɡɚɬɟɡɚʃɭ ɩɪɢ ɚɤɫɢʁɚɥɧɨɦ ɧɚɩɪɟɡɚʃɭ (АТllТКm КЧН Warnke, 1975). ɉɪɨʁɟɤɰɢʁɟ ɬɪɢ ɦɨɝɭʄɟ ɩɨɜɪɲɢ ɥɨɦɚ ɭ (σxp - σyp) ɪɚɜɧɢ ɩɪɢɤɚɡɚɧɟ ɫɭ ɧɚ ɋɥɢɰɢ 7- 5, ɝɞɟ ɫɭ (σxp) ɢ (σyp) ɝɥɚɜɧɢ ɧɚɩɨɧɢ ɤɨʁɢ ɫɭ ɪɚɡɥɢɱɢɬɢ ɨɞ ɧɭɥɟ ɭ ɩɪɚɜɰɭ (x) ɢ (y) ɨɫɟ. Ɉɛɥɢɤ ɥɨɦɚ ʁɟ ɮɭɧɤɰɢʁɚ ɡɧɚɤɚ ɝɥɚɜɧɨɝ ɧɚɩɨɧɚ ɭ ɩɪɚɜɰɭ (z) ɨɫɟ (σzp). ɇɚ ɩɪɢɦɟɪ, ɭɤɨɥɢɤɨ ɫɭ ɧɚɩɨɧɢ (σxp) ɢ (σyp) ɧɟɝɚɬɢɜɧɢ (ɩɪɢɬɢɫɚɤ), ɚ ɧɚɩɨɧ (σzp) ʁɟ ɭɦɟɪɟɧɨ ɩɨɡɢɬɢɜɚɧ (ɡɚɬɟɡɚʃɟ), ɦɨɝɭʄɚ ʁɟ ɩɨʁɚɜɚ ɩɪɫɥɢɧɚ ɭ ɩɪɚɜɰɭ ɭɩɪɚɜɧɨɦ ɧɚ ɩɪɚɜɚɰ ɧɚɩɨɧɚ (σzp). Ɇɟђɭɬɢɦ, ɭɤɨɥɢɤɨ ʁɟ (σzp = 0) ɢɥɢ ɭɦɟɪɟɧɨ ɧɟɝɚɬɢɜɚɧ, ɩɪɟɬɩɨɫɬɚɜɤɚ ʁɟ ɞɚ ʄɟ ɞɨʄɢ ɞɨ ɦɪɜʂɟʃɚ ɛɟɬɨɧɚ (ANSYS, 2014). ɋɥɢɤɚ 7-5: ɉɨɜɪɲɢɧɟ ɥɨɦɚ ɛɟɬɨɧɚ (ANSYS, 2014) ɉɪɫɥɢɧɟ ɫɟ ʁɚɜʂɚʁɭ ɭ ɤɨɧɚɱɧɨɦ ɟɥɟɦɟɧɬɭ ɛɟɬɨɧɚ ɤɚɞɚ ɝɥɚɜɧɢ ɧɚɩɨɧ ɡɚɬɟɡɚʃɚ ɭ ɛɢɥɨ ɤɨɦ ɩɪɚɜɰɭ ɥɟɠɢ ɜɚɧ ɩɨɜɪɲɢɧɟ ɥɨɦɚ. ɉɨɫɥɟ ɩɨʁɚɜɟ ɩɪɫɥɢɧɚ ɩɪɟɬɩɨɫɬɚɜʂɚ ɫɟ ɞɚ ʁɟ ɦɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ ɤɨɧɚɱɧɨɝ ɟɥɟɦɟɧɬɚ ɭ ɩɪɚɜɰɭ ɩɚɪɚɥɟɥɧɨɦ ɩɪɚɜɰɭ ɝɥɚɜɧɨɝ ɧɚɩɨɧɚ ɡɚɬɟɡɚʃɚ ʁɟɞɧɚɤ ɧɭɥɢ. Ɇɪɜʂɟʃɟ ɫɟ ʁɚɜʂɚ ɤɚɞɚ ɫɭ ɫɜɢ ɝɥɚɜɧɢ ɧɚɩɨɧɢ ɧɟɝɚɬɢɜɧɢ (ɧɚɩɨɧɢ ɩɪɢɬɢɫɤɚ) ɢ ɥɟɠɟ ɜɚɧ ɩɨɜɪɲɢɧɟ ɥɨɦɚ, ɚ ɭɫɜɚʁɚ ɫɟ ɞɚ ʁɟ ɦɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ ɤɨɧɚɱɧɨɝ ɟɥɟɦɟɧɬɚ ʁɟɞɧɚɤ ɧɭɥɢ ɭ ɫɜɢɦ ɩɪɚɜɰɢɦɚ (ANSYS, 2014) ɢ ɤɨɧɚɱɧɢ ɟɥɟɦɟɧɬ ɧɟɫɬɚʁɟ. ɍ ɛɪɨʁɧɢɦ ɢɫɬɪɚɠɢɜɚʃɢɦɚ ʁɟ ɭɨɱɟɧɨ ɞɚ ɭɤɨɥɢɤɨ ʁɟ ɭɤʂɭɱɟɧɚ ɨɩɰɢʁɚ ɦɪɜʂɟʃɚ ɛɟɬɨɧɚ ɞɨɥɚɡɢ ɞɨ ɩɪɟɪɚɧɨɝ ɥɨɦɚ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ ɦɨɞɟɥɚ ɛɟɬɨɧɫɤɟ ɝɪɟɞɟ (Kachlakev and Miller, 2001). Ɇɪɜʂɟʃɟ ɛɟɬɨɧɚ ɫɟ ɧɚʁɩɪɟ ʁɚɜʂɚ ɭ ɟɥɟɦɟɧɬɢɦɚ ɧɟɩɨɫɪɟɞɧɨ ɢɫɩɨɞ ɨɩɬɟɪɟʄɟʃɚ, ɚ, ɤɚɨ ɩɨɫɥɟɞɢɰɚ, ʁɚɜʂɚ ɫɟ ɦɪɜʂɟʃɟ ɢ ɨɤɨɥɧɢɯ ɟɥɟɦɟɧɚɬɚ ɛɟɬɨɧɚ ɱɢɦɟ ɫɟ ɉɪɫɤɚʃɟ ɉɪɫɤɚʃɟ (ɉɪɫɤɚʃɟ) (Ɇɪɜʂɟʃɟ) (Ɇɪɜʂɟʃɟ) ɉɪ ɫɤɚ ʃɟ 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 207 ɡɧɚɱɚʁɧɨ ɫɦɚʃɭʁɟ ɥɨɤɚɥɧɚ ɤɪɭɬɨɫɬ. ɇɚ ɤɪɚʁɭ ɫɟ ʁɚɜʂɚʁɭ ɜɟɥɢɤɚ ɩɨɦɟɪɚʃɚ ɦɨɞɟɥɚ ɢ ɪɟɲɟʃɚ ɞɢɜɟɪɝɢɪɚʁɭ. ɍ ɪɟɚɥɧɢɦ ɩɪɨɛɥɟɦɢɦɚ ɥɨɦ ɛɟɬɨɧɚ ɱɢɫɬɢɦ ɩɪɢɬɢɫɤɨɦ ʁɟ ɦɚɥɨ ɜɟɪɨɜɚɬɚɧ. ɋɟɤɭɧɞɚɪɞɧɟ ɞɢɥɚɬɚɰɢʁɟ ɡɚɬɟɡɚʃɚ ɩɪɨɭɡɪɨɤɨɜɚɧɟ ɉɨɚɫɨɧɨɜɢɦ ɟɮɟɤɬɨɦ ʁɚɜʂɚʁɭ ɫɟ ɭɩɪɚɜɧɨ ɧɚ ɩɪɚɜɚɰ ɞɟɥɨɜɚʃɚ ɨɩɬɟɪɟʄɟʃɚ. Ʉɚɤɨ ʁɟ ɱɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɡɚɬɟɡɚʃɭ ɢɡɭɡɟɬɧɨ ɦɚɥɚ, ɩɨʁɚɜɚ ɫɟɤɭɧɞɚɪɧɢɯ ɞɢɥɚɬɚɰɢʁɚ ɩɪɨɭɡɪɨɤɭʁɟ ɩɨʁɚɜɭ ɩɪɫɥɢɧɚ ɢ ɟɜɟɧɬɭɚɥɧɢ ɥɨɦ (MТЧНОss and Young, 1981; Shah et al., 1995). Ɂɛɨɝ ɬɨɝɚ ʁɟ ɭ ɨɜɨɦ ɢɫɬɪɚɠɢɜɚʃɭ ɦɨɝɭʄɧɨɫɬ ɥɨɦɚ ɦɪɜʂɟʃɟɦ ɢɫɤʂɭɱɟɧɚ. 7.2.2 Чɟɥɢɱɧɚ ɚɪɦɚɬɭɪɚ ɢ ɱɟɥɢɱɧɟ ɩɥɨɱɟ Кɚɪɚɤɬɟɪɢɫɬɢɤɟ ɱɟɥɢɱɧɟ ɚɪɦɚɬɭɪɟ ɤɨʁɟ ɫɭ ɤɨɪɢɲʄɟɧɟ ɭ ɧɭɦɟɪɢɱɤɨɦ ɢɫɬɪɚɠɢɜɚʃɭ ɦɟɬɨɞɨɦ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ ɭ ɨɜɨɦ ɪɚɞɭ, ɤɚɨ ɲɬɨ ɫɭ ɦɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ, ɝɪɚɧɢɰɚ ɪɚɡɜɥɚɱɟʃɚ (ɧɚɩɨɧ ɬɟɱɟʃɚ) ɢ ɱɜɪɫɬɨʄɚ ɩɪɢ ɡɚɬɟɡɚʃɭ ɞɨɛɢʁɟɧɟ ɫɭ ɨɞ ɫɬɪɚɧɟ ɩɪɨɢɡɜɨђɚɱɚ ɨɜɢɯ ɦɚɬɟɪɢʁɚɥɚ. ɍɫɜɨʁɟɧɚ ʁɟ ɛɢɥɢɧɟɚɪɧɚ ɡɚɜɢɫɧɨɫɬ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɟ ɡɚ ɚɪɦɚɬɭɪɧɢ ɱɟɥɢɤ ɫɚ ɢɞɟɧɬɢɱɧɢɦ ɨɫɨɛɢɧɚɦɚ ɩɪɢ ɩɪɢɬɢɫɤɭ ɢ ɡɚɬɟɡɚʃɭ (ɋɥɢɤɚ 7-6) ɢ ɉɨɚɫɨɧɨɜɢɦ ɤɨɟɮɢɰɢʁɟɧɬɨɦ ɨɞ 0,30 (Gere and Timoshenko, 1997). ɋɥɢɤɚ 7-6: Ⱦɢʁɚɝɪɚɦ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɟ ɡɚ ɚɪɦɚɬɭɪɧɢ ɱɟɥɢɤ Ɇɚɬɟɪɢʁɚɥɧɟ ɤɚɪɚɤɬɟɪɢɫɬɢɤɟ ɡɚ ɚɪɦɚɬɭɪɧɢ ɱɟɥɢɤ ɤɨʁɟ ɫɭ ɤɨɪɢɲʄɟɧɟ ɭ ɪɚɞɭ ɫɭ:  ɦɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ: Es= 210 GPa;  ɧɚɩɨɧ ɬɟɱɟʃɚ: fy= 400 MPa;  ɉɨɚɫɨɧɨɜ ɤɨɟɮɢɰɢʁɟɧɬ: ν=0,30. fy 1 ȿs 1 ȿsp ε σ fy εy 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 208 ɍ ɦɨɞɟɥɢɦɚ ɫɭ ɞɨɞɚɬɟ ɱɟɥɢɱɧɟ ɩɥɨɱɟ ɧɚ ɦɟɫɬɢɦɚ ɨɫɥɨɧɚɰɚ ɢ ɦɟɫɬɢɦɚ ɞɟɥɨɜɚʃɚ ɤɨɧɰɟɧɬɪɢɫɚɧɢɯ ɫɢɥɚ ɤɚɤɨ ɛɢ ɫɟ ɨɛɟɡɛɟɞɢɥɚ ɪɚɜɧɨɦɟɪɧɢʁɚ ɪɚɫɩɨɞɟɥɚ ɧɚɩɨɧɚ. ɉɪɟɬɩɨɫɬɚɜɤɚ ʁɟ ɞɚ ɫɭ ɱɟɥɢɱɧɟ ɩɥɨɱɟ ɨɞ ɥɢɧɟɚɪɧɨ ɟɥɚɫɬɢɱɧɨɝ ɦɚɬɟɪɢʁɚɥɚ ɫɚ ɢɫɬɢɦ ɦɚɬɟɪɢʁɚɥɧɢɦ ɤɚɪɚɤɬɟɪɢɫɬɢɤɚɦɚ ɤɚɨ ɢ ɚɪɦɚɬɭɪɧɢ ɱɟɥɢɤ. 7.2.3 ɎɊɉ ɚɪɦɚɬɭɪɚ Ʉɚɨ ɲɬɨ ʁɟ ɢ ɪɚɧɢʁɟ ɪɟɱɟɧɨ, ɎɊɉ ɦɚɬɟɪɢʁɚɥɢ ɫɚɫɬɨʁɟ ɫɟ ɨɞ ɞɜɚ ɦɚɬɟɪɢʁɚɥɚ ɤɨʁɢ ɫɟ ɤɨɦɛɢɧɭʁɭ ɧɚ ɦɚɤɪɨɫɤɨɩɫɤɨɦ ɧɢɜɨɭ. ɉɪɜɢ ɦɚɬɟɪɢʁɚɥ ɫɭ ɚɪɦɚɬɭɪɧɚ ɜɥɚɤɧɚ ɤɨʁɚ ɞɚʁɭ ɱɜɪɫɬɨʄɭ ɢ ɤɪɭɬɨɫɬ ɎɊɉ ɦɚɬɟɪɢʁɚɥɭ, ɤɨʁɚ ɫɭ ɭɬɨɩʂɟɧɚ ɭ ɤɨɧɬɢɧɭɚɥɧɢ ɩɨɥɢɦɟɪ (ɦɚɬɪɢɰɭ) ɤɨʁɚ ɢɯ ɩɨɜɟɡɭʁɟ (Ʉɚа, 1997). Ɉɫɨɛɢɧɟ ɎɊɉ ɚɪɦɚɬɭɪɟ ɧɢɫɭ ɢɫɬɟ ɭ ɫɜɢɦ ɩɪɚɜɰɢɦɚ. Ɉɧɚ ɩɪɢɩɚɞɚ ɝɪɭɩɢ ɬɡɜ. ɫɩɟɰɢʁɚɥɧɢɯ ɨɪɬɨɬɪɨɩɧɢɯ ɦɚɬɟɪɢʁɚɥɚ ɤɨʁɢ ɫɭ ɬɪɚɧɫɜɟɪɡɚɥɧɨ ɢɡɨɬɪɨɩɧɢ, ɤɨɞ ɤɨʁɢɯ ɫɭ ɦɚɬɟɪɢʁɚɥɧɟ ɨɫɨɛɢɧɟ ɩɪɢɛɥɢɠɧɨ ɢɫɬɟ ɭ ɛɢɥɨ ɤɨɦ ɩɪɚɜɰɭ ɭɩɪɚɜɧɨɦ ɧɚ ɩɪɚɜɚɰ ɜɥɚɤɚɧɚ (Gibson, 1994; Kaw, 1997). Ɂɚ ɞɚʂɭ ɚɧɚɥɢɡɭ ɩɪɟɬɩɨɫɬɚɜʂɟɧɟ ɫɭ ɝɥɚɜɧɟ ɦɚɬɟɪɢʁɚɥɧɟ ɨɫɟ ɬɚɤɨ ɞɚ ʁɟ (x) ɩɪɚɜɚɰ ɜɥɚɤɚɧɚ, ɚ (y) ɢ (z) ɫɭ ɩɪɚɜɰɢ ɭɩɪɚɜɧɢ ɧɚ (x) ɩɪɚɜɚɰ. ɍ ɨɜɨɦ ɢɫɬɪɚɠɢɜɚʃɭ ɩɪɟɬɩɨɫɬɚɜʂɟɧɟ ɫɭ ɥɢɧɟɚɪɧɨ-ɟɥɚɫɬɢɱɧɟ ɨɫɨɛɢɧɟ ɎɊɉ ɚɪɦɚɬɭɪɟ (ɋɥɢɤɚ 7- 7), ɬʁ. ɩɨʁɟɞɧɨɫɬɚɜʂɟɧɚ ɜɟɡɚ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɚ ɭ ɩɪɚɜɰɭ ɜɥɚɤɚɧɚ ɡɚ ɩɪɢɦɟʃɟɧɭ ɎɊɉ ɚɪɦɚɬɭɪɭ. ɋɥɢɤɚ 7-7: Ⱦɢʁɚɝɪɚɦ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɧɚɩɨɧɚ ɢ ɞɢɥɚɬɚɰɢʁɟ ɡɚ ɎɊɉ ɚɪɦɚɬɭɪɭ ɍɥɚɡɧɢ ɩɨɞɚɰɢ ɩɨɬɪɟɛɧɢ ɡɚ ɦɨɞɟɥɢɪɚʃɟ ɎɊɉ ɚɪɦɚɬɭɪɟ ɤɨɧɚɱɧɢɦ ɟɥɟɦɟɧɬɢɦɚ ɫɭ:  ɛɪɨʁ ɫɥɨʁɟɜɚ,  ɞɟɛʂɢɧɚ ɫɜɚɤɨɝ ɫɥɨʁɚ,  ɨɪɢʁɟɧɬɚɰɢʁɚ ɜɥɚɤɚɧɚ ɡɚ ɫɜɚɤɢ ɫɥɨʁ,  ɦɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ ɎɊɉ ɚɪɦɚɬɭɪɟ ɡɚ ɬɪɢ ɩɪɚɜɰɚ (Ex, Ey ɢ Ez),  ɦɨɞɭɥ ɫɦɢɰɚʃɚ ɎɊɉ ɚɪɦɚɬɭɪɟ ɡɚ ɬɪɢ ɪɚɜɧɢ (Gxy, Gyz ɢ Gxz), εfrp,u 1 ȿfrp ε σ ffrp 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 209  ɝɥɚɜɧɢ ɉɨɚɫɨɧɨɜ ɤɨɟɮɢɰɢʁɟɧɬ ɡɚ ɬɪɢ ɪɚɜɧɢ (νxy, νyz ɢ νxz). Ʌɨɤɚɥɧɢ ɤɨɨɪɞɢɧɚɬɧɢ ɫɢɫɬɟɦ ɡɚ ɎɊɉ ɫɥɨʁɟɜɢɬɢ ɩɨɜɪɲɢɧɫɤɢ ɟɥɟɦɟɧɬ ʁɟ ɞɟɮɢɧɢɫɚɧ ɬɚɤɨ ɞɚ ʁɟ x ɩɪɚɜɚɰ ɭ ɩɪɚɜɰɭ ɜɥɚɤɚɧɚ, ɞɨɤ ɫɭ y ɢ z ɩɪɚɜɰɢ ɭɩɪɚɜɧɢ ɧɚ x ɩɪɚɜɚɰ. Ɉɫɨɛɢɧɟ ɢɡɨɬɪɨɩɧɢɯ ɦɚɬɟɪɢʁɚɥɚ, ɤɚɨ ɲɬɨ ɫɭ ɦɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ ɢ ɉɨɚɫɨɧɨɜ ɤɨɟɮɢɰɢʁɟɧɬ, ɢɞɟɧɬɢɱɧɟ ɫɭ ɭ ɫɜɢɦ ɩɪɚɜɰɢɦɚ, ɡɛɨɝ ɱɟɝɚ ɢɧɞɟɤɫɢ ɧɢɫɭ ɩɨɬɪɟɛɧɢ. Ɉɜɨ ɧɢʁɟ ɫɥɭɱɚʁ ɫɚ ɫɩɟɰɢʁɚɥɧɢɦ ɨɪɬɨɬɪɨɩɧɢɦ ɦɚɬɟɪɢʁɚɥɢɦɚ ɤɨɞ ɤɨʁɢɯ ɫɭ ɢɧɞɟɤɫɢ ɧɟɨɩɯɨɞɧɢ ɞɚ ɞɟɮɢɧɢɲɭ ɨɫɨɛɢɧɟ ɭ ɪɚɡɥɢɱɢɬɢɦ ɩɪɚɜɰɢɦɚ. ɇɚ ɩɪɢɦɟɪ, Ex≠Ey ɢ νxy≠νyx. Ex ʁɟ ɦɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ ɭ ɩɪɚɜɰɭ ɜɥɚɤɚɧɚ ɞɨɤ ʁɟ Ey ɦɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ ɭ ɩɪɚɜɰɭ в ɭɩɪɚɜɧɨɦ ɧɚ ɩɪɚɜɚɰ ɜɥɚɤɚɧɚ. Кɨɪɢɲʄɟʃɟ ɉɨɚɫɨɧɨɜɢɯ ɤɨɟɮɢɰɢʁɟɧɚɬɚ ɡɚ ɨɪɬɨɬɪɨɩɧɟ ɦɚɬɟɪɢʁɚɥɟ ɭɡɪɨɤɭʁɟ ɡɚɛɭɧɭ, ɡɛɨɝ ɱɟɝɚ ɫɭ ɩɨɞɚɰɢ ɡɚ ɨɪɬɨɬɪɨɩɧɢ ɦɚɬɟɪɢʁɚɥɢ ɭ ɩɪɨɝɪɚɦɭ Ⱥɧɫɢɫ ɫɚɞɪɠɚɧɢ ɭ ɤɨɟɮɢɰɢʁɟɧɬɭ νxy ɢɥɢ ɝɥɚɜɧɨɦ (major) ɉɨɚɫɨɧɨɜɨɦ ɤɨɟɮɢɰɢʁɟɧɬɨɦ. Ƚɥɚɜɧɢ ɉɨɚɫɨɧɨɜ ɤɨɟɮɢɰɢʁɟɧɬ ʁɟ ɨɞɧɨɫ ɞɢɥɚɬɚɰɢʁɚ ɭ y ɢ x ɩɪɚɜɰɭ ɤɚɞɚ ʁɟ ɨɩɬɟɪɟʄɟʃɟ ɭ ɩɪɚɜɰɭ ɜɥɚɤɚɧɚ ɞɨɤ ʁɟ ɜɟɥɢɱɢɧɚ νyx ɦɚʃɢ (minor) ɉɨɚɫɨɧɨɜ ɤɨɟɮɢɰɢʁɟɧɬ ɤɨʁɢ ʁɟ ɦɚʃɢ ɨɞ νxy, ɞɨɤ ʁɟ ɦɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ Ex ɜɟʄɢ ɨɞ ɦɨɞɭɥɚ ɟɥɚɫɬɢɱɧɨɫɬɢ Ey. ɂɡɪɚɡɨɦ (7-5) ɞɚɬ ʁɟ ɨɞɧɨɫ ɢгɦɟђɭ νxy ɢ νyx (Kaw, 1997). xy x y yx E E   (7-5) ȼɪɟɞɧɨɫɬɢ ɨɜɢɯ ɤɨɟɮɢɰɢʁɟɧɚɬɚ ɭɫɜɨʁɟɧɟ ɫɭ ɧɚ ɨɫɧɨɜɭ ɩɪɨɫɩɟɤɚɬɚ ɩɪɨɢɡɜɨђɚɱɚ ɢ ɥɢɬɟɪɚɬɭɪɟ, ɚ ɩɪɢɤɚɡɚɧɟ ɫɭ ɬɚɛɟɥɚɪɧɨ (Ɍɚɛɟɥɚ 7-1). Ɍɚɛɟɥɚ 7-1: Ʉɚɪɚɤɬɟɪɢɫɬɢɤɟ ɎɊɉ ɦɚɬɟɪɢʁɚɥɚ (KКМСlКФОv Кnd MМCurrв, 2000) Ɇɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ Ƚɥɚɜɧɢ ɉɨɚɫɨɧɨɜ ɤɨɟɮɢɰɢʁɟɧɬ ɑɜɪɫɬɨʄɚ ɩɪɢ ɡɚɬɟɡɚʃɭ Ɇɨɞɭɥ ɫɦɢɰɚʃɚ Ⱦɟɛʂɢɧɚ ɥɚɦɟɥɟ (ɩɪɟɱɧɢɤ ɲɢɩɤɟ) ɎɊɉ (MPa) / (MPa) (MPa) (mm) ЦɎɊɉ Ex=150000 νxy=0,22 2000 Gxy=61475 1,4 (Ø8) Ey=115000 νxz=0,22 Gxz=61475 Ez=115000 νyz=0,30 Gyz=44234 ȽɎɊɉ Ex=40800 νxy=0,26 760 Gxy=16190 (Ø10) Ey=13600 νxz=0,26 Gxz=16190 Ey=13600 νyz=0,30 Gyz=5230 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 210 7.3 Ɍɢɩɨɜɢ ɭɫɜɨјɟɧɢɯ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 7.3.1 Ⱥɪɦɢɪɚɧɢ ɛɟɬɨɧ Ɂɚɩɪɟɦɢɧɫɤɢ ɤɨɧɚɱɧɢ ɟɥɟɦɟɧɬ ɋɨɥɢɞ 65 (Solid 65), ɤɨʁɢ ɢɦɚ ɨɫɚɦ ɱɜɨɪɨɜɚ ɫɚ ɩɨ ɬɪɢ ɫɬɟɩɟɧɚ ɫɥɨɛɨɞɟ ɭ ɫɜɚɤɨɦ ɱɜɨɪɭ (ɬɪɚɧɫɥɚɰɢʁɟ ɭ ɱɜɨɪɨɜɢɦɚ ɭ ɩɪɚɜɰɢɦɚ ɤɨɨɪɞɢɧɚɬɧɢɯ ɨɫɚ Б, В ɢ Г), ɤɨɪɢɲʄɟɧ ʁɟ ɡɚ ɦɨɞɟɥɢɪɚʃɟ ɛɟɬɨɧɚ. ɋɨɥɢɞ 65 ɫɟ ɤɨɪɢɫɬɢ ɡɚ ɦɨɞɟɥɢɪɚʃɟ ɛɟɬɨɧɚ ɩɪɢ ɱɟɦɭ ɩɨɫɬɨʁɢ ɦɨɝɭʄɧɨɫɬ ɞɚ ɫɟ ɭ ɨɤɜɢɪɭ ɨɜɨɝ ɤɨɧɚɱɧɨɝ ɟɥɟɦɟɧɬɚ ɦɨɞɟɥɢɪɚ ɢ ɚɪɦɚɬɭɪɧɢ ɱɟɥɢɤ. ɋɟɦ ɛɟɬɨɧɚ ɩɪɢɦɟʃɭʁɟ ɫɟ ɩɪɢ ɦɨɞɟɥɢɪɚʃɭ ɚɪɦɢɪɚɧɢɯ ɤɨɦɩɨɡɢɬɚ, ɤɚɨ ɲɬɨ ʁɟ ɮɢɛɟɪɝɥɚɫ, ɢ ɝɟɨɥɨɲɤɢɯ ɦɚɬɟɪɢʁɚɥɚ, ɤɚɨ ɲɬɨ ɫɭ ɫɬɟɧɟ. ɇɚʁɜɚɠɧɢʁК ɨɫɨɛɢɧɚ ɨɜɨɝ ɟɥɟɦɟɧɬɚ ʁɟ ɦɨɝɭʄɧɨɫɬ ɬɪɟɬɢɪɚʃɚ ɧɟɥɢɧɟɚɪɧɢɯ ɦɚɬɟɪɢʁɚɥɧɢɯ ɨɫɨɛɢɧɚ. Ɇɨɝɭʄɚ ʁɟ ɩɨʁɚɜɚ ɩɪɫɥɢɧɚ ɭ ɬɪɢ ɨɪɬɨɝɨɧɚɥɧɚ ɩɪɚɜɰɚ, ɦɪɜʂɟʃɟ ɛɟɬɨɧɚ, ɩɥɚɫɬɢɱɧɢɯ ɞɟɮɨɪɦɚɰɢʁɚ ɢ ɬɟɱɟʃɟ ɛɟɬɨɧɚ. Ⱥɪɦɚɬɭɪɚ ɦɨɞɟɥɢɪɚɧɚ ɨɜɢɦ ɟɥɟɦɟɧɬɨɦ ɢɦɚ ɫɩɨɫɨɛɧɨɫɬɢ ɡɚɬɟɡɚʃɚ ɢ ɩɪɢɬɢɫɤɚ ɚɥɢ ɧɟ ɢ ɫɦɢɰɚʃɚ ɚ ɦɨɝɭʄɚ ʁɟ ɢ ɚɧɚɥɢɡɚ ɩɥɚɫɬɢɱɧɢɯ ɞɟɮɨɪɦɚɰɢʁɚ ɢ ɬɟɱɟʃɚ. ɍ ɫɥɭɱɚʁɭ ɦɨɞɟɥɢɪɚʃɚ ɱɟɥɢɱɧɟ ɚɪɦɚɬɭɪɟ ɋɨɥɢɞ 65 ɟɥɟɦɟɧɬɨɦ ɨɝɪɚɧɢɱɚɜɚ ɫɟ ɫɥɨɛɨɞɚ ɮɨɪɦɢɪɚʃɚ ɦɪɟɠɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ ɢ ɬɚɱɧɨɝ ɞɟɮɢɧɢɫɚʃɚ ɩɨɥɨɠɚʁɚ ɚɪɦɚɬɭɪɟ (Кɭɤɚɪɚɫ, 2007). Ɂɛɨɝ ɬɨɝɚ ʁɟ ɭ ɨɜɨɦ ɪɚɞɭ ɱɟɥɢɱɧɚ ɚɪɦɚɬɭɪɚ ɦɨɞɟɥɢɪɚɧɚ ɥɢɧɢʁɫɤɢɦ ɟɥɟɦɟɧɬɨɦ Ʌɢɧɤ180 (Link180). Ƚɟɨɦɟɬɪɢʁɚ ɢ ɩɨɥɨɠɚʁ ɱɜɨɪɨɜɚ ɡɚ ɤɨɧɚɱɧɢ ɟɥɟɦɟɧɬ ɋɨɥɢɞ 65 ɩɪɢɤɚɡɚɧɢ ɫɭ ɧɚ ɋɥɢɰɢ 7-8. ɋɥɢɤɚ 7-8: Ƚɟɨɦɟɬɪɢʁɚ ɢ ɩɨɥɨɠɚʁ ɱɜɨɪɨɜɚ ɤɨɧɚɱɧɨɝ ɟɥɟɦɟɧɬɚ ɋɨɥɢɞ 65 (ANSYS, 2014) ȿɥɟɦɟɧɬ Ʌɢɧɤ 180 ɤɨʁɢ ʁɟ ɤɨɪɢɲʄɟɧ ɡɚ ɦɨɞɟɥɢɪɚʃɟ ɱɟɥɢɱɧɟ ɚɪɦɚɬɭɪɟ ʁɟ ɩɪɨɫɬɨɪɧɢ ɤɨɧɚɱɧɢ ɟɥɟɦɟɧɬ ɤɨʁɢ ɢɦɚ ɞɜɚ ɱɜɨɪɚ ɧɚ ɤɪɚʁɟɜɢɦɚ, ɫɜɚɤɢ ɫɚ ɩɨ ɬɪɢ ɫɬɟɩɟɧɚ ɫɥɨɛɨɞɟ (ɬɪɚɧɫɥɚɰɢʁɟ ɭ ɩɪɚɜɰɢɦɚ ɤɨɨɪɞɢɧɚɬɧɢɯ ɨɫɚ Б, В ɢ Г). Ɉɜɚʁ ɟɥɟɦɟɧɬ ɬɚɤɨђɟ ɢɦɚ ɫɩɨɫɨɛɧɨɫɬ ɩɥɚɫɬɢɱɧɢɯ ɞɟɮɨɪɦɚɰɢʁɚ, ɬɟɱɟʃɚ, ɨɦɟɤɲɚɜɚʃɚ ɤɚɨ ɢ ɦɨɝɭʄɧɨɫɬ ɜɟɥɢɤɢɯ 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 211 ɞɟɮɨɪɦɚɰɢʁɚ. Ƚɟɨɦɟɬɪɢʁɚ ɢ ɩɨɥɨɠɚʁ ɱɜɨɪɨɜɚ ɡɚ ɨɜɚʁ ɬɢɩ ɟɥɟɦɟɧɬɚ ɩɪɢɤɚɡɚɧɢ ɫɭ ɧɚ ɋɥɢɰɢ 7-9. ɋɥɢɤɚ 7-9: Ƚɟɨɦɟɬɪɢʁɚ ɢ ɩɨɥɨɠɚʁ ɱɜɨɪɨɜɚ ɤɨɧɚɱɧɨɝ ɟɥɟɦɟɧɬɚ Ʌɢɧɤ 180 (ANSYS, 2014) 7.3.2 ɎɊɉ ɚɪɦɚɬɭɪɚ ɋɨɥɢɞ 46 (Solid 46), ɫɥɨʁɟɜɢɬɚ ɜɟɪɡɢʁɚ ɤɨɧɫɬɪɭɤɬɢɜɧɨɝ ɟɥɟɦɟɧɬɚ ɋɨɥɢɞ 45 (Solid 45) ɩɪɨʁɟɤɬɨɜɚɧ ɡɚ ɦɨɞɟɥɢɪɚʃɟ ɬɚɧɤɢɯ ʂɭɫɤɢ ɢɥɢ ɬɟɥɚ, ɤɨɪɢɲʄɟɧ ʁɟ ɡɚ ɦɨɞɟɥɢɪɚʃɟ ɎɊɉ ɚɪɦɚɬɭɪɟ. ȿɥɟɦɟɧɬ ɦɨɠɟ ɞɚ ɫɚɞɪɠɢ ɞɨ 250 ɪɚɡɥɢɱɢɬɢɯ ɦɚɬɟɪɢʁɚɥɧɢɯ ɫɥɨʁɟɜɚ ɫɚ ɪɚɡɥɢɱɢɬɢɦ ɨɪɢʁɟɧɬɚɰɢʁɚɦɚ ɢ ɨɪɬɨɬɪɨɩɧɢɦ ɦɚɬɟɪɢʁɚɥɧɢɦ ɤɚɪɚɤɬɟɪɢɫɬɢɤɚɦɚ ɡɚ ɫɜɚɤɢ ɫɥɨʁ. ɍɤɨɥɢɤɨ ʁɟ ɩɨɬɪɟɛɧɨ ɮɨɪɦɢɪɚɬɢ ɜɢɲɟ ɨɞ 250 ɫɥɨʁɟɜɚ, ɞɨɫɬɭɩɧɚ ʁɟ ɭɥɚɡɧɚ ɤɨɧɫɬɢɬɭɬɢɜɧɚ ɦɚɬɪɢɰɚ. ȿɥɟɦɟɧɬ ɢɦɚ ɬɪɢ ɫɬɟɩɟɧɚ ɫɥɨɛɨɞɟ ɭ ɫɜɚɤɨɦ ɱɜɨɪɭ (ɬɪɚɧɫɥɚɰɢʁɟ ɭ ɩɪɚɜɰɢɦɚ ɤɨɨɪɞɢɧɚɬɧɢɯ ɨɫɚ Б, В ɢ Г). Ƚɟɨɦɟɬɪɢʁɚ ɢ ɩɨɥɨɠɚʁ ɱɜɨɪɨɜɚ ɡɚ ɨɜɚʁ ɬɢɩ ɟɥɟɦɟɧɬɚ ɩɪɢɤɚɡɚɧɢ ɫɭ ɧɚ ɋɥɢɰɢ 8-10. ɋɥɢɤɚ 7-10: Ƚɟɨɦɟɬɪɢʁɚ ɢ ɩɨɥɨɠɚʁ ɱɜɨɪɨɜɚ ɤɨɧɚɱɧɨɝ ɟɥɟɦɟɧɬɚ ɋɨɥɢɞ 46 (ANSYS, 2014) 7.3.3 Чɟɥɢɱɧɟ ɩɥɨɱɟ Кɨɧɚɱɧɢ ɟɥɟɦɟɧɬ ɫɚ ɨɫɚɦ ɱɜɨɪɨɜɚ, ɋɨɥɢɞ 45 (Solid 45), ɤɨɪɢɲʄɟɧ ʁɟ ɡɚ ɦɨɞɟɥɢɪɚʃɟ ɨɫɥɨɧɚɱɤɢɯ ɱɟɥɢɱɧɢɯ ɩɥɨɱɚ. ɋɜɚɤɢ ɱɜɨɪ ɨɜɨɝ ɟɥɟɦɟɧɬɚ ɢɦɚ ɬɪɢ ɫɬɟɩɟɧɚ 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 212 ɫɥɨɛɨɞɟ ɭ ɫɜɚɤɨɦ ɱɜɨɪɭ (ɬɪɚɧɫɥɚɰɢʁɟ ɭ ɩɪɚɜɰɢɦɚ ɤɨɨɪɞɢɧɚɬɧɢɯ ɨɫɚ Б, В ɢ Г). ȿɥɟɦɟɧɬɨɦ ɫɟ ɦɨɝɭ ɨɩɢɫɚɬɢ ɩɨʁɚɜɟ ɩɥɚɫɬɢɱɧɨɫɬɢ, ɬɟɱɟʃɚ, ɨɱɜɪɲʄɚɜɚʃɚ, ɜɟɥɢɤɢɯ ɞɟɮɨɪɦɚɰɢʁɚ ɢ ɜɟɥɢɤɢɯ ɞɢɥɚɬɚɰɢʁɚ. Ƚɟɨɦɟɬɪɢʁɚ ɢ ɩɨɥɨɠɚʁ ɱɜɨɪɨɜɚ ɡɚ ɨɜɚʁ ɬɢɩ ɟɥɟɦɟɧɬɚ ɩɪɢɤɚɡɚɧɢ ɫɭ ɧɚ ɋɥɢɰɢ 7-11. ɋɥɢɤɚ 7-11: Ƚɟɨɦɟɬɪɢʁɚ ɢ ɩɨɥɨɠɚʁ ɱɜɨɪɨɜɚ ɤɨɧɚɱɧɨɝ ɟɥɟɦɟɧɬɚ ɋɨɥɢɞ 45 (ANSYS, 2014) 7.4 ɍɫɜɨјɟɧɢ ɩɪɨɪɚɱɭɧɫɤɢ ɦɨɞɟɥ ɢɫɩɢɬɢɜɚɧɢɯ ɝɪɟɞɧɢɯ ɧɨɫɚɱɚ ɢ ɦɪɟɠɚ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ ɍ ɰɢʂɭ ɪɚɰɢɨɧɚɥɧɢʁɟɝ ɩɪɨɪɚɱɭɧɚ ɢɫɤɨɪɢɲʄɟɧɚ ʁɟ ɫɢɦɟɬɪɢʁɚ ɚɧɚɥɢɡɢɪɚɧɢɯ ɧɨɫɚɱɚ. Ɇɨɞɟɥɢɪɚɧɚ ʁɟ ɱɟɬɜɪɬɢɧɚ ȺȻ ɝɪɟɞɧɨɝ ɧɨɫɚɱɚ, ɭɡ ɫɢɦɭɥɚɰɢʁɭ ɝɪɚɧɢɱɧɢɯ ɭɫɥɨɜɚ ɡɚ ɢɡɚɛɪɚɧɢ ɫɬɚɬɢɱɤɢ ɫɢɫɬɟɦ (ɋɥɢɤɚ 7-12). Ɇɨɞɟɥɢɪɚʃɟ ʁɟ ɢɡɜɪɲɟɧɨ ɧɚ ɨɫɧɨɜɭ ɦɟɯɚɧɢɱɤɢɯ ɤɚɪɚɤɬɟɪɢɫɬɢɤɚ ɫɚɦɨɭɝɪɚђɭʁɭʄɟɝ ɛɟɬɨɧɚ, ɱɟɥɢɱɧɟ ɚɪɦɚɬɭɪɟ, ɟɩɨɤɫɢɞɧɨɝ ɥɟɩɤɚ ɢ ȽɎɊɉ ɚɪɦɚɬɭɪɟ ɤɨʁɟ ɫɭ ɞɟɮɢɧɢɫɚɧɟ ɭ ɩɨɝɥɚɜʂɭ 7.2 ɩɪɢ ɱɟɦɭ ʁɟ ɩɪɟɬɩɨɫɬɚɜʂɟɧɚ ɩɭɧɚ ɩɪɢɨɧʂɢɜɨɫɬ ɢɡɦɟђɭ ɦɚɬɟɪɢʁɚɥɚ. ɋɥɢɤɚ 7-12: ɉɪɨɪɚɱɭɧɫɤɢ ɦɨɞɟɥ ɱɟɬɜɪɬɢɧɟ ȺȻ ɝɪɟɞɟ ɦɨɞɟɥɢɪɚɧɟ ɤɨɧɚɱɧɢɦ ɟɥɟɦɟɧɬɢɦɚ 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 213 ȼɪɥɨ ɜɚɠɚɧ ɫɟɝɦɟɧɬ ɩɪɢ ɩɪɨɪɚɱɭɧɭ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ ʁɟ ɩɪɚɜɢɥɚɧ ɢɡɛɨɪ ɦɪɟɠɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ. ɍɤɨɥɢɤɨ ʁɟ ɦɪɟɠɚ ɩɪɟɜɢɲɟ ɝɭɫɬɚ ɪɚɩɢɞɧɨ ɪɚɫɬɟ ɩɨɬɪɟɛɧɨ ɜɪɟɦɟ ɡɚ ɩɪɨɪɚɱɭɧ, ɚ ɭɤɨɥɢɤɨ ʁɟ ɦɪɟɠɚ ɩɪɟɜɢɲɟ ɝɪɭɛɚ ɧɟ ɦɨɝɭ ɫɟ ɞɨɛɢɬɢ ɭɩɨɬɪɟɛʂɢɜɢ ɪɟɡɭɥɬɚɬɢ. Ɂɛɨɝ ɬɨɝɚ ʁɟ ɧɟɨɩɯɨɞɧɨ ɢɡɜɪɲɢɬɢ ɫɬɭɞɢʁɭ ɤɨɧɜɟɪɝɟɧɰɢʁɟ ɪɟɡɭɥɬɚɬɚ ɩɪɟɤɨ ɧɟɤɨɝ ɨɞ ɩɪɨɪɚɱɭɧɫɤɢɯ ɩɚɪɚɦɟɬɚɪɚ. ɍ ɨɜɨɦ ɢɫɬɪɚɠɢɜɚʃɭ ʁɟ ɢɡɜɪɲɟɧɚ ɫɬɭɞɢʁɚ ɤɨɧɜɟɪɝɟɧɰɢʁɟ ɭɝɢɛɚ ɩɪɟɫɟɤɚ ɭ ɩɨɥɨɜɢɧɢ ɪɚɫɩɨɧɚ (ɋɥɢɤɚ 7-13 ɢ Ɍɚɛɟɥɚ7-2) ɧɚ ɨɫɧɨɜɭ ɤɨʁɟ ʁɟ ɭɫɜɨʁɟɧɚ ɞɢɦɟɧɡɢʁɚ ɤɨɧɚɱɧɨɝ ɟɥɟɦɟɧɬɚ ɨɞ 10 mm. ɋɥɢɤɚ 7-13: ɉɪɨɪɚɱɭɧɫɤɢ ɦɨɞɟɥɢ ɱɟɬɜɪɬɢɧɟ ɤɨɧɬɪɨɥɧɟ ɝɪɟɞɟ ɫɚ 2587, 19736 ɢ 155968 ɟɥɟɦɟɧɚɬɚ Ɍɚɛɟɥɚ 7-2: ɋɬɭɞɢʁɚ ɤɨɧɜɟɪɝɟɧɰɢʁɟ ɪɟɡɭɥɬɚɬɚ ɩɪɟɦɚ ɝɭɫɬɢɧɢ ɦɪɟɠɟ ɟɥɟɦɟɧɚɬɚ Ɇɨɞɟɥ Ȼɪɨʁ ɟɥɟɦɟɧɚɬɚ Ⱦɢɦɟɧɡɢʁɟ ɟɥɟɦɟɧɚɬɚ (mm) ɍɝɢɛ (mm) 1 2587 20×20×20 5,850 2 19736 10×10×10 5,868 3 155968 5×5×5 5,878 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 214 7.5 Ɋɟɡɭɥɬɚɬɢ ɧɭɦɟɪɢɱɤɟ ɚɧɚɥɢɡɟ ɐɢʂ ɚɧɚɥɢɡɟ ɩɭɬɟɦ ɧɭɦɟɪɢɱɤɨɝ ɦɨɞɟɥɚ ʁɟ ɭɩɨɪɟђɟʃɟ ɫɚ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɦ ɪɟɡɭɥɬɚɬɢɦɚ ɢ ɩɪɢɤɚɡ ɤɚɪɚɤɬɟɪɢɫɬɢɱɧɢɯ ɮɚɡɚ ɤɪɨɡ ɤɨʁɟ ɩɪɨɥɚɡɢ ɧɨɫɚɱ ɬɨɤɨɦ ɧɚɧɨɲɟʃɚ ɨɩɬɟɪɟʄɟʃɚ. ɂɫɬɪɚɠɟɧɚ ʁɟ ɨɛɥɚɫɬ ɥɢɧɟɚɪɧɨɝ ɩɨɧɚɲɚʃɚ ɢ ɩɨʁɚɜɚ ɩɪɜɟ ɩɪɫɥɢɧɟ, ɧɟɥɢɧɟɚɪɧɚ ɨɛɥɚɫɬ ɞɨ ɩɨʁɚɜɟ ɬɟɱɟʃɚ ɭ ɡɚɬɟɝɧɭɬɨʁ ɱɟɥɢɱɧɨʁ ɚɪɦɚɬɭɪɢ ɢ ɨɛɥɚɫɬ ɨɞ ɩɨʁɚɜɟ ɬɟɱɟʃɚ ɞɨ ɥɨɦɚ. ɍɩɨɪɟђɟʃɟ ɪɟɡɭɥɬɚɬɚ ɧɭɦɟɪɢɱɤɟ ɢ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɟ ɚɧɚɥɢɡɟ ɩɨɤɚɡɚɧɨ ʁɟ ɩɪɟɤɨ ɞɢʁɚɝɪɚɦɚ ɭɝɢɛɚ ɢ ɞɢɥɚɬɚɰɢʁɚ ɭ ɎɊɉ ɚɪɦɚɬɭɪɢ. ɍɨɱɟɧɟ ɪɚɡɥɢɤɟ ɫɭ ɧɟɦɢɧɨɜɧɟ ɡɛɨɝ ɢɞɟɚɥɢɡɚɰɢʁɟ ɦɟɯɚɧɢɱɤɢɯ ɤɚɪɚɤɬɟɪɢɫɬɢɤɚ ɭɡɨɪɤɚ ɝɪɟɞɧɨɝ ɟɥɟɦɟɧɬɚ ɢ ɚɩɪɨɤɫɢɦɚɰɢʁɚ ɭ ɧɭɦɟɪɢɱɤɨɦ ɦɨɞɟɥɭ. Ʌɨɤɚɥɧɚ ɧɟɫɚɜɪɲɟɧɨɫɬ ɩɪɜɟɧɫɬɜɟɧɨ ɛɟɬɨɧɚ ɧɚ ɫɩɨʁɭ ɰɟɦɟɧɬɧɨɝ ɤɚɦɟɧɚ ɢ ɚɝɪɟɝɚɬɚ ʁɟ ʁɟɞɚɧ ɨɞ ɪɚɡɥɨɝɚ ɧɟɫɥɚɝɚʃɚ ɪɟɡɭɥɬɚɬɚ. ɉɨɪɟɞ ɬɨɝɚ, ɭ ɧɭɦɟɪɢɱɤɨɦ ɦɨɞɟɥɢɪɚʃɭ ɩɪɟɬɩɨɫɬɚɜʂɟɧɚ ʁɟ ɢɞɟɚɥɧɚ ɩɪɢɨɧʂɢɜɨɫɬ ɱɟɥɢɤɚ ɢ ɛɟɬɨɧɚ, ɟɩɨɤɫɢɞɧɨɝ ɥɟɩɤɚ ɢ ɛɟɬɨɧɚ, ɤɚɨ ɢ ɟɩɨɤɫɢɞɧɨɝ ɥɟɩɤɚ ɢ ɎɊɉ ɚɪɦɚɬɭɪɟ. Ɇɟђɭɬɢɦ, ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨ ʁɟ ɞɨɤɚɡɚɧɨ ɞɚ ɩɪɢ ɜɢɲɢɦ ɧɢɜɨɢɦɚ ɨɩɬɟɪɟʄɟʃɚ ɞɨɥɚɡɢ ɞɨ ɝɭɛɢɬɤɚ ɩɪɢɨɧʂɢɜɨɫɬɢ ɡɛɨɝ ɱɟɝɚ ɫɟ ʁɚɜʂɚʁɭ ɢɡɜɟɫɧɚ ɨɞɫɬɭɩɚʃɚ ɭ ɪɟɡɭɥɬɚɬɢɦɚ ɧɭɦɟɪɢɱɤɟ ɢ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɟ ɚɧɚɥɢɡɟ. Ʉɨɧɬɪɨɥɧɢ ɝɪɟɞɧɢ ɧɨɫɚɱ ɋɥɢɤɚ 7-14: ɉɪɨɪɚɱɭɧɫɤɢ ɦɨɞɟɥ ɤɨɧɬɪɨɥɧɨɝ ɝɪɟɞɧɨɝ ɧɨɫɚɱɚ Ɂɚ ɚɧɚɥɢɡɭ ɤɨɧɬɪɨɥɧɨɝ ɝɪɟɞɧɨɝ ɧɨɫɚɱɚ ɭɫɜɨʁɟɧ ʁɟ ɦɨɞɟɥ ɱɟɬɜɪɬɢɧɟ ɝɪɟɞɟ (ɋɥɢɤɚ 7-14) ɤɨʁɢ ɭ ɫɥɭɱɚʁɭ ɤɨɧɬɪɨɥɧɟ ɝɪɟɞɟ ɢɦɚ 92093 ɟɥɟɦɟɧɚɬɚ ɢ 19736 ɱɜɨɪɨɜɚ. 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 215 ɇɚ ɋɥɢɰɢ 7-15 ɩɪɢɤɚɡɚɧ ʁɟ ɞɟɮɨɪɦɢɫɚɧɢ ɨɛɥɢɤ ɧɨɫɚɱɚ ɫɚ ɜɪɟɞɧɨɫɬɢɦɚ ɭɝɢɛɚ ɩɪɢ ɪɚɡɥɢɱɢɬɢɦ ɫɬɟɩɟɧɢɦɚ ɩɪɨɛɧɨɝ ɨɩɬɟɪɟʄɟʃɚ. ɚ) ɛ) ɋɥɢɤɚ 7-15: ɉɪɢɤɚɡ ɞɟɮɨɪɦɢɫɚɧɨɝ ɧɨɫɚɱɚ ɫɚ ɜɪɟɞɧɨɫɬɢɦɚ ɭɝɢɛɚ ɩɪɢ ɩɪɨɛɧɨɦ ɨɩɬɟɪʄɟʃɭ ɨɞ: ɚ) P=50 ФN; ɛ) P=100 ФN ɇɚ ɨɫɧɨɜɭ ɞɨɛɢʁɟɧɢɯ ɜɪɟɞɧɨɫɬɢ ɭɝɢɛɚ ɩɪɢ ɪɚɡɥɢɱɢɬɢɦ ɧɢɜɨɢɦɚ ɨɩɬɟɪɟʄɟʃɚ ɭɪɚђɟɧ ʁɟ ɝɪɚɮɢɱɤɢ ɩɪɢɤɚɡ ɢ ɞɚɬɨ ɭɩɨɪɟђɟʃɟ ɫɚ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɦ ɪɟɡɭɥɬɚɬɢɦɚ (ɋɥɢɤɚ 7-16). ɇɚ ɞɢʁɚɝɪɚɦɭ ɫɟ ɦɨɠɟ ɭɨɱɢɬɢ ɢɡɜɟɫɧɨ ɧɟɫɥɚɝɚʃɟ ɪɟɡɭɥɬɚɬɚ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɟ ɢ ɧɭɦɟɪɢɱɤɟ ɚɧɚɥɢɡɟ ɩɪɢ ɱɟɦɭ ɦɨɞɟɥ ɆɄȿ ɩɨɤɚɡɭʁɟ, ɝɟɧɟɪɚɥɧɨ, ɜɟʄɭ ɤɪɭɬɨɫɬ ɩɪɟ ɫɜɟɝɚ ɡɛɨɝ ɢɞɟɚɥɢɡɚɰɢʁɚ ɤɨʁɟ ɫɭ ɭɫɜɨʁɟɧɟ ɩɪɢ ɦɨɞɟɥɢɪɚʃɭ ɛɟɬɨɧɚ ɢ ɱɟɥɢɱɧɟ ɚɪɦɚɬɭɪɟ. 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 216 ɋɥɢɤɚ 7-16: ɍɩɨɪɟɞɧɢ ɞɢʁɚɝɪɚɦ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɨɩɬɟɪɟʄɟʃɚ ɢ ɭɝɢɛɚ ɭ ɩɪɟɫɟɤɭ I (U1) ɢ ɩɪɟɫɟɤɭ II (U2 ) ɤɨɧɬɪɨɥɧɟ ɝɪɟɞɟ ɞɨɛɢʁɟɧɢ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨ ɢ ɩɪɢɦɟɧɨɦ MKE (Ansys) Ʉɨɧɬɢɧɭɚɥɧɢ ɝɪɟɞɧɢ ɧɨɫɚɱ Ȼ-Ƚ1 ɋɥɢɤɚ 7-17: ɉɪɨɪɚɱɭɧɫɤɢ ɦɨɞɟɥ ɝɪɟɞɧɨɝ ɧɨɫɚɱɚ Ȼ-Ƚ1 Ɂɚ ɚɧɚɥɢɡɭ ɝɪɟɞɧɨɝ ɧɨɫɚɱɚ Ȼ-Ƚ1 ɭɫɜɨʁɟɧ ʁɟ ɦɨɞɟɥ ɫɚ 20190 ɟɥɟɦɟɧɚɬɚ ɢ 94642 ɱɜɨɪɚ. ɇɚ ɋɥɢɰɢ 7-18 ɩɪɢɤɚɡɚɧ ʁɟ ɞɟɮɨɪɦɢɫɚɧɢ ɨɛɥɢɤ ɧɨɫɚɱɚ ɫɚ ɜɪɟɞɧɨɫɬɢɦɚ ɭɝɢɛɚ ɩɪɢ ɪɚɡɥɢɱɢɬɢɦ ɫɬɟɩɟɧɢɦɚ ɩɪɨɛɧɨɝ ɨɩɬɟɪɟʄɟʃɚ. ɇɚ ɨɫɧɨɜɭ ɧɭɦɟɪɢɱɤɢ ɨɞɪɟђɟɧɢɯ ɜɪɟɞɧɨɫɬɢ ɭɝɢɛɚ ɢ ɞɢɥɚɬɚɰɢʁɚ ɭ ɎɊɉ ɚɪɦɚɬɭɪɢ ɩɪɢ ɪɚɡɥɢɱɢɬɢɦ ɫɬɟɩɟɧɢɦɚ (ɤɨɪɚɰɢɦɚ) ɨɩɬɟɪɟʄɟʃɚ, ɢɡɜɪɲɟɧɨ ʁɟ ɩɨɪɟђɟʃɟ ɫɚ ɪɟɡɭɥɬɚɬɢɦɚ ɞɨɛɢʁɟɧɢɦ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɦ ɢɫɩɢɬɢɜɚʃɟɦ (ɋɥɢɤɟ 7-19 ɢ 7-20). ɇɚ ɞɢʁɚɝɪɚɦɭ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɨɩɬɟɪɟʄɟʃɚ ɢ ɭɝɢɛɚ ɫɟ ɭɨɱɚɜɚ ɞɟɥɢɦɢɱɧɨ ɨɞɫɬɭɩɚʃɟ 0 20 40 60 80 100 120 0 5 10 15 20 25 Ɉɩ ɬɟɪ ɟʄɟ ʃɟ (k N) ɍɝɢɛ (mm) U1 U2 Ansys 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 217 ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨ ɞɨɛɢʁɟɧɢɯ ɜɪɟɞɧɨɫɬɢ ɭɝɢɛɚ ɭ ɨɞɧɨɫɭ ɧɚ ɜɪɟɞɧɨɫɬɢ ɭɝɢɛɚ ɤɨʁɟ ɫɭ ɞɨɛɢʁɟɧɟ ɩɪɢɦɟɧɨɦ ɧɭɦɟɪɢɱɤɟ ɚɧɚɥɢɡɟ ɆɄȿ. Ɋɚɡɥɨɡɢ ɨɜɨɝ ɧɟɫɥɚɝɚʃɚ ɥɟɠɟ ɭ ɭɫɜɨʁɟɧɢɦ ɢɞɟɚɥɢɡɨɜɚɧɢɦ ɤɚɪɚɤɬɟɪɢɫɬɢɤɚɦɚ ɤɨɦɩɨɧɟɧɬɧɢɯ ɦɚɬɟɪɢʁɚɥɚ, ɤɚɨ ɢ ɭ ɢɞɟɚɥɢɡɚɰɢʁɢ ɜɟɡɚ ɢɡɦɟђɭ ɛɟɬɨɧɚ, ɱɟɥɢɱɧɟ ɚɪɦɚɬɭɪɟ, ɟɩɨɤɫɢɞɧɨɝ ɥɟɩɤɚ ɢ ɎɊɉ ɚɪɦɚɬɭɪɟ. ɚ) ɛ) ɜ) ɋɥɢɤɚ 7-18: ɉɪɢɤɚɡ ɞɟɮɨɪɦɢɫɚɧɨɝ ɧɨɫɚɱɚ ɫɚ ɜɪɟɞɧɨɫɬɢɦɚ ɭɝɢɛɚ ɩɪɢ ɩɪɨɛɧɨɦ ɨɩɬɟɪʄɟʃɭ ɨɞ: ɚ) P=40 ФN; ɛ) P=80 ФN; ɜ) P=120 kN 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 218 ɋɥɢɤɚ 7-19: ɍɩɨɪɟɞɧɢ ɞɢʁɚɝɪɚɦ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɨɩɬɟɪɟʄɟʃɚ ɢ ɭɝɢɛɚ ɭ ɩɪɟɫɟɤɭ I (U1) ɢ ɩɪɟɫɟɤɭ II (U2 ) ɝɪɟɞɟ Ȼ-Ƚ1 ɞɨɛɢʁɟɧɢ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨ ɢ ɩɪɢɦɟɧɨɦ MKE (Ansys) ɋɥɢɤɚ 7-20: ɍɩɨɪɟɞɧɢ ɞɢʁɚɝɪɚɦ ɞɢɥɚɬɚɰɢʁɚ ɭ ɎɊɉ ɚɪɦɚɬɭɪɢ ɭ ɩɪɟɫɟɤɭ III ɝɪɟɞɟ Ȼ-Ƚ1 ɞɨɛɢʁɟɧɢ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨ (MT6) ɢ ɧɭɦɟɪɢɱɤɨɦ ɚɧɚɥɢɡɨɦ ɩɪɢɦɟɧɨɦ ɆɄȿ (Ansвs) Ʉɨɧɬɢɧɭɚɥɧɢ ɝɪɟɞɧɢ ɧɨɫɚɱ Ȼ-Ƚ2 Ɂɚ ɚɧɚɥɢɡɭ ɝɪɟɞɧɨɝ ɧɨɫɚɱɚ Ȼ-Ƚ2 ɭɫɜɨʁɟɧ ʁɟ ɦɨɞɟɥ ɫɚ 20265 ɟɥɟɦɟɧɚɬɚ ɢ 95617 ɱɜɨɪɨɜɚ. ɇɚ ɋɥɢɰɢ 7-21 ɩɪɢɤɚɡɚɧ ʁɟ ɞɟɮɨɪɦɢɫɚɧɢ ɨɛɥɢɤ ɧɨɫɚɱɚ ɩɪɢ ɪɚɡɥɢɱɢɬɢɦ ɫɬɟɩɟɧɢɦɚ ɨɩɬɟɪɟʄɟʃɚ. 