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15 = 5 * 3;     = 15

5 = 15 / 3;     = 

125 =(5;3);     = 125

        0,3333..

5 =(125;0.33333); 125   0,33333 = 5

12 = (144);      = 144..

12 = sqrt(144);      = 144.. (   Word ).

90  = 1,570796327 . =Pii/2

180  = 3,14159265358979324. =Pii

ctg( a ) = tan ( 90  a )    ..    .

  (GR);       .

Inv(GR) = tan(GR)  (GR);



Pii = 3,14159265358979324   ..

.cosa= cos20 = 0,93969262078591   20 

.sinaa=sin40 = 0,64278760968654   40 

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  b = 128.

  h = 46.

  L = 235.

:

   : Q = 7,85 * b * h* L / 1000000..;

Q = 10,861888 

  = 7850  / .. ( 30  1050-88 ).

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 d = 127.

 L = 390.

:

  : S=d*d*Pii/4; S=127*127*Pii /4..;

S= 12667,68698.

 :

Q = 7,85 * S * L / 1000000..;

Q = 7,85 *12667,68698*390 / 1000000..;

Q = 38,782124 .

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  d = 200.

  dv = 100.

 L = 300.

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:

Sn=d*d*Pii/4; Sn= 200*200*Pii/4; Sn= 31415,92654..

Sv=dv*dv*Pii/4..;

Sv= 100*100*Pii/4; Sv=7853,981634..

Q=7,85*(Sn-Sv)*L / 1000000..; Q=7,85*(23561,9449)*300 / 1000000..;

Q= 55,48838 

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   S = 100.

  L = 300.

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:

Q=7,85 * 0,866025403 * S * S *L / 1000000..;

Sp= 0,866025403 * S * S ..  ..

Q=7,85 * 0,866025403 * 100 * 100 * 300 / 1000000..;

Q= 20,3949 

:           

        . =0,866025403

  

.

   .

 h = 200.

 b = 160.

   = 300.

.  .








   : Q = 7,85 * b * h*  / 2000000..;

Q=7,85 * 200 * 160 * 300 / 2000000..;

Q= 37,68 

:         

     . =0,5

     

    .

 a = 200.

 b = 160.

 c = 140.

  h = 300.

.  .








:

   q = 7,85  / ..

:

.x=(b*b+c*c-(a*a))/(2*b*c)..;

.x=((160*160+140*140-(200*200))/(2*160*140)..;

.x= 0,116071428

Ua = arccos(x)

Ua = 83,33457274

    ..

   b :

Hb = c * cos ( 90  Ua ); (90  = 1,570796327 . ).

Hb = 140 * 0,993240868 = 139,0537216

 :

S = b * Hb/2..; S = 160 * 139,0537216 / 2 = 11124,29773 

 :

Q = 7,85 * S * h..; Q = 7,85 * 11124,29773 * 300 / 1000000..;

Gsf = 461030/2725231222

Q = 26,19772 ..

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S = b * Hb/2;   9   9*8/2.      .

  9   S = 11124,29773        D6.

  D6..     = 13*5*9/1000000.      .

  D6   = 26,1977 .  :

Q = 7,85 * S * h; Q = 7,85 * 11124,29773 * 300 / 1000000; Q = 26,1977 .



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 b = 300.

 a = 140.

 h = 160.

  L = 400.

   q = 7,85  / ..

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:

 :

S=h*(b+a)/2..; S=160*(300+140)/2; S=h*(b+a)/2; S= 35200

:

Q=7,85 * S *L /1000000..; Q=7,85 * 35200 *400 /1000000..;

Q= 110,528 

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  d = 600.

  dv = 200.

  L = 300.

.  .








  :

V=(L * Pii / 3)*( Rb*Rb + Rm * Rm + Rb * Rm )..;

V=(300 * Pii / 3)*( 90000 + 10000 + 30000 )..;

V = 40840704,5

 :

Q= 7,85 * V / 1000000..; Q= 7,85 * 40840704,5 / 1000000..;

Q = 320,59953 ..

