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?????? ?1
???????????? ?????? ???????? ???????? ????????? ??? ????????? ??? P1 ? P2
?????? ????????? ?=2�105 ???
?????????:
??????? ?????? ??????? ?? ???????? ???????? ? ????????;
????????? ??? ??????? ??????? ????? ? ??????? ????????????? ????????? ????????? ??????????? ?????? N, ?????????? s ? ??????????? ?????????? ??????? ????? ?l;
????????? ????? ?????????? ?????? N, ?????????? s ? ??????????? ?????????? ??????? ????? ?l;
??????? ????? ? ????????? ??????? ??? [s]=160 ???
???????? ??????: P1, ??P2, ??a, ?b, ?c, ?A1, ??2A2, ??2A3, ??2[s], ???E, ???10110,50,80,52,12,02,11602�105
???????:
1)??? ??????????? ????????? ??????????? ???????? ???? ?? ??????? ? ??????? ?? ???????? ?? ???? ??????????????? ?????.
R_D=?. ???????? ??????? ????????????? ???????? ??? ???????:
?D=?l_D^P1+?l_D^P2+?l_D^x=0;
???????? ?????? ????: , ??? ?li - ???????????,
Ni - ?????? ??????????? ?? ???????,
li - ????? ???????,
E - ?????? ?????????? ?????????,
Ai - ??????? ??????????? ???????.
?l_D^P1=(P_1�0.5�a)/(E�A_3 )=(?10?^4�0.25)/(4.2�?10?^7 )=5.95�?10?^(-5)
?l_D^P2=-(P_2�b)/(E�A_2 )-(P_2�c)/(E�A_3 )=-(11�?10?^3�0.8)/(4�?10?^7 )-(11�?10?^3�0.5)/(4.3�?10?^7 )=-3.51�?10?^(-4)
?l_D^x=(x�c)/(E�A_3 )+(x�b)/(E�A_2 )+(x�a)/(E�A_1 )=x�(0.5/(4.2�?10?^7 )+0.8/(4�?10?^7 )+0.5/(4.2�?10?^7 ))=
=x�4.38�?10?^(-8)
5.95�?10?^(-5)-3.51�?10?^(-4)+x�4.38�?10?^(-8)=0
x=(-5.95�?10?^(-5)+3.51�?10?^(-4))/(4.38�?10?^(-8) )
x=6.65�?10?^3 ??
2) ???????? ????? ?????????? ???. ???????? ????? ??????? (???????? ?? ?????????? ????)
N_ED=x=6.65�?10?^3??
N_DC=6.65�?10?^3-P_2=6.65�?10?^3-11�?10?^3=-4.345�?10?^3 ??
N_BC=6.65�?10?^3-P_2=6.65�?10?^3-11�?10?^3=-4.345�?10?^3 ??
N_BA=x-P_2+P_1=-4.345�?10?^3+?10?^4=5.65�?10?^3 ??
3) ???????? ????? ?????????? ?????????? s=N/A
s_AB=N_AB/A_3 =(5.65�?10?^3)/(2.1�?10?^(-4) )=2.7�?10?^7 ??
s_BC=N_BC/A_3 =-(4.345�?10?^3)/(2.1�?10?^(-4) )=-2.07�?10?^7 ??
s_CD=N_DC/A_2 =-(4.345�?10?^3)/(2.0�?10?^(-4) )=-2.17�?10?^7 ??
s_DE=N_DE/A_1 =(6.65�?10?^3)/(2.1�?10?^(-4) )=3.17�?10?^7 ??
4)?????? ????? ??????????? ?????????? ??????? ?l=(N�l)/(E�A)
?A=0
?B=?A+?AB=0+(N_BA�0.5�a)/(E�A_1 )=0+(5.65�?10?^3�0.25)/(4.2�?10?^7 )=3.36�?10?^(-5) ?
?C=?B+?CB=3.36�?10?^(-5)+(N_CB�0.5�a)/(E�A_1 )=3.36�?10?^(-5)-
-(4.345�?10?^3�0.25)/(4.2�?10?^7 )=7.73�?10?^(-6) ?
?D=?C+?DC=7.73�?10?^(-6)+(N_DC�b)/(E�A_2 )=7.73�?10?^(-6)-(4.345�?10?^3�0.8)/(4�?10?^7 )=
=-8�?10?^(-5) ?
?E=?D+?ED=-8�?10?^(-5)+(N_ED�a)/(E�A_1 )=-8�?10?^(-5)+(6.65�?10?^3�0.5)/(4.2�?10?^7 )=
=-7.7?�10?^(-7) �0 ?
5) ???????? ????????? ??????? ??? ??????????? ?????????? s_???=31.7 ???
s_???<[s]
?????????????, ??????? ????????? ???????????.
W=([s]-s_???)/[s] �100%=(160-31.7)/160�100%=80.2%
???????? ??????? ?????????? 80.2%.
?????? ?2
?????????:
1) ??????? ?????? ???? ?? ???????? ???????? ? ????????;
2) ????????? ????? ???????? ???????? ?;
3) ????????? ????? ??????????? ?????????? t;
4) ????????? ????? ????? ???????????? f;
5) ??????? ????? ? ????????? ??????? ??? [t]=50 ???.
???????? ??????: T1 ??�?T2 ??�?a, ??b, ??c, ??d1, ??d2, ??d3, ??[t], ???G, ???1.0 0.110050010060206050
???????: 1) ???????? ??????? ? ??????? E. ?? ???????? ??????? ?????????? ???????? ?E = X. ???? ???????? ? ??????? ? ? ???? ??????? ?????? ??????? ?????? ????: f_?=0. ???????? ??????? ????????????? ???????? ???, ???????? ????????
f_E=f_E+f_(ET_2 )+f_(ET_1 )=0
f_E=(T�l)/(G�I_p )
f_E=(x�c)/(G�I_pIII )+(x�b)/(G�I_pII )+(x�a)/(G�I_pI )
f_(ET_2 )=-(T_2�c�0.4)/(G�I_pIII )-(T_2�b)/(G�I_pII )+(T_2�a)/(G�I_pI )
f_(ET_1 )=(T_1�a)/(G�I_pI )
I_pI=(p�d^4)/32=(3.14�(6�?10?^(-2) )^4)/32=127.17�?10?^(-8) ?^4
I_pII=(p�?d_2?^4)/32=(3.14�(2�?10?^(-2) )^4)/32=1.57�?10?^(-8) ?^4
I_pIII=(p�?d_3?^4)/32=(3.14�(6�?10?^(-2) )^4)/32=127.17�?10?^(-8) ?^4
x=(-(T_1�a)/(G�I_pI )+T_2/G ((c�0.4)/I_pIII +b/I_pII +a/I_pI ))/(1/G (c/I_pIII +b/I_pII +a/I_pI ) )=
=(-(?10?^3�0.1)/(0.8�?10?^11�127.17�?10?^(-8) ))/(1/(0.8�?10?^11 )�(0.1/(127.17�?10?^(-8) )+0.5/(1.57�?10?^(-8) )+0.1/(127.17�?10?^(-8) )) )+
+((0.1�?10?^3)/(0.8�?10?^11 )((0.1�0.4)/(127.17�?10?^(-8) )+0.5/(1.57�?10?^(-8) )+0.1/(127.17�?10?^(-8) )))/(1/(0.8�?10?^11 )(0.1/(127.17�?10?^(-8) )+0.5/(1.57�?10?^(-8) )+0.1/(127.17�?10?^(-8) )))=97.4 ?
2) ???????? ????? ???????? ????????: T_ED=x=97.4 ?�?
T_DC=x-T_2=97.4-0.1�?10?^3=-2.6 ?�?
T_CB=x-T_2=97.4-0.1�?10?^3=-2.6 ?�?
T_BA=x-T_2+T_1=97.4-0.1�?10?^3+1�?10?^3=997.4 ?�?
3) ???????? ????? ??????????? ??????????:
t=T/W_p W_p=(p�d^3)/16
t_ED=T_ED/W_pED =(97.4�16)/(3.14�(60�?10?^(-3) )^3 )=2.3�?10?^6
t_DC=T_DC/W_pDC =-(2.6�16)/(3.14�(60�?10?^(-3) )^3 )=6.13�?10?^4=0.0613�?10?^6
t_CB=T_CB/W_pCB =-(2.6�16)/(3.14�(20�?10?^(-3) )^3 )=-1.65�?10?^6
t_BA=T_BA/W_pBA =(997.4�16)/(3.14�(60�?10?^(-3) )^3 )=2.3�?10?^7=23�?10?^6
???????? ????? ????? ????????. ???????? ? ????????????? ????
