(. 5.8, ), , , , .
1. Qy Mx. Qy Mx , , , Qy Mx z .
. 5.8
, , , : - ; ( / ), . , , (. 5.8, ) : I - D, II - , III - .
Qy Mx
I-I, z 1, Qy Mx , , (. 5.9). , , .
S y = 0 = 0 , z 1 I (0 £ z 1 £ 1 ):
S y = 0, = 0;
, + m = 0, = - m = -10 ×.
, I - const. , I-I , , . 5.9.
II (1 £ z 2 £ 2 ).
S y = 0 II-II (. 5.10) :
S y = 0, ;
, + m - P (z 2 - 1) = 0, = - m + P (z 2 - 1).
, II , z 2 . , II-II , , . 5.10.
, z 2 II , , , .. Mx Qy (. 5.8, ).
z 2 = 1 ; = -30 ; = -10 + 30 (1 - 1) = -10 ×;
z 2 = 2 ; = -30 ; = -10 + 30 (2 - 1) = 20 ×.
III (2 £ z 2 £ 4 ).
S y = 0 III-III (. 5.11) , , ,
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S y = 0, ;
, + m - P (z 3 - 1) + 0,5 q (z 2 - 2)2 = 0,
= - m + P (z 3 - 1) - 0,5 q (z 2 - 2)2.
, III , - .
. 5.11 |
z 3 , , , (. 5.8, ).
z 3 = 2 = -30 + 20×(2 - 2) = - 30 ;
= -10 + 30 (2 - 1) - 0,5×20×(2 - 2)2 = 20 ×.
z 3 = 4 = -30 + 20×(4 - 2) = 10 ;
= -10 + 30 (4 - 1) - 0,5×20×(4 - 2)2 = 40 ×.
, , .. (. 5.8, ), . z 0 , = 0. , , :
- P + q (z 0 - 2) = 0, .
z 0 = 3,5 , M max:
×.
Qy Mx
(, ) Qy Mx , Qy Mx , Qy Mx (. 5.8, , ). Qy , - . Mx . Qy , Mx .
Qy Mx
. 5.12 |
Qy Mx , , Qy Mx . , II (. 5.8, ) Mx (. 5.12) :
.
, , , , Mx .
a , . :
1. Mx , , , , , , ;
2. Mx , , ;
3. Mx m , ;
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4. , , , . ;
5. Mx =
= M max , , .. , ;
6. Qy , Mx = const;
7. Qy , ;
8. Qy (, RA , RB) , , .
.
2.1. Mx, . Mx , . , , - . , , , .. . , .
Mx (. 5.8, ), , , , . , . , , Mx = 0, , .. . , (. 5.8, ).
2.2. . , . , M max = 42,5 ×. RH = 16×103 /2 h / b = 1,5:
,
:
= 2,66×10-3 3.
:
.
, =
= 0,288 , :
0,192 .
, h ´ b = 0,29´ ´0,19 2, (Wx = 2,663×10-33).
5.4.2. II. ( 7)
1. Qy Mx. (. 5.13, ) (. 5.8, ) , , , , . , . , , , , .
. , , .. y, , . S MA = 0; S MB = 0.
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S y = 0, .. , , .
S MA = 0 :
S MA = - ×1 + q ×5×4,5 - m - RB ×6 = 0,
.
S MB = 0 :
S MB = - P ×7 - m - q ×5×1,5 + RA ×6 =0; RA = 40 .
RA RB . , . .
. 5.13
S y = - P - q ×5 + RA + RB = 0; -10 - 20×5 + 40 + 70 = 0;
-110 + 110 = 0; 0 = 0.
.
, , , . : I - ; II - ; III - IV - D (. 5.13, ).
Qy, Mx
, I, z 1 (. 5.14, ). S y = 0 , Qy Mx I, z 1 0 £ z 1 £ 1 :
. 5.14
S y = 0, - - P = 0, = - P ( );
, - - P × z 1 = 0, = - P × z 1 ( ).
, , , . 5.14, , - , , , . 5.14, . z 1 :
z 1 = 0 = -10 , = -10×0 = 0;
z 1 = 1 = -10 , = -10×1 = -10×.
II, (. 5.14, ) S y = 0 , z 2 1 £ £ z 2 £ 3 :
S y = 0, - - P + RA = 0, = RA - P ( );
, - - P × z 2 + RA (z 2 - 1) = 0,
= RA (z 2 - 1) - P × z 2 ( ).
z 2 , II, , :
z 2 = 1 = 40 - 10 = 30 ,
= 40×(1 - 1)-10×1 = -10 ×;
z 2 = 3 = 30 , = 40×(3 - 1) - 10×3 = 50 ×.
III, S y = 0 (. 5.15), Qy Mx III, z 3 3 £ z 3 £ 7 :
S y = 0, - - P + RA - q ×(z 3 - 3) = 0,
= RA - P - q ×(z 3 - 3) - ;
, ,
- .
. 5.15 |
III: z 3 = 3 = 40 - 10 -
- 20×(3- 3) = 30 ,
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= 40×(3 - 1)-10×3 - = -50 ×;
z 3 = 7 = 40 - 10 - 20×(7 - 3) = -50 ,
= 40×(7 - 1) - 10×7 - = 10 ×.
, (. 5.13, ). , =
= 0, . z 0 , = 0. , :
RA - P - q ×(z 0 - 3) = 0, .
z 0 = 4,5 , M max = 72,5 ×.
Qy Mx IV D , .. , , , .
. 5.16 |
IV (. 5.16) (0 £ z 4 £ £ 1 ) :
S y = 0, - - q × z 4 = 0, = q × z 4 - ( );
, , - ().
D IV Qy Mx :
z 4 = 0 = 0, = 20 ×;
z 4 = 1 = 20×1 =20 , ×.
IV , Mx - . , z 4 = 0,5 , :
×.
Qy Mx
Qy Mx , , , Qy Mx , Qy Mx (. 5.13, , ).
2.1. Mx . Mx (. 5.13, ) , , . D , . . , Mx = 0, . , , (. 5.13, ).
2.2. . , M max = 72,5 ×. RH = 200×103 /2 ():
.
Wx :
3 .
( 8239-72) 27 Wx = 37,1×10-5 3. , 5%, .