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   dm  L    d  Lp.

 dm=d-dv.. dm=600-200.. dm=400..     Lp..

Lp=d*L/dm.. Lp=600*300/400.. Lp=450.. Lv=Lp-L.. Lv=450-300.. Lv=150..

         .

     d  dv: V = Pii*d*d*Lp*(1/3)/4..

V = Pii*600*600*450*(1/3)/4.. V = 424115001..  Vv=1570796..

      V = 424115001-1570796..

V =40840705..    Q = 320,599 .

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  R = 300.

  h = 200.

  L = 400.

   q = 7,85  / ..

.   .








:

 :

.d=R+R ; d= 300 + 300; d= 600

 :

Sk= d * d * Pii / 4..; Sk= 600 * 600 * Pii / 4..; Sk= 282743,3388

   :

.a=R-h..; a= 300  200; a= 100

  :

.b= sqrt((R*R)-(a*a))..; b= sqrt((300*300)-(100*100))..; b= 282,8427125

 :

St= a * b..; St= 100 * 282,8427125..; St= 28284,27125

      :

U = arctan( b / a )..; U = arctan( 282,8427125 / 100 );

U = 70,52877937

  

Ss=Sk * U * 2 / 360..; Ss= 282743,3388 * 70,52877937 * 2 / 360..;

Ss= 110786,3476

  

Sg=( Ss  St )..; Sg=( 55393,17378  28284,27125 )..; Sg= 82502,07631

Q = 7,85 * Sg * L / 1000000..; Q = 7,85 * 82502,07631 * 400 / 1000000..;

Q = 259,05652 ..

   Excel

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 :

Sk= d * d * Pii / 4; Sk= (R+R) * ( R+R) * Pii / 4; Sk= 600 * 600 * Pii / 4; Sk= 282743,3388

 Excel. D9 =(B7+B7)*(B7+B7)*()/4..

   : .a=R-h; .a= 300  200; .a= 100  Excel E14=B7-B5..

  :

.b= sqrt((R*R)-(a*a)); b= sqrt((300*300)-(100*100)); b= 282,8427125

 Excel E15=((B7*B7)-(E14*E14)) E16=(E15)

 : St= a * b;.. St= 100 * 282,8427125;.. St= 28284,27125

 Excel D11=E16*E14..

      :    .  @008.

U = arctan( b / a );.. U = arctan( 282,8427125 / 100 );..  Excel E17=E16/E14.. D6=ATAN(E17)..

      ( 2* = 360      ).

E18=D6/()..

  : D1=D9*E18..

  (      ): D4=D10-D11..

 : =D4*B9*B11/1000000 Q = 259,05652 

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 x1 = 10;  y1 = 20;

 x2 = 50;  y2 = 80;

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:

 :

L= sqrt((x1-x2)*(x1-x2))+((y1-y2)*(y1-y2));

L= sqrt((10-50)*(10-50))+((20-80)*(20-80));

L= sqrt( 5200 ); L= 72,11102551

   -  :

U= arctan((y2-y1)/(x2-x1));

U= arctan( 60 / 40 ); U= 56,30993247

..

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:  x1 = 10;  y1 = 20;

 x2 = 90;  y2 = 180;

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: RF-01.

Yy = (((y2-y1)*(x-x1)) / (x2-x1))+y1; Yy = (((180-20)*(50-10)) / (90-10))+20;..

Yy = ( 6400 / 80 )+20; Yy = 100;..

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.

:

       :

       .

(L1+L2)=( X2-X1)= 10.. L1=(L1+L2)/((M1/M2)+1); L1=10/((6/8)+1).. ;

L1 = 5,7142857  L2=4,285714..

    :

M=m1+m2; M= 6 + 8;.. M= 14 

: 1*L1=M2*L2 6*5,7142857=8*4,285714..  ..

( M1+M2)*(X1+L1)=(M1*X1)+(M2*X2).. (6+8)*(4+5,7142857)=(6*4)+(8*14)..

  ..

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  d.

  dv.

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   U.

 :

  d = 100

  dv = 80,90169943749474.

   n = 5

. .