0 20 40 60 80 100 120 140 0 5 10 15 20 25 30 Ɉɩ ɬɟɪ ɟʄɟ ʃɟ (k N) ɍɝɢɛ (mm) U1 U2 Ansys 0 20 40 60 80 100 120 140 0 5000 10000 15000 20000 Ɉɩ ɬɟɪ ɟʄɟ ʃɟ (k N) ɦɢɤɪɨ Ⱦɢɥɚɬɚɰɢјɟ MT6 Ansys 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 219 a) ɛ) ɜ) ɋɥɢɤɚ 7-21: ɉɪɢɤɚɡ ɞɟɮɨɪɦɢɫɚɧɨɝ ɧɨɫɚɱɚ ɫɚ ɜɪɟɞɧɨɫɬɢɦɚ ɭɝɢɛɚ ɩɪɢ ɩɪɨɛɧɨɦ ɨɩɬɟɪʄɟʃɭ ɨɞ: ɚ) P=50 ФN; ɛ) P=100 ФN; ɜ) P=145 kN ɇɚ ɋɥɢɤɚɦɚ 7-22 ɢ 7-23 ɩɪɢɤɚɡɚɧɢ ɫɭ ɭɩɨɪɟɞɧɨ ɞɢʁɚɝɪɚɦɢ ɭɝɢɛɚ ɢ ɞɢɥɚɬɚɰɢʁɚ ɭ ɎɊɉ ɚɪɦɚɬɭɪɢ ɞɨɛɢʁɟɧɢ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨ ɢ ɧɭɦɟɪɢɱɤɨɦ ɚɧɚɥɢɡɨɦ ɩɪɢɦɟɧɨɦ ɆɄȿ. 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 220 ɋɥɢɤɚ 7-22: ɍɩɨɪɟɞɧɢ ɞɢʁɚɝɪɚɦ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɨɩɬɟɪɟʄɟʃɚ ɢ ɭɝɢɛɚ ɭ ɩɪɟɫɟɤɭ I (U1) ɢ ɩɪɟɫɟɤɭ II (U2 ) ɝɪɟɞɟ Ȼ-Ƚ2 ɞɨɛɢʁɟɧɢ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨ ɢ ɩɪɢɦɟɧɨɦ MKE (Ansys) ɋɥɢɤɚ 7-23: ɍɩɨɪɟɞɧɢ ɞɢʁɚɝɪɚɦ ɞɢɥɚɬɚɰɢʁɚ ɭ ɎɊɉ ɚɪɦɚɬɭɪɢ ɭ ɩɪɟɫɟɤɭ I ɝɪɟɞɟ Ȼ-Ƚ2 ɞɨɛɢʁɟɧɢ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨ (MT6) ɢ ɧɭɦɟɪɢɱɤɨɦ ɚɧɚɥɢɡɨɦ ɩɪɢɦɟɧɨɦ ɆɄȿ (Ansys) ɍ ɩɨɱɟɬɧɨɦ, ɥɢɧɟɚɪɧɨɦ ɞɨɦɟɧɭ ɧɭɦɟɪɢɱɤɢ ɦɨɞɟɥ ɢ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢ ɪɟɡɭɥɬɚɬɢ ɫɟ ɩɨɬɩɭɧɨ ɩɨɤɥɚɩɚʁɭ. Ɏɚɡɚ ɞɨ ɩɨʁɚɜɟ ɬɟɱɟʃɚ ɭ ɱɟɥɢɱɧɨʁ ɚɪɦɚɬɭɪɢ ɩɨɤɚɡɭʁɟ ɜɪɥɨ ɞɨɛɪɨ ɫɥɚɝɚʃɟ ɪɟɡɭɥɬɚɬɚ ɤɚɞɚ ɫɭ ɭ ɩɢɬɚʃɭ ɭɝɢɛɢ (ɋɥɢɤɚ 7-22) ɢ ɢɡɜɟɫɧɚ ɨɞɫɬɭɩɚʃɚ ɭ ɫɥɭɱɚʁɭ ɞɢɥɚɬɚɰɢʁɚ ɭ ȽɎɊɉ ɚɪɦɚɬɭɪɢ (ɋɥɢɤɚ 7-23). ɉɨɫɥɟ ɩɨɱɟɬɤɚ ɬɟɱɟʃɚ ɱɟɥɢɱɧɟ ɚɪɦɚɬɭɪɟ ʁɚɜʂɚʁɭ ɫɟ ɡɧɚɬɧɢʁɚ ɨɞɫɬɭɩɚʃɚ ɭɫɥɟɞ ɜɟʄɟ ɤɪɭɬɨɫɬɢ ɧɭɦɟɪɢɱɤɨɝ ɦɨɞɟɥɚ. 0 20 40 60 80 100 120 140 160 0 10 20 30 40 Ɉɩ ɬɟɪ ɟʄɟ ʃɟ (k N) ɍɝɢɛ (mm) U1 U2 Ansys 0 20 40 60 80 100 120 140 160 0 5000 10000 15000 20000 25000 Ɉɩ ɬɟɪ ɟʄɟ ʃɟ (k N) ɦɢɤɪɨ Ⱦɢɥɚɬɚɰɢјɟ MT6 Ansys 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 221 Ʉɨɧɬɢɧɭɚɥɧɢ ɝɪɟɞɧɢ ɧɨɫɚɱ Ȼ-Ƚ3 Ɂɚ ɚɧɚɥɢɡɭ ɤɨɧɬɢɧɭɚɥɧɨɝ ɝɪɟɞɧɨɝ ɧɨɫɚɱɚ Ȼ-Ƚ3 ɭɫɜɨʁɟɧ ʁɟ ɦɨɞɟɥ ɫɚ 20335 ɟɥɟɦɟɧɚɬɚ ɢ 96955 ɱɜɨɪɨɜɚ. ɇɚ ɋɥɢɰɢ 7-24 ɩɪɢɤɚɡɚɧ ʁɟ ɞɟɮɨɪɦɢɫɚɧɢ ɨɛɥɢɤ ɧɨɫɚɱɚ ɩɪɢ ɪɚɡɥɢɱɢɬɢɦ ɫɬɟɩɟɧɢɦɚ ɨɩɬɟɪɟʄɟʃɚ. ɚ) ɛ) ɜ) ɋɥɢɤɚ 7-24: ɉɪɢɤɚɡ ɞɟɮɨɪɦɢɫɚɧɨɝ ɧɨɫɚɱɚ ɫɚ ɜɪɟɞɧɨɫɬɢɦɚ ɭɝɢɛɚ ɩɪɢ ɩɪɨɛɧɨɦ ɨɩɬɟɪʄɟʃɭ ɨɞ: ɚ) P=50 ФN; ɛ) P=100 ФN; ɜ) P=165 kN 7 ɇɭɦɟɪɢɱɤɨ ɦɨɞɟɥɢɪɚʃɟ ɩɪɢɦɟɧɨɦ ɦɟɬɨɞɟ ɤɨɧɚɱɧɢɯ ɟɥɟɦɟɧɚɬɚ 222 ɇɚ ɨɫɧɨɜɭ ɧɭɦɟɪɢɱɤɢ ɨɞɪɟђɟɧɢɯ ɜɪɟɞɧɨɫɬɢ ɭɝɢɛɚ ɢ ɞɢɥɚɬɚɰɢʁɚ ɭ ɎɊɉ ɚɪɦɚɬɭɪɢ ɩɪɢ ɪɚɡɥɢɱɢɬɢɦ ɫɬɟɩɟɧɢɦɚ (ɤɨɪɚɰɢɦɚ) ɨɩɬɟɪɟʄɟʃɚ, ɢɡɜɪɲɟɧɨ ʁɟ ɩɨɪɟђɟʃɟ ɫɚ ɪɟɡɭɥɬɚɬɢɦɚ ɞɨɛɢʁɟɧɢɦ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɦ ɢɫɩɢɬɢɜɚʃɟɦ (ɋɥɢɤɟ 7-25 ɢ 7-26). ɇɚ ɞɢʁɚɝɪɚɦɢɦɚ ɡɚɜɢɫɧɨɫɬɢ ɫɟ ɭɨɱɚɜɚ ɞɨɛɪɨ ɫɥɚɝɚʃɟ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨ ɞɨɛɢʁɟɧɢɯ ɜɪɟɞɧɨɫɬɢ ɫɚ ɜɪɟɞɧɨɫɬɢɦɚ ɞɨɛɢʁɟɧɢɦ ɩɪɢɦɟɧɨɦ ɧɭɦɟɪɢɱɤɟ ɚɧɚɥɢɡɟ ɆɄȿ ɋɥɢɤɚ 7-25: ɍɩɨɪɟɞɧɢ ɞɢʁɚɝɪɚɦ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɨɩɬɟɪɟʄɟʃɚ ɢ ɭɝɢɛɚ ɭ ɩɪɟɫɟɤɭ I (U1) ɢ ɩɪɟɫɟɤɭ II (U2) ɝɪɟɞɟ Ȼ-Ƚ3 ɞɨɛɢʁɟɧɢ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨ ɢ ɩɪɢɦɟɧɨɦ MKE (Ansys) ɋɥɢɤɚ 7-26: ɍɩɨɪɟɞɧɢ ɞɢʁɚɝɪɚɦ ɞɢɥɚɬɚɰɢʁɚ ɭ ɎɊɉ ɚɪɦɚɬɭɪɢ ɭ ɩɪɟɫɟɤɭ I ɝɪɟɞɟ Ȼ-Ƚ3 ɞɨɛɢʁɟɧɢ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨ (MT6) ɢ ɧɭɦɟɪɢɱɤɨɦ ɚɧɚɥɢɡɨɦ ɩɪɢɦɟɧɨɦ ɆɄȿ (Ansys) 0 20 40 60 80 100 120 140 160 180 0 5 10 15 20 25 Ɉɩ ɬɟɪ ɟʄɟ ʃɟ (k N) ɍɝɢɛ (mm) U1 U2 Ansys 0 20 40 60 80 100 120 140 160 180 0 5000 10000 15000 20000 Ɉɩ ɬɟɪ ɟʄɟ ʃɟ (k N) ɦɢɤɪɨ Ⱦɢɥɚɬɚɰɢјɟ MT6 Ansys 8 Ɂɚɜɪɲɧɟ ɧɚɩɨɦɟɧɟ 223 8 ЗАВɊШɇЕ ɇАɉɈɆЕɇЕ ɇɚ ɨɫɧɨɜɭ ɛɪɨʁɧɢɯ, ɩɪɟ ɫɜɟɝɚ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɯ, ɚ ɡɚɬɢɦ ɬɟɨɪɢʁɫɤɢɯ ɢ ɧɭɦɟɪɢɱɤɢɯ ɢɫɬɪɚɠɢɜɚʃɚ ɭɨɱɟɧɨ ʁɟ ɞɚ ɫɟ ɤɚɩɚɰɢɬɟɬ ɧɨɫɢɜɨɫɬɢ ɧɚ ɫɚɜɢʁɚʃɟ ɚɪɦɢɪɚɧɨɛɟɬɨɧɫɤɢɯ (ȺȻ) ɝɪɟɞɚ ɡɧɚɱɚʁɧɨ ɩɨɜɟʄɚɜɚ ʃɢɯɨɜɢɦ ɨʁɚɱɚɜɚʃɟɦ ɚɪɦɚɬɭɪɨɦ ɨɞ ɎɊɉ ɦɚɬɟɪɢʁɚɥɚ. ȼɟʄɢɧɚ ɨɜɢɯ ɢɫɬɪɚɠɢɜɚʃɚ ɛɚɜɢ ɫɟ ɩɨɧɚɲɚʃɟɦ ɧɨɫɚɱɚ ɫɬɚɬɢɱɤɨɝ ɫɢɫɬɟɦɚ ɩɪɨɫɬɚ ɝɪɟɞɚ, ɨɩɬɟɪɟʄɟɧɢɯ ɫɚ ɞɜɟ ɤɨɧɰɟɧɬɪɢɫɚɧɟ ɫɢɥɟ (four point load), ɚ ɦɧɨɝɨ ɱɟɲʄɢ ɫɥɭɱɚʁ ɭ ɪɟɚɥɧɢɦ ɤɨɧɫɬɪɭɤɰɢʁɚɦɚ ʁɟ ɫɬɚɬɢɱɤɢ ɫɢɫɬɟɦ ɤɨɧɬɢɧɭɚɥɧɨɝ ɧɨɫɚɱɚ, ɤɨʁɢ ʁɟ ɡɧɚɬɧɨ ɦɚʃɟ ɢɫɬɪɚɠɢɜɚɧ. ɉɨɪɟɞ ɬɨɝɚ, ɭ ɞɨɦɚʄɨʁ ɝɪɚђɟɜɢɧɫɤɨʁ ɪɟɝɭɥɚɬɢɜɢ ʁɨɲ ɭɜɟɤ ɧɟɦɚ ɩɪɚɤɬɢɱɧɢɯ ɩɪɟɩɨɪɭɤɚ, ɧɢ ɩɪɨɩɢɫɚ ɢ ɫɬɚɧɞɚɪɞɚ ɡɚ ɩɪɢɦɟɧɭ ɛɢɥɨ ɤɨɝ ɫɢɫɬɟɦɚ ɨʁɚɱɚʃɚ ɎɊɉ ɚɪɦɚɬɭɪɨɦ ɢ ɭɝɥɚɜɧɨɦ ɫɟ ɤɨɪɢɫɬɟ ɩɪɟɩɨɪɭɤɟ ɢ ɫɨɮɬɜɟɪɢ ɫɜɟɬɫɤɢ ɩɪɢɡɧɚɬɢɯ ɩɪɨɢɡɜɨђɚɱɚ ɨɜɢɯ ɩɪɨɢɡɜɨɞɚ. Ɂɛɨɝ ɬɨɝɚ ʁɟ ʁɟɞɚɧ ɨɞ ɰɢʂɟɜɚ ɢɫɬɪɚɠɢɜɚʃɚ ɛɢɨ ɞɚ ɫɟ ɨʁɚɱɚɜɚʃɟ ɤɨɧɬɢɧɭɚɥɧɢɯ ɝɪɟɞɧɢɯ ɧɨɫɚɱɚ ɚɪɦɚɬɭɪɨɦ ɨɞ ɎɊɉ ɦɚɬɟɪɢʁɚɥɚ ɞɨɞɚɬɧɨ ɢɫɬɪɚɠɢ ɬɟɨɪɢʁɫɤɢ ɢ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɨ ɢ ɩɪɢɛɥɢɠɢ ɧɚɭɱɧɨʁ ɢ ɫɬɪɭɱɧɨʁ ʁɚɜɧɨɫɬɢ ɭ ɨɛɥɚɫɬɢ ɝɪɚђɟɜɢɧɫɤɨɝ ɤɨɧɫɬɪɭɤɬɟɪɫɬɜɚ. Ɍɟɠɢɲɬɟ ɪɚɞɚ ɩɪɟɞɫɬɚɜʂɚʁɭ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɚ ɢɫɩɢɬɢɜɚʃɚ ɲɟɫɬ ȺȻ ɤɨɧɬɢɧɭɚɥɧɢɯ ɝɪɟɞɧɢɯ ɧɨɫɚɱɚ ɨʁɚɱɚɧɢɯ ɎɊɉ ɚɪɦɚɬɭɪɨɦ, ɢɡɥɨɠɟɧɢɯ ɭɬɢɰɚʁɭ ɤɪɚɬɤɨɬɪɚʁɧɨɝ ɫɬɚɬɢɱɤɨɝ ɨɩɬɟɪɟʄɟʃɚ. Ɉʁɚɱɚɜɚʃɟ ɤɨɧɬɢɧɭɚɥɧɢɯ ɧɨɫɚɱɚ ʁɟ ɢɡɜɪɲɟɧɨ ɧɚ ɞɜɚ ɧɚɱɢɧɚ: 1. ɭɝɪɚɞʃɨɦ ɚɪɦɚɬɭɪɧɢɯ ɲɢɩɤɢ ɧɚ ɛɚɡɢ ɫɬɚɤɥɟɧɢɯ (ȽɎɊɉ) ɢ ɤɚɪɛɨɧɫɤɢɯ (ЦɎɊɉ) ɜɥɚɤɚɧɚ ɭ ɡɚɲɬɢɬɧɨɦ ɫɥɨʁɭ ɛɟɬɨɧɚ (ɇɋɆ ɦɟɬɨɞɚ), ɢ 8 Ɂɚɜɪɲɧɟ ɧɚɩɨɦɟɧɟ 224 2. ɥɟɩʂɟʃɟɦ ɥɚɦɢɧɚɬɚ ɨɞ ɤɚɪɛɨɧɫɤɢɯ ɜɥɚɤɚɧɚ ɧɚ ɡɚɬɟɝɧɭɬɨʁ ɩɨɜɪɲɢɧɢ ɝɪɟɞɟ (ȿȻ ɦɟɬɨɞɚ). Ɋɟɡɭɥɬɚɬɢ ɦɟɪɟɧɢɯ ɭɝɢɛɚ ɧɨɫɚɱɚ ɭ ɫɪɟɞɢɧɢ ɨɛɚ ɩɨʂɚ, ɞɢɥɚɬɚɰɢʁɚ ɭ ɛɟɬɨɧɭ, ɱɟɥɢɱɧɨʁ ɢ ɎɊɉ ɚɪɦɚɬɭɪɢ ɩɪɢɤɚɡɚɧɢ ɫɭ ɭ ɜɢɞɭ ɞɢʁɚɝɪɚɦɚ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɨɩɬɟɪɟʄɟʃɚ ɢ ɦɟɪɟɧɢɯ ɩɚɪɚɦɟɬɚɪɚ ɡɚ ɫɜɟ ɢɫɩɢɬɚɧɟ ɝɪɟɞɟ, ɩɨɫɥɟ ɱɟɝɚ ʁɟ ɢɡɜɪɲɟɧɚ ɢ ʃɢɯɨɜɚ ɭɩɨɪɟɞɧɚ ɚɧɚɥɢɡɚ. ɉɪɢɤɚɡɚɧɢ ɫɭ ɨɛɥɢɰɢ ɥɨɦɚ ɢɫɩɢɬɢɜɚɧɢɯ ɧɨɫɚɱɚ ɡɚɜɢɫɧɨ ɨɞ ɦɟɬɨɞɟ ɢ ɩɨɫɬɭɩɤɚ ɨʁɚɱɚʃɚ. ɉɨɪɟɞ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɯ ɢɫɩɢɬɢɜɚʃɚ, ɪɚɡɜɢʁɟɧ ʁɟ ɦɚɬɟɦɚɬɢɱɤɢ ɦɨɞɟɥ ɡɚ ɩɪɨɪɚɱɭɧ ɧɨɫɢɜɨɫɬɢ ɩɪɟɫɟɤɚ ȺȻ ɝɪɟɞɟ ɨʁɚɱɚɧɟ ɎɊɉ ɚɪɦɚɬɭɪɨɦ, ɨɩɬɟɪɟʄɟɧɟ ɧɚ ɫɚɜɢʁɚʃɟ. ɇɚɩɢɫɚɧ ʁɟ ɩɪɨɝɪɚɦ ɆИɤ.m ɭ Ɇɚɬɥɚɛɭ (MATLAB R2014a) ɱɢʁɨɦ ɩɪɢɦɟɧɨɦ ɫɭ ɨɞɪɟђɟɧɟ ɤɪɢɜɟ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɦɨɦɟɧɬɚ ɢ ɤɪɢɜɢɧɟ ɩɪɟɫɟɤɚ ɨʁɚɱɚɧɢɯ ɪɚɡɥɢɱɢɬɨɦ ɤɨɥɢɱɢɧɨɦ ȽɎɊɉ, ɨɞɧɨɫɧɨ ЦɎɊɉ ɚɪɦɚɬɭɪɟ. Кɨɪɢɲʄɟʃɟɦ ɩɪɨɝɪɚɦɚ ɆИɤ.m ɚɧɚɥɢɡɢɪɚɧɢ ɫɭ ɭɬɢɰɚʁɢ ɪɚɡɥɢɱɢɬɢɯ ɩɚɪɚɦɟɬɚɪɚ (ɜɪɫɬɚ ɢ ɤɨɥɢɱɢɧɚ ɎɊɉ ɚɪɦɚɬɭɪɟ, ɱɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ ɢ ɩɪɨɰɟɧɚɬ ɚɪɦɢɪɚʃɚ ɭɧɭɬɪɚɲʃɨɦ ɱɟɥɢɱɧɨɦ ɚɪɦɚɬɭɪɨɦ) ɧɚ ɧɨɫɢɜɨɫɬ ɩɪɟɫɟɤɚ ɝɪɟɞɟ ɨʁɚɱɚɧɟ ɎɊɉ ɚɪɦɚɬɭɪɨɦ. ɇɭɦɟɪɢɱɤɨ ɢɫɬɪɚɠɢɜɚʃɟ ɨɛɭɯɜɚɬɚ ɧɟɥɢɧɟɚɪɧɭ ɚɧɚɥɢɢɡɭ ɟɤɫɩɟɪɢɦɟɧɬɥɧɨ ɢɫɩɢɬɢɜɚɧɢɯ ɧɨɫɚɱɚ ɩɪɢɦɟɧɨɦ ɫɨɮɬɜɟɪɚ Ⱥɧɫɢɫ (ANSВS). 8.1 Зɚкʂɭɱɰɢ ɫɩɪɨɜɟɞɟɧɢɯ ɢɫɬɪɚɠɢɜɚʃɚ ɍ ɨɜɨɦ ɪɚɞɭ, ɧɚ ɨɫɧɨɜɭ ɫɩɪɨɜɟɞɟɧɢɯ ɫɨɩɫɬɜɟɧɢɯ ɢɫɬɪɚɠɢɜɚʃɚ ɜɟɡɚɧɢɯ ɡɚ ɦɨɝɭʄɧɨɫɬ ɩɪɢɦɟɧɟ ɎɊɉ ɚɪɦɚɬɭɪɟ ɭ ɨʁɚɱɚɜɚʃɭ ȺȻ ɤɨɧɬɢɧɭɚɥɧɢɯ ɝɪɟɞɧɢɯ ɧɨɫɚɱɚ ɢɡɜɟɞɟɧɟ ɫɭ ɞɜɟ ɝɪɭɩɟ ɡɚɤʂɭɱɚɤɚ. ɉɪɜɚ ɝɪɭɩɚ ɡɚɤʂɭɱɚɤɚ ɨɞɧɨɫɢ ɫɟ ɧɚ ɚɧɚɥɢɡɭ ɩɪɟɫɟɤɚ ȺȻ ɝɪɟɞɟ ɨʁɚɱɚɧɟ ɎɊɉ ɚɪɦɚɬɭɪɨɦ ɩɪɢɦɟɧɨɦ ɩɪɨɝɪɚɦɚ ɆИɤ.m. Ⱦɪɭɝɭ ɝɪɭɩɭ ɱɢɧɟ ɡɚɤʂɭɱɰɢ ɤɨʁɢ ɫɟ ɨɞɧɨɫɟ ɧɚ ɝɪɚɧɢɱɧɚ ɫɬɚʃɚ ɤɨɧɬɢɧɭɚɥɧɢɯ ɧɨɫɚɱɚ ɨʁɚɱɚɧɢɯ ɎɊɉ ɚɪɦɚɬɭɪɨɦ, ɢɡɥɨɠɟɧɢɯ ɞɟʁɫɬɜɭ ɤɪɚɬɤɨɬɪɚʁɧɨɝ ɨɩɬɟɪɟʄɟʃɚ. ɇɚ ɨɫɧɨɜɭ ɚɧɚɥɢɡɟ ɞɨɛɢʁɟɧɢɯ ɞɢʁɚɝɪɚɦɚ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɦɨɦɟɧɬɚ ɫɚɜɢʁɚʃɚ ɢ ɤɪɢɜɢɧɟ ɩɪɟɫɟɤɚ ȺȻ ɝɪɟɞɟ ɨʁɚɱɚɧɟ ɎɊɉ ɚɪɦɚɬɭɪɨɦ (Сɥиɤе 5-12 ɞɨ 5-32), ɤɚɨ ɢ ɞɢʁɚɝɪɚɦɚ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɝɪɚɧɢɱɧɨɝ ɦɨɦɟɧɬɚ ɫɚɜɢʁɚʃɚ ɢ ɩɨɜɪɲɢɧɟ ɎɊɉ ɚɪɦɚɬɭɪɟ ɩɪɢ ɪɚɡɥɢɱɢɬɢɦ ɜɪɟɞɧɨɫɬɢɦɚ ɱɜɪɫɬɨʄɟ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ ɢ ɩɪɨɰɟɧɬɚ ɚɪɦɢɪɚʃɚ ɱɟɥɢɱɧɨɦ ɚɪɦɚɬɭɪɨɦ (Сɥиɤе 5-34 ɞɨ 5-78), ɢɡɜɟɞɟɧɢ ɫɭ ɫɥɟɞɟʄɢ ɡɚɤʂɭɱɰɢ:  Ɉɛɥɢɤ ɜɟɡɟ ɦɨɦɟɧɬ-ɤɪɢɜɢɧɚ ʁɟ ɛɢɬɧɚ ɤɚɪɚɤɬɟɪɢɫɬɢɤɚ ȺȻ ɩɪɟɫɟɤɚ ɨɞ ɤɨʁɟ ɭ ɡɧɚɱɚʁɧɨʁ ɦɟɪɢ ɡɚɜɢɫɢ ɩɨɧɚɲɚʃɟ ȺȻ ɝɪɟɞɟ ɭ ɰɟɥɢɧɢ. ɇɚ ɞɨɛɢʁɟɧɢɦ ɞɢʁɚɝɪɚɦɢɦɚ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɦɨɦɟɧɬɚ ɫɚɜɢʁɚʃɚ ɢ ɤɪɢɜɢɧɟ ɩɪɟɫɟɤɚ ȺȻ ɝɪɟɞɟ ɨʁɚɱɚɧɟ ɪɚɡɥɢɱɢɬɨɦ ɤɨɥɢɱɢɧɨɦ ɫɬɚɤɥɟɧɟ ɢ ɤɚɪɛɨɧɫɤɟ ɎɊɉ ɚɪɦɚɬɭɪɟ ɭɨɱɟɧɟ ɫɭ ɬɪɢ 8 Ɂɚɜɪɲɧɟ ɧɚɩɨɦɟɧɟ 225 ɤɚɪɚɤɬɟɪɢɫɬɢɱɧɟ ɨɛɥɚɫɬɢ: 1) ɞɨ ɩɨʁɚɜɟ ɩɪɫɥɢɧɟ ɭ ɩɪɟɫɟɤɭ, 2) ɨɞ ɩɨʁɚɜɟ ɩɪɫɥɢɧɟ ɞɨ ɩɨʁɚɜɟ ɬɟɱɟʃɚ ɱɟɥɢɱɧɟ ɚɪɦɚɬɭɪɟ ɢ 3) ɨɞ ɩɨʁɚɜɟ ɬɟɱɟʃɚ ɚɪɦɚɬɭɪɟ ɞɨ ɥɨɦɚ ɩɪɟɫɟɤɚ.  ɇɚ ɜɪɟɞɧɨɫɬ ɦɨɦɟɧɬɚ ɩɨʁɚɜɟ ɩɪɫɥɢɧɟ (Mcr) ɎɊɉ ɚɪɦɚɬɭɪɚ ɢɦɚ ɦɢɧɢɦɚɥɚɧ ɭɬɢɰɚʁ ɛɟɡ ɨɛɡɢɪɚ ɧɚ ɜɪɫɬɭ ɢ ɤɨɥɢɱɢɧɭ ɞɨɞɚɬɧɟ ɚɪɦɚɬɭɪɟ.  ɇɚ ɜɪɟɞɧɨɫɬ ɦɨɦɟɧɬɚ ɬɟɱɟʃɚ (Ɇy), ɤɚɨ ɢ ɧɚ ɜɪɟɞɧɨɫɬ ɝɪɚɧɢɱɧɨɝ ɦɨɦɟɧɬɚ ɫɚɜɢʁɚʃɚ (Ɇu) ɎɊɉ ɚɪɦɚɬɭɪɚ ɢɦɚ ɡɧɚɱɚʁɚɧ ɭɬɢɰɚʁ, ɩɪɢ ɱɟɦɭ ʁɟ ɩɨɜɟʄɚʃɟ ɦɨɦɟɧɬɚ ɬɟɱɟʃɚ ɢ ɝɪɚɧɢɱɧɨɝ ɦɨɦɟɧɬɚ ɫɚɜɢʁɚʃɚ ɜɟʄɟ ɭ ɫɥɭɱɚʁɭ ЦɎɊɉ ɚɪɦɚɬɭɪɟ, ɤɚɨ ɩɨɫɥɟɞɢɰɚ ɜɟʄɟ ɱɜɪɫɬɨʄɟ ɩɪɢ ɡɚɬɟɡɚʃɭ ɭ ɨɞɧɨɫɭ ɧɚ ȽɎɊɉ ɚɪɦɚɬɭɪɭ.  ɉɨɬɪɟɛɚɧ ɩɪɨɰɟɧɚɬ ɚɪɦɢɪɚʃɚ ɫɩɨʂɚɲʃɨɦ ɎɊɉ ɚɪɦɚɬɭɪɨɦ ɬɪɟɛɚ ɨɞɪɟɞɢɬɢ ɭ ɫɜɚɤɨɦ ɩɨʁɟɞɢɧɚɱɧɨɦ ɫɥɭɱɚʁɭ ɨʁɚɱɚɜɚʃɚ, ɫ ɨɛɡɢɪɨɦ ɞɚ ɧɚ ɦɨɦɟɧɚɬ ɧɨɫɢɜɨɫɬɢ ɩɪɟɫɟɤɚ ɭɬɢɱɭ ɢ ɱɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ ɢ ɩɪɨɰɟɧɚɬ ɚɪɦɢɪɚʃɚ ɭɧɭɬɪɚɲʃɨɦ ɱɟɥɢɱɧɨɦ ɚɪɦɚɬɭɪɨɦ. ɍ ɫɥɭɱɚʁɭ ɤɚɞɚ ʁɟ ɱɜɪɫɬɨʄɚ ɛɟɬɨɧɚ ɩɪɢ ɩɪɢɬɢɫɤɭ ɦɚɥɚ, ɤɚɨ ɢ ɭ ɫɥɭɱɚʁɭ ɤɚɞɚ ʁɟ ɜɟɥɢɤɢ ɩɪɨɰɟɧɚɬ ɚɪɦɢɪɚʃɚ ɭɧɭɬɪɚɲʃɨɦ ɱɟɥɢɱɧɨɦ ɚɪɦɚɬɭɪɨɦ, ɩɪɢɦɟɧɚ ɞɨɞɚɬɧɟ ɎɊɉ ɚɪɦɚɬɭɪɟ ɝɭɛɢ ɧɚ ɡɧɚɱɚʁɭ ʁɟɪ ɞɨɥɚɡɢ ɞɨ ɥɨɦɚ ɩɪɟɫɟɤɚ ɭɫɥɟɞ ɦɪɜʂɟʃɚ ɛɟɬɨɧɚ, ɩɪɢ ɱɟɦɭ ʁɟ ɦɚɥɨ ɢɫɤɨɪɢɲʄɟʃɟ ɧɨɫɢɜɨɫɬɢ ɎɊɉ ɚɪɦɚɬɭɪɟ. ɇɚ ɨɫɧɨɜɭ ɫɩɪɨɜɟɞɟɧɢɯ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɯ ɢɫɩɢɬɢɜɚʃɚ, ɤɚɨ ɢ ɧɭɦɟɪɢɱɤɟ ɚɧɚɥɢɡɟ, ɩɪɨɢɡɚɲɥɚ ʁɟ ɞɪɭɝɚ ɝɪɭɩɚ ɡɚɤʂɭɱɚɤɚ ɜɟɡɚɧɢɯ ɡɚ ɝɪɚɧɢɱɧɚ ɫɬɚʃɚ ɤɨɧɬɢɧɭɚɥɧɢɯ ɧɨɫɚɱɚ ɨʁɚɱɚɧɢɯ ɎɊɉ ɚɪɦɚɬɭɪɨɦ, ɢɡɥɨɠɟɧɢɯ ɞɟʁɫɬɜɭ ɤɪɚɬɤɨɬɪɚʁɧɨɝ ɨɩɬɟɪɟʄɟʃɚ. ɂɚɤɨ ʁɟ ɢɫɩɢɬɢɜɚɧ ɪɟɥɚɬɢɜɧɨ ɦɚɥɢ ɛɪɨʁ ɤɨɧɬɢɧɭɚɥɧɢɯ ɝɪɟɞɧɢɯ ɧɨɫɚɱɚ (ʁɟɞɚɧ ɤɨɧɬɪɨɥɧɢ ɢ ɩɟɬ ɨʁɚɱɚɧɢɯ) ɦɨɝɭ ɫɟ, ɫɚɝɥɚɫɧɨ ɰɢʂɟɜɢɦɚ ɢɫɬɪɚɠɢɜɚʃɚ, ɮɨɪɦɭɥɢɫɚɬɢ ɫɥɟɞɟʄɢ ɡɚɤʂɭɱɰɢ:  ɇɚ ɨɫɧɨɜɭ ɞɢʁɚɝɪɚɦɚ ɡɚɜɢɫɧɨɫɬɢ ɢɡɦɟђɭ ɨɩɬɟɪɟʄɟʃɚ ɢ ɭɝɢɛɚ, ɭɨɱʂɢɜɟ ɫɭ ɬɪɢ ɤɚɪɚɤɬɟɪɢɫɬɢɱɧɟ ɨɛɥɚɫɬɢ: 1) ɥɢɧɟɚɪɚɧɨ ɩɨɧɚɲɚʃɟ ɞɨ ɩɨʁɚɜɟ ɩɪɫɥɢɧɚ ɭ ɛɟɬɨɧɭ, 2) ɧɟɥɢɧɟɚɪɧɨ ɩɨɧɚɲɚʃɟ ɨɞ ɩɨʁɚɜɟ ɩɪɫɥɢɧɚ ɞɨ ɩɨʁɚɜɟ ɬɟɱɟʃɚ ɭ ɡɚɬɟɝɧɭɬɨʁ ɱɟɥɢɱɧɨʁ ɚɪɦɚɬɭɪɢ ɢ 3) ɢɡɪɚɡɢɬɨ ɧɟɥɢɧɟɚɪɧɨ ɩɨɧɚɲɚʃɟ ɨɞ ɩɨʁɚɜɟ ɬɟɱɟʃɚ ɭ ɱɟɥɢɱɧɨʁ ɚɪɦɚɬɭɪɢ ɞɨ ɥɨɦɚ.  ɍ ɞɨɦɟɧɭ ɟɥɚɫɬɢɱɧɢɯ ɞɟɮɨɪɦɚɰɢʁɚ, ɞɨ ɩɨʁɚɜɟ ɩɪɫɥɢɧɚ, ɧɟɦɚ ɛɢɬɧɢɯ ɪɚɡɥɢɤɚ ɭ ɩɨɧɚɲɚʃɭ ɧɨɫɚɱɚ, ɛɟɡ ɨɛɡɢɪɚ ɧɚ ɧɚɱɢɧ ɨʁɚɱɚɜɚʃɚ.  ɉɪɢɦɟɧɚ ɎɊɉ ɚɪɦɚɬɭɪɟ ɡɚ ɨʁɚɱɚɜɚʃɟ ȺȻ ɤɨɧɬɢɧɭɚɥɧɢɯ ɝɪɟɞɧɢɯ ɧɨɫɚɱɚ, ɱɚɤ ɢ ɩɪɢ ɦɚɥɨʁ ɤɨɥɢɱɢɧɢ ɞɨɞɚɬɧɟ ɚɪɦɚɬɭɪɟ ɦɨɠɟ ɡɧɚɱɚʁɧɨ ɞɚ ɩɨɜɟʄɚ ɧɨɫɢɜɨɫɬ ɧɚ ɫɚɜɢʁɚʃɟ. Ɉɜɨ ʁɟ ɩɨɬɜɪђɟɧɨ ɨʁɚɱɚɜɚʃɟɦ ɞɨɞɚɬɧɢɦ ɫɬɚɤɥɟɧɢɦ ɢ ɤɚɪɛɨɧɫɤɢɦ ɎɊɉ ɲɢɩɤɚɦɚ ɤɨʁɢɦɚ ʁɟ ɩɨɫɬɢɝɧɭɬɨ ɩɨɜɟʄɚʃɟ ɧɨɫɢɜɨɫɬɢ ɭ ɨɞɧɨɫɭ ɧɚ ɤɨɧɬɪɨɥɧɭ 8 Ɂɚɜɪɲɧɟ ɧɚɩɨɦɟɧɟ 226 (ɧɟɨʁɚɱɚɧɭ) ɝɪɟɞɭ ɨɞ 22% ɞɨ 82%, ɭ ɡɚɜɢɫɧɨɫɬɢ ɨɞ ɜɪɫɬɟ ɢ ɩɨɥɨɠɚʁɚ ɎɊɉ ɨʁɚɱɚʃɚ, ɤɚɨ ɢ ɨʁɚɱɚɜɚʃɟɦ ɎɊɉ ɬɪɚɤɚɦɚ, ɤɨʁɢɦɚ ʁɟ ɩɨɫɬɢɝɧɭɬɨ ɩɨɜɟʄɚʃɟ ɧɨɫɢɜɨɫɬɢ ɨɞ 50%.  