(??????? ?)
f_A=0
f_B=f_A+f_AB=0+(T_BA�a)/(G�I_pI )=(997.4�100�?10?^(-3))/(0.8�?10?^11�127.17�?10?^(-8) )=9.8�?10?^(-4) ???
f_c=f_B+f_CB=9.8�?10?^(-4)+(T_CB�b)/(G�I_pII )=9.8*?10?^(-4)-(2.6�0.5)/(0.8�?10?^11�1.57�?10?^(-8) )=
=-5.5�?10?^(-5) ???
f_D=f_C+f_DC=-5.5�?10?^(-5)+(T_DC�0.4�c)/(G�I_pIII )=
=-5.5�?10?^(-5)-(2.6�0.4�0.1)/(0.8�?10?^11�127.17�?10?^(-8) )=-5.6�?10?^(-5) ???
f_E=f_D+f_DE=-5.6�?10?^(-5)+(T_DE�0.6�c)/(G�I_pIII )=
=-5.6�?10?^(-5)+(97.4�0.6�0.1)/(0.8�?10?^11�127.17�?10?^(-8) )=1.4�?10?^(-6) ??? �0
???????? ????????? t_max=23 ???
[t]=50 ???
t_max<[t]
?????????????, ??????? ????????? ???????????.
W=([t]-t_max)/[t] �100%=(50-23)/50�100%=54%
???????? ??????? ?????????? 54%.
?????? ?3
??? ???????? ????? ?????????:
1. ???????? ????????? ?????????? ???? Q ? ??????????? ??????? ? ??? ??????? ??????? ? ????? ????;
2. ????????? ????? ?????????? ??? Q ? ??????????? ??????? ?;
3. ????? ? ????????? ???????? ????? ???????????? ??????????? ??????? ??? [s]=160 ???.
???????? ??????: P1, ??q, ??/?a, ?b, ?c, ?d, ??, ??�?[s], ???1,01,00,12,02,10,110160
???????: 1) ????????? ??????????? ??????? ???????:
?_(k=1)^n�?M_kA=0;?
M-q�2,1�3,05+R_B�4,1-P�4,2=0;
R_B=(-M+q�2,1�3,05+P�4,2)/4,1=(-?10?^4+1�2,1�3.05+1�4.2)/4,1=0,148 ??;
?_(k=1)^n�?M_kB=0;?
-P�0,1+q�2,1�1,05-R_A�4,1+M=0;
R_A=(-P�0,1+q�2,1�1,05+M)/4,1=(-1�0,1+1�2,1�1,05+?10?^4)/4,1=2,952 ??;
????????:
?_(k=1)^n�F_ky =0;
R_A-q�2,1+R_B-P=2,952-2,1+0,148-1=0;
2) ???????? ????? ?????????? ???:
0=z_1=0,1 ?;
Q_y=P=?10?^3 ?;
0=z_2=2.1 ?;
Q_y=P-R_B+q�z_2;
z_2=0 ?; Q_y=P-R_B=?10?^3-147,56=852,44 ?;
z_2=2,1?; Q_y=P-R_B+q�2,1=?10?^3-147,56+?10?^3�2,1=2952,44 ?;
0=z_3=2 ?;
Q_y=R_A=2952,44 ?;
0=z_4=0,1 ?; Q_y=0 ?;
3) ???????? ????? ?????????? ????????: 0=z_1=0,1;
M_x=-P�z_(1;)
z_1=0 ?;
M_x=0;
z_1=0,1 ?;
M_x=-?10?^3�0,1=-100 ?�? ;
0=z_2=2,1 ?;
M_x=-P�(0,1+z_2 )+R_B�z_2-q�?z_2?^2/2;
z_2=0?;
M_x=-P�0,1=-100 ?�?; z_2=2,1 ?;
M_x=-2200+147,56�2,1-?10?^3�?2,1?^2/2=-4095,12 ?�? ;
0=z_3=2 ?;
M_x=-P�(2,2+z_3 )+R_B�(2,1+z_3)-q�2,1�(1,05+z_3)
z_3=0 ?;
M_x=-P�2,2+R_B�2,1-q�2,205=-4095,12 ?�?; z_3=2 ?;
M_x=-P�4,2+R_B�4,1- q�6,405=-10000 ?�?; ?????? ?4
??? ???????? ????? ????????? ????????? ???????? ????? ???????????? ??????????? ??????? ??? [s]=160 ???.
a, ??b, ???, ??�?[s], ???283010160
????????? ????????? ?????? ??????? ??????? ??????? ???????????? ??????????? ??? ??:
y_c=(?�?A_i y_ci ?)/(?�A_i )=(A_1 y_c1+A_2 y_c2)/(A_1+A_2 );
y_c=((2�a+2�b)�(1,5�a+b)�(1,5�a+b)/2-2�b�1,5�a�(1,5�a)/2)/((2�a+2�b)�(1,5�a+b)-2�b�1,5�a)=
=(116�72�36-60�42�21)/(116�72-60�42)=42,48 ??;
2) ?????????? ?????????? ??? ?????? ?? ?????? ??????? ?????????????? ?? ????????? ?????? ? ???????????? ? ????? ????? ??????? ?? ???????: s_max=M_xmax/I_x �y_i, ??? M_xmax-???????????? ???????? ??????????? ??????? ? ?????????????? ???????;
Ix-?????? ??????? ??????? ???????????? ??????????? ???;
y-??? ?????????? ?? ??????????? ??? ?? ?????????????? ?????. I_xc=I_x1+?a_1?^2�A_1+I_x2+?a_2?^2�A_2;
a_1=-y_c1+y_c=-((1,5�a+b)/2)+42,48=-36+42,48=6,38 ?? ;
a_2=-y_c2+y_c=-((1,5�a)/2)+42,48=-21+42,48=21,48 ?? ;
I_x1=(b_1�h^3)/12=((2�a+2�b)�?72?^3)/12=(11,6�?72?^3)/12=360,80 ????^4 ;
I_x2=(b_2�h^3)/12=(2�b�h^3)/12=(6�?4,2?^3)/12=37,04 ????^4 ;
I_xc=((2�a+2�b)�?72?^3)/12+(-y_c1+y_c )^2�(2�a+2�b)�(1,5�a+b)-
-(2�b�h^3)/12-(-y_c2+y_c )^2�2�b�1,5�a=360,60+?0,648?^2�11,6�7,2-37,04-
-?2,148?^2�6�4,2=242,56 ????^4 ;
3) ?????? ????? ?????????? ?????????? ??? ???????? ???????:
s_max=M_xmax/I_x �y_i ;
M_xmax=10 ??�? ;
y_A=y_c=42,48 ?? ;
y_B=?(1,5�a+b)-y?_c=72-42,48=29,52 ;
s_A=M_xmax/I_xc �y_A=(?10?^4�y_c)/I_xc =(?10?^4�42,48�?10?^(-3))/(242,56�?10?^(-8) )=175,13 ??? ;
s_B=M_xmax/I_xc �y_B=(?10?^4�(?(1,5�a+b)-y?_c ))/I_xc =(?10?^4�29,52?�10?^(-3))/(242,56�?10?^(-8) )=121,70 ??? ;
4) ????????? ??????? ??????????? ??????? ????? ? ????? ????????:
[s]=160 ???
?? ??????? ?????????: s_max=[s]
s=M_xmax/W_x ;
Wx= M_xmax/[s] =?10?^4/(160�?10?^6 )=62,5 ????^3;
?? ???? 8239 - 72 ? 14 ?? ???? ??? ??????? ????????:
Wx=81,7 ????^(3;)
A=17,4 ??? ?^4;
5) ????????? ?????????? ??????? ????? ? ????? ?????:
W_x= (p�d^3)/32;
d=?((32�M_xmax)/(p�[s] ));
d=?((32�?10?^4)/(3,14�160�?10?^6 ))=0,086?=86 ??;
d=90??=9 ??;
A_??=(p�d^2)/4=(3,14�9^2)/4=63,6 ????^2;
6) ????????? ?????????? ??????? ????? ? ????? ??????:
W_x= (p�d^3 (1-c^4 ))/32; c=d_0/d=0,8;
d=?((32�M_xmax)/(p�[s]�(1-c^4 ) ))=?((32�?10?^4)/(3,14�160�?10?^6�(1-?0,8?^4 ) ))=0,103?=103 ??
d=105??=10,5 ??;
d_0=0,8�105=84??;
A_???=(p�(d^2-?d_0?^2 ))/4=(3,14�(?10,5?^2-?8,4?^2 ))/4=31,16 ????^2;
???????? ??????? ????? ? ????? ??????????????:
W_x=(b�h^2)/6;
h=1,7�b;
W_x=(b�?(1,7�b)?^2)/6=0,482�b^3;
b=?(M_xmax/([s]�0,482))=?(?10?^4/(160�?10?^6�0,482))=51??;
h=1,7�b=1,7�51=86,7??;
A_????=b�h=5,1�8,67=44,23 ????^2
??????
