:
120301
120302
120303
280402
2010
539.3
30.121
( 1 27
2010 .)
: ..., ..
: ..., ..
: , ..., ..
1 . 酅...4
2 充..6
3 ......8
4 ᅅ..10
4.1 ...12
4.2 酅.13
ꅅ.24
: - -, .
: .
.
( ) , .
, , .
, , , : , (.1.1).
, , , , .
, , , .
1.1 .
, , - , R. . Z Y X, : - Nz, , - z, (.1.2).
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1.2 .
Nz - ( ); y - Y X; z- ; - (XZ YZ). :
Nz - ;
;
z- ;
- .
, ( ) :
å Fkx = 0; åFky =0; åFkz = 0
åMx = 0; åMy = 0; åMz = 0.
, . :
1. .
2. , .
3. .
4. Nz, , , , , z.
- Nz, , .
, ..
N= åFiz
1. (.2.1) .
2.1 .
1. . :
åFkx=0 - +ql + F + 2q1,5l-F = 0 =4ql.
1. . :
N=åFix
:
( , .2.2), "-". , , "+" ( , .2.2)
2.2 .
. . , .
1-1 (). (.2.3)
åFkx=0; - + q1+N1=0.
2.3 1-1().
N1 = q1 ( ), 0 £ x1 £ l.
x1=0 N1=HA=4ql.
x1=l N1=HA-ql=4ql-ql=3ql.
2-2 (). åFkx=0; - +q1 + F+N2=0; N2=H -q1-F = 4q1-2q1 = 2q1.
2.4 2-2
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3-3 () åFkx= 0; -N3 +2qx3-F=0
N3= - F + 2qx3 ( ), 0£3£1,5l.
2.5 3-3 ().
3 = 0 N3 = -ql.
x3=1,5l N3=-F + 2q-1,5l = 2ql.
. . , , ; N , - (.2.1).
. ( ) ( ) . - "". "" .
2
, -
3.1
Mk. , . ( ), .
, , . , . , : , (.3.1 ). .
1. .3.2 : m1= 2ml, m2= 3ml, m3=1,5ml.
: 1-1 Mk1 = -m1 = -2ml.
2-2 k2 =-m1 + m2=-2ml+3ml=ml.
3-3 Mk3=-m1+2+m3= -2ml + 3ml + 1,5ml= 2,5ml.
3.2 .
(.3.2). , , , .
2. , .3.3, .
. , () , , . , .
1. Mk1 = -mx1 0 £x1£
x1=0 Mk1=0
x1=a Mk1=-m a
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3.3 .
2-2. Mk2 = -m a + M = 0
3-3. Mk3 =-m a + M+M +mx3 0 £x3 £ a
x3=0 Mk3 = -m a + m a +m a = m a
x3=a Mk3= m a +m a = 2m a
. 3.3
4
, .
. , , , . , , , . , , , : ) N, , ; ) Q , ; ) , , .
Q , , (.4.1 ). - (.4.16).
, . (.4.1 ). , (.4.1 ), .
4.1 .
Q Y , :
Q = åFiy
, , , , ,
Mu = åM(Fi)
, . , , .
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.
1. (.4.2). ( ) , . , . : ( R-.4.2), ; ( ), , .
2. - (.4.2). , . R, , . , , .
4.2
3. - (.4.2). , , I-I , . R, .
.
, ( ), ( Q) ( N).
, ,
1. Q , , .4.3.
4.3 .
. , ( ), . I, II, III, IV, . 4. 3. 1.
I. 1-1 (): (. 4.4, ):
Q1 Y = -G = -qx1,
G- , .
4.4 1-1.
M1 1-1 1, :
M1=åM=-G×x1/2=-qx1×x1/2=-qx12; ( 2- ), 0£x1£2 l
1=0 Q1=0 M1=0
x1=2 l Q1=-q×2 l =-2q l;
M1=-q/2×(2 l)2=-2q l 2
M1 Q1 .4.3 Q I .
, , , ( ). .
. 2-2 (.4.5, )
4.5 2-2.
Q2=åY=-G=-2q l; M2=åM=-G(l+x2)=-2q l (l +x2) 0£x2£ l
2=0 Q2=-2q l M2= -2q l 2
2 =2 Q2= -2q l M2=-2q l (l+l)=-4q l 2
Q2 M2 .4.3 Q II .
III. 3-3 (. 4.6, )
4.6 3-3.
Q3= åY=-2q l + F = -2q l +5q l =3q l; M3=åM=-2q l (2 l +x3)+Fx3; 0< 3< l.
3=0 Q3=3q l; M3=-2q l ×2 l =-4q l 2.
x3= l Q3=3q l M3 = -2q l × (2l + l)+5q I×I = -q l 2.
Q3 3 .4.3 Q III .
I\/ 4.4 (. 4.7, ):
4.7 4-4.
Q4 =
M4 = 0≤4≤ l
4 = 0 Q4 = 3ql, .
4 = l Q4 = 3q l, .
Q4 4 . 4.3 Q I\/ .
Q , . , Q . σmax , σmax . , Q=3ql M=4ql2.
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2 Q . 4.8.
:
1) .
, , :
åFkx=0 HA=0; åMD=0;ql×0,5l+M-RA×3l=0;
åMA=0; M-ql×2,5l+RD×3l=0; RA=(0,5ql2+ql2)/3l=0,5ql.
RD=(2,5ql2-ql2)/3l=0,5ql.
:
åFky=0 RA-ql+RD=0; 0,5ql-ql+0,5ql=0.
.
4.8 .
2) .
, : , . .
.
1-1. .
Q1=RA=0,5ql
M1=RAx1=0,5ql×x1 ( ), 0£x1£ l
1=0 1=0.
1=1 1=0,5ql2.
.