:

   :

Ur = 180 / n; Ur = 180 / 5; Ur = 36

    .

  :

R=d / 2; R=100 / 2; R= 50

  :

Rv=(d/2)*cos( Ur ); Rv= 50 * cos( 36 );

Rv= 40,45084972

 :

.dv=Rv+Rv; .dv= 40,45084972 + 40,45084972;

.dv= 80,90169944

   :

X = d * ( cos ( 90 / n ))

 :

Sg= 2*(sqrt( R * R  Rv * Rv )); Sg= 2*(sqrt( 50 * 50  40,45084972 * 40,45084972 ));

Sg= 58,77852523

 :

S= ( Sg * Rv * n ) / 2; S= ( 58,77852523 * 40,45084972 * 5 ) / 2; S= 5944,103227

   Excel.

    Excel   _12. (   ).

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@010.  180    Pii = 3,1415926 ..

    :  = *Pii/180

    :  = *180/Pii

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:

:

    = P..

  .

 :

 = P.. ..

:  =   ;  = ..

 =sqrt( * + * );  =   ;  =  / 2;

  :  /  = E / ; :

E = * / ; :  = (  +  )*  / ;

E =   E;  =   ;  =  +  = AX + BT;

Rm=(XT*AB)/OA..  ..

Rb=BK=(AB*(XT+PB))/OB  ..

X=OB/OA..

UA=ATan(X)..   ..

UB=(Pii/2)-UA   ..

SB=Pii*BK*BK..    .R..

SM=Pii*Rm*Rm..     .R..

SBS=SB*2*UA/Pii..

SMS=SM*2*UB/Pii..

KO=BK-OB..

OO1=OA-Rm..

STR=2*KO*OO1..

SO=(SMS+SBS)-STR..

XU=UA*360/Pii..

X=4*SO/Pii..

DS= sqrt(X)..

      :

  Rb = ;          W.

  Rb    W   .

    E      

      Rb.

  Rm = E;   W  

     :

G = 90  W; :     .

    .

        :

.d =sqrt( 4*S / Pii );  S     .

 :

:

  = 80;   = 60;

.  .

.








.

:

  = 100,0..

    .  = 40,0..

  = 50,0..

    M.  = 30,0..

  .  = 73,739795..

    = 15106,498;

.    = 138,687;

   Excel

    Excel   _12. (   ).

    14.       :

 .      @002. @003. @004. @004.

:      .      .

@010.  180    Pii = 3,1415926 ..

    :  = *Pii/180

    :  = *180/Pii

       .

           .

     Excel.      14.

     F    .

      D.

   ,    @013.

        14.     14_Z.

      @007.

  

      :

 L;  ;  R;  G.

           .

.   .








    :

 = sqrt( R*R  X*X); L = X + X; H = R  B; G = rcsin ( X / R );

  = Pii * R * G / 90;

  Ss = Pii * R * R * G / 180;

    St = L * B /2;

  (  ) Sg = Ss  St;

      ,

    .

 :

 R = 1000;

 D = R+R; D = 2000;  L = 765,3668647;

   H = 76,12046749;

:   : 2 * G = Au = 45 ..

     = Au:

Sk=Pii*D*D* Au /(4*360); Sk = 392699,0816987241;

   :

St=(L/2)* B; St = 353553,3905932738;

   :

S = Sk-St; S = 39145,69110545033;

   :

L=Pii*D*Au /360; L = 785,3981634;

   Excel.

    Excel   _12. (   ).

    15.       :

  ..      @002. @003. @004. @004.

   .

:                 .  Excel          .     Python..

  

      ,    

  ,      .

        ,   ,  ,             2.

.   .

,,,,








    .

:

    L.

    L   1.

1 = L / 2;  = sqrt( R*R  X1*X1); H1 = R  B;

     H1.

       2.

   2 = R  ( sqrt( R*R  X2*X2));

     2: Hm = H1  H2;

    2      Hm

   ,

        .

 :

 :

 R = 10000;

   L = 8000;

     = 834,8486100883201.

  :

       - = 3000,0.

