CongThuc_PTHH

CC CNG THC S DNG TRONG PHNG PHP PHN T

HU HN - M HNH CHUYN V - BI TON H THANH

1. Thit lp ma trn cng phn t

1.1 Ma trn cng phn t trong h to a phng

1.1.1 Phn t thanh hai u nt cng (NN)

l

EJ

l

EJ

l

EJ

l

EJl

EJ

l

EJ

l

EJ

l

EJl

EF

l

EFl

EJ

l

EJ

l

EJ

l

EJl

EJ

l

EJ

l

EJ

l

EJl

EF

l

EF

Ke

460

260

6120

6120

0000

260

460

6120

6120

0000

][

22

2323

22

2323

(1)

1.1.2 Phn t thanh u i nt cng, u j khp (NK)

000000

03

033

0

0000

03

033

0

03

033

0

0000

][

323

22

323

l

EJ

l

EJ

l

EJl

EF

l

EFl

EJ

l

EJ

l

EJl

EJ

l

EJ

l

EJl

EF

l

EF

Ke (2)

1.1.3 Phn t thanh u i khp, u j nt cng (KN)

l

EJ

l

EJ

l

EJl

EJ

l

EJ

l

EJl

EF

l

EF

l

EJ

l

EJ

l

EJl

EF

l

EF

Ke

3300

30

3300

30

0000

000000

3300

30

0000

][

22

233

233

(3)

1.2 Ma trn cng phn t trong h to tng th

1.2.1 Ma trn chuyn phng

100000

0cossin000

0sincos000

000100

0000cossin

0000sincos

][

T (4)

1.2.2 Ma trn cng phn t trong h to tng th

]].[.[][]'[ TKTK eT

e (5)

2. Quy i ti trng phn t thnh lc nt tng ng

2.1 Quy i ti trng tc dng trn phn t (theo phng h to a phng) v

thnh lc nt tng ng theo phng h to a phng

2.1.1 Phn t thanh hai u nt cng (NN)

* Do lc phn b u px:

( )

1 1. 0 0 . 0 0

2 2x

T

e x xpR p l p l

(6)

* Do lc phn b u py:

2 2( )

1 1 1 10 . . 0 . .

2 12 2 12y

T

e y y y ypR p l p l p l p l

(7)

* Do ti trng tp trung T:

( )

. .0 0 0 0

T

e T

T b T aR

l l

(8)

* Do ti trng tp trung P:

2 2 2 2

3 2 3 2( )0 ( 2 ) 0 (3 2 )

T

e P

Pb Pab Pa Pa bR l a l a

l l l l

(9)

* Do moment tp trung M:

3 2 3 2( )

6 60 (2 ) 0 (2 )

T

e M

Mab Mb Mab MaR a b b a

l l l l

(10)

2.1.2 Phn t thanh u i nt cng, u j khp (NK)

* Do lc phn b u px:

( )

1 1. 0 0 . 0 0

2 2x

T

e x xpR p l p l

(11)

* Do lc phn b u py:

2( )

5 1 30 . . 0 . 0

8 8 8y

T

e y y ypR p l p l p l

(12)


( )

. .0 0 0 0

T

e T

T b T aR

l l

(13)


2 2

2 2 2( )0 (3 ) (2 ) 0 (3 ) 0

2 2 2

T

e P

Pb b Pab Pa aR l a

l ll l l

(14)


2 2 2

2 2 2( )

3 30 (1 ) (1 3 ) 0 (1 ) 0

2 2 2

T

e M

M b M b M bR

l ll l l

(15)

2.1.3 Phn t thanh u i khp, u j nt cng (KN)

* Do lc phn b u px:

( )

1 1. 0 0 . 0 0

2 2x

T

e x xpR p l p l

(16)

* Do lc phn b u py:

2( )

3 5 10 . 0 0 . .

8 8 8y

T

e y y ypR p l p l p l

(17)


( )

. .0 0 0 0

T

e T

T b T aR

l l

(18)


2 2

2 2 2( )0 (3 ) 0 0 (3 ) (2 )

22 2

T

e P

Pb b Pa a PabR l b

l ll l l

(19)


2 2 2

2 2 2( )

3 30 (1 ) 0 0 (1 ) (1 3 )

2 2 2

T

e M

M a M a M aR

l ll l l

(20)

Vect ti trng nt tng ng do ti trng tc dng trn phn t quy i thnh

lc nt tng ng theo phng h to a phng:

( ) ( ) ( ) ( ) ( )x y

e e e e e ep p T P MR R R R R R (21)

2.2 Quy i ti trng tc dng trn phn t (theo phng h to a phng) v

thnh lc nt tng ng theo phng h to tng th:

eT

e RTR .][' (22)

3. Lp ma trn cng tng th, xc nh chuyn v nt, xc nh ni lc:

3.1 Lp ghp:

Ma trn ]'[ eK ca tng phn t ma trn ][ SK .