???????Ai , ???i/A117,41,0263,63,66331,161,79444,232,54
?????? ?5
??? ???????? ?????????? ?????????????? ????? ????????? ????? ?????????? ???? ? ??????????? ???????, ??????? ???????????????? ????????, ?????????? ?????? ? ??????? D.
[s]=160 ???.
P, ??M, ??�??, ?[s], ???1102.11601.????????? ??????? ??????????? ??????????????? ????? ??? ???????? ????? ?????? ??????????? ???? ??????? ? ?????? ??????????? ?????????
??????????:
n=4-3=1
2. ???????? ???????? ???????
3. ???????? ???????????? ????????? ?????? ???, ??? ????? ??? d_11�X_1+?_1p=0, ??? d_11- ??? ??????????? ????? ?????????? ????????? ????
?? ???????? ???? ?? ????, ?_1p- ??????????? ????? ?????????? ????????? ????
?? ???????? ??????? ????????,
X_1- ??????????? ????.
??? ??????????? d_11 ???????? ?????? ?.?. ?????? ????? X_1=1 ?? ?????? ??? ?????? ????? ????????? ????? (�_1 ) �.
M_DC=X_1�c/2=1�1,05=1,05 ??�?; M_CB=X_1�(c/2+c)=1�(1,05+2,1)=3,15 ??�?;
M_BA=X_1�(c/2+c+c/2)=1�(1,05+2,1+1,05)=4,2 ??�?;
4. ???? ????????? ??????????? d_11, ??????? ???????????? ????:
d_11=1/(E�J_x ) (�_1 ) �׵ �=
=1/(E�J_x )�(1,05/6�(2�4,2�4,2+2�3,15�3,15+4,2�3,15+3,15�4,2)+
+2,1/6�(2�3,15�3,15+2�1,05�1,05+3,15�1,05+3,15�1,05)+
+1,05/6�(2�1,05�1,05))=1/(E�J_x )�24,695;
5. ????????? ??????????? ?_1p ???????????? ???? (�_p ) ��(�_1 ) �; ??? �_p- ??? ????? ?? ???????? ??????? ?????? ??????? ?????????. M_DC=0 ??�?; ?0=z?_2=2,1 ?;
M_CB=-P�z_2;
z_2=0 ?;
M_CB=0 ?�?;
z_2=2,1 ?;
M_CB=-P�2,1=-?10?^3�2,1=-2,1�?10?^(3 ) ?�?;
?0=z?_3=1,05 ?;
M_BA=-P�(2,1+z_3 )+M;
z_3=0 ?;
M_BA=-P�2,1+M=-?10?^3�2,1+?10?^4=7,9?�10?^3 ?�? ;
z_3=1,05 ?;
M_BA=-P�(2,1+1,05)+M==-?10?^3�3,15+?10?^4=6,85�?10?^(3 ) ?�?;
?_1p=1/(E�J_x ) �_p�(�_1 ) �=
=1/(E�J_x )�((1,05/6�(2�4,2�6,85+2�3,15�7,9+4,2�7,9+3,15�6,85)+
+2,1/6�(-2�3,15�2,1-1,05�2,1))=1/(E�J_x )�22,96;
?????????? X_1:
24,695/(E�J_x )�X_1+22,96/(E�J_x )=0;
X_1=-0,93 ??;
????????? ???????? ????? ?????? ? ????????? ????????? X_1 ??????? ??? ??????????? ?? ???????????????.
?????? ?????????????? ????? ?????????? ??? Q_y? ?????????? ???????? M_x ??? ???????? ?????.