ɍɩɨɬɪɟɛɨɦ ȽɎɊɉ ɲɢɩɤɢ ɦɨɠɟ ɫɟ ɨɫɬɜɚɪɢɬɢ ɩɨɜɟʄɚʃɟ ɧɨɫɢɜɨɫɬɢ ɤɨɧɬɢɧɭɚɥɧɢɯ ɧɨɫɚɱɚ ɛɟɡ ɨɛɡɢɪɚ ɧɚ ɩɨɥɨɠɚʁ ɨʁɚɱɚʃɚ ɲɬɨ ʁɟ ɩɨɬɜɪђɟɧɨ ɫɩɪɨɜɟɞɟɧɢɦ ɟɤɫɩɟɪɢɦɟɧɬɨɦ. Ɉʁɚɱɚɜɚʃɟɦ ɭ ɝɨɪʃɨʁ ɡɨɧɢ ɢɡɧɚɞ ɫɪɟɞʃɟɝ ɨɫɥɨɧɰɚ ɩɨɫɬɢɝɧɭɬɨ ʁɟ ɧɟɡɧɚɬɧɨ ɩɨɜɟʄɚʃɟ ɧɨɫɢɜɨɫɬɢ ɡɚ 22%, ɞɨɤ ɫɟ ɨʁɚɱɚɜɚʃɟɦ ɭ ɞɨʃɨʁ ɡɨɧɢ ɨɛɚ ɩɨʂɚ ɧɨɫɢɜɨɫɬ ɩɨɜɟʄɚɜɚ ɡɚ 48%, ɚ ɨʁɚɱɚɜɚʃɟɦ ɢ ɭ ɝɨɪʃɨʁ ɡɨɧɢ ɢɡɧɚɞ ɫɪɟɞʃɟɝ ɨɫɥɨɧɰɚ ɢ ɭ ɞɨʃɨʁ ɡɨɧɢ ɨɛɚ ɩɨʂɚ ɩɨɫɬɢɝɧɭɬɨ ʁɟ ɩɨɜɟʄɚʃɟ ɨɞ 67%, ɭ ɨɞɧɨɫɭ ɧɚ ɧɨɫɢɜɨɫɬ ɤɨɧɬɪɨɥɧɟ (ɧɟɨʁɚɱɚɧɟ) ɝɪɟɞɟ.  ɍɩɨɬɪɟɛɨɦ ЦɎɊɉ ɲɢɩɤɢ, ɡɚɯɜɚʂɭʁɭʄɢ ʃɢɯɨɜɨʁ ɜɟʄɨʁ ɱɜɪɫɬɨʄɢ ɩɪɢ ɡɚɬɟɡɚʃɭ, ɦɨɠɟ ɫɟ ɡɧɚɱɚʁɧɢʁɟ ɩɨɜɟʄɚɬɢ ɧɨɫɢɜɨɫɬ ɤɨɧɬɢɧɭɚɥɧɢɯ ɧɨɫɚɱɚ ɭ ɩɨɪɟђɟʃɭ ɫɚ ɭɩɨɬɪɟɛɨɦ ȽɎɊɉ ɲɢɩɤɢ. ɂɩɚɤ, ɭɨɱɟɧɨ ʁɟ ɩɨɜɟʄɚʃɟ ɧɨɫɢɜɨɫɬɢ ɨɞ ɫɜɟɝɚ 9 % ɤɨɞ ɝɪɟɞɟ ɨʁɚɱɚɧɟ ЦɎɊɉ ɲɢɩɤɚɦɚ ɭ ɨɞɧɨɫɭ ɧɚ ɧɨɫɢɜɨɫɬ ɝɪɟɞɟ ɨʁɚɱɚɧɟ ȽɎɊɉ ɲɢɩɤɚɦɚ. Ɋɚɡɥɨɡɢ ɧɟɡɧɚɬɧɨɝ ɩɨɜɟʄɚʃɚ ɧɨɫɢɜɨɫɬɢ ɥɟɠɟ ɭ ɩɪɟɜɪɟɦɟɧɨɦ ɨɬɤɚɡɭ ɝɪɟɞɧɨɝ ɧɨɫɚɱɚ ɨʁɚɱɚɧɨɝ ЦɎɊɉ ɲɢɩɤɚɦɚ.  ɂɚɤɨ ɫɟ ɢ ɫɬɚɤɥɟɧɟ ɢ ɤɚɪɛɨɧɫɤɟ ɎɊɉ ɲɢɩɤɟ ɦɨɝɭ ɤɨɪɢɫɬɢɬɢ ɭ ɨɤɜɢɪɭ ɇɋɆ ɦɟɬɨɞɟ ɡɚ ɩɨɜɟʄɚʃɟ ɧɨɫɢɜɨɫɬɢ ɤɨɧɬɢɧɭɚɥɧɨɝ ɧɨɫɚɱɚ, ɧɚ ɢɡɛɨɪ ɦɚɬɟɪɢʁɚɥɚ ɦɨɝɭ ɭɬɢɰɚɬɢ ɢ ɞɪɭɝɢ ɱɢɧɢɨɰɢ. ɇɚ ɩɪɢɦɟɪ, ɡɛɨɝ ɧɢɠɟ ɰɟɧɟ ɭ ɨɞɧɨɫɭ ɧɚ ЦɎɊɉ ɚɪɦɚɬɭɪɭ, ȽɎɊɉ ɚɪɦɚɬɭɪɚ ɦɨɠɟ ɛɢɬɢ ɟɤɨɧɨɦɢɱɧɢʁɚ ɭ ɜɟʄɢɧɢ ɫɥɭɱɚʁɟɜɚ ɨʁɚɱɚɜɚʃɚ, ɚɥɢ ɭ ɫɥɭɱɚʁɟɜɢɦɚ ɤɚɞɚ ʁɟ ɞɟɮɨɪɦɚɛɢɥɧɨɫɬ ɨɝɪɚɧɢɱɚɜɚʁɭʄɢ ɭɫɥɨɜ, ɬɪɟɛɚ ɤɨɪɢɫɬɢɬɢ ЦɎɊɉ ɚɪɦɚɬɭɪɭ ɡɛɨɝ ʃɟɧɨɝ ɜɟʄɟɝ ɦɨɞɭɥɚ ɟɥɚɫɬɢɱɧɨɫɬɢ.  ɉɪɢɦɟɧɚ ɇɋɆ ɦɟɬɨɞɟ ɨʁɚɱɚʃɚ ɢɦɚ ɧɢɡ ɩɪɟɞɧɨɫɬɢ ɭ ɨɞɧɨɫɭ ɧɚ ȿȻ ɦɟɬɨɞɭ ɨʁɚɱɚʃɚ, ɤɚɤɨ ɫɚ ɚɫɩɟɤɬɚ ɝɪɚɧɢɱɧɨɝ ɫɬɚʃɚ ɧɨɫɢɜɨɫɬɢ, ɬɚɤɨ ɢ ɭ ɩɨɝɥɟɞɭ ɞɟɮɨɪɦɚɛɢɥɧɨɫɬɢ. ɉɪɟɞɧɨɫɬ ɩɪɢɦɟɧɟ ȿȻ ɦɟɬɨɞɟ ɭ ɨɞɧɨɫɭ ɧɚ ɇɋɆ ɦɟɬɨɞɭ ʁɟ ɭ ɩɨɝɥɟɞɭ ɟɤɨɧɨɦɢɱɧɨɫɬɢ, ɫ ɨɛɡɢɪɨɦ ɞɚ ʁɟ ɩɨɬɪɟɛɧɚ ɤɨɥɢɱɢɧɚ ɟɩɨɫɤɢɞɧɟ ɢɫɩɭɧɟ ɡɧɚɬɧɨ ɦɚʃɚ.  Ɉʁɚɱɚɜɚʃɟ ȽɎɊɉ ɲɢɩɤɚɦɚ ɧɟ ɭɬɢɱɟ ɧɟɝɚɬɢɜɧɨ ɧɚ ɞɭɤɬɢɥɧɨɫɬ ɤɨɧɬɢɧɭɚɥɧɢɯ ɧɨɫɚɱɚ, ɲɬɨ ɩɨɬɜɪђɭʁɟ ɢ ɢɧɞɟɤɫ ɞɭɤɬɢɥɧɨɫɬɢ ɢɫɩɢɬɚɧɢɯ ɧɨɫɚɱɚ (ɂȾ>4). Ɂɚ ɪɚɡɥɢɤɭ ɨɞ ʃɢɯ, ɞɭɤɬɢɥɧɨɫɬ ɧɨɫɚɱɚ ɨʁɚɱɚɧɨɝ ЦɎɊɉ ɲɢɩɤɚɦɚ ɧɢʁɟ ɡɚɞɨɜɨʂɚɜɚʁɭʄɚ (ɂȾ<2). Ɋɚɡɥɨɝ ɜɟʄɟ ɞɭɤɬɢɥɧɨɫɬɢ ɧɨɫɚɱɚ ɨʁɚɱɚɧɢɯ ȽɎɊɉ ɚɪɦɚɬɭɪɨɦ ɥɟɠɢ ɭ ɦɚʃɟɦ ɦɨɞɭɥɭ ɟɥɚɫɬɢɱɧɨɫɬɢ ɬɟ ɚɪɦɚɬɭɪɟ ɭ ɨɞɧɨɫɭ ɦɨɞɭɥ ɟɥɚɫɬɢɱɧɨɫɬɢ ЦɎɊɉ ɚɪɦɚɬɭɪɟ. Ɇɚɥɚ ɞɭɤɬɢɥɧɨɫɬ ɧɨɫɚɱɚ ɨʁɚɱɚɧɢɯ ɤɚɪɛɨɧɫɤɢɦ ɲɢɩɤɚɦɚ ɢ ɥɚɦɢɧɚɬɢɦɚ ɥɟɠɢ ɭ ɩɪɟɜɪɟɦɟɧɨɦ ɨɬɤɚɡɭ ɨɜɢɯ ɧɨɫɚɱɚ ɭɫɥɟɞ ɫɦɚʃɟɧɟ 8 Ɂɚɜɪɲɧɟ ɧɚɩɨɦɟɧɟ 227 ɩɪɢɨɧʂɢɜɨɫɬɢ ЦɎɊɉ ɲɢɩɤɢ ɨɞɧɨɫɧɨ, ɨɞɜɚʁɚʃɚ ɎɊɉ ɥɚɦɢɧɚɬɚ ɨɞ ɩɨɜɪɲɢɧɟ ɛɟɬɨɧɚ.  ɍ ɫɥɭɱɚʁɭ ɨʁɚɱɚɜɚʃɚ ɇɋɆ ɦɟɬɨɞɨɦ, ɭɨɱɟɧɢ ɨɛɥɢɰɢ ɨɬɤɚɡɚ ɫɭ ɛɢɥɢ ɪɚɡɥɢɱɢɬɢ ɡɚ ɞɜɚ ɬɢɩɚ ɎɊɉ ɲɢɩɤɢ. Кɨɞ ɝɪɟɞɧɢɯ ɧɨɫɚɱɚ ɨʁɚɱɚɧɢɯ ȽɎɊɉ ɲɢɩɤɚɦɚ, ɨɬɤɚɡ ɫɟ ʁɚɜɢɨ ɭ ɡɨɧɢ ɫɢɞɪɟʃɚ ɭɫɥɟɞ ɝɭɛɢɬɤɚ ɩɪɢɨɧʂɢɜɨɫɬɢ ɧɚ ɦɟђɭɜɟɡɢ ɛɟɬɨɧ-ɟɩɨɤɫɢɞɧɚ ɢɫɩɭɧɚ, ɞɨɤ ɤɨɞ ɝɪɟɞɟ ɨʁɚɱɚɧɟ ЦɎɊɉ ɲɢɩɤɚɦɚ, ɞɨ ɨɬɤɚɡɚ ʁɟ ɞɨɲɥɨ ɭɫɥɟɞ ɝɭɛɢɬɤɚ ɩɪɢɨɧʂɢɜɨɫɬɢ ɢɡɦɟђɭ ЦɎɊɉ ɲɢɩɤɟ ɢ ɨɤɨɥɧɨɝ ɟɩɨɤɫɢɞɧɨɝ ɥɟɩɤɚ. ɍ ɫɥɭɱɚʁɭ ЦɎɊɉ ɚɪɦɚɬɭɪɟ, ɝɭɛɢɬɚɤ ɩɪɢɨɧʂɢɜɨɫɬɢ ɫɟ ɦɨɠɟ ɨɛʁɚɫɧɢɬɢ ɦɚɥɨɦ ɚɞɯɟɡɢʁɨɦ ɢɡɦɟђɭ ɝɥɚɬɤɟ ɩɨɜɪɲɢɧɟ ЦɎɊɉ ɲɢɩɤɢ ɢ ɟɩɨɤɫɢɞɧɟ ɢɫɩɭɧɟ.  Ɉɬɤɚɡ ɧɨɫɚɱɚ ɨʁɚɱɚɧɨɝ ȿȻ ɦɟɬɨɞɨɦ ʁɟ ɧɚɫɬɚɨ ɨɞɜɚʁɚʃɟɦ ɥɚɦɢɧɚɬɚ ɧɚ ɫɩɨʁɭ ɛɟɬɨɧɚ ɢ ɟɩɨɤɫɢɞɧɨɝ ɥɟɩɤɚ, ɡɛɨɝ ɩɪɟɤɨɪɚɱɟʃɚ ɧɚɩɨɧɚ ɡɚɬɟɡɚʃɚ ɭ ɛɟɬɨɧɭ. ɉɪɢɦɟʃɟɧ ʁɟ ɧɚʁɱɟɲʄɢ ɨɛɥɢɤ ɨɛɪɚɞɟ ɜɟɡɟ, ɛɟɡ ɩɨɫɟɛɧɟ ɨɛɪɚɞɟ ɩɨɜɪɲɢɧɟ ɛɟɬɨɧɚ ɧɚ ɤɨɧɬɚɤɬɭ ɫɚ ɥɚɦɢɧɚɬɨɦ.  ɇɭɦɟɪɢɱɤɢ ɩɨɫɬɭɩɚɤ ɧɟɥɢɧɟɚɪɧɟ ɚɧɚɥɢɡɟ ȺȻ ɤɨɧɬɢɧɭɚɥɧɢɯ ɝɪɟɞɧɢɯ ɧɨɫɚɱɚ ɨʁɚɱɚɧɢɯ ɎɊɉ ɚɪɦɚɬɭɪɨɦ ɢɡɭɡɟɬɧɨ ʁɟ ɤɨɦɩɥɟɤɫɚɧ ɚɥɢ ɞɚʁɟ ɭɩɨɬɪɟɛʂɢɜɟ ɪɟɡɭɥɬɚɬɟ, ɲɬɨ ʁɟ ɭ ɞɢɫɟɪɬɚɰɢʁɢ ɭɩɨɪɟђɟʃɟɦ ɫɚ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɦ ɜɪɟɞɧɨɫɬɢɦɚ ɢ ɩɨɤɚɡɚɧɨ.  Ɋɟɡɭɥɬɚɬɢ ɞɨɛɢʁɟɧɢ ɆКȿ ɚɧɚɥɢɡɨɦ ɦɨɞɟɥɚ ɝɪɟɞɧɢɯ ɧɨɫɚɱɚ ɩɨɤɥɚɩɚʁɭ ɫɟ ɫɚ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɦ ɫɜɟ ɞɨ ɩɨʁɚɜɟ ɬɟɱɟʃɚ ɡɚɬɟɝɧɭɬɟ ɱɟɥɢɱɧɟ ɚɪɦɚɬɭɪɟ. ɉɨɫɥɟ ɩɨʁɚɜɟ ɬɟɱɟʃɚ ɱɟɥɢɤɚ, ɫɪɚɱɭɧɚɬɢ ɭɝɢɛɢ ɢ ɞɢɥɚɬɚɰɢʁɟ ɩɪɢɦɟɧɨɦ ɆКȿ ɫɭ ɦɚʃɟ ɭ ɨɞɧɨɫɭ ɧɚ ɭɝɢɛɟ ɢ ɞɢɥɚɬɚɰɢʁɟ ɞɨɛɢʁɟɧɟ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɦ ɢɫɩɢɬɢɜɚʃɟɦ. Ɋɚɡɥɨɡɢ ɧɟɫɥɚɝɚʃɚ ɪɟɡɭɥɬɚɬɚ ɞɨɛɢʁɟɧɢɯ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɦ ɢɫɩɢɬɢɜɚʃɟɦ ɢ ɩɪɢɦɟɧɨɦ ɆКȿ ɫɭ ɩɪɟ ɫɜɟɝɚ ɭ ɥɨɤɚɥɧɨʁ ɧɟɫɚɜɪɲɟɧɨɫɬɢ ɩɪɜɟɧɫɬɜɟɧɨ ɛɟɬɨɧɚ ɧɚ ɫɩɨʁɭ ɰɟɦɟɧɬɧɨɝ ɤɚɦɟɧɚ ɢ ɚɝɪɟɝɚɬɚ, ɤɚɨ ɢ ɩɪɟɬɩɨɫɬɚɜʂɟɧɨʁ ɢɞɟɚɥɧɨʁ ɩɪɢɨɧʂɢɜɨɫɬɢ ɢɡɦɟђɭ ɛɟɬɨɧɚ, ɟɩɨɤɫɢɞɧɨɝ ɥɟɩɤɚ ɢ ɎɊɉ ɚɪɦɚɬɭɪɟ.  ɋɜɢ ɡɚɤʂɭɱɰɢ ɡɚɫɧɨɜɚɧɢ ɫɭ ɧɚ ɚɧɚɥɢɡɢ ɪɟɡɭɥɬɚɬɚ ɫɩɪɨɜɟɞɟɧɢɯ ɢɫɬɪɚɠɢɜɚʃɚ. Ɂɚ ɢɡɜɨђɟʃɟ ɨɩɲɬɢʁɢɯ ɡɚɤʂɭɱɚɤɚ ɧɟɨɩɯɨɞɧɨ ʁɟ ɫɬɜɨɪɢɬɢ ɜɟʄɭ ɛɚɡɭ ɟɤɫɩɟɪɢɦɟɧɬɚɥɧɢɯ ɩɨɞɚɬɚɤɚ ɤɨʁɢ ɛɢ ɫɟ ɞɨɛɢɥɢ ɢɫɩɢɬɢɜɚʃɢɦɚ ɭ ɥɚɛɨɪɚɬɨɪɢʁɫɤɢɦ ɢ ɬɟɪɟɧɫɤɢɦ ɭɫɥɨɜɢɦɚ. 8 Ɂɚɜɪɲɧɟ ɧɚɩɨɦɟɧɟ 228 8.2 ɉɪɟɩɨɪɭкɟ ɡɚ ɛɭɞɭʄɚ ɢɫɬɪɚɠɢɜɚʃɚ Ɉʁɚɱɚɜɚʃɟ ɚɪɦɢɪɚɧɨɛɟɬɨɧɫɤɢɯ ɤɨɧɫɬɪɭɤɰɢʁɚ ɩɪɢɦɟɧɨɦ ɎɊɉ ɚɪɦɚɬɭɪɟ ɢɦɚ ɦɧɨɝɨ ɩɪɟɞɧɨɫɬɢ ɭ ɨɞɧɨɫɭ ɧɚ ɤɨɧɜɟɧɰɢɨɧɚɥɧɟ ɧɚɱɢɧɟ ɨʁɚɱɚɜɚʃɚ. ɉɪɢɦɟɧɚ ɇɋɆ ɦɟɬɨɞɟ, ɤɨʁɚ ɭ ɧɚɲɨʁ ɡɟɦʂɢ ʁɨɲ ɭɜɟɤ ɧɢʁɟ ɡɚɫɬɭɩʂɟɧɚ ɭ ɩɪɚɤɫɢ, ɩɪɟɞɫɬɚɜʂɚ ɜɪɥɨ ɚɬɪɚɤɬɢɜɧɨ ɩɨʂɟ ɡɚ ɛɭɞɭʄɚ ɢɫɬɪɚɠɢɜɚʃɚ. ɍ ɨɜɨɦ ɪɚɞɭ ʁɟ ɞɚɬ ɨɞɝɨɜɨɪ ɧɚ ɧɟɤɚ ɩɢɬɚʃɚ ɜɟɡɚɧɚ ɡɚ ɨʁɚɱɚɜɚʃɟ ɤɨɧɬɢɧɭɚɥɧɢɯ ɝɪɟɞɧɢɯ ɧɨɫɚɱɚ ɧɚɩɪɚɜʂɟɧɢɯ ɨɞ ɫɚɦɨɭɝɪɚђɭʁɭʄɟɝ ɛɟɬɨɧɚ. ɉɪɜɟɧɫɬɜɟɧɢ ɰɢʂ ʁɟ ɛɢɨ ɞɚ ɫɟ ɞɨђɟ ɞɨ ɪɚɰɢɨɧɚɥɧɨɝ ɢɡɛɨɪɚ ɜɪɫɬɟ ɎɊɉ ɚɪɦɚɬɭɪɟ, ɦɟɬɨɞɟ ɢ ɧɚɱɢɧɚ ɨʁɚɱɚʃɚ ɤɨɧɬɢɧɭɚɥɧɢɯ ɝɪɟɞɧɢɯ ɧɨɫɚɱɚ. ɂɫɬɪɚɠɢɜɚʃɚ ɛɢ ɬɪɟɛɚɥɨ ɭɫɦɟɪɢɬɢ ɭ ɫɥɟɞɟʄɢɦ ɩɪɚɜɰɢɦɚ:  ȿɤɫɩɟɪɢɦɟɧɬɚɥɧɨ ɢɫɩɢɬɢɜɚʃɟ ɩɨɧɚɲɚʃɚ ȺȻ ɤɨɧɬɢɧɭɚɥɧɢɯ ɝɪɟɞɧɢɯ ɧɨɫɚɱɚ ɨʁɚɱɚɧɢɯ ɎɊɉ ɚɪɦɚɬɭɪɨɦ ɩɪɢ ɞɢɧɚɦɢɱɤɨɦ ɨɩɬɟɪɟʄɟʃɭ;  ɂɫɬɪɚɠɢɜɚʃɟ ɩɪɢɦɟɧɟ ɭɫɤɢɯ ɬɪɚɤɚ ɢ ɢɫɩɭɧɚ ɩɪɨɪɟɡɚ ɧɚ ɛɚɡɢ ɰɟɦɟɧɬɚ ɡɚ ɨʁɚɱɚɜɚʃɟ ɭ ɨɤɜɢɪɭ ɇɋɆ ɦɟɬɨɞɟ;  ɂɫɬɪɚɠɢɜɚʃɟ ɧɚɱɢɧɚ ɡɚ ɫɩɪɟɱɚɜɚʃɟ ɨɞɜɚʁɚʃɚ ɫɩɨʂɚ ɡɚɥɟɩʂɟɧɢɯ ɥɚɦɢɧɚɬɚ ɤɨɞ ȿȻ ɦɟɬɨɞɟ;  Ɏɨɪɦɢɪɚʃɟ ɧɭɦɟɪɢɱɤɢɯ ɦɨɞɟɥɚ ɤɨʁɢɦ ɛɢ ɫɟ ɪɚɡɥɢɱɢɬɢ ɨɛɥɢɰɢ ɥɨɦɚ, ɤɨʁɢ ɫɟ ʁɚɜʂɚʁɭ ɤɨɞ ɧɨɫɚɱɚ ɨʁɚɱɚɧɢɯ ɎɊɉ ɚɪɦɚɬɭɪɨɦ, ɦɨɝɥɢ ɚɧɚɥɢɡɢɪɚɬɢ ɢ ɩɪɟɞɜɢɞɟɬɢ;  Ɋɟɚɥɧɚ ɧɭɦɟɪɢɱɤɚ ɫɢɦɭɥɚɰɢʁɚ ɦɟђɭɫɨɛɧɢɯ ɜɟɡɚ ɢɡɦɟђɭ ɛɟɬɨɧɚ ɢ ɟɩɨɤɫɢɞɧɟ ɢɫɩɭɧɟ, ɤɚɨ ɢ ɟɩɨɤɫɢɞɧɟ ɢɫɩɭɧɟ ɢ ɎɊɉ ɚɪɦɚɬɭɪɟ.  