Vect }'{ eR ca tng phn t vect }'{ SR

Cng vect }'{ SR vi vect ti trng tc dng trc tip ti nt }{ PR vect

lc tng cng ti nt }{ SR

}{}'{}{ PSS RRR (23)

3.2 Xt iu kin bin, kh trng lp:

Ma trn ][ SK ma trn ]*[ sK

Vect }{ SR vect }*{ SR

3.3 Gii h phng trnh: SSS RuK **.*

}*{*}*{ 1 SSS RKu

(24)

3.4 Vect chuyn v nt ca phn t:

Lp ghp cc chuyn v nt (gm nhng chuyn v ti cc lin kt v nhng

chuyn v xc nh t kt qu gii h phng trnh) vect chuyn v nt ca phn t trong

h to tng th eu' .

Vect chuyn v nt ca phn t trong h to a phng eu .

}'{}{ ee uTu (25)

3.5 Vect ni lc ca phn t:

eeee RuKF }{}{ (26)

Ni lc ti 2 u thanh:

)1(ei

FN ; )2(ei

FQ ; )3(ei

FM (27)

)4(ej

FN ; )5(ej

FQ ; )6(ej

FM

1. Ri rc ha kt cu v lp bng s liu:

+ Tin hnh ri rc kt cu thnh 2 phn t v 3 nt.

+ Bng s liu phn t:

Phn t Nt i Nt j E.J E.F l Cos() Sin() Loi PT

1 1 2 2'560 192'000 4 1 0 NN

2 2 3 1'080 144'000 5 0.8 -0.6 NK

+ Bng s liu ti trng trn phn t:

Phn t px py T a b P a b M a b

1 -1.8

2 2.4 2.5 2.5 -3.2 2.5 2.5

+ Bng s liu ti trng tc dng ti nt:

Nt PX PY MZ

2 -5

+ Bng s liu iu kin bin:

Nt uX uY rZ

1 0 0 0

2 0 0 0

3 0 0 khng x

2. Thit lp ma trn cng phn t:

2.1. Phn t 1: (p dng cng thc 1, 4, 5)

Ma trn [Ke]

48'000 0 0 -48'000 0 0

0 480 960 0 -480 960

0 960 2'560 0 -960 1'280

-48'000 0 0 48'000 0 0

0 -480 -960 0 480 -960

0 960 1'280 0 -960 2'560

Ma trn [T]

1 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

Ma trn [T]T

1 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

K'e (1) (2) (3) (4) (5) (6)

(1) 48'000.0 0.0 0.0 -48'000.0 0.0 0.0

(2) 0.0 480.0 960.0 0.0 -480.0 960.0

(3) 0.0 960.0 2'560.0 0.0 -960.0 1'280.0

(4) -48'000.0 0.0 0.0 48'000.0 0.0 0.0

(5) 0.0 -480.0 -960.0 0.0 480.0 -960.0

(6) 0.0 960.0 1'280.0 0.0 -960.0 2'560.0

2.2. Phn t 2: (p dng cng thc 2, 4, 5)

Ma trn [Ke]

28'800.0 0.0 0.0 -28'800.0 0.0 0.0

0.0 25.9 129.6 0.0 -25.9 0.0

0.0 129.6 648.0 0.0 -129.6 0.0

-28'800.0 0.0 0.0 28'800.0 0.0 0.0

0.0 -25.9 -129.6 0.0 25.9 0.0

0.0 0.0 0.0 0.0 0.0 0.0

Ma trn [T]

0.8 -0.6 0 0 0 0

0.6 0.8 0 0 0 0

0 0 1 0 0 0

0 0 0 0.8 -0.6 0

0 0 0 0.6 0.8 0

0 0 0 0 0 1

Ma trn [T]T

0.8 0.6 0 0 0 0

-0.6 0.8 0 0 0 0

0 0 1 0 0 0

0 0 0 0.8 0.6 0

0 0 0 -0.6 0.8 0

0 0 0 0 0 1

K'e (4) (5) (6) (7) (8) (9)

(4) 18'441.3 -13'811.6 77.8 -18'441.3 13'811.6 0.0

(5) -13'811.6 10'384.6 103.7 13'811.6 -10'384.6 0.0

(6) 77.8 103.7 648.0 -77.8 -103.7 0.0

(7) -18'441.3 13'811.6 -77.8 18'441.3 -13'811.6 0.0

(8) 13'811.6 -10'384.6 -103.7 -13'811.6 10'384.6 0.0

(9) 0.0 0.0 0.0 0.0 0.0 0.0

3. Quy i ti trng phn t thnh lc nt tng ng:

3.1. Phn t 1: (p dng cng thc 7, 21, 22)

( )

0 3.6 2.4 0 3.6 2.4y

T

e pR

0 3.6 2.4 0 3.6 2.4T

eR

T{ 0 3.6 2.4 0 3.6 2.4' }(1) (2) (3) (4) (5) (6)

eR

3.1. Phn t 2: (p dng cng thc 13, 14, 21, 22)

( )