Q_DC=+X_1=0,93 ??;
Q_CB=+X_1+P=0,93+1=1,93 ??;
Q_CB=+X_1+P=0,93+1=1,93 ??;
M_DC=-X_1�1,05=-0,93�1,05=-0,976 ??�?;
?0=z?_2=2,1 ?;
M_CB=-X_1�(1,05+z_2 )-P�z_2;
z_2=0 ?;
M_CB=-X_1�1,05=-0,93�1,05=-0,976 ??�?;
z_2=2,1 ?;
M_CB=-X_1�(1,05+2,1)-P�2,1=-0,93�3,15-2,1=-5,029 ??�?;
?0=z?_3=1,05 ?;
M_BA=-X_1�(3,15+z_3 )-P�(2,1+z_3 )+M;
z_3=0 ?;
M_BA=-X_1�3,15-P�2,1+M=-0,93�3,15-2,1+10=2,944 ??�?;
??????? ???????? ?.?. ???????? ???????? ?????????? ???????? X_1 ????????? ?????? ???????? ???????.??? ????? ?????? ???????? ???????
???????? ?????? ????????? ????????.
X_2=1??;
??????? ????????? ??????????:
?�?M_A=0?;
?�?M_D=0;?
?-R?_D�4,2+X_2=0;
?-R?_A�4,2+X_2=0;
R_A=R_D=1/4,2 ??;
?????? ????? ?? ?????????? ??????? (�_2 ) �:
M_DC=-R_D�1,05=-1/4,2�1,05=-0,25 ??�?;
M_CB=-R_D�3,15=-1/4,2�3,15=-0,75 ??�?;
M_BA=-R_D�4,2=-1/4,2�4,2=-1 ??�?;
???????? ???????????????? ????????.
f_A=0 ?? ??????? ? ????? ?;
f_A=1/(E�J_x ) �_x�(�_2 ) �=
=1/(E�J_x )((1,05/6�(-2�2,944-2�4,971�0,75-2,944�0,75-4,971�4,2)+
+2,1/6�(2�5,029�3,15+2�1,05�0,976+3,15�0,976+5,029�1,05)+
+1,05/6�(2�1,05�0,976))=0;
?????? ???????? ??????????? ??????? ????? D.
??? ????? ???????? ?????? ???????? ??????? ????????? ????? X_3=1. ???????? ????????? ????? �_3:
? ????? D,M_D=0;
? ????? C,M_C=-X_3�1,05=-1,05 ??�?;
? ????? B,M_B=-X_3�3,15=-3,15 ??�?;
? ????? A,M_A=-X_3�4,2=-4,2 ??�?;
?D=1/(E�J_x ) �_x׵_3=
=1/(E�J_x )((1,05/6�(-2�2,944�4,2-2�3,15�4,971-2,944�3,15-4,971�4,2)+
+2,1/6�(2�5,029�3,15+2�1,05�0,976+3,15�0,976+5,029�1,05)+
+1,05/6�(2�1,05�0,976))=1/(E�J_x )�0,005;
??????? ??????? ????????? ?? ?????:
s_max=M_xmax/W_x =[s];
[s]=160 ???;
W_x=M_xmax/[s] =(5,029�?10?^3)/(160�?10?^6 )=0,031�?10?^(-3) ?^3=31????^3;
???????? ??????? ? ???? ???????? ?? ???? 8237-72;
W_x=39,7 ????^3; J_x=198 ????^4 ;
?D=(0,005�?10?^3)/(2�?10?^11�198�?10?^(-8) )=1,26�?10?^(-5) ?
?????? ?6
???????? ??? ????????? ? ?????????? ???????? n ? ???????? ???????? N.
?????????:
1. ?????????? ????????, ??????????? ?? ???;
2. ????????? ????? ???????? ????????, ????? ?????????? ???????? ? ???? ??????????(???????????? ? ??????????????);
3. ????????? ??????? ????, ????????? ?????? ?????? ?????????(?????? ?????????? ??????????? ??????????) ??? ????? ?????? ?????????(?????????????? ??????), ???? ???????? ??????????? ?????????? [s].
N,
???n,
??/???
[s],
????????? ?????????a,
??
b,
??
???????? ???????? ?????d_1,??d_2,??12700160?????20010080160
1.????????? ???????? ??????:
M_??=N/?
?=(p�n)/30
M_??=(30�N)/(p�n)=(12?�10?^3�30)/(3.14�700)=164 ?�?
M_??=(F_t�d)/2
F_t1=(2�M_??)/d_1 =(2�164)/(80�?10?^(-3) )=4100 ?
F_t2=(2�M_??)/d_2 =(2�164)/(160�?10?^(-3) )=2080 ?