229   1:   M_k.m %Skrip datoteka za odredjivanje dijagrama zavisnosti izmedju momenta savijanja (M) i %krivine preseka (k) disp(' ') disp('GEOMETRIJSKE KARAKTERISTIKE POPRECNOG PRESEKA') disp(' ') b=input(' Unesite sirinu poprecnog preseka u mm b='); h=input(' Unesite visinu poprecnog preseka u mm h='); Ab=b*h; disp(' ') fprintf(' Povrsina poprecnog preseka grede Ab= %f mm^2',Ab ) disp(' ') Ib=b*h^3/12; disp(' ') fprintf(' Moment inercije grede Ib= %f mm^4',Ib ) disp(' ') disp(' ') c_dole=input(' Unesite debljinu zastitnog sloja u donjoj zoni u mm c_dole='); c_gore=input(' Unesite debljinu zastitnog sloja u gornjoj zoni u mm c_gore='); disp(' ') disp('DIMENZIJE ARMATURE') disp(' ') Fi_uzeng=input(' Unesite precnik uzengije u mm Fi_uzeng='); Fi_dole=input(' Unesite precnik armature u donjoj zoni u mm Fi_dole='); Fi_gore=input(' Unesite precnik armature u gornjoj zoni u mm Fi_gore='); disp(' ') disp('UDALJENJA ARMATURE OD PRITISNUTE IVICE PRESEKA') disp(' ') d_dole=h-c_dole-Fi_uzeng-Fi_dole/2; d_gore=c_gore+Fi_uzeng+Fi_gore/2; fprintf(' Udaljenje armature u gornjoj zoni d_gore= %f mm',d_gore ) disp(' ') fprintf(' Udaljenje armature u donjoj zoni d_dole= %f mm',d_dole ) disp(' ') d_frp=input(' Unesite udaljenje frp armature od pritisnute ivice u mm d_frp='); disp(' ')  230 y_dole=h-d_dole; y_gore=h-d_gore; y_frp=h-d_frp; disp(' ') disp('KARAKTERISTIKE CELICNE ARMATURE') disp(' ') As1=input(' Unesite povrsinu armature u donjoj zoni u mm^2 As1='); As2=input(' Unesite povrsinu armature u donjoj zoni u mm^2 As2='); Es=input(' Unesite modul elasticnosti celika u MPa Es='); f_s_y=input(' Unesite granicu tecenja celika u MPa f_s_y='); Eps_s_y=f_s_y/Es; fprintf(' Dilatacija tecenja celika Eps_s_y= %f',Eps_s_y ) disp(' ') Esp=input(' Unesite procenat ojacanja celika:'); Esp=Esp/100; disp(' ') Dilatacija_celik=[0; Eps_s_y; 0.01]; Napon_celik=[0; f_s_y; f_s_y+(0.01-Eps_s_y)*Esp*Es]; plot(Dilatacija_celik,Napon_celik) xlabel('Dilatacija ()') ylabel('Napon (MPa)') title('Veza napona i dilatacija za armaturni celik') disp(' ') disp('KARAKTERISTIKE FRP ARMATURE') disp(' ') Afrp=input(' Unesite povrsinu frp armature u donjoj zoni u mm^2 Afrp='); Efrp=input(' Unesite modul elasticnosti FRP armature u MPa Efrp='); f_frp_ult=input(' Unesite zateznu cvrstocu frp armature u MPa f_frp_ult='); disp(' ') Eps_frp_ult=f_frp_ult/Efrp; fprintf(' Dilatacija kidanja frp armature Eps_frp_ult= %f',Eps_frp_ult ) disp(' ') Dilatacija_FRP=[0; Eps_frp_ult]; Napon_FRP=[0; f_frp_ult]; plot(Dilatacija_FRP,Napon_FRP) xlabel('Dilatacija ()') ylabel('Napon (MPa)') title('Veza napona i dilatacija za FRP armaturu') disp(' ') Kapa=input(' Unesite redukcioni faktor odnosno pretpostavljeni stepen iskoriscenja FRP armature Kapa='); Eps_frp_ult_red=Kapa*Eps_frp_ult; fprintf(' Redukovana dilatacija kidanja frp armature Eps_frp_ult_red= %f',Eps_frp_ult_red ) disp(' ') Dilatacija_FRP=[0; Eps_frp_ult]; Napon_FRP=[0; f_frp_ult]; Dilatacija_FRP_red=[0; Eps_frp_ult_red]; Napon_FRP_red=[0; f_frp_ult*Kapa]; plot(Dilatacija_FRP,Napon_FRP,':r',Dilatacija_FRP_red,Napon_FRP_red,'-b','linewidth',2) xlabel('Dilatacija ()') ylabel('Napon (MPa)') title('Veza napona i dilatacija za FRP armaturu sa redukcionim faktorom') disp(' ') disp(' ') disp('KARAKTERISTIKE BETONA') disp(' ') f_c_prim=input(' Unesite pritisnu cvrstocu betona u MPa f_c_prim='); Ec=3202*((f_c_prim+8)^(0.587)); fprintf(' Modul elasticnosti betona Ec= %f MPa',Ec ) disp(' ') Eps_c_fcprim=2*f_c_prim/Ec;  231 fprintf(' Dilatacija betona pri pritisnoj cvrstoci Eps_c_fcprim= %f',Eps_c_fcprim ) disp(' ') GranicaElasticnostiBetona=0.3*f_c_prim; fprintf(' Granica elasticnosti betona 0.3*f_c_prim= %f MPa',GranicaElasticnostiBetona ) disp(' ') Eps_c_elast=GranicaElasticnostiBetona/Ec; fprintf(' Dilatacija betona na granici elasticnosti Eps_c_elast= %f',Eps_c_elast ) disp(' ') n=Es/Ec; n_frp=Efrp/Ec; f_c_r=0.6*(f_c_prim^(1/2)); fprintf(' Zatezna cvrstoca betona fcr= %f MPa',f_c_r ) disp(' ') Atransf1=(n-1)*As1; Atransf2=(n-1)*As2; Atransf_frp=(n_frp-1)*Afrp; y_td=(b*h^2/2+Atransf1*y_dole+Atransf2*y_gore+Atransf_frp*y_frp)/(b*h+Atransf1+Atransf2+Atransf_frp); y_tg=h-y_td; Ig=b*y_tg^3/12+b*y_tg*(y_tg/2)^2+b*y_td^3/12+b*y_td*(y_td/2)^2+Atransf1*(d_dole- y_tg)^2+Atransf2*(y_tg-d_gore)^2+Atransf_frp*(y_tg-d_frp)^2; Mcr=f_c_r*Ig/y_td; Mcr=Mcr/1e6; fprintf(' Moment pojave prsline Mcr= %f kNm',Mcr ) disp(' ') Eps_c_cr=f_c_r/Ec; RO_c=Eps_c_cr/y_tg fprintf(' Dilatacija betona pri pojavi prsline Eps_c_cr= %f',Eps_c_cr ) disp(' ') Eps_c_ult=input(' Unesite granicnu dilataciju betona u mikrodilatacijama Eps_c_ult='); disp(' ') md=input(' Unesite broj mikrodilatacija na kojima se vrsi iteracija='); disp(' ') BrojIteracija=Eps_c_ult/md; Eps_c_ult=Eps_c_ult*1e-6; disp(' ') fprintf(' Broj iteracija je: %f',BrojIteracija ) disp(' ') disp(' ') fprintf(' Prava-parabola dijagram zavisnosti' ) disp(' ') f_c_mat=zeros(BrojIteracija,1); Eps_c_mat=zeros(BrojIteracija,1); Eps_c=0; f_c_mat(1)=0; for k=1:BrojIteracija; Eps_c=Eps_c+md*1e-6; if