tablas reistencia de materiales

7/23/2019 Tablas Reistencia de materiales

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MÉTODO DE TRES MOMENTO

P a L b

4 4 5 1

28.800

M a L b

8 3 7 4

25.143

W L

3 4

48.000

W L b c

2 5 3 2

36.900

W L a d

5 7 5 2

102.857

W L

2 6

57.600 50.400

W L

3 4

22.400 25.600

W L

3 4

30.000 30.000

6 Aa L = Pa

L ( L2−a2)=

6 Aa

L =

− M

L (3a2− L2 )=

6 Aa

L

= w

4 L

[b2(2 L2−b2)]= 6 Ab

L =

w

4 L[ L4−c

2(2 L2−c2)]=

6 Aa

L = w

4 L [ L4−a

2(2 L2−a2) ]= 6 Ab

L =

w

4 L[d2(2 L2−d2) ]=

WL 3

4=

6 Ab L

= Pb L ( L2−b2)=

6 Ab

L =

+ M

L (3b2− L2 )=

6 Aa

L =

6 Ab

L =

WL 3

4

6 Aa

L

= 8WL

3

60

= 6 Ab

L

= 7WL

3

60

=

6 Aa

L= 7WL

3

60=

6 Ab

L= 8WL

3

60=

6 Aa

L =

5WL 3

32 =

6 Ab

L =

5WL 3

32 =



w L a b c d

3 5 2 4 1 3

54.000

w L a b

3 5 3 2

20.070

27.180

Colocar los valores de: w, L, a, b y c.w L a b c d e

2 5 0 3 2 2 3

23.520

25.980

Colocar los valores de: w, L, a, b y c.

w L a b c d2 4 0 3 1 2

1.500

1.500

15.900

15.600

w L a b c d

2 30 3 25 5 27

11970.933

12273.067

MOMENTOS DE EMPOTRAMIENTO PE

6 Aa

L= w

4 L [ b

2(2 L2−b2)−a2(2 L2−a2)

] = 6 Ab

L =

w

4 L [d2

(2 L

2

−d

2

)−c

2

(2 L

2

−c

2

)]=

6 Ab

L= wa

2

60 L [20 L2−3a( 4 L+b )]=

6 Aa

L= wa2

60 L [10 L2−3 a2 ]=

6 Aa

L=wbe(b+3d )3

27 L2

+wbdc

2 (b+c+3 d )

2 L2

−wb

3(5a+4 b )20 L

=

6 Ab

L=wbe(b+3d )2(b+9c+3d )