1.2 0 0 1.2 0 0T

e TR

( )

0 2.2 3.0 0 1.0 0T

e PR

1.2 2.2 3.0 1.2 1.0 0T

eR

T{ 0.36 2.48 3.0 0.36 1.52 0' }(4) (5) (6) (7) (8) (9)

eR

4. Lp ma trn cng tng th, xc nh chuyn v nt, xc nh ni lc:

4.1 Lp ghp:

+ Ma trn cng ton h SK :

(1) (2) (3) (4) (5) (6) (7) (8) (9)

(1) 48000.0 0.0 0.0 -48000.0 0.0 0.0 0.0 0.0 0.0

(2) 0.0 480.0 960.0 0.0 -480.0 960.0 0.0 0.0 0.0

(3) 0.0 960.0 2560.0 0.0 -960.0 1280.0 0.0 0.0 0.0

(4) -48000.0 0.0 0.0 66441.3 -13811.6 77.8 -18441.3 13811.6 0.0

(5) 0.0 -480.0 -960.0 -13811.6 10864.6 -856.3 13811.6 -10384.6 0.0

(6) 0.0 960.0 1280.0 77.8 -856.3 3208.0 -77.8 -103.7 0.0

(7) 0.0 0.0 0.0 -18441.3 13811.6 -77.8 18441.3 -13811.6 0.0

(8) 0.0 0.0 0.0 13811.6 -10384.6 -103.7 -13811.6 10384.6 0.0

(9) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

+ Vect lc nt ton h SR :

- Lp ghp cc vect lc nt do ti trng tc dng trn phn t quy i v nt:

T{ 0 3.6 2.4 0.36 6.08 0.6 0.36 1.52 0' }(1) (2) (3) (4) (5) (6) (7) (8) (9)

SR

- Cng vi lc tc dng trc tip ti nt:

T{ 0 3.6 2.4 0.36 11.08 0.6 0.36 1.52 0 }(1) (2) (3) (4) (5) (6) (7) (8) (9)

SR

4.2 Xt iu kin bin, kh trng lp:

- B cc hng v ct trong ma trn SK c s th t tng ng vi bc t do ca nt c

lin kt, hoc khng xc nh (1, 2, 3, 7, 8, 9) *SK

Ma trn cng [K*]S

66'441.33 -13'811.56 77.76

-13'811.56 10'864.59 -856.32

77.76 -856.32 3'208.00

- B cc hng trong vect SR c s th t tng ng vi bc t do ca nt c lin kt,

hoc khng xc nh (1, 2, 3, 7, 8, 9) *SR

T{ 0.36 11.08 0.6* }(4) (5) (6)

SR

- B cc hng trong vect SR c s th t tng ng vi bc t do ca nt c lin kt,

hoc khng xc nh (1, 2, 3, 7, 8, 9) *SR

4.3 Gii h phng trnh: SSS RuK **.*

}*{*}*{ 1 SSS RKu

Ma trn [K*]-1S

2.0594E-05 2.6702E-05 6.6285E-06

2.6702E-05 0.00012864 3.3692E-05

6.6285E-06 3.3692E-05 0.00032055

T{ 0.0003073 0.0014552 0.000568* }(4) (5) (6)

Su

4.4 Vect chuyn v nt ca phn t:

Lp ghp cc chuyn v nt (gm nhng chuyn v ti cc lin kt v nhng

chuyn v xc nh t kt qu gii h phng trnh) vect chuyn v nt ca phn t trong

h to tng th eu' .

Xc n vect chuyn v nt ca phn t trong h to a phng eu .

{ } { ' }e e eu T u

+ Phn t 1:

T{ 0 0 0 0.0003073 0.0014552 0.000568' }(1) (2) (3) (4) (5) (6)

eu

0 0 0 0.0003073 0.0014552 0.000568T

eu

+ Phn t 2:

T{ 0.0003073 0.0014552 0.000568 0 0 0' }(4) (5) (6) (7) (8) (9)

eu

0.0006273 0.0013485 0.000568 0 0 0T

eu

3.5 Vect ni lc ca phn t:

eeee RuKF }{}{

Ni lc ti 2 u thanh:

)1(ei

FN ; )2(ei

FQ ; )3(ei

FM

)4(ej

FN ; )5(ej

FQ ; )6(ej

FM

+ Phn t 1:

14.748 3.753 3.070 14.748 3.447 2.457T

eF

Ni lc ti 2 u thanh:

14.748iN ; 3.753iQ ; 3.070iM

14.748jN ; 3.447jQ ; 2.457jM

+ Phn t 2:

16.867 2.091 2.457 19.267 1.109 0T

eF

Ni lc ti 2 u thanh:

16.867iN ; 2.091iQ ; 2.457iM

19.267jN ; 1.109jQ ; 0jM

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