Eps_c0&c10&c1Eps_s_y; syms c; hcr=(1+Eps_c_cr/Eps_c)*c; c_elast=c*Eps_c_elast/Eps_c; c_plast=c-c_elast; Eps_s2=Eps_c*(1-d_gore/c); Eps_s1=Eps_c*(d_dole/c-1); f_c=f_c_prim*(2*Eps_c/Eps_c_fcprim-(Eps_c/Eps_c_fcprim)^2); f_c_elast=0.3*f_c_prim; C_c_elast=1/2*Eps_c_elast*Ec*b*c_elast; C_c_plast_pravougaonik=Eps_c_elast*Ec*b*c_plast; C_c_plast_trougao=1/2*(f_c-f_c_elast)*b*c_plast; C_s2=Eps_s2*Es*As2; T_s1=(Eps_s_y*Es+Esp*Es*(Eps_s1-Eps_s_y))*As1; T_c=0.5*Eps_c_cr*Ec*b*(hcr-c); Eps_frp=Eps_c*(d_frp/c-1); T_frp=Eps_frp*Efrp*Afrp; c=solve(C_c_elast+C_c_plast_pravougaonik+C_c_plast_trougao+C_s2-T_s1-T_frp-T_c ); c1=c(1); c2=c(2); c1=double(c1); c2=double(c2); if c1>0&c10.01; syms c; hcr=(1+Eps_c_cr/Eps_c)*c; c_elast=c*Eps_c_elast/Eps_c; c_plast=c-c_elast; Eps_s2=Eps_c*(1-d_gore/c); Eps_s1=Eps_c*(d_dole/c-1); f_c=f_c_prim*(2*Eps_c/Eps_c_fcprim-(Eps_c/Eps_c_fcprim)^2); f_c_elast=0.3*f_c_prim; C_c_elast=1/2*Eps_c_elast*Ec*b*c_elast; C_c_plast_pravougaonik=Eps_c_elast*Ec*b*c_plast; C_c_plast_trougao=1/2*(f_c-f_c_elast)*b*c_plast; C_s2=Eps_s2*Es*As2; T_s1=(Eps_s_y*Es+Esp*Es*(Eps_s1-Eps_s_y))*As1; T_c=0.5*Eps_c_cr*Ec*b*(hcr-c); Eps_frp=Eps_c*(d_frp/c-1); T_frp=Eps_frp*Efrp*Afrp; c=solve(C_c_elast+C_c_plast_pravougaonik+C_c_plast_trougao+C_s2-T_s1-T_frp-T_c ); c1=c(1); c2=c(2); c1=double(c1); c2=double(c2); if c1>0&c10&c1Eps_s_y; syms c hcr=(1+Eps_c_cr/Eps_c)*c; c_elast=c*Eps_c_elast/Eps_c; c_prom=c*Eps_c_fcprim/Eps_c; c_plast=c_prom-c_elast; c_const=c-c_prom; Eps_s2=Eps_c*(1-d_gore/c); Eps_s1=Eps_c*(d_dole/c-1); f_c=f_c_prim*(2*Eps_c/Eps_c_fcprim-(Eps_c/Eps_c_fcprim)^2); f_c_elast=0.3*f_c_prim; C_c_elast=1/2*Eps_c_elast*Ec*b*c_elast; C_c_plast_pravougaonik=0.3*f_c_prim*b*c_plast; C_c_plast_trougao=0.35*f_c_prim*b*c_plast; C_c_const=f_c_prim*b*c_const; C_s2=Eps_s2*Es*As2; T_s1=(Eps_s_y*Es+Esp*Es*(Eps_s1-Eps_s_y))*As1; T_c=0.5*Eps_c_cr*Ec*b*(hcr-c); Eps_frp=Eps_c*(d_frp/c-1); T_frp=Eps_frp*Efrp*Afrp; c=solve(C_c_elast+C_c_plast_pravougaonik+C_c_plast_trougao+C_c_const+C_s2-T_s1-T_frp-T_c); c1=c(1); c2=c(2); c1=double(c1); c2=double(c2);  238 if c1>0&c1Eps_frp_ult_red; T_frp=0; end M=C_c_elast*2/3*c_elast+C_c_plast_pravougaonik*(c_elast+c_plast/2)+ +C_c_plast_trougao*(c_elast+2/3*c_plast)+C_c_const*(c_prom+c_const/2)+ +C_s2*(c-d_gore)+T_s1*(d_dole-c)+T_c*2/3*(hcr-c)+T_frp*(d_frp-c); M=M/1e3; RO=Eps_c/c; RO_mat(k,1)=RO; c_mat(k,1)=c; M_mat(k,1)=M; Ief=b*hcr^3/12; Ief_mat(k,1)=Ief; hcr_mat(k,1)=hcr; Eps_c_mat(k,1)=Eps_c; Eps_s2_mat(k,1)=Eps_s2; Eps_s1_mat(k,1)=Eps_s1; Eps_frp_mat(k,1)=Eps_frp; else Eps_s1>0.01; syms c hcr=(1+Eps_c_cr/Eps_c)*c; c_elast=c*Eps_c_elast/Eps_c; c_prom=c*Eps_c_fcprim/Eps_c; c_plast=c_prom-c_elast; c_const=c-c_prom; Eps_s2=Eps_c*(1-d_gore/c); Eps_s1=Eps_c*(d_dole/c-1); f_c=f_c_prim*(2*Eps_c/Eps_c_fcprim-(Eps_c/Eps_c_fcprim)^2); f_c_elast=0.3*f_c_prim; C_c_elast=1/2*Eps_c_elast*Ec*b*c_elast; C_c_plast_pravougaonik=0.3*f_c_prim*b*c_plast; C_c_plast_trougao=0.35*f_c_prim*b*c_plast; C_c_const=f_c_prim*b*c_const;  239 C_s2=Eps_s2*Es*As2; T_s1=(Eps_s_y*Es+Esp*Es*(Eps_s1-Eps_s_y))*As1; T_c=0.5*Eps_c_cr*Ec*b*(hcr-c); Eps_frp=Eps_c*(d_frp/c-1); T_frp=Eps_frp*Efrp*Afrp; c=solve(C_c_elast+C_c_plast_pravougaonik+C_c_plast_trougao+C_c_const+ +C_s2-T_s1-T_frp-T_c); c1=c(1); c2=c(2); c1=double(c1); c2=double(c2); if c1>0&c1Eps_frp_ult_red; T_frp=0; end M=C_c_elast*2/3*c_elast+C_c_plast_pravougaonik*(c_elast+c_plast/2)+ +C_c_plast_trougao*(c_elast+2/3*c_plast)+C_c_const*(c_prom+c_const/2)+ +C_s2*(c-d_gore)+T_s1*(d_dole-c)+T_c*2/3*(hcr-c)+T_frp*(d_frp-c); M=M/1e3; RO=Eps_c/c; RO_mat(k,1)=RO; c_mat(k,1)=c; M_mat(k,1)=M; Ief=b*hcr^3/12; Ief_mat(k,1)=Ief; hcr_mat(k,1)=hcr; Eps_c_mat(k,1)=Eps_c; Eps_s2_mat(k,1)=Eps_s2; Eps_s1_mat(k,1)=Eps_s1; Eps_frp_mat(k,1)=Eps_frp; end end end end disp(' ') fprintf(' Granicno stanje betona' )  240 disp(' ') M_gr_betona=M plot(RO_mat,M_mat) xlabel('Krivina ()') ylabel('Moment savijanja (kNm)') title('Dijagram zavisnosti momenta i krivine') disp(' ') fprintf(' Granicno stanje momenta' ) disp(' ') [d e]=max(M_mat); Mgr=d RO_gr=RO_mat(e) Eps_c_gr=Eps_c_mat(e) Eps_s1_gr=Eps_s1_mat(e) Eps_frp_gr=Eps_frp_mat(e) M_mat_gr=M_mat(1:e); RO_mat_gr=RO_mat(1:e); Eps_c_mat_gr=Eps_c_mat(1:e); Eps_s1_mat_gr=Eps_s1_mat(1:e); Eps_frp_ma_grt=Eps_frp_mat(1:e); Ief_mat_gr=Ief_mat(1:e); hcr_mat_gr=hcr_mat(1:e); plot(RO_mat_gr,M_mat_gr) xlabel('Krivina ()') ylabel('Moment savijanja (kNm)') title('Dijagram zavisnosti momenta i krivine') A=[M_mat Ief_mat]; AB=Eps_s_y-Eps_s1_mat; AB=abs(AB); [d e]=min(AB); M_tecenja=M_mat(e) RO_tecenja=RO_mat(e) Eps_s1_tecenja=Eps_s1_mat(e) Eps_c_tecenja=Eps_frp_mat(e) ABC=0.01-Eps_s1_mat; ABC=abs(ABC); [d e]=min(ABC); M_gr_dil_cel=M_mat(e) RO_gr_dil_cel=RO_mat(e) Eps_s1_gr_dil_cel=Eps_s1_mat(e) Eps_c_gr_dil_cel=Eps_c_mat(e) Eps_frp_gr_dil_cel=Eps_frp_mat(e) M_mat_gr_dil_cel=M_mat(1:e); RO_mat_gr_dil_cel=RO_mat(1:e); ABCD=Eps_frp_ult_red-Eps_frp_mat; ABCD=abs(ABCD); [d e]=min(ABCD); M_gr_dil_frp=M_mat(e) RO_gr_dil_frp=RO_mat(e) Eps_s1_gr_dil_frp=Eps_s1_mat(e) Eps_c_gr_dil_frp=Eps_c_mat(e) Eps_frp_gr_dil_frp=Eps_frp_mat(e) M_mat_gr_dil_frp=M_mat(1:e); 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