  (  ) = 374,2406242577763.



       - = 2000,0.

  (  ) = 632,8075812210318.



       - = 1000,0.

  (  ) = 784,7229811545203.



       - = 500,0.

  (  ) = 822,3407878074104.



       - = 0,001.

  (  ) = 834,848610088271.

   Excel.

    Excel   _15. (   ).

    16.       :

  ,   ,   Excel   

    .

  

     .

.  .

,,,








   

     .

 = a.  = b.  = c.

:

.x=((b*b)+(c*c)-(a*a))/(2*b*c) au=rccos(x)  .

.x=((a*a)+(c*c)-(b*b))/(2*a*c) bu=rccos(x)  .

.cu=180-(au+bu)  .

      

 = a;  = b;  = cu..

:

.= sqrt ((a*a)+(b*b))-(2*a*b*(cos(cu)))  .

.x=((b*b)+(c*c)-(a*a))/(2*b*c) au=arccos(x)  .

.x=((a*a)+(c*c)-(b*b))/(2*a*c) bu=arccos(x)  .

      

 = a;  = bu;  = cu;

: .au=180-(bu+cu)  . .b=(a*(sin(bu)))/(sin(au))  .

.c=(b*(sin(cu)))/(sin(bu))  .

    

:

R=a/(2*(sin(au)) R    .

.hc=b*(sin(au))    .

.hb=a*( sin(cu))    B.

.ha=c*(sin(bu))    A.

S=a*ha/2..  .

Pe=a+b+c.. .

.rv=(S+S)/Pe   .

..

 :

     .

  = 15,77350269;

  = 14,14213562;

  = 11,54700538;

  = 75;   = 60;   = 45..

 = 10;   = 11,1535507;

  = 13,66025403;

  = 8,164965804;

  = 3,804268442;

 = 78,86751346;

   Excel.

      17.. (   ).




 


  



  

  d.

 :

 :  = 80;

S=5026,548246; Jxx =2010619,298; Wx=50265,48246.. .i=20,0

:

.s=d*d*Pii/4  .

.wr=Pii*d*d*d/16   .

.wx=wr/2   .

.jr=wr*d/2   .

.jx=jr/2      -.

.rm=sqrt(jx/s)    -.

   .

   Excel.

      18.. (   ).

  

  d.

  dv.

.   .








.x=(d-dv)/2   .

.sn=d*d*Pii/4  .

.sv=dv*dv*Pii/4    .

.s=sn-sv   .

.jrn=Pii*(d**4)/32

.jrv=Pii*(dv**4)/32

.jr=jrn-jrv   .

.jx=jr/2     -.

.wr=jr*2/d   .

.wx=wr/2   .

.rm=0,25*(sqrt(d*d+dv*dv))    -.

 :

  :  = 80; .  = 60..

  S=2199,11485751;

Jxx =1374446,785946; Wx=34361,1696486.. .i=25,0..

   Excel.

      19.. (   ).

  



  

  h.

  b.

 :

 :  = 80;  = 60..

S=4800; Jxx =2560000; Wx= 64000..

Jyy =1440000; Wyy= 48000.. .i=17,320510

 = 100..

.  .








.s=h*b  .

.dg =sqr ((b*b)+(h*h))  .

.jx=b*h*h*h/12      -.

.wx=b*h*h/6      -.

.jy=h*b*b*b/12     Y-Y.

     j min.

.rm=sqrt(j min/s)   .

    .



   Excel.

      20.. (   ).



   

  h.

  b.

  hm.

  bm.

.   .








:

.s=(h*b)-(hm*bm)    .

.jx=(b*h*h*h/12)-(bm*hm*hm*hm/12)     -.

.wx=2*jx/h     -.

.jy=(h*b*b*b/12)-(hm*bm*bm*bm/12)     Y-Y.

.wy=2*jy/b     Y-Y.

     j min.

.rm=sqrt(j min/s)   .

.rmm= sqrt(((b*h*h*h)  (bm*hm*hm*hm))/(12*.s))..

 :

 .