54 L2

+wbdc 3

L2

−wb

3(b+5c)20 L

=

6 Aa

L=(

6

L)[ R1

81(3d+b )3+

R2c2

6(b+c+3 d )−

wb 3

120(5a+4b)]=

6 Ab

L =( 6

L )[ R

1

162 (3 d+b )2

(b+9c+3d )+

R2c3

3 −wb

3

120 ( 5c+b)]=

R1=wb

2 L(c+

b

3)=

R2=wb

2 L(a+

2b

3)=

6 Aa

L= w

4 L[ b2(2 L2−b

2)−a2(2 L2−a

2) ]=

6 Aa

L= w

4 L[ d 2(2 L2−d

2)−c2(2 L2−c

2 ) ]=



Colocar los valores de: w, L, a y b

w L a b d e !o" #oda

2 5 0 3 2 3

1.898

+1.896

1.404

1.102

w L a

2 5 3

+3.420

1.980

w L a b

2 30 3 25

+139.724

129.653

P L a b

4 5 4 1

+0.640

2.560

W L

2 6

+3.600 2.400

W L

6 6

R1= wb

540 L3 [56b

3

−45b2

( L−2a )+270e2

( L+2d )]=

M 1= wb

540 L2 [ b2(30 L−45a−28b )−270de2 ]=

M 2= M

1+ R

1 L−

wbe

2=

R2=

wb

2 − R

1=

M A =−wa

2

12 L2 (3a2−8aL+6 L2 )=

M B= wa 3

12 L2 (4 L−3a )=

M A=

−w

12 L2 (

3b

4

−8b

3

L+6b

2

L

2

−3a

4

+8a

3

L−6a

2

L

2

)=

M B=

w

12 L2(4 b3

L−3b4−4 a3

L+3a4 )=

M A=− Pab2

L2 =

M B= Pa

2

b

L2 =

M A=−WL2

20= M

B=WL

2

30=

M A=−WL2

12= M

B=WL

2

12=



+18.000 18.000

W L

4 4

+3.667 1.667

w L a b

3 5 2 3

+0.864

2.286 -/

Colocar los valores de: a, b, c y w

a b c d e w L

2 6 1 5 4 4.5 9

+23.667

11.593

27.333

15.407

w L a

2 5 3

+3.420

1.980

L

6 6 4

+15.600

14.400

M A=−WL2

12= M

B=WL

2

12=

M B=

5

192WL2= M

A=−11

192WL

2=

M A=wb

3

60 L 5−3

b

L =

R A = wb

4 L3 [4e2 ( L+2d )−b

2 (c−a)]=

M A =

wb

24 L2 {b2 [ L+3(c−a )]−24 e

2

d }= M A=

R A= M

B= RB= M B= R A L−wbe+ M A=

RB=wb− R A

M B=−wb2

60 [3(b

L)2

+10 a L ]=

M A=−wa

2

12 [6− a

L(8−3

a

L)]=

M B=wa 3

12 L( 4−3

a

L)=

M A= L2

60(3w

1+2w

2)=

w2w

1

M B= L2

60(2w

1+3w

2)=



w L c

2 7 2

+1.654

0.441

M a b L

8 3 4 7

1.306

2.449

CÁLCULO DE REACCIONES

L

4 5 5 100

+0.200

0.200

W L a

54.8 +85.4 0 30 +18.37 81.39 1.5

4.673 28.373

+4.673 31.627

M A = wc

2

30 L2(10 L2+6c2−15 cL)=

M B= wc 3

20 L2 (5 L−4 c )=

M A

M B

A y=

B y=

M A

A y=

B y=

M A

M B

A y=

B y=

M A

M B

A y=

B y=

M A

M B

M A =− Mb

L2 ( L−3 a)=

M B= Ma

L2 ( 2 L−3a )=



a b L P w

205.7 0 15 15 30 0 2

36.857 P'ede colocar:

P 0 % W 0 % M 0

23.14333

a b c L

1 12.71 3.5 0.5 1 5 6 4.5

0.35800 P'ede colocar:

P 0 % W 0 % M 0

10.14200

M A

M B

A y=

B y=

M A

M B

A y=

B y=

P1

P2



19.200

+1.143

+2.841

5.651

44.100

L1 L2 L3

5 7 5

67.143

M1L1 2M2L1L2* M3L2

+53.96 24 7

M2L2 2M3L2L3* M4L3

7 24 5

M3L3 2M4L3L4* M5L4

5 10 0

!-!#M CC-/

M2 M3 M4

24 7 0

7 24 5

0 5 10



48.000

RFECTO

c

2

(2 L

2

−c

2

) ]=



s $%r&'las Correc(as y co&)robadas*

+9.376



-/



L

115.9 20

10.795

10.795

b L P

4.5 6 60

M B

A y=



c'adro de ardy croos

0 1 0.512 0.488 0.41710.792 +3.703 4.877 +4.173 11.304

0 +7.089 -3.5445

1.454 1.386 0.693

-1.178 +2.357

0.603 0.575 0.287

-0.060 +0.120

0.031 0.029 0.015

+0.006

10.792 -10.792 3.421 -3.421 9.817

L4 61a1L1 62a2L2 62b2L2 63a3L3 63b3L3 64b4l4

0 67.284 187.462 137.538 85.77 90.48 0

61a1L1 62b2L2

67.284 137.538

62a2L2 63b3L3

187.462 90.48

63b3L3 64b4l4

85.77 0

+150.862

+277.942

+85.77

1 2 3



0.583 0+6.346 5.404

+3.295 -1.647

+0.168 -0.084

+0.009 -0.004

-9.817 3.669

M1 M5

+10.792 0

4



ah av ab ad ac bc be cf de df ef cv

MATRIZ 1

-1 0 0.53 -0.7071 1 0 0 0 0 0 0 0

0 -1 0.848 -0.7071 0 0 0 0 0 0 0 0

0 0 0 0 -1 0.53 0 0.9285 0 0 0 0

0 0 0 0 0 -0.848 0 -0.3714 0 0 0 1

0 0 -0.53 0 0 -0.53 -0.2425 0 0 0 0 0

0 0 -0.848 0 0 0.848 0.9701 0 0 0 0 0

0 0 0 0 0 0 0 -0.9506 0 -0.4472 0.4472 0

0 0 0 0 0 0 0 0.3714 0 0.8944 0.8944 0

0 0 0 0.7071 0 0 0 0 -1 0.4472 0 0

0 0 0 0.7071 0 0 0 0 0 -0.8944 0 0

0 0 0 0 0 0 0.2425 0 1 0 -0.4472 0

0 0 0 0 0 0 -0.9701 0 0 0 -0.8944 0

MATRIZ INVERSA 1

-1 0 -1 0 -1 -5.551E-017 -0.978173 -0.0036380166 -0.990299 -0.009701 -0.990299 0.002425

0 -1 0 0 -0.8 -0.5 -0.195637 -0.5007340554 -0.3980563 -0.601944 -0.398056 -0.399524