F_r1=0,364�F_t1=0,364�4100=1,5�?10?^3 ?
F_r2=0,364�F_t2=0,364�2080=0,75?�10?^3 ?
2. ????????? ??????? ??????? ? ?????????
2.1. ? ?????????????? ????????? ZOX:
?_(k=1)^n�?M_kA=0;?
F_t1�200�?10?^(-3)+B_H�400�?10?^(-3)+F_r2�500�?10?^(-3)=0;
B_H=(-F_t1�200�?10?^(-3)-F_r2�500�?10?^(-3))/(400�?10?^(-3) )=
=-(0,75�?10?^3�500?�10?^(-3)-4,09?�10?^3�200?�10?^(-3))/(400�?10?^(-3) )=-2,9825?�10?^3 ?;
?�?X_k=0?;
A_H-F_t1-B_H ?-F?_r2=0;
A_H=F_t1+B_H ?+F?_r2;
A_H=4,09?�10?^3-2,9825?�10?^3+0,75�?10?^3=1,8575�?10?^3 ?;
?_(k=1)^n�?M_kB=0;?
A_H�400?�10?^3-F_t1�200�?10?^(-3)+F_r2�100�?10?^(-3)=
=1,8575?�10?^3�400?�10?^(-3)-4,09?�10?^3�200?�10?^(-3)+
+0,75�?10?^3�100?�10?^(-3)=0;
0=0;
2.2. ? ???????????? ????????? ZOY:
?_(k=1)^n�?M_kA=0?;
-F_r1�200�?10?^(-3)-B_V�400�?10?^(-3)-F_t2�500�?10?^(-3)=0;
B_V=(-F_r1�200�?10?^(-3) ?-F?_t2�500�?10?^(-3))/(400�?10?^(-3) );
B_V=(-1,5�?10?^3�200�?10?^(-3)-2,08�?10?^3�500�?10?^(-3))/(400�?10?^(-3) )=-3,35�?10?^3 ?;
?�?Y_k=0?;
A_V-F_r1-B_v ?-F?_t2=0;
A_V=F_r1+B_v ?+F?_(t2;)
A_V=1,5�?10?^3-3,35�?10?^3+2,08�?10?^3=0,23�?10?^3 ?;
?_(k=1)^n�?M_kB=0;?
?-A?_V�400?�10?^(-3)+F_r1�200�?10?^(-3)-F_t2�100�?10?^(-3)=0;
-0,23�?10?^3�400?�10?^(-3)+1,5?�10?^3�200?�10?^(-3)-2,08�?10?^3�100�?10?^(-3)=
=0;
0=0;
3.???????? ????? ?????????? ? ???????? ????????.
3.1. ????? ???????? ??????????? ? ???????????? ????????? ????? ??????? 1:
M_X=A_V�200?�10?^(-3)=0,23?�10?^3�200?�10?^(-3)=0,046 ??�?;
?????? ??????? 3:
M_X=?-F?_t2�100?�10?^(-3)=-2,08?�10?^3�100?�10?^(-3)=-0,208 ??�?;
3.2. ????? ???????? ??????????? ? ?????????????? ????????? ????? ??????? 1:
M_Y=?-A?_H�200?�10?^(-3)=-1,8575?�10?^3�200?�10?^(-3)=-0,371 ??�?;
?????? ??????? 3:
M_Y=F_r2�100?�10?^(-3)=0,75?�10?^3�100?�10?^(-3)=0,075 ??�?;
4.????????? ???????? ??????:
T=(F_t1�d_1)/2=(4,09?�10?^3 ?�80�10?^(-3))/2=163,6 ?�?;
5.????????? ??????? ???? ? ??????? ???????? ??????:
???????? 1: M?_?=v(?M_X?^2+?M_Y?^2 )=v((0,046)^2+(-0,371)^2 )=0,374 ??�?;
???????? 2: M?_?=v(?M_X?^2+?M_Y?^2 )=v((0,208)^2+(0,075)^2 )=0,221 ??�?;
??????? ??????? 1;
M_???=v(?M_??^2+?M_???^2 )=v((0,374)^2+(0,164)^2 )=0,408 ??�?;
W_x=(p�d^3)/32;
W_x=M_???/[s] ;
d=?((32�M_???)/(p�[s] ))=?((32�0,408�?10?^3)/(3,14�160�?10?^6 ))=0,0296 ?;
????????? d=30 ??
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