 = 80;

 .= 60;

 = 60..

 .= 40..

S=2400; Jxx =1840000; Wx= 46000.. Jyy =1120000; Wyy= 37333,(3)..

.rm=21,60246899 .rmm=21,6025.  = 100..

   Excel.

      21.. (   ).



  

  h.

  b.

  .      Z.

         .

 -   ..  .

 Y-Y   ..  .

.  .








:

Sk=(h*b)/2  .

Jxk=b*h*h*h/36     -.

   :

Mik=Jxk/(h*2/3)      -.

   :

Mio=Jxk/(h*1/3)      -.

Rk=sqrt(Jxk/Sk)   .

Z=h/3  ..  .

 :

 : =80; =60;

S=2400; Z =26,6(6);     ..

Jxx =853333,3(3); Wxn=32000,0;   ..

Wxv=16000,0;   ..

.i=18,85618083..



Jy=h*b*b*b/48

   Excel.

      22.. (   ).



  

  h.

  b.

  hm.

  bm.

  .      xc.

 -   ..  .

 Y-Y   ..  .

. .








 :

 :

  = 80..   =20..

  = 60..   = 40..

 S=4000.;

XC=44,0..;     ..

Jxx =4629333,(3)..

-   ..

Wxx=60912,28070175;.. ..

Jyy=773333,(3)..;

Wyy=25777,(7);..

  .i= 13,90444.. ..

.

:

.s=(h*b)+(hm*bm)   .

.j1=b*h*h*h/12     .. .

.j2=bm*hm*hm*hm/12     .. .

.f1=h*b  .

.f2=hm*bm  .

.x1=(h/2)+hm

.x2=hm/2 Gsf = 461030/2725231222

      xc.

.xc=((f1*x1)+(f2*x2))/(f1+f2)

.r1=(((h/2)+hm)-xc)  ..   .. .

.r2=xc-(hm/2)  ..   .. .

.jx1=j1+(r1*r1*f1)    .

.jx2=j2+(r2*r2*f2)    .

.jx=jx1+jx2     .

.wx=jx/((h+hm)-xc)      .

.jy1=h*b*b*b/12

.jy2=hm*bm*bm*bm/12

.jy=jy1+jy2     Y.

.wy=jy/(bm/2)      YY.

     j min.

.rm=sqrt(j min/s)   .

   Excel.

      23.. (   ).

  Ż  .



  

  = h.

  = b.

  = hs.

  = bs.

  = bm.

  = hm.

 -   ..   (  ).

 Y-Y   ..  .

. .








 :

  :

  = 40..

  =60..

  = 80..

  =20..

  = 100..

  = 10..

S=5000.;

XC =69,80..;     ..

Jxx =9886466,(6)..

-   ..

Wxx=141639,923591;.. ..

Jyy=1606666,(6)..

Wyy=32133,(3);..

.i= 17,925773.. ..



:

.s=(h*b)+(hm*bm)+(hs*bs)   .

.j1=b*h*h*h/12      ..

.j2=bs*hs*hs*hs/12       ..

.j3=bm*hm*hm*hm/12      ..

.f1=h*b   .

.f2=hs*bs   .

.f3=hm*bm  .

.x1=(h/2)+hs+hm 

.x2=(hs/2)+hm

.x3=hm/2

     xc.

.xc=((f1*x1)+(f2*x2)+(f3*x3))/(f1+f2+f3)

.r1=((h+hs+hm)-h/2)-xc  ..   .. .

.r2=((hs/2)+hm)-xc  ..   .. .

.r3=xc-(hm/2)  ..   .. .

.jx1=j1+(r1*r1*f1)    .

.jx2=j2+(r2*r2*f2)    .

.jx3=j3+(r3*r3*f3)    .

.jx=jx1+jx2+jx3     .

.wx1=jx/((h+hs+hm)-xc)      .

.wx=jx/xc      .

   W   

.jy1=h*b*b*b/12

.jy2=hm*bm*bm*bm/12

.jy3=hs*bs*bs*bs/12

.jy=jy1+jy2+jy3     Y.