0 0 0 0 -0.9433962 -0.58962264 -0.08652 -0.2214473684 0.1187917 -0.118792 0.118792 -0.324103

0 0 0 0 0 0 0.1729154 0.4425776934 0.7054047 0.708822 0.705405 0.176333

0 0 -1 0 -0.5 0.3125 -0.810049 0.4266757757 -0.5544669 0.554467 -0.554467 0.2988847

0 0 0 0 -0.9433962 0.58962264 0.2018593 0.5166598024 -0.2771534 0.277153 -0.277153 0.7561662

0 0 0 0 0 0 -0.252083 -0.6452065569 0.3461102 -0.34611 0.34611 -0.944303

0 0 0 0 0 0 -0.987652 0.164616134 -0.4389613 0.438961 -0.438961 -0.109729

0 0 0 0 0 0 0.1834027 0.4694200305 -0.2518125 0.251812 0.748188 0.1870276

0 0 0 0 0 0 0.1367045 0.3498956697 0.557683 -0.557683 0.557683 0.1394064

0 0 0 0 0 0 0.2734183 0.6998153856 -0.3754042 0.375404 -0.375404 -0.093841

0 0 0 1 -0.8 0.5 -0.195637 0.4992659446 -0.3980563 0.398056 -0.398056 0.6004756

1

2

3

4

5

!6

7

8

!9

10

11

!12



MATRIZ 2

0.00

0.00

0.00

0.00

" # - 20 -90.00

0.00

0.00

$ # 30 135.00

0.000.00

0.00

0.00

MM%&T

89.51

4.40

55.01

59.75

102.60

154.65

-87.10

22.22

63.37

47.24

94.48

139.40

!1 #

!2 #

!3 #

!4 #

!5 #

!6 #

!7 #

!8 #

!9 #

!10

#

!11

#

!12

#



0.1 100

0.2 +100

0.1 0

0.2 0

0.26667 0.13333 150

0.13333 0.26667 +150

0.2 225

M#-; 1

0.46667 0.13333 +50.00000

0.13333 0.66667 +75.00000

M-/<! 1 92.05

+115.91

2.27273 +0.45455 +9.66

+0.45455 1.59091 +19.32

115.91

MML# +186.36

M AC

=

M CA=

M CD=

M DC =

M BD=

M DB=

M ED=

M DE=

EI θ D

EI θC

M ij

M CA

+ M CD

=0

M DB

+ M DC

+ M DE

=0

EI θ D

EI θC

bi

EI θC =

EI θ D

EI θC

M AC =

M CA=

M CD= M DC =

M BD= M DB=

M DE=



+79.5455 205.68

+96.5909 0

EI θC =

EI θ D

=

M DC = M

DE=

M ED=



TABLA DE DISTRIBUCIÓN DE MOMENTOS'a( ac ,

E'e/( de )/( *eb'/ AC A E E

ac/'e( de d*('*bc*+, 0 0.429 0.571 0.4 0.3 0.3 1 0

1. M/e,/( e, e'e/( 100 -100 150 -150 150 ###

2. E*)*b'*/ de )/( ,d/( -21.45 -29 150

3. T'a()ac*+, -11 -14.28 754. E*)*b'*/ de )/( ,d/( -24.29

5. T'a()ac*+, -12

6. E*)*b'*/ de )/( ,d/( 5.21 6.93

7. T'a()ac*+, 2.61 3.47

8. E*)*b'*/ de )/( ,d/( -1.39 -1.04 -1.04

9. T'a()ac*+, -0.69 -0.5

10. E*)*b'*/ de )/( ,d/( 0.30 0.40

11. T'a()ac*+, 0.15 0.20

12. E*)*b'*/ de )/( ,d/( -0.08 -0.06 -0.06

13. M/e,/( ,a)e( 92 ### ### ### -19 206 0 ###



1 0.39 0.62 0.5 0.5 0

32 -16.8 19.2 0.32 5.12 -9.13 10.57

-15.2 -7.6 1 2.005 2.01 1

0 -5 -8 -4

1 2 1.99 1

0 -1 0

0 0 0 0

0 0

-32 6.21 -6.21 5 -5 12.64

1 2 3 4



0 1 0.38 0.63 0.5 0.5 0

6 -2.27 7.88 -6 6 -3.95 4.2

0 -3.73 -1.87 -0.51 -1

0.19 0.31 0.16

-0.04 -0.08

0 0.02

6 -6 6.22 -6.22 5.05 -5.05 3.65

1 2 3 4

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