      Y-Y.

.wy=jy/(b/2)      YY.

.wy=jy/(bm/2)      YY.

   W   

     j.

.rm=sqrt(jx/s)

.rm=sqrt(jy/s)

   Excel.

      24.. (   ).

  Ż  .



  

  = h.

  = a.

  = b.

 -   ..  .

 Y-Y   ..  .

.  .








#      14-03-2020 ..

Pii = 3,141592654  .

.x=(b-a)/2..

.y=(h*h)+(x*x)..

.ab=sqrt(y).. #   (    ).

.xx=((a+x)*(a+x))+(h*h)..

.dt=sqrt(xx).. #   (  ).

Ugrx=h/x..

Ugr=arctan(Ugrx).. #  Ugrx  .

Ug=Ugr*180/Pii.. #  (    ).

.s=h*(b+a)/2..  .

    - (  -   ).

       .

Sp=a*h.. # .

Jp=h*h*h*a/12.. #  .

St=((b-a)/2)*h/2.. #  .

.x=(b-a)/2.. #  .

Jt=h*h*h*x/36.. #   .

.yt=h/3.. #    .

#      (   ).

.z=(((St+St)*yt)+(Sp*h/2))/(St+St+Sp).. (  z   V ).

#       .

.at=z-yt.. #     .. .

     -   .

Jts=2*(Jt+at*at*(St))..

#     -   .

.ap=z-(h/2).. #    .. .

Jps=Jp+ap*ap*Sp..     -   .

.jx=Jps+Jts.. #     .

.v=z.. #      .

.wxv=jx/(h-v).. #      X-X.

.wxn=jx/v.. #      X-X.

.xr=jx/(Sp+St+St).. #jx /  .

Rix=sqrt(xr).. #   (   ).

    YY.

#        .

Sp=a*h.. # .

Jpy=a*a*a*h/12.. #  .

# 

St=((b-a)/2)*h/2.. #  .

.hy=(b-a)/2.. #  .

Jty=hy*hy*hy*h/36.. #    Y-Y.

.yty=hy/3.. #    .

.ytyc=yty+(a/2).. #     Y-Y.

#       .

# .ytyc       Y-Y.

Jtsy       Y-Y   .

Jtsy=2*(Jty+ytyc*ytyc*(St))..

# Jpy     (   ).

.jyy=Jpy+Jtsy.. #     Y-Y.

.wyv=jyy/(b/2).. #    Y-Y.

.xr=jyy/(Sp+St+St).. # ( jx /   ).

Riy=sqrt(xr).. #   (    Y-Y ).

 :

    .

  = 30.

  = 50.

  = 20.



   = 33.54102.

  = 46.097722.

   = 63.434949 .

  = 1050.0.

    -.

   -   Jt = 11250.0.

   -   = 12.8571.

     -   . =26173.4694.

    -   . =47755.102.

     . =73928.5714.

 .   . =4312.5 ; 5750.0 ;

   - = 8.391..

    YY.

   Y-Y   Jt = 2812.5..

     Y-Y   . =106875.0..

     Y-Y (   ) = 20000.0..

     Y-Y. =126875.0..

 .   Y-Y. =5075.0..

   Y-Y = 10.9924..

   Excel.

      25.. (   ).

  Ż   .



  

. .








 -   ..         do.

 Y-Y   ..   -.

.d    (    ).

.ss=0,866025403*d*d      .

.do=1,154700538*d   .

.ss=0,6495190528*do*do      .

.ls=do/2   .

    .

    .

     .

.h=d/2   .

.a=do/2   (   ).

.b=do  .

  :

.s=h*(b+a)/2..  .

    - (  -   )..

       .

Sp=a*h.. # .

Jp=h*h*h*a/12.. #  .

St=((b-a)/2)*h/2.. #  .

.x=(b-a)/2.. #  .

Jt=h*h*h*x/36.. #   .

.yt=h/3.. #    .

#    (  )   (   )..

.z=(((St+St)*yt)+(Sp*h/2))/(St+St+Sp).. (  z   V ).

#       .

.at=z-yt.. #     .. .

     -   .

Jts=2*(Jt+at*at*(St))..

#     -   .

.ap=z-(h/2).. #    .. .

Jps=Jp+ap*ap*Sp..     -   .

.jx=Jps+Jts.. #     .

          V  z.

Jtz          V.

Jtz= jx + V*V*s..

Jse= Jtz+ Jtz..      .

Wse=Jse*2/d..       .

.rm=sqrt(Jse/(s+s))    -.

 :

  (    ) d = 86,60254038..

  do = 100..

  = 6495,190528..

   Excel.

      26.. (   ).

  Ż  .



  

             ,  , .     .

.  .

.








.

 :   10 .. =100  = 55 . Wx= 39,7 ..

      L = 50 .   10 .

  =100 *.. =10000 *..

      10     ,      .

   = 0,7   .       :  = 30.

  7 .    S = 210 ..     =107 .

  _27    ; J = 1203860   .

       .

          ..  

    Y.  Wx= J/Y..

J = 120,3860   . Wx=21120,35 .. Wx=21,12035 ..

    =/W.. =10000/21,12035.. = 473,48 /..

    .

    : =/W.. =10000/39,7.. = 251,9 /..

    ..

        .         

   Y  .      , 

    .        .

  Ż        .

             .

       .                 Y . W = J / Y 

,,,,

       .

  v-v       .

        .

         .

 ,      v-v 

   .  [ 1 ].

 ,      v-v 

   .

         v-v.

 -        .

       -

    .  [ 2 ].

        .

   ..      .

          .

 .

     .

        .

 ,       .

:    , ,     

(  )       .

Excel    .     .

   = h.

   = b.

.j1=b*h*h*h/12    .  [ 1 ].

.w1=j1/(h/2)    .

.s1=h*b    .

.xc1=h/2        -.

.m1=s1*(h/2)       -.

#    1

   = h1.

   = b1.

  

    - = hx.

.j2=b1*h1*h1*h1/12    .

.w2=j2/(h1/2)    .

.s2=h1*b1    .

.xc2=(h1/2)+hx        -.

.m2=s2*((h1/2)+hx)       -.

.xx=(m1+m2)/(s1+s2)  ..   v-v   .

R1=xx-xc1   ..   ..  .

R2=xc2-xx   ..   ..  .

 [ 2 ].

.j1x=j1+( R1*R1*s1)     .. .

.J2x=j1+( R2*R2*s2)     .. .

.Jx=j1x+j2x       .. .

Sx=s1+s2    .

.... .....

        ,    :

.s1=Sx xc1=xx j1=Jx m1=Sx*xx

   :

(      )     ,

  #    1

        .

..

       .

     Python 3    ..

         ..

      Excel.

   Excel.

      27..  28.. (   ).

  Ż  .

DŻ        D2  D28   

    ,    ,  16,  .

 Ż   .

   28             .

    .     ..

@014.    2.

    27.. (   ).

    27 ..        27..

              .

      27    27,     2.

      (     )    -

    -

.  Excel  1.












    .

.  Excel  .












  2           28

         (  )  .

@015.   .

#    2

              .

          2..

      .

     .

.  Excel  .












   2   D1   D15      

.  123.       .         .

.  Excel  .












    2    4          4.   D15      .     

D15.. D21 ..     D15..       

  D15.. (   )      4 

     4.   123.    D15..

.  Excel  .

,,,








,,,

     6  8      D21  D16.      .

  10, 12, 14     .   D4.. D10       .      

  .     ,    D15.. D21   

      #    2

        .

:                .                .

    ,   .

.  .

..








,,,,,

         :

     .

        . Xv  Xv

 ѻ          Xv-Xv.

   27  1..       1.  .

     2.  .

      27  2..      27  2..

     .

          

    = 150,  = 30..

        Xv-Xv.

,,,,

@016.  (  )  .

   ,         

      .

           .

.01-   _27    _27_.

  1  3-24   .       




  .


   .

   ,     (https://www.litres.ru/pages/biblio_book/?art=66861928)  .

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